High Power Impulse Magnetron Sputtering: Fundamentals, Technologies, Challenges and Applications [1 ed.] 0128124547, 9780128124543

Table of contents :
Cover
High Power Impulse
Magnetron Sputtering:

Fundamentals, Technologies, Challenges
and Applications
Copyright
Contents
Contributors
Preface
1 Introduction to magnetron sputtering
1.1 Fundamentals of sputtering
1.1.1 DC glow discharge
1.1.2 Electrical breakdown
1.1.3 The cathode sheath
1.1.4 Secondary electron emission
1.1.5 Electron energy distribution function
1.1.6 Electric potentials
1.1.7 Sputter yield
1.1.8 Energy distribution of sputtered atoms
1.1.9 Collisions in gases
1.1.10 DC glow sputter source
1.2 Magnetron sputtering
1.2.1 DC magnetron sputtering
1.2.2 Addition of magnetic fields
1.2.3 Electron confinement and target utilization
1.2.4 Electron heating
1.3 Magnetron sputtering configurations
1.3.1 Balanced and unbalanced magnetrons
1.3.2 Rotating magnetrons
1.4 Pulsed magnetron discharges
1.4.1 Definition of pulsed magnetron sputtering discharges
1.4.2 Asymmetric bipolar mid-frequency pulsing
1.4.3 Magnetron sputtering with a secondary discharge
1.4.4 High power impulse magnetron sputtering
1.4.5 Modulated pulse power magnetron sputtering
1.4.6 Summary
References
2 Hardware and power management for high power impulse magnetron sputtering
2.1 Brief history of high power pulsed magnetron sputtering
2.2 Pulse generators
2.2.1 Basic pulse generators
2.2.2 Thyristor-diode-based pulsers
2.2.3 IGBT-based pulsers
2.2.4 Pre-ionization
2.2.5 Pulse delay
2.3 Substrate bias
2.3.1 Bias solutions
2.3.2 Synchronized pulsed HiPIMS bias
2.4 Advanced HiPIMS configurations
2.4.1 Multicathode configurations
2.4.2 Superposition
2.4.3 Pulse trains/multipulses/chopped pulses
2.4.4 Summary
References
3 Electron dynamics in high power impulse magnetron sputtering discharges
3.1 Techniques for characterizing plasma electrons
3.1.1 Langmuir probe
3.1.2 Emissive probe
3.1.3 Triple probe
3.2 Fundamental electron characteristics
3.2.1 Electron energy, density, and temperature
3.2.2 Plasma expansion and reflection
3.3 Influence of target material and working gas
3.3.1 Electron energy, density and temperature
3.3.2 Plasma potential
3.3.3 Reactive plasmas
3.4 Multiple sources and hybrid systems
3.4.1 Electron properties in multisource systems
3.4.2 Electron properties in hybrid systems
References
4 Heavy species dynamics in high power impulse magnetron sputtering discharges
4.1 The plasma ions
4.1.1 Techniques for characterizing plasma ions
4.1.1.1 Energy-resolved mass spectrometry
4.1.1.2 Retarding field energy analyzers
4.1.1.3 Modified quartz crystal microbalance (ion meter)
4.1.1.4 Laser-based methods for ion detection
4.1.2 Spatial and temporal distribution of ions in the bulk plasma
4.1.3 Ion energy distribution in the vicinity of the substrate
4.1.3.1 Time-averaged IEDF
4.1.3.2 Time-resolved IEDF
4.1.3.3 Reactive HiPIMS
4.1.3.4 Time-evolution of the ion flux
4.1.4 Ionized fraction of depositing particles
4.1.5 Ionized flux fraction in HiPIMS
4.1.5.1 Reactive HiPIMS discharges
4.1.5.2 Hybrid systems
4.1.5.3 Influence of the magnetic field
4.1.5.4 Mass spectrometry results
4.1.6 Ionized density fraction
4.2 The plasma neutrals
4.2.1 Spatial and temporal evolution of plasma neutrals
4.2.2 Gas rarefaction
References
5 Modeling the high power impulse magnetron sputtering discharge
5.1 Modeling approaches
5.1.1 Pathway models
5.1.2 Steady-state global models
5.1.2.1 Ionization and return of sputtered target material
5.1.2.2 Deposition parameters
5.1.2.3 Limitations of this approach
5.1.3 Time-dependent global model, IRM
5.1.3.1 Particle balance
5.1.3.2 Neutral particle balance
5.1.3.3 Ion particle balance
5.1.3.4 Electron balance
5.1.3.5 Power balance
5.1.3.6 Plasma chemistry
5.1.4 Particle-in-cell
5.1.4.1 Challenges of HiPIMS PIC simulations
5.1.4.2 Pseudo-3D PIC
5.1.5 Monte Carlo simulations
5.1.5.1 Monte Carlo collision simulations
5.1.5.2 Monte Carlo simulation of neutral particle transport
5.1.5.3 Direct simulation Monte Carlo (DSMC) for neutral particles transport
5.1.5.4 A posteriori Monte Carlo
5.1.6 Other models
5.1.6.1 A feedback model
5.1.6.2 EEDF as solution of Boltzmann's equation
5.1.6.3 Models for spokes
5.1.6.3.1 A phenomenological model
5.1.6.3.2 The wave coupling model
5.2 Important modeling results
5.2.1 Deposition rate
5.2.2 Current and voltage waveforms
5.2.2.1 Time-dependent global models
5.2.2.2 Self-consistent PIC model
5.2.3 Time-dependent plasma properties
5.2.3.1 Temporal evolution of neutral and charged species
5.2.3.2 Excited states evolution
5.2.3.3 Electron energy distribution function (EEDF)
5.2.3.4 Ion energy distribution function (IEDF)
5.2.3.5 Electron transport coefficients and plasma deconfinement
References
6 Reactive high power impulse magnetron sputtering
6.1 Introduction to reactive sputter deposition
6.1.1 Working point
6.1.2 Process control
6.2 Fundamentals of reactive sputtering
6.2.1 Molecular gas and plasma chemistry
6.2.2 Secondary electron emission
6.2.3 Sputter yields for compounds
6.2.4 Reactive gas implantation and thickness of the compound layer
6.2.5 Balance (Berg) model of hysteresis reactive sputtering
6.3 Hysteresis in reactive HiPIMS
6.3.1 Experimental observations
6.3.2 Dynamics of the hysteresis
6.3.3 Models of hysteresis in reactive HiPIMS
6.4 Important aspects of reactive HiPIMS
6.4.1 Discharge waveforms
6.4.2 Process stability and deposition rate
6.4.3 Dynamics of the sputter target surface
6.4.4 Plasma characteristics in the metal and compound mode
6.4.5 Negative ions in R-HiPIMS
References
7 Physics of high power impulse magnetron sputtering discharges
7.1 The discharge current
7.1.1 The discharge current composition
7.2 Discharge modes
7.2.1 The discharge current amplitude
7.2.1.1 The generalized recycling model (GRM)
7.2.1.2 Discharge analysis
7.2.2 Temporal evolution of the discharge current
7.2.3 Ohmic heating versus sheath acceleration
7.3 Transport of charged particles
7.3.1 Classical ion and neutral species transport
7.3.1.1 Ion transport
7.3.1.2 Classical electron transport
7.3.2 Anomalous transport
7.3.2.1 Anomalous electron transport
7.3.2.2 Anomalous ion transport
7.4 Plasma Instabilities
7.4.1 Spokes and breathing instabilities in magnetron sputtering discharges
7.4.2 The potential structure
7.4.3 Effect of spokes on charged particle transport
7.4.3.1 Transport near the target
7.4.3.2 Transport in the bulk plasma
7.4.3.3 Transport near the substrate
7.5 Deposition rate
7.5.1 Physics of deposition rate loss
7.5.2 Increasing the deposition rate
7.5.3 Deposition rates in reactive HiPIMS
References
8 Synthesis of thin films and coatings by high power impulse magnetron sputtering
8.1 Introduction to the fundamentals of thin film growth
8.1.1 Thin film growth from an atomistic point of view
8.1.2 Effect of energetic ions on thin film microstructural evolution
8.1.3 Effect of pulsed vapor fluxes on thin film growth dynamics
8.2 Deposition on complex-shaped substrates
8.3 Interface engineering
8.4 Thin film microstructure and morphology
8.4.1 Film density and surface roughness
8.4.2 Film texture and morphological evolution
8.4.3 Synthesis of self-organized nanostructures
8.5 Stress generation and evolution
8.5.1 Atomistic view on stress generation and evolution
8.5.2 Effect of highly ionized fluxes on stress generation evolution
8.5.3 Tailoring of stress in optical coatings by HiPIMS
8.6 Phase composition
8.6.1 Phase composition tailoring in elemental thin film materials: the Ta case
8.6.2 Phase composition tailoring in functional oxide films
8.6.3 Phase composition tailoring in metastable ternary ceramic films
8.6.4 Phase formation tailoring via control of chemical composition
8.7 Time-domain effect of HiPIMS on film growth
8.8 Summary
References
Index
Back Cover

Citation preview

High Power Impulse Magnetron Sputtering

High Power Impulse Magnetron Sputtering Fundamentals, Technologies, Challenges and Applications Edited by

Daniel Lundin Laboratoire de Physique des Gaz et Plasmas - LPGP UMR 8578 CNRS, Université Paris–Sud Université Paris–Saclay, Orsay Cedex, France

Tiberiu Minea Laboratoire de Physique des Gaz et Plasmas - LPGP UMR 8578 CNRS, Université Paris–Sud Université Paris–Saclay, Orsay Cedex, France

Jon Tomas Gudmundsson Department of Space and Plasma Physics School of Electrical Engineering and Computer Science KTH Royal Institute of Technology Stockholm, Sweden Science Institute, University of Iceland Reykjavik, Iceland

Elsevier Radarweg 29, PO Box 211, 1000 AE Amsterdam, Netherlands The Boulevard, Langford Lane, Kidlington, Oxford OX5 1GB, United Kingdom 50 Hampshire Street, 5th Floor, Cambridge, MA 02139, United States Copyright © 2020 Elsevier Inc. All rights reserved. No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or any information storage and retrieval system, without permission in writing from the publisher. Details on how to seek permission, further information about the Publisher’s permissions policies and our arrangements with organizations such as the Copyright Clearance Center and the Copyright Licensing Agency, can be found at our website: www.elsevier.com/permissions. This book and the individual contributions contained in it are protected under copyright by the Publisher (other than as may be noted herein). Notices Knowledge and best practice in this field are constantly changing. As new research and experience broaden our understanding, changes in research methods, professional practices, or medical treatment may become necessary. Practitioners and researchers must always rely on their own experience and knowledge in evaluating and using any information, methods, compounds, or experiments described herein. In using such information or methods they should be mindful of their own safety and the safety of others, including parties for whom they have a professional responsibility. To the fullest extent of the law, neither the Publisher nor the authors, contributors, or editors, assume any liability for any injury and/or damage to persons or property as a matter of products liability, negligence or otherwise, or from any use or operation of any methods, products, instructions, or ideas contained in the material herein. Library of Congress Cataloging-in-Publication Data A catalog record for this book is available from the Library of Congress British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library ISBN: 978-0-12-812454-3 For information on all Elsevier publications visit our website at https://www.elsevier.com/books-and-journals Publisher: Mathew Deans Acquisition Editor: Christina Gifford Editorial Project Manager: Gabriela D. Capille Production Project Manager: Selvaraj Raviraj Designer: Christian Bilbow Typeset by VTeX Cover photo by Dr. Marcus Morstein displaying a HiPIMS plasma near the surface of a cylindrical rotatable magnetron inside a PLATIT industrial PVD coating chamber equipped with an Ionautics HiPIMS power supply.

Contents

Contributors Preface 1

2

Introduction to magnetron sputtering Jon Tomas Gudmundsson, Daniel Lundin 1.1 Fundamentals of sputtering 1.1.1 DC glow discharge 1.1.2 Electrical breakdown 1.1.3 The cathode sheath 1.1.4 Secondary electron emission 1.1.5 Electron energy distribution function 1.1.6 Electric potentials 1.1.7 Sputter yield 1.1.8 Energy distribution of sputtered atoms 1.1.9 Collisions in gases 1.1.10DC glow sputter source 1.2 Magnetron sputtering 1.2.1 DC magnetron sputtering 1.2.2 Addition of magnetic fields 1.2.3 Electron confinement and target utilization 1.2.4 Electron heating 1.3 Magnetron sputtering configurations 1.3.1 Balanced and unbalanced magnetrons 1.3.2 Rotating magnetrons 1.4 Pulsed magnetron discharges 1.4.1 Definition of pulsed magnetron sputtering discharges 1.4.2 Asymmetric bipolar mid-frequency pulsing 1.4.3 Magnetron sputtering with a secondary discharge 1.4.4 High power impulse magnetron sputtering 1.4.5 Modulated pulse power magnetron sputtering 1.4.6 Summary References Hardware and power management for high power impulse magnetron sputtering Zdenˇek Hubiˇcka, Jon Tomas Gudmundsson, Petter Larsson, Daniel Lundin 2.1 Brief history of high power pulsed magnetron sputtering

xi xiii 1 1 2 8 10 11 14 15 16 18 19 22 23 25 25 26 27 30 31 31 32 33 34 36 37 38 38 39

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Contents

2.2 Pulse generators 2.2.1 Basic pulse generators 2.2.2 Thyristor-diode-based pulsers 2.2.3 IGBT-based pulsers 2.2.4 Pre-ionization 2.2.5 Pulse delay 2.3 Substrate bias 2.3.1 Bias solutions 2.3.2 Synchronized pulsed HiPIMS bias 2.4 Advanced HiPIMS configurations 2.4.1 Multicathode configurations 2.4.2 Superposition 2.4.3 Pulse trains/multipulses/chopped pulses 2.4.4 Summary References 3

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Electron dynamics in high power impulse magnetron sputtering discharges ˇ Martin Cada, Jon Tomas Gudmundsson, Daniel Lundin 3.1 Techniques for characterizing plasma electrons 3.1.1 Langmuir probe 3.1.2 Emissive probe 3.1.3 Triple probe 3.2 Fundamental electron characteristics 3.2.1 Electron energy, density, and temperature 3.2.2 Plasma expansion and reflection 3.3 Influence of target material and working gas 3.3.1 Electron energy, density and temperature 3.3.2 Plasma potential 3.3.3 Reactive plasmas 3.4 Multiple sources and hybrid systems 3.4.1 Electron properties in multisource systems 3.4.2 Electron properties in hybrid systems References Heavy species dynamics in high power impulse magnetron sputtering discharges ˇ Martin Cada, Nikolay Britun, Ante Hecimovic, Jon Tomas Gudmundsson, Daniel Lundin 4.1 The plasma ions 4.1.1 Techniques for characterizing plasma ions 4.1.1.1 Energy-resolved mass spectrometry 4.1.1.2 Retarding field energy analyzers 4.1.1.3 Modified quartz crystal microbalance (ion meter) 4.1.1.4 Laser-based methods for ion detection

52 52 55 57 63 63 64 64 68 69 69 71 74 75 75

81 81 82 86 88 91 91 94 95 95 98 102 103 103 104 106

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4.1.2 Spatial and temporal distribution of ions in the bulk plasma 4.1.3 Ion energy distribution in the vicinity of the substrate 4.1.3.1 Time-averaged IEDF 4.1.3.2 Time-resolved IEDF 4.1.3.3 Reactive HiPIMS 4.1.3.4 Time-evolution of the ion flux 4.1.4 Ionized fraction of depositing particles 4.1.5 Ionized flux fraction in HiPIMS 4.1.5.1 Reactive HiPIMS discharges 4.1.5.2 Hybrid systems 4.1.5.3 Influence of the magnetic field 4.1.5.4 Mass spectrometry results 4.1.6 Ionized density fraction 4.2 The plasma neutrals 4.2.1 Spatial and temporal evolution of plasma neutrals 4.2.2 Gas rarefaction References

118 123 124 127 127 130 132 133 136 137 138 139 140 141 141 146 151

Modeling the high power impulse magnetron sputtering discharge Tiberiu Minea, Tomáš Kozák, Claudiu Costin, Jon Tomas Gudmundsson, Daniel Lundin 5.1 Modeling approaches 5.1.1 Pathway models 5.1.2 Steady-state global models 5.1.2.1 Ionization and return of sputtered target material 5.1.2.2 Deposition parameters 5.1.2.3 Limitations of this approach 5.1.3 Time-dependent global model, IRM 5.1.3.1 Particle balance 5.1.3.2 Neutral particle balance 5.1.3.3 Ion particle balance 5.1.3.4 Electron balance 5.1.3.5 Power balance 5.1.3.6 Plasma chemistry 5.1.4 Particle-in-cell 5.1.4.1 Challenges of HiPIMS PIC simulations 5.1.4.2 Pseudo-3D PIC 5.1.5 Monte Carlo simulations 5.1.5.1 Monte Carlo collision simulations 5.1.5.2 Monte Carlo simulation of neutral particle transport 5.1.5.3 Direct simulation Monte Carlo (DSMC) for neutral

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particles transport

5.1.5.4 A posteriori Monte Carlo 5.1.6 Other models 5.1.6.1 A feedback model 5.1.6.2 EEDF as solution of Boltzmann’s equation 5.1.6.3 Models for spokes

159 160 162 162 163 165 165 166 168 171 172 172 175 177 179 183 184 185 185 186 187 188 188 189 190

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5.2 Important modeling results 5.2.1 Deposition rate 5.2.2 Current and voltage waveforms 5.2.2.1 Time-dependent global models 5.2.2.2 Self-consistent PIC model 5.2.3 Time-dependent plasma properties 5.2.3.1 Temporal evolution of neutral and charged species 5.2.3.2 Excited states evolution 5.2.3.3 Electron energy distribution function (EEDF) 5.2.3.4 Ion energy distribution function (IEDF) 5.2.3.5 Electron transport coefficients and plasma deconfinement

References 6

7

Reactive high power impulse magnetron sputtering Tomáš Kubart, Jon Tomas Gudmundsson, Daniel Lundin 6.1 Introduction to reactive sputter deposition 6.1.1 Working point 6.1.2 Process control 6.2 Fundamentals of reactive sputtering 6.2.1 Molecular gas and plasma chemistry 6.2.2 Secondary electron emission 6.2.3 Sputter yields for compounds 6.2.4 Reactive gas implantation and thickness of the compound layer 6.2.5 Balance (Berg) model of hysteresis reactive sputtering 6.3 Hysteresis in reactive HiPIMS 6.3.1 Experimental observations 6.3.2 Dynamics of the hysteresis 6.3.3 Models of hysteresis in reactive HiPIMS 6.4 Important aspects of reactive HiPIMS 6.4.1 Discharge waveforms 6.4.2 Process stability and deposition rate 6.4.3 Dynamics of the sputter target surface 6.4.4 Plasma characteristics in the metal and compound mode 6.4.5 Negative ions in R-HiPIMS References Physics of high power impulse magnetron sputtering discharges Daniel Lundin, Ante Hecimovic, Tiberiu Minea, André Anders, Nils Brenning, Jon Tomas Gudmundsson 7.1 The discharge current 7.1.1 The discharge current composition 7.2 Discharge modes 7.2.1 The discharge current amplitude

192 192 195 196 201 202 202 207 208 211 212 214 223 223 224 227 227 228 231 232 235 236 240 241 244 245 246 247 249 250 253 256 257 265

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7.2.1.1 The generalized recycling model (GRM) 7.2.1.2 Discharge analysis 7.2.2 Temporal evolution of the discharge current 7.2.3 Ohmic heating versus sheath acceleration 7.3 Transport of charged particles 7.3.1 Classical ion and neutral species transport 7.3.1.1 Ion transport 7.3.1.2 Classical electron transport 7.3.2 Anomalous transport 7.3.2.1 Anomalous electron transport 7.3.2.2 Anomalous ion transport 7.4 Plasma Instabilities 7.4.1 Spokes and breathing instabilities in magnetron sputtering discharges 7.4.2 The potential structure 7.4.3 Effect of spokes on charged particle transport 7.4.3.1 Transport near the target 7.4.3.2 Transport in the bulk plasma 7.4.3.3 Transport near the substrate 7.5 Deposition rate 7.5.1 Physics of deposition rate loss 7.5.2 Increasing the deposition rate 7.5.3 Deposition rates in reactive HiPIMS References 8

Synthesis of thin films and coatings by high power impulse magnetron sputtering Kostas Sarakinos, Ludvik Martinu 8.1 Introduction to the fundamentals of thin film growth 8.1.1 Thin film growth from an atomistic point of view 8.1.2 Effect of energetic ions on thin film microstructural evolution 8.1.3 Effect of pulsed vapor fluxes on thin film growth dynamics 8.2 Deposition on complex-shaped substrates 8.3 Interface engineering 8.4 Thin film microstructure and morphology 8.4.1 Film density and surface roughness 8.4.2 Film texture and morphological evolution 8.4.3 Synthesis of self-organized nanostructures 8.5 Stress generation and evolution 8.5.1 Atomistic view on stress generation and evolution 8.5.2 Effect of highly ionized fluxes on stress generation evolution 8.5.3 Tailoring of stress in optical coatings by HiPIMS 8.6 Phase composition 8.6.1 Phase composition tailoring in elemental thin film materials: the Ta case

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8.6.2 Phase composition tailoring in functional oxide films 8.6.3 Phase composition tailoring in metastable ternary ceramic films 8.6.4 Phase formation tailoring via control of chemical composition 8.7 Time-domain effect of HiPIMS on film growth 8.8 Summary References Index

355 357 358 360 361 362 375

Contributors André Anders Leibniz Institute of Surface Engineering (IOM), Leipzig, Germany Nils Brenning Department of Space and Plasma Physics, School of Electrical Engineering and Computer Science, KTH Royal Institute of Technology, Stockholm, Sweden Nikolay Britun Chimie des Interactions Plasma-Surface (ChIPS), CIRMAP, Université de Mons, Mons, Belgium ˇ Martin Cada Institute of Physics v. v. i., Academy of Sciences of the Czech Republic, Prague, Czech Republic Claudiu Costin Alexandru Ioan Cuza University, Faculty of Physics, Iasi, Romania Jon Tomas Gudmundsson Department of Space and Plasma Physics, School of Electrical Engineering and Computer Science, KTH Royal Institute of Technology, Stockholm, Sweden Science Institute, University of Iceland, Reykjavik, Iceland Ante Hecimovic Max-Planck-Institut for Plasma Physics, Garching, Germany Zdenˇek Hubiˇcka Institute of Physics v. v. i., Academy of Sciences of the Czech Republic, Prague, Czech Republic Tomáš Kozák Department of Physics and NTIS–European Centre of Excellence, University of West Bohemia, Plzeˇn, Czech Republic Tomáš Kubart Solid State Electronics, The Ångström Laboratory, Uppsala University, Uppsala, Sweden

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Contributors

Petter Larsson Ionautics AB, Linköping, Sweden Daniel Lundin Laboratoire de Physique des Gaz et Plasmas - LPGP, UMR 8578 CNRS, Université Paris–Sud, Université Paris–Saclay, Orsay Cedex, France Ludvik Martinu Department of Engineering Physics, Polytechnique Montréal, Montréal, Quebec, Canada Tiberiu Minea Laboratoire de Physique des Gaz et Plasmas - LPGP, UMR 8578 CNRS, Université Paris–Sud, Université Paris–Saclay, Orsay Cedex, France Kostas Sarakinos Nanoscale Engineering Division, Department of Physics, Chemistry and Biology, Linköping University, Linköping, Sweden

Preface

High Power Impulse Magnetron Sputtering: Fundamentals, Technologies, Challenges and Applications is an in-depth introduction to High Power Impulse Magnetron Sputtering (HiPIMS) with an emphasis on how this novel sputtering technique differs from conventional magnetron processes in terms of hardware, discharge physics, thin film growth, and resulting thin film characteristics. The book is a result of an invitation from Elsevier in 2016 to write a first book entirely dedicated to HiPIMS. Roughly two and a half years later this is the result. There is undoubtedly work that has been overlooked or not sufficiently dealt with in this book. Our ambition, however, has been to present a comprehensive text on the HiPIMS process, rather than a collection of loosely connected results found in the scientific literature. The main motivation is that HiPIMS, like so many topics in science, is a field in rapid development. With a great number of new findings presented every year, results are sometimes misinterpreted or contradictory. In addition, different descriptions of HiPIMS use their own terminology, which unfortunately varies depending on what source you are looking at. Altogether this presents a significant threshold for someone new to the field. If this book in any way can lower that threshold and stimulate more work on HiPIMS, then we have succeeded in our task. So who should read this book? We hope that anyone involved in ionized physical vapor deposition will benefit from reading it, or at least a few chapters, depending on interest and expertize. The material, however, is aimed at a broader audience of professionals, practitioners, and students, who are familiar with basic concepts of plasma physics and thin films. We have tried to introduce various topics in such a way that someone new to HiPIMS will still be able to follow and possibly be even more motivated to try out this promising (but challenging) technology. We start this book by an introduction to magnetron sputtering in Chapter 1, where we introduce the basic concepts needed to explore HiPIMS. Chapter 2 presents an overview of the historical development of the HiPIMS technique along with various high power pulsers that have been developed over the years. Chapters 3 and 4 are focused on experimental process characterization in HiPIMS and describe the role of electrons and heavy species (neutrals and ions), respectively. Typical characteristics of these species are presented to provide a solid understanding of the most important fundamental properties of the HiPIMS discharge. These findings are followed up in Chapter 5 using computational modeling. The main models are presented and compared to each other when possible. We also highlight some important modeling results, which have been selected to emphasize the added understanding brought by computational modeling, but also to validate certain model approaches or highlight model-specific results. Chapter 6 extends the fundamental knowledge gained in the previous chapters to reactive HiPIMS processes, which involves an introduction of

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Preface

basic sputtering physics in reactive gas mixtures as well as more specific aspects of surface and discharge processes related to reactive HiPIMS. Chapter 7 is an attempt at unifying and summarizing the most important concepts presented in mainly Chapters 3 – 6, and describes the underlying physical and chemical mechanisms giving rise to the observed process results and the consequences thereof. Finally, Chapter 8 discusses the use of HiPIMS to deposit thin films. The chapter is subdivided into several sections, each focusing on a different process-specific aspect related to certain film characteristics, where HiPIMS have been shown to have a great impact. Each chapter contains an extensive list of references to stimulate further reading. A book like this one would not be possible without the contributions and invaluable input by all the expert coauthors and by many colleagues and friends. We do not list all the authors of the individual chapters, who have, besides their own texts, made great contributions to the book as a whole. With the risk of forgetting someone, we would still like to mention a few colleagues outside the author list, who deserve special recognition. In particular, we are deeply grateful to the talented T.J. Petty, who patiently listened to our descriptions and discussions and converted them into fantastic illustrations. We also acknowledge Felipe Cemin, who read and commented some of the chapters, while writing his Ph.D. thesis at Université Paris-Sud. Adrien Revel is acknowledged for his input on the numerical modeling, mainly related to the 2D and 3D particle simulations of short HiPIMS pulses. Finally, we would like to conclude by thanking our families for all the support they have shown us during the course of writing this book and, in particular, for understanding why we had to work all those evenings (and most weekends). Daniel Lundin Tiberiu Minea Jon Tomas Gudmundsson Paris–Linköping–Stockholm, June 2019

Introduction to magnetron sputtering

1

Jon Tomas Gudmundssona,b , Daniel Lundinc a Department of Space and Plasma Physics, School of Electrical Engineering and Computer Science, KTH Royal Institute of Technology, Stockholm, Sweden, b Science Institute, University of Iceland, Reykjavik, Iceland, c Laboratoire de Physique des Gaz et Plasmas LPGP, UMR 8578 CNRS, Université Paris–Sud, Université Paris–Saclay, Orsay Cedex, France

Plasma-based physical vapor deposition (PVD) methods have found widespread use in various industrial applications. In plasma-based PVD processes, the deposition species are either vaporized by thermal evaporation or by sputtering from a source (the cathode target) by ion bombardment. Sputter deposition has been known for decades as a flexible, reliable, and effective coating method. Initially, the dc glow discharge or the dc diode sputtering discharge was used as a sputter source followed by the magnetron sputtering technique, which was developed during the 1960s and 1970s. Magnetron sputtering has been the workhorse of plasma-based sputtering applications for the past four decades. In the planar configuration, the magnetron sputtering discharge is simply a diode sputtering arrangement with the addition of magnets directly behind the cathode target. With the introduction of magnetron sputtering, the disadvantages of diode sputtering, such as poor deposition rate, were overcome as the operating pressure could be reduced while maintaining the energy of the sputtered species, often resulting in improved film properties. Here we discuss the basics of the sputtering process, give an overview of the dc glow discharge, and review the basic physics relevant to the maintenance of the discharge and the sputter processes. Then we discuss the dc glow discharge and its role as a sputter source and how it evolves into the magnetron sputtering discharge. We also discuss various magnetron sputtering configurations in use for a wide range of applications both under laboratory and industrial arrangements. Finally, we introduce pulsed magnetron discharges including high power impulse magnetron sputtering (HiPIMS) discharges.

1.1 Fundamentals of sputtering An important process that takes place in a glow discharge is sputtering, which can occur if the voltage applied to the cathode is sufficiently high. When the ions and fast neutrals from the plasma bombard the cathode target, they not only release secondary electrons, but also atoms of the cathode material. This is referred to as sputtering. When species are sputtered off a cathode target and subsequently used as film forming material, the process belongs to what is referred to as a physical vapor deposition High Power Impulse Magnetron Sputtering. https://doi.org/10.1016/B978-0-12-812454-3.00006-1 Copyright © 2020 Elsevier Inc. All rights reserved.

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High Power Impulse Magnetron Sputtering

(PVD). Sputtering is most easily performed by exposing a cathode target to a gas discharge: either a dc discharge (Kay, 1962) or a magnetron sputtering discharge (Waits, 1978), whereas ion beam sputter deposition is also a well-established PVD technique (Bundesmann and Neumann, 2018). Other PVD techniques include evaporation, pulsed laser deposition, cathodic arc deposition, and ion plating. Sputtering in gas discharges was discovered in the mid-19th century (Grove, 1852). Film formation utilizing sputter deposition, where the cathode target is the source of the film forming material, was first reported by Wright in the 1870s (Wright, 1877a,b). Sputter deposition of thin films had already found commercial application by the 1930s (Fruth, 1932, Hulburt, 1934), but gained significant interest in the late 1950s and early 1960s with improved vacuum technology and the realization that a wide range of materials could be deposited using dc sputtering (Kay, 1962, Westwood, 1976) as well as rf sputtering utilized mainly for dielectrics (Anderson et al., 1962). Here we discuss some of the fundamentals of discharge physics and sputtering. We introduce the dc glow discharge, including its voltage–current characteristics and the various regions observed in its operation, and their properties and role. We discuss some of the fundamentals of plasma physics relevant to sputtering discharges, including electrical breakdown, the relation between the sheath voltage drop and the sheath thickness, and the secondary electron emission, essential for the maintenance of the dc glow discharge. The sputter yield is then discussed in Section 1.1.7, the energy distribution of the sputtered atoms in Section 1.1.8, and collisions within plasma discharges in Section 1.1.9. Finally, we introduce the dc glow sputtering discharge or the dc diode sputtering device in Section 1.1.10. This discussion is intended to give an overview of the fundamental concepts and parameters that are needed to understand the operation of the magnetron sputtering discharge.

1.1.1 DC glow discharge The term gas discharge refers to a flow of electric current through a gaseous medium. For a current to flow, some of the gas atoms and molecules have to be ionized. Furthermore, this current, the discharge current, has to be driven by an electric field. The discharge current, which provides power to the discharge, has to be continuous throughout the length of the discharge. There is a transition in the discharge with regards to which charged species carries the discharge current. In front of the cathode, there is a region, the cathode glow, in which most of the ionization occurs. Outside this region the discharge current is mainly carried by electrons toward the anode and by ions toward the cathode. Energy is needed for the ionization in the cathode glow. In the dc discharge, this is resolved by secondary electron emission from the cathode target. This electron emission is essential for the maintenance of the discharge (see Section 1.1.4). The discharge current is built up by ionization within the cathode sheath, which is due to the secondary electrons that are accelerated by the large electric fields in this region. Thus to describe the current in a dc discharge, the interaction of charged particles with the electrode surfaces has to be taken into account. Let us assume two parallel electrodes separated by a distance L and with applied potential VD . The gap between the electrodes is filled with gas at pressure p, the

Introduction to magnetron sputtering

3

Figure 1.1 The discharge current ID versus the discharge voltage VD for a low-pressure dc discharge. The various operating regimes are noted, with increasing current, Townsend regime, subnormal glow, normal glow, abnormal glow, and arc regime. Reprinted from Gudmundsson and Hecimovic (2017). ©IOP Publishing. Reproduced with permission. All rights reserved.

working gas pressure. The type of discharge that is formed between the two electrodes depends upon the pressure of the working gas, the nature of the working gas, the applied voltage, and the geometry of the discharge. In the following discussion of the dc discharge, we follow the discussion given in a recent review on the foundations of the dc discharge (Gudmundsson and Hecimovic, 2017). The discharge current is shown versus the voltage across a low-pressure dc discharge in Fig. 1.1. A description of the relation between the current and voltage for the dc discharge can be found in review papers such as by Francis (1956) and Ingold (1978) and in a number of textbooks including those of Howatson (1976, Chapter 4), Raizer (1991, Section 8.2), and Roth (1995, Chapter 9) and can be summarized as follows: When a voltage is first applied, the discharge current is very small. This current consists of contributions from various external sources such as cosmic radiation generating free electrons and ions. When the voltage has become large enough to collect all these charged particles, this current remains nearly constant with increased voltage. As the voltage is further increased, the charged particles eventually achieve enough energy to produce more charged particles through collisions with the working gas atoms or by bombardment of the electrodes leading to generation of secondary electrons. As more charged particles are created, the current increases, whereas the voltage is limited by the output impedance of the power supply and remains roughly constant. This region is commonly referred to as the Townsend discharge. The characteristics of the Townsend discharge are very small discharge currents. The Townsend discharge is not luminous since the electron density is low, and therefore the density of excited atoms, which emit visible light, is correspondingly small. Furthermore, it

4

High Power Impulse Magnetron Sputtering

is not a self-sustained discharge in the sense that it does not entirely provide its own ionization but requires some external assistance to produce electrons either within the gas itself or from a negatively biased electrode. If the applied voltage is increased further, then the discharge current increases, and eventually this leads to a situation where the plasma density is high enough for the discharge to reorganize the vacuum potential structure and form a cathode sheath, which enables more efficient ionization and therefore a higher current at a given voltage. Then the current increases sharply by several orders of magnitude and becomes independent of the external seed. This is what is referred to as the breakdown point VB (see Fig. 1.1) or subnormal glow and occurs at voltages ranging from two or three hundred volts and upward, depending on the nature of the working gas, the gas pressure, and the separation of the electrodes. Once breakdown has occurred, the discharge becomes self-sustaining and takes the form of a glow, and the gas becomes luminous. As ions bombard the electrode, secondary electrons are emitted. These electrons impact and ionize the atoms of the working gas. Thus more ions are available to bombard the cathode and create more secondary electrons. At this point, the voltage drops, and the discharge current increases abruptly. Electron impact excitation collisions followed by deexcitation with the emission of radiation are responsible for the characteristic glow. This regime is referred to as the normal glow or the dc glow discharge. The ion bombardment of the cathode surface is initially not uniform. The discharge current arranges an optimum current density, and, as the current increases further, more and more of the cathode target surface is subject to ion bombardment. This continues with increased supplied power until a nearly uniform density is achieved covering the entire cathode area. When the whole cathode is covered by ion bombardment, further increase in the power leads to a discharge with a current density at the cathode, which is no longer optimal. Higher currents can therefore only be achieved with higher voltages over the cathode sheath. There is therefore an increase in both voltage and current. This operation regime is referred to as the abnormal glow and is the regime used for sputtering, which is further discussed in Section 1.1.10. The abnormal glow discharge looks much like the normal glow discharge but is more intensely luminous, and sometimes the structures near the cathode merge into one another. As the current density at the cathode becomes large enough for the formation of cathode spots, the discharge makes a transition into the arc regime. The cathode spots can, through a combination of field emission and thermoionic emission, emit electrons more efficiently than the secondary electron emission process, which leads to a second avalanche, increased discharge current, and a drop in the discharge voltage as seen in Fig. 1.1. Eventually a low-voltage high-current arc discharge forms. The dc glow discharge is important historically both for studying the properties of the plasma and for various applications where the dc discharge is used to provide a weakly ionized plasma. The simplicity of the dc glow discharge geometry made it a commonly used plasma generation method for fundamental research in both discharge physics and atomic and molecular physics (Gudmundsson and Hecimovic, 2017). As seen in Fig. 1.1, the dc glow discharge operates in the current range from µA to hun-

Introduction to magnetron sputtering

5

Figure 1.2 A schematic of the dc glow discharge showing several distinct regions that appear between the cathode and the anode. The colors of the various regions assume a neon discharge. The dark spaces are abbreviated as DS.

dreds of mA (current density range 10−5 – 10−3 A/cm2 ), and the working gas pressure is typically in the range 0.5 – 300 Pa. Early studies of the dc glow discharge revealed that it consists of several different regions between the electrodes, which have been illustrated in more or less the same way by several authors (Francis, 1956, Ingold, 1978, Raizer, 1991, Roth, 1995, Nasser, 1971). In Fig. 1.2, we present a schematic of the normal glow discharge in a 0.5 m long tube using neon at 133 Pa as the working gas, which is due to Nasser (1971). The cathode is typically made of an electrically conductive metal. The cathode metal has an influence on the voltage required to maintain the discharge. For a metal that is a good emitter of electrons (see discussion in Section 1.1.4) lower voltages are sufficient. Immediately next to the cathode is a thin dark layer, the Aston dark space. The Aston dark space is followed by the cathode glow, which has a relatively high ion density. The secondary electrons released from the cathode surface are accelerated away from the cathode. These high-energy electrons undergo collisions with neutral working gas atoms at a distance away from the cathode corresponding to the ionization mean free path. In this region the secondary electrons participate in excitation and thereby generate the cathode glow. The cathode glow is followed by the cathode (Crookes or Hittorf) dark space. The regions that extend from the Aston dark space to the cathode dark space together constitute the cathode sheath. Here the electric field is directed toward the cathode, and the space charge is positive and of relatively high density. The cathode dark space is followed by the negative glow (in fact, a region with positive potential), which exhibits a significant light intensity. Most of the ionization occurs here. The boundary toward the cathode dark space is rather abrupt while it is diffuse on the anode side toward the Faraday dark space. The electric field and the energy of the electrons are low in the Faraday dark space. The electron energy available for excitation and ionization is here exhausted. Before entering this dark region, the potential gradient is slightly negative as the space charge reverses. Here the density of electrons has become high enough to carry the entire discharge current and to make the space charge negative. The electron density falls within this dark space region due to recombination and diffusion until the net space charge is zero and the electric field approaches a small constant value and the positive column begins. The positive column is a quasineutral plasma where the electric field is very low. The positive column is simply a long uniform glow, except when striations are formed. The positive column acts as a conducting path between the negative glow region and the anode. The anode

6

High Power Impulse Magnetron Sputtering

Table 1.1 The color of selected luminous zones in the dc glow discharge. Gas He Ne Ar H2 N2 Air

Cathode layers red yellow pink red/brown pink pink

Negative glow pink orange dark blue pale blue blue blue

Positive column red/pink red/brown dark red pink red/yellow red/yellow

Based on Francis (1956).

glow is a bright region that appears at the end of the positive column. Often a thin dark space is observed at the end of the positive column (the anode dark space), and a glow close to the surface of the anode (the anode glow). The size, intensity, and color of all the regions described above depend on the nature of the working gas, gas pressure, and applied voltage. Also, some of the features may be absent over particular parameter ranges. The various gases give a discharge of a characteristic color. The colors of the light emitted from the various zones of the dc glow discharge are listed in Table 1.1. If the pressure is reduced, then the cathode dark space expands at the expense of the positive column. This is due the fact that now the electrons have to travel farther (mean free path is longer) to produce efficient ionization. For a secondary electron emission yield in the range 0.05 – 0.1, each secondary electron must initiate an avalanche that produces roughly 10 – 20 ions to maintain the discharge. An electron avalanche is possible within the cathode sheath of glow discharges, because the electron mean free path for ionizing collisions is here smaller than the sheath thickness. As we will see in Section 7.2.3, ionization avalanches within the sheath region are not possible in HiPIMS discharges due to lower pressures and thinner cathode sheaths. How many ions each secondary electron actually produces depends on the ionization mean free path and the distance between the anode and cathode. This relation is qualitatively the statement of Paschen’s law, which relates the breakdown voltage VB to the product of gas pressure and electrode separation and will be discussed in Section 1.1.2. This also shows that the ionization processes in the cathode dark space are essential for the maintenance of the discharge. The potential difference applied between the two electrodes is generally not equally distributed between cathode and anode. The spatial variations of the potential, the electric field, particle densities, space charge, and current densities along the axis of a dc glow discharge are shown in Fig. 1.3. The spatial variation of the plasma parameters shown here was found by particle-in-cell simulation of an argon dc discharge at 50 Pa when a voltage of 400 V is applied across the 5 cm discharge gap (Budtz-Jørgensen, 2001). As the potential profile indicates (Fig. 1.3A), the electric field is large in the vicinity of the electrodes and almost zero within the positive column. Thus almost all the applied voltage drops completely within the first few millimeters in front of the cathode. This region adjacent to the cathode, which is thus characterized by a strong electric field, is the cathode fall, or often referred to as the cathode sheath. We see in

Introduction to magnetron sputtering

7

Figure 1.3 Spatial profiles of (A) the plasma potential, (B) the electric field, (C) ion and electron density, (D) space-charge density, and (E) ion and electron current density. From particle-in-cell simulation of an argon dc discharge at 50 Pa, electrode separation of 5 cm, and −400 V applied to the cathode. Reprinted from Budtz-Jørgensen (2001). ©Budtz-Jørgensen. Reproduced with permission. All rights reserved.

Fig. 1.3C that the sheath region is depleted of electrons, and in Fig. 1.3D, we see that the net space charge is positive in the sheath region in line with our previous discussion of the dark space. The space charge shown in Fig. 1.3D is found by subtraction of the electron density from the ion density. In the plasma bulk, the plasma is quasineutral, and the electron and ion densities are the same. This space charge density leads to the electric field distribution seen in Fig. 1.3B.

8

High Power Impulse Magnetron Sputtering

1.1.2 Electrical breakdown Electrical breakdown is an important phenomenon in discharge physics. Here we derive the breakdown voltage as a function of the product pL, where p is the working gas pressure, and L is the distance between the electrodes, which is commonly referred to as the Paschen curve. A similar discussion can be found in various textbooks such as by Lieberman and Lichtenberg (2005, Section 14.3), Raizer (1991, Chapter 7), and Roth (1995, Section 8.6). The electron density and flux grow exponentially as we move axially away from the cathode. Thus the increase in the electron flux is proportional to the flux, or de = α(z)e (z), dz

(1.1)

where e is the electron flux, and α is known as Townsend’s first ionization coefficient and is the inverse of the mean free path for ionization, that is, α(z) ≡ 1/λiz . The electron flux in the direction along the discharge axis (or the direction of the electric field) is  z  e (z) = e (0) exp α(z )dz . (1.2) 0

Due to the continuity of the total charge (creation of equal numbers of electron–ion pairs), we can write 



i (0) − i (L) = e (0) exp

L



α(z )dz





 −1 ,

(1.3)

0

where e (L) from Eq. (1.2) has been inserted. Since the discharge must be selfsustaining, we have e (0) = γsee i (0) and i (L) = 0. Then  exp 0

L

 1 α(z )dz = 1 + γsee

(1.4)

is the condition for self-sustainability. In a vacuum region, the electric field E is a constant, and it follows that the electron drift velocity μe E is also a constant. Hence the electron energy Ee is a constant, allowing us to treat α as a constant in Eq. (1.4). In that case, taking the logarithm of both sides of Eq. (1.4) gives   1 αL = ln 1 + , (1.5) γsee which is the breakdown condition for a dc discharge. The ionization coefficient is usually expressed in the form   Bp α = A exp − , (1.6) p E

Introduction to magnetron sputtering

9

Table 1.2 Constants for the Townsend ionization coefficient. Gas Air H2 Ar N2

A [cm−1 Torr−1 ] 14.6 5.0 13.6 11.8

B [V/(cm Torr)] 365 130 235 325

Range of E/p [V/(cm Torr)] 150 – 600 150 – 400 100 – 600 100 – 600

From Lieberman and Lichtenberg (2005).

where A and B are determined experimentally and found to be roughly constant over a range of pressures and fields for a given gas type. The coefficients A and B for various common gases are listed in Table 1.2. If the minimum voltage at which the discharge initiates, the breakdown voltage, is written as VB = EL, then     BpL 1 ApL exp − = ln 1 + , (1.7) VB γsee which solved for VB gives VB =

BpL

ln(ApL) − ln ln(1 + 1/γsee )

(1.8)

which is a function of the product pL. The product of pressure and distance between the electrodes (pL) is a suitable parameter to characterize the discharge. The curve that shows VB as a function of the product pL is called the Paschen curve. Thus for a fixed discharge length L, there is an optimum gas pressure for plasma breakdown. By differentiating the expression for the breakdown voltage, Eq. (1.8), with respect to pL and setting the derivative equal to zero, we can find the value of pL that corresponds to the minimum breakdown voltage (Raizer, 1991, Chapter 7)   exp(1) 1 (pL)min = ln 1 + , (1.9) A γsee and the minimum voltage is   B 1 , VB,min = exp(1) ln 1 + A γsee

(1.10)

which is referred to as the minimum sparking potential, and is the minimum voltage at which electrical breakdown can occur in a given gas. According to Eq. (1.8), the breakdown voltage is high for low and high pressure and a minimum at pL given by Eq. (1.9). At the lower pressures the ionization process is ineffective due to the low electron-neutral collision probability, whereas at higher pressures elastic collisions prevent the electrons from reaching high enough energy for ionization to occur. The number of gas atoms or molecules in the space between

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High Power Impulse Magnetron Sputtering

the electrodes is proportional to pL. At lower pressure, the distance between cathode and anode has to be longer to create a discharge with properties comparable to those of high pressure with small distance between the electrodes. For low pressure, the electron mean free path is large, and most electrons reach the anode without colliding with gas atoms or molecules. Thus, at low pressure, a higher value of VB is required to generate enough electrons to cause the breakdown of the gas. At higher pressures, the electron mean free path is short. The electrons do not gain enough energy from the electric field to ionize the gas atoms or molecules due to their frequent collisions with the gas molecules. Therefore VB increases as the pressure increases.

1.1.3 The cathode sheath All plasmas are separated from the surrounding walls by a sheath. We have seen in Section 1.1.1, and in particular in Fig. 1.3A, that most of the potential drop over a dc glow discharge appears across the cathode sheath. The relation between the sheath thickness dc , the discharge current density J , and the voltage drop across the cathode sheath Vc was derived by Child (1911), assuming that the initial ion energy is negligible compared to the sheath potential (see also Lieberman and Lichtenberg (2005, Section 6.2)), giving  1/2 3/2 4 Vc 2e J = 0 , 9 Mi dc2

(1.11)

where Mi is the ion mass. Eq. (1.11) is referred to as the Child law or the collisionless Child–Langmuir law. The Child law is valid when the sheath potential is large compared to the average energy of the electrons. A similar relation was derived by Langmuir (1913) for electrons emitted from a hot cathode approaching a cold anode (no thermionic emission). In the collisional regime, where the pressure is high enough that the charged species interact frequently with neutral gas species, we can assume that the ion-neutral mean free path λi is independent of the ion velocity (Lieberman and Lichtenberg, 2005, Section 6.6). This gives the collisional Child law J=

   3/2   3/2 2 5 2eλi 1/2 Vc 0 . 5/2 3 3 πMi dc

(1.12)

Alternatively, assuming that the diffusion of ions is negligible, compared to the drift due to an electric field, and assuming that the ion mobility μi is independent of the ion velocity, we get 9 V2 J = 0 μi c3 , 8 dc

(1.13)

which is referred to as the Mott–Gurney law. It was derived to describe the current at the interface of a semiconductor and insulator (Mott and Gurney, 1948, Chapter V) and later adapted to describe the current through the discharge sheath by Cobine (1958).

Introduction to magnetron sputtering

11

Equation (1.13) is valid only at very high pressures (low drift velocities). The relation between the current density, sheath voltage drop, and the sheath thickness given by Eqs. (1.12) and (1.13) is sometimes referred to as the collisional Child–Langmuir law. We note here that the scalings of the current density with both Vc and dc in Eq. (1.12) are different from Eq. (1.13). It has been demonstrated by experiments that the Mott–Gurney law (Eq. (1.13)) applies to a dc glow discharge in hydrogen (Lisovskiy et al., 2016) and nitrogen (Lisovskiy et al., 2014) for most of the pressure range from 10 to 333 Pa.

1.1.4 Secondary electron emission The emission of secondary electrons as a result of ions or neutrals bombarding a metallic surface plays an important role in discharge physics. The secondary electron emission yield or coefficient γsee is defined as the number of secondary electrons emitted per incident species. The secondary electron emission yield generally depends on the material being bombarded, its surface condition, the type of bombarding species, and the kinetic energy of the bombarding species. The sputter targets are held at high negative potentials, and thus the secondary electrons are accelerated away from the target surface with initial energy equal to the target potential. In many cases, these electrons sustain the discharge by ionization of the neutral working gas. These ions then bombard the cathode target and subsequently release more secondary electrons. As a first approximation, the secondary electron emission yield is independent of the velocity of the bombarding particle while their energy is low, since the electron emission occurs due to transfer of the potential energy of the incoming ion or atom to an electron in the target (Hagstrum, 1954, Abroyan et al., 1967). This constant secondary electron emission yield is attributed to an Auger process and is referred to as potential emission. The energy-dependent portion of the secondary electron emission yield is called kinetic emission. Kinetic emission occurs when a bombarding particle transfers sufficient kinetic energy to an electron in the target. Typically, it starts contributing to the total secondary electron emission yield at a threshold energy of around a few hundred electron volts. This process dominates at higher energies. Both experimental data and theory predict a linear dependence of the secondary electron emission yield on the bombarding particle energy close to the threshold energy, and linear dependence on the bombarding velocity at higher energies (Abroyan et al., 1967, Parilis and Kishinevskii, 1960, Cawthron, 1971, Baragiola et al., 1979, Hasselkamp, 1992). At much higher energies, experimental data show that the electron yield starts decreasing with increasing bombarding velocity. This occurs for a bombarding energy of around 100 keV for H+ (Hasselkamp, 1992). The two different mechanisms are considered to be detachable, so the total electron emission yield is written as γsee = γp + γk ,

(1.14)

where γp and γk are the contributions from potential and kinetic emission to the total yield, respectively. In addition to the energy of the impacting particle, the secondary

12

High Power Impulse Magnetron Sputtering

Figure 1.4 Secondary electron emission yields for Ar+ ions and neutral Ar beams incident on various dirty metal surfaces versus particle energy. The solid lines show the secondary electron emission yields for dirty metals, and dashed lines show the secondary electron emission yields for clean metals. After Phelps and Petrovi´c (1999) and Phelps et al. (1999).

electron emission yield depends on the cathode material but rarely exceeds 0.2 for metallic targets bombarded by ions with energy below 1 keV. The condition of the target significantly affects the ion-induced secondary electron emission yield. For clean surfaces, kinetic emission is dominant for projectile energies exceeding about 300 eV/amu (Winter et al., 1991, 2001) and has been observed down to an energy in the range 10 eV/amu (Eder et al., 2000). For Ar+ ion projectiles, this would mean a lower threshold of ∼ 0.4 keV, although kinetic emission would only play a dominant role for impinging ion energies above ∼ 12 keV. However, the threshold for kinetic emission may be reduced in case of dirty or technological surfaces (Phelps and Petrovi´c, 1999). Still, for an energy range of 0.5 – 1.0 keV, relevant in magnetron sputtering discharges, potential emission is expected to dominate. Clean metals, that is, metals free of oxidation, gas adsorbtion, and other contamination generally have a lower kinetic emission yield than contaminated metals (Phelps and Petrovi´c, 1999). The secondary electron emission yields for argon ions γsee,i and argon neutrals γsee,a bombarding “dirty” metal electrodes and “clean” metal electrodes are shown versus the ion or atom kinetic energy of the incident particle in Fig. 1.4. The secondary electron emission yields γsee,i and γsee,a are calculated using the formulas given by Phelps and Petrovi´c (1999) and Phelps et al. (1999). For “clean” surfaces, equations B10 and B12 in Phelps and Petrovi´c (1999) are used, whereas for “dirty” surfaces, equations B15 and B17 in Phelps and Petrovi´c (1999) are used (a correction to B15 is given by Phelps et al. (1999)). For the typical ion bombarding energies expected in magnetron sputtering discharges, including HiPIMS discharges, the secondary electron emission is determined by the potential energy of the arriving ion projectile rather than its kinetic energy. For a potential emission to occur, the potential energy (ionization potential) of the projectile has to exceed twice the work function of the target material. A fit to experimentally

Introduction to magnetron sputtering

13

Table 1.3 The work function φ and the first and second ionization energies for several common elements. Element Ar Al Cu Ti Cr W

φ [eV] N/A 4.08 – 4.28 4.9 4.1 – 4.3 4.5 4.55

Eiz,1 [eV] 15.76 5.99 7.73 6.82 6.77 7.98

Eiz,2 [eV] 27.63 18.83 20.29 13.58 16.50 17.62

From Anders et al. (2007).

determined secondary electron emission yields for various ions on clean surfaces is given as (Baragiola et al., 1979, Baragiola and Riccardi, 2008) γsee = 0.032 (0.78Eiz − 2φ) ,

(1.15)

where Eiz is the ionization energy of the ion, and φ is the work function of the target surface. This process can only occur when the condition 0.78Eiz > 2φ is fulfilled. Another empirical expression is also frequently used (Raizer, 1991): γsee = 0.016(Eiz − φ).

(1.16)

This condition is not fulfilled for most metal ions sputtering a target of the same metal. The work function φ and the first and second ionization energies for several common elements are shown in Table 1.3. Thus, as pointed out by Anders (2008) for a typical metallic magnetron sputtering target, singly charged metal ions cannot perform potential emission. During self-sputtering of a metal target, no secondary electrons are emitted, and the secondary electron emission coefficient is practically zero. We also note looking at Table 1.3 that for some of the common metals like Cr and Ti, the ionization energy to create doubly charged ions is relatively low, compared to the ionization energy of argon. In that case the concentration of the doubly charged ions of the sputtered material is expected to be high. These doubly charged ions can fulfill the condition 0.78Eiz > 2φ and thus create secondary electrons. The presence of a magnetic field close to the cathode surface, such as in the case of magnetron sputtering discharges (see Section 1.2.2), may have a strong influence on the secondary electron emission. Once emitted, the secondary electron motion is governed by the Lorentz equation, which results in helicoidal (arch-shaped) trajectories above the cathode. A fraction of the secondary electrons can thereby return to the cathode surface despite the strong repulsive electric field. Here they are either reflected or (re)captured, which will reduce the secondary electron emission yield. We therefore have to make a distinction between the standard γsee , which is a material-dependent property, and the effective secondary electron emission yield γsee,eff as seen by the discharge. Thornton was one of the first to study this issue in magnetron sputtering discharges (Thornton, 1978). He considered a coaxial cylindrical post magnetron and

14

High Power Impulse Magnetron Sputtering

estimated the recapture probability to be r = 0.5 based on a qualitative model for calculating the discharge voltage. Later on Buyle et al. (2004) calculated the recapture probability to be in the range 0.65 – 0.75 for a planar magnetron sputtering discharge configuration. For HiPIMS discharges, the recapture probability has been investigated more recently by Huo et al. (2013) and Gudmundsson et al. (2016), where values of r = 0.50 – 0.86 are reported. In general, the recapture probability is expected to depend on the geometry of the system, the magnetic field configuration, target erosion, and operational parameters, such as working gas pressure (Buyle et al., 2003, Costin et al., 2005). Finally, it should be noted that many of the secondary electrons are thermalized by collisions with the atoms of the working gas, but even at relatively high pressures a substantial number of the electrons retain the full target potential as they impact the anode.

1.1.5 Electron energy distribution function Knowledge of the electron dynamics in technological plasmas helps us to identify which elementary processes are involved in the discharge. The temporal evolution of the electron dynamics is particularly important for pulsed discharges, since it provides information on changes taking place in the plasma when, for example, the cathode voltage is intentionally altered or plasma instabilities occur. Spatial homogeneity of the electron distribution (which also influences other plasma properties) is very important in plasmas where thin films are deposited or surfaces are treated. Electrons constitute the lightest particles in glow discharges, which implies that electrons collide either with particles of the same mass or with particles having a considerably greater mass (neutrals or ions). A distribution function f (t, r, v) gives detailed information on a particle population for a given time t, at a certain position in space, described by the vector r and velocity v, i.e., a six-dimensional phase space of the particle position and velocity. The knowledge of this function allows for calculation of the number of electrons at time t in the volume element d3 r and having a velocity in the range from v to v + dv. For electrons, the electron distribution function (EDF) describes both isotropic and anisotropic electron populations. The electron density ne can be calculated from the electron distribution function as  (1.17) ne (t, r) = fe (t, r, v)dv, v

where fe (t, r, v) is the electron distribution function. The analytical expression of the EDF is often very complicated due to the complexity of low-temperature plasmas. However, from a practical point of view, some experimental techniques provide measurements of the electron energy distribution function (EEDF) ge (t, r, E). This distribution function also describes the electron population, but instead of using the velocity vector, we only gain knowledge of the kinetic energy of the electrons in an interval from E to E + dE. For determination of the EEDF, the electron population must be isotropic in the velocity space, and therefore we lose

Introduction to magnetron sputtering

15

information on the angular distribution. In the case of an isotropic EDF the following expression holds: fe (t, r, v) = fe0√(t, r, v), where we have used the relation between kinetic energy and velocity v = 2E/me , where me is the electron mass. Then the equation for expressing the EEDF as a function of an isotropic EDF is  ge (t, r, E) = 2π

2e me

3/2



E 1/2 fe0 t, r, 2E/me .

(1.18)

When the EEDF is known, the electron density ne can be calculated using Eq. (1.18) or  ∞ ne = ge (E)dE. (1.19) 0

We often use the electron energy probability function (EEPF) gp (t, r, E) = E −1/2 ge (t, r, E)

(1.20)

for visualization of evaluated Langmuir probe characteristics because it allows us to directly determine whether the measured electron distribution is Maxwellian or not (see also Chapter 3, Section 3.1.1 on Langmuir probes).1 When the EEPF is displayed on a semilog plot, it exhibits a straight line if the electron energy distribution is Maxwellian (Godyak and Demidov, 2011). Although the electron energy distribution provides full information on the kinetic properties of an electron gas, it is often convenient to describe the average dynamics of electrons for a given time and location. The effective electron temperature  2 2 1 ∞ Ege (E)dE (1.21) Teff = E = 3 3 ne 0 is often used as a measure of the average electron energy. In the case the EEDF is Maxwellian, we can refer to Te = 23 E as the electron temperature. In the following chapters, we often use the roman typeface symbol T for the voltage equivalent of the temperature such that kB Te [K] = eTe [V].

1.1.6 Electric potentials In Section 1.1.1, we discussed plasma sheaths being established in glow discharge plasmas to maintain plasma quasineutrality. A similar behavior is found in the plasma bulk, which is charged positive to prevent escape of electrons out of the plasma. The potential observed in the plasma bulk or at the plasma boundaries is called the plasma potential Vpl (see Fig. 1.3A), which, in the present context, is an important plasma parameter from the point of view of sheath electron energization (Brenning et al., 2016) 1 Maxwellian electron distributions can be found, for example, in plasmas with high plasma density and

higher pressures, where many collisions between electrons are expected leading to thermalization of the electron population.

16

High Power Impulse Magnetron Sputtering

and for ion acceleration (Hershkowitz, 1994). The plasma potential can theoretically be calculated by solving the Poisson equation, which in the case of no magnetic field and steady-state conditions is written as ∇ 2ϕ = −

e(ni − ne ) , 0

(1.22)

where ni is the ion density, ne is the electron density, e is the elementary charge, and 0 is the permittivity of vacuum. It can easily be shown that the plasma potential is constant when variations in charge neutrality are negligible and the plasma potential is changing significantly only at length scales comparable to or smaller than the Debye length for which charge neutrality is not preserved. Electrically isolated objects inserted into the plasma are bombarded by plasma electrons and ions and will in general take on a slightly negative potential with respect to the plasma potential due to the higher mobility of the electrons. Since neither electrons nor ions can be drained, the charging continues until a sufficiently negative potential balances out the electron and ion fluxes. This potential is known as the floating potential Vfl and gives rise to a zero net current to the inserted object. The magnitude of the floating potential Vfl can be determined by setting the absolute values of the ion and electron fluxes at the electrically isolated object to be identical, that is, |i | = |e |. The floating potential has a repulsing effect on the electron current, which decreases exponentially according to the Boltzmann distribution. Then the equality of ion and electron current densities can be expressed as   Vfl − Vpl 1 i = ns uB = ns v¯e exp , (1.23) 4 Te where uB = (eTe /Mi )1/2 is the Bohm velocity, v¯e = (8eTe /πme )1/2 is the mean electron speed, and Vfl − Vpl is the difference between the floating potential Vfl and the plasma potential Vpl . Solving Eq. (1.23) for Vfl − Vpl , we find Vfl − Vpl = −

  Te Mi ln , 2 2πme

(1.24)

where Mi is the ion mass.

1.1.7 Sputter yield Sputtering is the ejection of atoms due to bombardment of a solid or a liquid surface (the target) by energetic particles, often ions (Ruzic, 1990). The sputter yield Y is defined as the mean number of atoms removed from the target surface for each incident ion. In general the sputter yield depends on the energy of the incoming projectile ion, the ion incident angle (in relation to the target normal), the bombarding ion mass, and the target material. The maximum transferable energy in a collision has to be larger than the surface binding energy or Eth + Esp > Esb / , where Esb is the surface binding

Introduction to magnetron sputtering

17

energy (heat of sublimation) of the target material, Eth is the threshold energy for sputtering, Esp is the binding energy of a projectile to the target surface (Esp = 0 for noble gas ions), = 4Mi Mt /(Mi + Mt )2 is the energy transfer factor in a binary collision, and Mi and Mt are the masses of the projectile and the target atom, respectively (Eckstein, 2007). The minimum ion energy required for sputtering to take place is known as the threshold energy for sputtering and is given by Yamamura and Tawara (1996) as

  i Esb 1 + 5.7 M Mt / if Mi ≤ Mt , Eth = (1.25) if Mi ≥ Mt , Esb × 6.7/

and is typically in the range from some 10 eV to a few hundred eV. For example, if an Ar+ ion bombards a titanium target, then Mi < Mt and Eth ≈ 6.75 × Esb , and if an Ar+ ion bombards an aluminum target, then Mi > Mt and Eth ≈ 9.82 × Esb . There exist in the literature a number of semiempirical models that describe the energy and angular dependence of the sputter yield (see e.g. Sigmund (1969), Bohdansky (1984), Yamamura and Shindo (1984), and Yamamura and Tawara (1996)). Yamamura and Tawara (1996) give various empirical formulas for the sputter yield as a function of ion bombarding energy and data for various combinations of ions and target materials. In the energy range of interest here, 20 – 5000 eV, the sputter yield increases with increasing incident ion energy. The sputter yield is also strongly target material dependent. Sputter yields for Ar+ ions versus bombarding energy, in the energy range 0 – 1000 eV, for various target materials are shown in Fig. 1.5. In this energy range the sputter yield can be approximated by Y (Ei ) = aEib ,

(1.26)

where a, material dependent, and b (roughly 0.5) are fitting parameters that are given for a particular combination of bombarding ion and target materials (Anders, 2010, 2017). For Ar+ bombarding a Cu target, a = 0.1421 and b = 0.468, whereas for the self-sputtering Cu+ bombarding a Cu target, a = 0.0691 and b = 0.556. In addition, the sputter yield increases with increasing angle of incidence, and maximum occurs in the range between 60◦ and 80◦ and falls off rapidly as the angle is increased further (Oechsner, 1975). When the cathode surface is struck by a particle in this energy range, some atoms, referred to as primary knock on atoms, may gain substantial amount of the energy from the incoming ion through the collision. They in turn sputter or strike other atoms transferring momentum yet again. It is of great interest to track these mechanisms and evaluate their combined effects. Computer codes such as TRIM (Transport of Ions in Matter) (Biersack and Haggmark, 1980), SRIM (Stopping and Range of Ions in Matter) (Ziegler et al., 2008, 2010), and TRIDYN (a TRIM simulation code including dynamic composition changes) (Möller and Eckstein, 1984, Möller et al., 1988) are commonly used to calculate the sputter yield. They use a binary collision model and follow the incident particles and all of its cascade atoms until they sputter or their energy is too low to escape the surface potential.

18

High Power Impulse Magnetron Sputtering

Figure 1.5 Sputter yields for Ar+ ions in the energy range 0 – 1000 eV impinging on various target materials. The yields are calculated using a sputter yield calculator from the Surface Physics Group at TU Wien (Surface Physics Group at TU Wien, 2017), which is based on empirical equations for sputter yields at normal incidence by Matsunami et al. (1983).

It should be noted, however, that projectile-target combinations resulting in modifications of the target will lead to a lower accuracy, when using the empirical sputter yield equations discussed. This is particularly relevant for sputtering in reactive gas mixtures, such as N2 or O2 , which may form compounds on the sputter target and thereby altering the material properties. As an example, the sputter yield of Ti when bombarding a pure Ti target and a completely oxidized TiO2 target exhibits a difference in the Ti sputter yield by a factor 15 – 20 between the pure metal and compound targets at 500 eV incident ion energy. Thus target poisoning can have significant influence on the sputter yield as will be discussed further in Section 6.2.3. Using the sputter yield, we can now calculate the sputter rate Rsputter =

Y (Ei )Ji , entarget

(1.27)

where Y (Ei ) is the sputter yield, Ji is the ion current density at the target surface, and ntarget is the atomic density of the target. This can be used to estimate how deep the sputtering process digs into the target surface for a given operation time.

1.1.8 Energy distribution of sputtered atoms The atoms sputtered off the cathode target are considerably more energetic than thermally evaporated atoms (a few eV as compared to about a tenth of an eV). Usually it is desirable to maintain this initial kinetic energy of the sputtered atoms, because of its effect on the film growth (Petrov et al., 1993). Relatively low working gas pressures are typically desired to minimize scattering of the sputtered atoms. The sputter process is, therefore, normally a line-of-sight process where the deposition flux cannot be

Introduction to magnetron sputtering

19

easily controlled, since it consists of neutral atoms. This broad distribution has been measured for sputtered neutrals (Stuart et al., 1969) and is predicted by the Thompson random collision cascade model (Thompson, 1968, 1981). According to the Sigmund– Thompson theory, the energy distribution function can be approximated by fS−T ∝

E , (E + Esb )3−2m

(1.28)

where Esb is the surface binding energy of the target material, and m is the exponent in the interaction potential applied V (r) ∝ r −m (Hofer, 1991). This model predicts an energy spectrum that peaks sharply at 12 Esb , followed by a gradual decrease to higher energies (∝ 1/E 2 ). The energy distribution of atoms ejected from a target is expected to be independent of the nature of the incident ion and the crystal structure of the target. It should be noted that the original Sigmund–Thompson sputter energy distribution function, given in Eq. (1.28), slightly overestimates the probability to sputter-eject energetic atoms. A modified distribution function was later introduced by Stepanova and Dew (2004), where they added a cutoff energy Emax to better reflect experimentally measured profiles     E + Esb n . (1.29) fS−D = fS−T 1 − Emax + E Typical values of the constants are n = 1, m = 0.2 (Stepanova and Dew, 2004), and Emax = 20 eV (Lundin et al., 2013). The angular distribution of the sputtered atoms is often described as a cosine distribution. It means that the relative amount of material sputtered at any particular angle can be compared to the amount sputtered at normal incidence times the cosine of the angle from normal incidence. The overall distribution can thereby be drawn as an ellipse, and in three dimensions, the distribution would appear as an ellipsoid centered on the ion impact point. For a more detailed discussion of the energy and angular distribution of the sputtered material, the reader should consult the reviews given by Hofer (1991) and Gnaser (2007) or the original work by Thompson (1968, 1981) and by Sigmund (1969). If the sputtered material is subsequently ionized, then the ion energy distribution generally shows a narrow low-energy peak, due to thermalized atoms, which are ionized and then accelerated by the plasma potential, and a broad distribution at higher energies, which originates from the sputtered neutrals, which have been ionized by electron impact within the plasma (see e.g. Andersson et al. (2006)). Due to the small mass of the electron, the electron impact ionization does not change the energy of the resulting ion by much. More details on ion energy distributions in HiPIMS discharges are given in Section 4.1.3.

1.1.9 Collisions in gases The glow discharge contains electrons, different types of ions, neutral atoms, and molecules, as well as photons. In principle, we should consider collisions/interaction

20

High Power Impulse Magnetron Sputtering

between all these species, but fortunately some of these collisions are more important than others for the type of low-pressure glow discharges that are used for sputter applications. Before discussing the various collisions, it is necessary to examine the physics involved. The working gas pressure is an important parameter in discharge physics. At low pressure, only a few collisions occur, and the energy transfer between species is inefficient. At high pressure, many collisions occur between the various plasma species, which result in more equal temperatures of the species. The fundamental quantity that characterizes a collision between particles is the cross section σ (vR ), where vR is the relative velocity between the particles before collision. In the definition of the collisional cross section, an element of probability for a certain reaction to occur is implicitly included. The mean free path λ is the average distance traveled by a particle between collisions with other particles and is reciprocal to the product of the gas density (or pressure) and the collisional cross-section σ (vR ): λ=

1 . nσ (vR )

(1.30)

For argon gas at 0.13 Pa (1 mTorr) and room temperature, the average distance traveled by an Ar atom before a collision to another Ar atom is about 8 cm, and most other gases are within a factor of three of this value (provided gas atoms of thermal energy) (Chapman, 1980). When two particles collide, one or both particles may change their momentum or their energy, neutral particles can become ionized, and ionized particles can become neutral. Collision processes can be divided into elastic and inelastic collisions, depending on whether the internal energies of the colliding particles are maintained or not. The total energy, which is the sum of the kinetic and potential (internal) energy, is conserved in a collision. When the internal energies of the colliding particles do not change, then the sum of kinetic energies is conserved, and the collision is said to be elastic. In this case, the kinetic energy is generally exchanged between particles, whereas the total kinetic energy is conserved. Using the energy transfer function 4Mi Mt /(Mi + Mt )2 , it is found that the energy transfer is negligible in electron collisions with heavy particles, such as neutral atoms. For these cases, the electron just changes direction without significantly changing speed. When the sum of kinetic energies is not conserved, the collision is referred to as inelastic. The most important inelastic collisions are listed in Table 1.4. The inelastic collisions often involve excitation or ionization of the colliding particles, so that the sum of kinetic energies after collision is less than that before collision. Inelastic collisions involving electrons are essential to the maintenance of a glow discharge. The most important of these collisions is electron impact ionization. For electron impact ionization of an argon atom, this is written e + Ar −→ Ar+ + 2e, through which an Ar+ ion is formed along with two electrons. Thus a bound electron on the atom is ejected. It is through this multiplication of the electrons and subse-

Table 1.4 The most important inelastic collision types in glow discharges. Chemical symbols are used where appropriate. M refers to any type of metal atom and e refers to an electron. Inelastic reaction Ionization

Reaction example e + Ar −→ Ar+ + 2e

Excitation

e + Ar −→ Ar∗ + e

Recombination

e + Ar+ + body −→ Ar + body

Relaxation Dissociation

Ar∗ −→ Ar + hν e + O2 −→ O + O + e

Dissociative electron attachment Charge transfer Penning ionization

e + O2 −→ O− + O + e Ar + Ar+ −→ Ar+ + Ar Arm + M −→ Ar + M+ + e

Comments A bound electron in the atom is ejected from the atom. Threshold energy for ionization to occur (ionization potential φiz ). For Ar, φiz = 15.76 eV. Excitation of a bound electron to a higher energy level within an atom. Threshold energy for excitation to occur. For Ar, φexc = 11.56 eV. Inverse of ionization. Three body collision (with a wall for example) is typically required. Inverse of excitation. Release of photon with energy hν. Breaking apart a molecule. Requires overcoming the bond strength in the molecule, which is 5.15 eV for oxygen. Often the primary mechanism for negative ion formation in molecular gas. For oxygen, the threshold energy for dissociative attachment is 4.2 eV. Ion-neutral collision. Involves long-lived excited species called metastables, such as Arm with energy levels at 11.56 eV and 11.72 eV.

22

High Power Impulse Magnetron Sputtering

Figure 1.6 Low aspect ratio dc glow discharge used for sputtering.

quent acceleration by the electric field that the glow discharge is maintained. This process has a threshold referred to as ionization energy Eiz below which no ionization occurs. The ionization threshold for a few common gases and metals is given in Table 1.3. It is referred to as excitation when a transfer of energy to a bound electron on the atom allows the electron to jump to a higher energy level within the atom with a corresponding quantized absorption of energy. For ions colliding with atoms, the main processes are elastic scattering in which momentum and energy are exchanged. However, also inelastic collisions leading to resonant charge transfer can occur; see Table 1.4. In molecular gases, there are a number of additional important processes that can occur. These may include inelastic collisions, such as vibrational and rotational excitation, dissociation, and dissociative recombination. When negative ions are present, the processes can include attachment, detachment, ion–ion mutual neutralization, and positive–negative ion charge transfer.

1.1.10 DC glow sputter source For decades, the dc glow discharge was used as a sputter source, and there have been a number of reviews written on dc glow discharge sputter deposition (Kay, 1962, Westwood, 1976, Vossen and Cuomo, 1978, Thornton and Greene, 1994). In Fig. 1.6, we show a schematic of such a setup. The upper electrode is the cathode, which serves as a target for ion impact sputtering. In sputter deposition the cathode surface (the target) is the source of the film forming material. The material is then transported through the low-pressure gaseous environment, before it condenses on a substrate to form a film. Such processes can be used to deposit thin films of elemental, alloy, and compound materials as well as some polymeric materials. For sputter applications with the dc glow discharge, the distance between cathode and anode is generally short, so that normally only a short anode zone is present along with the cathode dark space and the negative glow, where the slightly positive plasma potential returns back to zero at the anode. The positive column is commonly absent in these short discharges. The diode sputter sources are often low aspect ratio dc glow discharges (L/R < 1 for a cylindrical configuration) and mainly used for sputtering of metals. Cathode diameters are typically in the range 10 – 30 cm, whereas the spacing between the cathode and anode is 5 to 10 cm. This configuration is referred to as an obstructed dc glow discharge.

Introduction to magnetron sputtering

23

The low pressure dc discharge will adjust the width of the cathode fall region, dc , such that a minimum value of the product dc p = (dp)min is established, referred to as the Paschen minimum. If the length of the dc discharge is less than dc at the Paschen minimum value, then the voltage drop over the cathode fall rises above the Paschen minimum Vc,min . This is desired in some plasma processing applications, where a large voltage drop across the cathode sheath is needed. Almost all the voltage appears across the cathode sheath (dark space or cathode fall). Typical dc glow discharges for sputter deposition require a negatively charged cathode at 2000 – 5000 V and a grounded surface anode. The substrates on which the sputtered atoms are deposited are placed on a substrate holder which is often the lower electrode or the anode. However, the substrate holder may be separate from the anode which then can be grounded, floating, biased, heated, cooled, or some combination of these. A typical dc glow discharge is maintained by secondary electron emission, and the operating pressure must be high enough so that the secondary electrons are not lost to the anode or to the grounded surfaces before performing ionization. These pressures are higher than preferred for optimum transport of the sputtered atoms due to scattering by the working gas atoms. Hence, there is a narrow pressure range around 2 – 4 Pa for dc glow discharge sputtering to be viable. At this pressure, the cathode dark space is about 1 – 2 cm wide. The discharge current density can be as high as 1 mA/cm2 , and the deposition rate is below 10 nm/min at best. The dc sputter source is generally weekly ionized with an ionization fraction of the order of 10−4 . In the dc sputter diode configuration the ions that impinge on the target surface do not have the full cathode fall potential. This is due to the working gas pressure that is high enough to allow charge-exchange collisions and momentum transfer collisions (thermalization) between the accelerating ions and the working gas neutrals. The consequence is that there is a broad energy spectrum of ions and high energy neutrals that impinge on the target surface. The higher the gas pressure, the lower the mean energy of particles that bombard the target. The disadvantages of dc diode sputter deposition include low sputter rate and thus low deposition rate, target poisoning by reactive contaminants, substrate heating due to electrons accelerated away from the cathode target, and that only electrically conductive materials can be used as sputter targets. Also the sputter power efficiency (sputtered atoms/ion-volt) is relatively low in these discharges as they operate at high voltage, and this efficiency decreases with increasing energy.

1.2 Magnetron sputtering To lower the discharge voltage and expand the operational pressure range, the lifetime of the electrons in the target vicinity has to increase. In the 1930s, Penning had proposed the use of magnetic fields in a sputtering system to extend the lifetime of the electrons escaping from the cathode, and trap them in the vicinity of the cathode target (Penning, 1936). Further exploration of the effects of a magnetic field on a dc glow discharge in diode configuration led to the discovery of an additional ionization

24

High Power Impulse Magnetron Sputtering

Figure 1.7 A schematic of the dc planar magnetron discharge used for sputtering.

region in the negative glow in the presence of a magnetic field and increased ion intensity at the cathode target (Kay, 1963). This idea was developed into a cylindrical hollow cathode device in which an axial magnetic field is used to trap electrons, coined as magnetron sputtering (Gill and Kay, 1965). The enhanced ionization due to the addition of a magnetic field leads to acceptable deposition rates and makes operation possible at working gas pressures significantly lower than 4 Pa (Gill and Kay, 1965). These coaxial cylindrical magnetron sputter sources (Thornton, 1978, Thornton and Penfold, 1978) were demonstrated in both hollow cathode (Gill and Kay, 1965, Thornton, 1974) and center cathode configuration (Wasa and Hayakawa, 1967, 1969). This work was followed by the introduction of the planar magnetron sputtering device by Chapin in 1974 (Chapin, 1974, 1979, Waits, 1978). A schematic of a dc planar magnetron sputtering configuration is shown in Fig. 1.7. In the planar magnetron sputtering discharge the cathode target is either a circular or a rectangular plate. In this configuration, the magnetic field can be created by permanent magnets (Waits, 1978), electromagnets (Window and Savvides, 1986a, Wendt and Lieberman, 1990), or a combination of both (Solov’ev et al., 2009, Kozyrev et al., 2011). The center portion of the magnet is of one polarity (north in Fig. 1.7), and the outer periphery is of the other polarity (south in Fig. 1.7). So the assembly consists of an outer annular magnet and an inner magnet of opposite polarity, and the magnetic field lines go out from the center of the cathode and go back into the cathode at the annular. Since the electrons spend more time where the electric field is perpendicular to the magnetic field, the ideal geometry would be to have the magnetic field parallel to the cathode surface. However, in reality the magnetic field produced by the magnet and its associated pole pieces comprise field lines, which extend from the sputter surface and return thereto to form an arch over what is referred to as the erosion region. Within this arch, ionizing electrons and ionized gas are confined forming a dense glow discharge and consequently a high level of sputter activity. We refer to this region as the ionization region. If the cathode plate is circular (can also be rectangular) the magnetic confinement leads to a luminous torus shaped plasma that hovers next to the target. Sometimes a planar magnetron discharge consists of a planar cathode (sputtering source or target) parallel to an anode surface. However, in most cases the anode is

Introduction to magnetron sputtering

25

a grounded shield around the magnetron target (as seen in Fig. 1.7) as well as the walls of the deposition system. Since the electrons move along magnetic field lines with ease, the magnetic field lines closest to the cathode target that go through a grounded structure, for example, the grounded shield, will define a “virtual anode” for the magnetron discharge. The position of the anode, including the virtual anode, is very important for the interaction between the plasma and the substrate. If the anode shields the plasma generated at the cathode from the substrate, then the plasma will be very weak in the substrate vicinity, and the possibility to utilize the plasma to modify the growing film, with, for example, low-energy ion bombardment, will be limited.

1.2.1 DC magnetron sputtering In a conventional dc magnetron sputtering (dcMS) discharge the cathode is kept at a constant negative voltage. Positive ions generated in the plasma are accelerated toward the cathode target generating a vapor of atoms and molecules from the target surface through sputtering (see Section 1.1.7). In the magnetron sputtering discharge the secondary electrons are accelerated by the potential difference between the cathode and the bulk plasma. The main advantage of the planar magnetron sputtering discharge is that the sputtered material flows in the direction normal to the cathode plane. Conventional planar dcMS sources are commonly operated using argon as the working gas in the pressure range 0.1 – 1.5 Pa and an applied cathode voltage in the range of 300 – 700 V, whereas the confining magnetic field strength at the target surface is in the range 20 – 60 mTesla. This leads to current densities of the order of 4 – 60 mA/cm2 and power densities of several tens of W/cm2 (Waits, 1978). This pressure regime and operation parameters define a collision-free sputter deposition process, where the deposition rate is limited by the target power density, and the sputtered atoms almost maintain their energy of a few eV obtained from the sputtering event. The electron density in the substrate vicinity is typically in the range 1015 – 17 10 m−3 (Rossnagel and Kaufman, 1986, Sheridan et al., 1991, Seo et al., 2004, Sigurjonsson and Gudmundsson, 2008). The static deposition rate is in the range 20 – 200 nm/s. The degree of ionization of the sputtered material is generally very low, often of the order of 0.1% or less (Petrov et al., 1994). The majority of the ions bombarding the substrate are ions of the noble working gas. Also, the density of the sputtered particles is much lower than the density of the noble working gas (Naghshara et al., 2011). The primary mechanism for the ionization of the sputtered metal atoms in a dcMS discharge is Penning ionization through impact with the working noble gas atoms that are in the metastable state (Christou and Barber, 2000). The mean free path for the sputtered material with respect to electron impact ionization is over 50 cm (Gudmundsson, 2010).

1.2.2 Addition of magnetic fields The path of the electrons in magnetron sputtering discharges is more complicated due to the presence of both a magnetic field B and an electric field E. As seen in Fig. 1.7,

26

High Power Impulse Magnetron Sputtering

the magnetic field is arched, and the electrons are reflected back into the ionization region (IR) above the race track (discussed in Section 1.2.3) whenever they encounter the cathode sheath edge. They bounce back and forth along the magnetic field lines in cycloid-like trajectories until a collision occurs. The majority of the ionization events occur in this region where the energetic electrons are trapped. That is why it is sometimes referred to as the ionization region. In the absence of an electric field, an electron will gyrate in the magnetic field with the electron cyclotron angular frequency eB , me

ωce =

(1.31)

and the corresponding gyration radius is rce =

ue,⊥ ue,⊥ me = , ωce eB

(1.32)

where ue,⊥ is the electron speed perpendicular to the magnetic field B. Typical values for rce are 1 – 10 mm. This means that electrons in the target vicinity are magnetized, that is, their gyration radius is much smaller than the characteristic size of the confining magnetic field structure. As a comparison, ions have a gyration radius rci of the order of 1 m, which is larger than the characteristic size of the system, and thus the ions are not magnetized by the relatively weak static magnetic field. In the presence of an electric field the electron exhibits a net drift perpendicular to both the B and E field vectors, often referred to as the Hall drift or the E × B-drift (Lieberman and Lichtenberg, 2005, Chen, 2016), which is given by vE =

E×B , B2

(1.33)

and the electrons perform trochoid movements. For a planar magnetron discharge, this drift is in the azimuthal direction, with typical drift velocities around 104 m/s within the ionization region. The resulting azimuthal current is often referred to as the Hall current (Thornton, 1978, Rossnagel and Kaufman, 1987). In addition, there is a drift driven by the electron pressure gradient (or diamagnetic drift) written as v∇p =

∇pe × B . ene B 2

(1.34)

The Hall drift (Eq. (1.33)) and the diamagnetic drift (Eq. (1.34)) result in an azimuthal current flowing above the target race track. Notice that, as pointed out by, for example, Thompson (1964, pp. 160–164), the curved vacuum B field drifts (the drifts of the gyro centers that are proportional to the electron energies E and E⊥ ) give no contribution to the macroscopic current in a homogeneous plasma.

1.2.3 Electron confinement and target utilization Due to the magnetic confinement, a torus-shaped dense plasma hovers in front of the cathode target. Thus in the planar magnetron configurations the sputter-erosion

Introduction to magnetron sputtering

27

is not uniform and leads to the formation of a circular groove-like erosion pattern (the “race track”). This is one of the characteristic features of conventional planar magnetron sputter tools and is a consequence of the charged particle confinement in the magnetic field. For a planar magnetron sputtering discharge, the target utilization is often in the range 26 – 45% (Chapin, 1974, Waits, 1978, Nakano et al., 2017). This race track formation limits the target utilization, resulting in higher operating costs. This also means that the deposition pattern can be non-uniform. Film thickness uniformity must be accomplished by substrate (or target) movement. This issue has been resolved to a large degree by using rotating magnetic assemblies that increase the target utilization and improve the deposited film thickness homogeneity dramatically (Iseki, 2006). Target utilization of up to 77% has been reported using an asymmetric yoke magnet structure (Iseki, 2010). Another option is the rotatable magnetron, which will be discussed in more detail in Section 1.3.2.

1.2.4 Electron heating If the discharge is sustained by secondary electron emission from the cathode and by ion bombardment, then the discharge current at the cathode target consists of electron current Ie and ion current Ii , or ID = Ie + Ii = Ii (1 + γsee ),

(1.35)

where γsee is the secondary electron emission coefficient (see also Section 1.1.4). Note that γsee ∼ 0.05 – 0.2 for most metals (Depla et al., 2009), so at the target the dominating fraction of the discharge current is due to ions. The number of electron–ion pairs created by each secondary electron that is trapped in the target vicinity is then N≈

VD , Ec

(1.36)

where Ec is the energy loss per electron–ion pair created with the flow of secondary electrons into the plasma as the source of energy (Lieberman and Lichtenberg, 2005, Thornton and Penfold, 1978, Depla et al., 2010) and VD is the discharge voltage. As we discussed in Section 1.1.4, not all the secondary electrons are confined in the target vicinity. To account for the electrons that are not trapped, we define the effective secondary electron emission coefficient γsee,eff = me (1 − r)γsee , where e is the fraction of the electron energy that is used for ionization before being lost, m is a factor that accounts for secondary electrons ionizing in the sheath, and r is the recapture probability of secondary electrons. To sustain the discharge, the condition γsee,eff N = 1

(1.37)

28

High Power Impulse Magnetron Sputtering

has to be fulfilled. This defines the minimum voltage needed to sustain the discharge as VD,min =

Ec βγsee,eff

(1.38)

,

where β is the fraction of ions that return to the cathode. Equation (1.38) is often referred to as the Thornton equation. The basic assumption is that acceleration across the sheath is the main source of energy for the electrons (Thornton, 1978). Above breakdown, the parameters m, β, e , and r can vary with the applied discharge voltage, so we can rewrite the Thornton equation for any voltage as (Depla et al., 2009) 1 βme (1 − r) = γsee . VD Ec

(1.39)

Thus a plot of the inverse discharge voltage 1/VD against γsee should then give a straight line through the origin. Depla et al. (2009) measured the discharge dc voltage for a magnetron sputtering discharge with a 5 cm diameter target of 18 different target materials with argon as the working gas while keeping the working gas pressure and discharge current constant. Since all the data are taken in the same magnetron at the same discharge current and working gas pressure, the discharge parameters m, β, e , and Ec are independent of γsee . The authors plotted 1/VD against γsee for working gas pressure of 0.4 and 0.6 Pa and discharge currents 0.4 A and 0.6 A, that is, total of four cases. It was found that for all cases, a straight line indeed results, but that it does not pass through the origin. It has been proposed that the intercept is due to Ohmic heating, that is, the dissipation of locally deposited electric energy J · E to the charged particles that carry the current density J (Brenning et al., 2016). Then the inverse discharge voltage 1/VD can be written in the form of a generalized Thornton equation β H m(1 − r)(1 − δIR ) eC Ie /ID IR δIR 1 = e γ + see VD EcH EcC       a

(1.40)

b

or V1D = aγsee + b, where the intersect is associated with the Ohmic heating process. Here eC is the fraction of the electron energy for the plasma bulk electrons that is used for ionization before being lost from the discharge process, eH is the fraction of the electron energy for the hot secondary electrons that is used for ionization before being lost from the discharge process, and δIR = VIR /VD is the fraction of the total discharge voltage that is dropped across the dense plasma next to the target, the ionization region. Using this formulation, Ohmic heating is thereby the energy gain of an average electron moved across a fraction Ie /ID IR of the potential VIR . It follows that the fraction of the total ionization that is due to Ohmic heating can be obtained directly from the line fit parameters a and b of the measured 1/VD versus γsee . This

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Figure 1.8 The relative contributions to the total ionization ιtotal due to Ohmic heating ιOhmic and sheath energization ιsheath . The curves show Eq. (1.40) using a and b from the four combinations of pressure and discharge current in the dc magnetron studied by Depla et al. (2009). They are plotted in the same top-down order as the labels and are drawn solid only in the range of γsee , where they are supported by the measurements of Depla et al. (2009). A blue circle (black in print version) marks the value from the HiPIMS study by Huo et al. (2013). Reprinted from Brenning et al. (2016). ©IOP Publishing. Reproduced with permission. All rights reserved.

ratio can be written as a function of only the secondary electron yield γsee : b ιOhmic = . ιtotal aγsee + b

(1.41)

This relation is plotted in Fig. 1.8 for the four cases studied by Depla et al. (2009). We see that the contribution of Ohmic heating is in the range 30 – 70%, and its contribution decreases with increased secondary electron emission coefficient. Furthermore, Fig. 1.8 also shows a high-power example from an aluminum HiPIMS discharge operated at an argon pressure of 1.8 Pa modeled by Huo et al. (2013), marked by a circle. It is taken at the end of a 400 µs long pulse when the discharge was deep into the selfsputter mode (the current composition of this discharge is discussed in Section 7.1.1). A large fraction of Al+ ions here give an effective γsee close to zero (see also discussion in Section 7.1.1). Note that this HiPIMS case is perfectly consistent with the dcMS cases. The fraction of the discharge voltage that falls over the ionization region δIR =

VIR VD

(1.42)

can be estimated from b=

eC Ie /ID IR δIR . EcC

(1.43)

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High Power Impulse Magnetron Sputtering

Huo et al. (2013, 2017) assume that eC = 0.8, Ie /ID IR ≈ 0.5, and EcC = 53.5 V for Te = 3 V, which gives δIR = 0.15 – 0.19, or 15 – 19% of the applied discharge voltage falls over the ionization region. These results are supported by recent measurements, which have revealed strong electric fields parallel and perpendicular to the target of a dc magnetron sputtering discharge (Panjan and Anders, 2017). The measurements show that the potential can be as high as 30 – 70 V (δIR = 11 – 25%) in the region up to 20 mm over the race track area for a dcMS discharge operated at 270 V and 0.27 Pa. The largest E-fields (and potential drops) result from a double layer structure at the leading edge of an ionization zone. It is suggested that the double layer plays a crucial role in the energization of electrons since electrons can gain several tens of eV when crossing the double layer (Panjan and Anders, 2017). Electrons gain energy when they encounter an electric field, a potential gradient, such as the field in the double layer. The electron heating power Je · E is associated with an acceleration of electrons in the electric field—this electron energization in a double layer is Ohmic heating.

1.3 Magnetron sputtering configurations The planar magnetron sputtering discharge is well established for deposition of thin films of both metallic and dielectric materials. It is widely used in both laboratory settings (using small circular targets) and in industrial applications where the targets are often linear (rectangular and larger). The magnetron sputtering technique can be applied to a large variety of materials and is easily scalable to large areas. The coating uniformity can be in the range of a few percent even for cathodes in the range of meters. Over the past decades, magnetron sputtering has become an extremely important technology for thin film deposition in a wide range of industrial applications. These include metallization in integrated circuits (Hopwood, 1998, Rossnagel, 2008), coatings for wear resistance and corrosion protection (Kelly et al., 1996), large area coating of architectural glass (Nadel et al., 2003), and display applications (KrempelHesse et al., 2009). Depending on the application the applied target voltage can be constant (dc), radio frequency (Nowicki, 1977), or pulsed (Schiller et al., 1993). The configuration can be planar, cylindrical with axial magnetic field, or rotating around a fixed magnetic assembly (discussed in Section 1.3.2). Much of the early exploration of the magnetron sputtering phenomena was made on cylindrical magnetron configurations with axial magnetic field, which were either in the cylindrical post, with the inner cylinder as the cathode target, or the cylindrical-hollow (or inverted magnetron), with the outer cylinder as the cathode target (Thornton, 1978, Thornton and Penfold, 1978). The E × B drift paths go around the cylinder, either on the inside or the outside, depending on the configuration. These configurations are not in much use nowadays except for the hollow cathode magnetron configuration, which is well suited for coating wires or fibers that are allowed to pass through it.

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Figure 1.9 A schematic of the magnetic design commonly used in magnetron sputtering discharges. The three cases, (A) all the field lines originate from the central magnet and pass into the annular magnet (Balanced), (B) all the field lines originate from the central magnet, with some not passing into the annular magnet (Unbalanced type I), and (C) all the field lines originate from the annular magnet, with some not passing into the cylindrical central magnet (Unbalanced type II).

1.3.1 Balanced and unbalanced magnetrons The conventional planar magnetron sputtering discharge is considered to be balanced if the magnetic fluxes through the pole faces of the outer poles and through the pole face of the inner pole are the same, as seen in Fig. 1.9A. If the condition is fulfilled, then the magnetic trap confines the plasma just in front of the cathode target. The substrate thus experiences very little impingement by ions. That is useful when depositing on, for example, heat sensitive substrates. To increase the ion flux to the substrate, an unbalanced magnetron was developed by Window and Savvides (Window and Savvides, 1986a,b, Savvides and Window, 1986). It is based on strengthening or weakening of the magnetic flux through one of the poles, which leads to an unbalance in the magnetic circuit. Window and Savvides (1986a) define two types of unbalancing. In type I, all field lines originate from the central magnet with some not passing into the annular magnet, as seen in Fig. 1.9B. For this case, the unbalanced field lines are directed toward the chamber walls leading to low plasma density in the substrate vicinity. In type II, all field lines originate from the annular magnet with some not passing into the central magnet, as seen in Fig. 1.9C. These unbalanced field lines extend into the substrate vicinity. Some of the secondary electrons can follow these magnetic field lines away from the target toward the substrate. Thus the plasma is not strongly confined to the cathode target region, but is allowed to flow out toward the substrate. This leads to a significant increase in the ion current density in the vicinity of the substrate (Savvides and Window, 1986, Sproul, 1998). As a consequence, the energy of the ions bombarding the substrate during film growth, can be tuned by a substrate bias.

1.3.2 Rotating magnetrons For a few decades, large cylindrical targets have been used for large area coatings. In this configuration the cathode target is a cylindrical tube, and the magnet assembly is installed inside the cylinder, as seen in Fig. 1.10. The rotatable cylindrical mag-

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High Power Impulse Magnetron Sputtering

Figure 1.10 The rotating magnetron sputtering discharge. The cathode target is a tube that rotates around the fixed magnet assembly with a rotation frequency of roughly 1 Hz. After Wright and Beardow (1986).

netron target was originally proposed to alleviate the problem of low target utilization (Wright and Beardow, 1986). In this configuration the target life increases substantially, and the target utilization can be as high as 90%. The target can rotate during sputtering, so the target erodes uniformly as the target material is continuously exposed to the plasma zone resulting in a uniform erosion around 360◦ of the target surface. These rotatable targets are essential for deposition on large area glass for architectural and automotive applications and for the production of flat panel displays and photovoltaic solar cells (Blondeel et al., 2009). For large area coatings, using a typical inline coater, the substrate is moved relative to the magnetron cathode target in a linear fashion. In particular for reactive sputtering, the active region of the rotatable target is maintained free of dielectric layer build up due to continuous sputtering with rapid rotation speeds (20 rev/min) (Nadel et al., 2003). In the cylindrical configuration the target surface area may be in hundreds and up to tens of thousands of square cm. In some cases the magnet assembly is wobbled for improved layer thickness distribution (Krempel-Hesse et al., 2009).

1.4 Pulsed magnetron discharges Over the years, various modifications have been made to improve the magnetron sputtering technology (see e.g. the reviews by Kelly and Arnell (2000) and Sproul (1998)), in particular, to increase the flux of ions to the substrate and to allow deposition of dielectric films. We will first address the issue of depositing insulating thin films by pulsing the magnetron discharge.

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33

1.4.1 Definition of pulsed magnetron sputtering discharges The pulsed magnetron sputtering (pMS) arrangement can be either asymmetric bipolar pulsed (Kelly et al., 2000, Sellers, 1998, Scholl, 1998) or a unipolar pulsed (Kouznetsov et al., 1999). The asymmetric bipolar pulsing was developed to address issues in reactive sputtering. These issues will be discussed in detail in Chapter 6. The parameter range is much wider in the pulsed system compared to conventional dc and radio frequency (rf) operation, and the pulsing of the discharge allows for a much greater flexibility due to additional control parameters, such as pulse width, duty cycle (the percentage of the time that the pulse is on), and pulse frequency. In reactive sputtering, the deposited film is a compound and redeposition on the target will therefore result in a different material compared to the composition of the bulk target. If the compound film is an insulator, such as Al2 O3 or Si3 N4 , then a capacitor is formed: The pure metal target (cathode) acts as one conductor, the plasma acts as the other conductor, and in between the insulating film forms the dielectric of the capacitor (Sellers, 1998). The metal cathode target is negatively charged, and a positive charge is collected on the plasma facing side of the insulator film. This is problematic for several reasons: (i) The dc current cannot flow through a capacitor. As we have seen in Section 1.2.4, the discharge current is mainly carried by positive ions impinging on the target. For the part of the target covered by the insulating compound, it means that very few ions will arrive at this zone and sputter the compound. Consequently, this area of the target is poisoned. (ii) The parasitic capacitor may not be able to charge up all the way to the applied discharge voltage. If this is the case, there will be a breakdown of the insulator, which will cause a sudden release of charge carriers. It forces the localized current density to increase into the arc discharge regime, which is not desired (see also Section 1.1.1). (iii) If the entire cathode is covered by the insulating film, then the discharge will be extinguished as soon as the insulator surface voltage drops below the voltage required to sustain the discharge (see also discussion on minimum voltage required in Section 1.2.4). One solution is to use pulsed magnetron sputtering and in particular bipolar pulsed discharges, so that the positive charge accumulated during the negative voltage pulse can be neutralized by electron bombardment during the positive voltage pulse. For this purpose, let us estimate the charging time of an insulator assuming a constant discharge current density J0 = 1 mA/cm2 . The capacitance can thereby be calculated as C = Q/V = (J0 At)/V , and therefore the charging time t = CV /(J0 A), where Q is the charge. Using a typical capacitance per area unit of C/A = 1 pF/cm2 and an applied voltage of V = 1000 V, we find that t = 1 µs. It is thereby possible to generate an almost continuous discharge with a pulse frequency of about 1 MHz. In practice, it is found that the charging time is somewhat longer, since the current is not constant and pulsing frequencies ≥ 100 kHz are typically sufficient (Chapman, 1980, pp. 10–11).

34

High Power Impulse Magnetron Sputtering

Alternatively, it is also possible to use rf magnetron sputtering (usually operated at 13.56 MHz) to deposit dielectric compound films. In particular, when depositing from thick electrically insulating (often compound) target materials, rf power is the only option. Rf sputtering can indeed produce high-quality insulating thin films, such as Al2 O3 from an insulating Al2 O3 target (Voigt and Sokolowski, 2004), but the deposition rates are in most cases considerably lower compared to pulsed magnetron sputtering. Rf power can also be used for reactive sputtering of Al to form aluminum oxide films. However, reactive deposition of aluminum oxide with rf power deposits only at 2 – 3% of the metal deposition rate (Sproul, 1998). Also, rf driven magnetron sputtering systems are complex and difficult to scale up for commercial applications.

1.4.2 Asymmetric bipolar mid-frequency pulsing The asymmetric bipolar dc sputtering discharge was developed to optimize the deposition of insulating films from conductive targets through reactive sputtering (Sellers, 1998). Pulsing the magnetron sputtering discharge in the medium frequency range (10 – 250 kHz) when depositing insulating films can significantly reduce the formation of arcs and, consequently, reduce the number of defects in the resulting film (Schiller et al., 1993). The duty cycle is typically 50 – 90% (Kelly and Bradley, 2009). Asymmetric bipolar pulsing, during which reversed voltage pulses of about +50 to +150 V (or roughly 10 – 20% of the negative voltage amplitude) are added to the normal dc waveform (see Fig. 1.11), are often claimed to be the optimum solution to the target poisoning problem (Sellers, 1998). The reason is that this technique allows for preferential sputtering of the insulating layer that forms on the target surface during reactive sputtering. The working mechanism has been described by Sellers (1998) and can be summarized as follows: First, a typical discharge voltage of VD = −400 V is applied to the cathode target (Fig. 1.11A), which leads to positive ions being accelerated toward the target sputtering predominantly the metal target. The insulating area will not be significantly sputtered, since it collects low-energy ions and the top surface of the dielectric of this parasitic capacitor is thereby charged towards +400 V and thus limits ion acceleration and ultimately reduces the sputter yield. Next, the polarity is rapidly reversed to about +100 V (Fig. 1.11B), which leads to the plasma-facing surface of the insulator to be charged toward −100 V. As the pulse once more reverses and the metal target reaches −400 V, the parasitic capacitor is charged to −100 V (Fig. 1.11C). The effective voltage on the plasma-facing side of the insulator is now −500 V, and consequently the positive ions can sputter this region with an increased energy compared to the pure metal target and thereby reduce the compound fraction of the target. This process requires a high enough frequency to avoid build-up of voltage on the compound covered regions to not cause a breakdown of these parasitic capacitors (Schiller et al., 1993), as described in item (ii) in Section 1.4.1. In practice, this means pulsing frequencies around 100 kHz, which is also in line with our previous frequency estimation concerning sustaining the discharge. Deposition rates during pMS approach those obtained for the deposition of pure metal films. In the case of Al2 O3 , Sproul (1998) reports deposition rates as high as

Introduction to magnetron sputtering

35

Figure 1.11 Preferential sputtering by asymmetric bipolar sputtering. Three points in time are displayed: (A) normal sputter mode, (B) reversal mode, and (C) return to sputter mode. After Sellers (1998).

78% of the metal deposition rate. Note that this technology has also been applied to deposit resistive (not insulating) thin films. In these cases, slightly higher frequencies have been required due to the tendency of the resistive film to self-discharge (Sellers, 1998). Asymmetric bipolar pulsing has rather complex process characteristics due to the steep transients in the voltage waveforms on the µs scale in combination with the spatial variations in the magnetic field and plasma density (Kelly and Bradley, 2009). For ease of comparison with HiPIMS, covered in detail in this book, here we summarize some of the most striking features. From Langmuir probe studies (Glocker, 1993, Bradley et al., 2001) it has been established that the time averaged effective electron temperature Teff is generally greater in pMS compared to dcMS. This is also seen in Fig. 1.12A, where Teff is increased by 33% compared to dcMS values by pulsing at 100 kHz. It is believed that the increased electron heating is due to the pulsed nature of the discharge. The mechanism is likely stochastic heating by the advancing sheathedge during pulse-on, which may then heat the plasma globally through subsequent collisions (Glocker, 1993). In addition, Bradley et al. (2001) show that there is a burst of hot or beam-like electrons shortly after the initiation of the negative voltage pulse, which is probably due to electrons coming directly from the target and accelerated in the cathode sheath. Pulsing the discharge also increases the time-averaged electron density. One example is shown in Fig. 1.12B, where there is an 18% increase at 100 kHz compared to dcMS, although values of up to 300% increase have been reported (Glocker, 1993). However, electron density on the order of ne ∼ 1016 m−3 is too low for the pMS discharge to generate a substantial fraction of ionized sputtered material. As an example, we can estimate the degree of ionization of sputtered Ti by looking at the probability for the sputtered neutral to undergo electron impact ionization when traveling a distance z (see e.g. Lundin et al. (2015) and Gudmundsson (2010) for details on the calculations). By taking the time-averaged values Te = 4.5 eV and ne = 8.4 × 1015 m−3 for the pMS discharge characterized in Fig. 1.12, an estimated velocity of the neutral of 500 m/s, and a typical distance of z = 0.05 cm, we find an ionization probability of

36

High Power Impulse Magnetron Sputtering

Figure 1.12 Langmuir probe measurements at a typical substrate position in pMS. The variation of the electron density ne , and the effective electron temperature Teff during one pMS cycle at 100 kHz pulse frequency. The solid red line (gray in print version) represents the average value from the time-resolved measurements and the dashed blue line (black in print version) represents the value measured in a dcMS equivalent discharge. Data taken from Bradley et al. (2001).

< 1% with a corresponding electron impact ionization mean free path of about 25 cm. It is therefore concluded that although the pMS technique is suitable for reactive sputtering of insulating or poorly conductive thin films, it does not lead to a significant increase of the flux of ions of the sputtered material to the substrate, although some increase of the substrate bias current compared to dcMS has been reported (Kelly and Arnell, 2000).

1.4.3 Magnetron sputtering with a secondary discharge For many applications, a high degree of ionization of the sputtered material is desired as the ion flux to the substrate is known to have a significant influence on the overall quality of the resulting film (Rossnagel and Cuomo, 1988, Colligon, 1995). Furthermore, the energy of the ions bombarding the substrate can be controlled. Over

Introduction to magnetron sputtering

37

the past three decades, there has been significant progress in enhancing the level of ionization in the magnetron sputtering discharge. This was initially achieved by the application of a secondary discharge to a conventional magnetron sputtering discharge (Gudmundsson, 2008), either an inductively coupled plasma assisted magnetron sputtering (ICP-MS) (Yamashita, 1989, Rossnagel and Hopwood, 1994, 1993, Joo, 2000, Hopwood, 2000a) or a microwave amplified magnetron sputtering source (Gorbatkin et al., 1996, Musil et al., 1991, Yoshida, 1992, Xu et al., 2001, Wendt, 2000, Holber, 2000). The secondary discharge typically creates a plasma with an electron density in the range of 1017 – 1018 m−3 and with electron temperatures in the range of 1.5 – 4.5 V (Hopwood and Qian, 1995, Yamashita et al., 1999), which correspond to an electron impact ionization mean free path for the sputtered vapor of a few cm (Hopwood, 1998, Gudmundsson, 2010). The ICP-MS discharge is currently widely used in the semiconductor industry for deposition of metal and compound lines, pads, vias, and contacts (Rossnagel, 2008). The combination of magnetron sputtering and secondary high-density discharges have also been applied to demonstrate a collisionless deposition process at pressures below 0.1 Pa (Yoshida, 1992, Musil, 1998). When the deposition flux consists of more ions than neutrals, that is, M+ > M , then the process is referred to as ionized physical vapor deposition (IPVD) (Hopwood, 2000b). Common to all the IPVD techniques is a very high electron density, typically, ≥ 1018 m−3 . The plasma density increases with increased power density supplied to the target. However, an increased power density leads to overheating and eventually melting of the sputter target. Thus, there is an upper limit to the power that can be delivered through the discharge cathode target.

1.4.4 High power impulse magnetron sputtering More recently, a method using high power pulsed magnetron sputtering discharges in unipolar mode, referred to as high power impulse magnetron sputtering (HiPIMS), or less often as high power pulsed magnetron sputtering (HPPMS), has been proposed as one solution to stay below the power limit for target/magnetron damage, while at the same time achieving a highly ionized flux of the sputtered material (Kouznetsov et al., 1999, Macák et al., 2000). In HiPIMS, this is accomplished using pulsed plasma discharges with a peak power density in the range 0.5 – 10 kW/cm2 (averaged over the target surface) at a low duty cycle in the range of 0.5 – 5%, that is, considerably lower than the 50 – 90% in pMS discussed in Section 1.4.2. The HiPIMS discharge operates by applying square voltage pulses of about 500 – 2000 V, which generates peak current densities of up to 3 – 5 A/cm2 (Helmersson et al., 2006, Gudmundsson et al., 2012). The pulse length is in the range 20 – 500 µs, but typically 30 – 100 µs when depositing thin films, with a repetition frequency of 50 – 5000 Hz. To distinguish this technique from other pulsed magnetron processes, Anders (2011) defines HiPIMS as pulsed magnetron sputtering where the peak power exceeds the time-averaged power by typically two orders of magnitude. Through the use of very high applied instantaneous power densities to the magnetron cathode target, there is a significant increase in the charge carrier density in front of the target during the HiPIMS pulse. In numbers, this means that for the

38

High Power Impulse Magnetron Sputtering

HiPIMS discharge, the electron density in the ionization region close to the target surface is on the order of 1018 – 1019 m−3 (Gudmundsson et al., 2001, 2002), which corresponds to an electron impact ionization mean free path for a sputtered metal atom on the order of 1 cm or less (Gudmundsson, 2010). The characteristics and technical aspects of HiPIMS will be thoroughly dealt with in the following chapters of this book. However, let us first compare this method to the previously discussed dcMS and pMS techniques as well as other HiPIMS-type solutions. First, we already here stress that a few variations of high power pulsed magnetron sputtering discharges exist. For example, superposition of dcMS and HiPIMS discharges (on one magnetron target) have been reported by several authors (Mozgrin, 1994, Samuelsson et al., 2012, Ganciu et al., 2005, Bandorf et al., 2007) and is sometimes referred to as pre-ionized HiPIMS (Va˘sina et al., 2007). Also, decomposition of a single HiPIMS pulse into several individual pulses to produce a pulse sequence (pulse train) has been investigated to some extent (Barker et al., 2013, 2014, Antonin et al., 2015). For this configuration, there is a delay of a few tens of µs between each individual pulse while maintaining typical HiPIMS off-times of milliseconds between each sequence. These and various other hybrid configurations will be described in more detail in Chapter 2.

1.4.5 Modulated pulse power magnetron sputtering Another approach to high power pulsed magnetron sputtering consists of modulating the pulse such that in an initial stage (a few hundred microseconds) the power level is moderate (similar to dcMS levels), followed by a high power pulse (lasting a few hundred microseconds up to a millisecond). Such type of longer pulses are referred to as modulated pulse power magnetron sputtering (MPPMS). This method uses longer pulses, with pulse widths up to 3 ms, at similar repetition rates as found in HiPIMS, that is, in the range between several 10 Hz and a few 100 Hz, leading to duty cycles well above 5% (up to 25%). The main feature of this approach is the superimposition of a macropulse, that is, the previously described longer voltage pulse, with a train of shorter micropulses with frequencies in the range of several 10 kHz. The “on”- and “off”-time of these micropulses, which are typically up to several 10 µs, as well as their frequency can be altered within the macropulses. Using this approach, varying the micropulse frequency and the “on”- and “off”-times arbitrarily, target voltage and discharge current waveforms can be created (Chistyakov and Abraham, 2009, Liebig et al., 2011). Although this technique is not the focus of the book, we will still compare the HiPIMS/MPPMS plasma process characteristics in Chapter 3.

1.4.6 Summary As a summary, we present an overview of the discussed magnetron sputtering discharges in terms of duty cycle versus peak power density (at the target) pt illustrated in Fig. 1.13. We take pt = 0.05 kW/cm2 to be a typical upper limit for a dcMS discharge before target damage sets in. Pulsed magnetron sputtering discharges operated below

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39

Figure 1.13 An overview of dc and pulsed magnetron sputtering discharges based on the peak power density at the target pt , and the duty cycle. Reprinted with permission from Gudmundsson et al. (2012). Copyright 2012, American Vacuum Society.

this limit are referred to as pulsed dcMS and include the bipolar asymmetrically pulsed discharges, discussed in Section 1.4.2. For all discharges operating above the dcMS limit, the higher peak power must be compensated for by a lower duty cycle. Pulsed magnetron sputtering discharges that are operated at the higher peak power with a low duty cycle are referred to as high power pulsed magnetron sputtering (HPPMS) discharges. For square-shaped pulses, this gives the power density limit line shown in Fig. 1.13. The HiPIMS range in peak power density is defined to lie above a HiPIMS limit of pt > 0.5 kW/cm2 . MPPMS pulses typically begin at a low power level, often in the dcMS range, followed by a stronger pulse of intermediate power density (0.05 < pt < 0.5 kW/cm2 ) or even into the HiPIMS range. These definitions are used throughout the book.

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Anders, A., 2017. Tutorial: reactive high power impulse magnetron sputtering (R-HiPIMS). Journal of Applied Physics 121 (17), 171101. Anders, A., Andersson, J., Ehiasarian, A., 2007. High power impulse magnetron sputtering: current–voltage–time characteristics indicate the onset of sustained self-sputtering. Journal of Applied Physics 102 (11), 113303. Anderson, G.S., Mayer, W.N., Wehner, G.K., 1962. Sputtering of dielectrics by high-frequency fields. Journal of Applied Physics 33 (10), 2991–2992. Andersson, J.M., Wallin, E., Münger, E.P., Helmersson, U., 2006. Energy distributions of positive and negative ions during magnetron sputtering of an Al target in Ar/O2 mixtures. Journal of Applied Physics 100 (3), 033305. Antonin, O., Tiron, V., Costin, C., Popa, G., Minea, T.M., 2015. On the HiPIMS benefits of multi-pulse operating mode. Journal of Physics D: Applied Physics 48 (1), 015202. Bandorf, R., Falkenau, S., Schmidt, V., Mark, G., 2007. Modifications of coatings by DCsputtering with superimposed HPPMS. In: Proceedings of the 50th Society of Vacuum Coaters Annual Technical Conference. Louisville, Kentucky, April 28–May 3, 2007. Society of Vacuum Coaters, Albuquerque, New Mexico, pp. 477–479. Baragiola, R.A., Alonso, E.V., Ferron, J., Oliva-Florio, A., 1979. Ion-induced electron emission from clean metals original research article. Surface Science 90 (2), 240–255. Baragiola, R.A., Riccardi, P., 2008. Electron emission from surfaces induced by slow ions and atoms. In: Depla, D., Mahieu, S. (Eds.), Reactive Sputter Deposition. Springer Verlag, Berlin–Heidelberg, pp. 43–60. Barker, P.M., Konstantinidis, S., Lewin, E., Britun, N., Patscheider, J., 2014. An investigation of c-HiPIMS discharges during titanium deposition. Surface and Coatings Technology 258, 631–638. Barker, P.M., Lewin, E., Patscheider, J., 2013. Modified high power impulse magnetron sputtering process for increased deposition rate of titanium. Journal of Vacuum Science and Technology A 31 (6), 060604. Biersack, J.P., Haggmark, L.G., 1980. A Monte Carlo computer program for the transport of energetic ions in amorphous targets. Nuclear Instruments and Methods 174 (1–2), 257–269. Blondeel, A., Persoone, P., De Bosscher, W., 2009. Rotatable magnetron sputter technology for large area glass and web coating. Vakuum in Forschung und Praxis 21 (3), 6–13. Bohdansky, J., 1984. A universal relation for the sputtering yield of monatomic solids at normal ion incidence. Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms 2 (1–3), 587–591. Bradley, J., Bäcker, H., Kelly, P.J., Arnell, R.D., 2001. Time-resolved Langmuir probe measurements at the substrate position in a pulsed mid-frequency DC magnetron plasma. Surface and Coatings Technology 135 (2–3), 221–228. Brenning, N., Gudmundsson, J.T., Lundin, D., Minea, T., Raadu, M.A., Helmersson, U., 2016. The role of Ohmic heating in dc magnetron sputtering. Plasma Sources Science and Technology 25 (6), 065024. Budtz-Jørgensen, C.V., 2001. Studies of Electrical Plasma Discharges. Ph.D. thesis. Aarhus University, Aarhus, Denmark. Bundesmann, C., Neumann, H., 2018. The systematics of ion beam sputtering for deposition of thin films with tailored properties. Journal of Applied Physics 124 (23), 231102. Buyle, G., De Bosscher, W., Depla, D., Eufinger, K., Haemers, J., De Gryse, R., 2003. Recapture of secondary electrons by the target in a DC planar magnetron discharge. Vacuum 70 (1), 29–35.

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Hardware and power management for high power impulse magnetron sputtering

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ˇ Hubicka ˇ a , Jon Tomas Gudmundssonb,c , Petter Larssond , Daniel Lundine Zdenek a Institute of Physics v. v. i., Academy of Sciences of the Czech Republic, Prague, Czech Republic, b Department of Space and Plasma Physics, School of Electrical Engineering and Computer Science, KTH Royal Institute of Technology, Stockholm, Sweden, c Science Institute, University of Iceland, Reykjavik, Iceland, d Ionautics AB, Linköping, Sweden, e Laboratoire de Physique des Gaz et Plasmas - LPGP, UMR 8578 CNRS, Université Paris–Sud, Université Paris–Saclay, Orsay Cedex, France

The historical development of the high power impulse magnetron sputtering (HiPIMS) technique is here reviewed, and the various high power pulsers developed over the years are discussed. The work that led to the development of the HiPIMS technique was initiated at the Moscow Engineering and Physics Institute (MEPhI) in the late 1960s, where high power pulses were applied to diode sputter sources. Magnetic confinement was added in the 1980s, and the high power pulsed magnetron technique was developed into various applications, including electron emitters. A pre-ionized HiPIMS discharge was reported in the early 1990s and demonstrated as a tool to deposit thin films and for ion-stimulated etching. The first HiPIMS power supplies utilized a high power thyristor and a rather small capacitor that was charged through a diode circuit from a 50 Hz (or a transformer) source and discharged through an inductor. In the past two decades, there has been a significant improvement of the pulsing technology. These improvements include the introduction of the insulated-gate bipolar transistor (IGBT) as a high power switch along with larger capacitors or capacitor banks and more sophisticated arc handling. These developments have led to improvements in the discharge voltage and current waveforms, as well as allowing variation of the repetition frequency, and a better defined pulse length.

2.1 Brief history of high power pulsed magnetron sputtering The design of the pulse generators used for HiPIMS is based on the technology developed to drive radars in the 1940s (Glasoe, 1948), xenon flash-lamp pump sources for solid state lasers in the 1960s (Markiewicz and Emmett, 1966), and for high power lasers in the 1980s (Christie et al., 1982, Whitham et al., 1987). They have more reHigh Power Impulse Magnetron Sputtering. https://doi.org/10.1016/B978-0-12-812454-3.00007-3 Copyright © 2020 Elsevier Inc. All rights reserved.

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cently been developed to drive pulsed cathodic arc deposition sources (Siemroth et al., 1994, Anders et al., 1999). The historical development of the power supplies for the HiPIMS discharge has been reviewed by Ochs et al. (2009). The development of high power pulse magnetron sputtering is traced to the Moscow Engineering and Physics Institute (MEPhI). The initial works were on glow discharges or diode type sputter tools (without magnetic confinement) in the late 1960s and the early 1970s (Malkin and Pyshnov, 1972). There they applied a cathode voltage of 5 kV in 140 µs-long pulses, which resulted in peak currents of 1 – 140 kA through a nitrogen discharge in the pressure range 13 Pa – 13 kPa, between aluminum electrodes of diameter 19 – 30 mm corresponding to current densities in the range 1 – 5 kA/cm2 . When operating at these high current densities, the plasma could be maintained for up to 100 µs before transitioning into an arc. The authors referred to this plasma as quasi-steadystate stage of the discharge. By the early 1980s an axial magnetic field had been added to create a pulsed magnetron type discharge. This allowed performing experiments at lower pressures 0.1 – 10 Pa (Tyuryukanov et al., 1981, 1982). Discharge currents of up to 1500 A for an applied cathode voltage of 400 – 500 V were reported for an argon discharge, where the pulse length was up to 100 µs. In Tomsk during the 1980s, there were also studies of hollow cathode magnetron systems in the coaxial cylindrical geometry to be used as electron emitters (Oks and Chagin, 1988). These pulsed hollow cathodes reached discharge currents of 1 kA during 10 µs-long pulses. Through these experiments, it was demonstrated that there are discharge regimes that do not transition into an arc despite of very high currents in a magnetron setting. The first published record on what we now refer to as a pre-ionized HiPIMS discharge was presented in the early 1990s (Fetisov et al., 1991) by the group at MEPhI. The development of this first HiPIMS discharge is discussed in much detail by Mozgrin (1994). It is there referred to as a high-current low-pressure quasistationary discharge in a magnetic field and was demonstrated for two configurations, a planar magnetron device and two hollow axisymmetric electrodes immersed in a cusp-shaped magnetic field. For the planar magnetron device, Mozgrin et al. (1995) reported a peak power of 200 kW (200 A) onto a 120 mm diameter target giving peak a power density of 1.8 kW/cm2 and discharge current densities of up to 25 A/cm2 at a repetition rate of 10 Hz in a pre-ionized discharge. It was demonstrated that this technique could be used to grow thin films of various metals (Mozgrin, 1994, Mozgrin et al., 1995). Furthermore, etching of silicon in an Ar/SF6 mixture was demonstrated using this technique (Mozgrin, 1994, Mozgrin et al., 1996). Around the same time in Tomsk, Bugaev et al. (1996) reported on a pulsed power supply that operated at repetition frequency 5 – 20 Hz and pulse duration 2 – 10 ms for pulsing a filament-assisted hollow cathode magnetron with a pulse voltage up to 800 V and a peak current of 450 A. They reported cathode current densities as high as 2.8 A/cm2 . This setup was used to deposit Cu and Ti films, and it was noted that the deposition rate was much lower for pulsed operation compared to dc operation at the same average power. Also, they recognized that the drop in deposition rate could be lowered by decreasing the magnetron confining magnetic field strength. In the late 1990s, Kouznetsov et al. (1999) discussed a thyristor-based power supply capable of peak power pulses of up to 2.4 MW at repetition frequency 50 Hz and pulse

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width 50 – 100 µs generating a peak target power density as large as 2.8 kW/cm2 on a planar magnetron target. A few years later, Christie et al. (2004a,b) reported on a power supply capable of peak powers of up to 3 MW operating from a single shot to 500 Hz repetition frequency and pulse width of 100 – 150 µs. These early HiPIMS power supplies are characterized by an initial voltage peak in the kilovolt range due to the resonant charging of the unloaded capacitance at the output, followed by a drop in the voltage to several hundred volts, typical of the operating voltage of a conventional dcMS. After a slight delay from the initial voltage peak, the target current increases up to a peak value, which also decays with falling voltage (see the discussion by Gudmundsson et al. (2002) and further discussion in Section 2.2.2). More recently, a power supply that provides a constant voltage (a nearly rectangular waveform) throughout a pulse length of few hundred µs, due to a large storage capacitance, has been developed for HiPIMS applications (SPIK2000A) (Mark, 2001) (see e.g. Anders et al. (2007)) and is discussed in Section 2.2.3. Musil et al. (2001) reported on experiments with a pulsed power supply (Rübig MP120) that works in the frequency range 0.5 – 50 kHz with maximum peak voltage of 1000 V and a peak current of 120 A, and thus maximum pulse power of 120 kW. Ehiasarian and Bugyi demonstrated a pulse generator (HMP 6/16) that supplied up to 3000 A at 2000 V in up to 200 µs long pulses for variable repetition frequency up to 100 Hz on linear magnetron targets of 400 cm2 area (Ehiasarian and Bugyi, 2004) and later of 1200 cm2 area (Ehiasarian et al., 2006, Ehiasarian, 2010) intended for industrial applications. Leroy et al. (2010) have demonstrated HiPIMS operation using a rotating cylindrical magnetron. They operated the discharge up to power densities of 2.7 kW/cm2 . It should be noted however that for applications in glass and web coating, the cylindrical target area can be as large as a several times 10000 cm2 , and thus the peak power has to be in tens of MW. A power supply that operates at voltages up to 3 kV and can give a peak current of 6 kA and thus a pulse power of 18 MW is in production (Ochs, 2008). Another approach to high power pulsed magnetron sputtering (HPPMS) is to apply arbitrary tailored pulse shape utilizing multistep pulses, as introduced by Chistyakov et al. (2006, 2007) and referred to as modulated pulse power magnetron sputtering (MPPMS) (see Fig. 1.13). MPPMS pulses typically begin at a low power level, often in the dcMS range, followed by a stronger pulse of intermediate power density (0.05 < pt < 0.5 kW/cm2 ) or even in the HiPIMS range. Typically, a stable weakly ionized discharge is formed with a low power density (typical for dcMS operation) prior to a transition to a strongly ionized discharge created with a power density of 0.1 – 1.5 kW/cm2 with a pulse length up to 3 ms and pulse frequency in the range 4 – 400 Hz (Lin et al., 2011). The MPPMS pulse is sometimes referred to as a macropulse, and it can consist of series of micropulses. The micropulses determine the applied power by varying the on/off time (Lin et al., 2009, Liebig et al., 2011, Meng et al., 2011). Another approach is using voltage oscillation packages with short off-time periods to modulate the peak power, referred to as deep oscillation magnetron sputtering (DOMS) (Ferreira et al., 2014). The pulse duration is in ms, whereas the ton is a few µs, and the oscillation period is a few tens of µs.

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Pulse generators

The pulse generators are at the core of the pulsed magnetron sputter technology. Pulser technology was originally based on a switched capacitor bank, in which a thyristor (historically, a vacuum tube) switch was used to connect an energy storage capacitor to the load to initiate the pulse, and then at the end of the pulse, it was disconnected. Sometimes this was arranged into what is referred to as line-type pulsers. Then the energy storage device is essentially a lumped element network approximating a transmission line (White et al., 1948b). This lumped element network of the line-type pulser served both as the source of the electrical energy during the pulse and as the pulse-shaping element and is generally referred to as the pulse-forming network (PFN). The basic manifestation of a single-mesh PFN is composed of a capacitor and an inductor. The initial description of the design of a power supply for a high power pulsed magnetron sputtering was given by Christie et al. (2004a,b), Sproul et al. (2004), and Kouznetsov (2001). The energy for the pulse is stored in an electrostatic field in the amount (1/2)Cs V02 , were Cs is the network storage capacitance, and V0 is the peak charge voltage on the capacitor. The charging circuit generally consists of a power supply and a charging element. The addition of an inductance makes it possible to design a highly efficient resonant charging circuit (White et al., 1948a). Resonance charging of the capacitor was in the early days most often accomplished from a dc voltage source through a thyristor switch (Mozgrin et al., 1995, Bugaev and Sochugov, 2000) or by a transformer that has its primary winding connected to the line mains and its secondary winding connected to the discharge capacitor through a diode and a thyristor switch (Kouznetsov, 2001). The pulse-forming line is switched to the magnetron discharge through another thyristor. Here we discuss how the pulser technology has evolved over the past few decades and the improvements that have been made in order to better maintain the cathode voltage and to better define the pulse length. We also show the typical VD –ID characteristics for a few generations of HiPIMS power supplies.

2.2.1 Basic pulse generators We start by looking at the general basic concepts of power supplies for pulsed magnetron discharges, which can be seen in Fig. 2.1. A pulse-forming network serves the dual purpose of storing the energy required for a single pulse and defining the shape of the pulse (White et al., 1948b). The energy may be stored either in a capacitor, or in an inductor, or in combinations of these circuit elements. The pulse-forming network shown in Fig. 2.1A utilizes a large capacitor C, which is charged from a regular dc power supply VZ . A transistor switch S connects the capacitor to the magnetron cathode via an inductor L during the time of the active pulse when a discharge is generated between the cathode and anode. The discharge voltage and current waveforms for this circuit are shown in Fig. 2.2A. The high discharge current in the pulse ID , as seen in Fig. 2.2A, can be achieved because the capacitor, when charged to the voltage VC , can

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Figure 2.1 Two basic concepts of discharge pulsing with, (A) a capacitor C, and (B) tapped inductance L1 –L2 and M, as accumulating elements.

supply a large pulse current ID into the discharge. This pulse current ID can be many times higher than the maximum dc current supplied by the dc source because a large energy 1 EC = CVC2 2

(2.1)

can be stored in the capacitor C. The current accumulation in the pulse is a great advantage of this configuration. The inductor L added between the switch S and the cathode (Fig. 2.1A) controls (slows down) the rate of current increase in the discharge and partially protects the transistor switch from large current surges. When the discharge current ID grows, the inductance L induces a voltage Vi , which is oriented against the current change Vi = −

dID L. dt

(2.2)

The inductance L also partially prevents the generation of an undesirable arc characterized by a very high discharge current and a low discharge voltage (see also Section 1.1.1). We can see that the typical current and voltage waveforms in Fig. 2.2A for this configuration exhibit rather rectangular voltage pulse VD and a slow growth of the discharge current ID during the pulse. The rate of growth of ID during the pulse is determined by the size of the inductor L and the plasma impedance of the magnetron sputtering discharge. The second concept of discharge pulsing can be seen in Fig. 2.1B. This concept is preferably used in the classical medium frequency pulsed magnetron technology (see Section 1.4.2) and is described by Drummond (1996). A large tapped inductance

54

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Figure 2.2 The discharge voltage and current waveforms measured on the magnetron cathode from a pulsed power supply with (A) capacitor bank depicted in Fig. 2.1A, and (B) with pulsed power supply with tapped inductor depicted in Fig. 2.1B.

L1 –L2 (L1 > L2 ) with a mutual inductance M is used as an accumulating element. The transistor switch S connects periodically the tap of this inductor directly back to the positive pole of the dc source VZ and simultaneously shunts a series connection between the magnetron discharge and the inductor L2 . During the time S is switched on, the current IL flows through the inductance L1 and the switch S (ID = 0), and at this stage a significant energy is accumulated by the inductor L1 or 1 EL = L1 IL2 . 2

(2.3)

Once S is switched off, the inductor L1 will generate a high voltage Vi across L1 or Vi = −

dIL1 L1 dt

(2.4)

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with the same orientation as VZ in order to maintain the current flow through L1 (the current IL1 through L1 now decreases). This high voltage peak at the beginning of the pulse (as seen in Fig. 2.2B) will make it easier to generate a plasma breakdown in the vicinity of the magnetron target (see also Section 1.1.2). When the switch S is switched on at the end of the active pulse, the current IL1 starts to increase through L1 , and, due to the mutual inductance M between L1 and L2 , a temporary positive voltage VD is generated on the magnetron cathode (i.e. the magnetron cathode potential is positive relative to the anode), which is expressed by VD =

dIL1 M. dt

(2.5)

This temporal positive voltage VD is valuable in reactive pulsed magnetron sputtering, since it will generate a high electron flux onto a poisoned magnetron target, as previously discussed in Section 1.4.2. This type of pulsed power supply is called a chopper. It should be noted that the first concept with the capacitor bank (Fig. 2.1A) is historically more important for the design of HiPIMS power supplies because high currents in the pulse are easily generated due to the large capacitance C. On the other hand, a chopper (Fig. 2.1B) is sometimes implemented in HiPIMS sources as an antiarcing circuit in some realizations of industrial HiPIMS sources that are to be operated up to very high pulse currents (Kadlec and Weichart, 2016).

2.2.2 Thyristor-diode-based pulsers We now turn to discuss one of the first HiPIMS power supplies. It was designed for very high magnetron discharge currents in the pulse (ID > 1 kA). We follow the description of Kouznetsov (2001) of the circuit diagram that is shown in Fig. 2.3. This is more or less the same concept as described by Mozgrin (1994) and Bugaev et al. (1996) a few years earlier. The construction is quite simple and employs a high power thyristor rated up to 9 kA as a switch. The capacitor C has a value around 10 – 20 µF. There are two transformers Tr1 and Tr2 working with the line frequency 50 – 60 Hz. The transformer Tr1 has the same direction of the primary and secondary windings, but the transformer Tr2 has the secondary winding wound in the opposite direction of the primary winding. Thus the voltages Vr and V1 have the opposite phase. This means that during the first half period of the line voltage, the capacitor C is charged through the diode D2 by a current Ich . During the second half period, while the positive signal of voltage V2 appears between the gate and the cathode of the thyristor, the gate current Ig will grow above a critical value, and the thyristor will become conductive. A high voltage VD will thereby be applied between the cathode and anode of the magnetron sputtering discharge, and a high pulse discharge current ID will flow through the inductor L as the capacitor C discharges. The inductor L, with a typical value of L ≈ 25 µH, works as a limiting element to prevent fast discharge current growth and any undesirable arc transitions. The protective diode D3 also partially eliminates high voltage overshoots, which can appear between the cathode of the thyristor and the

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High Power Impulse Magnetron Sputtering

Figure 2.3 The original concept of a HiPIMS power supply, which was based on thyristor switches and can deliver extremely high currents during the pulse. Redrawn from Kouznetsov (2001).

magnetron cathode. During the active pulse, the capacitor C is completely discharged and the discharge current and voltage, ID and VD , respectively, decrease gradually to zero. When the discharge current ID decreases below a certain threshold limit, the thyristor will switch back to a nonconductive state, and the capacitor C accumulates charge again. This type of HiPIMS power supply is capable of delivering pulse powers of up to Pp ≈ 1 MW. One disadvantage of this construction is the difficulty to control the length of the active pulse, since it is given by the time constant of the plasma impedance and the values of C and L. Furthermore, the pulse repetition frequency is fixed by the frequency of the ac line supply. This type of power supply was used in the early demonstration of the HiPIMS technique performed at Linköping University (Kouznetsov et al., 1999, Macák et al., 2000, Gudmundsson et al., 2002). The exact shapes of the discharge current and voltage waveforms are to a great extent determined by the size of the storage capacitor C, but it also depends on whether the circuit inductance L or the resistance of the plasma discharge dominate in limiting the current. When the inductance L is relatively small, the output voltage rises rapidly to a sharp peak. An example of the temporal variations of the cathode voltage and discharge current can be seen in Fig. 2.4, measured using the same pulser unit (SINEX I) as used in the seminal work of Kouznetsov et al. (1999), and similar to that shown by the circuit diagram in Fig. 2.3. We see clearly an initial voltage peak in the kilovolt range due to the resonant charging of the unloaded capacitance at the output, which is followed by a drop in the voltage to several hundred volts. The voltage then drops even further to values that are typical operating voltages for a dcMS discharge. As the voltage drops, the discharge current increases up to a peak value followed by a gradual decay of the current. Generally, the discharge does not reach stationary plasma discharge conditions for pulse lengths of 100 µs or less. Furthermore, it can be seen that the waveforms of the cathode voltage and the discharge current depend on the discharge working gas pressure. The pulse length is dictated by the plasma impedance along with the size of the inductor L and capacitance C, so it is not easily predicted.

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Figure 2.4 The discharge (A) voltage VD and (B) current ID for an argon discharge at 0.27 and 2.67 Pa from an early thyristor-based power supply. The target is made of tantalum 150 mm in diameter. Based on data from Gudmundsson et al. (2002).

2.2.3 IGBT-based pulsers Fortunately, the current and voltage waveforms can be improved by modern concepts of pulsed power supplies, which utilize insulated-gate bipolar transistors (IGBTs) as high power switches (Baliga et al., 1984). Also, the previously used small capacitor C can be substituted by a large capacitor bank composed of low-impedance electrolytic capacitors. In addition, a more sophisticated circuit solution is required for arc handling in HiPIMS operation, mainly in the case of large magnetron targets, which require very high pulse currents. IGBTs are indeed very suitable for this application due to their short switching time, which is in the range 1 – 2 µs. Furthermore, they have a high input impedance and can be controlled by a simple voltage driver in a similar way as power MOSFETs, that is, by applying a low voltage signal (VGE ≈ 15 – 20 V) between the gate electrode and the emitter electrode. The IGBT behaves as a bipolar transistor with regards to the output impedance and can thus deliver high currents. Recently, IGBT modules are available in compact blocks rated up to high currents in the range 1 – 2 kA at a reasonable price. They are often connected in parallel, which mainly applies to the types exhibiting a positive temperature coefficient of the saturation voltage VCEsat and having equivalent specifications. A typical circuit diagram of a HiPIMS power supply based on IGBT switches is shown in Fig. 2.5. This concept was partially described by Zahringer et al. (2003) and Kuzmichev et al. (2003) for a single magnetron target and by Mark (2001) for a different topology using two magnetrons. This design uses a large capacitor bank C2 charged by a dc power supply to a high voltage VDC . A capacitor C1 and inductor L1 are added as a filter, which should protect the dc power supply electronics from para-

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High Power Impulse Magnetron Sputtering

Figure 2.5 The basic concept of a HiPIMS power supply with IGBT transistors as switches and an antiarcing circuit.

sitic sharp voltage spikes from the IGBT pulsing unit. The IGBT is switched on during a well-defined time tON (e.g. tON ≈ 50 – 150 µs) and then switched off. The switching of the IGBT is taken care of by a proper IGBT driver, which is described further in this section. The IGBT connects the charged capacitor C2 with the magnetron cathode via inductor L. The inductance L ≈ 20 µH has a similar function as in the previously discussed cases, that is, as a current limiter, partially preventing a transfer of the magnetron discharge into the arc regime. To increase the maximum discharge current delivered in the pulse, two equivalent lines with IGBTs are connected in parallel, as can be seen in Fig. 2.5. This solution is very efficient, provided that proper current sharing through both IGBTs is guaranteed. Suitable equivalent IGBTs should therefore be used with similar characteristics, such as similar saturation voltages VCEsat and a positive temperature coefficient of VCEsat . Fig. 2.6 shows the discharge voltage and current waveforms from the SINEX 2 pulser unit, which was an IGBT-based pulser, but the capacitor was rather small, and the pulse width would vary strongly with the current at turn-off as the internal charge took a long time to drain out at lower current. As seen in Fig. 2.6, the actual pulse width decreases with increasing working gas pressure. Some pulser units have a storage capacitor C2 that is large enough to keep a constant voltage for a relatively long pulse. When a larger storage capacitor is placed in the circuit, a square voltage pulse is achieved. This is shown in Fig. 2.7, where we see the discharge voltage and current waveforms for Ar/N2 discharges operated at different nitrogen flow rates while the argon flow rate was kept fixed at 40 sccm to achieve 0.9 Pa and 150 W average power for 200 µs pulses. By using a large capacitor C2 , the voltage pulse VD on the cathode can be almost square even for high discharge currents ID during the full pulse length. Indeed, the voltage waveforms are almost square in all cases as seen in Fig. 2.7A. The pulser applied here (Melec SPIK2000A) has a large capacitor bank and IGBT switch as discussed by Mark (2001) and shown on the circuit diagram in Fig. 2.5. The discharge current waveforms are shown in Fig. 2.7B, and it is noticeable that higher nitrogen flow rates contribute to more delay on plasma ignition and

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Figure 2.6 The discharge (A) voltage VD and (B) current ID for an argon discharge at 0.4 and 2.7 Pa driven by an IGBT pulser with a small capacitor. The target is made of copper 150 mm in diameter. Based on data from Gudmundsson et al. (2009).

to a higher discharge current (the delay to the onset of the discharge current is discussed in Section 2.2.5). The initial peak in the discharge current is a result of strong gas compression due to the sudden large flux of atoms from the target. Oscillations are often detected on the voltage applied between anode and cathode VD at the beginning of a pulse and are caused by the inductance L, which creates a resonant circuit with the capacitance of the magnetron cathode relative to ground plus the parasitic capacitance of the cable connecting the magnetron with the power supply. This ringing disappears when the parasitic capacitance is shunted by the developed magnetron plasma later on in the pulse. Using this kind of a pulse power supply, that keeps a constant voltage throughout the pulse length, Anders et al. (2007) recorded a set of discharge current waveforms, each taken at a fixed voltage for various target materials. An example of the discharge current waveforms for an Al target from this study are shown in Fig. 5.9A. They find that the shape of the discharge current waveform depends on the target material and demonstrate that the discharge current waveform for the HiPIMS discharge typically exhibits an initial pressure-dependent peak followed by a second phase that depends on the applied power and target material. They claim that the initial peak is dominated by the ions of the working gas, whereas the later phase has a strong contribution from self-sputtering. To reach the latter phase, the pulse length has to be longer than 100 – 200 µs depending on the target material, which we will return to in Section 7.2.2. The circuit shown in Fig. 2.5 contains some typical protective elements for IGBT switches. The most important element is the fast recovery diode D1 placed between emitter and collector of the IGBT transistor. This diode prevents the appearance of any

60

High Power Impulse Magnetron Sputtering

Figure 2.7 The discharge (A) voltage VD and (B) current ID for an argon discharge mixed with nitrogen

at different flow rates and vanadium target (area of 45 cm2 ) driven by an IGBT based power supply with a large capacitor bank. The total gas pressure is 0.9 Pa, the argon flow rate is 40 sccm, the voltage pulse is 200 µs long and the pulse frequency is 100 Hz. Reprinted from Hajihoseini and Gudmundsson (2017). ©IOP Publishing. Reproduced with permission. All rights reserved.

voltage overshoot in the reverse direction on the IGBT transistor. A capacitor CS and a resistor RS can further help eliminating any other voltage overshoots between the collector and emitter of the IGBT. To correctly switch on and off the IGBT transistor, it is necessary to apply suitable voltage pulses VGE between the gate and emitter of the IGBT. These pulses are provided by an IGBT driver. However, there are some technical issues with the realization of IGBT drivers, and many types of circuits exist for this purpose (Rashid, 2011). An example of an IGBT driver suitable for HiPIMS power supplies, as the one shown in Fig. 2.5, is presented in Fig. 2.8. This IGBT driver is floating and has a floating dc supply connected together with a secondary winding of transformer Tr. The external pulse signal is transferred into the driver optically through an optocoupler Op (Rashid, 2011). The dc supply is isolated from the ground by an insulating transformer Tr designed for high voltages of several kV between the primary and secondary windings. Thus the whole driver together with the dc supply circuit can be on a very high voltage and can be connected with the emitter of the IGBT. Although the input impedance of the IGBT is very high, the IGBT driver has to be able to charge the capacitance CG very quickly when the IGBT is switched on and to quickly discharge CG when the IGBT is switched off. For this reason, the IGBT driver should be able to provide a high instant current for fast charging/discharging of CG . It is achieved by including a current amplifier composed of a complementary pair of NPN and PNP bipolar transistors T1 and T2 , both working in the common collector mode. Another issue is the capacitance CS between the gate and the collector of the IGBT. This capacitance CS is sometimes referred to as the Miller capacitance.

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Figure 2.8 One example of an IGBT driver with optical coupling and floating supply.

Each change of voltage between the collector and emitter VCE has to be accompanied by the charging/discharging of CS . These capacitive transient currents have to flow through the output stage of the IGBT driver; in our case, this means through transistors T1 and T2 . There is a risk that the capacitive current charging CS would flow through the open T2 and a voltage drop could be created on the internal impedance of T2 during the switching off of the IGBT. Thus the IGBT could be parasitically reopened and again closed. Consequently, some oscillations could appear on the IGBT. This effect could potentially be harmful for the IGBT and thereby for the entire HiPIMS power supply. There are several possibilities how to overcome this problem. In the presented IGBT driver (Fig. 2.8), the voltage VGE is always negative relative to the emitter of the IGBT during the off-time (VGE = −VE ≈ −10 V). Thus, the IGBT cannot be reopened due to the Miller capacitance CS . Although the inductance L is included in the circuit, this solution cannot always help to prevent the development of an arc. For a proper HiPIMS pulser, an active antiarcing circuit should be implemented as well, as can be seen in Fig. 2.5. The arc can be detected by a fast current sensor, which gives an arc signal once the discharge current ID grows above a defined level. If it occurs, then the IGBT driver quickly switches off the IGBT transistors for a certain predefined time τarc . The time τarc should be long enough so that the arc plasma completely dies out. The second possibility is to detect a sudden cathode voltage VD decrease due to the arc and simultaneously observe the discharge current ID above a certain defined limit. The above presented solution of arc suppression is suitable for medium pulse discharge currents limited by ID ≈ 600 – 1000 A in the pulse. Keep in mind that for large magnetron targets, the current in a pulse can be as high as ID ≈ 1 – 2 kA in a HiPIMS discharge. We should consider that the energy EL stored in the inductance L grows with ID according to 1 EL = LID2 . 2

(2.6)

In the case of an arc event, the current ID can be very high. To properly extinguish the arc, the energy EL should be transferred or removed from the inductor L in the way that EL cannot be further delivered into the already existing arc and consequently prolong its existence. There are several methods how to technically solve this problem,

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High Power Impulse Magnetron Sputtering

Figure 2.9 The concept of an industrial IGBT-based HiPIMS power supply with antiarcing circuit for extremely high currents during the pulse. Redrawn from Kadlec and Weichart (2016).

Figure 2.10 The discharge voltage and current waveforms from an industrial IGBT-based HiPIMS power supply with antiarcing circuit.

which are described in various patents (Kadlec and Weichart, 2016, Zahringer et al., 2003, Bulliard et al., 2014, Christie, 2004). The method described by Kadlec and Weichart (2016) can be seen as implemented in the circuit shown in Fig. 2.9. The inductor L has a tap. This tap is connected to the IGBT switch S2 , which is also connected to the magnetron anode and simultaneously to the positive pole of the dc power supply. Once the arc is detected by current and voltage probes, the IGBT switch S2 is switched on, and after some defined delay τ , the IGBT switch S1 is switched off. Once S2 is switched on, the discharge current ID drops fast to zero because the magnetron is practically shunted, as seen in Fig. 2.10. Thus the major part of the energy stored in the inductor L is released, not through the magnetron discharge, but through the path consisting of S2 , L, and a diode DA . It is clear that after S2 is switched on and before S1 is switched off, the current in L will grow, and a positive voltage VD will appear on the magnetron cathode (Fig. 2.9) due to the mutual inductance M of the coil L with the tap. The temporary positive target voltage VD will extinguish the arc rapidly.

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2.2.4 Pre-ionization Some of the high power pulse systems include a pre-ionizer (Mozgrin et al., 1995, Fetisov et al., 1999, Bugaev and Sochugov, 2000, Va˘sina et al., 2007, Poolcharuansin et al., 2010). Here a dc power supply maintains a conventional dcMS discharge, and a high power pulse is superimposed. The dc power supply usually provides a current of a few hundred mA that maintains a dc type magnetron sputtering discharge with electron density in the range 1014 – 1016 m−3 . Other means of pre-ionization have been suggested, such as an rf discharge (Mozgrin et al., 1995). For a HiPIMS discharge that is operated without pre-ionization, the delay time between the initiation of the discharge voltage and the onset of the discharge current can be significant when the operating pressure is very low (see also Section 2.2.5). Then in some cases the plasma cannot fully develop within the pulse, and if the delay is longer than the actual pulse width, then the plasma will not ignite at all. The role of the pre-ionizer is providing a seed of charge in the discharge volume between the pulses. This allows for the HiPIMS discharge to be operated at low enough pressure to reach the region of ballistic transport of sputtered particles (Poolcharuansin and Bradley, 2011). Poolcharuansin et al. (2010) have demonstrated how a dc pre-ionizer can be used to reduce or eliminate the ignition delay time in a HiPIMS discharge when operating at pressures below 0.1 Pa.

2.2.5 Pulse delay In a typical HiPIMS discharge that is operated without pre-ionization, a delay td is always noticed between the onset of the target voltage and the onset of discharge current. This delay depends on the working gas pressure (Gudmundsson et al., 2002), the gas composition (Hála et al., 2010), the target material (Hecimovic and Ehiasarian, 2011), and the applied voltage (Yushkov and Anders, 2010). This can be clearly seen in Fig. 2.4, where this delay time decreases as the pressure is increased from 0.27 to 2.67 Pa. The delay time increases with decreasing pressure and can be in the range of a few µs to over 100 µs (Gudmundsson et al., 2002, Poolcharuansin et al., 2010). In Fig. 2.7, we see that for reactive HiPIMS operation, the delay also depends on the partial pressure of the reactive gas. Yushkov and Anders (2010) explore the dependence of the delay on the target voltage VD and gas mixing both experimentally and theoretically. They suggest that the delay of current onset consists of a statistical time lag ts and a formative time lag tf such that td = ts + tf .

(2.7)

It is known that the fluctuation in the delay time in the HiPIMS discharge is very small, and it can be assumed that ts  tf . By treating the initiation of the discharge as a vacuum breakdown, Yushkov and Anders (2010) derive an equation for the formative time lag   a b tf ≈ exp , (2.8) VD − VB VD

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where VB is the static breakdown voltage, VD is the applied voltage, a = Ap, and b = Bpd, where A and B are constants that depend on the gas type and have been determined experimentally and are listed in Table 1.2 for common working gases.

2.3

Substrate bias

HiPIMS is an ionized physical vapor deposition (IPVD) process where the sputtered material is highly ionized (Helmersson et al., 2006). This implies that by applying a substrate bias voltage the energy of these ions, as they strike the substrate, can be controlled. The substrate bias voltage can thus be a key parameter during film deposition since bombarding energetic ions enhance adatom migration, promote desorption of physically adsorbed atoms and shallow ion implantation, and trap impinging atoms (Takagi, 1984). Substrate biasing is therefore an effective method to control the microstructural evolution such as film texture and grain size, and thus to tailor the film properties, which is explored in Chapter 8. Not only dc biasing is of relevance in HiPIMS. Synchronizing the substrate bias with the pulse power supply was first demonstrated for deposition of diamond-like carbon (DLC) films on large substrates in a HiPIMS discharge with a cylindrical cathode (Bugaev and Sochugov, 2000). The substrate bias voltage was applied with a delay of 60 µs with respect to the voltage pulse applied to the magnetron target. Bugaev and Sochugov (2000) showed that the negative bias voltage falls with time during the pulse. Thus there are two important issues that need to be kept in mind while discussing substrate bias in HiPIMS: • The largely neglected issue of a drop in the applied substrate bias voltage during the HiPIMS discharge pulse, which prevents the user from maintaining a desired bias voltage. It also leads to the obvious question of what bias voltage was actually used during deposition. • The possibility to synchronize a pulsed substrate bias with the HiPIMS discharge pulse to selectively attract certain ionic species, that is, bias optimization in the time domain. We will further address these challenges and possibilities from a physical point of view (what is happening in the plasma?) and from a technical point of view (what equipment is needed and how does this equipment work?). Note that this chapter is mainly dedicated to the HiPIMS hardware, and we will therefore refer to the detailed descriptions of the plasma characterization and the applications given later on in this book, where appropriate.

2.3.1 Bias solutions During HiPIMS deposition of thin films, the applied substrate bias voltage may decrease toward zero during the HiPIMS discharge pulse (pulse-on) and then slowly

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Figure 2.11 Time-resolved discharge characteristics from a 40 µs HiPIMS pulse on a 2” Cu target with argon working gas at 0.5 Pa showing (A) the discharge voltage and current measured at the cathode, and (B) the bias voltage and current measured at the substrate table having an area of 47.8 cm2 and located approximately 10 cm from the cathode. The dashed vertical lines in (B) show the duration of the cathode discharge pulse shown in figure (A).

recover during the pulse-off period. One example is seen in Fig. 2.11, where a 40 µs HiPIMS pulse is applied to a 2” Cu target (area of 20 cm2 ) with argon as the working gas at 0.5 Pa. It generates a peak discharge current of about ID,peak = 40 A for an applied discharge voltage VD ≈ −800 V, as shown in Fig. 2.11A. A dc substrate bias of Vbias = −50 V using a regular dc power supply (SR1.5-N-1500, Technix, France) is applied to the substrate table (the table area is 47.8 cm2 and it is located approximately 10 cm from the cathode). By monitoring the bias voltage Vbias (t) and the substrate current Ibias (t) it is found that Vbias = −50 V, but rather decreases from about −77 V to −22 V as the substrate current increases during the end of the HiPIMS (cathode) pulse as seen in Fig. 2.11B. In the present example, the bias current peaks at t ≈ 50 µs and reaches 2.7 A, which roughly coincides with the minimum bias voltage value. During the discharge pulse, the plasma density increases (approximately in proportion to the discharge current), which loads the bias power supply down as any deviation

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from the floating potential requires more and more current drive. In HiPIMS, this load arises from the considerable ion flux generated, as discussed in Section 4.1, which constitutes an ion current to the bias power supply. Under these conditions, the bias voltage drops due to the gradual discharge of the smoothing capacitance internal to the bias power supply and also due to the voltage drop over the output impedance of the power supply. The inductive drop can be seen in the recovery of the bias voltage as the bias current rapidly decreases after the pulse. In some types of power supplies made for driving plasma discharges, the rapidly changing current can also trigger arcsuppression features in the power supply. After the pulse, the plasma density decays rapidly, and the substrate load quickly becomes a very high impedance. Now the average bias voltage increases as the slowly changing supply current recharges the smoothing capacitance. As the voltage control loop in the bias power supply loses control of the output voltage, there may be an overshoot or ringing in the bias voltage as control is regained, depending on the damping behavior of the loop. The large majority of power supplies used for substrate bias are only one-quadrant supplies, meaning that they can only draw current from the substrate and that any overvoltage will only slowly be bled away from the output by leakage resistances. A simple remedy to reduce the time constant of the high-impedance load is to add an external shunt resistance of suitable size. The behavior of the bias voltage changes somewhat in character when using midfrequency pulsed dc voltage for substrate bias, but the problem of reduced bias voltage when the ion current is large during the pulse remains. Pulsed dc power supplies tend to be good low-impedance voltage sources as required to drive high-frequency pulses on a capacitive plasma load, but they also tend to have more sophisticated arc-suppression features compared to most dc power supplies, and this increases the risk of false detection of arcs due to the high ion flux density during the HiPIMS pulse. With higher pulsed bias frequencies, such as when using an rf source, there is still the issue of the bias voltage dropping during the HiPIMS discharge pulse. This is due to self-biasing (negative charging) of the substrate table due to the impinging electrons in combination with a blocking capacitor in the rf circuitry, which does not allow the charge collected on the substrate table to discharge to ground. The way the self-bias builds up by rectifying properties of the plasma along with heating of the electrons, rather than the more straight rectification at lower frequencies (see discussion on sheath formation in Section 1.1.3), means that the bias voltage is much more sensitive to the plasma conditions at the substrate table. There is also the issue of how much of the rf power provided by the generator is actually absorbed by the plasma due to the matching between generator and plasma. The change in plasma properties between a quiescent, fully rf-driven plasma, and the high-density HiPIMS plasma is so large that both the rf power required to drive the desired self-bias and the matching conditions are vastly different at different times. This makes the rf bias method the most difficult one to use in a HiPIMS process. In fact, when applying rf bias (13.56 MHz), the bias voltage can be observed to drop completely to zero very early in the pulse and stay low for a long while afterwards. One challenging way to some-

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Figure 2.12 Synchronized pulsed rf bias applied on the substrate (A) discharge current and voltage waveforms on the magnetron cathode, and (B) pulsed modulated synchronized rf voltage on the substrate together with induced pulsed dc self-bias on the substrate.

what remedy this issue is synchronizing the rf bias with the HiPIMS pulse, which is shown in Fig. 2.12. This particular result required manual tuning of the matching unit to match the impedance of the HiPIMS discharge. Still, the self-bias level is not stable as shown in Fig. 2.12B. The key to successfully generate a well-defined bias signal or bias pulses during HiPIMS operation is to present the substrate with a low-impedance voltage source, switched on and off by a fast switch. A low-impedance voltage source is most easily achieved with a regular dc power supply and a smoothing capacitance that can handle the pulse current without too much drop in the output voltage. The smoothing capacitance necessitates some form of arc-limiting function to prevent the energy stored in the smoothing capacitance from being dissipated through a substrate arc. A convenient way of handling arcs is to use the bias switch to disconnect the bias source in case of an arc. The switching needs both on and off control, so in the relevant voltage

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range 0 – 1000 V, IGBTs or MOSFETs are suitable. There is no big difference in the requirements of the bias power supply to the HiPIMS power supply, and a smaller version of the HiPIMS pulser is often a suitable choice, which results in pulsing the bias voltage using typical HiPIMS pulse lengths and repetition rates.

2.3.2 Synchronized pulsed HiPIMS bias It is well known that rare gas ion bombardment of the growing film during conventional sputter deposition is widely employed to increase film density (Thornton, 1986), improve film/substrate adhesion via interfacial mixing (Pawel et al., 1990), enhance crystallinity (Shin et al., 2002), and so on. However, at high ion energies, such ion bombardment leads to detrimental residual ion-induced compressive stress of several GPa (Daniel et al., 2010). On the other hand, in HiPIMS, it is straightforward to generate a substantial metal ion flux to the substrate in addition to the working gas ions (see Section 4.1 for details). Furthermore, studies of mass, flux, and energy distribution of each ion species incident at the film growth surface have shown that there is a significant difference in arrival time of the ionic inert working gas versus metal species (see Section 4.1 and Greczynski et al. (2014)). In Section 8.4.2, we will show that such metal-ion irradiation during film growth plays a crucial role in determining the film microstructure, phase content, and mechanical properties. For now, it suffices to say that the existence of a metal-ion-dominated phase in HiPIMS provides an opportunity to separate metal ion from working gas ion-induced effects on the film microstructure and film properties. One solution is synchronizing the substrate bias to only the metal ion-rich portion during the HiPIMS pulse. This requires the user to select when to activate a bias pulse with respect to the HiPIMS discharge pulse (i.e. a delay of the bias pulse in the time domain) and repeat the process at a common frequency. Such operation is schematically shown in Fig. 2.13, where a proper HiPIMS substrate bias (discussed in the previous section), with a constant pulsed bias voltage, is synchronized to the HiPIMS discharge voltage pulses on two magnetron targets. Note that there is a (user-defined) delay between the onset of the HiPIMS voltage pulse and the HiPIMS substrate bias voltage pulse, as seen in Fig. 2.13B. Furthermore, one can also combine such synchronization of the substrate bias voltage with co-sputtering compounds from several magnetrons. In such a configuration, it is desirable to individually synchronize the magnetron sources and the substrate bias source as shown in Fig. 2.13. Other ways of implementing co-sputtering are discussed in more detail in Section 2.4.2. A more sophisticated solution is to not only synchronize the bias timing with the sputter sources, but also to apply different voltages at different times. If only square voltage pulses of different amplitudes are needed, then we can simply repeat the bias pulsing described earlier with different pulsers set to different voltages. If full waveform control is needed, then a high-bandwidth voltage source has to be used instead, which can be cost-prohibitive.

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Figure 2.13 Synchronized HiPIMS operation. (A) A schematic illustration of how to set up synchronized HiPIMS on two magnetron targets for co-sputtering, including synchronization of the pulsed HiPIMS bias voltage. After a synchronized HiPIMS solution from Ionautics AB, Sweden (http://ionautics.com/). (B) An example of the synchronized output voltage signals in time for the setup given in (A).

2.4

Advanced HiPIMS configurations

The standard unipolar HiPIMS discharge configuration as presented in Section 2.2 has been modified to achieve other, often more complex, discharge pulse schemes to address issues such as arcing, reactive sputtering, deposition rate, and/or tailoring of the process plasma characteristics. We further review a selection of the most important configurations.

2.4.1 Multicathode configurations Bipolar, sometimes referred to as dual, HiPIMS operation refers to alternatingly applying a pulse voltage on two magnetron targets, which take turns acting as cathode and anode. This can be achieved by employing a bipolar (dual) HiPIMS pulsed power supply with a so-called H-bridge configuration (Baliga, 2008, Section 10.1). The H-bridge works with two independently controlled dc power supplies. The basic concept of this pulsed power supply can be seen in Fig. 2.14. This system is described by Mark (2001), and it has been demonstrated with magnetron sputter tools working in HiPIMS mode as presented by Aijaz et al. (2010) for example. The basic version of the system contains four high power IGBT switches T1 , T2 , T3 , and T4 and two independent dc power supplies Vz1 , Vz2 with controlled dc voltages at the outputs. It operates as follows. When the TTL pulse unit provides VPM1 = 5 V (high level) and VPM2 = 0 V (low level), the IGBT drivers of T2 and T3 will open the transitors T2 and T3 , whereas the transistors T1 and T4 will remain closed. Thus the discharge current ID will be positive (Fig. 2.14) and will flow from the positive pole of the dc power supply Vz2 through the

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Figure 2.14 Bipolar dual IGBT-based HiPIMS pulsed power supply with H-bridge and two magnetron cathodes.

Figure 2.15 The discharge voltage and current waveforms from the bipolar dual HiPIMS pulsed power supply with H-bridge and two magnetron cathodes.

opened T3 , the inductance L2 , the target of magnetron M2 working as an anode, the target of magnetron M1 working as a cathode, through the inductance L1 , the opened transistor T2 , and back to the negative pole of the dc power supply Vz2 . A large lowimpedance capacitor bank C2 helps to provide the charge for the high current in the pulse as already described in Section 2.2.1. The magnetron target M1 in Fig. 2.14 works as the cathode and is sputtered during this phase of the pulsing cycle, whereas the magnetron target M2 works as the anode. In the next phase of the pulsing cycle, the pulse TTL unit sets VPM2 = 5 V (high level) and VPM1 = 0 V (low level). The transistors T1 and T4 will thereby open, and transistors T2 and T3 will now close. The discharge current ID will be negative (opposite direction as shown in Fig. 2.14) and will flow from the positive pole of the dc power supply Vz1 through T1 , through the inductor L1 , the target M1 , the target M2 , the inductor L2 , the opened transistor T4 , and back to the negative pole of Vz1 . The target M2 now works as the cathode and is sputtered, whereas the target M1 works as the anode. The discharge voltage and current waveforms from the bipolar dual HiPIMS pulsed power supply are shown in Fig. 2.15.

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Using the described solution allows independent control of dual HiPIMS magnetron sputtering of two targets made of different materials (Aijaz et al., 2010, Stranak et al., 2010). This can be useful for the deposition of alloy thin films, such as investigated by Stranak et al. (2014) in the case of TiCu. This method has also been demonstrated to suppress arcs in reactive sputter deposition of Al2 O3 , and then both targets are of the same metal (Zhou et al., 2018). Note that the current sensor included between L1 and M1 works as an arc detector for both directions of the pulse discharge current. In case of an arc event, the conducting pair of transistors will quickly switch off during a predefined time period to extinguish the arc (see also Section 2.2.1). Note that this H-bridge system requires that the dc power supplies Vz1 and Vz2 always have floating outputs relative to ground.

2.4.2 Superposition A similar HiPIMS power supply employing the H-bridge circuit, as described above, can easily be operated in the single magnetron mode with unipolar pulses (Fig. 2.16) (Mark, 2001, Mark and Mark, 2014). In this case, only a single dc power supply Vz1 is needed, and the target of magnetron M1 works as the cathode and is sputtered. Only transistors T2 and T3 are required for the switching of HiPIMS pulses, and the pulsed discharge current ID is always positive. Again, the dc power supply Vz1 has to have a floating output relative to ground. Based on such a configuration, it is now possible to superimpose a dc signal (Ganciu-Petcu et al., 2011, Bandorf et al., 2008, Va˘sina et al., 2007), such as presented in Fig. 2.16. An additional dc power supply is connected in parallel with the H-bridge HiPIMS power supply to the magnetron M1 . The HiPIMS and the dc power supplies are connected to the magnetron M1 over diodes D1 and D2 , respectively. These two diodes will guarantee a reliable operation of the power supplies in the parallel connection. In fact, the current from the two power supplies can only flow in the direction from the positive pole to the negative pole in the outer circuit. The main advantage of such a parallel combination of dcMS and HiPIMS is a preionization of the discharge plasma before the HiPIMS pulse ignition (Ganciu-Petcu et al., 2011, Va˘sina et al., 2007). Pre-ionization is mainly important for the operation of HiPIMS at very low pressures or with very short HiPIMS pulses as discussed in Section 2.2.4. The ignition of a HiPIMS discharge is much faster with the pre-ionization. The second advantage of this hybrid combination is a higher deposition rate (Bandorf et al., 2008, Mark and Mark, 2014). Samuelsson et al. (2012) have shown that when combining dcMS and HiPIMS on a single cathode, the two processes can be operated independently with regard to deposition rates and ionization in the deposition flux. This allows for tuning the amount of ions of the sputtered material, keeping the deposition rate and ion energy distribution unchanged by adjusting the dcMS and HiPIMS powers independently. Increasing the HiPIMS power fraction, an experimentally found threshold of ≥ 40% resulted in marginal improvement of the film quality, whereas a significant reduction in deposition rate efficiency was observed. By decoupling the ionization from the ion energies and average deposition rate, the degree of ionization can be isolated and controlled independently.

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Figure 2.16 IGBT-based HiPIMS pulsed power supply with H-bridge and superimposed dc power supply.

Figure 2.17 The discharge voltage and current waveforms of a HiPIMS pulsed power supply with H-bridge and superimposed dc power supply.

The current and voltage waveforms of when superimposing a HiPIMS discharge onto a (weak) dc discharge can be seen in Fig. 2.17. During the HiPIMS pulse-off, the dc discharge is active, and the current and voltage to the magnetron M1 are delivered from the dc power supply through the diode D2 in Fig. 2.16. The HiPIMS power supply with closed T2 and T3 is isolated from the dc power supply circuit by the diode D1 . When the HiPIMS power supply is activated by opening T2 and T3 , the magnetron cathode will be connected to the high negative potential of Vz1 (|Vz1 | > |Vdc |), and the dc power supply will be isolated from the discharge circuit by D2 . As the HiPIMS power supply transitions into pulse-off, the current to the magnetron will again be delivered from the dc power supply once the potential at the anode of D2 will be positive relative to the potential of the cathode of D1 , and the diode D2 will become conductive again. The plasma impedance is usually very low immediately after the end of the HiPIMS pulse. For this reason, the regulating circuit of the dc power supply will reduce the

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Figure 2.18 Dual IGBT-based HiPIMS pulsed power supply with superimposed mf power (two magnetron targets).

voltage at the magnetron to a very low value to stabilize the set discharge current (see the voltage and current waveforms in Fig. 2.17). As the HiPIMS plasma decays after the end of the active HiPIMS pulse, the plasma impedance grows, and the voltage at the magnetron cathode target will again stabilize at the typical voltage VDC of the dc magnetron discharge. In addition, it has also been shown that it is possible to superimpose dual HiPIMS onto a mid-frequency (mf) magnetron discharge (see also Section 1.4.2 for details on mid-frequency pulsing). The mf power is applied during the off-time of HiPIMS operation (Bandorf et al., 2009, Mark and Mark, 2014). One possible configuration of such a power supply can be seen in Fig. 2.18. In this configuration, the HiPIMS power supply essentially consists of the H-bridge circuit with two independent dc power supplies, which is similar to the system presented in Fig. 2.14. Both magnetron cathode targets are connected in parallel with the mf power supply as can be seen in Fig. 2.18. Another option is to connect the magnetron targets in parallel with the mf power supply over a transformer and through resistors as proposed by Stranak et al. (2012). Those two resistors should have a substantially higher resistance than the impedance of the active HiPIMS plasma. During the HiPIMS pulse off-time, an ordinary mf discharge is generated between the two magnetron targets working in dual mode. During HiPIMS pulse-on, a dual HiPIMS discharge is generated between the magnetron targets. Note that the mf power is still supplied to the magnetron targets, but does not show up in the voltage characteristics, since the mf discharge voltage has decreased to significantly lower values compared to the HiPIMS discharge voltage. Benefits of this mf plasma generation include stable operation of dual HiPIMS at lower working gas pressures, more intensive ion bombardment of growing films during the HiPIMS pulse off-time, and, in some cases, a higher deposition rate at the same average power due to the contribution of mf pulsed magnetron sputtering during HiPIMS

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Figure 2.19 The discharge voltage and current waveforms from a dual IGBT-based HiPIMS pulsed power supply with superimposed mf power (two magnetron targets) (power supply from Fig. 2.18).

pulse off (provided that the deposition rate in pure mid-frequency pulsed magnetron sputtering is higher compared to the HiPIMS rate) (Samuelsson et al., 2012, Sittinger et al., 2013, Diyatmika et al., 2018). The discharge voltage and current waveforms are shown in Fig. 2.19.

2.4.3 Pulse trains/multipulses/chopped pulses Sometimes the discharge current and voltage waveforms are arranged in the so-called chopped HiPIMS operation. For this purpose, the HiPIMS power supply presented in Fig. 2.16 can be operated giving train of short pulses (micropulses) (tpulse ≤ 5 – 100 µs) within a longer pulse packet (t ≈ 100 – 600 µs). Here a macropulse refers to the total “on” pulse sequence within one repetition frequency (Barker et al., 2013). The voltage and current waveforms for chopped HiPIMS are presented in Fig. 2.20. Technically, this operation is achieved by modulating the TTL signal VPM1 (Fig. 2.16), which has the shape of the defined burst of short pulses and which results in the high power switching IGBT transistors following the driving signal VPM1 . It was shown by Antonin et al. (2015) and Barker et al. (2013) that chopped HiPIMS can substantially increase the deposition rate. This phenomenon was explained by the reduction of the returned flux of ionized sputtered particles back to the target (back-attraction), which will be dealt with in more detail in Chapter 4 (see Section 4.1.2). Furthermore, Antonin et al. (2015) also showed that by controlling the length of the micropulses and the off-time in between, the plasma diffusion away from the target, and, consequently, the ion flux to the substrate can be influenced. Chopped HiPIMS is also beneficial for the reactive HiPIMS process, since an arc event can be partially or entirely eliminated by interrupting the discharge current after each micropulse.

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Figure 2.20 The discharge current and voltage waveforms of a chopped HiPIMS pulse generated using a HiPIMS power supply with superimposed dc power (power supply from Fig. 2.16).

2.4.4 Summary We have discussed the development and construction of high power pulsers and their applications in magnetron sputtering. The high power pulsers have developed from the initial thyristor-switched capacitors to pulsers that are based on IGBT switches with large capacitor banks. For the early pulser with thyristor-switched capacitors, the voltage and current waveforms were dependent on the plasma impedance, and the pulse length was not well defined. With IGBT switching and larger capacitors and capacitor banks, square voltage waveforms are possible with a well-defined pulse length. Various combinations of HiPIMS pulsers with dc and mf power supplies have been suggested and tested.

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Ehiasarian, A.P., Bugyi, R., 2004. Industrial size high power impulse magnetron sputtering. In: Proceedings of the 47th Society of Vacuum Coaters Annual Technical Conference. Dallas, Texas, April 24–29, 2004. Society of Vacuum Coaters, Albuquerque, New Mexico, pp. 486–490. Ehiasarian, A.P., Reinhard, C., Hovsepian, P.E., Colton, J.M., 2006. Industrial-scale production of corrosion-resistant CrN/NbN coatings deposited by the combined high power impulse magnetron sputtering etching unbalanced magnetron sputtering deposition (HIPIMS/UBM) process. In: Proceedings of the 49th Society of Vacuum Coaters Annual Technical Conference. Washington, DC, April 22–27, 2006. Society of Vacuum Coaters, Albuquerque, New Mexico, pp. 349–353. Ferreira, F., Serra, R., Oliveira, J.C., Cavaleiro, A., 2014. Effect of peak target power on the properties of Cr thin films sputtered by HiPIMS in deep oscillation magnetron sputtering (DOMS) mode. Surface and Coatings Technology 258, 249–256. Fetisov, I.K., Filippov, A.A., Khodachenko, G.V., Mozgrin, D.V., Pisarev, A.A., 1999. Impulse irradiation plasma technology for film deposition. Vacuum 53 (1–2), 133–136. Fetisov, I.K., Khodachenko, G.V., Mozgrin, D.V., 1991. Quasi-stationary high current forms of low pressure discharge in magnetic field. In: Palleschi, V., Vaselli, M. (Eds.), Proceedings of the XX International Conference on Phenomena in Ionized Gases. Barga, Italy, July 8–12, 1991, pp. 474–475. Ganciu-Petcu, M., Hecq, M., Dauchot, J.-P., Konstantinidis, S., Bretagne, J., De Poucques, L., Touzeau, M., 2011. Pulsed magnetron sputtering deposition with preionization. U.S. Patent no. 7,927,466 B2 (April 19, 2011). Glasoe, G.N., 1948. Introduction. In: Glasoe, G.N., Lebacqz, J.V. (Eds.), Pulse Generators. In: Massachusetts Institute of Technology Radiation Laboratory Series, vol. 5. McGraw Hill, New York, pp. 1–17. Greczynski, G., Lu, J., Jensen, J., Bolz, S., Kölker, W., Schiffers, C., Lemmer, O., Greene, J.E., Hultman, L., 2014. A review of metal-ion-flux-controlled growth of metastable TiAlN by HIPIMS/DCMS co-sputtering. Surface and Coatings Technology 257, 15–25. Gudmundsson, J.T., Alami, J., Helmersson, U., 2002. Spatial and temporal behavior of the plasma parameters in a pulsed magnetron discharge. Surface and Coatings Technology 161 (2–3), 249–256. Gudmundsson, J.T., Sigurjonsson, P., Larsson, P., Lundin, D., Helmersson, U., 2009. On the electron energy in the high power impulse magnetron sputtering discharge. Journal of Applied Physics 105 (12), 123302. Hajihoseini, H., Gudmundsson, J.T., 2017. Vanadium and vanadium nitride thin films grown by high power impulse magnetron sputtering. Journal of Physics D: Applied Physics 50 (50), 505302. Hála, M., Viau, N., Zabeida, O., Klemberg-Sapieha, J.E., Martinu, L., 2010. Dynamics of reactive high-power impulse magnetron sputtering discharge studied by time- and spaceresolved optical emission spectroscopy and fast imaging. Journal of Applied Physics 107 (4), 043305. Hecimovic, A., Ehiasarian, A.P., 2011. Temporal evolution of the ion fluxes for various elements in HIPIMS plasma discharge. IEEE Transactions on Plasma Science 39 (4), 1154–1164. Helmersson, U., Lattemann, M., Bohlmark, J., Ehiasarian, A.P., Gudmundsson, J.T., 2006. Ionized physical vapor deposition (IPVD): A review of technology and applications. Thin Solid Films 513 (1–2), 1–24. Kadlec, S., Weichart, J., 2016. Arc suppression and pulsing in high power impulse magnetron sputtering (HIPIMS). U.S. Patent no. 9,355,824 B2 (May 31, 2016).

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Kouznetsov, V., 2001. Method and apparatus for magnetically enhanced sputtering. U.S. Patent no. 6,296,742 B2 (October 2, 2001). Kouznetsov, V., Macák, K., Schneider, J.M., Helmersson, U., Petrov, I., 1999. A novel pulsed magnetron sputter technique utilizing very high target power densities. Surface and Coatings Technology 122 (2–3), 290–293. Kuzmichev, A.I., Melnyk, Y.I., Kulikovsky, V.Y., Bohac, P., Jastrabik, L., 2003. Characteristics of pulse magnetron discharge with power supply from a capacitor energy storage. In: Proceedings of the 26th International Conference on Phenomena in Ionized Gases, vol. 4. Greifswald, Germany, July 15–20, 2003, pp. 123–124. Leroy, W.P., Mahieu, S., Depla, D., Ehiasarian, A.P., 2010. High power impulse magnetron sputtering using a rotating cylindrical magnetron. Journal of Vacuum Science and Technology A 28 (1), 108–111. Liebig, B., Braithwaite, N.S.J., Kelly, P.J., Chistyakov, R., Abraham, B., Bradley, J., 2011. Time-resolved plasma characterisation of modulated pulsed power magnetron sputtering of chromium. Surface and Coatings Technology 205, S312–S316. Lin, J., Moore, J.J., Sproul, W.D., Mishra, B., Rees, J.A., Wu, Z., Chistyakov, R., Abraham, B., 2009. Ion energy and mass distributions of the plasma during modulated pulse power magnetron sputtering. Surface and Coatings Technology 203 (24), 3676–3685. Lin, J., Sproul, W.D., Moore, J.J., Wu, Z., Lee, S., Chistyakov, R., Abraham, B., 2011. Recent advances in modulated pulsed power magnetron sputtering for surface engineering. JOM Journal of the Minerals, Metals and Materials Society 63 (6), 48–58. Macák, K., Kouznetsov, V., Schneider, J., Helmersson, U., Petrov, I., 2000. Ionized sputter deposition using an extremely high plasma density pulsed magnetron discharge. Journal of Vacuum Science and Technology A 18 (4), 1533–1537. Malkin, O.A., Pyshnov, A.V., 1972. Dependence of parameters of a high-current pulsed discharge on current and on initial pressure. High Temperature 9 (5), 802–807. Mark, G., 2001. Power supply unit for bipolar power supply. U.S. Patent no. 6,735,099 B2 (April 17, 2001). Mark, M., Mark, G., 2014. MELEC’s pulse book: circuits and applications. http://www.melecgmbh.de/wp-content/uploads/MelecPulseBook.pdf. Markiewicz, J.P., Emmett, J.L., 1966. Design of flashlamp driving circuits. IEEE Journal of Quantum Electronics 2 (11), 707–711. Meng, L., Cloud, A.N., Jung, S., Ruzic, D.N., 2011. Study of plasma dynamics in a modulated pulsed power magnetron discharge using a time-resolved Langmuir probe. Journal of Vacuum Science and Technology A 29 (1), 011024. Mozgrin, D.V., 1994. High-current Low-pressure Quasi-stationary Discharge in a Magnetic Field: Experimental Research. Ph.D. thesis. Moscow Engineering Physics Institute (MEPhI), Moscow, Russia. Mozgrin, D.V., Fetisov, I.K., Khodachenko, G.V., 1995. High-current low-pressure quasistationary discharge in a magnetic field: experimental research. Plasma Physics Reports 21 (5), 400–409. Mozgrin, D.V., Fetisov, I.K., Khodachenko, G.V., 1996. Interaction of plasma with surfaces of conductive and dielectric solids in high current quasi steady state discharges of low pressure in magnetic fields. Izvestiya Akademii Nauk, Seriya Fizicheskaya 60 (4), 191–194. Musil, J., Leština, J., Vlˇcek, J., Tölg, T., 2001. Pulsed dc magnetron discharge for high-rate sputtering of thin films. Journal of Vacuum Science and Technology A 19 (2), 420–424. Ochs, D., 2008. HIPIMS power for improved thin film coatings. Vakuum in Forschung und Praxis 20 (4), 34–38.

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Ochs, D., Ozimek, P., Ehiasarian, A., Spencer, R., 2009. The historical development of HIPIMS power supplies: from laboratory to production. SVC Bulletin, (Spring), 36–39. Oks, E.M., Chagin, A.A., 1988. High-current magnetron discharge in a plasma electron emitter. Soviet Physics – Technical Physics 33 (6), 702–704. Pawel, J.E., McHargue, C.J., Wert, J.J., 1990. The influence of ion bombardment on the adhesion of thin films to substrates. Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms 46 (1–4), 392–396. Poolcharuansin, P., Bradley, J.W., 2011. The evolution of the IEDFs in a low-pressure HiPIMS discharge. Surface and Coatings Technology 205, S307–S311. Poolcharuansin, P., Liebig, B., Bradley, J.W., 2010. Plasma parameters in a pre-ionized HIPIMS discharge operating at low pressure. IEEE Transactions on Plasma Science 38 (11), 3007–3015. Rashid, M.H., 2011. Power Electronics Handbook: Devices, Circuits and Applications, 3 ed. Elsevier, Amsterdam, The Netherlands. Samuelsson, M., Lundin, D., Sarakinos, K., Björefors, F., Wälivaara, B., Ljungcrantz, H., Helmersson, U., 2012. Influence of ionization degree on film properties when using high power impulse magnetron sputtering. Journal of Vacuum Science and Technology A 30 (3), 031507. Shin, C.-S., Gall, D., Kim, Y.-W., Hellgren, N., Petrov, I., Greene, J.E., 2002. Development of preferred orientation in polycrystalline NaCl-structure δ-TaN layers grown by reactive magnetron sputtering: role of low-energy ion surface interactions. Journal of Applied Physics 92 (9), 5084–5093. Siemroth, P., Schülke, T., Witke, T., 1994. High-current arc – a new source for high-rate deposition. Surface and Coatings Technology 68–69, 314–319. Sittinger, V., Lenck, O., Vergöhl, M., Szyszk, B., Bräuer, G., 2013. Applications of HIPIMS metal oxides. Thin Solid Films 548, 18–26. Sproul, W.D., Christie, D.J., Carter, D.C., Tomasel, F., Linz, T., 2004. Pulsed plasmas for sputtering applications. Surface Engineering 20 (3), 174–176. ˇ Stranak, V., Cada, M., Hubiˇcka, Z., Tichý, M., Hippler, R., 2010. Time-resolved investigation of dual high power impulse magnetron sputtering with closed magnetic field during deposition of Ti–Cu thin films. Journal of Applied Physics 108 (4), 043305. ˇ Stranak, V., Drache, S., Bogdanowicz, R., Wulff, H., Herrendorf, A.-P., Hubiˇcka, Z., Cada, M., Tichý, M., Hippler, R., 2012. Effect of mid-frequency discharge assistance on dualhigh power impulse magnetron sputtering. Surface and Coatings Technology 206 (11–12), 2801–2809. ˇ Stranak, V., Wulff, H., Ksirova, P., Zietz, C., Drache, S., Cada, M., Hubiˇcka, Z., Bader, R., Tichý, M., Helm, C.A., Hippler, R., 2014. Ionized vapor deposition of antimicrobial Ti–Cu films with controlled copper release. Thin Solid Films 550, 389–394. Takagi, T., 1984. Ion-surface interactions during thin film deposition. Journal of Vacuum Science and Technology A 2 (2), 382–388. Thornton, J.A., 1986. The microstructure of sputter-deposited coatings. Journal of Vacuum Science and Technology A 4 (6), 3059–3065. Tyuryukanov, P.M., Fetisov, I.K., Nikolsky, A.D., 1981. Characteristics of pulsed discharge in axial-symmetric transverse magnetic field. Soviet Physics – Technical Physics 26 (10), 1182–1184. Tyuryukanov, P.M., Nikolskii, A.D., Fetisov, I.K., Tolstoi, I.N., 1982. Low-pressure pulsed discharge in a transverse axisymmetric magnetic field. Soviet Journal of Plasma Physics 8 (6), 693–697.

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a , Jon Tomas Gudmundssonb,c , Daniel Lundind ˇ Martin Cada a Institute of Physics v. v. i., Academy of Sciences of the Czech Republic, Prague, Czech Republic, b Department of Space and Plasma Physics, School of Electrical Engineering and Computer Science, KTH Royal Institute of Technology, Stockholm, Sweden, c Science Institute, University of Iceland, Reykjavik, Iceland, d Laboratoire de Physique des Gaz et Plasmas - LPGP, UMR 8578 CNRS, Université Paris–Sud, Université Paris–Saclay, Orsay Cedex, France

Electrons are the main energy carriers in HiPIMS discharges and their properties dictate the ionization processes and thus the discharge properties. The properties of the electrons are described by the fundamental plasma parameters, such as the electron density ne , the effective electron temperature Teff , the plasma potential Vpl , and the floating potential Vfl . Electrons are responsible for some of the most important inelastic collision processes taking place in the plasma volume, like ionization of working gas atoms and the atoms of the sputtered material, excitation of atoms to higher energetic levels, excitation of molecules to higher vibrational or rotational states, dissociation of molecules, occurring in particular in reactive sputtering processes, and creation of negative ions by attachment processes. Insight into the evolution of ne and Teff can help us determine if certain elementary processes are dominant (high rate) or if they are negligible (low rate). Here we give an extended overview of the measured fundamental plasma parameters related to electrons. The characterization methods applied, such as Langmuir probe, emissive probe, and triple probe, will be demonstrated as suitable methods for temporally and spatially resolved investigations. The analysis of the plasma characteristics reported in this chapter will help us identify desired discharge conditions and serves as important input to the discussion of the HiPIMS discharge physics given in Chapter 7.

3.1

Techniques for characterizing plasma electrons

Langmuir probes, emissive probes or triple probes are common diagnostic tools that are often applied to characterize the properties of plasma electrons in various plasma discharges including HiPIMS discharges. In this section, we provide brief descriptions of these techniques comprising what properties we can measure and/or estimate, limitations, and sources of errors. This is not an exhaustive discussion by any means, and High Power Impulse Magnetron Sputtering. https://doi.org/10.1016/B978-0-12-812454-3.00008-5 Copyright © 2020 Elsevier Inc. All rights reserved.

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the interested reader is referred to the books by Hutchinson (2009) or Huddlestone and Leonard (1965) and review papers by Godyak (1990) and Demidov et al. (2002) for more detail.

3.1.1 Langmuir probe One relatively straightforward technique to determine plasma parameters, such as electron density ne , effective electron temperature Teff , floating potential Vpl , and plasma potential Vfl is known as the Langmuir probe. It was introduced in 1923 by Langmuir (1923a), who later analyzed the technique in detail together with MottSmith (Mott-Smith and Langmuir, 1926). The basic assumption of this probe technique is that, unlike a large electrode surface affecting the plasma, the Langmuir probe is small and thus produces only small local plasma perturbations. Up to now, many Langmuir probe constructions have been developed together with a continuous improvement in the probe theory, measurement technique, and data acquisition. The principle of the Langmuir probe operation is very simple. A probe tip made of metal of a cylindrical, spherical, or planar shape with a diameter on the order of several tens of micrometers is typically used in low-temperature weakly ionized technological plasmas. The metal is chosen such that the secondary electron emission yield is as low as possible (typically tungsten, platinum, molybdenum, or graphite). The probe tip is inserted into a ceramic or quartz holder and electrically connected to the acquisition unit(s) via a feedthrough in the vacuum chamber. An overview of a basic arrangement for the entire probe construction and probe circuit is depicted in Fig. 3.1. A power supply for sweeping the probe voltage Vp is connected between the probe and a reference electrode. Since the cathode voltage is typically very high, the anode, which is often connected to the grounded vacuum chamber, is usually chosen as the reference electrode. An ammeter and a voltmeter are added to the probe circuit for measuring the probe current Ip at a given probe voltage Vp during the voltage sweep. In this way, a typical Ip –Vp (or probe) characteristics, as seen in Fig. 3.2, can be obtained. Details on the construction of the Langmuir probe circuits can be found in the literature, see, for example, Demidov et al. (2002) or Godyak (1990) and references therein. The probe voltage must be swept in such a range that the probe characteristics can be divided into three distinct parts separated by the floating potential Vfl and the plasma potential Vpl (see Fig. 3.2). For a sufficiently negative probe voltage (approximately less than 2Vfl ), only ions can reach the probe surface, and the measured current is referred to as the ion saturation current. A transition region for the probe characteristics lies between 2Vfl and Vpl . Here, both electrons and ions in the plasma are collected by the probe. When the probe voltage is higher than the plasma potential Vpl , practically only the electrons can reach the probe, and this part of the probe current characteristics is referred to as the electron saturation current. Interpretation of the probe characteristics, for example, calculating the plasma parameters based on the probe characteristics, is based on the theory on how charged particles traverse the space charge sheath that forms around the probe and reach the surface of the probe. A detailed description of the theory is provided by Pfau and Tichý (2008).

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Figure 3.1 A schematic of a Langmuir probe and the acquisition circuit. Voltmeter and ammeter measuring the probe voltage Vp and the probe current Ip are connected to a computer controlling the measurement procedure and data acquisition.

Figure 3.2 A typical current–voltage characteristics from a Langmuir probe immersed in a weakly ionized rf discharge.

The floating potential Vfl can easily be found, since this is the point on the probe Ip –Vp characteristics where the probe current is zero, that is, the electron and ion currents to the probe are equal. When the probe voltage is equal to the plasma potential, Vp = Vpl , the electric field between the probe and the plasma disappears, and the probe is at the same potential as the plasma itself and draws mainly the current from the more mobile electrons. At this point the probe characteristics have an inflection point, and the second derivative of the probe characteristics must be zero (Pfau and Tichý, 2008), which can typically be determined within an error of ±1 V. Furthermore, using the Druyvesteyn formulation (Druyvesteyn, 1930) (see e.g. Lieberman and Lichtenberg (2005, p. 189) for a more thorough description), we can also extract

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the electron density and the effective electron temperature as well as the electron energy distribution function (EEDF) ge (E) from the recorded Ip –Vp curves. The EEDF can be obtained from the second derivative of the electron probe current in the region where the probe voltage is negative with respect to the plasma potential according to ge (Vpl − Vp ) =

√ d2 Ipe 2 2me  e(Vpl − Vp ) , 2 e Ap d(Vpl − Vp )2

(3.1)

where Ap is the area of the probe surface, and Ipe is the electron probe current. Since the energy of the electrons E that overcome the retarding potential applied on the probe is proportional to (Vpl − Vp ), we can easily rescale the distribution function given by Eq. (3.1) to obtain the EEDF as a function of electron energy in units eV. Please note that, below the plasma potential, the measured probe current is a combination of the electron probe current Ipe and the ion probe current Ipi , which cannot easily be separated. However, a common approach is to extrapolate the ion probe current measured at a highly negative probe voltage to the point of interest (in Vp ), where Ipe and Ipi are comparable. The obtained ion probe current can then be subtracted from the total probe current resulting in the acquisition of the electron probe current only. Nevertheless, this procedure may not always be applicable and thus can introduce errors in the calculated EEDF. The reason lies in the fact that the theory describing a collection of ions by negatively biased probes is not accurately known for typical low-temperature plasmas (energy distribution of ions, number of ion collisions in the sheath, ion drift velocity, or structure of the space charge sheath around the probe are not fully known) (Godyak and Demidov, 2011). In many cases, it is more suitable to calculate the double derivative of the probe current Ip and to carry out the subtraction of the second derivative of the Ip extrapolated from a high negative probe voltage where the second derivative of the ion current to the probe Ipi dominates the second derivative of Ip . In this way, we obtain directly the second derivative of the electron current to the probe Ipe (Ivanov et al., 1977). Finally, once the EEDF is known, calculations of the electron density ne and effective electron temperature Teff can be carried out according to Eqs. (1.19) and (1.21), respectively, given in Section 1.1.5. When the EEDF is Maxwellian, we can talk about electron temperature, which is denoted by Te . The Druyvesteyn approach is essential when determining the electron properties in a discharge with non-Maxwellian electron energy distributions (Lieberman and Lichtenberg, 2005, p. 191), which is sometimes found in HiPIMS plasmas due to a highly energetic tail of electrons (see also Section 3.2). In a magnetron sputtering discharge a magnetic field is present in the target vicinity. The magnetic field is known to reduce the current collected by a Langmuir probe since the charged particles tend to follow the magnetic field lines (Laframboise and Rubinstein, 1976). The effect of the magnetic field on the collection of charged particles by a cylindrical or spherical probe depends on several parameters (Tichý et al., 1997, Passoth et al., 1997, 1999). In a collisionless plasma with large Debye length (low density plasma) the ratio of the probe radius to the gyroradius β = rp /rec is used to determine the influence of the magnetic field on the current collection. For β  1,

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we expect no distortion of the probe characteristic, whereas for β < 1, some distortion cannot be excluded (Tichý et al., 1997). Thus it is desirable to have a small probe radius. As discussed in Section 1.2.2, for a typical magnetron sputtering discharge, rce = 1 – 10 mm, and thus the probe radius has to be no larger than 50 – 100 µm for β < 0.1 to be fulfilled. The ratio β decreases with increasing velocity and mass of the charged particle, so that fast electrons and ions are less influenced by the magnetic field. Thus the presence of a magnetic field has predominant influence on the collection of low-energy electrons. For a collisionless plasma where the probe collecting surface is oriented parallel to the magnetic field lines, the mean gyroradius must be larger than the thickness of the space charge sheath around the probe. It is assumed that the electric potential changes within a mean gyroradius of a charged particle are small enough so that all orbits can be approximated by helices between any two intersections with the probe (Laframboise and Rubinstein, 1976). If this is fulfilled, then the effective electron mean free path is roughly equal to the gyroradius. However, when this condition is not satisfied, the collection of charged particles by the probe from the plasma is depleted. Thus, for a cylindrical Langmuir probe, the influence of the magnetic field is minimized when the probe is arranged perpendicular to the magnetic field lines. Also the presence of a magnetic field can lead to anisotropy in the EEDF. The ratio B/p, where p is the working gas pressure, characterizes the reduction of the diffusion coefficient for charged particles in direction across the field lines. Note that the degree of anisotropy depends on the ratio B/p and not on the magnetic field strength. This coefficient is important for plasmas in which the collisions of charged particles with neutrals cannot be neglected. At higher working gas pressures, the higher number of electron collisions with neutral particles leads to thermalization of the electrons, which shortens the relaxation time for the EEDF into its unaltered form and, consequently, reduces the influence of the magnetic field. Thus for B/p values below 0.01, no influence of the magnetic field on the EEDF is expected (Passoth et al., 1997). The Langmuir probe has several important advantages, such as a simple construction and implementation, a relatively uncomplicated electronic acquisition unit, even for time-resolved measurements, easily transportable hardware, and the possibility of obtaining several important plasma parameters from one measurement. Furthermore, the spatial resolution is proportional to the Debye length, and temporal resolution is given by the plasma frequency of ions. However, there are also some disadvantages, which must be taken into account when a Langmuir probe is used. Even when the probe tip is small (typical radius rp < 0.1 mm), the probe still disturbs the surrounding plasma by drawing charged particles. Other issues include covering of the probe tip by deposited material, material and dimensions of the probe stem can affect the discharge, charged/neutral particle interaction with the probe surface can produce secondary particles, a hot plasma can destroy the probe, as well as the previously discussed uncertainties in the theory used to describe the flux of the charged particles to the probe (Pfau and Tichý, 2008). Several commercial producers offer automated Langmuir probe systems enabling linear motion of the probe within the vacuum chamber and fully computer controlled measurements of the probe characteristics together with a semiautomatic interpreta-

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tion of the probe characteristics providing basic plasma parameters.1 These measuring systems allow time-resolved measurement of the probe characteristics with a resolution typically less than 1 µs and measurements in rf discharges with the probe compensated against an rf component of the probe current arising due to an rf bias between the probe and the plasma.

3.1.2 Emissive probe Electron emitting probes (often referred to as emissive probes) were suggested by Langmuir already in the 1920s for the measurement of plasma parameters (Langmuir, 1923b). During the last several decades, the emissive probe has been demonstrated as a powerful instrument for measuring the plasma potential in discharges under strong magnetic fields, during plasma instabilities in a flowing plasma or within ion or electron beams (Smith et al., 1979, Sheehan and Hershkowitz, 2011). Recent review papers discuss the practical use of the emissive probe in challenging environments (Sheehan and Hershkowitz, 2011, Sheehan et al., 2017), and provide a good starting point for those that desire to further explore this technique. Essentially, the emissive probe is a thin wire (typical diameter of 0.1 mm) forming a small loop, which is heated by electric current to emit electrons into the plasma. The wire should generate sufficiently high electron thermionic emission, and tungsten is a commonly used material. The hardware of the emissive probe is similar to the cold Langmuir probe discussed in Section 3.1.1, although the emissive wire has to be connected to a source that provides heating current. Most often, a transformer with rectified sinusoidal output voltage (one diode for rectifying is enough since the filament does not cool down during the line period) is used offering galvanic isolation of the heating voltage from an electronic circuit, which provides sweeping of the probe voltage and simultaneous probe current acquisition. The probe current acquisition unit must be capable of measuring the probe current during the short period when the heating voltage is off to ensure that the probe is kept at a defined potential (Smith et al., 1979). An emission current Iem can flow from the probe to the plasma as long as the probe voltage Vp fulfills the condition Vp ≤ Vpl , independently of the EEDF and of fluctuations in Teff . For Vp > Vpl , the emission current drops exponentially, and electron collection begins to dominate the probe current (compare with Fig. 3.2 for the Langmuir probe). Since the temperature of the emitted electrons Tem (temperature of the heated wire) is usually much smaller than that of the plasma electrons, this exponential drop is very abrupt. Therefore the floating potential Vfl,em of an emissive probe can be taken as a sufficiently accurate approximation for the plasma potential (Kemp and Sellen, 1966). Furthermore, the floating potential of the emissive probe tends to saturate as the emitted electron current increases, and this saturated floating potential can be taken as the plasma potential (Kemp and Sellen, 1966). However, it should be noted that a biased emissive probe immersed in a plasma collects both electrons 1 This includes Impedans https://www.impedans.com/langmuir_probes, Hiden Analytical http://www.

hidenanalytical.com/products/for-thin-films-plasma-and-surface-engineering/espion/, and Plasma Sensors http://plasmasensors.com/index.html.

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Figure 3.3 Typical Ip –Vp characteristics from a cold Langmuir probe (solid line) and a hot emissive probe (dashed line).

and ions from the plasma. Therefore the probe characteristics of the Langmuir and emissive probes are similar except that the Ip,em –Vp,em characteristic of the emissive probe is shifted down to a negative probe current (apparent ion current due to electron emission) as seen in Fig. 3.3. Additional procedures on how to determine the plasma potential from the Ip,em –Vp,em characteristics of the emissive probe have been developed. For example, we can plot the emitted current versus probe potential on a semilog scale, where the emitted current is obtained by subtraction of the probe current of the nonemitting probe from the probe current of the emissive probe versus the probe potential. Then the plasma potential is given by the intersection of two straight lines extrapolating the plotted emitting electron current (Sellen et al., 1965). The plasma potential at the emitting wire can in such a way be estimated with an accuracy on the order of kB Tem /e. Since the temperature of the emitting wire is roughly 1500 – 3000◦ C, the error of the measured Vpl is about 0.1 – 0.2 V (Kemp and Sellen, 1966). Another method is based on measuring the probe voltage, where the nonemitting and the emitting probe characteristics are separated. This point indicates the position of the plasma potential. The accuracy of this method is somewhat worse, approximately 0.5 V (Chen, 1965). The emissive probe has several advantages. Unlike the cold Langmuir probe, the (hot) emissive probe does not suffer from contamination of the wire surface by impurities, such as from deposition of sputtered material. Another advantage of the emissive probe lies in the possibility to measure the plasma potential in magnetically confined plasmas, flowing plasmas, and in discharges where electron or ion beams are present. Also, by using the technique of directly measuring the plasma potential based on the recorded saturated floating potential, we can display the temporal evolution of the plasma potential in real time on, for example, a digital sampling oscilloscope, which then provides instant feedback on the plasma process. This enormously facilitates localized measurements of Vpl and is the only way to observe fluctuations of Vpl with high temporal resolution, which turns out to be of great value in HiPIMS discharges, as we will see later in this chapter.

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Figure 3.4 Schematic of a triple probe configuration. (A) The middle probe is connected to the outer probes via the voltage sources V2 and V3 . (B) The outer probe P2 is left floating, and the current flows through the probes P1 and P3 .

3.1.3 Triple probe The triple probe was introduced by Chen and Sekiguchi (1965) in the mid-1960s. The purpose of developing this probe method was to have a technique enabling fast, if possible direct, measurements of the basic plasma parameters, Teff , ne , Vpl , and Vfl . The triple probe consists of three equally sized probe tips placed as close as possible to each other without having overlapping space charge sheaths around adjacent probe tips. Generally, the outer probe tips P2 and P3 can be connected with the middle probe tip P1 via voltage sources V2 and V3 as seen in Fig. 3.4A. Depending on the voltages V2 and V3 , all the probe tips can be at the floating potential (V2 and V3 equal zero, and the net current must be zero as well), or the probe tips P2 and P3 collect ion saturation current, and the probe tip P1 collects electron saturation current if the outer probe tips P2 and P3 are biased negatively to the reference probe tip P1 or vice versa (Chen and Sekiguchi, 1965). According to Kirchhoff’s current law, we can write the current balance for the circuit in Fig. 3.4A as I 1 = I 2 + I3 ,

(3.2)

and based on Kirchhoff’s voltage law, the voltage fulfills 2 − 1 = V2 , 3 − 1 = V3 ,

(3.3) (3.4)

where 1 , 2 , and 3 are the probe tip potentials measured negatively referenced to the plasma potential. Assuming that (i) the EEDF is Maxwellian, (ii) the mean free path of the electrons is much larger than both the probe radii and the space charge sheath thickness around the probe tip, and (iii) the sheaths around the probe tips do not overlap, then the currents I1 , I2 , and I3 in Eq. (3.2) can be expressed by the wellknown equations for the electron and ion saturation currents collected by the Langmuir probe (Chen, 1965). If we also assume that the variation in the ion saturation current with the change in the probe potential is negligible in comparison to the electron current (i.e. the ion current flowing to each probe is independent of the probe potential

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Ii (1 ) ≈ Ii (2 ) ≈ Ii (3 ) ≡ Ii ), then Eq. (3.2) can be rewritten in the form (Chen and Sekiguchi, 1965)   eV2 I1 + I2 1 − exp − kB Te  . = (3.5) I1 + I3 1 − exp − eV3 kB Te

Equation (3.5) can be applied directly to calculate the electron temperature if the current flowing through each probe tip is measured along with the voltages V2 and V3 (in fact, any two currents of the three probe currents can be measured, and the last one can be estimated from Eq. (3.2)). Let, for example, probe tip P2 be at floating potential (by removing the fixed voltage source V2 ; see Fig. 3.4B); and the current I2 = 0. Then the current I has to flow between probe tips P1 and P3 , I1 = I3 = I , the left-hand side of Eq. (3.5) is reduced to 1/2, and Eq. (3.5) can be simplified to   eV2 1 − exp − kB Te 1  . (3.6) = 2 1 − exp − eV3 kB Te

Since the voltage V3 is fixed externally by the voltage source and we expect the bias voltage on the probe tip P3 to be sufficiently large to ensure collection of only the ion saturation current, that is, V3 ≥ 3kB Te /e, then the denominator in Eq. (3.6) converges to 1, and Eq. (3.6) can be rewritten as k B Te V2 = . e ln 2

(3.7)

In this way, the electron temperature can be directly displayed, for example, on a digital sampling oscilloscope, with high-input impedance, by measuring a potential difference between probe tips P2 and P1 . We should note that the electron temperature determined in this way is independent of the type of ions arriving at the probe. We can show that the electron current component can be eliminated from the total probe currents I1 , I2 , and I3 by a simple rearrangement of Eq. (3.2). Then the ion saturation current Ii can be expressed as   2) I3 − I2 exp − e(Vk3B−V Te   , (3.8) Ii = e(V3 −V2 ) 1 − exp − kB Te where the fixed voltages V2 and V3 , the measured electron temperature according to Eq. (3.7), and the measured currents flowing through the probe tips are used (Chen and Sekiguchi, 1965). For instantaneous measurements of the ion saturation current, it is advantageous to leave the probe tip P2 again at floating potential (similarly as in the derivation of Eq. (3.6); see Fig. 3.4B), and the current I2 must be zero and I1 = I3 = I . If we substitute this condition into Eq. (3.8), then we yield, by using

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Eq. (3.6), an expression for the ion saturation current Ii , which practically equals to the measured current I , provided that the fixed voltage V3 ≥ 3kB Te /e: 

Ii = exp

I eV2 kB Te



−1

(3.9)

.

To be able to determine the electron density from the measured ion saturation current Ii , we have to assume that the electron density at the space charge sheath edge nes and the density of positive ions nis are approximately equal on the boundary of the space charge sheath around the probe tip. The electron density nes at the space charge sheath edge depends on the electron density ne in the plasma bulk according to nes = ne exp(−1/2) ≈ nis =

Ii , √ eAp kB Te /Mi

(3.10)

where nis is the ion density at the sheath edge, Mi is the ion mass, and Ap is the probe area. The electron density ne can be calculated in this way from the measured ion saturation current Ii (Chen and Sekiguchi, 1965): ne =

Ii . √ 0.61eAp kB Te /Mi

(3.11)

The possibility to directly acquire the basic plasma parameters without the need to sweep the probe voltage is a major advantage of the triple probe technique. The plasma parameters are acquired by a simple measurement of the voltage between probe tips P2 and P1 and the current flowing through the probe tips P3 and P1 . This operation can easily be carried out on an oscilloscope and allows for a high time resolution. On the other hand, we must keep in mind that Eqs. (3.7) and (3.11) were derived under plasma conditions, which may not always be fulfilled. Especially in HiPIMS discharges, the EEDF is not always strictly Maxwellian, and the ion sheath thickness increases as the probe potential decreases with respect to the floating potential. Growing sheath thickness implies an increase in the ion saturation current Ii , which is expected to be independent on the change of the probes’ potential when Eq. (3.5) is derived. The error can be quantified if the increase of the ion saturation current with decreasing probe potential is known. Details on how to treat and quantify the errors of measured electron density ne by the triple probe can be found in the seminal work of Chen and Sekiguchi (1965). Also, the effective electron temperature in HiPIMS discharges can vary between several tens of eV down to a tenth of eV during the pulse period, as will be discussed in Section 3.3. Under such conditions, it is difficult to fulfill the requirements of the triple probe method. Nevertheless, the triple probe technique can still be used to acquire relative trends in the plasma parameters, in particular, in pulsed discharges or when investigating plasma instabilities.

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Fundamental electron characteristics

We now turn to a discussion of the spatial and temporal variations of the electron density ne and the effective electron temperature Teff in HiPIMS discharges based on the extensive investigations carried out using the previously described diagnostic techniques. We will also address the electron energy distribution function (EEDF) and how it evolves during and after the HiPIMS discharge pulse.

3.2.1 Electron energy, density, and temperature The first report on Langmuir probe measurement to capture the properties of the electrons in the HiPIMS discharge was published by Gudmundsson et al. (2001) relatively soon after Kouznetsov and coworkers’ seminal HiPIMS paper (Kouznetsov et al., 1999) using the same discharge chamber and power supply. They carried out timeresolved measurements on a HiPIMS discharge operated with 100 µs long pulses at 50 Hz repetition frequency at an average power of 300 W, which was applied to a 6” (150 mm) circular Ta target. The argon working gas pressure was maintained at pAr = 0.27 Pa. The probe was placed at a distance of 20 cm from the target and revealed an electron density increase during the discharge pulse reaching a peak in electron density of close to 1018 m−3 at 30 µs after the end of the pulse, which was followed by a two-step plasma density decay. On the contrary, the average electron energy was found to decrease rapidly from 4.5 eV at the beginning of the pulse to 2.5 eV at 92 µs followed by an increase up to 3.5 eV at the end of the pulse. During the pulse off-time (afterglow), the average electron energy was found to reach a minimum value of 1.5 eV approximately 240 µs after the ignition of the plasma pulse (140 µs after pulse-off) followed by a gradual increase to a plateau value corresponding to 2.4 eV. The measured EEDFs demonstrated that toward the end of the pulse, two energy groups of electrons were present (bi-Maxwellian distribution). Furthermore, it was also observed that the EEDF was Maxwellian during the peak in electron density, which was followed by a Druyvesteyn-like EEDF with slightly higher average electron energy (see also Section 1.1.5). Further measurements of the EEDF in the same system with a Cu target over the race track area was in fact close to being Maxwellian during the entire plasma pulse (with the possible exception of the pulse-initiation stage, which was difficult to probe) (Gudmundsson et al., 2009). Pajdarová et al. (2009) reported on the temporal evolutions of the electron energy distribution and the local plasma parameters in the substrate position with a planar Cu target of 100 mm diameter. They found electron energy distributions with two groups of electrons and sharply truncated high-energy tails during the pulse. The hot electrons decreased rapidly in numbers in the initial stage of the pulse approaching the kinetic temperature approximately 100 µs after pulse initiation. As a comparison, for dcMS, the EEDF is commonly observed to be bi-Maxwellian in the substrate vicinity (Sheridan et al., 1991, Sigurjonsson and Gudmundsson, 2008, Seo and Chang, 2004, Seo et al., 2004). Due to the limited spatial resolution in the first attempts to characterize the HiPIMS plasma, additional Langmuir probe studies were carried out on the same deposition

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Figure 3.5 Temporal and spatial variation of the electron density ne in the vicinity of the target at (A) 40, (B) 160, (C) 280, and (D) 640 µs after pulse ignition, respectively. ©2005 IEEE. Reprinted, with permission, from Bohlmark et al. (2005).

system as used by Gudmundsson et al. (2001, 2009). A detailed study by Bohlmark et al. (2005) of the spatial and temporal plasma density distribution can be seen in Fig. 3.5. They applied 9 J HiPIMS pulses, 100 µs long, at a repetition frequency of 50 Hz to a 6” (150 mm) circular Ti target, but for higher argon working gas pressure, pAr = 2.7 Pa, compared to the earlier studies. The space above the target (2 – 28 cm in the axial z direction and 0 – 14 cm in the parallel y direction) was scanned using a time-resolved Langmuir probe. It was found that the electron density was the highest above the target race track during the first 160 µs from the onset of the plasma pulse with a peak density > 1019 m−3 close to the target and that the electron density steeply decreases when moving away from the race track region (Bohlmark et al., 2005). This is roughly two orders of magnitude higher electron density than commonly observed in the substrate vicinity for a conventional dcMS discharge. From Fig. 3.5 it is also seen that the plasma pulse on-time is characterized by an expansion of the plasma from the target and into the vacuum chamber as the discharge current increases, which is discussed in more detail in the next section. The obtained results show that the plasma density at a typical substrate position can be more than one order of magnitude lower compared to the electron density close to the target surface. During the plasma pulse off-time (t > 100 µs in the present case), the plasma further expands away from the target, and the electron density above the race track decreases, whereas the plasma density in the magnetic null point (y = 0 cm and z = 7 cm) moderately increases. Note that the plasma density remains at a relatively high level of 1017 – 1018 m−3 even 540 µs (Fig. 3.5D, t = 640 µs) after the pulse is off. In fact, a high plasma density ∼ 1017 m−3 is commonly observed to linger at large distances from the target surface for a rather long time, up to a few milliseconds

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Figure 3.6 The time evolution of the electron temperatures for the different identified electron components. The HiPIMS pulse was 100 µs long with a peak discharge current density of 1.1 A/cm2 , which was reached at t ≈ 35 µs. A few different groups of electrons are observed, namely superthermal Test , hot Teh , and cold Tec electrons. The superthermal or beam-like electrons are generated by the dynamic motion of the sheath, and they have Test values up to 100 eV and persist for a duration of 3 µs. The argon working gas pressure was 0.5 Pa. Data taken from Poolcharuansin and Bradley (2010).

(Gudmundsson et al., 2002, Horwat and Anders, 2010). It is also worth noting that a monotonic rise in plasma density with discharge working gas pressure (Gudmundsson et al., 2002) and applied power (Alami et al., 2005), as well as an approximately linear increase in electron density with increased discharge current (Ehiasarian et al., 2008, Lundin et al., 2015), is observed. From effective electron temperature measurements it is generally found that Teff is rather stable in the range 1 – 6 eV at about a few tens of microseconds into the pulse, which is in line with the early reports discussed before, except for the afterglow, where most reports agree on Teff values in the range of 0.3 – 1 eV (Gudmundsson et al., 2009, ˇ Vetushka and Ehiasarian, 2008, Ehiasarian et al., 2008, Lundin et al., 2015, Cada et al., 2011). Furthermore, detailed studies on the effective electron temperature variation during the onset of the discharge pulse have been carried out by Poocharuansin et al. (Poolcharuansin and Bradley, 2010, Poolcharuansin, 2012). A Langmuir probe was placed 10 cm above the center of a 6” (150 mm) circular Ti target. The plasma parameters were investigated for pulse power densities of 500 W/cm2 and 1000 W/cm2 and at three different argon working gas pressures (0.5, 1.1, and 1.6 Pa). The time evolution of the electron temperatures for the different electron components identified are shown in Fig. 3.6. Three distinct groups of electrons were found in the initial stages of the pulse (< 4 µs). The authors describe these groups as superthermal, hot, and cold electrons with effective electron temperatures in the ranges 70 – 100, 5 – 7, and 0.8 – 1 eV, respectively. The explanation given by Poolcharuansin and Bradley (2010) for the existence of the superthermal electrons assumes that initially the sheath is very thin or nonexisting, depending on the off-time remnant plasma. After the pulse initiation, the sheath expands rapidly due to increasing target cathode voltage. The electrons from the remnant off-time plasma are accelerated in the increasing axial field of the forming sheath. This results in an E × B-drift and azimuthal current. As the sheath edge

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advances, these electrons may then bounce from the leading edge of the sheath, similar to what is referred to as stochastic heating in capacitively coupled rf discharges (Lieberman and Lichtenberg, 2005, Lieberman and Godyak, 1998). Thus, beamlike electrons are formed and are detected as having a very high effective electron temperature in the first few microseconds after the voltage initiation. These electrons have a strong impact on the floating potential, which is further discussed in Section 3.3.2. However, it should be noted that the mentioned electron groups were indistinguishable after approximately 5 µs into the pulse, after which only one group of electrons was observed, and the electron gas was gradually cooled down to around 2 eV during the pulse, which is in line with other reported values of Teff . As a comparison with the reported electron density and electron temperature values observed in HiPIMS discharges, we also provide typical data obtained in the MPPMS discharge discussed in Chapter 1 (Section 1.4.5). Meng et al. (2011) used three identical triple probes, which were placed parallel to a 14” (360 mm) circular Ti target at the substrate position. The obtained results demonstrate that the electron density reached values of about 5 × 1017 m−3 and Teff ≤ 10 eV for standard discharge conditions. Furthermore, a higher repetition frequency of the macropulse resulted in a drop in electron density due to the limited instantaneous peak power, whereas higher argon working gas pressures (in the range from 0.13 Pa to 4.0 Pa) resulted in a somewhat increased ne , but lower Teff . Also, Liebig et al. (2011) investigated the plasma parameters in an MPPMS system, which was equipped with a circular Cr target, 150 mm in diameter. A Langmuir probe was placed above the center of the magnetron target at a distance of 10 cm (∼ substrate position). The authors recorded typical electron densities in the range 2.5 × 1017 – 4.5 × 1017 m−3 . The effective electron temperature during the first 50 µs reached up to 100 eV, in line with the previously discussed beam-like electrons in HiPIMS, but rapidly decreased to 3 eV during the first stage of the macropulse. We therefore conclude that MPPMS discharges generally have an electron density that is about one order of magnitude lower compared to HiPIMS discharges, which scales rather well with the instantaneous peak power applied (see Fig. 1.13). However, the effective electron temperatures are found to be in the same range as in HiPIMS discharges.

3.2.2 Plasma expansion and reflection In Fig. 3.5, it is shown how the plasma expands from the target and into the vacuum chamber when the pulse is on and continues to do so also during the afterglow (pulseoff). Gudmundsson et al. (2002) found that the peak in the electron density travels away from the target at a speed that decreases with increased working gas pressure from 4 km/s at pAr = 0.07 Pa to 0.9 km/s at pAr = 2.7 Pa while sputtering a Ta target. At the higher working gas pressures, they also observed a second peak in the measured time-resolved electron density at larger distances from the target. Typically, the second peak was observed at roughly 400 µs from initiation of the plasma pulse (pulse width 100 µs). However, the exact timing of this peak depended on the dimensions of the vacuum chamber, the pulse power density, and the target material (Alami et al., 2005). Thus they concluded that the second peak in the electron density during the plasma

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off-time is caused by reflection of neutral particles from the chamber walls, implying a local increase in gas density and subsequently in the plasma density (Alami et al., 2005). Gylfason et al. (2005) measured the time-resolved electron saturation current at different positions from a Ti target with the intention to study expansion of ion acoustic solitary waves propagating from the target. Their observations revealed that the time-resolved electron saturation current (which is proportional to the electron density) consisted of one peak traveling away from the magnetron target. The speed of the moving electron saturation current peak depended significantly on the working gas pressure and on the energy of the plasma pulse and ranged from circa 5 km/s at pAr = 0.13 Pa to 1 km/s at pAr = 2.7 Pa. It is interesting that for the highest investigated pressure, a second peak in the electron saturation current emerged. However, its position in time was stationary for all the investigated distances from the target. Other authors have reported a similar behavior during plasma expansion. Vetushka and Ehiasarian (2008) investigated HiPIMS discharges for Cr and Ti targets both with a diameter of 75 mm at an Ar pressure of 0.28 Pa and 2.7 Pa. The HiPIMS pulse duration was always set to 70 µs with a repetition frequency of 100 Hz. The Langmuir probe tip was placed 10 cm above the target. Surprisingly, a second peak in the plasma density was only observed at pAr = 2.7 Pa at approximately 110 µs after the plasma pulse, which is much earlier after pulse-off compared to the previous reports. The authors correlated this second peak to the main plasma expanding from the target to the probe with typical ion velocities of 700 m/s. Ehiasarian et al. (2008) investigated the plasma expansion as a function of different pulse discharge currents ranging from 14 A (JD,peak = 0.3 A/cm2 ) to 80 A (JD,peak = 1.8 A/cm2 ) in the same system using a Ti target. They clearly demonstrate that a first peak in the electron density appeared approximately at the end of the pulse independent of the discharge current amplitude. Again, a second peak in the electron density was observed at about 80 µs after pulseoff. It was found being more pronounced with increasing pulse discharge current and in line with the observations in the earlier work (Vetushka and Ehiasarian, 2008) discussed previously. A more in-depth analysis of the plasma expansion and composition is given in Section 7.2.2.

3.3

Influence of target material and working gas

The influence of the target material on the spatial and temporal evolution of the plasma parameters has been investigated by several research groups. We will first look at how the fundamental electron properties (EEDF, ne , and Teff ) change depending on the choice of target material. Also, the plasma potential will be addressed as well as the impact on the electron dynamics when adding a reactive gas.

3.3.1 Electron energy, density and temperature One of the earliest reports, where the plasma parameters are compared for discharges operated with different target materials, is from Vetushka and Ehiasarian (2008), who

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studied Ar/Cr and Ar/Ti discharges. They found that the electron density at an argon working gas pressure of 0.28 Pa is a factor ∼2 higher for Cr compared to Ti at the same distance from the target (10 cm), that is, ne,Cr ≈ 8 × 1017 m−3 and ne,Ti ≈ 4 × 1017 m−3 , respectively. Furthermore, the electron density started to grow at the same time as the discharge current for the Cr target, whereas there was a delay of about 25 µs when using the Ti target. However, the peak of the plasma density was reached at the same time ∼16 µs after the end of the pulse (length 70 µs) for both targets. The authors linked this behavior to a higher sputter yield of Cr and a higher cathode voltage on the Cr target compared to the Ti case. It implies a stronger gas rarefaction of argon atoms in the vicinity of the target (see Section 4.2.2 for gas rarefaction) and simultaneously a presence of electrons with higher kinetic energy due to higher cathode voltage for the Cr target. Under such conditions, it is more probable that a significant fraction of the Cr atoms will be ionized near the probe, even when the plasma density is comparable in the vicinity of the target (observed discharge current waveforms were practically identical for both target materials) (Vetushka and Ehiasarian, 2008). Also, the Ar/Cu discharge has been characterized. Pajdarová et al. (2009) used a Langmuir probe to study 200 µs long HiPIMS pulses at a repetition frequency of 1 kHz applied to a 100 mm-diameter Cu target. The plasma density was determined for peak pulse discharge currents of 5 A (JD,peak = 0.06 A/cm2 ) and 50 A (JD,peak = 0.6 A/cm2 ) at a distance of 10 cm from the target at an argon working gas pressure of pAr = 1 Pa. The electron density was approximately 70 times larger for the higher discharge current pulse. For the first 100 µs of the high-current case (50 A), the electron density increased to 1017 m−3 , followed by a steep increase up to 1018 m−3 at 150 µs, and being almost constant up to the end of the discharge pulse. A similar trend was observed also for the 5 A discharge pulses. The authors also report that the electron temperature oscillated between 0.95 eV to 1.1 eV during the high-current part of the pulse independently of the magnitude of the discharge current. Lundin et al. (2015) carried out time-resolved Langmuir probe measurements using 50-mm circular targets of Al, C, and Ti. The probe was located above the race track at a distance of 4 cm. The length of the discharge pulse was 100 µs or 400 µs, and the argon working gas pressure was set to pAr = 0.5 Pa or pAr = 2.0 Pa. The average discharge power was kept constant at 200 W, and the pulse discharge current density JD,peak was varied from 0.5 A/cm2 to 2.0 A/cm2 by changing the pulse repetition frequency. The electron density peaked at the end of the pulse and was generally found to be in the range 1 × 1018 – 5 × 1018 m−3 . By increasing the discharge current density the electron density increased linearly with a tendency to level out at higher JD,peak . Increasing the working gas pressure resulted in a significant increase in the electron density in the Ar/Ti discharges, whereas the changes in electron density were not so pronounced for the Ar/Al discharges. The measured effective electron temperature was around 2 – 4 eV, independently of the target material. As an extended comparison, the electron density normalized to the HiPIMS peak discharge current density JD,peak , averaged over the entire target for various HiPIMS discharges, is plotted in Fig. 3.7 for different target materials: Ti, Cu, Cr, Al, C, Ta, Nb, and W. All the discharges were operated with pure argon as the working gas over a rather wide range of operating pressures (0.27 – 2.7 Pa). Even though

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Figure 3.7 Electron (plasma) density normalized to the HiPIMS peak discharge current density averaged over the entire target surface for eight different target materials (Ti, Cu, Cr, Al, C, Ta, Nb, and W). All the discharges were operated with pure argon as the working gas with the pressure given above each bar (0.27 – 2.7 Pa). The values inside the bars denote the discharge current density (0.06 – 2 A/cm2 ). The data were compiled from several authors (Vetushka and Ehiasarian, 2008, Pajdarová et al., 2009, Lundin et al., 2015, Gudmundsson et al., 2001, Spagnolo et al., 2016, Lockwood Estrin et al., 2017).

the process conditions (pressure, target size, and target material), the HiPIMS pulse configuration, and the exact location of the density measurement varied, the electron density still scales rather well with the peak current density (JD,peak in the range 0.06 – 2 A/cm2 ); that is, for typical peak current densities around 1 A/cm2 , a plasma density of 1 – 3 × 1018 m−3 can be expected in the region close to the cathode target. However, the Ar/Nb and Ar/W discharges seem to deviate somewhat from this value and produce an electron density closer to 1019 m−3 at the same peak current density. These two discharges were characterized using a triple probe placed much closer to the target surfaces (10 – 15 mm) compared to the other discharges, investigated by Langmuir probes, which is likely the reason for the slightly higher normalized electron density values. There is also a weak tendency of increasing electron density when increasing the total pressure from 0.5 Pa to 2.0 Pa, as seen in Fig. 3.7 for the Ar/Ti and Ar/Al discharges. However, increasing the pressure beyond 2.0 Pa does not seem to increase the electron density. So far, we have mainly discussed changes in the plasma density. However, a novel approach to increase the electron temperature during HiPIMS operation was proposed by Aijaz et al. (2012) when trying to increase the ionization fraction of sputtered carbon atoms during HiPIMS deposition of amorphous carbon (a-C) (the thin film properties of this material is discussed in Section 8.4.1). The authors showed that the number of high-energy electrons can indeed be increased by using a working gas with high ionization potential. Neon was identified as a suitable candidate, since Eiz = 21.56 eV, and the sputter yield for Ne+ ions bombarding graphite is significantly higher in comparison with, for example, He+ ions (Eiz = 24.58 eV) bombarding graphite. HiPIMS pulses with a repetition frequency of 600 Hz and a pulse length of

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25 µs were used for sputtering a graphite target, 50 mm in diameter, at a peak power of 2.7 kW. The working gas pressure in the chamber was kept constant at 2 Pa with an Ar/Ne gas mixture ranging from 0% Ne to 83% Ne. EEDFs were obtained from Langmuir probe measurements recorded at 60 mm from the target at t = 60 µs after the plasma pulse initiation (i.e. during plasma afterglow). They were characterized as being bi-Maxwellian with two electron populations with temperatures Teff,c and Teff,h corresponding to cold and hot electrons, respectively. It was observed that an increase of the Ne content from 0% to 83% resulted in an approximately linear increase in both Teff,c and Teff,h from Teff,h = 2.5 eV to Teff,h = 4.5 eV and Teff,c = 0.54 eV to Teff,c = 0.60 eV. Using mass spectrometry, a substantial increase in the C+ ion flux was verified as compared to a conventional HiPIMS process with pure argon as the working gas (see also Section 4.1).

3.3.2 Plasma potential In addition to the EEDF and the estimated ne and Teff values, there are also reports of the spatial and temporal variation of the plasma potential as well as the floating potential obtained from measured Ip –Vp characteristics of the Langmuir probe (Gudmundsson et al., 2001, 2002, Pajdarová et al., 2009, Poolcharuansin and Bradley, 2010) and from emissive probe measurements (Mishra et al., 2011). These reports generally show that during the initial stages of the pulse, the plasma potential exhibits negative values of several tens of volts close to the target. The absolute value decreases with increased distance, but does never reach ground potential. As the discharge current rises and a dense plasma is established, Vpl attains a slightly positive value of around 2–3 V. During the HiPIMS afterglow, the plasma potential decreases to a value close to zero. Note, however, that the situation when using hybrid HiPIMS sources (see Section 3.4) can be somewhat different. For example, Stranak et al. (2012b) indeed found that Vpl is fairly constant around 5 V, 45 mm from the target, during the HiPIMS plasma pulse, whereas the addition of an ECWR plasma during pulse-off led to plasma potential values of around 30 V. The floating potential, on the other hand, is typically found to be negative, up to several hundred volts, at the initial phase of the plasma pulse (Poolcharuansin and Bradley, 2010). During the remainder of the pulse, the floating potential rapidly increases and commonly reaches values of approximately 0 V (or slightly negative (Lundin et al., 2015)) at the end of the plasma pulse. During the pulse off-time, the floating potential is oscillating around 0 V. Two detailed investigations of the spatial and temporal evolution of the plasma potential in HiPIMS discharges were carried out by Mishra et al. (2010, 2011) using an emissive probe. In the first study (Mishra et al., 2010), the probe was placed above the race track at a distance from 2 mm to 100 mm from the 6” (150 mm) Ti target surface. They found that the plasma potential evolution was insensitive to a pressure change in the range from pAr = 0.54 Pa to pAr = 1.08 Pa. However, the study revealed that the plasma potential exhibits very high negative values in the vicinity of the target (< 10 mm), around −100 V to −200 V, depending on the discharge conditions, during the initial phase of the plasma pulse (pulse length 100 µs). During the second half

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of the plasma pulse, the plasma potential increased to a value between −15 V and −25 V. On the other hand, Vpl outside the magnetic trap (> 50 mm from the target) only showed small changes during the entire discharge pulse and was found to be in the range −20 V to +5 V. During the plasma-off phase, the plasma potential oscillated around 3 V. The obtained results indicate a strong spatial inhomogeneity in the plasma potential in the axial direction. This may have a significant impact on the deposition rate. The negative potential barrier in the vicinity of the target during more or less the entire plasma pulse impedes ionized sputtered particles reaching the substrate located outside the magnetic trap, which is discussed in detail in Section 7.5.1. In the follow-up study, the authors extended the previous investigation to include 2D spatial mapping of the plasma potential, which is shown in Fig. 3.8 (Mishra et al., 2011). This work proved that the plasma potential stays negative within the entire plasma pulse up to a distance of about 10 mm from the target surface. With increasing axial distance, Vpl diminishes in magnitude, approaching but not reaching ground potential at distances up to 80 mm, demonstrating the existence of bulk electric field strengths of several kV/m. Rauch et al. (2012) also mapped out the plasma potential in a HiPIMS discharge with a 3” (76 mm) circular Nb target operating at a repetition frequency of 100 Hz with a pulse on-time of 100 µs and a peak current of 170 A (JD,peak = 3.7 A/cm2 ). 2D mapping of the temporal evolution of the plasma potential and derived electric fields in the radial range 0 – 38 mm and in the axial range 1 – 72 mm, was carried out. The obtained results confirmed the discussed findings of Mishra et al. (2010, 2011). The main fraction of the applied discharge voltage on the cathode drops within a distance of up to 40 mm, that is, in the cathode sheath and the magnetic presheath, with approximately 10 – 20% of VD seen as a potential drop over the presheath region (often referred to as the ionization region), which will be of great importance later on when modeling the plasma chemistry in HiPIMS (see Section 5.1.3). The plasma potential inside the plasma bulk (outside the ionization region) was again close to zero. In addition, the effect of magnetic field configuration in terms of magnetic field geometry (balanced versus unbalanced magnetron) and substrate conditions were investigated by Liebig and Bradley (2013). They found that the plasma potential within the magnetic trap close to the magnetron was systematically lower (3 V to 5 V more negative) when the substrate was kept floating in comparison to a grounded substrate. Due to the negative plasma potential (Vpl ≈ −20 V during the main part of the discharge pulse), the bulk plasma strongly repels low-energy electrons entering this region. It was also concluded that the use of a floating substrate results in a limited amount of electrons entering this region due to a reduced (positive) ion flux out of the magnetic trap. On the other hand, an unbalanced magnetic field was found to cause a decrease in the axial electric field. Then the potential barrier between the target and substrate is reduced implying more effective transport of ionized sputtered particles to the substrate. Consequently, optimization of the magnetron magnetic field can lead to increased deposition rates in HiPIMS.

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Figure 3.8 2D plots of the measured plasma potential Vpl measured in volts during (A) the initial current rise (t = 7 µs), and (B) at the time of maximum discharge current (t = 40 µs). The direction of the magnetic field lines is indicated by the arrows of unit length. The target was titanium 150 mm in diameter, the pressure was 0.54 Pa, and the peak current density was 1.3 A/cm2 . From Mishra et al. (2011). ©IOP Publishing. Reproduced with permission. All rights reserved.

The effect of changing the absolute magnetic field strength of the magnetron sputtering discharge has been investigated to some degree (Mishra et al., 2010, Bradley et al., 2015). The evolution of the plasma potential along an axial distance between 5 mm and 100 mm from the surface of a Ti target, 150 mm in diameter, for three different absolute magnetic field strengths in the range from 25 mT to 38 mT measured in the vicinity of the target was studied by Mishra et al. (2010) and is shown in Fig. 3.9. The magnitude of the total magnetic field was approximately 2.5 mT at an axial distance of 100 mm (typical substrate position) for all investigated magnetic field configurations. The measurements were carried out at two different working gas

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Figure 3.9 The plasma potential Vpl versus axial distance z from the cathode surface at two different times during the pulse: (A) during the initial current rise (t ≤ 10 µs) and (B) at peak current (t = 40 µs). Results for three different B-field configurations are shown: profiles A (weakest |B|), B, and C (strongest |B|). All the measurements were carried out at an average discharge power of 750 W, a gas pressure of 1.08 Pa, and above the race track (r = 45 mm) of a planar circular magnetron equipped with a Ti target, 15 cm in diameter. Data from Mishra et al. (2010).

pressures pAr = 0.54 Pa and pAr = 1.08 Pa using peak current densities in the range 1 – 3 A/cm2 depending on B-field strength (highest current for the strongest B-field). Axial profiles of the plasma potential, as measured by the emissive probe for three different magnetic field configurations, demonstrated that a weaker magnetic field resulted in systematically lower absolute plasma potential values in comparison with a stronger magnetic field. At the beginning of the plasma pulse, the plasma potential reached up to −80 V in the vicinity of the target for a total magnetic field strength of 38 mT compared to −40 V measured at the same position for a magnetic field strength of 25 mT. The measured plasma potential was in the range from −30 V to −2 V at an axial distance of 100 mm. Similar results were obtained when the HiPIMS discharge current reached its maximum. In this case the plasma potential varied from −25 V

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(strong B-field) to −10 V (weak B-field) close to the target, while reaching −10 V (strong B-field) and −5 V (weak B-field) 100 mm from the target surface. As previously discussed, the lower potential barrier across the plasma may lead to an enhanced sputtered particle flux to the substrate and thereby increasing the deposition rate. We will return to the subject of deposition rate in Section 7.5.1 and further analyze the impact of the B-field configuration.

3.3.3 Reactive plasmas Reactive HiPIMS is a promising method for depositing compounds, which is described in more detail in Chapter 6. Plasma characterization of this process is essential for optimized deposition conditions. However, up to now, there are only a few reports ˇ devoted to the investigation of ne and Teff in reactive HiPIMS discharges. Cada et al. (2011) analyzed a reactive atmosphere of Ar/O2 when sputtering a 50 mm circular Ti target in compound (poisoned) mode using a Langmuir probe positioned at the substrate location 70 mm above the race track. Two different total pressures 2 Pa and 20 Pa and two different pulse discharge current densities JD,peak = 3.2 A/cm2 and 5.8 A/cm2 were investigated while the Ar/O2 mixture flow rate ratio was kept at 60 sccm/15 sccm. The effective electron temperature during the plasma pulse was found to be in the range 1 – 1.7 eV and was practically independent of the pulse discharge current density. The higher pressure gave rise to a systematic decrease of Teff by approximately 0.5 eV. During the plasma off-time, an exponential-like decrease of Teff to 0.1 eV was measured for all the plasma conditions. The results on the effective electron temperature are thus in line with the previously reported results in nonreactive HiPIMS discharges. The electron density peaked approximately 10 µs after the discharge pulse (100 µs long) independent of the total gas pressure. For the higher pulse discharge current density JD,peak = 5.8 A/cm2 , a peak value of ne = 7 × 1017 m−3 was recorded. ˇ Recently, an extended time-resolved study was carried out by Cada et al. (2017), again in a reactive atmosphere of Ar/O2 when sputtering a 50 mm circular Ti target. The process was investigated for two different pulse discharge currents at a constant time-averaged power of 200 W and different argon-to-oxygen mass flow ratios to explore the various reactive process regimes: metal mode, transition mode, and compound mode. Peak values of ne in the range 2 × 1018 – 5 × 1018 m−3 were recorded 40 mm away from the cathode target for the highest discharge current case (JD,peak ≈ 1.2 – 1.7 A/cm2 , depending on oxygen mass flow rate) with a weak trend of decreasing ne when increasing the O2 flow rate. However, Teff generally increased by about 0.5 eV with increasing oxygen flow rate and with a typical absolute value around 2 eV. The increase in Teff is likely an effect of the reduction of sputtered Ti due to increased compound formation on the target (decreased sputter yield). Having fewer sputtered Ti neutrals forces the discharge to increase the electron energy to increase the ionization rate of the working gas (Ar/O2 ), as both Ar and O2 have a higher ionization potential than Ti, to maintain a high HiPIMS discharge current.

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3.4 Multiple sources and hybrid systems From an industrial point of view, a combination of several magnetron targets utilizing HiPIMS power sources is crucial for mass production of thin films and coatings. In addition, various hybrid approaches consisting of combinations of dc, rf, medium frequency (mf), pulsed dc, inductively coupled plasma (ICP), microwave surfatron, or electron cyclotron wave resonance (ECWR) plasmas with HiPIMS discharges have been developed to enhance the performance of the HiPIMS deposition systems. Also, the MPPMS technology can be incorporated into the hybrid HiPIMS plasma sources. Details on several of these hybrid HiPIMS technologies can be found in Section 2.4. In this section, we provide an overview of the electron plasma characteristics for multiple target arrangements and a few hybrid systems.

3.4.1 Electron properties in multisource systems Stranak et al. (2010, 2011) investigated an unbalanced dual magnetron sputtering system with a closed magnetic field configuration equipped with Ti and Cu targets. The cathodes were connected to a dual sputter system, which was based on a parallel combination of two identical HiPIMS units, which allowed pulsing the targets independently with a user-defined delay between subsequent pulses. During pulsing, each cathode was alternately employed as anode (ground) or cathode. A Langmuir probe was placed between both magnetrons at a distance of 55 mm below the targets. A preionization effect using the remnant plasma from the plasma decay on the Ti cathode preceding the HiPIMS pulse on the Cu cathode was explored by choosing different delay times between subsequent pulses, namely 15 µs and 500 µs. To achieve the desired Ti/Cu film composition, a higher discharge power was delivered to the Ti target. The peak in the plasma density during the HiPIMS pulse on the Ti cathode reached 8 × 1018 m−3 , independently on the delay between pulses for JD,peak ≈ 2 A/cm2 . Peak plasma densities of 4 × 1018 m−3 and 2 × 1018 m−3 were reached during pulseon of the Cu cathode (JD,peak ≈ 0.5 A/cm2 ) for a pulse delay time of 15 µs and 500 µs, respectively. The effective electron temperature was estimated to be 3 eV during pulseon of the Ti plasma and about 1.5 eV during pulse-on of the Cu plasma, independently of the applied pulse delay. Evaluated EEDFs demonstrated that the electron energy distribution somewhat deviated from a Maxwellian distribution. Vozniy et al. (2011) investigated the operation of four identical 2” (50 mm) circular magnetrons equipped with Ti targets in a mirrored configuration at a working gas pressure of pAr = 2 Pa. A Langmuir probe was placed in the center of the sputtering system. The sputtering system worked in two different regimes: (i) all four cathodes were simultaneously ignited by a sequence of two HiPIMS pulses each 20 µs long with a delay time of 20 µs between the pulses, or (ii) two adjacent magnetrons were ignited simultaneously by a 20 µs HiPIMS pulse, during which the opposite pair of magnetrons served as anode and vice versa during subsequent HiPIMS pulses. Such sequences of HiPIMS pulses were repeated at a frequency of 1 kHz for both regimes. The average power was always kept constant at 200 W. In the case of simultaneous

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pulsing of the four magnetrons, the electron density in the center of the sputtering system peaked at 1.4 × 1017 m−3 approximately 24 µs after the first HiPIMS pulse and was essentially constant during the following 20 µs delay. During the subsequent HiPIMS pulse, the electron density further increased up to about 2.5 × 1017 m−3 . The second mode of operation was characterized by a gradual increase in the electron density up to 1.3 × 1017 m−3 at 26 µs from pulse initiation, which was followed by a decrease in the electron density up to the beginning of the second HiPIMS pulse. During the second pulse, the electron density increased faster in comparison with the first regime of operation reaching a maximum at 3.9×1017 m−3 . During the pulse off-time, the electron density decreased in both regimes to about 6 × 1016 m−3 . A probable explanation of such a behavior of ne is that the mirrored configuration of the magnetrons’ magnetic field causes accumulation of electrons in the middle of the discharge volume. Further increase in the electron density during the subsequent HiPIMS pulse is related to the presence of remnant charge, which cannot fully recombine during short delay times between the subsequent HiPIMS pulses.

3.4.2 Electron properties in hybrid systems We will now turn to the hybrid HiPIMS systems. Drache et al. (2013) explored a combination of a simultaneously driven (superimposed) mf pulsed dc discharge and a HiPIMS discharge on two magnetron targets with a closed magnetic field configuration. The mf pulsed dc power supply was connected in parallel to the dual HiPIMS power supply and separated by a transformer (see also Section 2.4.2). The magnetron targets were mounted parallel to each other and equipped with Ti and Cu targets, both with a diameter of 50 mm. A Langmuir probe was placed between the magnetron targets at a distance of 50 mm from the target surface (typical substrate position for this system). The repetition frequency of the HiPIMS pulses was 100 Hz with a pulse on-time of 100 µs. The delay between subsequent HiPIMS pulses on the two cathodes was 15 µs. The mf pulsed dc power supply was operated at a repetition frequency of 94 kHz, that is, about three orders of magnitude higher frequency compared to the HiPIMS pulses. Typical voltage waveforms measured on the cathodes with Ti target and with Cu target, together with a waveform of the discharge current measured on the Ti cathode, are shown in Figs. 3.10A and B, respectively. The authors found that such a configuration resulted in maintaining a weak plasma in between HiPIMS pulses, which led to a pre-ionization effect supporting faster increase in the electron density during the HiPIMS pulse and simultaneously an increase of the electron density by 30% at the end of the HiPIMS pulse. Another benefit of this configuration was the possibility of reducing the working gas pressure in the vacuum chamber down to pAr ≈ 0.1 Pa, which is more than one order of magnitude lower pressure compared to conventional dual HiPIMS, which required pAr ≈ 3 Pa at otherwise similar discharge conditions to maintain a stable discharge (Stranak et al., 2010). The authors also found that the effective electron temperature reached a peak value around 8 – 9 eV at 25 µs after HiPIMS pulse ignition, which rapidly decreased to a steady level of 2 – 3 eV. Attempts have been made to operate HiPIMS discharges below typical minimum process gas pressures, approximately 0.1 Pa, due to the interest in enhancing the film

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Figure 3.10 The temporal evolution of the (A) cathode voltage on the Ti and Cu cathodes and (B) discharge current waveform on the Ti cathode as measured in the hybrid dual HiPIMS discharge. Reprinted from Drache et al. (2013), with permission from Elsevier.

properties by reducing the number of collisions between the sputtered particles and the working gas (pronounced high-energy tail of neutral and ionized particles or higherionization fractions of the working gas). Stranak et al. (2012b) developed a solution combining an electron cyclotron wave resonance (ECWR) discharge and a HiPIMS discharge. The ECWR effect is based on the interaction of an electromagnetic wave (in this case, at a frequency of 13.56 MHz) with plasma electrons in the presence of a weak homogeneous magnetic field (typically of the order of mT). Since the magnetic field causes a slight plasma anisotropy, the polarized electromagnetic wave can propagate through the plasma. The resonant plasma excitation occurs when odd multiples (tunable by the strength of the magnetic field) of the electron cyclotron wave fit into the plasma dimensions in the direction of wave propagation (Stranak et al., 2012a). In such a configuration a discharge could be maintained at working gas pressures as low

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as 0.03 Pa. Stranak et al. (2012a) operated such a HiPIMS discharge using 100 µs pulse on-time at a repetition frequency of 100 Hz and at a peak discharge current density of 3.5 A/cm2 . The ECWR discharge was running with an absorbed rf power of 350 W. The magnetron assembly was equipped with a Ti target. A Langmuir probe was placed on the same axis as the magnetron and an rf electrode. Axial movement of the probe allowed measuring the plasma parameters along the distance 30 – 180 mm from the target surface. Apart from the plasma buildup during the first 20 µs of the HiPIMS pulse, the electron density at 45 mm was found to be constant at 2 × 1018 m−3 during the whole HiPIMS plasma pulse, which was followed by a gradual decrease to 3 × 1016 m−3 during 100 µs after the end of the pulse. During the HiPIMS pulse-off, the electron density was constant at 1017 m−3 for a pressure of 0.05 Pa. The effective electron temperature between HiPIMS pulses was roughly 7 eV, which decreased to a steady value of about 4 eV within the first 20 µs of the HiPIMS pulse. The effective electron temperature also exhibited a linear decrease with increasing distance from the target, and Teff was about 1.5 eV at 100 mm from the target. In addition, hybrid HiPIMS sources have been developed for the purpose of reactive sputtering (see also Section 3.3.3 for the basic electron plasma characteristics in reactive HiPIMS mode). A combination of a microwave surfatron discharge as a source for activated reactive species (oxygen, nitrogen, etc.), and a HiPIMS discharge has shown promising results for high-rate deposition of dielectric stoichiometric thin films (Stranak et al., 2017). The plasma parameters were measured for several process conditions. The magnetron was equipped with a Ti target, and the Ar/O2 mass flow rates were adjusted for operation in the regime between metallic and transition mode. The measured electron density reached 1018 m−3 at the end of the HiPIMS pulse for a discharge current of 40 A corresponding to JD,peak = 2 A/cm2 . The surfatron discharge was running continuously, and the electron density during the HiPIMS pulse-off was roughly 1017 m−3 . As such, those results were not different from the previously discussed hybrid systems. However, it was found that the effective electron temperature was systematically increased by about 15% when the surfatron discharge was added, which increases the dissociation, excitation, and ionization rates leading to greater amounts of active species, such as oxygen atoms, atomic oxygen ions and metastable oxygen atoms and molecules, which are more reactive on the Ti surface compared to the neutral reactive O2 gas in the ground state (Kutasi et al., 2011). Teff attained a value of about 6 eV, 20 µs from the start of the HiPIMS pulse, which was followed by a gradual decrease during the entire pulse reaching a value of 3 eV. During the plasma off-time, Teff was constant at 3.5 eV when only running the surfatron.

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ˇ Stranak, V., Herrendorf, A.-P., Drache, S., Cada, M., Hubiˇcka, Z., Tichý, M., Hippler, R., 2012b. Highly ionized physical vapor deposition plasma source working at very low pressure. Applied Physics Letters 100 (14), 141604. ˇ Stranak, V., Kratochvi, J., Olejnicek, J., Ksirova, P., Sezemsky, P., Cada, M., Hubiˇcka, Z., 2017. Enhanced oxidation of TiO2 films prepared by high power impulse magnetron sputtering running in metallic mode. Journal of Applied Physics 121 (17), 171914. Tichý, M., Kudrna, P., Behnke, J., Csambal, C., Klagge, S., 1997. Langmuir probe diagnostics for medium pressure and magnetised low-temperature plasma. Journal de Physique IV 7 (C4), C4-397 – C4-411. Vetushka, A., Ehiasarian, A.P., 2008. Plasma dynamic in chromium and titanium HIPIMS discharges. Journal of Physics D: Applied Physics 41 (1), 015204. Vozniy, O.V., Duday, D., Lejars, A., Wirtz, T., 2011. Ion density increase in high power twincathode magnetron system. Vacuum 86 (1), 78–81.

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a , Nikolay Britunb , Ante Hecimovicc , Jon Tomas Gudmundssond,e , ˇ Martin Cada Daniel Lundinf a Institute of Physics v. v. i., Academy of Sciences of the Czech Republic, Prague, Czech Republic, b Chimie des Interactions Plasma-Surface (ChIPS), CIRMAP, Université de Mons, Mons, Belgium, c Max-Planck-Institut for Plasma Physics, Garching, Germany, d Department of Space and Plasma Physics, School of Electrical Engineering and Computer Science, KTH Royal Institute of Technology, Stockholm, Sweden, e Science Institute, University of Iceland, Reykjavik, Iceland, f Laboratoire de Physique des Gaz et Plasmas LPGP, UMR 8578 CNRS, Université Paris–Sud, Université Paris–Saclay, Orsay Cedex, France

The film forming material consists of neutral atoms sputtered off the target and its ions. In the case of reactive sputtering atoms, molecules and ions of the reactive gas also contribute to the film. The energy and the composition of the film forming species strongly influences the properties of the films being deposited. One of the key differences between dcMS and HiPIMS is the ionization fraction of the sputtered material. We discuss the methods applied to determine the ionization fraction of the sputtered material and the different ways it is quantified, and then survey the ionized flux fraction determined for the HiPIMS discharge. Furthermore, the method of laser-induced fluorescence is utilized to explore the spatio-temporal behavior of the ions and neutrals, and the observations are discussed. We also discuss and compare the ion energy distribution from dcMS and HiPIMS discharges.

4.1 The plasma ions It is well known that thin film deposition in plasma-based synthesis highly depends on the interaction between the deposited material and the plasma ions, where low-energy ion-bombardment is a well-established tool to synthesize dense and homogeneous coatings with controlled texture and physical properties. In this context, the key parameters are the ion number density and the ion energy (velocity), which together constitute the ion flux. However, it is not always straightforward to generate a significant fraction of ions at sufficient energy required in thin film growth. Ideally, we would like to have massive amounts of monoenergetic ions while at the same time be able to select what species in the deposition flux are ionized. Furthermore, the temporal behavior of the ion density and the composition in the vicinity of the magnetron High Power Impulse Magnetron Sputtering. https://doi.org/10.1016/B978-0-12-812454-3.00009-7 Copyright © 2020 Elsevier Inc. All rights reserved.

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target helps us to interpret cathode voltage and discharge current waveforms measured in HiPIMS discharges and to explain trends and changes in the sputter yield and secondary electron emission. In this section, we focus on the spatial and temporal ion density and ion energy distributions of the ionized working gas and the ions of the target material due to their importance for understanding and optimizing sputter processes. Such investigations also require insight into characterization techniques, and we present some of the most commonly used methods.

4.1.1 Techniques for characterizing plasma ions Two of the most important parameters describing the ion dynamics are the ion energy distribution function (IEDF) and the ion flux to the substrate, since they provide information on the energy deposited into the growing thin film. In Section 3.1.1, we saw that electrostatic probes are able to measure the ion current, which can be used to estimate the ion flux. However, the ion current signals are typically two orders of magnitude smaller than the electron component when the Langmuir probe is biased at the plasma potential, and the voltage range where a retarding potential is applied to discriminate ions with different energies is overlapped with a contribution from accelerated plasma electrons. It is therefore very difficult to obtain reliable results on the ion component from the probe current. To analyze the ions of the plasma, we instead need an instrument that is capable of repelling the plasma electrons and sample only the plasma ions. The IEDF is commonly measured using an energy-resolving mass spectrometer or a retarding field energy analyzer (RFEA), which are both briefly described in Sections 4.1.1.1 and 4.1.1.2. In addition, the ionized flux fraction of depositing particles is another important parameter in HiPIMS, since the large amount of ionized sputtered material is what fundamentally distinguishes this technique from conventional magnetron sputtering. One of the most reliable techniques of measuring the ionized flux fraction is the gridded (or grid-less) quartz crystal microbalance (QCM), which is described in Section 4.1.1.3.

4.1.1.1

Energy-resolved mass spectrometry

Particle energy/mass analyzers are suitable tools for measuring ion velocity distributions and for obtaining mass spectra of the heavy species in the plasma volume at a given energy. In HiPIMS, these mass spectrometers are mainly used to investigate ions incident on the substrate by replacing the substrate with an analyzer. However, due to the larger size of these devices, the disturbance of the plasma will be more significant compared to electrostatic probes. Using energy-resolved mass spectrometry, atoms, molecules, or ions are extracted from the plasma through a sampling orifice. A small orifice is needed to keep the inner space of the analyzer free of deposited material and at the same time ensure limited plasma penetration. The pressure in the analyzer must be below 10−2 Pa to avoid any collisions between the particles in order to (i) preserve the energy distribution of particles from the plasma and (ii) not to disturb the

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ion trajectories that determine the reliability and reproducibility of the measurement. For this reason, the number of orifices for plasmas at high pressures (atmospheric or higher) can be two or more, with differential pumping after each orifice (Benedikt et al., 2012). The methods of sampling atoms and ions differ significantly. Ionized particles are attracted by the space charge sheath existing in front of the orifice resulting in a measurement of the ion flux  = nv (not the density!). The ion flux is higher for lighter ions due to a higher velocity at the same density and energy, which must be taken into account when quantitatively comparing measurements of different ionic species. After the orifice, ions are focused and guided through the analyzer by ion optics consisting of electrostatic lenses. It is important to note that the focal length of the electrostatic lenses can change with ion energy leading to chromatic aberration (failure to focus on the same convergence point), which adversely affects quantitative measurements (Hamers et al., 1998). Furthermore, a consequence of using the ion extraction optics is that only ions in line-of-sight with the sampling orifice are detected. We should also take into account that the acceptance angle of the analyzer depends on the energy of the ions (Hamers et al., 1998). The acceptance angle has been reported to be between 5 and 20 degrees for ions with energy below 1 eV and about 3 degrees for ions with energy above 1 eV (see e.g. Lundin et al. (2008)). In case of neutral species, the neutral density is measured. Upon entering the analyzer, the atoms pass through an ionization chamber, where the atoms are ionized. The source of ionization is most commonly electrons emitted from a heated filament (often made of tungsten or thoriated iridium) and accelerated by a potential difference between the filament and the walls of the ionization chamber. There are also other ionization methods, although less used: dissociative electron attachment chemical ionization, thermal ionization, or photo ionization. Beyond the ionization chamber, only ionized particles are guided through the analyzer toward an energy analyzer. The two most commonly used designs for selection of ions based on their energy are sector-field electrostatic analyzers and Bessel-box energy analyzers. The sector-field electrostatic analyzer is based on an electrostatic field between two electrodes, which can have parallel, cylindrical, toroidal, or spherical configuration. The centripetal force generated by the electric field balances the centrifugal force of the traversing ion, and therefore only ions with a selected energy will pass the energy analyzer, whereas ions with higher or lower kinetic energy will be lost to the electrodes. The advantage of the sector field electrostatic analyzer is 100% transmission of ions with the selected energy and energy resolution better than 0.1 eV. The disadvantage is that the sector-field analyzer requires much more space due to its design. The Bessel-box type energy analyzer comprises of a cylindrical chamber closed with two endcaps. Both endcaps have an orifice in the center. In the middle of the cylindrical chamber, there is a round obstacle, preventing high-energy ions to pass through the cylinder. The trajectory of ions with selected energy is guided by the electric field created by potentials applied on the cylinder and its endcaps. The advantages of the Bessel-box type energy analyzer are the simple design and energy resolutions below 0.5 eV. The disadvantage is the low transmission, which is typically about 10%

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(Downie et al., 1995). Only ions with the selected mass to charge ratio Mi /z will pass the mass analyzer, where z is the number of elementary charges. There are several types of mass analyzers (linear quadrupole, time of flight, electrical or magnetic sector field), but most commonly used is the quadrupole mass spectrometer (QMS), sometimes referred to as the quadrupole mass analyzer. The QMS comprises of four parallel conducting rods. The rods are biased by dc and rf voltages with the opposite rods being at the same potential. The ions travel down the quadrupole between the rods. Determined by the ratio of applied voltages, only ions of a certain mass-to-charge ratio Mi /z will reach the detector, whereas the remaining ions have unstable trajectories and will collide with the rods (Dawson and Whetten, 1970, Dawson, 1976). The light masses (small Mi /z) are resonantly accelerated sideways by the rf fields, whereas the heavy masses (large Mi /z) are deflected sideways by the dc field, allowing only selected masses to pass the mass analyzer. The advantages of the QMS are its compact design and light weight, high scan speed, and simple operation. The disadvantage is the difficulty to perform quantitative measurements of light ions. At the end of the ion’s path through the analyzer, the ions interact with an ion detector to generate current that can be measured and quantified. There are two commonly used detectors, a Faraday cup or a secondary electron multiplier. The Faraday cup is a cup-like detector collecting ions and recapturing the secondary electrons generated by ion impact. The advantages are a simple design and an ion sensitivity that does not deteriorate over time. The disadvantages are slow response time and low sensitivity. The secondary electron multiplier is built on the principle of amplification of the secondary electrons generated by ions reaching the detector. The secondary electrons are multiplied by a set of discrete dynodes or by one continuous dynode to reach a gain of typically 105 . The electron current is detected by an electrode and then converted into a voltage signal that is proportional to the number of impinging ions. The advantages of a secondary electron multiplier are high sensitivity and fast response time. The disadvantage is deterioration over time due to contamination of the dynodes. One of the main issues with the energy/mass analyzer is that several components change performance over time (such as the ionizer efficiency, the secondary electron multiplier sensitivity, etc.). Thus, absolute calibration should be performed at regular intervals. Quantitative determination of the number of ions of a specific mass is therefore a rather challenging task when using energy/mass analyzers, since only the number of counts on a multiplier detector with unknown transmission characteristics is recorded. Furthermore, if neutrals are to be analyzed, then they must first be ionized inside the ionization cage, where the information on the initial number of neutrals entering the analyzer is lost. It is therefore practically impossible to reliably determine the ratio between the number of ions and neutrals of the same mass (Ellmer et al., 2003). Note that the energy scale measured by a mass spectrometer is represented in volts. To change the energy scale to eV, it is necessary to multiply it by the charge of the particle, for example, in the case of doubly charged ions the energy scale should be multiplied by two to obtain the energy scale in eV.

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Figure 4.1 Scheme of a typical retarding field energy analyzer (RFEA) for measuring the ion energy distribution function. The first grid is connected to the housing. The second grid is biased negatively with respect to the analyzer housing and repels the electrons from entering the analyzer. The third grid selects the ions according to their kinetic energy. The third grid potential is swept from the dc potential of the first grid to a potential of several tens of volts above the plasma potential to cover the entire kinetic energy range of the plasma ions. The collecting grid current is recorded as a function of the bias potential on the third grid.

4.1.1.2

Retarding field energy analyzers

The retarding field energy analyzer (RFEA) is a small, inexpensive, and simple device to sample the IEDF. The basic design is based on a parallel plate geometry of two electrodes, one acting as collector and the other as a retarding electrode having a small hole so that the charged particle beam can enter into the analyzer (Simpson, 1961). An applied potential V0 between the electrodes determines if a charged particle entering the analyzer with a kinetic energy Ek will be collected (Ek > eV0 ) or repelled (Ek < eV0 ). The charged particles that reach the collector electrode are subsequently detected as an electric current. This simple configuration of the RFEA is suitable only for measurements of positively or negatively charged particles existing separately in the investigated system, such as charged particle beams. Unfortunately, this prerequisite is not valid for low-temperature plasmas where electrons and ions of different masses and charge are mixed. To resolve this issue, the RFEA must be able to repel all the negative charges and collect only positive charges with selected energy. This requires the addition of at least one more electrode, which can be biased independently. A typical design of such an RFEA can be seen in Fig. 4.1. The RFEA is comprised of three fine grids and one collector in a metallic housing, which can serve as a dummy substrate. In this case, the electric field between the housing and the plasma reflects

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a majority of the plasma electrons, and only those from the high-energy tail of the electron energy distribution function (EEDF) can enter the RFEA. The first top grid is connected to the housing and can thereby simulate a situation where the substrate is grounded or at floating potential or biased to an arbitrary negative potential. The second grid is biased negatively with respect to the analyzer housing and serves as electron suppressor to repel all the plasma electrons entering the analyzer. The third grid serves as a selector of ions according to their kinetic energy. The third grid potential is swept from the dc potential of the first grid (all the ions are going through the grid, and no discrimination occurs) to a potential of several tens of volts above the plasma potential to cover the entire kinetic energy range of plasma ions. Only ions with kinetic energy higher than the retarding potential applied on the third grid can be detected on the collector. The collector electrode is typically biased to about −10 V with respect to the first grid to attract all the ions passing the third grid. The accelerating voltage applied on the collector must be low enough to suppress ion-induced secondary electron emission from the collector material. If the secondary electron emission is not negligible, then it will distort the collected current. In such a case, a fourth grid should be inserted in front of the collector having a slightly negative bias with respect to the collector electrode. The collector grid current is recorded as a function of the bias potential on the third grid. The derivative of the collector current with respect to the bias potential gives the ion energy distribution function. It is important to note that the size of the grid holes plays a crucial role for proper operation of the RFEA. The collector electrode has to sample only selected plasma ions, and the plasma must not penetrate into the RFEA, which requires that the hole diameter dh must fulfill the condition dh ≤ 2λD , where λD is the Debye length (Böhm and Perrin, 1993). On the other hand, the grid transmission should be as high as possible or at least 50% to measure a reasonably strong signal on the collector and to minimize the generation of secondary electrons on the electron suppressor grid. Furthermore, attention must be paid to (i) the grid spacing and (ii) the total thickness of the analyzer. The spacing between the grids has to be smaller than the thickness of the space charge sheath, which is formed around the biased grids. This means that ion collection should not be limited by the space charge sheath but only by the ion temperature (velocity). The second point requires that ions measured on the collector electrode should not have undergone any collisions with neutrals inside the RFEA, which would have an impact on the measured IVDF. To fulfill this requirement, the total thickness of the RFEA must be smaller than the mean free path for ion-neutral interaction. This condition limits the use of an RFEA to working gas pressures below roughly 10 Pa for a typical analyzer thickness of 3 mm (Gahan et al., 2008, Hayden et al., 2009). For operation above this pressure limit, then the analyzer must be differentially pumped to keep an acceptable internal pressure inside the RFEA. For further reading on the aspects of modern RFEA construction and measurements, see for example, the discussion by Gahan et al. (2008).

4.1.1.3

Modified quartz crystal microbalance (ion meter)

One of the most robust techniques to measure the ionized flux fraction in situ is the use of a modified quartz crystal microbalance (QCM) with two grids added in front

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of the crystal, often referred to as a gridded QCM (g-QCM) (Fox and Krupanidhi, 1994, Green et al., 1997, Rossnagel and Hopwood, 1993, Kubart et al., 2014). This device is also sometimes referred to as an ion meter. The ion meter is operated in two different configurations: (i) For measuring neutral particle flux only. Then the bottom grid is biased positively (typically +60 V) to repel all the ions from being deposited on the sensor, whereas the upper grid is biased negatively to about −30 V to repel plasma electrons from reaching the QCM. This gives the mass deposition rate (proportional to the flux) of neutral particles Rn only. (ii) For measuring both ion and neutral flux, the grids are connected to ground resulting in no discrimination of particles reaching the sensor, and the total mass deposition rate Rt is determined. This allows the determination of the ionized flux fraction of the depositing particles Fflux according to Lundin et al. (2015) Fflux =

Rt − Rn . Rt

(4.1)

An advantage of using a QCM is that only depositing particles condensing on the electrode contribute to the measured mass. In other words, we do not have to worry about atoms or ions from the inert working gas. We should also note that the flux of depositing particles on the electrode of the ion meter is recorded for a period much longer than the typical HiPIMS plasma pulse. This implies that the ion meter is not suitable for time-resolved measurements of the ionized flux fraction of depositing particles. When the plasma pulse is off, ions are recombining quickly. Thereby the ionized flux fraction of depositing particles decreases during the pulse off-time. It is therefore assumed that the measured ionized flux fraction over many plasma pulses is somewhat lower in comparison with the instantaneous ionized flux fraction during the pulse. The grids in front of the QCM significantly decrease the amount of collected particles arriving on the quartz crystal. Thus, in situations where the deposition rate is significantly reduced, for instance, during reactive sputtering in the compound mode, the signal can be rather weak. To improve the signal level, a gridless QCM (m-QCM) was developed by Kubart et al. (2014). The quartz crystal electrode is then either directly biased at +60 V or grounded to measure only neutrals or all depositing particles, respectively. Instead of an electron repelling grid, a homogeneous magnetic field parallel with the quartz crystal is generated by two SmCo magnets placed at the front of the QCM, thus preventing electrons from reaching the crystal top electrode. The magnets are conductively connected with the grounded anode, which further assists in transporting the plasma electrons to the anode without affecting the QCM measurements. It is shown by Kubart et al. (2014) that there is a good agreement between the g-QCM and the m-QCM by comparing the recorded ionized flux fractions (see Section 4.1.5), which also implies that the ionized flux is not significantly affected by ambipolar diffusion due to electron transport to the magnet poles when using the m-QCM.

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4.1.1.4

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Laser-based methods for ion detection

Our study of ions in HiPIMS will start by an attempt to visualize and comment the ion dynamics in the vicinity of the magnetron target. It also serves as a good introduction to the discussion on the physics of HiPIMS and, in particular, the mechanisms responsible for ion generation and acceleration, which we will deal with in Chapter 7. When visualizing the plasma species spatially and temporally, it is important to keep in mind that: (i) both ground and excited ion states contribute to the total ion density, (ii) the contribution of the ground state ions dominates outside the ionization region (magnetic trap) as electron excitation drops, and (iii) in a discharge with highly nonuniform electric and magnetic field distributions, such as in HiPIMS discharges, we may expect non-uniform distributions of the ion density. To visualize ground state (i.e. nonemitting) species in any discharge, they have to be excited by an external source in the area of interest, which should in turn result in a minimal discharge perturbation. One of the most reliable techniques for measuring the spatial distribution of the ground-state particles in gaseous discharges is laser-induced fluorescence (LIF) imaging (Lochte-Holtgreven, 1968, Kirkbright and Sargent, 1974, Britun et al., 2015b). This technique combines a resonance excitation of the atomic or molecular states in the plasma volume by external laser radiation with a subsequent detection of spontaneous emission produced by the excited states (Stern and Johnson, 1975). Usually short-pulsed (∼ 10 ns) dye laser systems are used for this purpose to clearly observe the fluorescence decay after the laser pulse. When using LIF imaging, the plasma may be considered mostly unperturbed, as only a relatively small part of the discharge species experience laser excitation from the ground state. Moreover, since the laser energy itself is small (within the so-called linear mode of LIF operation (Amorim et al., 2000)), the percentage of the excited species is often negligible (Britun et al., 2014).

4.1.2 Spatial and temporal distribution of ions in the bulk plasma Let us consider an example of ion propagation above the magnetron target in a shortpulse (20 µs) HiPIMS discharge using a Ti target (10 cm in diameter) and argon as the working gas. In our example the discharge is operated at a working gas pressure of either pAr = 0.7 or 2.7 Pa at a pulse repetition rate of 1 kHz and about 0.26 J of energy delivered per pulse (corresponding to a peak power density of ∼ 0.4 kW/cm2 and peak discharge current density of ∼ 1.2 A/cm2 ). The magnetron assembly was balanced with a |B|-field value of about 0.1 T near the target center and with a nullpoint located at ∼ 8 cm away from the target surface. The experimental setup with the laser-based imaging geometry used is shown schematically in Fig. 4.2. A rectangular 7 × 10 cm2 region of interest (ROI) with a depth of about 2 mm (corresponding to the laser beam width) located perpendicularly to the target surface was investigated. The typical discharge current–voltage waveforms measured are shown in Fig. 4.3. As we can see, the discharge current does not saturate during the discharge current evolution due to the short plasma pulse duration used in the present case (see Section 7.2.2 for

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Figure 4.2 Schematic layout of a magnetron sputter source and a flat laser beam located perpendicularly to the target for visualization of ground state particles in HiPIMS discharges.

Figure 4.3 The discharge current and voltage waveforms registered in an argon HiPIMS discharge with Ti target investigated by LIF. Pulse duration is 20 µs, and the working gas pressure pAr = 2.7 Pa. The discharge voltage is shown inverted. The peak current density is JD,peak ≈ 1.2 A/cm2 .

details on the discharge current evolution). The excitation parameters used for LIF analysis for the three main species are summarized in Table 4.1, where here we focus on Ti+ ions. The neutral species are discussed in Section 4.2. Other experimental parameters can be found in the literature (Britun et al., 2015b). In the described geometry, each LIF image corresponding to a 2D distribution of the Ti+ ion density has been averaged over 20 ns intervals and accumulated using about 100 discharge pulses. The time delay is counted from the beginning of the discharge pulse. The temporal evolution of the Ti+ ion density above the target obtained by LIF imaging is presented in Fig. 4.4. Note that a logarithmic color scheme is chosen here. From the obtained data it is clear that the appearance of ions in the HiPIMS discharge is strongly correlated with the discharge current. From Fig. 4.4A we find that the ion density increases during the plasma on time, peaking at about 5 µs after the plasma pulse is off. Several more features of the ion behavior can also be noticed: • Ions do not disappear completely between the discharge pulses (980 µs off-time), especially at higher pressure. • At the beginning of the discharge pulse the remaining ion density from the previous pulse is instantaneously depleted near the target as the positive ions are attracted to the negatively charged cathode.

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Table 4.1 Spectral transitions for Ti atoms, Ti+ ions, and metastable argon atoms Arm probed by LIF. Spectral parameter Lower state Energy Intermediate state Energy Higher state Energy Lower state nature Excitation (laser) wavelength, λexc Fluorescence wavelength, λfluor Optical filter (central wavelength/width)

Ti 3d2 4s2 a3 F2 0.000 eV 3d3 (4 F)4s b3 F2 1.430 eV 3d2 (3 P)4s4p(3 Po )v3 Do1 3.886 eV Ground 320.58 nm

Ti+ 3d2 (3 F)4s a4 F3/2 0.000 eV 3d3 a2 P1/2 1.221 eV 3d2 (3 F)4p z2 Do3/2 3.937 eV Ground 314.80 nm

Arm 3p5 4s (1s5 ) 11.548 eV 3p5 4s (1s4 ) 11.624 eV 3p5 4p(2p2 ) 13.328 eV Metastable 696.54 nm

508.70 nm

456.38 nm

727.29 nm

510/10 nm

460/10 nm

730/10 nm

The data is based on Payling and Larkins (2000) and the NIST Atomic Spectra Database Lines Form.

Figure 4.4 The temporal evolution of the relative ground state density of Ti+ ions above the magnetron target in a HiPIMS discharge at two different argon working gas pressures (A) 0.7 Pa and (B) 2.7 Pa. Pulse duration is 20 µs. Time delay from the pulse initiation (in µs) is indicated next to each subfigure. All images are normalized to the same value. The investigated region is located immediately above the target surface and extends 7 cm in the axial direction. Logarithmic color scheme is used.

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• As the ionization of sputtered species evolves, the Ti+ ions are mainly concentrated in front of the target race track (the area corresponding to the magnetic trap). • At the lower Ar working gas pressure the Ti+ ions appear earlier in the race track vicinity. The Ti+ ion density is evolving quickly after the discharge pulse. • Considerable redistribution of Ti+ ions takes place during the pulse off-time leading to a more uniform ion distribution in the region of interest The fact that the ions originate from the race track vicinity corroborates with the magnetic trap acting as a reservoir for captured electrons (see Section 3.2 and in particular Fig. 3.5). Here, the electrons bounce back and forth along the magnetic field lines in cycloidal-like trajectories until a collision occurs with a heavy particle, leading to extensive electron impact ionization in this region, as previously discussed in Section 1.1.5. After ionization of the sputtered Ti atoms in the magnetic trap (ionization region), the Ti+ ions propagate away from the target surface, forming a density maximum above the race track at the end of the discharge pulse. During the afterglow the ions continue to propagate away from the cathode target. The estimated ion propagation velocity at pAr = 2.7 Pa is about 103 m/s (Britun et al., 2015b, 2008a,b). For the 2.7 Pa case, the continuous redistribution of the ion density is particularly striking. Two zones are apparent: During the pulse and just after the pulse, the ion density is strong above the target race track. Later, after the pulse is off, an elongated region above the target center can be observed, where the ions are mainly concentrated as the discharge evolves into the afterglow (t ≥ 60 µs). The appearance of a central zone seems to depend on the working gas pressure, and its nature is not quite clear. One possible reason for its formation is likely the redistribution of residual electrons (which ionize the sputtered neutrals) during the plasma pulse afterglow, which was discussed earlier in Section 3.2 (see Fig. 3.5) when investigating the spatio-temporal evolution of the electron density. Both race track and central zones, where Ti+ ions are mainly concentrated, get considerably blurred during the off-time interval due to ion diffusion, as can be observed in Fig. 4.4B after t = 80 µs. This results in a nearly uniform Ti+ ion density at the end of the off-time (t > 700 µs). At the lower working gas pressure (0.7 Pa), the ion density distribution is rather uniform already at ∼ 300 µs, presumably due to a faster diffusion. Another striking feature is that the ions are always present in the discharge volume, until the very end of the pulse off time (i.e. up to 1 ms in the present case). These remaining ions linger well into the plasma afterglow and have also been detected by mass spectrometry, as discussed in Section 4.1.3.2, and act as seed ions (pre-ionization) for the next plasma pulse. To study the absolute density of the atomic states in the plasma volume, the 2D distributions presented should be calibrated by another technique capable of providing the atomic number density of states. Atomic absorption spectroscopy (AAS) can be used for this purpose (Britun et al., 2015c). In spite of the fact that AAS only produces line-of-sight averaged results, it represents a reliable way for calibration of the number density, as long as the density distribution is spatially uniform, which is typically the case at the end of the pulse off-time as can be seen in Fig. 4.4 (see also the neutral evolution in Fig. 4.13). In the considered example the AAS measurements were performed ∼ 5 cm above the magnetron target using a standard hollow cathode lamp as

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Figure 4.5 The temporal evolution of the ground-state Ti+ ion number density at 5 cm above the magnetron target in a HiPIMS discharge obtained by atomic absorption spectroscopy at pAr = 2.7 Pa. Pulse duration is 20 µs. The discharge current and voltage waveforms are shown in Fig. 4.3.

reference source and the resonant Ti, Ti+ , and Ar transitions available from the literature (Payling and Larkins, 2000). The obtained evolution of the ion number density for four Ti+ ion ground-state sublevels, measured at 2.7 Pa is shown in Fig. 4.5. The data also reveal the main features already seen in the 2D density imaging data shown in Fig. 4.4, such as the Ti+ ion density drop at the beginning of the off time at 5 cm above the target (compare Fig. 4.4B at t = 0 and 25 µs with Fig. 4.5) and the Ti+ ion density decay after t ∼ 300 µs. Based on the AAS analysis, the Ti+ ion density is found in the interval 0.7 – 2 × 1017 m−3 for the 2.7 Pa case 5 cm away from the target surface. For the Ti+ ions recorded at 2.7 Pa in Fig. 4.4B the 100 mark corresponds to 1018 m−3 for the number density of the 0.000 eV state of Ti+ (the lowest among 4 sublevels). For the total Ti+ ion density we have to multiply by roughly 4. The highest ion density measured under these conditions (detected close to the target race track at t = 30 µs) is ∼ 1018 m−3 . For the low-pressure case (0.7 Pa), the peak Ti+ ion density is comparable to that obtained in the high-pressure case, whereas the background density is only ∼ 1016 m−3 (green color (gray in print version) in Fig. 4.4A). It is important to note that the AAS method may lead to rather high measurement uncertainty at the end of the plasma pulse, making the determination of the ion number density rather complicated (as indicated by the dotted gray line in Fig. 4.5). In the HiPIMS case, this is a result of very high Ti+ ion emission at the end of the plasma pulse (at the same spectral lines that are used in the AAS method) or/and the presence of plasma instabilities, also known as ionization zones or spokes, which are inherent in HiPIMS plasma discharges and widely studied in the literature (Kozyrev et al., 2011, Andersson et al., 2013, Hecimovic et al., 2014, 2017a) (for details, see Section 7.4). The spoke appearance may significantly affect the emission intensity of the atomic spectral lines of interest and thus dramatically increase the uncertainty of the AAS data (Britun et al., 2015c). However, in the present case, this contribution is supposed to be minor taking into account our comparably low discharge current values (Hecimovic et al., 2017a). The AAS data is expected to be affected to a larger extent by high plasma

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emission, which increases nearly exponentially at the end of the HiPIMS plasma pulse for short pulses, as shown by Britun et al. (2015a). It is also interesting to estimate the ion flux toward a virtual substrate located in a plane parallel to the target surface some distance away from the target, as this quantity is important during film growth. In the present case, assuming the net velocity of the sputtered particles to be ∼ 103 m/s and the typical Ti+ ion density measured at the beginning of the off-time to be about 1018 m−3 near the race track (close to the magnetron target), we obtain an ion flux of the order of ∼ 1021 ions m−2 s−1 . Further away from the target, however, where the sputtered particles have undergone considerable scattering in collisions with the argon working gas and thereby lost their directionality (uniform velocity distribution) (Lundin et al., 2013); this value should be defined by the well-known nvave /4 expression, giving a flux estimation of about 1017 m−3 × vave /4, that is, ∼ 1019 ions m−2 s−1 (at about 7 cm above the target surface, that is, at the top of the imaging area shown in Fig. 4.2). As we can see, the total ion flux may vary by two orders of magnitude within the area of interest depending on the distance from the target, which may significantly affect ion bombardment and substrate heating.

4.1.3 Ion energy distribution in the vicinity of the substrate We will now look closer at the ion energies of the ionized sputtered species and of the ionized working gas in HiPIMS discharges by studying experimentally obtained ion energy distribution functions (IEDFs). The IEDF of ions in HiPIMS discharge is initially determined by two possible distributions: (i) a distribution of thermalized cold particles, typically the working gas (often described by assuming a Maxwell distribution) and (ii) a distribution of atoms sputtered from the target (described by a Thompson distribution or a Stepanova–Dew distribution (Thompson, 1968, Stepanova and Dew, 2004)), which were discussed in Section 1.1.8. Commonly the ion energy distribution comprises both distributions with different weight factors, appearing as a peak at low energy (corresponding to the Maxwellian distribution) and a high energy tail (from the sputtered particles). Sometimes, there are additional peaks in the IEDF from ions accelerated in possible potential structures in the plasma, for example, an ion peak at about 20 eV for singly charged ions (Maszl et al., 2014). These highenergy peaks are commonly attributed to ion acceleration by plasma instabilities due to collective plasma effects (Maszl et al., 2014, Ni et al., 2012, Lundin et al., 2008, Hecimovic et al., 2017b), which we introduce in the following Section 4.1.3.1 with full details given in Sections 7.3 and 7.4. The Maxwell distribution describes the energy spectrum of the particles in thermal equilibrium:    E E exp − , (4.2) FM (E) = 2 kB T π(kB T )3 where E is the particle energy, kB is the Boltzmann constant, and T is the temperature of the system (300 – 1200 K). It is considered that if the ions (or atoms before

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ionization) undergo sufficient number of collisions with the background gas, then the ions become thermalized. In the case where the gas/plasma mixture in front of the target is heated due to collisions with energetic sputtered particles (see Section 4.2.2), or by the hot target surface, the ion distribution is still Maxwellian, but shifted toward higher energies. Note that also ions of the sputtered species can exhibit thermalized energy distributions, provided that they undergo a sufficient amount of collisions. This typically requires long travel distances and/or high working gas pressures. Increasing the working gas pressure reduces the mean free path of ions and increases the collision frequency, resulting in a lower average energy and narrower IEDF. Similarly, by placing the substrate further away from the target the ions will experience more collisions before appearing at the substrate, again resulting in a low-energy narrow IEDF. However, the disadvantage of increasing pressure and distance is that the density of ions reaching the substrate will be proportionally reduced due to scattering (Kadlec et al., 1997, Burcalova et al., 2008, Atiser et al., 2009).

4.1.3.1

Time-averaged IEDF

Typical IEDFs of the working gas ions (Ar+ ) and ionized sputtered species (Ti+ ) from a dcMS discharge are shown in Fig. 4.6. The working gas pressure was 0.40 Pa, and the applied power was 1 kW (VD = 400 V). IEDFs exhibit a peak at an ion energy of about 2 eV and contain a high-energy tail that extends up to roughly 20 and 40 eV for Ar+ and Ti+ ions, respectively. In the case of Ti+ , the high-energy tail is related to the original energy distribution of the sputtered neutrals at the cathode (Kadlec et al., 1997). The corresponding time-averaged IEDFs for a HiPIMS discharge in the same system are shown in Fig. 4.7. These measurements were made at working gas pressure of 0.4 Pa in argon, and the HiPIMS discharge was generated by applying 3 and 10 J pulses. We note that the ion energy distributions are similar for the two different pulse energies. The IEDFs for Ar+ are rather similar to the dcMS case. The most striking feature is the existence of a high-energy tail of the sputtered metal extending beyond 100 eV, which is not seen in the dcMS case. Bohlmark et al. (2006) stated that about 50% of the Ti+ ions have an energy > 20 eV. The energy distribution of the background working gas is often considered to be in thermal equilibrium (thermalized) due to collisions within the gas and with the walls of the vacuum chamber. The gas temperature of the background gas is thereby estimated to be in the range from 300 K (room temperature) to an upper limit of around 1200 K (Vitelaru et al., 2012, Kanitz et al., 2016), that is, significantly lower than what is seen in Fig. 4.7 (and also in Fig. 4.6). However, when measuring such IEDFs by mass spectrometry, the peak of the IEDF is commonly shifted (increased) by a few eV and is equal to the value of the plasma potential. This is due to (positive) ions being accelerated by the potential difference between the plasma potential and the grounded orifice of the mass spectrometer. In Fig. 4.7, we also see that the IEDF for Ar+ ions comprises a small tail that exhibits a strong dependence on the discharge power (compare the 3 J/pulse and 10 J/pulse HiPIMS discharges). The appearance of high-energy Ar+ ions is a consequence of heating of the Ar working gas by collisions with the more energetic metal flux. High powers applied in HiPIMS discharges will result in

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Figure 4.6 The ion energy distributions for Ar+ and Ti+ ions taken from a conventional dcMS discharge. The Ar working gas pressure was 0.4 Pa, the applied power 1 kW, and the target material was Ti. The recorded counts have been adjusted with the corresponding isotope abundance. Reprinted from Bohlmark et al. (2006), with permission from Elsevier.

Figure 4.7 The ion energy distributions for Ar+ and Ti+ ions measured from a HIPIMS discharge. The Ar pressure was 0.4 Pa, the pulse energy 3 and 10 J, and the target was made of Ti. The recorded counts have been adjusted with the corresponding isotope abundance. Reprinted from Bohlmark et al. (2006), with permission from Elsevier.

higher densities of sputtered material, higher collision rates between metal and working gas species, and consequently will extend IEDFs to higher energies (Bohlmark et al., 2006, Aiempanakit et al., 2011, Burcalova et al., 2008, Ehiasarian et al., 2011, Ferrec et al., 2016, Franz et al., 2014, Hecimovic et al., 2008, Hecimovic and Ehiasarian, 2009, Kudláˇcek et al., 2008, Lazar et al., 2010, Mishra et al., 2009, Vlˇcek et al., 2007a,b, Ehiasarian et al., 2008). However, at pressures above about 1 Pa, the increase in power does not seem to influence the average ion energy, as the increase in energy by the sputtered flux is counteracted by an increasing number of collisions (Burcalova et al., 2008). There are several processes in the plasma that contribute to the generation of high-energy ions in HiPIMS discharges. First, the previously discussed Thompson or Stepanova–Dew energy distribution functions of sputtered particles are likely less reduced to lower energies by gas scattering in HiPIMS due to strong gas rarefaction

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(depletion of working gas in front of the target) when operating at high instantaneous discharge powers (see Section 4.2.2 for details). The previously described thermalization processes are thereby less efficient (Hecimovic et al., 2008, Ehiasarian et al., 2008). Second, ions reflected from the target will return to the plasma bulk as fast neutrals, where the higher discharge voltage used in HiPIMS results in more energetic neutrals (Yamamura and Ishida, 1995, Drüsedau et al., 1999, Rudolph et al., 2018). Note that the neutral reflection probability from the target is much higher for argon atoms than for metal atoms. The reflected atoms may then be ionized when passing through the dense plasma, although with a low probability due to the short time that they spend in the dense plasma region. Such reflected and ionized species will retain a relatively high energy and thereby contribute to the observed high-energy tail (Hecimovic et al., 2008). The above two processes imply that the IEDF of sputtered species will extend to higher energies with increasing discharge power, which has been confirmed by Hecimovic et al. (2008) and Ehiasarian et al. (2008). The third process in the plasma contributing to the generation of high-energy ions in HiPIMS is the presence of plasma instabilities, such as non-stationary double-layer potential structures (i.e. potential humps) associated with rotating dense plasma zones (spokes), which accelerate ions in the ionization region near the target surface. These are expected to have a strong effect on the primarily ionized sputtered species (see Section 7.4 for details). The ionization zones/spokes appear in dcMS (Panjan and Anders, 2017), rfMS (Panjan, 2019), and HiPIMS (Kozyrev et al., 2011, Panjan et al., 2015, Hecimovic et al., 2016) discharges. The higher plasma densities found in HiPIMS discharges, and thus probably more dense spokes, appear to generate potentials high enough to accelerate ions away from the target (Maszl et al., 2014, Yang et al., 2015, Panjan et al., 2014). In addition to the singly charged ions, there are also several reports of multiply charged ions in HiPIMS discharges (Ehiasarian et al., 2002, Bohlmark et al., 2006, Ehiasarian et al., 2007, Anders et al., 2007, Andersson et al., 2008, Ehiasarian et al., 2008, Greczynski and Hultman, 2010, Poolcharuansin et al., 2010, Lazar et al., 2010, Hecimovic and Ehiasarian, 2010). As was discussed in Section 1.1.4, multiply charged ions can create secondary electrons when self-sputtering dominates. Bohlmark et al. (2006) report that, for a Ti target, a significant fraction of the ion flux is due to the Ti2+ ion, and an observation of the Ti4+ ion has been reported (Andersson et al., 2008, Poolcharuansin et al., 2010). Poolcharuansin et al. (2010) claim that there is an increase in multiply charged ions with decreasing operating pressure, in particular, in the low-pressure regime below 0.5 Pa. Greczynski and Hultman (2010) find that the number of doubly charged Cr2+ ions increased almost linearly with increased pulse energy in an Ar/N2 industrial scale discharge with Cr target. Lazar et al. (2010) see a significant fraction of doubly charged zirconium ions in the total ion flux when operating with Zr target. There the flux fraction of doubly charged zirconium ions was higher than the fraction of singly charged zirconium ions. It increased with increased distance from the cathode target and could become dominant. Furthermore, Ross et al. (2011), point out that there is an optimum condition for the HiPIMS discharge where the maximum number of singly charged ions are created per unit energy. The sputtering efficiency decreases as energy is spent creating the more highly ionized species.

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Time-resolved IEDF

The IEDFs of metal and working gas ions change during the pulse and in the afterglow of the HiPIMS discharges, and therefore time-averaged measurements do not provide a complete understanding of the ion dynamics during a HiPIMS pulse. An example of time-resolved measurements of the IEDFs of Cr+ and Ar+ ions in a HiPIMS discharge is shown in Fig. 4.8. We see that the metal ions during and shortly after the end of the discharge pulse (tpulse = 70 µs) exhibit highly energetic tails extending up to 70 eV for Cr+ ions (Hecimovic and Ehiasarian, 2009). After the pulse, the high-energy tail slowly diminishes with time as a result of losses to the substrate and surrounding walls as well as collisions with the surrounding low-energy gas particles. The low-energy part of the IEDF of the ionized sputtered species is thus preserved over longer times. On the other hand, during the pulse, the working gas IEDF comprises a main lowenergy peak and a small high-energy group of ions, which is probably created through collisions with high-energy metal ions. The high-energy tail of the working gas ions is found to disappear shortly after the end of the pulse and only the low-energy peak remains, as shown in Fig. 4.8 for Ar+ ions (Bohlmark et al., 2006, Hecimovic and Ehiasarian, 2009). Not only the ion energy, but also the life span of ions has been found to depend strongly on collisions of the sputtered flux with the surrounding gas, and as such depend on the target material. Hecimovic and Ehiasarian (2011) report that the life span of heavy ions are generally found to be the longest. Typical life spans for singly charged ions at 0.3 Pa are 4 ms for C+ ions, 5 ms for Al+ , Ti+ , and Cu+ ions, about 6 ms for Cr+ ions, and 10 ms for Nb+ ions. At higher pressure of 3 Pa, a second peak appears for singly charged metal ions around 1.2 ms, which could be the signal of bulk plasma slowly diffusing away from the target indicating a life span for C+ ions being about 7 ms, and more than 10 ms for Al+ , Cu+ , Cr+ , Ti+ , and Nb+ ions. The long lifespan of ions impinging on the substrate could be beneficial for reducing residual stress and inhibit the incorporation of contaminants in the coating (Mishra et al., 2009, Hecimovic and Ehiasarian, 2009, Aiempanakit et al., 2011, Hecimovic and Ehiasarian, 2011, Cemin et al., 2017).

4.1.3.3

Reactive HiPIMS

In reactive mode the reactive gas reacts with the target surface and creates a compound layer (see Section 6.1 for details on reactive sputtering). Therefore the ions impinging on the target sputter both metal atoms of the target material and atoms of the reactive gas. Apart from atomic ions from the target,1 there are molecular ions that are ionized in the plasma bulk by electron impact ionization (Lundin et al., 2016), which is described in more detail in Section 6.2.1. Typically, the reactive atomic gas ions (such as N+ or O+ ) constitute the primary source of nitrogen/oxygen ions detected (Greczynski and Hultman, 2010, Schmidt et al., 2012). This is in contrast to 1 There is also a smaller contribution of atomic reactive gas ions resulting from dissociation of the reactive

gas molecules followed by ionization in the volume plasma (Lundin et al., 2017).

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Figure 4.8 Time-resolved measurement of the IEDF of Cr+ ions (A) in the early stages of the pulse and

(B) in the later part of the pulse and Ar+ ions (C) in the early stages of the pulse and (D) in the later part of the pulse, measured in a HiPIMS discharge with 20 µs gate width. The pulse duration was 70 µs (shaded region in the figures). Note that Cr+ ions are measured up to 2.4 ms from the start of the pulse and Ar+ ions up to 5 ms from the start of the pulse. From Hecimovic and Ehiasarian (2009). ©IOP Publishing. Reproduced with permission. All rights reserved.

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Figure 4.9 The ion energy distribution functions (IEDFs) from Al and Ti targets operated in both dcMS and HiPIMS modes. The dcMS data are time-averaged. For HiPIMS, the IEDFs correspond to the 20 µs highest target current density portions of the 200 µs pulses investigated. Reprinted from Greczynski et al. (2012b), with permission from Elsevier. + what is commonly observed for reactive dcMS, where molecular ions (N+ 2 , O2 ) dominate (Greczynski and Hultman, 2010). As a result of the different origins of reactive atomic gas ions (mainly from the target) and reactive molecular gas ions (from the plasma bulk), they often exhibit different IEDFs. In Fig. 4.9, it is, for example, seen that the N+ ions in HiPIMS have a similar IEDF as the sputtered metal ions with a low-energy peak and a high-energy tail. However, the IEDF of N+ 2 ions resembles closer to the Ar+ distribution with a significantly reduced energetic tail. In the afterglow, the metal and reactive gas ion fluxes reduce faster than the inert working gas ion flux (Greczynski and Hultman, 2010). The IEDFs in a wide range of reactive HiPIMS processes have been studied, including TiO (Aiempanakit et al., 2011, Alami et al., 2015, Aiempanakit et al., 2013), TiN (Ehiasarian et al., 2007, 2011, Lattemann et al., 2010), CrN (Greczynski and Hultman, 2010, Greczynski et al., 2010), AlO (Andersson et al., 2006), AlN (Jouan et al., 2010), CrAlN (Bobzin et al., 2017), TiAlN (Greczynski et al., 2014), AlSiN (Lewin et al., 2013), NiO (Kubart et al., 2014), CuO (Kubart et al., 2014), and NbO (Franz et al., 2016). The results follow the general trends established before and shown in Fig. 4.9. To complete our picture on the IEDF in reactive HiPIMS, we also need to mention the presence of negative ions. For example, when the working gas is a mixture of Ar

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and O2 , negative O− ions may be formed either due to electron transfer in surface processes at the target or due to dissociative attachment in the plasma bulk (Zeuner et al., 1998, Bowes et al., 2013, Bowes and Bradley, 2014). Typically, the IEDF of O− comprises three groups of ions: low-, medium-, and high-energy ions. The high-energy group consists of O− ions that are created at the target surface and accelerated in the sheath and extended presheath. The negative ions at the target surface are generated through desorption of O− ions or O atoms followed by electron attachment, and these ions gain an energy equivalent to the voltage applied to the target (Zeuner et al., 1998, Bowes et al., 2013). Such high-energy ions can give rise to defects in the coatings and significant residual stress, as discussed in Section 8.5. The medium-energy group has an energy that corresponds to about half the target potential, and it is most probably − − generated by O− 2 and other clusters (e.g. TiO , TiO2 , etc.) that are sputtered from the target followed by acceleration over the entire discharge potential. Due to collisions en route to the mass spectrometer, the clusters subsequently dissociate into Ti and O atoms and O− ions, which share the kinetic energy. The low-energy group of ions is most probably formed in the extended presheath in front of the magnetron target and will thereby experience limited acceleration during transport out into the volume (Mráz and Schneider, 2006, Welzel et al., 2011). Bowes et al. (2013) find the O− ion to be the most abundant of the negative ion species across the entire energy range when operating a reactive Ar/O2 HiPIMS discharge with Ti target. Furthermore, they − find that TiO− 2 and TiO3 ions are only observed at the highest energies corresponding approximately to the average target potential, which suggests that such ions are produced exclusively at the target surface and not in the plasma bulk.

4.1.3.4

Time-evolution of the ion flux

We have so far seen that the IEDF in nonreactive and reactive HiPIMS strongly depends on the type of ionic species investigated and on the time during (or after) the discharge pulse. The understanding of how the IEDF changes is very important when using a substrate bias to control the energy of ions impinging on the substrate. A synchronized pulsed HiPIMS bias, such as described in Section 2.3.2, can be tailored to adjust the energy of ions and, more importantly, control the metal/gas ion ratio. Ideally, the bias should be used during the part of the pulse when the metal/gas ion ratio is the highest (metal-ion-dominated phase), and the bias voltage should be set to enhance adatom mobility in order to optimize the desired properties of the deposited films (Greczynski et al., 2012a), which will be described in more detail in Section 8.6.3. To identify the metal-ion-dominated phase, consider Fig. 4.10, where the energy+ integrated ion flux intensity of Al+ , Ar+ , N+ 2 , and N ions are plotted during a 200 µs HiPIMS pulse (again recall that only qualitative trends can be established, since quantitative measurements are generally beyond the limit of mass spectrometry). In the early stages of the HiPIMS pulse, the ion flux reaching the substrate is dominated by working gas ions (Bohlmark et al., 2006, Greczynski et al., 2012a). In Fig. 4.10, we see that the Ar+ and N+ 2 fluxes increase during the early stage of the pulse, which is in line with our finding in the previous section that the reactive molecular gas ions mainly follow the plasma chemistry from the plasma volume, and not the plasma chemistry

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+ Figure 4.10 Time evolution of the energy-integrated ion flux intensity of Al+ , Ar+ , N+ 2 , and N ions

recorded by a mass spectrometer located at the substrate position during a 200 µs HiPIMS pulse. The peak current density was 0.5 A/cm2 at t = 47 µs. Data from Greczynski et al. (2012a).

due to target related processes. As the discharge current rapidly increases, more sputtering takes place, and the working gas ion flux saturates or even reduces (seen as a drop of the Ar+ intensity at around t = 50 µs in Fig. 4.10), whereas the metal flux increases and dominates the ion flux reaching the substrate. In the present example, this results in a metal-ion-dominated flux during t = 40 – 90 µs, although we will postpone the discussion on the physical mechanisms responsible to Section 7.2.2 to get a better overview of the entire plasma evolution. After the end of the pulse, the voltage at the cathode falls to zero, and the sputtering process stops. The atoms and ions continue colliding among themselves and with the surrounding gas. This leads to a situation where the total ion flux decreases with time during the afterglow. In Fig. 4.10, note that the ion flux decay starts already during the end of the discharge pulse, which in this example is due to a strong decrease of the discharge current after reaching a peak value at t = 47 µs. Based on the time-resolved IEDFs and the energy-integrated ion flux analyzed before, the temporal evolution of the IEDF for different species can be summarized as follows: IEDF of inert working gas ions: • Early in the pulse – strong increase of working gas ion flux exhibiting a low-energy peak only; • During the pulse – saturation or reduction of ion flux exhibiting a low-energy peak with a second ion population at higher energies; • In the afterglow – decay of ion flux exhibiting a low-energy peak only. IEDF of metal ions: • Early in the pulse – no clear signal due to very few ions present; • During the pulse – increased ion flux, which follows rather closely the discharge current, and is characterized by a low-energy peak and a high-energy tail; • In the afterglow – decay of ion flux exhibiting a low-energy peak only.

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IEDF of reactive atomic and molecular gas ions: • Early in the pulse – increase of mainly molecular gas ion flux exhibiting a lowenergy peak only; • During the pulse – saturation or reduction of the molecular gas ion flux, whereas the atomic gas ion flux may still show an increase. The atomic gas ions exhibit a low-energy peak and a high-energy tail similar to the metal ions; • In the afterglow – decay of ion flux exhibiting a low-energy peak only.

4.1.4 Ionized fraction of depositing particles One of the key features of HiPIMS is the significant fraction of ionized metallic particles generated in the vicinity of the target (Helmersson et al., 2006, Gudmundsson et al., 2012). Describing this requires knowledge of the absolute fraction of ionized sputtered particles. There is unfortunately some confusion in the literature concerning the ionized fraction, and it is therefore necessary to clarify the situation before going into the reported results. Three approaches are typically used to describe the degree (or fraction) of ionization: the ionized flux fraction Fflux , the ionized density fraction Fdensity , and the fraction αt of the sputtered metal atoms that become ionized in the plasma (sometimes referred to as probability of ionization). First, following Hopwood (1998), we define the ionized flux fraction of species s as (s)

(s) Fflux =

i (s)

(s)

i + n

(s)

(4.3)

,

(s)

where i and n are the ion and neutral fluxes of the species s arriving at the substrate or detector, respectively, in unit of m−2 s−1 . Second, the ionized density fraction of species s is defined as (s)

(s) Fdensity ≡

(s)

ni (s)

(s)

n i + nn (s)

,

(4.4)

where ni and nn are the ion and neutral densities of the species s in the volume, (s) respectively. Third, the probability of ionization αt of species s was originally introduced by Christie (2005) (although he used the notation β for this quantity) when describing his well-known target material pathways model for HiPIMS (see Section 5.1.1). It is defined as the fraction of the total amount of sputtered atoms that are ionized by the magnetron plasma. Fflux is the easiest to measure, as discussed in Section 4.1.5, and consequently the most commonly reported fraction of ionization. These different ways to quantify the degree of ionization are discussed further by Butler et al. (2018), who compared ionization in the HiPIMS discharge to the often used method of combining dcMS with a secondary inductively coupled plasma (ICP) discharge to achieve ionized-PVD.

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4.1.5 Ionized flux fraction in HiPIMS The earliest attempt to estimate the ionized flux fraction Fflux in HiPIMS discharges was made already by Kouznetsov et al. (1999) in their pioneering work, where they deposited Cu on a substrate at a distance of 6 cm from the target (15 cm in diameter). The experiment was carried out at an Ar working gas pressure of 0.065 Pa with a pulse discharge peak power density of 2.8 kW/cm2 . Comparing the thickness of two thin copper films deposited on a conductive Si substrate using either an applied bias of +140 V (repelling positive ions) or −50 V (depositing both neutrals and ions), they could estimate the ionized flux fraction. The deposition rate for +140 V bias comprised of only 30% of the rate measured with the applied negative bias on the substrate. A rough estimate was thereby Fflux ≈ 70%. It should be noted that such measurements assume that the density of both deposited films is the same, which is not necessarily the case when depositing from a combination of ions and neutrals or from neutrals only. Furthermore, the error resulting from thickness measurements by a profilometer is not negligible due to film roughness. We therefore estimate that the error in the reported ionized flux fraction is at least 10%. Macák et al. (2000) followed up on these measurements using the same HiPIMS system, but now equipped with a Ti0.5 Al0.5 target, 15 cm in diameter. They applied a pulse with peak power density of 0.6 kW/cm2 at an Ar working gas pressure of 0.13 Pa with 50 Hz repetition frequency and a pulse on-time of 100 µs. A planar probe with an area of 1.77 cm2 was placed at a distance of 10 cm from the target and biased to −70 V. The temporal evolution of the measured ion current on the probe revealed a two-peak structure, which could be deconvoluted to separate argon and metal ions. Integrating the area below the metal and argon component of the measured ion current enabled the authors to calculate the number of ionized particles depositing on the probe. By measuring the total deposition rate the ionization flux fraction of deposited particles could be estimated to 40% ± 20%, where the large error is due to the fitting of the measured ion current. More accurate measurements of the ionized flux fraction were carried out more than a decade later by using the previously described gridded and grid-less QCM. These measurements were carried out by several authors using various targets and discharge conditions. We have summarized these measurements in Fig. 4.11. Before we go into the details of these measurements, we would like to comment on a few general features: • The ionized flux fraction is ≥ 50% for typical peak current densities around 1 A/cm2 and working gas pressures in the range of 0.5 – 2.0 Pa, but is somewhat reduced for pressures closer to 2.0 Pa and exhibits a strong decrease at around 4.0 Pa. As a comparison, the measured ionized flux fraction in dcMS is close to 0% at otherwise similar discharge conditions (Kubart et al., 2014). • It is possible to identify an increase in the ionized flux fraction with increasing discharge peak current density, at least when comparing within the same experimental series (see also further for details).

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Figure 4.11 Compiled data on ionized flux fraction measurements in HiPIMS for eight different material systems (Ti, TiO2 , TiAl, Cu, Al, Fe, Fe2 O3 , Ni). The discharges were operated in either pure Ar or in an Ar/O2 mixture with the pressure given above each bar (0.05 – 4.0 Pa). The values inside the bars denote the discharge current density averaged over the entire target (0.03 – 6 A/cm2 ). The letters beside the discharge current densities refer to results from different authors i.e. (a) Kouznetsov et al. (1999), (b) Macák et al. (2000), (c) Vlˇcek et al. (2007a), (d) Kudláˇcek et al. (2008), (e) Poolcharuansin and Bradley (2010), (f) Lundin et al. (2015), (g) Hubiˇcka et al. (2013), (h) Kubart et al. (2014), (i) Meng et al. (2014), (k) Stranak et al. (2014) (HiPIMS+ECWR), and (m) Stranak et al. (2014) (HiPIMS).

• There are no strong variations between the target materials investigated (taking into account the differences in distance between target and probe at otherwise similar process conditions) although Al and Ti exhibit a slightly higher ionized flux fraction than Cu, which is likely due to the higher ionization potential for Cu compared to Ti and Al and to a considerably lower electron impact ionization collision cross-section (Samuelsson et al., 2010). We also note that the ionized flux fraction values found when using a mass spectrometer (cases (c) and (d) in Fig. 4.11) are unexpectedly high as compared to the gridded QCM and grid-less QCM measurements, which is discussed in more detail below. The first measurements of the ionized flux fraction in HiPIMS using a gridded QCM were carried out by Poolcharuansin et al. (2012) in an argon discharge with Ti target. The g-QCM was positioned 13 cm above the race track and facing the target. They modified the g-QCM by removing the grid suppressing ions from reaching the quartz crystal and directly biasing the upper electrode of the quartz crystal to +20 V when only measuring the deposition rate of neutral particles. The grid reflecting plasma electrons was biased to −40 V. The experiments were conducted using a planar magnetron with a target diameter of 15 cm at an Ar pressure of 0.53 Pa. The ionized flux fraction of Ti was investigated for different average discharge powers in the range from 0.3 kW to 1.25 kW at rather low discharge peak current densities by varying: (i) pulsing frequency from 200 Hz to 600 Hz, (ii) pulse length from 40 µs to 100 µs, and (iii) initial cathode voltage from 404 V to 450 V (only one parameter changed at a time). In the frequency series, the cathode voltage was fixed at 465 V, re-

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sulting in an estimated peak discharge current density of 0.18 A/cm2 at a pulse length of 100 µs. The increase in frequency increased the average discharge power from 0.3 kW to 0.9 kW, but the ionized flux fraction decreased from 50% to about 30% although the total deposition rate increased. Exactly the same trend in Fflux was seen also in the second case when increasing the pulse width at a fixed frequency of 500 Hz. The cathode voltage was always set to 510 V although the estimated peak discharge current density increased with pulse width from 0.17 A/cm2 to 0.28 A/cm2 (corresponding to an increase in the average discharge power from 0.3 kW to 1.25 kW). A smaller decrease of the ionized flux fraction from 40% to 35% was also somewhat surprisingly reported in the third case, when increasing the cathode voltage from 404 V to 450 V, which resulted in an increase of the estimated pulse discharge current density from roughly 0.08 A/cm2 to 0.3 A/cm2 (corresponding to an increase in the average discharge power from 0.3 kW to 1.25 kW). The authors attributed the overall decrease in the ionized flux fraction with increasing average discharge power to increased probability of back-attraction of the target material, denoted βt , which is discussed in more detail in Sections 5.1 and 7.5.1. For example, a higher cathode voltage results in a greater ion retarding potential in the vicinity of the target and an extended presheath region, which leads to a higher probability of metal ions returning to the target. However, it is difficult to see this effect for a constant voltage case, such as when increasing the frequency. Instead, the authors speculate that it may be attributed to the thermalization of metal ions in the afterglow plasma (Hecimovic and Ehiasarian, 2011), which requires long enough off-times for ions to reach the g-QCM. However, more work is likely needed to clarify this effect. Kubart et al. (2014) explored the ionized flux fraction in argon discharges with Ti and Ni targets using a g-QCM (two-grid configuration) for various pulse power densities, 0.1 – 1.9 kW and 0.1 – 1 kW/cm2 , respectively, which approximately corresponded to peak current densities in the range JD,peak ≈ 0.3 – 4.1 A/cm2 for Ar/Ti and JD,peak ≈ 0.3 – 2.5 A/cm2 for Ar/Ni. They used 50 mm diameter circular Ti and Ni targets, which were mounted on a magnetron with a high-strength magnetic field suitable for sputtering of ferromagnetic materials (magnets were approximately 50% stronger than standard magnets). The Ar pressure was set to 0.8 Pa for the Ni target and increased to 1.0 Pa for the Ti target to improve the discharge stability. The average discharge power was kept constant at 200 W, and the pulse on-times were 50 µs, 100 µs, and 300 µs. The ionized flux fraction of Ni deposited at a distance of 43 mm from the target increased with increasing pulse power density and reached up to 50% with a tendency to saturate when approaching the highest applied pulse power density (1 kW/cm2 ). For comparison, Fflux ≈ 0% in dcMS at an average power of 200 W (however, the total deposition rate was almost 5 times higher compared to HiPIMS). In contrast to Poolcharuansin et al. (2012), they show that the pulse width in the Ar/Ni case did not influence the measured ionized flux fraction, which is not so surprising considering that they used the same pulse duty cycle and thereby not significantly changing the peak currents achieved. In the Ar/Ti case the ionized flux fraction reached 60%, with an increasing trend with increasing peak power density (and peak current density). Here shorter pulses resulted in somewhat higher ionized flux fractions together with the same total deposition rate.

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Figure 4.12 Ionized metal flux fraction of Ar/Ti (filled symbols) and Ar/Al (hollow symbols) HiPIMS discharges as a function of average pulse current density (close to peak current densities). The argon pressure was set to either 0.5 Pa or 2.0 Pa. The lines only serve to guide the eye. Based on data from Lundin et al. (2015).

Lundin et al. (2015) followed up on the previous investigation by focusing on the influence of the peak current density and working gas pressure. They investigated Fflux in HiPIMS discharges with Ti and Al targets (50 mm in diameter) using an mQCM placed at a distance of 40 mm from the target. The discharges were operated at an Ar working gas pressure of either 0.5 Pa or 2.0 Pa and at an average discharge power of 200 W using 100 µs pulses. An increase in the pulse average current density from 0.5 A/cm2 to 2.0 A/cm2 (corresponding to a peak current density from 0.7 to 2.5 A/cm2 ) generally resulted in a clear increase in the ionized flux fraction from about Fflux ≈ 20% to Fflux ≈ 60% for both Ar/Ti and Ar/Al discharges as seen in Fig. 4.12. The authors could correlate this to increasing electron density and electron temperature and therefore an increased ionization probability, as determined by Langmuir probe measurements (see also Section 3.1.1). However, the ionized flux fraction was always roughly 10 percentage points higher at 0.5 Pa in comparison with 2.0 Pa. The reason was found to be a decrease of the effective electron temperature during the discharge pulse when increasing the pressure, resulting in a decreased probability for electron impact ionization. The authors also investigated the effect of extending the discharge pulse to 400 µs while maintaining the same peak current densities and average power by decreasing the pulse frequency. Similar to Kubart et al. (2014), they did not observe any strong changes in the ionized flux fraction, again highlighting the importance of the peak current density. In one case, however, prolonging the plasma pulse to 400 µs in Ar/Al discharge at 0.5 Pa led to an increase in the ionized flux fraction to 78%, which the authors correlated to somewhat higher electron density and effective electron temperature.

4.1.5.1

Reactive HiPIMS discharges

The ionized flux fraction in reactive Ar/O2 mixtures has also been investigated. Kubart et al. (2014) studied an Ar/O2 discharge with Ti target using an m-QCM. The sensor

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was placed 35 mm from the target. The pulse on-time was set to 100 µs, and the discharge was kept in the compound mode (fully oxidized target) at a total pressure of 1.1 Pa. The ionized flux of depositing particles was measured for different pulse power densities in the range 0.1 – 2 kW/cm2 (JD,peak ≈ 0.2 – 4.0 A/cm2 ). The reactive process was compared to a discharge running in pure argon atmosphere under otherwise equivalent conditions. It was found that the total deposition rate in the compound mode was around 8 times lower in comparison with operating in pure argon (see also Section 6.1 for a more thorough discussion of deposition rates in reactive magnetron sputtering). The results clearly revealed that the ionized flux fraction was systematically higher in the compound mode, where a maximum value of 67% was reached at the highest pulse power density compared to 40% for pure metal sputtering. Even for lower pulse power densities, the ionized flux fraction was still relatively high in the compound mode, Fflux ≈ 33% at 0.5 kW/cm2 (Fflux ≈ 10% in pure metal mode under the same conditions). Based on our discussion in Section 3.3.3 and the results ˇ of Cada et al. (2017), the increased ionized fraction in the compound mode is likely related to a higher effective electron temperature when operating in the compound mode. Also, an increase in the electron density is expected due to the higher peak currents reported by the authors (Kubart et al., 2014) (see also Section 3.3), which will also increase the ionization probability. The ionized flux fraction was also measured when reactively depositing hematite (α-Fe2 O3 ) thin films (Hubiˇcka et al., 2013). Also here an m-QCM was employed at a distance of 60 mm from the target. A circular Fe target, 50 mm in diameter, was mounted on a strongly balanced planar magnetron. The mass flow rates of Ar and O2 were 26 sccm and 20 sccm, respectively, at a constant pressure of 1 Pa. For all experiments, the time-averaged discharge current and pulse on-time were kept constant at 0.6 A and 100 µs, respectively. The impact of the pulse power density in the range 0.01 – 1.8 kW/cm2 , corresponding to a peak current density of 0.03 – 5.4 A/cm2 , was studied by changing the pulse frequency. It was found that Fflux increases with increasing pulse power density for both the reactive and pure metallic modes reaching 44% and 32%, respectively, at the highest pulse power density. Excluding the lowest pulse power density, the ionized flux fraction of depositing particles was always higher in reactive sputtering, in agreement with our previous discussion.

4.1.5.2

Hybrid systems

The ionized flux fraction for a hybrid HiPIMS system, consisting of an ECWR plasma source and a HiPIMS source, was studied by Stranak et al. (2014) due to the advantages of operating at low Ar working gas pressures (< 0.5 Pa); see also Section 3.4. A planar magnetron was equipped with a 50 mm circular Ti, Al, Cu, or Fe target. The studied HiPIMS process conditions were: pulsing frequency 100 Hz, pulse ontime 100 µs, and average discharge current 0.5 A, giving JD,peak ≈ 2 A/cm2 in pure HiPIMS discharge mode and JD,peak ≈ 2.3 A/cm2 for the hybrid ECWR-HiPIMS discharge. The ionized flux fraction was investigated for different Ar pressures in the range from 0.05 Pa to 4.0 Pa using an m-QCM placed 150 mm from the target. In pure HiPIMS mode an exponential-like decrease in Fflux was observed when increasing the pressure. At 0.5 Pa the ionized flux fraction of depositing particles was found

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between 40% (Al target) and 50% (Ti target), which is in line with the values reported by Kubart et al. (2014) and Lundin et al. (2015). At 4.0 Pa the Ar/Fe discharge yielded Fflux ≈ 16%, whereas Fflux ≈ 10% for the other target materials. The authors attributed the decrease in Fflux with increasing pressure to a thermalization of the electron gas, which decreases the rate coefficient for electron impact ionization of the sputtered material. However, the ECWR-HiPIMS discharge was able to operate down to a pressure of 0.05 Pa, where Fflux ≈ 45% for all investigated target materials. Furthermore, by optimizing the working gas pressure in this hybrid sputtering system the authors reached Fflux ≈ 80% at a pressure of 0.5 Pa for the Ti target, which is significantly higher than in pure HiPIMS mode under the same process conditions. The other target materials showed a similar behavior with a maximum in the ionized flux fraction at around 0.5 Pa and reaching 46%, 55%, and 62% for Al, Cu, and Fe targets, respectively. Again, the ionized flux fraction rapidly decreased for pressures higher than 0.5 Pa to about 15% at 4.0 Pa. To explain their observations, the authors assumed that the ionization mean free path increased significantly for the lowest pressure (0.05 Pa), resulting in lower ionization rate of sputtered atoms. The generally higher ionized flux fractions measured in the ECWR-HiPIMS system compared to the pure HiPIMS system might be due to a more effective transport of ions of sputtered atoms to the substrate, where they contribute to the measured higher values, as suggested by Konstantinidis et al. (2006). On the other hand, the measured values of Fflux for pressures higher than 2.0 Pa were comparable with those measured in pure HiPIMS. This might be due to a limited effect of the ECWR at higher pressures.

4.1.5.3

Influence of the magnetic field

The ionized flux fraction also depends on the magnetic field strength |B| and geometry (degree of balancing). The influence of the magnetic field strength |B| on the ionized flux fraction has been investigated in a few studies (Meng et al., 2014, Hajihoseini et al., 2019). Meng et al. (2014) studied an Ar/Cu discharge using a circular target, 36 cm in diameter, where |B| was set to 20, 50, or 80 mT (measured just above the race track). A g-QCM was placed at 14 cm from the target center. The HiPIMS discharge was operated at 100 Hz pulsing frequency and 50 µs pulse on-time with Ar working gas pressure that was kept constant at 0.67 Pa. We should note that typical HiPIMS peak currents were only achieved for the 80 mT case, where the peak current density was JD,peak ≈ 0.5 A/cm2 . Weaker magnetic fields produced JD,peak ≈ 0.2 A/cm2 at 50 mT and JD,peak ≈ 0.08 A/cm2 at 20 mT. Overall, the highest ionization flux fraction of Cu was 46%, which was observed for |B| = 20 mT and a peak cathode voltage of −900 V, whereas Fflux ≈ 24% and Fflux ≈ 20% were observed for 50 mT and 80 mT, respectively, at the same peak cathode voltage. Based on triple probe measurements, the authors propose a simple 1D empirical model calculating the ionization probability per distance unit of Cu atoms. The model shows that the weakest magnetic field (20 mT) results in the highest ionization probability over the whole distance between the target and substrate. On the other hand, the 80 mT magnetic field demonstrates a very high plasma density, low Teff , and wider presheath, which suppresses ion extrac-

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tion to the substrate (increased back-attraction). By adding up the Cu+ ion fluxes and comparing with the Cu atom flux the ionization fraction of depositing particles was also estimated from the model. Predicted ionized flux fractions Fflux were 51%, 25%, and 15% for magnetic field strengths of 20, 50, and 80 mT, respectively. We see that the measured quantities are in good agreement with results obtained from the empirical model. These results may seem somewhat counterintuitive based on our earlier discussion on how Fflux increases with increasing JD,peak . Hajihoseini et al. (2019) recorded both the ionized flux fraction and the deposition rate in a HiPIMS discharge that was operated in two different operating modes: ‘fixed voltage mode’ where the cathode voltage was kept fixed at 625 V while the pulse repetition frequency is varied and ‘fixed peak current mode’ carried out by adjusting the cathode voltage to maintain a fixed peak discharge current and by varying the frequency to achieve the desired time average power (300 W). The magnetic field strength |B| 11 mm above the race track was varied from 11 to 24 mT. For HiPIMS operated in the fixed voltage mode opposing trends were observed with increasing |B| in the studied range: a trade-off between the deposition rate (decreases by more than a factor of two) and the ionized flux fraction (increases by a factor 4 to 5). In fact, the deposition rate during HiPIMS operated in fixed voltage mode changed from 30% to 90% of the dcMS deposition rate as |B| was decreased. In contrast, when operating the HiPIMS discharge in fixed peak current mode the deposition rate increased by 38% when decreasing |B| by 53%. In the fixed peak current mode both deposition rate and Fflux increased with decreasing |B|. For a peak discharge current density of JD,peak = 0.5 A/cm2 the measured Fflux values were in the range 14.2 – 20.5%. The authors claim that the fraction of the ions of the sputtered material that escape back attraction increased by 30% when |B| was reduced during operation in fixed peak discharge current mode. Clearly, more investigations are needed to explore the effect of |B| on the ionized flux fraction and the deposition rate.

4.1.5.4

Mass spectrometry results

An alternative way to estimate the ionized flux fraction is using a mass spectrometer. Vlˇcek et al. (2007a) utilized an energy-resolved mass spectrometer placed 10 cm from the target surface (facing the target) to study an Ar/Cu discharge. They applied 200 µs long HiPIMS pulses at a pulsing frequency of 1 kHz to the Cu target, 10 cm in diameter, at a working gas pressure of 0.5 Pa. The total depositing particle flux was calculated from the measured deposition rate. The total ion flux was determined from integration of measured time-averaged ion energy distributions of Ar+ , Ar2+ , Cu+ , and Cu2+ . The ionized flux fraction Fflux was then determined from the flux ratio of copper ions and all depositing particles. The calibration of integrated ion energy distributions was carried out by comparing with the measured ion flux density integrated over the entire pulse period on a substrate placed at the same distance as the mass spectrometer. In this way the total number of counts from the mass spectrometer over the investigated energy range could be related to the measured ion flux on the substrate. From this information a fraction of the ion flux on the substrate was assigned to the value corresponding to the integral of the energy distribution of a specific ion.

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We have to note that such a calibration procedure is not fully reliable because we cannot directly compare count rates between different atoms from an ion detector in the mass spectrometer (see also Section 4.1.1.1). The reason is that the ion–electron secondary emission coefficient depends on the ionization energy of the measured ion (elemental-dependent). In other words, we cannot be sure that the flux of Cu+ ions is estimated correctly, and we have to assume a nonnegligible error. Although the error is unknown, their results confirmed that the ionized flux fraction Fflux increases with increasing peak current density reaching 56% for JD,peak ≈ 0.8 A/cm2 at a distance of 10 cm from the target. Kudláˇcek et al. (2008) followed up on the mass spectrometry measurements, but this time in an Ar/Ti discharge, using the same pulse parameters and working gas pressure as Vlˇcek et al. (2007a). At the 10 cm distance from the target, they measured Fflux ≈ 81% (JD,peak ≈ 0.8 A/cm2 ), whereas increasing the distance resulted in a decrease of Fflux to around 61% at 20 cm. If the plasma pulse length was increased to 500 µs with repetition frequency 1 kHz (duty cycle 50%), then Fflux ≈ 99% even for JD,peak ≈ 0.4 A/cm2 at a distance of 10 cm and a pressure of 0.5 Pa. It is not clear why this is so, and a situation with almost complete ionization of the depositing titanium atoms seems unrealistic at these conditions. The authors did not comment on this last result, which we believe could be attributed to the error resulting from the method determining Fflux .

4.1.6 Ionized density fraction We now turn to measurements of the ionized density fraction in the volume, ni /(ni + nn ), although very few measurements have been reported. Bohlmark et al. (2005) used time-averaged optical emission spectroscopy (OES) to record the emitted light from an Ar/Ti discharge 3 cm above the Ti target (15 cm in diameter). The emitted light was integrated over space within the line of sight parallel to the target surface. The HiPIMS repetition frequency was 50 Hz, and the plasma pulse length was 100 µs at a working gas pressure of 1.3 Pa. Under the assumption of limited thermodynamic equilibrium over the range of energies relevant to the excitation and first ionization of titanium atoms, models of the emitted spectrum for neutrals and ions were calculated (including 964 neutral and 215 ionic spectral lines). The modeled spectra were fitted to the measured spectra by varying the relative contribution of Ti neutrals and Ti+ ions. In such way the degree of ionization in the vicinity of the target was calculated for pulse power densities in the range from 0.05 kW/cm2 to 1.4 kW/cm2 (JD,peak ≈ 0.1 – 3.1 A/cm2 ). The degree of ionization was observed to be higher than 90% at a pulse power density of 0.2 kW/cm2 and saturated at almost 100% for higher measured pulse powers densities. At the lowest studied pulse power density of 0.05 kW/cm2 the degree of ionization reached around 50%. Lastly, besides measurements of the ionization flux fraction and the ionized density fraction in the volume, some effort has been devoted to calculating these values from computational modeling. Detailed descriptions of these attempts along with comparisons with some of the presented experimental results are given in Section 5.2.1.

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4.2 The plasma neutrals The ground state neutral species, both those sputtered from the target and those of the working gas, are of special interest in HiPIMS as they have a strong influence on the discharge kinetics. This is in particular the case where the ionization fraction is well below 100%, which is generally the situation for sputtered species during the pulse-off period and for the working gas during both pulse-on and pulse-off periods. The working gas neutrals also play an important role as they are the main source of ions in the discharge, at least during the early stages of the HiPIMS pulse (see Section 4.1.3.4), and strongly participate in gas heating, quenching of the excited and metastable states, Penning ionization, and so on. On top of this, the gas neutrals along with the ions also contribute to the total heat flux toward the growing film (Cormier et al., 2013). The motion of the neutral sputtered species has been studied by several authors, mainly based on Monte Carlo simulations (Turner et al., 1989, Yamamura and Ishida, 1995, Van Aeken et al., 2008, Lundin et al., 2013). This involves injecting test particles at z = 0 with a prescribed sputtered energy and angular distribution and then following them in time in a uniform neutral gas (see Section 5.1.5 for model details). The resulting velocity or energy distribution is then extracted as a function of z. Using this approach, Msieh et al. (2010) identified two distinct populations: one not collided population retaining the original sputter distribution, with density decreasing approximately as exp(−z/λcoll ), and another collided population, approximately thermal with the ambient gas temperature.

4.2.1 Spatial and temporal evolution of plasma neutrals We give an example of 2D density distributions of sputtered Ti neutrals in Fig. 4.13A. This data was obtained under the same HiPIMS conditions as presented for the Ti+ ions in Fig. 4.4 and discussed in Section 4.1.2. The density maps for metastable Ar atoms (Arm ) captured at the same time delays are also given for comparison in Fig. 4.13B. Already at a first glance the obtained evolution of the neutral particles is rather different from that of the ions. The main observations are as follows: • The sputtered Ti neutrals appear mainly after the plasma pulse is off (at t > 20 µs), unlike the Ti+ ions, which appear during pulse-on and peaked about 5 µs after pulse-off. • The metastable Arm density, on the other hand, is mainly peaking during pulse-on. • The Ti neutral density is higher in areas where Ti ionization is rather low (compare Figs. 4.13A and 4.4B). • A significant density depletion of the Ti density takes place at the end of the pulse above the race track. • The density distributions for Ti and Arm during the off-time are much more uniform than that of Ti+ ions. • The Arm metastable density somewhat increases during the pulse-off time (at about 300 µs).

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Figure 4.13 The spatio-temporal evolution of the relative ground state density of (A) Ti neutrals and (B) Ar (1s5 ) metastables (Arm ) above the magnetron target in a HiPIMS discharge at pAr = 2.7 Pa for a pulse duration of 20 µs. Time delay (in µs) is indicated next to each figure. The Ti and Arm data are normalized separately. The ROI dimensions are 7 × 10 cm2 , and a logarithmic color scheme is used. The discharge current and voltage waveforms are shown in Fig. 4.3.

From Fig. 4.13 we can see, that the Ti neutrals propagate in the direction away from the magnetron target with an estimated net velocity of about 1 km/s. This value is in a good agreement with the results obtained in a dcMS discharge by Vitelaru et al. (2010), where velocities of about 2 km/s at 1 cm away from the target for an Ar/Ti discharge were found at 0.8 Pa. The reason for the slightly higher velocity is likely due to the shorter distance to the target and the lower pressure. Let us note that the velocity should be lower as pAr increases, as shown by Fabry–Perot interferometry (Britun et al., 2008a), where values comparable to this work were found for Ti atoms. Depending on the electron temperature and electron density distribution, an intensive excitation and ionization of the sputtered atoms will occur, redistributing the ground state densities observed experimentally, as previously shown by Britun et al. (2015b). From the time-evolution of the Ti density shown in Fig. 4.13A, we can observe that there are essentially two depleted zones: (i) A low Ti density in the race track region immediately in front of the target (z < 1 cm) at t = 20 – 40 µs, and (ii) voids in the Ti density around z ≈ 3 cm above the race track observed at t = 15 – 20 µs. Concerning the first case, we know that electrons confined in the magnetic trap give rise to an intensive Ti ionization, resulting in two strong Ti+ ion density maxima already observed in Fig. 4.4 at t = 20 – 30 µs. Assuming electron impact ionization to be the main Ti ionization mechanism (e + Ti −→ Ti+ + 2e) during the HiPIMS pulse (Gudmundsson et al., 2015), it is reasonable that this ionization is a loss channel for

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Ti neutrals and hence leads to the observed reduction in Ti density around the same time and position as seen in Fig. 4.13A. The voids in the Ti density seen at larger z distances in the second case cannot, however, be linked to local electron trapping. Instead, these voids observed at t = 15 – 20 µs in Fig. 4.13A correlate with the Arm maxima in Fig. 4.13B observed nearly at the same time delays and location. This might be the result of Penning ionization of Ti (i.e. Ti + Arm −→ Ti+ + Ar), which should be accompanied by a loss of Ti neutrals as Arm propagate away from the target resulting in a Ti density depletion. This effect, however, does not considerably affect the overall Ti+ ion density distribution, as shown in Fig. 4.4. Concerning the Arm data, a density increase during the pulse-off time is observed in Fig. 4.13B at t = 300 µs. This phenomenon is related to Ar gas refill followed by electron impact excitation due to the remnant electrons (which should be even more prominent at higher pulse energies) having a typical refill time scale of hundreds of microseconds according to available estimations (Lundin et al., 2009). This effect has been directly visualized for Arm in HiPIMS by Vitelaru et al. (2012), who reported comparable refill times (see also Section 5.2.3.2). Interestingly, the same phenomenon seems to occur in reactive HiPIMS, affecting the production of O atoms during the plasma off time, as studied by Britun et al. (2017). According to our earlier discussion on Penning ionization of Ti, such an Arm density increase may also be accompanied by a limited increase of the Ti+ ion density (Gudmundsson et al., 2015). In our case, this effect is likely the reason behind the slight increase in the Ti+ ion density in the center of our investigated region as seen in Fig. 4.4B at t = 300 µs. At a pressure of 0.7 Pa, the Ar refill is not visible (see Britun et al. (2015b)), and the Ti+ ion density decay is much more uniform during the off time, as shown in Fig. 4.4A. The absolute number densities between two consecutive plasma pulses for both Ti and Arm were determined by AAS in the same way as was done for Ti+ ions and discussed in Section 4.1.2, and the results are presented in Fig. 4.14. For the neutral Ti atoms recorded at 2.7 Pa in Fig. 4.13A the 100 mark corresponds to 2 × 1018 m−3 for the number density of the 0.000 eV state of Ti (the lowest among 3 sublevels). For the total Ti density we have to multiply by 3. For the metastable Arm atoms recorded at 2.7 Pa in Fig. 4.13B the 100 mark corresponds to 1018 m−3 for the number density of the 1s5 state, while the 1s3 state is neglected. A reduction of the total Ti density is observed toward the end of the pulse followed by an increase in the afterglow. This behavior is likely caused by the combination of intensive ionization of sputtered Ti and depletion of the bottom ground state energy sublevel during this time interval (as also shown in Fig. 4.14). In the case of sputtered Ti the background density value is quite high, being about 2 × 1017 m−3 , whereas for the Arm density, it is only about 3 × 1015 m−3 , as we can see at the very beginning of the pulse and at the end of the off-time. The depletion of the lowest ground state sublevel is much more pronounced for the Ti neutral case (green line (dark gray in print version) in Fig. 4.14 at t = 20 – 200 µs). The Arm density is generally less stable during the afterglow, and a strong density reduction is detected after the HiPIMS pulse has been switched off (Fig. 4.14, gray line). This is a result of Ar rarefaction during this time interval (see also Section 4.2.2) together with continuous quenching of Arm states by (mainly) Ar

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Figure 4.14 The temporal evolution of the ground state Ti neutral and Arm metastable number densities at 5 cm above the magnetron target in a HiPIMS discharge obtained by atomic absorption spectroscopy at pAr = 2.7 Pa. Pulse duration is 20 µs. The discharge current and voltage waveforms are shown in Fig. 4.3.

ground state atoms. The Ar refill starts at t ∼ 300 µs, resulting in an overall Arm number density increase by a factor of ∼ 2, which is well correlated with the Arm density increase obtained by LIF imaging in Fig. 4.13B at this time. By combining the density distributions for Ti and Arm neutrals from the LIF measurements shown in Fig. 4.13 with the AAS measurements shown in Fig. 4.14 we can also estimate the absolute densities at any point within the considered region. In this way the yellow color (light gray in print version) in Fig. 4.13A corresponds to ∼ 2 × 1017 m−3 of the total Ti ground state density, representing the three sublevels. The Ti density peaks at ∼ 2 × 1018 m−3 (red color (dark gray in print version) at t = 40 µs). For Arm metastables (1s5 state only), the number density at the beginning of the off-time corresponds to ∼ 1016 m−3 (orange color (mid gray in print version) at t = 25 µs in Fig. 4.13B) and peaking at ∼ 1017 m−3 (red color (dark gray in print version) at t = 10 µs). The contribution of the Ar 1s3 state to the total Ar metastable density can be neglected in most cases, except for the end of the pulse on-time, where they are comparable, as demonstrated by Britun et al. (2015c). Another interesting aspect of the particle dynamics in HiPIMS is the direction of the particle motion. By using LIF imaging, virtually, any particle group with a particular velocity in the discharge volume can be visualized by introducing a corresponding deviation of the laser wavelength from its resonant value. Such an approach (referred to as Doppler-shifted LIF (DS-LIF)) can visualize the dynamics of the sputtered ground state atoms in the discharge volume, as shown by Britun et al. (2015b). To illustrate the particle motion asymmetry in the HiPIMS discharge, typical 2D density distributions above the magnetron target obtained for Ti neutrals and Ti+ ions using the DS-LIF technique are presented in Fig. 4.15. The Ti neutral and Ti+ ion density distributions are recorded after the HiPIMS pulse on-time, at the time delays t = 25 µs and t = 40 µs, respectively. One of the more striking features seen in this figure is the pronounced Ti/Ti+ density redistribution showing the densified areas and the density voids (depleted zones), as discussed earlier. Similar to what we discussed in Section 4.1.2, the Ti+ ion density maxima, adjacent to the race track, coincide with

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Figure 4.15 The spatial distribution of the ground state Ti atoms (left) and Ti+ ions (right) above the magnetron target in a HiPIMS discharge as a function of laser wavelength shift (indicated in the left-top corner, along with horizontal velocity to which it corresponds). Time delays are 25 µs for Ti and 40 µs for Ti+ ions. The working gas pressure is pAr = 0.7 Pa, and the pulse duration is 20 µs. Each image is normalized individually. Three arrows indicate the dominant directions of density propagation. The ROI dimensions are 7 × 10 cm2 . Linear color scheme is used.

the depleted density regions of Ti neutrals. This effect is much more pronounced at low pressure (0.7 Pa) than at high pressure (2.7 Pa), as shown previously. Before discussing the results in Fig. 4.15 in detail, let us first note that the thermalization of the sputtered species, and thereby their exact velocity distribution, drastically depends of the mass ratio between the target metal atoms and the working gas atoms. In the case of light metals the thermalization is very fast, whereas in the opposite case (heavy metal atoms) the energetic metal particles survive longer (Desecures et al., 2015). In the latter case, up to three populations of sputtered species can be identified: (i) energetic sputtered particles (following Thompson or Stepanova– Dew distributions; see Section 1.1.8) characterized by a ballistic transport, (ii) directed transport corresponding to the energetic particles after less than three collisions with the gas particles such as they could not reach equilibrium yet (i.e. they preserve a group velocity toward the substrate), and (iii) the thermalized particles characterized by a diffusive transport. To study the particle propagation in the discharge volume, the direction of the laser beam should be taken into account. Since the laser beam propagates from left to right in our case (see Fig. 4.2), the atoms having the opposite horizontal velocity component will be blue-shifted relative to the laser so that the laser frequency should be decreased (i.e. wavelength increased) to excite the blue-shifted atoms in a resonant way. A positive laser wavelength shift (defined as λ = λlaser − λresonant ) corresponds to the blue-shifted atoms, moving in our case from right to left. The shift values are

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indicated in the upper-right corners in Fig. 4.15. As we can see, both blue- and redshifted groups of atoms, represented here, reveal a spatial asymmetry. In our case the group of sputtered Ti adjacent to the left part of the race track consists of the Ti atoms preferentially moving to the right side of the ROI, whereas near the opposite side of the race track the Ti population is mainly formed by the atoms moving in the opposite direction (marked by large yellow arrows (white in print version) in Fig. 4.15). Let us note that the DS-LIF density patterns in Fig. 4.15 are normalized individually, thus somewhat exaggerating the contribution of high-speed atoms to the total density distribution. In reality, both blue- and red-shifted Ti atomic groups have a rather broad velocity distribution in the horizontal direction, with a typical FWHM = 6.3 km/s at 0.7 Pa, as shown by Britun et al. (2015b). Thus the Ti data displayed in Fig. 4.15 should be considered qualitative. Despite the visible asymmetry in the neutral Ti case the Ti+ ion data is nearly symmetrical, as shown in Fig. 4.15 (right column). The observed symmetry in the Ti+ ion case is likely closely related to the particle motion in the target vicinity. It is however probable that the azimuthal drift of charged particles (discussed in Section 1.2.2) above the target race track will induce a velocity component out of the imaging plane in our case, which may blur the anisotropy of the velocity distribution in the plane of imaging and turn the total ion sputtering pattern to a more symmetric one.

4.2.2 Gas rarefaction One important process related to the neutral particle dynamics is gas rarefaction, which results in a depletion of the working gas density in the near-cathode region and can thus have a great impact on the deposition process. A localized reduction in gas density in the target vicinity can occur due to gas heating. This gas heating can be caused by the discharge itself or by the presence of the hot target surface. This density reduction can be further enhanced by the flow of sputtered species from the target. Gas rarefaction has been extensively investigated both experimentally and theoretically in dcMS (Hoffman, 1985, Rossnagel, 1988, Kersch et al., 1994, Palmero et al., 2005, 2006, Kolev and Bogaerts, 2008). The mechanism for gas rarefaction discussed in these works is assumed to be mainly through heating followed by thermal expansion, where the heating is due to collisions (momentum transfer) between the working gas and the sputter-ejected target atoms, sometimes referred to as the sputter wind effect (Hoffman, 1985), as well as collisions between the working gas and reflected sputtering gas atoms. Furthermore, we will investigate gas rarefaction in HiPIMS and evaluate its impact on the HiPIMS process by studying several discharges in Ar although the conclusions are readily extended to include other working gases as well. A first Monte Carlo simulation of the neutral particle flow in HiPIMS discharges, taking into account only elastic collisions between the Ar gas atoms and the sputtered Ti atoms (Ar–Ar, Ar–Ti, Ti–Ti), was made by Kadlec (2007) using a self-consistent direct simulation Monte Carlo (DSMC) code discussed in Section 5.1.5.3. By applying a 200 µs-long HiPIMS pulse with ID (t) = 1 kA (corresponding to approximately a peak current density of 3 A/cm2 ) and an initial Ar pressure of pAr = 0.2 Pa, the neutral gas temperature was found to increase from 0.026 eV to 1 eV after 50 µs, at which time

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the neutral gas density had decreased by 60 – 70% in a region extending 2 cm above the race track. This is consistent with observations using optical emission spectroscopy in HiPIMS, where Vlˇcek et al. (2004) report almost an order of magnitude decrease in the density of neutral Ar. They also report a slightly less dramatic decrease in the density of the Ar+ ions at roughly 50 – 70 µs into a 200 µs-long pulse while sputtering a Cu target. Also, Alami and coworkers (Alami et al., 2006) observed a decrease in the optical emission spectroscopy intensity measured from neutral Ar at high discharge voltages. Lundin et al. (2009) studied the discharge ID –VD characteristics for HiPIMS pulses longer than 100 µs using a Cr target with Ar as the working gas. They identified two different current regimes: (i) a high-current transient during the first ∼ 100 µs followed by (ii) a plateau at lower currents. In Fig. 4.16, we see that at high applied discharge voltages the high-current transient had the characteristics of a HiPIMS discharge pulse (JD,peak ≥ 0.5 A/cm2 ), whereas the plateau current values are more in line with the currents observed in dcMS discharges using the same applied voltage. The current evolution was found to be strongly correlated with gas rarefaction, where the observed high-current transients cause a depletion of the working gas in the area in front of the target (i.e. loss of source for ions to carry the discharge current) and thereby a transition to a dcMS-like high-voltage lower-current regime (Lundin et al., 2009). To understand the observed current evolution, the authors stressed the need to include also plasma-based effects, such as a direct loss of ionized gas, where ionization of the working gas followed by transport to the cathode and subsequent neutralization leads to significant loss, up to 40% in their case, assuming that the returning Ar atoms from the target are energetic enough to pass the ionization region near the cathode without interacting with it (Lundin et al., 2009). In a follow-up theoretical study, Huo et al. (2012) provided a comprehensive summary on the various mechanisms leading to gas rarefaction in HiPIMS discharges when modeling an Al discharge with Ar as the working gas at VD = 450 V (we will discuss this discharge again in Section 7.1.1, and Fig. 7.1 shows the current composition at the target for various discharge voltages) using the ionization region model (IRM) discussed in detail in Section 5.1.3. These results are shown in Fig. 4.17, and the ID –VD characteristics are shown in Fig. 5.9. The rate of gas rarefaction dnAr /dt is the fastest at the maximum in discharge current, and a highest absolute value of the gas rarefaction nAr /nAr,0 ≈ 50% (top black curve, Fig. 4.17) appears 40 – 60 µs after the discharge current maximum. Here nAr,0 refers to the unperturbed neutral working gas density. Beyond this stage, the gas density increases again to a constant value during the current plateau phase. After the pulse is turned off (t = 400 µs) the gas refills and, with a time constant of 100 – 120 µs, returns to the initial value nAr,0 . In Fig. 4.17, we see that the dominating loss terms are electron impact ionization and the sputter wind kick-out. Of these two, the ionization term is larger by more than a factor of two throughout the pulse. The reason for the smaller impact of the sputter wind is that λmfp for elastic neutral–neutral collisions is on the order of a few cm for typical HiPIMS conditions taking into account significant gas rarefaction (Huo et al., 2012). Most of the sputter wind would therefore pass through the dense ionization region without colliding with a working gas atom. Let us compare this result with

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Figure 4.16 (A) Discharge voltage and current characteristics for a 400 µs-long pulse with an off-time of 9.9 ms between pulses. (B) Measured values of the initial high-current peak (black squares) and current plateau (red circles) versus the applied discharge voltage. Reference current values for the dcMS case are also given (green triangles). The measurements were performed using a Cr target 50 mm in diameter at an Ar pressure of 0.4 Pa. From Lundin et al. (2009). ©IOP Publishing. Reproduced with permission. All rights reserved.

the direct ionization losses. All argon atoms that are ionized disappear from the cold Ar population. The fraction of Ar+ ions that are not attracted to the target (1 − βg ) leaves to the bulk plasma and is lost, whereas the remaining fraction βg impinges on the target, picks up an electron, and returns to the ionization region as a part of a hot population nArH (see Section 5.1.3 for more detail on ArH ). This is an influx which is smaller by about a factor βg (typically around 0.9 (Huo et al., 2012)) than the ionization losses. In the modeling performed, Huo et al. (2012) assumed that ArH returned to the ionization region from the target with an equivalent temperature of 2 eV, giving an average speed of about 3 km/s. For the same reason as the sputtered species, the majority does not collide inside the ionization region and pass through it in about 2 – 4 µs. This gives a loss flux term, which almost balances the influx. The result is that argon atoms can be regarded as in practice lost upon ionization, as proposed by Lundin et al. (2009). It is also clear that the long mean free path is the basic reason why rarefaction by ionization losses dominates over the sputter

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Figure 4.17 A study of gas rarefaction and refill processes for a 400 µs-long HiPIMS discharge pulse in pure Ar at 1.8 Pa with Al target using the IRM code. The peak discharge current was 12 A, which corresponds to a peak discharge current density of 0.6 A/cm2 . The top-most curve shows for reference the argon gas density. The lower panel shows the reaction rates for losses and gains of neutral argon atoms due to collisions inside the ionization region, Ar+ + M −→ Ar + M+ charge exchange term × 10, the electron impact ionization of the hot ArH component, the kick-out of cold argon atoms by the sputter wind and the electron impact ionization of cold Ar. The ID –VD characteristics for this discharge are given in Fig. 5.9. From Huo et al. (2012). ©IOP Publishing. Reproduced with permission. All rights reserved.

wind in the modeled discharge. For higher working gas pressures, the sputter wind contribution would become more important although the investigated working gas pressure of pAr = 1.8 Pa is already high for commonly used deposition conditions. An easy way to make a rough estimation of gas rarefaction due to only direct loss of ionized gas was proposed by Huo et al. (2012), who introduce an ionization loss rarefaction time trarefaction from the pulse start assuming that: (i) all produced Ar+ ions go to the target, (ii) these ions carry the whole discharge current, (iii) the returning recombined Ar atoms are quickly lost to the plasma outside the ionization region, and (iv) there is negligible refill of gas. Complete gas rarefaction then would result when each of the Ar atoms that was originally in the ionization region has transported the charge e to the target and when this total charge equals the integrated discharge current, that is,  trarefaction ID (t)dt. (4.5) nAr,0 VIR e = tstart

In the Al discharge with Ar as working gas studied in Fig. 4.17, the authors found that nAr,0 VIR e = 4.5 × 1020 [m−3 ] × 6.35 × 10−4 [m3 ] × e = 4.6 × 10−4 [As] (Huo et al., 2012). By evaluating Eq. (4.5) with the experimental curve ID (t) gives a rarefaction time trarefaction ≈ 70 µs, which compares rather well with the time around 120 µs to reach maximum gas rarefaction in Fig. 4.17. Now, when we understand the fundamentals of gas rarefaction, we will look at some other factors determining the amplitude of the density reduction. Kozák and Lazar (2018) studied rarefaction of the Ar working gas for several consecutive 200 µs-

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Figure 4.18 Cross-section of the simulation domain showing the Ar density distribution at the end of a 200 µs long HiPIMS pulse using a Zr target with a maximum discharge current of 10 A (current was constant between 50 and 200 µs), which corresponds to a peak current density of 0.5 A/cm2 . The initial Ar pressure was 1.0 Pa, which corresponds to nAr,0 = 2.4 × 1020 m−3 at 300 K. From Kozák and Lazar (2018). ©IOP Publishing. Reproduced with permission. All rights reserved.

long HiPIMS pulses and 1.8 ms pulse-off intervals using a 3D DSMC method (binary collisions, but no plasma-based effects, as discussed before). The initial working gas pressure was pAr,0 = 1.0 Pa, which corresponds to nAr,0 = 2.4 × 1020 m−3 at 300 K. One example of the Ar density distribution at the end of a 200 µs pulse, when assuming a Zr target, is shown in Fig. 4.18, where a significant density reduction is observed close to the target. By investigating three different discharge pulse currents they observed a maximum reduction of the Ar density, nAr /nAr,0 , in the ionization region (extending 2 cm from the target surface) of 41%, 57%, and 66% when sputtering Zr atoms at 5, 10, and 15 A, respectively (equivalent to a pulse current density of 0.25, 0.50, and 0.75 A/cm2 ). Also, Huo et al. (2014) report a stronger (and faster) depletion of neutral Ar gas in the ionization region with increasing peak discharge current. It also results in a lower Ar+ ion current and a more rapid decrease of ID (t) after the peak in the discharge current, in line with the results of Lundin et al. (2009), which will be further explored in Section 7.2. Lastly, Kozák and Lazar (2018) have also investigated the impact on gas rarefaction in the ionization region for three different target materials at a current of 10 A (current density 0.50 A/cm2 ): C (12.01 amu), Al (26.98 amu), and Zr (91.22 amu). The difference of the maximum density reduction is surprisingly small with nAr /nAr,0 of 43%, 50%, and 57% for C, Al, and Zr, respectively. However, the authors point out that the size of the ionization region is small compared to the real extent of the region with significant Ar rarefaction, which in their case extends approximately up to 8 cm, as seen in Fig. 4.18.

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Modeling the high power impulse magnetron sputtering discharge

5

Tiberiu Mineaa , Tomáš Kozákb , Claudiu Costinc , Jon Tomas Gudmundssond,e , Daniel Lundina a Laboratoire de Physique des Gaz et Plasmas - LPGP, UMR 8578 CNRS, Université Paris–Sud, Université Paris–Saclay, Orsay Cedex, France, b Department of Physics and ˇ Czech Republic, NTIS–European Centre of Excellence, University of West Bohemia, Plzen, c Alexandru Ioan Cuza University, Faculty of Physics, Iasi, Romania, d Department of Space and Plasma Physics, School of Electrical Engineering and Computer Science, KTH Royal Institute of Technology, Stockholm, Sweden, e Science Institute, University of Iceland, Reykjavik, Iceland

Modeling has the possibility to capture the main interacting mechanisms in a plasma discharge, which are typically very difficult to identify (isolate) in experiments. A large variety of computer models describing the plasma behavior in HiPIMS discharges have been developed and used to gain insight into various physical and chemical mechanisms operating in these discharges. Here we give an extended overview and, when possible, a comparison of the theoretical and numerical methods used to tackle the different challenges encountered in HiPIMS discharges, from the cathode through the ionization region, the diffusion region, and, finally, to the substrate and chamber walls. We also highlight some important modeling results, which have been selected to emphasize the added understanding brought by computational modeling, but also to validate certain model approaches, or highlight model-specific results. Examples include how various models reproduce the discharge current (and sometimes the discharge voltage) often obtained from the time-dependent plasma parameters (electron density and temperature, ionization probability, etc.). With the help of the models, it is possible to probe the plasma parameters within the ionization region, where most experimental techniques fail. Such models can, for example, show how electrons are released from the target and become energized in the cathode sheath and in the ionization region, and how they contribute to ionization of neutral species, the atoms of the working gas or the atoms of the sputtered material. The time evolution of the electron energy distribution function, the electron temperature, and the ion energy distribution function are also discussed and compared to experimental results.

5.1

Modeling approaches

Various modeling approaches have been applied to describe the HiPIMS discharge. Models of various complexity including analytical formulae describing the relations High Power Impulse Magnetron Sputtering. https://doi.org/10.1016/B978-0-12-812454-3.00010-3 Copyright © 2020 Elsevier Inc. All rights reserved.

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between target current and fluxes of individual plasma species, including steady-state and time-dependent global models, Monte Carlo simulations, particle simulation using the particle-in-cell method, will be discussed. Steady-state global models were introduced to explain, at first only qualitatively, the trends observed in deposition rate and ionized fraction of the sputtered species as a function of the target power density. The main motivation was to explain the decrease in the power-normalized deposition rate of HiPIMS discharges compared to conventional dc magnetron sputtering (see Section 7.5) and to evaluate the fraction of target material ions in the particle flux onto the substrate (see further discussion in Section 4.1.5). The time-dependent global models were developed with the aim to explain the shape of the discharge current waveform, determine the ionization mechanisms, and to calculate the composition of the species in the plasma volume and the various particle fluxes to the target and substrate. The time-dependent global models are volume-averaged models based on time-dependent particle and energy balance equations. When modeling magnetron sputtering discharges, they are often restricted to the ionization region (IR), that is, the high-density plasma in front of the magnetron sputtering target where electrons are confined by the static magnetic field (magnetic trap). Multidimensional models, such as 2D models, aim to give a more detailed picture of the HiPIMS plasma dynamics during the pulse and afterglow. The 3D approaches, even if they are in their early stages, are giving the first insights into the azimuthal plasma structures, the origin of plasma instabilities, including spokes formation, and the mechanisms involved (see also Sections 7.3 and 7.4).

5.1.1 Pathway models The first model of the HiPIMS discharge was the pathway model which was originally introduced by Christie (2005) to explain the reduction in the deposition rate when compared to conventional dcMS. Fig. 5.1 shows the pathways of working gas and target material atoms and ions in a HiPIMS discharge (Christie, 2005, Vlˇcek and Burcalová, 2010, Brenning et al., 2017) and serves as a good starting point for the following discussion of the steady-state global models. For simplicity, we assume that only singly charged ions are present in the discharge; however, multiply charged ions can be added if needed. The pink box (light gray in print version) indicates the ionization region (IR). The IR is the high density region next to the target where the electrons are confined by the static magnetic field. The diagram shows two recycling loops, one for the working gas and the other for the target material. The target material atoms are ejected from the target by sputtering induced by ions originating from the + working gas (G+ t ) and from the target material (Mt ), respectively. After neutralization, the inert working gas atoms are released from the target (denoted Gt in Fig. 5.1). Fractions of the working gas atoms and target material atoms leaving the target can be ionized with probabilities αg and αt , respectively, and after some time can return back onto the target as ions of the working gas or ions of the sputtered material with probabilities βg and βt , respectively. This approach to modeling the HiPIMS discharge will be analyzed in detail in Section 7.2.1.1. The diagram also shows the pathways of

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Figure 5.1 The pathways of working gas and target material atoms and ions in a HiPIMS discharge. Based on Christie (2005), Vlˇcek and Burcalová (2010), and Brenning et al. (2017). IR stands for ionization region and DR for diffusion region. The symbols are defined in the main text.

target material atoms and ions toward the substrate where a film is deposited. This region is referred to as the diffusion region (DR) in Fig. 5.1. In the DR the effect of the magnetic field can be neglected and the particles leaving the IR travel in a weaker plasma (typically one to two orders of magnitude below the plasma density in the IR) dominated by neutral gas species. The discharge current density JD is composed of ions of both the working gas (Jg ), which release secondary electrons from the target, and ions of the target material (Jt ),1 and we can write JD = e(1 + γsee,eff )G+ + eM+ = (1 + γsee,eff )Jg + Jt , t

(5.1)

t

where γsee,eff is the effective secondary electron emission coefficient (Buyle et al., 2003, Costin et al., 2005, Vlˇcek and Burcalová, 2010), and G+ and M+ are fluxes t t of the working gas and target material ions incident onto the target, respectively. Both ion species contribute to the sputtering of the target proportional to their corresponding sputter yields. The total flux of sputtered target material atoms is given by Mt = G+ Ytg + M+ Yss = [(1 − ζ )Ytg + ζ Yss ](G+ + M+ ) , t

t

t

t

(5.2)

where Ytg and Yss are the sputter yields induced by working gas and target material ions, respectively, and ζ is the fraction of target material ion flux and the total ion flux 1 The secondary electron emission yield for singly charged metal ions is zero in the ion energy range studied

here, as discussed in Section 1.1.4.

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to the target, ζ=

M+ t

G+ + M+ t

(5.3)

.

t

We can then define Yt = (1 − ζ )Ytg + ζ Yss

(5.4)

as the effective sputter yield of the target. Let us note that ζ is a convenient parameter for the evaluation of the discharge regime, since ζ  0 for conventional dc magnetron sputtering, where the plasma density is too low to produce significant ionization of the sputtered target species (M+ → 0), and ζ = 1 for pure self-sputtering of the tart get, where the discharge current is dominated by the ions originating from the target (G+ → 0). t

5.1.2 Steady-state global models The models described in this section are based on the pioneering work of Christie (2005), who proposed a pathway diagram similar to that given in Fig. 5.1. Following the pathways of this diagram, relations for the fluxes of atoms and ions in steady state can be derived from fundamental balance equations. This approach was later on extended by Vlˇcek and Burcalová (2010), who introduced additional ionization in the plasma bulk and used an energy balance equation for secondary electrons to estimate the ion return probability. These two models focused only on the pathways of the sputtered target material atoms (right-hand side loop in Fig. 5.1). The concept of working gas recycling (left-hand side loop in Fig. 5.1) was further developed and unified by Brenning et al. (2017) and is described in Section 7.2.1.1 when discussing the temporal evolution of the discharge current. Here, a unified and comprehensive model description of a steady-state HiPIMS discharge is presented, so the resulting formulae can be applied to HiPIMS discharges with a long current plateau or with respect to averaged discharge characteristics. Multiply charged ions incident onto the target are not treated as separate species, but they can be accounted for by assuming effective fluxes of ions with mixed properties.

5.1.2.1

Ionization and return of sputtered target material

We define the probability αt that a sputtered target material atom is ionized and the probability βt that the ion returns back onto the target. Then the target material ion flux onto the target is expressed as M+ = Mt αt βt ,

(5.5)

t

where M+ is the metal ion flux to the target, and Mt is the metal atom flux from the t target. Substituting Eq. (5.2) into Eq. (5.5), we obtain M+ (1 − αt βt Yss ) = G+ Ytg αt βt . t

t

(5.6)

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By introducing the self-sputter parameter (Anders, 2008, Gudmundsson et al., 2016) πss = αt βt Yss

(5.7)

Eq. (5.6) takes the form M+ = G+ t

t

Ytg πss . Yss 1 − πss

(5.8)

This equation shows that the flux of target ions onto the target is proportional to the flux of working gas ions multiplied by the factor πss /(1 − πss ) incorporating the probabilities of ionization and return of the target material as ions. Note that this equation is valid only for πss < 1. For πss > 1, the sputtering and subsequent ionization and return of the target material is so high that it leads to an unlimited self-amplification of the sputtered material ion flux, the so-called self-sputter runaway (Anders, 2011, Brenning et al., 2017) (see also Section 7.2.1 for a detailed description). Such a regime can be achieved but cannot be described by Eq. (5.8), since it contradicts the steady-state assumption. By rearranging Eq. (5.6) to express the probability αt of ionization of sputtered target atoms it is found that (Vlˇcek and Burcalová, 2010) αt =

1 ζ ζ = , βt Ytg + ζ (Yss − Ytg ) βt Yt (ζ )

(5.9)

where ζ is given by Eq. (5.3) and Yt (ζ ) denotes the effective sputter yield given by Eq. (5.4). The target ion return probability βt can be estimated from the energy balance equation under the following assumptions: (i) the energy of secondary electrons in the IR is due to the entire applied voltage VD , (ii) the sheath is very thin (no multiplication of electrons inside the sheath), (iii) the ion return probability is taken the same for both ion species (βg = βt ), and (iv) Ec,eff is the effective collisional energy lost per ion–electron pair produced by a secondary electron (including potential loss of secondary electrons from the magnetic trap) (Vlˇcek and Burcalová, 2010). This translates into γsee,eff βt

eVD = 1, Ec,eff

(5.10)

where γsee,eff is the effective secondary electron emission coefficient of the target. Combining Eqs. (5.9) and (5.10) both αt and βt are expressed as functions of ζ . In Section 5.2.1, we will see how this rather limited set of equations still can provide valuable insight into the internal discharge parameters.

5.1.2.2

Deposition parameters

The deposition rate coefficient is defined as the number of deposited atoms per ion incident onto the target, that is, ρ=

Ms + M+s G+ + M+ t

t

=e

Ms + M+s Ji

,

(5.11)

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where Ms and M+s are target material atom and ion fluxes onto the substrate, respectively, as shown in Fig. 5.1. These fluxes can be expressed as Ms = Mt (1 − αt )(1 − γ )ξn

(5.12)

M+s = Mt [αt (1 − βt ) + γ (1 − αt )]ξi ,

(5.13)

and

where ξn and ξi are fractions of target neutrals and ions, respectively, incident onto the substrate, and γ is a parameter (0 ≤ γ ≤ 1) characterizing the degree of additional ionization of the sputtered target atoms within the plasma bulk. Note that these ions are not necessarily directed back to the target. Substituting Eqs. (5.12) and (5.13) into Eq. (5.11), gives the deposition rate coefficient   ρ = Yt (ζ ) (1 − αt )(1 − γ )ξn + [αt (1 − βt ) + γ (1 − αt )]ξi . (5.14) The normalized deposition rate coefficient expressing the ratio of the deposition rate coefficients for a HiPIMS and a conventional dcMS, that is, = ρHiPIMS /ρdcMS = ρ/ραt =0,γ =0 , can be expressed as

(ζ ) =

 Yt (ζ )  (1 − αt )(1 − γ + γ ηi ) + αt (1 − βt ηi ) , Ytg

(5.15)

where we used the substitution ηi = ξi /ξn . Using the approximate scaling Ytg ∝ VD0.5 (see Section 1.1.7) and the fact that the average target power density is given by SD = VD JD , we can express the scaling aD

(ζ ) , ∝√ SD VD (1 + γsee,eff (ζ ))

(5.16)

where aD is the deposition rate. This equation expresses the scaling of the efficiency of the deposition process including the effect of ionization and return of the sputtered target atoms and the fact that the sputter yield scales with the square root of the target voltage. These are the two most important processes responsible for the decrease of the normalized deposition rate aD /Sd , which is explored in Section 5.2.1. The ionized flux fraction of the target material atoms in the flux onto the substrate, which is very important for effective and controllable delivery of energy into the growing film, is defined as the ratio of target material ions to all target material particles incident onto the substrate, that is, Fflux =

M+s Ms + M+s

,

(5.17)

which is Eq. (4.3) discussed in Section 4.1.4. After substitution of Eqs. (5.12) and (5.13) into Eq. (5.17), we obtain Fflux =

[αt (1 − βt ) + γ (1 − αt )]ηi . (1 − αt )(1 − βt ) + [αt (1 − βt ) + γ (1 − αt )]ηi

(5.18)

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The deposition parameters and Fflux can be calculated for a given VD , ζ , γ , and ηi , provided that the values of Ec,eff (ζ ) and γsee,eff (ζ ) (see Eq. (5.10)) are evaluated for the given target material. Relevant examples for copper and titanium targets are provided in Section 5.2.1, where it is shown that Fflux is very different for these two materials independent of the assumed fraction of metallic ions.

5.1.2.3

Limitations of this approach

The pathway model is a steady-state model based on the fundamental particle balance equations in the HiPIMS discharge. Because of the steady-state assumption, the model can be applied to discharges with a long discharge current plateau or with respect to averaged discharge characteristics, as the balance equations for the total fluxes of atoms and ions during the whole pulse period can be written in the same way as it is done for the instantaneous fluxes. The return probability βt of target material ions to the target is evaluated from the energy balance equations for secondary electrons based on several assumptions (see the text above Eq. (5.10) for details). The value of βt is influenced by the effective energy needed for the production of an ion–electron pair, which is expected to depend on the mode of electron energization in the ionization region. This is generally a combination of sheath energization and Ohmic heating (Brenning et al., 2016) in the presheath where the electric field is constantly changing due the motion of spokes (Anders et al., 2012a). More details on electron energization are found in Section 7.2.3.

5.1.3 Time-dependent global model, IRM The most advanced and well established among the time-dependent global models that have been developed is the ionization region model (IRM). It was introduced by Raadu et al. (2011) and continuously improved over the last decade. IRM is a flexible modeling tool for studying the plasma behavior during a HiPIMS pulse and the afterglow. This model was initially applied to a discharge operated with argon as the working gas and Al target to study gas rarefaction (Raadu et al., 2011) and refill processes (Huo et al., 2012) and to explain the loss in deposition rate (Brenning et al., 2012). Furthermore, a large set of HiPIMS experimental observations could be explained using the IRM, such as the electron heating mechanism (Huo et al., 2013), and the onset of self-sputtering (Huo et al., 2014). For the case of titanium targets, IRM calculations of the discharge parameters during the pulse and the afterglow have been directly compared with experiments after implementing the detailed kinetics of argon metastable species (Stancu et al., 2015); see Section 5.2.3.2. This was followed by a study of the role of metastable argon atoms and stepwise ionization in the HiPIMS discharge (Gudmundsson et al., 2015). More recently, the IRM has been extended to model a reactive Ar/O2 HiPIMS discharge with Ti target by adding a reaction set for oxygen to the discharge model and by adding oxygen-related surface processes (Gudmundsson et al., 2016, Lundin et al., 2017), which we address in Section 6.4.4. The IRM has also been adapted and applied to explore other types of discharges, such as

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the hollow cathode discharge (Hasan et al., 2013). An overview of the development of the IRM and its different versions is given in a recent review by Huo et al. (2017). The IRM gives the time evolution of neutral and charged species and of the electron temperature in pulsed magnetron sputtering discharges. The model is based on a separation of the discharge volume into distinct regions defined by the dominating physics, as shown in Fig. 5.1. The model is limited to the ionization region (IR), which, in the IRM, is defined as an annular cylinder with outer radius rc2 , inner radius rc1 marking the race track region, and length L = z2 − z1 , extending from z1 to z2 axially away from the target. The IRM is a volume-averaged global model of the plasma chemistry, and the model assumes only volume-averaged values over the whole IR volume for the electron, ion, and neutral densities and the electron temperature. Geometrical effects are included indirectly as loss and gain rates across the boundaries of this annular cylinder to the target and the bulk plasma (Raadu et al., 2011). The temporal development is defined by a set of ordinary differential equations giving the first time derivatives of the electron energy and the particle densities for all the heavy particles. The electron density is found assuming quasineutrality of the plasma. The model is constrained by experimental data input in the sense that it first needs to be adapted to an existing discharge (the geometry and pressure, the process gas, sputter yields, target species, and a reaction set for these species) and then fitted to two or three parameters to reproduce the measured discharge current and voltage curves, ID (t) and VD (t), respectively. Examples of the fitting procedure are given in Section 5.2.2.1. Much of the early IRM development was based on discharges with Al targets (Huo et al., 2012, Brenning et al., 2012), and for this case two model fitting parameters were found to be sufficient. One of these, the voltage drop across the IR, VIR in the present IRM version, accounts for the power transfer to the electrons, and the other, β, accounts for the probability of back-attraction of ions to the target. The basic reason why these two quantities are so difficult to model is that they both depend on the rapidly varying time- and space-dependent electric forces acting on the charged particles within spoke structures, which are known to spontaneously arise in magnetron discharges (Hecimovic et al., 2015, 2016, 2017, Panjan and Anders, 2017). As the IRM is a volume averaged model, densities are averaged over the azimuthal direction, and thus spatial variations in particle density and potentials (potential humps) associated with these spokes are averaged out. Thus the results of the IRM should be taken as more representing qualitative trends rather than giving quantitative values. Besides the use of VIR and β as fitting parameters, recent IRM-modeling with other target materials (Gudmundsson et al., 2016) has revealed that sometimes a third fitting parameter needs to be added to the list, the probability r of back-attraction of secondary-emitted electrons from the target. Also this parameter is extremely difficult to predict theoretically (Thornton, 1978, Buyle et al., 2003, Revel et al., 2016). In the two discharges studied here, argon working gas with either Al or Ti target, only two fitting parameters are needed.

5.1.3.1

Particle balance

The species assumed in the IRM are electrons, ground state argon atoms Ar, hot argon atoms in the ground state ArH , warm argon atoms in the ground state ArW , metastable

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Table 5.1 The species considered in the non-reactive ionization region model. Species eC

Physics cold electron

eH

hot electron

Ar ArH

argon atom hot argon atom

ArW

warm argon atom

Arm

metastable argon atom

Al Al+ Al2+ Ti Ti+ Ti2+

aluminum atom singly ionized aluminum doubly ionized aluminum titanium atom singly ionized titanium doubly ionized titanium

Comment Bulk electrons assumed to have Maxwellian EEDF Hot population energized by secondary electrons emitted from the target Cold (thermal) argon atoms in the ground state Argon ions that after recombination return as atoms from the target with a few eV energy Argon ions that penetrate the target surface, displace atoms, and then slowly diffuse to the surface and escape as atoms at lower energy ≤ 0.1 eV (the target temperature) (Anders et al., 2012b) Cold (thermal) argon atoms in the metastable state Sputtered particle Sputtered and ionized particle Sputtered and twice ionized particle Sputtered particle Sputtered and ionized particle Sputtered and twice ionized particle

argon atoms Arm , argon ions Ar+ , metal neutrals M, singly ionized metal ions M+ , and doubly ionized metal ions M2+ . Collectively, the electrons are denoted by e, the neutral gas species are denoted by g, and the ions are denoted by i. The species considered in the model are listed in Table 5.1. In a generalized form, the particle balance equation for species X is given by  (X) dn(X)  (X) RGeneration,l − RLoss,j . = dt l

(5.19)

j

The terms RGeneration,l and RLoss,j are the reaction rates of various generation and loss processes related to the plasma chemistry in the IR of species X. The reaction rate Rj for a given reaction j in the volume is calculated as the product of the densities of the reactants and the rate coefficient kj of the reaction, Rj = k j ×



nreactant,l

[m−3 s−1 ],

(5.20)

l

where nreactant,l is the density of the lth reactant. The reaction rates in Eq. (5.19) can also describe additional generation and loss processes due to sputtering Rn,sputt , neutral flux diffusion Rn,diff , gas refill Rg,refill , gas kick-out Rg,kick-out , ion loss out of the IR or to surfaces Ri,loss , and return of recombined positive gas ions Rg,return from the

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target. Each term is discussed in detail in Sections 5.1.3.2 – 5.1.3.4. Note that not all terms are applicable for all species.

5.1.3.2

Neutral particle balance

The rate at which species are sputtered off the target (Al and Ti in the present work) is given by the generation term  RT  SRT Yi (Ei ) , (5.21) Rn,sputt = i i VIR where n stands for a neutral atom sputtered off the target, i stands for the ion involved in the process, iRT is the flux of ion i toward the target with i = Ti+ , Ti2+ , Al+ , Al2+ , or Ar+ , SRT is the area of the sputtered region (race track), Yi (Ei ) is the energydependent sputter yield for ion i bombarding the target, and VIR is the total volume of the IR. The sputter yields depend on the ion energies Ei , which we take to be the discharge voltage VD (t). Thus the sputter yield follows the discharge voltage waveform and is time-dependent (see Gudmundsson (2008)). In addition, neutral atoms produced through volume reactions in the IR and coming from the target are lost as they diffuse out of the IR, described by the loss term Rn,diff =

n,diff , L

(5.22)

where n,diff is the flux of neutral atoms or molecules, and L = z2 − z1 is the distance through the IR, which represents the typical length that species with a directed flow from the target travel when diffusing out of the IR. The flux is

−L n,diff = n,0 exp , (5.23) λn,G where λn,G is the mean free path for a target atom traveling through the working gas, and n,0 is the random flux governed by the thermal velocity of the particle coming off the target. We herein approximate the sputtered Ti and Al neutral-neutral cross sections with a typical effective momentum-exchange cross section of 2 × 10−19 m−2 (Phelps et al., 2000). Approximating with billiard-ball collisions, this value is taken to be independent of the energies of the neutral populations. The velocity of the particle coming off the target is  2eTn vran = |vz | = , (5.24) πmn and Tn is the temperature of the neutral species n. The cathode target of a magnetron is heated by ion bombardment, which leads to an elevated gas temperature close to the target. In addition, during the pulses, there can be a time variation of the gas temperature due to the sputter wind. Both processes have been measured by tunable diode laser absorption spectroscopy (TD-LAS) in a discharge for which an elevated

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169

gas temperature was included in the IRM (Vitelaru et al., 2012, Stancu et al., 2015); see also Fig. 7.9. For the terms Rg,refill , Rg,kick-out , and Rg,return , we will focus on the neutral species of the working gas (here argon). It is well known that gas rarefaction, described in Section 4.2.2, lowers the density of the working gas inside the IR below the gas density of the surrounding gas reservoir, ng,0 (Hoffman, 1985, Rossnagel, 1988, Kolev and Bogaerts, 2008, Lundin et al., 2009). This gives a back-diffusion (gain) term (ng,0 − ng )SBP 1 , Rg,refill = vg,ran 2 VIR

(5.25)

where the subscript g stands for the atoms of the working gas, and vran is their random thermal velocity as defined in Eq. (5.24). In the present case, the argon gas diffusional refill term is determined by the gas temperature and the gas density difference (ng,0 − ng ) between the IR and the surrounding volume. By definition only atoms moving toward the boundary, characterized by the area SBP , are involved so that the densities are taken to be one half of the volume densities. In the IRM, gas rarefaction by the effect of the sputter wind (Hoffman, 1985) is implemented as an argon kick-out term by collisions with fast sputtered particles coming from the target (see also Section 4.2.2). For each of the neutrals G of the working gas, including the metastable states, the particle balance includes the loss term  MM i nM,i 1 vran,M  nG (5.26) Fcoll Rn,kick-out = 2 L MG i nG,i where M here stands for the species sputtered off the target and their ions, singly and doubly ionized. The sum is taken over all the states of that sputtered species. A multiplication of the flux reductions by the mass ratio MM /MG accounts for the conservation of momentum, Fcoll = 1−exp(−L/λM,G ) is the probability of a collision inside the IR (Raadu et al., 2011), and λM,G is the mean free path. As an example, the kick-out term for the ground state neutral argon density equation is, in the IRM, given as   RAr,kick-out = (M,0 − M,diff ) + (M+ ,0 − M+ ,diff ) + (M2+ ,0 − M2+ ,diff ) SBP MM nAr × , (5.27) VIR MAr nAr + nArm   where we have replaced (1/2)vran,M i nM,i in Eq. (5.26) with the flux i M,i , and SBP is the area of the annular cylinder facing the lower density plasma outside the IR (bulk plasma). The outward argon momentum gain is thereby obtained through the reduction of metal outward momentum flow and is therefore proportional to the flux difference between the metal (atoms and ions) outward fluxes that would be obtained in the absence of collisions with argon (indexed “0” in the equation) and the actual metal fluxes reduced by momentum exchange collisions (indexed “diff”). In the IRM, not only cold argon neutrals with density nArC and metastable argon atoms with density nArm , but also two populations originating from argon ions that

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High Power Impulse Magnetron Sputtering

bombard the target and then return to the discharge volume as neutrals, warm argon atoms with density nArW and hot argon atoms with density nArH , are considered. The hot component is assumed to return almost immediately after mixing in the hot spot created by the ion impact. It is therefore ascribed a temperature with an energy of the same order as the sputtered species, typically a few eV. The warm population ArW is assumed to first penetrate the target surface and then to slowly diffuse back as atoms. Its energy is taken to be the thermal energy of the target surface with about 0.1 eV (∼ 1000 K) as an upper bound (Anders et al., 2012b). Furthermore, a fraction ξpulse ξH of the recombined Ar+ ions is assumed to return as hot neutrals ArH during the pulse, and a fraction ξpulse (1 − ξH ) is assumed to return as warm neutrals ArW during the pulse. The hot argon atoms are approximated to have an effective temperature of 4/3 eV (average energy of 2 eV) based on computer simulations (Huo et al., 2012). Here ξpulse is a parameter that tells how much of the trapped Ar is returning during the pulse. In the present case, ξpulse = 1 is assumed (i.e. 100% of the Ar atoms return during the pulse). The choice of ξpulse = 1 is motivated elsewhere (Huo et al., 2012, 2013). A default standard set is as follows: 50% are ArW with TArW = 0.1 eV, and 50% are ArH with TArH = 2 eV. Thus, for hot argon neutrals ArH , there is a generation term RT RArH ,return = ξpulse ξH Ar +

SRT , VIR

(5.28)

RT is the flux of Ar+ ions toward the target. For the generation of warm where Ar + neutrals, in Eq. (5.28), ξH is replaced by (1 − ξH ). Coming from the target, the hot argon neutrals ArH and the warm argon neutrals ArW have a directed flux away from the target, giving a loss out of the IR at random velocity (Eq. (5.24)), and thus the loss rate

RArZ ,loss = vran nArZ

SRT , VIR

(5.29)

where Z is H for hot and W for warm argon atoms. The need to assume the two parameters ξpulse and ξH for the recombined Ar atoms from the target is one of the weak points of the IRM. If accurate modeling of gas recycling is desired, then these should either be varied to test their influence as in Huo et al. (2012, 2013, 2014) or assessed separately. For the present discharges, a sensitivity analysis showed a small effect of gas recycling (Huo et al., 2017). The parameter ξH is therefore put in the middle of the possible range from 0 to 1. We want to stress, however, that it sometimes might be important to choose the parameters for the ArH and ArW populations with more care. This would typically be the case if the magnetron sputtering discharge has a larger size or if the plasma density and/or electron temperature are higher. These changes should increase the probability of ionization of the hot and warm argon gas components, followed by back-attraction to the target. The existence of discharges where this process is even dominating has been demonstrated by Anders et al. (2012b). Using a discharge with a graphite target, they demonstrated that an argon gas recycling trap can develop if the discharge current is high enough. Working gas recycling is dealt with in Section 7.2.1.

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5.1.3.3

171

Ion particle balance

For each ion, there is a loss rate given as Ri,loss =

iBP SBP + iRT SRT , VIR

(5.30)

where i stands for the particular ion, and iBP is the flux of ion i across the boundary toward the lower density plasma in the DR. However, even though most of the potential falls across the sheath, a fraction of the potential generally penetrates into the ionization region (Bradley et al., 2001). Thus the ions have a larger probability to be attracted back to the target. To account for this, an adjustable probability β that accounts for the back-attraction of ions is used in the IRM. Thus the flux density out of the IR toward the lower density plasma is reduced as required to obtain the assumed ion back-attraction probability β:

1 SRT RT BP  . (5.31) −1 i = β SBP i In earlier versions of the model (Gudmundsson, 2008, Raadu et al., 2011), it was assumed that the ions cross the sheath edge at the race track with the Bohm speed. This assumption turns out to be inconsistent with a significant potential drop over the extended presheath, in the range 10 – 100 V, as has been observed experimentally in the HiPIMS discharge (Mishra et al., 2011, Rauch et al., 2012). Therefore, here, as in more recent versions of the IRM, we present an improved treatment. Instead of accounting for spread-out ionization within the IR at various distances from the target, an approximation based on average quantities is made. The main assumptions are that the average ion that ends up at the target was produced in the middle of the IR, at a distance (z2 − z1 )/2 from the sheath edge, and that the potential difference from this position to the sheath edge is VIR /2. The loss time in the IR for this average ion under these assumptions is z2 − z1 . tloss = qi VIR mi

(5.32)

The number of ions i in the IR is ni VIR = ni SRT (z2 − z1 ),

(5.33)

where ni is the density of ion i. Since only a fraction β of the ions are destined to go to the race track, the total flux toward the race track can be written as β×(number of ions in IR)/(loss time). Note that this implies that tloss of Eq. (5.32) is valid also for ions that go to the bulk plasma. This gives iRT SRT =

βni SRT (z2 − z1 ) . tloss

(5.34)

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High Power Impulse Magnetron Sputtering

Division by SRT gives the flux to the race track:  qi VIR , iRT = βni mi

(5.35)

where qi is the ion charge.

5.1.3.4

Electron balance

Two electron populations are implemented in the IRM: one cold, eC , and one hot, eH . The cold electrons are created in the IR volume, and the hot secondary electrons are ejected from the cathode and are described in more detail in Section 5.1.3.5, where the power balance is discussed. The quasineutrality approximation holds with good precision in the IR, and the cold electron density can be written as   nec = Zi n+,i − n−,j − neh , (5.36) i

j

where Zi is the charge state of the positive ion i, n+,i is the density of the positive ion i, n−,j is the density of the negative ion j , and where the density of hot electrons is obtained from their effective electron temperature Teh and their electron energy density peh (see Section 5.1.3.5) as neh =

peh . eTeh

(5.37)

The quasineutrality approximation in the IRM is used only to obtain the electron density in the ionization region from the total ion charge density through Eqs. (5.36) and (5.37). When used for this limited purpose, it is valid under the condition λDe / lc 1, where λDe is the electron Debye length, and lc is the system length scale, which, for HiPIMS discharges, is satisfied by typically more than three orders of magnitude. Notice that the quasineutrality assumption gives neither values nor constraints regarding the electric fields and potentials. In the IRM the electric fields and potentials are assessed through the power balance as described in Section 5.1.3.5.

5.1.3.5

Power balance

The power balance equates the power absorbed by the plasma electrons to power losses due to processes, such as elastic and inelastic collisions, de-excitation, and Penning ionization. Before treating the power balance, we will first describe the cold and hot electron populations and how electrons are heated. The use of two electron populations has essentially two effects. First, this treatment gives a more accurate account of the cost of ionization as a function of electron energy. For example, metal ionization degree, degree of self-sputtering, and bulk electron temperature tend to decrease, whereas gas rarefaction and plasma density tend to increase if two electron populations are assumed, as compared to the first version of the IRM, where only one electron population is assumed (Raadu et al., 2011). These trends can be understood from the

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173

lower energy cost of ionization by the now introduced population of hot electrons. Second, this makes it possible to quantify two mechanisms of electron heating: secondary electron acceleration across the sheath and Ohmic heating within the IR, which is discussed in detail in Section 7.2.3. The power transfer to the electrons is given by Pe = PSH + POhm ,

(5.38)

where Pe is split up into sheath energization PSH and Ohmic heating POhm within the IR. This is achieved by splitting the discharge voltage up into the potential drop over the cathode sheath and the potential drop over the ionization region, VD = VSH + VIR . In each volume, the electrons get a part of the total electric power, ID VSH and ID VIR , respectively, which is given by the fraction of the current the electrons carry. The electron current in the sheath is obtained from the model-calculated ion currents to the target as

1 PSH = Ie,SH VSH = IAr+ γAr+ ,eff + IM2+ γM2+ ,eff VSH , (5.39) 2 where γAr+ ,eff = γAr+ m e (1 − r) is the effective secondary electron emission yield for Ar+ ions bombarding the target, γM2+ ,eff = γM2+ m e (1 − r) is the effective secondary electron emission yield for doubly ionized metal ions bombarding the target, and e represents the fraction of the electron energy that is used for ionization before being lost from the discharge process (Thornton, 1978). The terms within the parentheses give the numbers of secondary electrons that are emitted by argon ions IAr+ γAr+ and twice ionized metal ions IM2+ γM2+ from the target. The number of electrons that actually leave the cathode is reduced by the recapture probability r, whereas the factor m (equal to or greater than unity) accounts for ionization within the sheath (Depla et al., 2009). Here we assume that m e = 1. The factor 1/2 in front of the second term accounts for the fact that each M2+ ion carries a charge 2e. There is no IM+ γM+ term because the secondary emission coefficient of the single ionized metal γM+ = 0 for the ion energy range studied here, below 1 keV (Baragiola et al., 1979) as discussed in Section 1.1.4. Within the IR the electrons are heated by Ohmic heating (Huo et al., 2013) given by

 Ie POhm = Ie,IR VIR = (5.40) ID VIR . ID Here Ie /ID  is the volume average of the fraction of the discharge current in the IR carried by electrons. As an average over the ionization region, we typically take Ie /ID  ∼ 1/2 (Huo et al., 2013). The sheath potential is given by VSH = VD − VIR . In the IRM, VIR is defined as a fraction of the total applied discharge voltage, VIR = f VD . The two routes of electron heating are depositing energy into different parts of the electron energy distribution function (EEDF). These electron populations have different ionization rate coefficients and different effective costs of ionization and therefore are treated separately as one hot and one cold component. As shown and discussed in

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detail by Huo et al. (2013), a combination of two fortunate circumstances: (i) the cold population is kept Maxwellian mainly due to the high plasma density, and (ii) the ionization rates for the hot population exhibit only small variations in the energy range 30 – 1000 V, which means that there is no need to resolve the details of the high-energy EEDF. This makes it possible to put forward a quite accurate and yet simple model for the ionization rate for the complicated EEDF in HiPIMS discharges. Further details of the cold and hot electron populations are given by Huo et al. (2017). The temporal development of the cold electron temperature is followed by the rate equation I  3 dTec ID VD e f nec = Ehtc νizH + 2 dt ID IR eVIR

3 C + Edex kdex nArm − Edex − Eiz,M − Tec kP nArm nM 2



3 3 Ar C Arm C − Ec,C,eff + Tec kiz,Ar nec nAr − Ec,C,eff + Tec kiz,Ar m nec nArm 2 2



3 3 ArH C ArW C − Ec,C,eff + Tec kiz,Ar Tec kiz,Ar H nec nArH − Ec,C,eff + W nec nArW 2 2



3 3 M C M+ C − Ec,C,eff + Tec kiz,M nec nM − Ec,C,eff + Tec kiz,M + nec nM+ , 2 2 (5.41) where f is used as the first fitting parameter, as defined below Eq. (5.40). An ionization then gives an energy loss Ec,eff +Ehtc , where Ec,eff is the effective cost of ionization (Lieberman and Lichtenberg, 2005, pp. 81–82), and the term Ehtc (htc for hot-to-cold) provides an energy input into the cold electron energy equation. Also,  H H H W nAr + kiz,Ar n + kiz,Ar νizH = neh kiz,Ar m nArm + k W nArW iz,ArH ArH  H H + kiz,M nM + kiz,M + n M+

(5.42)

is the ionization frequency [ionizations m−3 s−1 ] of the hot electron population. The first two terms on the right-hand side of Eq. (5.41) correspond to the energy gain from hot electrons and the total input power, respectively. The remaining terms describe the inelastic electron collisions. The third term is due to electron impact de-excitation of metastable argon atoms, which represents an energy gain term for electrons, the fourth term is to account for Penning ionization of the metal atom, the terms five to eight are due to electron impact ionization of argon atoms, the ninth term represents electron impact ionization of the metal atom, and the tenth term represents electron impact ionization of the metal ion that creates M2+ . The terms (3/2)TeC in Eq. (5.41) refer to the average energy required for a new free electron to obtain the average cold electron temperature. For further details and additions of negative ions to the model, we refer to Gudmundsson et al. (2016).

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The hot electrons are followed by a rate equation for the density rather than for the temperature or average energy: 

dneh 1 1 (1 − f )VD = (1 − r) e m γAr+ IAr+ + γM2+ IM2+ dt FWHe VD 2 eVIR   H Ar H + Edex kdex neh nArm − Ec,C,eff + Ehtc kiz,Ar nArm neh  m  H   Ar H Ar H − Ec,C,eff + Ehtc kiz,Ar n n m nArm neh − Ec,C,eff + Ehtc k iz,ArH ArH eh  W    Ar H M H − Ec,C,eff + Ehtc kiz,Ar W nArW neh − Ec,C,eff + Ehtc kiz,M nM neh   +  M H − Ec,C,eff + Ehtc kiz,M+ nM+ neh . (5.43) The square brackets keep track of the rate of change of the total energy in the hot population. The first term inside the bracket is the energy obtained by the hot electrons through the sheath. The other terms describe the inelastic collisions of the hot electrons. Losses across the boundaries are neglected. Dividing the total energy by the average energy of the hot electrons (FWHe VD ) gives the density. Here FWeH = 0.5 is used as a default value.

5.1.3.6

Plasma chemistry

The working gas Ar+ ions are treated as one population in all versions of IRM. The rate equation for nAr+ therefore contains gain terms representing ionization from the hot and warm populations of argon atoms. The energy loss per electron–ion pair created by the cold electron population for the argon atom in the ground state is calculated as discussed by Hjartarson et al. (2010). The argon reaction set and rate coefficients used in the model are listed in Table 5.2. The rate coefficients are calculated assuming a Maxwellian EEDF for the cold electrons valid in the range 1 – 7 eV and for the hot electrons valid in the range 200 – 1000 eV. The argon reaction set is rather simple as we consider only argon atoms in the ground state and metastable argon atoms, where the two 4s metastable levels (3 P0 and 3 P2 ) are combined to give one effective metastable species. Metal ions are created by electron impact ionization, by Penning ionization, collisions of metal atoms with electronically excited argon atoms (Arm + M −→ M+ + Ar + e) with rate coefficient kP = 5.9 × 10−16 m3 /s for Al (Lu and Kushner, 2000) and 3.17 × 10−15 m3 /s for Ti (Stancu et al., 2015), and through charge exchange Ar+ + M −→ M+ + Ar with rate coefficient kchexc = 1 × 10−15 m3 /s (Lu and Kushner, 2000). The rate coefficient for the electron impact ionization of aluminum is calculated from the electron impact ionization cross sections given by Freund et al. (1990). The rate coefficient for electron impact ionization of Al+ to create Al2+ is based on the cross sections given by Hayton and Peart (1994) and McGuire (1982). The first ionization potential of Al is 5.99 eV, whereas the second ionization potential is 18.8 eV. The collisional energy loss EcAl per electron–ion pair created for the aluminum atom is

Table 5.2 A reaction set for electron–argon, argon–argon, electron–metal, and argon–metal reactions included in the ionization region model. The rate coefficients are calculated assuming a Maxwellian electron energy distribution function and fit in the range Te = 1 – 7 V for cold electrons and 200 – 1000 V for hot electrons. Reaction e + Ar →

Ar+

+e+e

Rate coefficient [m3 /s]

Ref.

2.34 × 10−14 Te 0.59 e−17.44/Te (cold)

(Gudmundsson and Thorsteinsson, 2007)

8 × 10−14 Te 0.16 e−27.53/Te (hot) e + Arm → Ar+ + e + e

6.8 × 10−15 Te 0.67 e−4.2/Te (cold)

(Lee and Chung, 2005)

5.7 × 10−13 Te −0.33 e−6.82/Te (hot) 2.5 × 10−15 Te 0.74 e−11.56/Te (cold)

e + Ar → Arm + e

(Lee and Chung, 2005)

3.85 × 10−14 Te −0.68 e−22/Te (hot) 4.3 × 10−16 Te 0.74 (cold)

e + Arm → Ar + e

(Ashida et al., 1995)

4.3 × 10−16 Te 0.74 + 4.957 × 10−14 Te −0.39 e−7.78/Te + 2.67 × 10−15 (hot) e + Ti → Ti+ + e e + Ti+ → Ti2+ + e

2.8278 × 10−13 Te −0.0579 e−8.7163/Te (cold)

(Deutsch et al., 2008)

1.1757 × 10−12 Te −0.3039 e−21.1107/Te (hot)

(Bartlett and Stelbovics, 2004)

1.8556 × 10−14 Te 0.4598 e−12.9927/Te (cold)

(Diserens et al., 1988)

8.1858 × 10−12 Te −0.669 e−200.93/Te (hot) Ar+ + Ti → Ar + Ti+

1 × 10−15

Estimated due to lack of data

3.17 × 10−15

(Stancu et al., 2015)

e + Al → Al+ + e

1.3467 × 10−13 Te0.3576 exp(−6.7829/Te ) (cold)   exp −0.074347[log(Te )]2 + 0.637867 log(Te ) − 29.516747 if Te > 81 eV (hot)

(Freund et al., 1990)

e + Al+ → Al2+ + e

2.34 × 10−14 Te0.59 exp(−17.44/Te ) (cold)   exp −0.1008[log(Te )]2 + 1.2011 log(Te ) − 34.5841 if Te > 7 eV (hot)

(Hayton and Peart, 1994, McGuire, 1982)

e + Al → Al(4s) + e

1.821 × 10−12 Te0.8679 exp(−6.975/Te ) (cold)

(Wells and Miller, 1975)

e + Al → Al(3d) + e

5.7148 × 10−12 Te−1.2858 exp(−6.975/Te ) (cold)

(Wells and Miller, 1975)

e + Al → Al(4p) + e

1.7195 × 10−12 Te−1.3692 exp(−9.0616/Te ) (cold)

(Wells and Miller, 1975)

e + Al+ → Al + e

10[−0.0104(log(E))

(Wells and Miller, 1975)

Arm

+ Ti → Ar +

Ti+

+e

Ar+ + Al → Ar + Al+ Arm

+ Al → Ar +

Al+

+e

2 +0.1134(log(E))−11.700]

(cold)

1 × 10−15

(Lu and Kushner, 2000)

5.9 × 10−16

(Lu and Kushner, 2000)

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calculated using the electron impact ionization cross section, electron impact excitation cross section (to levels 4s, 3d, and 4p only), and elastic cross sections calculated by Wells and Miller (1975). The electron impact ionization cross section for Ti is taken from Bartlett and Stelbovics (2004) and Deutsch et al. (2008), and the electron impact ionization cross section for Ti+ to create Ti2+ is taken from the measurements of Diserens et al. (1988). The first ionization potential of Ti is 6.82 eV, whereas the second ionization potential is 13.58 eV. The rate coefficients for ionization of Ti and Ti+ are listed in Table 5.2. To calculate the collisional energy loss EcTi for Ti, the electron impact ionization cross section (Bartlett and Stelbovics, 2004, Deutsch et al., 2008) with ionization potential of 6.828 eV was used. Furthermore, the nine lowest excited levels located at 0.81, 0.9, 1.43, 1.97, 2.09, 2.29, 2.40, 2.47, and 2.66 eV are included, and it is assumed that each excitation cross section follows the Thomson cross section (Lieberman and Lichtenberg, 2005, p. 72) with a peak at 1/5 of the peak of the ionization cross section. The cross section for electron elastic scattering by Ti is assumed to be the same as for nitrogen atoms (Neynaber et al., 1963, Ramsbottom and Bell, 1994). For the secondary electron emission yield for argon ions bombarding an aluminum target, the values measured by Yamauchi and Shimizu (1983) are used. A fit to their measured values in the range 700 – 1500 V gives γAr+ = 0.0769 + EAr+ × 1.1823 × 10−5 , where EAr+ is the Ar+ ion bombarding energy in eV, which is extended to zero 2/3 energy. For self-sputtering Al+ −→ Al, the sputter yield used is YSS,Al = 0.016EAl+ , based on the data collected by Hayward and Wolter (1969) and the calculation by the SRIM code given by Anders et al. (2007). For argon sputtering aluminum Ar+ −→ Al, the sputtering data collected by Ruzic (1990) are used, which up to 1000 eV is well fitted as Ysput,Al = 2.16 × 10−3 EAr+ . For self-sputtering Ti+ −→ Ti and Ti2+ −→ Ti and for argon sputtering titanium Ar+ −→ Ti, a fit to the data given by Anders et al. (2007) is used.

5.1.4 Particle-in-cell The particle-in-cell (PIC) method is probably the most powerful technique for simulating the magnetron sputtering discharge. When the PIC method is coupled to the Monte Carlo collision scheme (discussed in Section 5.1.5), the combined method is referred to as particle-in-cell Monte Carlo collision (PIC/MCC) method. The PIC modeling technique was extensively described in the reference book of Birdsall and Langdon (2004). Application of this technique to simulate dcMS discharges, including a discussion of advantages and drawbacks, were presented by Bogaerts et al. (2008), offering a large bibliography on the subject. In addition to the direct current or radio-frequency operation modes, the HiPIMS regime comes with its own challenges that the PIC method has to overcome, such as a high plasma density (above 1018 m−3 ), strong gas rarefaction (discussed in Section 4.2.2), time-dependent changes of the magnetic field due to large discharge currents (tens – hundreds Amperes), and so on. The basic idea of the PIC method is to allow typically a few hundred thousands computer-simulated particles (superparticles or macroparticles) to represent a significantly higher number

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of real particles (density in the range 1014 – 1018 m−3 ) (Birdsall, 1991, Verboncoeur, 2005, Tskhakaya et al., 2007). The PIC technique consists of following the macroparticles in time and space, considering for each macroparticle the local electric and magnetic field. The particle interaction is handled through macroforces acting on the particles that are calculated using the field equations at points on a computational grid. Usually, the electric field is self-consistently calculated and constantly updated, whereas the magnetic confinement field is often assumed to be static when simulating a magnetron sputtering discharge. The plasma potential is calculated by solving the Poisson equation at every time step. Both time and space are discretized, and the velocity space is treated fully (3D). Along their trajectory, the macroparticles can experience different types of collisions, which are treated by the Monte Carlo method (Metropolis et al., 1953) discussed in Section 5.1.5. After each time-step, the macroparticles accounted for in each space cell and the space charge are estimated assigning each macroparticle to the surrounding mesh nodes. Each macroparticle has an associated weight corresponding to a given number of real particles. As a result, the method can deliver, in a temporal sequence, the distribution function of the charged particles (and neutrals if considered in the model) in phase space (coordinates–velocity). By integrating the latter ones different macroscopic plasma parameters can be obtained: particle density, particle flux, mean kinetic energy for each particle (which, in the case of thermodynamic equilibrium, is a measure of the temperature), and discharge current. PIC/MCC has been successfully applied to simulate dcMS discharges in noble gases (Kondo and Nanbu, 1999) and reactive mixtures (Nanbu et al., 2000), as well as radio frequency (rf) magnetron sputtering discharges (Minea, 1998), mostly in 2D configurations assuming axial symmetry, that is, the azimuthal component of the magnetic field is zero. The tremendous advance in computing power and programming facilitated the extension to fully 3D simulations of dcMS discharges in recent years (Pflug et al., 2014), although the first attempts of this kind were already made in the 1990s (Nanbu and Kondo, 1997), but still at low power and hence limited plasma density (< 1016 m−3 ). As an example, simulation of a dcMS discharge in 2D requires about 20 µs of discharge time to reach a steady state (Bogaerts et al., 2008, Yusupov et al., 2012) and takes about one week of computing time on 32 cores (parallel computer). The simulation starts with an arbitrary initial condition, and the discharge evolves toward the steady state. For an rf discharge, at least 100 rf periods are necessary to reach convergence, which corresponds to about 8 µs for an excitation frequency of 13.56 MHz (Minea, 1998). The reason for the need to simulate several periods is due to the unknown initial conditions. The simulation must run until the memory of the arbitrary initial conditions is lost, taking into account that the beginning and the end of the same period are identical. Note that the rf steady state is given by the current balance onto the cathode between electrons and positive ions, leading to a constant self-bias (similar to dcMS). If the initial conditions were completely known (including here also the self-bias voltage), a single period simulation would be enough to achieve the full solution.

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In the case of a HiPIMS discharge, a time span of the order of 10 µs barely covers the width of very short pulses found in the literature (Ganciu et al., 2005), whereas most of the HiPIMS power supplies deliver longer pulses, i.e., a time span in the range of several tens of µs, which is required to obtain a significant discharge current rise, as discussed in Section 2.2.5. For these HiPIMS discharges, the plasma parameters at the beginning of the pulse are not known. Still, the different species of active particles at the beginning of the pulse are those that survived through the off-time phase of a HiPIMS period (or from the previous pulse) (see also Section 4.1.2). Neither the number of species nor their density is well defined, so the simulation of such a case should start with an arbitrary initial condition, and it should be treated similarly to an rf discharge. However, as the HiPIMS repetition frequency can be of the order of kHz, it is quite challenging to simulate even one period (of the order of ms), not to mention several periods, due to limitations in available computing power. Fortunately, there is a solution that makes it possible to obtain meaningful results from the simulation of a single pulse only. It is based on using a power supply with pre-ionization of the gas before the application of the high power pulse (Ganciu-Petcu et al., 2011) (see also Section 2.2.4). Pre-ionization refers to maintaining a low power dc discharge (voltage below 300 V and a current of a few mA) that provides the seeds of charge at the beginning of the HiPIMS pulse. This ensures a very fast rise of the discharge current, which is of the order of µs, as shown in Fig. 5.2. This represents a huge advantage allowing us to reach the discharge current plateau much faster (∼ 2 µs) while only simulating a single short pulse of a few µs, as reported by Minea et al. (2014) and Revel et al. (2018). In the examples discussed here, the pre-ionization stage starts at about 0.8 ms after the previous pulse ends, and it is on until the onset of the following pulse. Increased pulsing frequency results in a reduced pre-ionization dc voltage (Fig. 5.2A) until the voltage vanishes when the number of charged particles surviving from the previous pulse are numerous enough to ensure a fast rise of the current. For the simulation of a HiPIMS discharge with pre-ionization, the input (initial conditions) is the result of a PIC/MCC simulation of a low-power dcMS discharge.

5.1.4.1

Challenges of HiPIMS PIC simulations

There exists a large amount of information on PIC simulations of plasma discharges in the literature (Birdsall, 1991, Verboncoeur, 2005, Tskhakaya et al., 2007), which will not be discussed here. Instead, we will focus on the challenges of simulating a HiPIMS discharge by PIC/MCC. Let us first underline some important differences between dcMS discharges and pulsed magnetron sputtering discharges, as already discussed in Chapters 1 and 3. The density of the charged particles is at least two orders of magnitude higher in HiPIMS discharges compared to dcMS discharges, which results in a significant ionization of the sputtered species. Additional challenges include transitory, out of equilibrium discharge regimes (nano-to-microsecond scale) including also instabilities that are present in the HiPIMS discharge. Other differences involve the large discharge currents in HiPIMS discharges, which may potentially modify the magnetic trap. Furthermore, strong sputtering leads to gas rarefaction. Some of these aspects are discussed further below.

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Figure 5.2 The discharge (A) voltage and (B) current waveforms for HiPIMS pulses with pre-ionization and of different pulse lengths. The discharge was operated with argon as the working gas at p = 1.33 Pa with a FINEMET-type target, where an average power of 30 W was ensured for all pulses by changing the repetition frequency in the range of 0.05 – 2 kHz. Republished with permission of Elsevier, from Velicu et al. (2014); permission conveyed through Copyright Clearance Center, Inc.

In the HiPIMS discharge, the peak plasma density in the negative glow (or the IR (Raadu et al., 2011)) exceeds 1018 m−3 (Meier et al., 2018), whereas in the diffusion region (DR) (extending from the IR to the substrate) the plasma density is about 1016 m−3 (Minea et al., 2014). The Debye length corresponding to such densities is plotted in Fig. 5.3 with respect to the electron temperature. We recall here that the Debye length in cm is given by  Te λD ≈ 744 , (5.44) n0 where the electron temperature Te is given in eV, and the plasma density n0 is given in cm−3 . For typical HiPIMS discharge conditions, with an electron temperature of 5 eV and a plasma density of 1018 m−3 , the Debye length is λD ≈ 16 µm. An increase in

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Figure 5.3 The Debye length as a function of the electron temperature.

Figure 5.4 The spatial distribution of the Debye length in a typical HiPIMS discharge, obtained from PIC/MCC simulation. A rectangular magnetron cathode 40 mm wide (in the x direction) and infinite length (in the y direction), centered at (x, z) = (0, 0) is simulated. The anode is situated at z = 25 mm from the cathode. The discharge was operated with 0.4 Pa Ar as the working gas, short 6 µs HiPIMS pulses with pre-ionization and a pulse voltage VD = 800 V. The color scale shown is defined in terms of the Debye length for Teff = 5 eV and ne = 1018 m−3 or λD0 ≈ 16 µm. From Revel et al. (2018). ©IOP Publishing. Reproduced with permission. All rights reserved.

the plasma density by two orders of magnitude will reduce the Debye length by one order of magnitude, whereas an increase of the electron temperature by two orders of magnitude will increase the Debye length by one order of magnitude. Since HiPIMS discharges are strongly inhomogeneous with considerable gradients in electron/ion density and particle energy (see Sections 3.2 and 4.1.2 for details on the electron and ion density evolution, respectively), the Debye length also exhibits a large variation across the plasma volume. An illustrative example is given in Fig. 5.4, which shows a 2D map of the Debye length calculated using the result of a prior PIC/MCC simulation of a HiPIMS discharge pulse (Revel et al., 2018). Within the IR the Debye length is found to be in the range between ten and one hundred µs, whereas in the DR, it is about 0.5 – 1 mm. This aspect will introduce a strong limitation on the simulation process since an important stability criterion of the explicit PIC scheme is to have the spatial

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cell size comparable with the Debye length (Birdsall and Langdon, 2004). Simulations of a discharge at comparable high density show that the PIC results stay valid up to 3 times the Debye length (Okuda, 1972). The reduction of the Debye length affects at least three important parameters that determine the time step and the simulation time. Firstly, if a uniform space grid is used, then the cell size should be correlated to the shortest Debye length. For a small but significant plasma volume (at least 20 mm radius and 30 mm height), considering axial symmetry, the number of mesh nodes would be 6 × 106 . As the electric field is updated every time step, Poisson’s equation must be solved for each step as well, which requires tremendous computational resources. As an example, for the mesh corresponding to the representation shown in Fig. 5.4, the iterative Poisson solver takes about 1 second (the direct method would take several seconds), and the typical time-step is 10−11 s. A simulation of a 10 µs HiPIMS pulse in real time therefore requires 106 s. This rough estimate ignores the time required to move the particles in the plasma. Secondly, a small cell size (≈ λD ) requires a smaller time step. According to the Courant–Friedrichs–Lewy (CFL) stability criterion (Courant et al., 1928), the time step should provide an upper limit so that each simulated particle moves a distance smaller than the cell size during one time step. Otherwise, the particle energy will be affected by numerical heating, a nonphysical mode that increases the energy of the charged particles by moving the particles in an electric field, which is assumed constant during one time step, whereas, in reality, the electric field is changing when the particle moves from one cell to another. In the cathode sheath (but not only in this region), electrons can attain hundred of eVs, and thus the time step has to be significantly reduced. One solution to this problem is to use time-dependent uniform grids: the cell size of the grid is modified each time when the Debye length becomes larger than the cell size (Minea et al., 2014). The time step should be adjusted accordingly. For example, for a low plasma density with a maximum of 1016 m−3 , the cell size can be 50 µm, and a reasonable time step can be 5 × 10−12 s (assuming that the highest energy of the electrons is 100 eV). When the plasma density reaches 1018 m−3 , the cell size should be 10 µm or less, and the time step should be shorter than 1 × 10−12 s. Since the discharge voltage is of the order of a few hundred volts during the HiPIMS pulse (see Section 2.2 for examples), it is expected that the highest energy of the electrons in the cathode fall to be much larger than 100 eV. In such a case, the order of magnitude of the time step becomes 10−13 s. Another solution is to use nonuniform grids, preferably time-dependent (Revel et al., 2018). In this situation the grid must be very fine in the high-density region and in the cathode fall (for an accurate description of the cathode fall) and coarse in the rest of the plasma volume. The number of macroparticles per cell has to be high enough to give consistency to the PIC model (typically 50 or higher). Hence, a small cell size (≈ λD ) requires more test particles to simulate the discharge and thus larger storage capacity (> 10 Gb) in addition to longer computing time. In the simulation, the nonuniform grid reduces both the number of mesh nodes and the number of total macroparticles. It is also worth noting that the very high discharge currents can potentially lead to modifications of the magnetic trap. This question was addressed by Bohlmark et al. (2004). They found that for discharge currents up to 100 A, the change of the confining

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magnetic field in front of the target due to the Hall current is negligible. Only a 2 mT shift of the magnetic field strength was observed for 160 A peak discharge current. Thus the magnetic field can be taken as a constant for discharge currents up to 50 A. However, with increased computer capacity, higher discharge currents could become accessible with numerical simulation that would solve Maxwell’s equations instead of the Poisson equation. Another challenge is related to the neutral particle dynamics. The working gas density during the HiPIMS pulse may decrease significantly due to mechanisms such as the sputter wind and direct ionization losses, discussed in Section 4.2.2 and collectively referred to as gas rarefaction. The effect of gas rarefaction is more important for long discharge pulses (longer than 10 µs). Taking into account gas rarefaction in PIC/MCC simulations requires treating the neutrals as individual species, with an inhomogeneous and time-dependent particle density (and even temperature). This means that neutrals have to be followed as well, in time and space, which will require more computing time. A less time-consuming approach would be to define a space–time map of the density/temperature of the neutrals. In this case, the simulation might lose its self-consistent character, unless the map is calculated in accordance with the experimental findings. In the case of very short pulses (< 5 µs), gas rarefaction can however be neglected (Kadlec, 2007, Minea et al., 2014).

5.1.4.2

Pseudo-3D PIC

In most cases, axisymmetric systems are treated by 2D approaches, obtaining good averaged results. However, the 2D models assume a uniform plasma along the third dimension, which is not acceptable when transitory phenomena propagating in the azimuthal direction (plasma instabilities or spokes) have to be investigated (see Sections 7.3 and 7.4 concerning these phenomena). For such a purpose, the 2D PIC/MCC technique was extended to the so-called Pseudo-3D PIC (Revel et al., 2016). A precise simulation of spokes requires the full 3D treatment, which is so far inaccessible for high-density plasmas and large dimensions as in HiPIMS and hardly compatible with the computing power of present computers.2 The extended method instead uses the results of a 2D PIC/MCC simulation as input, keeps these results unchanged, and investigates the plasma behavior along the third spatial dimension (azimuthal direction). The numerical treatment is identical to PIC/MCC, the only difference being that the Poisson equation is solved only in 2D in the two other orthogonal planes that include the azimuthal direction. Hence, it is possible to obtain an estimation of the dependence of the electric field in 3D (Revel et al., 2016). The spatial and temporal domains can be reduced with respect to the primary PIC/MCC simulation to the space region or time interval characteristic for the required investigation. For example, in the axial direction the spatial domain can be limited to the ionization region over the race track, where spokes have been observed (Anders, 2014). Hence, the simulation time can be drastically reduced, since 2 The full explicit 3D PIC simulation of a dcMS discharge on 100 cores (parallel computer) would take

roughly 3 days/µs. In the case of a HiPIMS discharge, the full 3D computation time would exceed 30 days/µs.

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the plasma phase is well established and known in 2D. This Pseudo-3D PIC scheme only updates the azimuthal component of the electric field, which is mainly modified due to fluctuations of the plasma density, that is, exactly the phenomena at the origin of spokes (Tsikata and Minea, 2015, Revel et al., 2016). The resulting algorithm runs much faster (at least ten times) than a full 3D PIC code.3 The Pseudo-3D PIC code does not offer the advantages of a full 3D code, but it allows obtaining valuable qualitative results on transitory phenomena or instabilities associated with the third dimension.

5.1.5 Monte Carlo simulations Monte Carlo simulations (Metropolis and Ulam, 1949, Metropolis et al., 1953) are very powerful and largely used in various fields of physics, including plasma physics. There are some important differences between the kinetic approach and the Monte Carlo (MC) algorithm, although both can give a numerical solution for the electron energy distribution function (EEDF). In kinetic modeling the Boltzmann (or Fokker– Planck) equation is solved numerically, whereas in the Monte Carlo method, no equation is solved. The Monte Carlo method approaches the solution (the shape) of the EEDF without solving any equation, but instead takes into account all the interactions of the electrons within the plasma discharge. The Monte Carlo routines follow a large set of test particles in the simulated plasma volume. Each particle follows a different path, depending on the interaction it experiences, but finally, repeating the same experiment for a large amount of particles, the most frequent events are observed, and hence the behavior of the whole set of test particles becomes representative for the considered species (electrons, ions, neutrals, etc.). The transport of these particles assumes the knowledge of the local force field. If this field is known, then the MC method can be used in a predictive manner. Most of the time, the field is imposed, and the results consequently depend on the used field. To overcome this drawback, the Monte Carlo method can be incorporated into PIC modeling (discussed in Section 5.1.4). Coupling these two techniques gives one of the most powerful modeling approaches, known as the particle-in-cell Monte Carlo collision method. It is particularly powerful as a technique to explore low-pressure plasma discharges. However, another piece of information is required to correctly treat the particle interaction, the appropriate interaction cross sections. Reliable atomic and molecular data are essential for any plasma modeling. We further introduce the Monte Carlo collision (MCC) technique and other related Monte Carlo schemes below. We also show how Monte Carlo routines are used to obtain the interaction cross section and the fraction of ionization of sputtered metal. We also describe direct simulation Monte Carlo (DSMC) since it can be used to simulate the neutral particle transport. Finally, we describe a posteriori Monte Carlo since this is an attempt to overcome the intrinsic limitations of conventional Monte Carlo methods. 3 Pseudo-3D PIC takes typically less than 1 day to simulate a 10 cm-long race track for 2 µs.

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185

Monte Carlo collision simulations

Theoretically, the MCC method consists of checking the probability of particle collisions at every time step. However, in practice, the probability for a collision is randomly generated and presented as a number in the range between 0 and 1 allowing calculation of the collision moment. It is difficult to implement the MCC technique in this way since the estimation of the collision time involves the integration of the collision frequency over the entire time interval from the last collision (Haile, 1992). Note that the collision frequency depends on the energy of the macroparticle and hence on time. Therefore, the MCC method is often coupled to the null collision technique (Skullerud, 1968, Brennan, 1991). Using this latter approach, a time-of-flight is defined for each test particle (macroparticle in PIC/MCC), τcoll = ln(rnd)/νtot , where rnd is a randomly generated number between 0 and 1, and νtot is a constant greater than the maximum value of the total collision frequency. Note that νtot sums the collision frequencies of all possible collisions and typically depends on the energy of the macroparticle (since the collision cross section depends on the energy). After moving through the time interval τcoll , a second random number is generated to check if the macroparticle collides (real) or not (null). If a collision occurs, then the type of collision is assigned, followed by the collision treatment (momentum and energy conservation). The selection process is made by comparing the random number to the progressive sum of the collision frequencies normalized to νtot . A new time-of-flight is subsequently calculated, and the particle continues its movement except if it is ionized or reaches an electrode (wall).

5.1.5.2

Monte Carlo simulation of neutral particle transport

Most of the works using the Monte Carlo technique aim to quantify the statistical behavior of one type of particle species followed in time and space. Generally, a Monte Carlo simulation is run in three dimensions (3D) in space and also in the velocity space. Hence the MC method contains information on the velocity distribution function for each velocity direction, but also for the particle crossing a given surface, for instance, the substrate (Depla and Leroy, 2012), or the chamber walls. In this section, we focus on different approaches of using Monte Carlo methods to evaluate the microscopic information related to particle interaction, namely the cross section for collisions between the working gas and sputtered species. We will use the example of argon and titanium (Lundin et al., 2013). It is based on the inverse approach and starts with a guess of the interaction cross section. Using this guess, the velocity distribution function (VDF) of metal neutrals is evaluated by MC, and the output is directly compared to a measured VDF (Vitelaru et al., 2011). If the results are different, the cross section is adjusted until both VDFs are in good agreement. This algorithm exploits the uniqueness of the cross section, that is, independent of the way it is evaluated. To test the validity of the calculated cross section, the transport of sputtered metal atoms can be simulated for other plasma conditions (different pressure, different distance from the target, etc.). This time the cross section remains unchanged, and the Monte Carlo simulation becomes predictive (Lundin et al., 2013). Indeed, very good agreement between the calculated and measured VDFs in dcMS

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discharge supports the new reported Ar–Ti collision cross sections (both angular and energy dependent) (Lundin et al., 2013). The argon–titanium cross sections are typically four times larger than the known argon–argon cross sections (Somekh, 1984). This technique can be extended to any metal sputtered from the target. This Monte Carlo algorithm can be further extended by adding new reaction paths. For HiPIMS modeling, the most important reaction is electron impact ionization of the sputtered metal atoms as they cross the ionization region. The probability of metal ionization can be evaluated using the combination of momentum transfer toward the argon atoms (slowing down the metal) and electron impact ionization. However, the ionization frequency requires the knowledge of the electron density and temperature in the ionization region. Density and temperature maps can either be taken from simulations, such as the IRM (Raadu et al., 2011), from PIC simulations (Minea et al., 2014), or directly from measurements, such as those presented in Chapter 3. When the Monte Carlo technique depends on other self-consistent models, it is referred to as a posteriori Monte Carlo and is discussed in Section 5.1.5.4. This method has been used to evaluate the ionized density fraction of sputtered titanium, and the result has been compared to reported flux fractions of ionized metal (Hopwood, 2000) with a fairly good agreement for Te = 5 eV (Minea et al., 2014).

5.1.5.3

Direct simulation Monte Carlo (DSMC) for neutral particles transport

When simulating the target material species and its interaction with the working gas atoms, another approach derived from the Monte Carlo method can be applied, referred to as direct simulation Monte Carlo (DSMC) (Bird, 1994). The DSMC method is similar to the PIC method, but designed exclusively for neutral gases to study rarefied gas flows (e.g. around space probes reentering into upper layers of the Earth atmosphere). In the case of PIC simulations the particles are driven by the Lorentz force, whereas the neutrals exhibit elastic interactions, at least in the absence of reactive species that can form compounds. The interaction cross sections that are needed for Ar–Ar and Ti–Ar interactions can be found in the works of Somekh (1984) and Lundin et al. (2013), respectively. The method uses discrete macroparticles (each with an associated position and momentum vector) that represent an arbitrary distribution function of the investigated species in the phase space. Thus, contrary to the fluid method, the distribution function is not a priori assumed. A computational grid is superimposed over the simulation domain, which speeds up the selection of potentially colliding particles on a per cell basis. The evaluation of the collision probability and the postcollision velocities of particles is then performed in the same manner as in the Monte Carlo collision method. This method evaluates mutual collisions between particles of the same type and also between different species when present in the simulation. The energy and momentum are conserved for each collision. The DSMC method is slower than MCC and more difficult to implement. Similarly to the PIC method, there must be enough macroparticles in each cell (typically 50 or higher), and the integration time step is limited by the velocity of particles and the grid size. However, since neutrals are not influenced by the electric field, the proper grid size is mainly determined by the mean free path of neutral atoms, which is on the

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order of centimeters for pressures on the order of Pascals. This results in typical time steps on the order of 10−7 s and corresponding lengths of simulation up to the order of seconds (depending on the size of the problem). A particular challenge related to magnetron sputtering is that the density of sputtered atoms is typically more than one order of magnitude lower than the working gas density. Thus a constant macroparticle weight used for both species needs to be kept low to ensure there is enough target material particles in each cell. At the same time, the number of working gas particles would be unnecessarily high and slowing the simulation down. The proposed solution is to use a different weight for each particle species or even for each individual particle. This, however, makes the implementation of the binary collisions more difficult. Results of using DSMC to explore the HiPIMS discharge were already presented in Section 4.2.2 when studying gas rarefaction and will not be repeated here.

5.1.5.4

A posteriori Monte Carlo

For certain specific problems, such as obtaining transport coefficients of charged particles, there is no need for very complex methods such as PIC/MCC. Usually, transport coefficients are calculated in stationary and homogeneous combined electric and magnetic fields (Dujko et al., 2006), by applying a Monte Carlo method to a particle swarm experiment. In the particle swarm experiment a low particle density population is moved through a much higher particle density environment. When performing such calculations for HiPIMS discharges, the big challenge is the complex configuration of both the electric and magnetic fields (inhomogeneous, large gradients, variable angle between the two fields, nonstationary, at least for the electric field, etc.), which makes the charged particle transport to be spatio-temporal dependent. As a solution, a numerical method referred to as a posteriori Monte Carlo was proposed by Costin et al. (2014) for investigating electron transport in HiPIMS discharges. The method consists of following a large number of test electrons along their collisional trajectories in an electrical discharge, in a fully 3D time-dependent code. The collisions are treated by Monte Carlo simulation coupled to the null collision technique, as already described in Section 5.1.5.1. The discharge parameters, such as charged particle density and electric field, which are important for the treatment of the test electrons, have been previously obtained from a self-consistent PIC/MCC simulation. Thus, the calculations of the code are made in a self-consistent predetermined environment, which is why the technique is referred to as a posteriori Monte Carlo simulations. For a spatial description of electron transport coefficients, namely the drift velocity and diffusion coefficient, the test electrons are released at different points of the simulation domain. The transport coefficients can be obtained in each of the three space dimensions by mathematical manipulation of the coordinates of all test electrons, calculated in the real three-dimensional (3D) space and in time, as shown in Section 5.2.3.5. Besides the calculation of electron transport coefficients in HiPIMS discharges (Costin et al., 2014), the technique has been used to investigate dense plasma structures (spokes) traveling along the race track in magnetron sputtering discharges (Brenning et al., 2013).

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An advantage of this method is a very short computation time with respect to the more complex PIC/MCC technique, yet benefiting from the results of the PIC/MCC simulation. The computation time for a single run, with 105 electrons moved for 0.1 µs, is about one hour on a desktop computer with a 3 GHz processor. The disadvantage is that the results of the a posteriori MC simulation are obtained with electrons released at a specific point in space, whereas PIC/MCC results include the collective effect of the electrons coming from a much larger area.

5.1.6 Other models A few more HiPIMS-specific models have also been developed. They are typically aimed at investigating a single HiPIMS phenomenon/result and are thus less general than the previously described models. Here we discuss some of these models and connect them to the relevant physics.

5.1.6.1

A feedback model

The purpose of the feedback model proposed by Ross et al. (2015) is to describe the temporal trace of the discharge current as response to an applied voltage. The model is not focused on describing the discharge in detail, such as the IRM or the PIC/MCC simulation, but aims to include the principal plasma processes responsible for the discharge current behavior. The external circuit is considered in the model as well. The discharge is described as a time-dependent circuit containing three elements and is shown in Fig. 5.5. The strong electric field in the cathode fall (the first element of the circuit) drives the ions from the plasma to the cathode, which leads to secondary electron emission from the cathode to the plasma. The second element of the circuit is a quasineutral glow plasma of a given density, which corresponds to the ionization region. The third element is the series resistance R, the plasma resistance. The internal resistance R of the power supply is included in the external circuit. The discharge current is evaluated as the sum of two components, ion current to and secondary electron current from the cathode, both changing with time. The rate equation for the ion population contains two production mechanisms and one loss process. The positive feedback is ensured by the electron production mechanisms: ionization of neutral working gas by secondary electrons and ionization of the sputtered material. The two mechanisms are considered having a certain delay, which is caused by the transit time of various particles (ions, secondary electrons, and sputtered atoms) in the cathode fall. The model uses the cathode voltage waveform as input and adjusts the model parameters described earlier (which have much less physical meaning compared to other models such as IRM or PIC/MCC) to obtain different features of the discharge current. The model is able to reproduce a number of features of the different discharge currents obtained experimentally, such as an initial current peak followed by a current plateau with a variety of concave-up and concave-down rises, by adjusting the parameters of the model (Ross et al., 2015). The feedback model uses several fitting parameters, such as the secondary electron emission yield, the number of ions created by each

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Figure 5.5 A plasma discharge circuit model. A strong electric field in the cathode fall (the first element of the circuit) drives the ions from the plasma to the cathode, and secondary electron emission occurs from the cathode to the plasma. The second element is a quasineutral glow plasma, and the third element is the plasma resistance R. The internal resistance of the power supply is denoted by R . From Ross et al. (2015). ©IOP Publishing. Reproduced with permission. All rights reserved.

secondary electron, the sputter yield, the fraction of ions leaving for the cathode in one time step, and the fraction of sputtered material that is ionized.

5.1.6.2

EEDF as solution of Boltzmann’s equation

One method to obtain the electron energy distribution function (EEDF) in an electrical discharge is solving the Boltzmann equation. This task can be very difficult for a typical magnetron discharge due to the presence of a strongly inhomogeneous magnetic field and even more complicated for the HiPIMS discharge due to the temporal behavior of the discharge. Yet, for simplified cases (such as a stationary discharge, homogeneous magnetic field, etc.), obtaining the EEDF as a numerical solution of the Boltzmann equation requires much less computational resources compared to PIC, for example. The disadvantage of the method is a large number of assumptions that has to be made in comparison with a self-consistent method. There are two attempts in the literature to directly calculate the EEDF for the quasistationary phase of a HiPIMS discharge (Vašina et al., 2008, Gallian et al., 2015) (see also Section 5.2.3.3). Both of these methods use a 0D model, which was initially developed for a dcMS discharge (Guimarães et al., 1991) and was later adapted for HiPIMS (Vašina et al., 2008). In a first attempt, Vašina et al. (2008) used the simplified Boltzmann equation ∂Je−A ∂Je−e ∂F (E, t) =− + + kex + kiz + S − L , ∂t ∂E ∂E

(5.45)

which was solved numerically for the electrons within the ionization region, where F (E, t) is the electron energy distribution function expressed in m−3 eV−1 . The terms on the right-hand side are electron fluxes due to different collisions: elastic (electron– atom) ∂Je−A /∂E, Coulomb (electron–electron) ∂Je−e /∂E, inelastic excitation kex , and ionization kiz . The terms S and L account for the source (gain) and loss of electrons, respectively. The electron source term S is composed of secondary electrons emitted at the cathode surface by ion bombardment and accelerated in the cathode sheath: S(E) = G(E)

Ies , eV

(5.46)

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where Ies is the current due to secondary electrons, V is the volume of the magnetic trap (the IR), and G(E) is the distribution function of the secondary electrons, normalized as G(E)dE = 1. The mean energy of the secondary electrons is eVD , where VD is the discharge voltage. The loss term is determined by electron–ion recombination collisions, LR , and by scattering of electrons out of the ionization region, LS . The second loss term is expressed as  Ar (E) 1  el L in LS (E) = + νC νe−A + νe−A F (E) , (5.47) 4 V el , ν in , and ν are the collision frequencies for electron–atom (e-A) elaswhere νe−A C e−A tic and inelastic collisions and for electron–ion Coulomb collisions, respectively, A is the effective loss area for electrons corresponding to the limit of the magnetic trap, and rL (E) is the Larmor radius for an electron of energy E. More details about the terms included in the Boltzmann equation can be found in the work of Guimarães et al. (1991). A homogeneous and constant magnetic field is assumed within the ionization region. The Boltzmann equation is coupled to a set of balance equations for different heavy species (Guimarães and Bretagne, 1993), such as the excited states of the working gas (Ar) and sputtered metal (Cu). This combination is referred to as the collisional radiative model (CRM). For more details on balance equations for different heavy species, see the description of the IRM in Section 5.1.3. The CRM code introduced by Vašina et al. (2008) was used to explain the “space charge compensation of the ion transport”: it was assumed that the ion transport to the substrate is not affected by any space charge, the positive charge corresponding to the moving ions being fully compensated by electrons. The second model was developed by Gallian et al. (2015) and focused only on the energetic part of the EEDF, corresponding to the highly energetic electrons. The authors derived an analytical solution for the Boltzmann equation written for the energetic electrons, an equation which is almost identical to that solved by Vašina et al. (2008). The difference is that the first term of the equation (due to elastic electron– neutral interaction) and the loss term component LR are neglected for the energetic electrons. In this model the bulk electrons are treated as a Maxwellian population at low temperature, of the order of a few eV. The model was applied for the discharge current plateau phase of a HiPIMS discharge.

5.1.6.3

Models for spokes

Rotating dense plasma structures, spokes, that hover above the cathode are described in detail in Section 7.4. There have been some modeling efforts to describe spokes, notably using the previously discussed a posteriori MC technique (Costin et al., 2014) and the pseudo-3D PIC technique (Revel et al., 2016). In addition, a couple of spokespecific models have also been developed, which are summarized here.

5.1.6.3.1 A phenomenological model The structure of a spoke was investigated by Gallian et al. (2013) using a simplified phenomenological model, which calculates the distribution of particles along the azimuthal direction of the discharge. The aim of the model was to qualitatively reproduce

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a stable configuration of a spoke, in which an electron density peak remains unchanged as it rotates with a constant angular velocity while it diffuses. The continuity equation for electrons is written as ∂ne + ∇ ·  e = Re , ∂t

(5.48)

where ne is the electron density, and Re includes all the terms that describe creation and destruction of electrons. The electron flux is written as  e = ue ne − De ∇ne with ue the electron drift velocity and De the diffusion coefficient for electrons. The working gas (Ar) and the sputtered metal (Al) densities are obtained by solving rate equations in a similar way as discussed for the IRM in Section 5.1.3.1. The drift and diffusion of the heavy particles are neglected due to their longer time scale with respect to electrons or to the spoke rotation period. The elementary processes included in the model are: electron impact ionization, Penning ionization, charge exchange collisions, excitation and de-excitation of Ar metastables, loss of working gas atoms due to the metal sputter wind, and generation of metal atoms by gas ion sputtering or selfsputtering. A global loss/gain term is used for the heavy particles due to the particle transport toward/from the regions outside the spoke. The solution for the electron density equation is assumed to be Gaussian, with the amplitude and width treated as free parameters. With this assumption, an analytical solution is derived for the neutral density in a frame co-moving with constant angular velocity with the high plasma density region (Gallian et al., 2013). The variable parameters of the analytic solution are adjusted until the model results match the experimental conditions. This model gives the electron density and the spatial distribution of the neutrals.

5.1.6.3.2 The wave coupling model A first attempt at linking plasma instabilities in HiPIMS discharges with wave coupling was proposed by Lundin et al. (2008). They phenomenologically described how the modified two-stream instability gives rise to long wavelength (several cm) drift instabilities in the MHz range. More recently, a novel approach was proposed by Luo et al. (2018) to describe the spokes in HiPIMS discharges based on wave coupling. The electrons are assumed to be magnetized, whereas the ions are not magnetized but controlled by the equilibrium and perturbation potential distributions. In this scenario the free energy only comes from electron drift, and the studied plasma behavior is a result of the interaction between noncollisional azimuthal waves. The plasma wave interaction is analyzed via a dispersion relation. The ion contribution (i.e., ion density perturbation) in the HiPIMS discharge is expressed as (Luo et al., 2018) ni1 =

ky eni0  ky2 cs2 e = 2 ni0 , ω2 M ω Te

(5.49)

in which ky is the wave number along the azimuthal direction, cs is the ion sound velocity,  is the plasma perturbed potential, e is the elementary charge, and ni0 is the equilibrium ion density. The ion density perturbation ni1 and the electron drift are

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considered in the dispersion relation of the electron Bernstein wave (Chen and Smith, 2008). Two solutions are particularly interesting. The first is a Doppler-shifted electron Bernstein (DSEB) wave (Chen and Smith, 2008), and the second is an ion sound (IS) wave (Bussac et al., 1978). The frequencies of these waves are well within the range from 1 to 6 MHz, in line with measured plasma instabilities in the ionization region (Tsikata and Minea, 2015). The authors find that the coupling of the DSEB wave and the IS wave induces long-scale (centimeters) electric field oscillations and ultimately leads to an electric field structuring in the azimuthal direction (Luo et al., 2018). This coupling wave model thus reconciles the plasma instabilities experimentally observed when studying spokes and demonstrates a possible relation between them. Further discussions on spokes are found in Section 7.4.

5.2 Important modeling results In this section, we present and discuss some of the main physical phenomena that govern the HiPIMS discharge and can be derived from the different models presented in Section 5.1. These results have primarily been selected to emphasize the added understanding brought by computational modeling, validate certain modeling approaches, or highlight model-specific results. However, HiPIMS discharge modeling is not limited to only these aspects. Other modeling results are found elsewhere in the book when discussing different mechanisms in HiPIMS discharges.

5.2.1 Deposition rate One of the main issues with HiPIMS is that the deposition rate is commonly lower when compared to dcMS operated at the same time-averaged discharge power (Helmersson et al., 2006, Samuelsson et al., 2010). An important research effort has therefore been devoted to understand and further propose solutions to overcome this drawback of HiPIMS discharges. This issue of the low deposition rate will be addressed in more detail in Section 7.5. However, here we will look at modeling results of external and internal process parameters that may influence the deposition rate by introducing the concept of back-attraction of the ionized sputtered species, to the target which is believed to be the main reason for the reported rate loss (Christie, 2005). Let us start by analyzing results from the steady-state pathway models introduced in Sections 5.1.1 and 5.1.2 (Christie, 2005, Vlˇcek and Burcalová, 2010). Fig. 5.6 shows model calculations by Vlˇcek and Burcalová (2010) for copper and titanium targets. The independent variable in these graphs is the fraction of target material ions in the total ion flux to the target, ζ , that is, the fraction of metal ions contributing to the discharge current (assuming singly charged working gas and metal ions), which is defined by Eq. (5.3). This fraction can only be evaluated for given discharge conditions from a detailed balance of electron ionization and ion losses in the ionization region. However, it is reasonable to expect ζ to increase with increasing average target power

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Figure 5.6 Calculated values of the fraction βt of ionized sputtered atoms directed back to the target, the fraction αt of ionized sputtered atoms (ionization probability), the normalized deposition rate coefficient , and the ionized flux fraction of target material atoms Fflux onto the substrate as functions of the fraction ζ of target material atoms in the ion flux onto the target for sputtering of copper and titanium. From Vlˇcek and Burcalová (2010). ©IOP Publishing. Reproduced with permission. All rights reserved.

density in a pulse (resulting in increased sputtering and ionization of target material).4 Therefore, the dependence on ζ also provides trends of the discharge parameters as a function of the average target power density in a pulse. The upper panel of Fig. 5.6 shows that increasing ζ leads to increasing probability of ionization of target material atoms, αt , given by Eq. (5.9), as expected, and to a slight decrease of the returning fraction βt of target material ions given by Eq. (5.10). This is in agreement with an experimental evaluation of βt performed by Andersson and Anders (2009). As can be seen in the bottom panel, the model predicts an almost linear decrease of the normalized deposition rate constant with increasing ζ . This appears to be a direct consequence of the return of ionized target material atoms onto the target (back-attraction), and thus the model quantitatively evaluates the dominant mechanism responsible for the reported decrease of deposition rate in HiPIMS compared to dcMS. Note that this model predicts, in the case of Ti, an ionized sputtered metal flux fraction Fflux to the substrate, which reaches 100%, (seen in the lower right panel of Fig. 5.6), that is, considerably higher values compared to those we earlier found and shown in Fig. 4.11. However, this does not necessarily mean that the limit values of Fflux are accessible in practice, since the metallic fraction ζ cannot attain arbitrarily large values (e.g. the target power density is limited by the capability of the power supply, target cooling, etc.). Fig. 5.6 also shows that the ion return probability βt decreases with increasing target voltage for the same fraction ζ . This is due to the secondary electron balance 4 Recall that in Fig. 4.12 we saw that the ionized flux fraction to the substrate, F flux (Eq. (4.3)), was found

to increase with increasing average pulse current density (which also means increasing average target power density in a pulse).

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Figure 5.7 (A) The ionized flux fraction Fflux from Eq. (5.50), plotted as function of β for three different

HiPIMS pulses with peak current densities in the range 0.7 – 2.5 A/cm2 . The stars on the curves mark measured Fflux values from Lundin et al. (2015) and modeled by the IRM. The shaded area indicates typical HiPIMS values of β. (B) The normalized deposition rate plotted as function of Fflux for the three discharge pulses studied. The total number of Ti atoms and ions reaching a virtual substrate facing the Ti target at the edge of the IR (z2 = 20 mm), Ndep , has here been divided by the total number of sputtered Ti, Nsput . From Butler et al. (2018). ©IOP Publishing. Reproduced with permission. All rights reserved.

equation implemented in the model. A higher energy of electrons due to the increased sheath (and likely also presheath) electric fields means that more electron–ion pairs are produced for each electron in the IR. Consequently, these extra ions can be directed onto the substrate without lowering ζ . The same effect was reported experimentally by ˇ Capek et al. (2013), who evaluated the difference in βt in two cases with different magnetic field strengths (manifested also by different cathode target voltages). In addition, from Fig. 5.6 it is also seen that the fraction ζ of target material ions contributing to the discharge current is limited to 0.3 – 0.4 in the case of the titanium discharge, which is not the case for the investigated copper discharge. The authors ascribe this to the higher probability of ionization (higher ionization cross section and lower ionization threshold) and lower sputter yield for Ti than for Cu. Indeed, from Eq. (5.9) it follows that a lower effective sputter yield results in a higher ionization probability αt for the same fraction of ionized target material in the ion flux onto the target ζ . Consequently, this leads to a lower normalized deposition rate coefficient and a higher degree of ionization in the flux onto the substrate Fflux (as seen in Fig. 5.6) at the same ζ . Similar results for the ionization fractions have been found by Butler et al. (2018), who used the time-dependent IRM, introduced in Section 5.1.3, on titanium discharges in argon to investigate the differences and relations between Fflux , Fdensity , and αt

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(defined in Section 4.1.4). They found a simple analytical expression for Fflux as a function of αt and βt : Fflux =

1 t 1 + 2 αt1−α (1−βt )

,

(5.50)

which is plotted in Fig. 5.7A. The three different ionization probabilities αt were taken from three different HiPIMS pulses with peak current densities in the range 0.7 – 2.5 A/cm2 , and the stars in Fig. 5.7A represent the IRM results. First, in Fig. 5.7A, we again see that Fflux is increasing with increasing αt , which is consistent with the previous findings shown in Fig. 5.6 and with results from another time-dependent model by Kozák and Vlˇcek (2013). However, this comes at a cost of a reduced deposition rate, which is illustrated in Fig. 5.7B, where the normalized deposition rate is plotted as a function of Fflux for the three discharge pulses studied. The explanation is straightforward and in line with what we found earlier when investigating the normalized rate coefficient in Fig. 5.6: at higher αt , the flux of neutrals to the substrate is reduced due to the extra ionization, and this flux loss is only partially replaced by ions since the majority of these ions (85% ± 5%) are drawn back to the target. Second, Fflux shows a continuous decrease with increasing βt . This decrease is slow for βt < 0.5 but very steep for higher βt . The authors therefore suggest to operate HiPIMS discharges in a low βt range, since this would allow increasing Fflux without significantly decreasing the deposition rate. Three ways are proposed (Butler et al., 2018): (i) decrease the magnetic field intensity in front of the target (Mishra et al., 2010) (discussed in Section 7.5.1), (ii) modify the magnetic field topology (Raman et al., 2016) (discussed in Section 7.5.2), or (iii) modify the time-pattern of the pulse by using, for example, chopped HiPIMS (Barker et al., 2013) or pulse trains (Antonin et al., 2015) (discussed in Sections 2.4.3 and 7.5.2).

5.2.2 Current and voltage waveforms We now turn to modeling the time-dependent discharge current and the applied discharge voltage during the pulse, since these are the experimental parameters of the HiPIMS discharge that are easiest to access. By comparing two approaches, the volume averaged global IRM (Stancu et al., 2015, Huo et al., 2013, 2014, Butler et al., 2018) and the self-consistent PIC/MCC model (Revel et al., 2018), it is possible to isolate the specific contributions to the shape and amplitude of the discharge current. Specific attention is paid to explain the reliability of the two approaches, the IRM and the high-density PIC/MCC, where modeling results are directly compared with measurements when data are available. Note that most numerical models describe the temporal evolution of the discharge current as a response to a well-defined applied voltage pulse. The steady-state pathway models discussed in Section 5.1.2 deal only with the stationary state of the plasma attained when the discharge current and voltage both reach a plateau, and hence they cannot describe the discharge current waveform.

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5.2.2.1

High Power Impulse Magnetron Sputtering

Time-dependent global models

Time-dependent global models can reproduce the current waveform. Even if not self-consistent, the IRM and similar codes can recover the experimentally recorded discharge current evolution using the (experimental) voltage pulse as input. The experimentally determined discharge current ID (t) is thereby used to iterate the plasma parameters in the ionization region (IR) until convergence is achieved (Raadu et al., 2011). This fitting procedure is necessary for the reason that there are important discharge parameters for which there usually exist no good theoretical or experimental motivation for a specific value (in case such a value can be obtained, it can, however, be directly implemented in the code). In general, it is assumed that a good fit of the discharge current is a guarantee for finding a reliable time-evolution of the microscopic parameters of the plasma, such as electron density and temperature, positive ion densities, and their relative contribution to the discharge current, secondary electron production, metal generation by sputtering, etc. (see Section 5.1.3). We will later on in this chapter investigate the validity of such an assumption, but let us first focus on the fitting parameters of the IRM, which play a key role ensuring, on the one side, model consistency and, on the other side, providing a predictive feature. In the initial IRM codes (Raadu et al., 2011, Brenning et al., 2012, Huo et al., 2012, Stancu et al., 2015), two model fitting parameters are used. The first fitting parameter FPWR = Pe (t)/PD (t) is the fraction of the total discharge power PD (t) = ID (t)VD (t), which goes to energizing the electrons within the ionization region (Brenning et al., 2012). The second fitting parameter is the probability β for ions to leave the ionization region toward the target (back-attraction); the same value of β is used here for Ar+ and M+ ions. This gives a two-dimensional parameter space for model fitting. An illustrative example is given by Stancu et al. (2015). In their case, the axial extension of the ionization region (z2 − z1 ) was taken consistent with the bright light emission region of the plasma (where the electrons are effectively trapped). The discharge current waveform is reported in Fig. 5.8 together with the best fit values for FPWR and β (panel (C)). It is seen that β is in the range from 0.3 to 0.6 and FPWR is varied from 0.05 to 0.3. To identify suitable values to lock the model, Stancu et al. (2015) investigated the shape of the calculated discharge current waveform. They found that the rise time of the discharge current is delayed if β is too large (panel (E)) and the current decay beyond its maximum occurs too early if β is too small (panel (A)). On the other hand, the maximum of the calculated discharge current is not high enough if the electrons do not receive enough energy (low FPWR , panel (D)) or this maximum is overestimated if the electrons are too energized (high FPWR , panel (B)). In this way a best current fit was attained for FPWR = 0.195 and β = 0.4, as seen in panel (F). Moreover, the kinetics of the argon metastable was introduced in this version of the IRM, and the experimental results of the argon metastable evolution (Vitelaru et al., 2012) have been directly compared with the IRM predictions (Stancu et al., 2015). The good agreement found was taken as a first step for validating the IRM and is discussed in detail in Section 5.2.3.2. In more recent IRM version, FPWR has been replaced, since it does not distinguish between different mechanisms energizing the electrons. Instead, current versions of

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Figure 5.8 An example of how the IRM is locked (β and FPWR fixed constant) on experimental data for a pulse with a maximum discharge current of 40 A (JD,peak ≈ 0.5 A/cm2 ). Blue full line (panel (C)) indicates a low error level of current fitting, and the blue circle shows the locked values used for the best fit (panel (F)). Panels (A), (B), (D), and (E) show wrong values of the pair (β, FPWR ) outside of the solid curve. The discharge was operated with argon as the working gas at 1.33 Pa with a 4 inch Ti target. From Stancu et al. (2015). ©IOP Publishing. Reproduced with permission. All rights reserved.

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the IRM consider heating the electrons by (i) acceleration over the cathode sheath and (ii) Ohmic heating due to the potential drop over the IR, VIR (Huo et al., 2013), which was introduced in Section 5.1.3 and is further investigated in Section 7.2.3 when discussing the physics of electron energization. The energy balance is thereby expressed with respect to the fraction f = VIR /VD , instead of FPWR . VD is the total discharge voltage, which may vary during the discharge pulse (although f is typically constant in the model runs). Finally, the recapture probability r of secondary electrons released from the target upon ion bombardment has been identified as the third important fitting parameter (Gudmundsson et al., 2016). It depends on the geometry of the system, the magnetic field configuration, target erosion, and operational parameters such as the pressure, as shown by Costin et al. (2005). However, it has been found that for many HiPIMS discharges, the recapture probability can be varied in a wide range (typically 0.4 < r < 0.9), since it only has a small effect on the calculated discharge current. Current fitting using this updated set of fitting parameters (β, f = VIR /VD , and r) have been reported by several authors (Huo et al., 2013, 2014, Gudmundsson et al., 2016, Lundin et al., 2017, Butler et al., 2018). Note that for physical reasons, these three parameters have to fall within the range between 0 and 1, but the permitted ranges are determined in the model fitting procedure. In Fig. 5.9, we show an example of current fitting by Huo et al. (2014), since these important results are used in several places throughout this book. The experimental discharge characteristics (Fig. 5.9A), here used as an input to the IRM, were recorded by Anders et al. (2007) using a planar balanced magnetron equipped with an Al target. The target was 50 mm in diameter, and argon was used as working gas at a pressure of 1.8 Pa. Further details concerning the experimental conditions can be found elsewhere (Anders et al., 2007). The values of the three parameters β, f = VIR /VD , and r that lock the model for the Al discharge explored here are β = 0.9, f = 0.163 – 0.289, and r = 0.5. The authors found, however, that the third fitting parameter, the electron recapture probability r, could be varied in the range 0.25 ≤ r ≤ 0.75 without influencing the model output significantly and therefore used r = 0.5 (see Huo et al. (2013)). A sensitivity analysis was also carried out for this discharge (Huo et al., 2013) and later on also for a Ti discharge in argon (Huo et al., 2017), where it was concluded that the IRM model is indeed robust against changes of additional internal parameters (within reasonable ranges) and that the two fitting parameters β and f = VIR /VD are often sufficient. Butler et al. (2018) went even further in their attempt to lock the IRM when modeling an experiment by Lundin et al. (2015), who investigated the ionized flux fraction Fflux of Ti and Al using a gridless QCM sensor (see Fig. 4.12). In the IRM study, only Ti was investigated. The experiments were carried out using a standard planar circular Ti target with a diameter of 50 mm with argon as the working gas maintained at a pressure of 0.5 Pa. Three different peak current densities JD,peak were investigated at the same average power by varying the discharge voltage and pulse frequency: 0.7 A/cm2 , 1.0 A/cm2 , and 2.5 A/cm2 (averaged over the entire target area). Further experimental details are found elsewhere (Lundin et al., 2015). Similarly to the other IRM cases presented, Butler et al. (2018) also used the discharge current waveform ID (t) for fitting. The requirement that the model should

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Figure 5.9 (A) Experimental and (B) numerical IRM current waveforms for a discharge with argon as the working gas and Al target. The transitions to self-sputtering are marked by stars in (B), i.e., where the Al metal ion current to the target is half the discharge current. The curves are shaded blue (gray in print version) in the argon-dominated phase. From Huo et al. (2014). ©IOP Publishing. Reproduced with permission. All rights reserved.

reproduce ID (t) with less than ±10% total error, constrained the available (β, f ) parameter space as shown by the blue hollow circles in Fig. 5.10. The obtained crescent-shaped “best-fit” area is a typical result for current-fitting of the IRM (Huo et al., 2012, Stancu et al., 2015). As additional experimental data, they also used the measured ionized flux fraction as a second set of data for fitting. This gives a separate constraint of the available (β, f ) parameter space, which is shown by the green crosses in Fig. 5.10. Note that this second area gives the correct flux fraction only and not everywhere a good current fit: both current and flux fraction are correctly modeled only in the quite small area marked with red encircled crosses, where the blue hollow circles and the green crosses overlap, as seen in Fig. 5.10. This area defines the final constrained IRM model. In this study the recapture probabilities for electrons were assumed to be r = 0.7. Last, Bretagne et al. (2015) developed another version of the global model, initially to describe dcMS discharges (Guimarães et al., 1991) and further extended to HiPIMS discharges. Even if it looks similar to the IRM, the main difference resides in the simultaneous calculation of the balance equations for plasma species and the electron energy distribution function (EEDF) as a solution of the Boltzmann equation. Hence the convergence of the model gives the EEDF (which is not necessarily a Maxwellian distribution) and the density of species. This approach is the CRM dis-

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Figure 5.10 Constraining the IRM model with experimental data. Both the discharge current waveform ID (t) and the ionized flux fraction Fflux are correctly modeled only in the quite small area marked with red encircled crosses, where the blue hollow circles and the green crosses overlap. This area gives the final constrained IRM model. From Butler et al. (2018). ©IOP Publishing. Reproduced with permission. All rights reserved.

Figure 5.11 Discharge voltage and current evolution during the pulse from the CRM. Black lines represent the experimentally recorded discharge characteristics, and the red lines (gray in print version) the model results. After Bretagne et al. (2015).

cussed in Section 5.1.6.2. The main difference of this approach compared to the IRM is the self-consistent quality of the CRM. Indeed, CRM is able to predict the discharge current carried at the cathode during the pulse using as input the recorded voltage waveform, as Fig. 5.11 shows. In the CRM, the secondary electrons leaving the target are assumed to be very energetic, forming a monoenergetic beam entering the IR, since it is assumed that the entire discharge voltage VD falls over the cathode sheath, that is, VSH = VD and VIR = 0. Consequently, the discharge current is very sensitive to the pulse voltage (ionization is driven by the energetic electron beam), as can be seen in Fig. 5.11, where the first voltage peak gives rise to a peak in the modeled current waveform (∼ 10 µs after the beginning of the pulse), although such a feature is not present in the experiment. In spite of this, a good general agreement is obtained between the predicted current waveform by the CRM and the measured one.

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Figure 5.12 Current and voltage waveforms of a short-pulse HiPIMS discharge, obtained by PIC/MCC simulation, for three different values of the resistance in the external circuit. The parameters are Vapp = −800 V, pulse width 6 µs, rectangular metallic magnetron target 4 cm wide, and argon as working gas at 0.4 Pa. From Revel et al. (2018). ©IOP Publishing. Reproduced with permission. All rights reserved.

5.2.2.2

Self-consistent PIC model

PIC/MCC is a self-consistent modeling approach by default. In these simulations, the evolution of the cathode voltage and discharge current is part of the output, the input being the applied pulse voltage Vapp from the power supply to the external circuit, including the HiPIMS discharge. The simplest circuit considers the resistance R in series with the cathode, which limits the discharge current (Revel et al., 2018). The discharge current and voltage waveforms of a short-pulse HiPIMS discharge with pre-ionization, obtained by PIC/MCC simulations (Revel et al., 2018), are shown in Fig. 5.12. The discharge current strongly depends on the resistance of the external circuit. The transition from low current (low-power pulsed regime) to high current (HiPIMS regime) can be obtained by reducing the value of the external resistance. Revel et al. (2018) find that the trend and pulse shape are in qualitative good agreement with corresponding experimental discharge characteristics. The peak current density is 0.87 A/cm2 for 250  resistance in the model. The results of the plateau current obtained by simulation (Fig. 5.12) for the three external resistances suggest a quasilinear dependency between ID and R −1 . Extrapolating this linear dependence, to reach a maximum current of 100 A, which has been recorded experimentally by Ganciu et al. (2005) and used to benchmark the code, it is found that the external resistance of the circuit should be about 6.5 . On the other hand, only the discharge current ID and voltage VD are experimentally measured (Ganciu et al., 2005). So, the voltage applied from the power supply can be estimated as Vapp = VD + Rexp ID ≈ 1100 V, and it is found that Vapp stays almost constant during the pulse, in line with Vapp in Fig. 5.12. The value of the external resistance used for this estimation is Rexp = 6.7 ± 0.2 , that is, very close to the extrapolated value from the PIC/MCC calculations. PIC/MCC simulations reproduce well the general behavior of the experimentally recorded discharge current and voltage signals (Ganciu et al., 2005, Vašina et al., 2007, 2008, Costin et al., 2011, Velicu et al., 2014).

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In conclusion, several models can capture the most important features of the physics of HiPIMS and provide reliable pulse currents based on the microscopic characteristics of the plasma. IRM and CRM use volume averaged values of the plasma parameters of the high-density plasma over the race track, whereas 2D space-resolved PIC/MCC modeling gives the macroscopic discharge current.

5.2.3 Time-dependent plasma properties The discussion of the fundamental plasma characteristics in HiPIMS discharges was presented from an experimental point of view in Chapters 3 and 4. In this section, we focus on the same plasma characteristics but explore the modeling results. The discussion is mainly based on the results given by the following three approaches: IRM, CRM, and PIC/MCC. Results obtained from other models are occasionally discussed when they can be compared to each other or when they bring novel insights of the HiPIMS discharge. First, we report on the neutral, electron, and ion densities and then on the energy distributions of electrons and ions and consequently on the electron temperature. These results serve as a good introduction to understanding the HiPIMS pulse evolution, which is discussed in Section 7.2.2. The high plasma density also affects the electron transport across the magnetic trap, and the first modeling results will be presented. A more extensive discussion on the transport of charged particles in HiPIMS plasmas is given in Section 7.3.

5.2.3.1

Temporal evolution of neutral and charged species

The first modeling results on the density evolution of charged species during the pulse were reported by Raadu et al. (2011) using the IRM. They provided detailed information on the volume averaged plasma parameters within the ionization region and their temporal evolution during the pulse and the afterglow. Here we will look at an example from Huo et al. (2012), where the IRM results for an Al discharge are shown in Fig. 5.13. The modeled current waveform is shown in Fig. 5.9B (VD = 450 V). For a given ID (t) waveform (Fig. 5.13(a), blue solid curve), the IRM provides the timeevolution of the electron density, electron temperature, and the ionization fraction of the working gas and sputtered metal. The first phase during which the discharge current increases is characterized by the build-up of the space charge (see the second panel), and this time interval is necessary in order to fill the IR with a high-density plasma. It takes typically 10 to 15 µs, and it was evaluated as the time necessary for ions to travel the axial length of the IR, assuming that ions move with the Bohm speed. However, the maximum of the discharge current is reached at about 100 µs (in this example) because several generations of ions should reach the cathode (for discussion on ion recycling, see Section 7.2.1.1). So, the time to reach equilibrium is longer than the simple transit time of the ions across the IR. The electron temperature behaves differently as can be seen in the third panel of Fig. 5.13. It increases very fast at the very beginning of the pulse (< 5 µs) and later re-

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Figure 5.13 Time evolution of plasma parameters obtained by the IRM. First panel shows (a) experimentally recorded discharge current and (b) IRM calculated discharge current. Second panel: electron density. Third panel: electron temperature. Fourth panel: (c) argon working gas density, (d) argon ion density nAr+ , (e) hot recombined argon density nArH , and (f) metastable argon density nArm . Fifth panel: (g) ionized density fraction of the sputtered species (aluminum), Fdensity,Al , (h) ionized density fraction of the argon working gas, Fdensity,Ar . The discharge was operated in argon at 1.8 Pa with a 2 inch Al target, with a pulse voltage of 450 V and a peak discharge current of 12 A. From Huo et al. (2012). ©IOP Publishing. Reproduced with permission. All rights reserved.

laxes when the quantity of electrons in the IR starts to be significant (≈ 10% of nmax e ). This is consistent with Langmuir probe measurements performed by Gudmundsson et al. (2002, 2009) in a similar discharge and with optical emission measurements in another HiPIMS device (Hála et al., 2010), which demonstrate a significant amount of fast electrons during the discharge ignition. Further details on the electron temperature at this early stage are found in Section 3.2. The second phase, around the maximum of the discharge current, is characterized by a strong increase of the plasma density that reaches its maximum around the same time as the peak discharge current. This huge amount of electrons results in very effective ionization of the neutral species (see bottom panel of Fig. 5.13), which cools down the electrons (reduces their effective temperature), which reaches a minimum

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(∼ 3.5 eV) slightly before the time of the peak discharge current. The peak plasma density is ne ≈ 3.5 × 1019 m−3 , which is in line with the peak electron density values found in Section 3.2. The IRM predicts an important rarefaction of the gas (fourth panel, curve (c)), the argon density being reduced below 50% of the initial value a little after the discharge current reaches its maximum. The ionized density fraction represents about 10% of the total argon density (bottom panel, curve (h)), and it is the main mechanism responsible for the neutral depletion (curve (d)) in the present example. The other contributions are discussed in more detail in Section 4.2.2. The third phase is characterized by the afterglow. For short pulses, this is when the applied discharge voltage is cut off. In the example shown in Fig. 5.13 the pulse is very long or 400 µs. Consequently, before the afterglow, there is an intermediate phase characterized by a current decay when all the plasma parameters relax (see also Section 7.2.2). One exception is observed for the electron temperature that stays almost constant until the end of the pulse. Time and 2D space evolution of the density of charged species using PIC/MCC modeling was first calculated by Minea et al. (2014) for the early stages of the pulse. They gave also the first 2D maps of the electron and ion evolution and an estimation of the time to build up the space charge. In their simulation, only 2 µs are necessary to increase the plasma density by two orders of magnitude, from 1016 m−3 (pre-ionized discharge) to 1018 m−3 , corresponding to the transition from dcMS to HiPIMS operation. A comparison can also be made with recent calculations by Revel et al. (2018) using 2D self-consistent PIC/MCC simulations of a HiPIMS discharge operated with short pulses (< 10 µs), including pre-ionized discharge and the afterglow. The first two phases of the pulse development can be well identified, in spite of the short pulse (5 µs). Qualitatively, PIC/MCC simulations confirm the behavior found by the IRM. The peak discharge current is reached in a very short time and is followed by a plateau (see Fig. 5.12). The typical time to build up the space charge is 2 to 3 µs in these PIC/MCC simulations, that is, the pre-ionization reduces the first phase of the pulse with at least 10 µs. Through this type of modeling, internal plasma parameters, such as charged particle density, plasma potential, and so on, become accessible, also within the magnetic trap, where experimental techniques typically fail (see Chapter 3). Hence, the spatial extension of the IR can be clearly identified using the PIC/MCC approach and its evolution during the pulse and the afterglow. Fig. 5.14 shows 2D maps for the Ar+ ion density nAr+ , the electron density ne , the plasma potential Vp , and the axial electric field Ez at t = 2 µs. For a better visualization of the cathode sheath, the z-axis is plotted on a logarithmic scale for the Vp and Ez maps. It is very easy to obtain the mean value of a plasma parameter once its spatial distribution is known. The mean value can be calculated for the entire simulation domain or for a specific discharge region. As an example, the electron density averaged over the ionization region (5 < x < 15 mm and 0.1 < z < 5 mm in Fig. 5.14) is plotted in Fig. 5.15 as a function of time (Revel et al., 2018). It is compared to the maximum electron density in the discharge. The current and voltage waveforms are also reported for easier analysis.

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Figure 5.14 2D maps of ion and electron density (upper row), plasma potential, and axial electric field (lower row) of a short-pulse HiPIMS discharge, obtained by PIC/MCC simulation, for the time 2 µs in Fig. 5.15 (top). The maps on the lower row have the axial distance plotted on a logarithmic scale, and the different regions of the discharge are indicated by labels (right): CS for cathode sheath, IR for ionization region, and DR for diffusion region. From Revel et al. (2018). ©IOP Publishing. Reproduced with permission. All rights reserved.

The temporal evolution of the averaged electron density in the IR is similar to that of the discharge current (Fig. 5.15). Similar trends between the discharge current and plasma density have been obtained both experimentally (Meier et al., 2018) and by modeling using the IRM (Raadu et al., 2011, Gudmundsson et al., 2016) and shown in Fig. 5.13, or from the CRM (Bretagne et al., 2015), although for different time-scales and magnitudes. A rough comparison between the PIC/MCC simulation (Fig. 5.15) and the IRM (Fig. 5.13) results shows a relatively good qualitative agreement. However, in the IRM example the current is about 10 times higher than in the PIC/MCC simulation, which is reflected in the plasma density. The electron density is about 50 times higher in the IRM compared to the PIC/MCC averaged value but only about 20 times higher compared to maximum density given by the PIC/MCC. This discrepancy can have several origins. The potential drop over the discharge volume VD is much smaller in the PIC/MCC simulation because the external resistance is

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Figure 5.15 (A) The discharge voltage and current waveforms, and (B) comparison of the maximum and average electron densities during a short-pulse HiPIMS discharge, obtained by a PIC/MCC simulation. The average density was computed over the ionization region seen in Fig. 5.14. The same simulation conditions as for Fig. 5.12, for R = 500 . From Revel et al. (2018). ©IOP Publishing. Reproduced with permission. All rights reserved.

high (500 ) and the potential drop over this resistance drastically increases with the discharge current, reducing VD (Fig. 5.15, top). The magnetic field strength is higher in the PIC/MCC simulation confining the electrons close to the cathode and reducing the ionization probability. Furthermore, the pulse in the PIC/MCC simulation is too short to provide a significant amount of metal atoms that considerably contribute to the current increase (self-sputtering). Metal ionization also produces more electrons in the IR, which after being energized can ionize even more neutrals. The values for the plasma density are in better agreement when comparing the PIC/MCC results with measurements performed by Bohlmark et al. (2005) with Langmuir probes (Fig. 3.5). The shortest time is 40 µs in Fig. 3.5 (a) when the average plasma density is in the range from 1 × 1018 to 5 × 1018 m−3 , whereas the maximum density, just in front of the race track, hardly exceeds 5 × 1018 m−3 . As the pulse is 5 µs in total, the values found for the average density about 0.7 × 1018 m−3 and the maximum density oscillates around 1.5 × 1018 m−3 seem acceptable. Note also that Bohlmark et al. (2005) used pulses of 9 J and repetition frequency of 50 Hz (the discharge current is not indicated in the paper).

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Figure 5.16 (A) The metastable argon density [Arm ] from laser measurements with different pulse cutoff times (from Vitelaru et al. (2012)) and (B) the metastable argon density [Arm ] from the IRM calculations. Operating conditions are the same as shown in Fig. 5.8. From Stancu et al. (2015). ©IOP Publishing. Reproduced with permission. All rights reserved.

In conclusion, the HiPIMS plasma density obtained by modeling is in rather good agreement with experimentally recorded values. The IRM can simulate long and energetic pulses, whereas the PIC/MCC approach is limited, for the moment, to short pulses and lower electron density (ne < 1019 m−3 ). PIC/MCC results confirm IRM findings, giving consistency to HiPIMS models.

5.2.3.2

Excited states evolution

Both the IRM and the PIC/MCC approaches give insights into the plasma kinetics and particularly the excited states generated during the pulse. The most interesting are the long-lived excited levels, metastable states, of the working gas atoms and sputtered metal atoms. Here we focus on the working gas (argon), but experiments have been performed that follow the excited metal states as well, and they can also be modeled. The kinetics of the argon metastable states (Arm ) was implemented in one of the IRM versions (Stancu et al., 2015). Furthermore, the evolution of Arm was also recorded by time-resolved tunable diode laser absorption spectroscopy (TD-LAS) (Vitelaru et al., 2012), and the results were compared with the IRM output (Stancu et al., 2015). The good agreement obtained, seen in Fig. 5.16, was taken as an additional indication of the validity of the IRM. The metastable state of argon reaches its first maximum very fast (≈ 20 µs), much earlier than the maximum in the discharge current (≈ 75 µs), for a 200 µs-long pulse (see Fig. 5.8). The explanation of this early peak of the excited states (creation-loss equilibrium) is the higher production of the metastable states during the ignition phase due to the higher electron temperature, but especially the lower effectiveness of the loss terms (see Section 7.2.2 for details). The Arm experiences a minimum at the same time as the discharge current reaches its maximum, and the density of the ground state

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of argon is reduced. The second peak observed for long pulses is due to an evolution similar to that at the beginning of the pulse, with a slight increase of the density of the Ar ground state favoring Arm production by direct electron impact excitation of Ar (Stancu et al., 2015). An important result was obtained with the same IRM model concerning the role played by the metastable argon atoms in argon ionization via a two-step ionization process (involving two electrons of lower energy compared to the single-step process with an ionization energy of 15.75 eV). It had been suggested that the argon metastables contribute significantly to Ar ionization in HiPIMS, but the model demonstrated the contrary (Gudmundsson et al., 2015). Indeed, stepwise ionization is found to be negligible during the breakdown phase of the HiPIMS pulse and becomes significant (but never dominating) only later in the pulse. In conventional dcMS, stepwise ionization can be an important route for ionization of the argon gas. Indeed, the electron energy is lower in dcMS compared to HiPIMS, and the direct ionization probability increases nonlinearly with increase in the effective electron temperature. Under these conditions, direct ionization is the major route for Ar+ production. These results are in line with experimental observations by Britun et al. (2015).

5.2.3.3

Electron energy distribution function (EEDF)

The first numerical work aiming to evaluate the electron energy distribution function (EEDF) in HiPIMS was using the collisional radiative model (CRM) reported by Vašina et al. (2008). The EEDF was computed for different discharge currents, with or without the presence of the sputtered metal (Cu), and the results are shown in Fig. 5.17 for the plateau phase of a HiPIMS discharge (pulse waveforms of the voltage and discharge current are given in Fig. 5.11). The model results showed that Coulomb electron–ion collisions are dominant in the low energy range (the limit depends on the discharge current but, in general, for energies below 7 eV). The presence of the metal (Cu) species reduces (cools down) the EEDF, that is, the number of electrons in the energy range from approximately 3 to 40 eV decreases, and the number of low energy electrons (≤ 2 eV) increases, as can be seen in Fig. 5.17. The authors assumed that the latter are responsible for the ion transport from the ionization region to the substrate (ambipolar diffusion), acting as a neutralizing background. The IRM gives the mean energy of electrons in the IR, assumed at equilibrium (Maxwell distribution), so characterized by one temperature (Raadu et al., 2011). Typical values of the electron temperature found by the IRM lie between 8 eV (or even higher) at the beginning of the pulse to about 4 eV when the peak (or plateau) current is established (see e.g. Fig. 5.13, third panel). More recent versions of the IRM considers two electron populations present in the plasma (Huo et al., 2013). The two populations are referred to as “cold” and “hot” electrons with temperature intervals for the fit in the range Te = 0.01 – 10 eV and 200 – 1000 eV, respectively. The details are given in Section 5.1.3.5. This approximation is based on the fact that the electron impact ionization rate coefficient is fairly flat for energies larger than a few tens of eV, which makes it rather insensitive to the actual shape of the energy distribution of the hot electrons.

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Figure 5.17 The EEDFs computed for different HiPIMS discharge currents, with or without the presence of the sputtered metal in a 0D collisional radiative model (CRM). The following conditions were assumed: argon working gas at 1.4 Pa, 50 mT average magnetic field, and a circular copper target 33 mm in diameter. The maximum electron energy for each discharge current indicates the applied discharge voltage. From Vašina et al. (2008). ©IOP Publishing. Reproduced with permission. All rights reserved.

PIC/MCC modeling contains information of the electron velocity at each time step and for each macroparticle in the plasma. The energy distribution function can be plotted at a given moment in the pulse or over a limited region in space (selecting the particles present in this region). Typical results are reported in Fig. 5.18 (integrated over the whole simulated volume). The moments in time correspond to the capital letters (B–D) of the current pulse indicated in Fig. 5.15 (upper panel). During the first phase (ignition, time B), two electron populations are observed (Fig. 5.18, top). The cold population has Tce ∼ 11 eV, whereas the hot one is characterized by Teh ∼ 43 eV, and it represents ∼10% of the plasma electrons. The hot component Teh has its origin in secondary electrons emitted from the target surface, which gain energy in the high voltage drop across the sheath. At this moment in time the space charge is not sufficiently high in the plasma volume, and the discharge voltage is almost entirely used to accelerate the electrons. The cold population is produced mainly by ionization within the IR. A similar evolution of the electron temperature for the two populations was found by Huo et al. (2017). For important discharge voltages (approaching 1000 V), the initial ionization peak value is very high. This result is connected to an initial burst of hot electrons, also seen experimentally (Pajdarová et al., 2009). Poolcharuansin and Bradley (2010) called these electrons “superthermal”, and they are active only at the beginning of the pulse, as shown in Fig. 3.6. These electrons contribute significantly to effectively ionize the argon working gas when the high power pulse is applied. Indeed, the presence of very hot electrons at the very beginning of the pulse can be understood as the faster way to build up the space charge. Their energy is at this stage of the pulse taken from the pulse voltage due to the absence of a significant voltage drop in the ionization region.

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Figure 5.18 Energy distribution functions for electrons and ions in a short-pulse HiPIMS discharge, obtained by PIC/MCC simulation, averaged over the entire simulation domain for the times 2 µs (B-ignition), 5 µs (C-plateau), and 6 µs (D-afterglow) shown in Fig. 5.15 (top). The dashed lines show fits using a Maxwellian distribution for the EEDF. The insets show a zoom over the first 20 eV, the typical energy range accessible for probe measurements. The same simulation conditions as for Fig. 5.15, for R = 500 . From Revel et al. (2018). ©IOP Publishing. Reproduced with permission. All rights reserved.

When the plasma reaches steady-state conditions (panel C of Fig. 5.18), corresponding to the plateau of the current in Fig. 5.15, both populations relax toward much lower values, namely Te ∼ 7 eV and Teh ∼ 11 eV. Electron temperatures found by the IRM (Huo et al., 2012) evolve during the pulse from its maximum of 11 eV to about 5 eV at the end of the pulse when the plasma density and the discharge current decrease significantly. The experimentally recorded electron temperature by Poolcharuansin and Bradley (2010), discussed in Section 3.2, shows an increase at the beginning of the pulse, characterized by an almost flat EEDF that reaches a maximum temperature at 10 µs, and relaxes afterward. These results are to be compared to the inset in Fig. 5.18. The time correspondence is not ensured because the PIC/MCC results are obtained with a pre-ionization voltage, but the trends are in qualitative good agreement.

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For the near afterglow phase (panel D of Fig. 5.18), the two electron populations continue to relax, and their temperatures get closer to each other, both dropping in the “cold” temperature range < 10 eV (Huo et al., 2013). The PIC/MCC values are Te ∼ 5.5 eV and Teh ∼ 8 eV, but they correspond to only 6 µs after the beginning of the pulse, whereas the relaxation time is in the range of tens of µs (Poolcharuansin and Bradley, 2010). Equilibrium of the temperatures of the two electron populations is estimated to about 5 µs after pulse initiation by Poolcharuansin and Bradley (2010), but their measurement is local and relatively far from the IR (10 cm away from the cathode). In the IR the time for electrons to all be in equilibrium is expected to be longer.

5.2.3.4

Ion energy distribution function (IEDF)

An extended discussion on the plasma ions is presented in Section 4.1, including a discussion on ion energy measurements. However, here we only focus on the modeling results and the new insights they bring for the understanding of the HiPIMS discharge. PIC/MCC simulations contain also all the information regarding the ions, including their velocity (energy). Revel et al. (2018) investigated the ion energy distribution function (IEDF) for Ar+ ions striking the cathode at four different points in time (A–D) shown in Fig. 5.15 (top). This information is particularly important because it is a key to sputtering. At the very beginning of the pulse the ions exhibit energy in the range 200 – 500 eV, and there is practically no slow ions reaching the target (with an energy < 200 eV) (not shown). A similar energy distribution, between 250 and 500 eV, is recorded during the initial current increase, but the number of ions reaching the cathode is already one order of magnitude higher than at time A (not shown). In the plateau region of the discharge current (time C) the potential drop over the discharge (VD ) decreases to only 200 V, the remaining part of Vapp being lost on the external resistance (1.2 A through 500 ). Consequently, the energetic ions bombarding the target are contained within this maximum energy. The authors also found that the lower energy limit, which is only 40 eV, could be correlated to the potential drop over the cathode sheath. This unexpected result shows that a significant fraction of the plasma ions are not accelerated by the total discharge voltage (VD ), and consequently the ions are not forming a monoenergetic beam, as often assumed in the literature. Moreover, the continuous IEDF between the two limits (not shown) indicates that some ions are created in the presheath region where the potential is not zero, that is, this is the effect of a potential drop over the IR. In the afterglow the plasma potential relaxes toward zero, but the ions reaching the cathode preserve some of their kinetic energy (inertia). In light of modeling results of the IEDF, two main conclusions can be drawn. First, the ions bombarding the target are not monoenergetic. Second, they are accelerated in the IR reaching high energies before entering the sheath. Further discussions on the potential distribution are found in Section 7.2.3.

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Figure 5.19 (A) Drift velocity wz and (B) diffusion coefficient Dzz in the axial direction (z) as functions of the releasing position x of the cloud of secondary electrons for two different instantaneous powers, low (L) and high (H), of a short-pulse HiPIMS discharge. The simulated discharge conditions were: argon working gas at 5 mTorr, rectangular metallic target of 40 mm width, 105 test electrons followed during 100 ns. From Costin et al. (2014). ©IOP Publishing. Reproduced with permission. All rights reserved.

5.2.3.5

Electron transport coefficients and plasma deconfinement

HiPIMS discharges present a paradigm shift compared to other types of sputtering discharges, and this originates mainly from the very high ionization degree together with the effectiveness of the magnetic trap for electrons. Indeed, the very high discharge current operation (discharge current density can easily exceed 2 A/cm2 ) constrains the electrons to satisfy two contradictory requirements at the same time: (i) they must be energetic enough to effectively ionize the working gas and the sputtered metal atoms in spite of the low working gas pressure, and this is possible only using magnetic confinement, but (ii) they should increase their capability to escape from the magnetic trap to ensure closing the electric circuit and thereby enable large discharge currents. It is possible to evaluate via modeling the transport parameters of electrons crossing the magnetic barrier from the cathode to the anode. They have to be compared to the conventional values obtained for dcMS, and in this way, we can better understand the requirements formulated. Fig. 5.19 shows the results for the electron drift velocity wz and diffusion coefficient Dzz for two different instantaneous HiPIMS powers, low (L) and high (H) (Costin et al., 2014). The two discharge conditions correspond to two different times during the pulse: (L) is at 75 ns after the pulse power is on, that is, practically the dcMS discharge condition with a cathode voltage of 322 V; (H) is 1.4 µs later, which is assumed a typical case for the HiPIMS operation regime, with a cathode voltage of 600 V. The transport coefficients are estimated for the secondary electrons released at different points across the target (x-axis). The target was assumed rectangular, with a width of 40 mm along the x-axis and an infinite length along the y-axis. The center of the target is at x = 0 mm, and the center of the race track is at x ∼ 9.5 mm. In Fig. 5.19, we see that the diffusion coefficient is more sensitive to the discharge regime, increasing in the HiPIMS mode (H) by roughly 3.5 – 4.5 times with respect to the dcMS mode (L). One exception is recorded at x = 6 mm, where the increase

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Figure 5.20 Comparison of the drift velocity wy in the direction of E × B drift obtained by three methods: PIC/MCC, a posteriori MC, and calculated as E × B/B 2 for two different instantaneous powers, low (L) and high (H), of a short-pulse HiPIMS discharge. Calculations are made above the race track (x ∼ 9.5 mm). The same simulation conditions as for Fig. 5.19. From Costin et al. (2014). ©IOP Publishing. Reproduced with permission. All rights reserved.

is only 2 times, which is a position closer to the center of the target where the magnetic field line is not parallel to the cathode. It is surprising that the increase of Dzz is slightly larger (a factor of 4) on the other side of the target (moving away from the race track to the cathode edge). The electron drift velocity wy is well oriented in the direction of E × B, and it was estimated by three different methods (PIC/MCC, a posteriori MC, and calculated as E × B/B 2 using averaged values for E and B). The comparison is reported in Fig. 5.20 for the same two different instantaneous powers as before, low (L) and high (H). The drift velocity wy is calculated at different points along the z-axis, right above the race track (x ∼ 9.5 mm). The cathode sheath (z < 1 mm) is characterized by high values of the drift velocity wy , induced by the strong sheath electric field. In the IR, a posteriori MC results are in good agreement with the analytical drift velocity E × B/B 2 , whereas the PIC/MCC simulation overestimates the drift velocity. The difference is assigned to the fact that a posteriori MC simulates only electrons released in a specific point in space (the same point for which the quantity E × B/B 2 is estimated), whereas PIC/MCC simulation considers the electrons coming from different regions of the discharge, which cross the point of interest at a certain moment and contribute to the average value of the drift velocity wy . The HiPIMS regime is characterized by higher values of wy in the IR, which is a sign of a higher axial electric field compared to the dcMS regime. To summarize, due to the increase in the plasma density, in the HiPIMS operation regime the plasma electrons increase their capacity to escape from the magnetic trap, a phenomenon called de-confinement. Another mechanism that seems to play an important role for keeping the high density plasma is likely the Coulomb interaction between electrons and ions, proposed by Vašina et al. (2008). Hence the local density increases, and the higher diffusion across the magnetic barrier allows the current increase in the pulse. The E × B drift of electrons is slightly faster in HiPIMS discharge compared to dcMS discharge. Topics related to plasma deconfinement are discussed

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in detail in Section 7.3, and 3D plasma structuring (spokes) in Section 7.4 including both experimental observations and modeling results.

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Reactive high power impulse magnetron sputtering

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Tomáš Kubarta , Jon Tomas Gudmundssonb,c , Daniel Lundind a Solid State Electronics, The Ångström Laboratory, Uppsala University, Uppsala, Sweden, b Department of Space and Plasma Physics, School of Electrical Engineering and Computer Science, KTH Royal Institute of Technology, Stockholm, Sweden, c Science Institute, University of Iceland, Reykjavik, Iceland, d Laboratoire de Physique des Gaz et Plasmas LPGP, UMR 8578 CNRS, Université Paris–Sud, Université Paris–Saclay, Orsay Cedex, France

Reactive magnetron sputtering is essential in many industrial processes where it is applied to deposit compound films or coatings. Reactive sputtering is attractive because a range of compounds can be prepared from a low-cost metal target by addition of an appropriate reactive gas to the noble working gas. Using reactive HiPIMS adds several beneficial effects through ion assistance during growth of compound thin films (the material properties are discussed in detail in Chapter 8). To understand the reactive HiPIMS process, we here start with an overview of reactive sputtering and an introduction to process hysteresis in dcMS, which is followed by an overview of fundamental surface and plasma processes focusing on the behavior specific for reactive sputtering. In the second half of the chapter, HiPIMS-specific aspects of reactive sputtering will be reviewed. This includes hysteresis in reactive HiPIMS operation, which is the subject of much debate, as some report reduction or elimination of the hysteresis effect, while others claim that a feedback control is essential. To provide a deeper insight into the process physics, a combination of experimental and computational model results are presented and discussed throughout the text.

6.1 Introduction to reactive sputter deposition In reactive sputter deposition, compound thin films are deposited on a surface where a chemical reaction between the sputtered precursor, typically a metal, and a reactive gas introduced into the process atmosphere takes place (Depla and Mahieu, 2008). The deposition process hence contains elements of physical and chemical vapor deposition (Smith, 1995), and the plasma chemistry is thereby of great importance. The use of a gas precursor makes reactive sputtering very flexible, and a wide range of compounds can be synthesized from the same sputter target by simply changing the reactive gas. In addition to the flexibility, less expensive and more robust metal targets are used instead of brittle ceramic ones. Although oxides and nitrides are the most common materials deposited by reactive sputtering (Safi, 2000) with materials such as TiN, CrN, or TiO2 widely used, other High Power Impulse Magnetron Sputtering. https://doi.org/10.1016/B978-0-12-812454-3.00011-5 Copyright © 2020 Elsevier Inc. All rights reserved.

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compounds such as carbides (Zehnder and Patscheider, 2000) and sulfides (Thornton et al., 1984) can also be synthesized. The properties of the deposited films can be tuned by the deposition process as will be discussed in Chapter 8. In fact, magnetron sputtering provides several means for control of the film growth. Stoichiometry, the ratio between metal and reactive gas atoms, is the first factor determining the properties of a compound and therefore has to be carefully controlled. Control of the compound stoichiometry is achieved by controlling the ratio between the flux of metal atoms and reactive gas atoms and molecules in reactive sputter deposition. Simple control of the reactive gas supply, however, is not sufficient to control the deposition process. When a compound layer is formed on the sputter target surface, the sputter rate of the target changes, altering the flux ratio even without a change in the external process parameters (Berg and Nyberg, 2005). The growth conditions are therefore also a function of the process history exhibiting the so-called hysteresis effect. Maintaining the deposition process at a desired working point, that is, providing optimum and stable growth conditions, is a major challenge. The deposition rate is another important factor that determines productivity. Ensuring the process stability and increasing the deposition rate remain the main engineering challenges in reactive magnetron sputter deposition with the process hysteresis representing the main issue (Berg and Nyberg, 2005). The microstructure is also of critical importance and is sensitive to the growth conditions (Sundgren et al., 1983). In addition, the temperature stability of the substrate materials may limit the deposition temperature in many cases. Careful selection of the growth conditions can help to achieve the desired performance of the deposited materials despite reduced substrate temperature (Fortier et al., 2014, Vlˇcek et al., 2017).

6.1.1 Working point The first task in the development of a deposition process is identifying a stable working point that provides suitable growth conditions resulting in a material with the desired properties. Process curves that display different process parameters as functions of the reactive gas flow provide a first guidance in determining the working point without analyzing film properties. Representative process curves of the deposition rate, discharge voltage, and partial pressure of the reactive gas are shown in Fig. 6.1 for the case of Ti sputtering in Ar/O2 atmosphere. A typical evolution of the deposition rate with reactive gas flow is displayed in Fig. 6.1A, which shows the well-known hysteresis loop. When the reactive gas flow is increased above a certain value, the deposition rate decreases suddenly and equally abruptly returns to the high deposition rate regime when the reactive gas supply is sufficiently reduced. A hysteresis is also observed in the discharge voltage (Fig. 6.1B) and in the oxygen partial pressure (Fig. 6.1C) versus oxygen flow rate. The hysteresis is most severe for oxides where an order of magnitude reduction of the deposition rate is common (Berg and Nyberg, 2005). A schematic sketch of the mass deposition rate curve is shown in Fig. 6.2, where the three main regions of operation of a reactive magnetron process are indicated. For low reactive gas flows, a metal mode is maintained with predominantly metallic film deposited at a high rate.

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Figure 6.1 Evolution of process parameters (A) deposition rate, (B) discharge voltage, and (C) oxygen partial pressure with the oxygen flow rate in reactive sputtering of Ti in Ar/O2 atmosphere. The arrows indicate the direction of the transition.

Figure 6.2 Deposition rate evolution with reactive gas flow. Pronounced hysteresis (wide transition region) defined by the transitions A–B and C–D is shown.

All the supplied reactive gas is incorporated into the deposited metal, the surface of the sputter target is free from compound, and the addition of the reactive gas does not affect significantly the sputter process. The mass deposition rate increases somewhat with increasing flow of the reactive gas as the mass of the gas atoms adds to that of the deposited metal. With further increase in the reactive gas flow, the deposition rate drops abruptly as a transition from metal to compound mode takes place, seen as a jump from point A to point B in Fig. 6.2. At this reactive gas flow rate, all the sputtered metal is converted into compound material, and the excess reactive gas reacts with the sputter target surface covering it with a layer of compound material. Films deposited in the compound mode are stoichiometric, and further addition of reactive gas does not have any significant effect (except an increase of the partial pressure

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of the reactive gas, as seen in Fig. 6.1C). The compound mode is maintained even when the reactive gas supply is reduced until a point C in Fig. 6.2 is reached. Here the reactive gas supply no longer maintains the compound layer on the sputter target surface, and a transition to the metal mode (point D) occurs. The presence of hysteresis means that the working point in the transition region A–B–C–D is ill defined. For the same reactive gas flow rate, the deposition process may be in the metal (D–A) or compound mode (C–B), depending on the process history. Furthermore, a disturbance in the sputtering can cause a transition from one to the other mode. Deposition in the transition region, however, is very attractive because it offers the possibility of tuning the film stoichiometry, and the deposition rate may be increased (Sproul, 1998), which we will explore further in Section 6.3. When there is a large difference in the sputter yield of metal (YM ) and compound (YC ), compound formation results in a significant reduction of sputtered metal (YM  YC ). This in turn leads to further reduced consumption of the reactive gas and thus increased formation of the compound layer. Such a positive feedback explains the abrupt change in the deposition rate observed in Fig. 6.1A (down arrow). Transition back to the metal mode occurs when the reactive gas flow is reduced so that there is not enough reactive gas to convert all the sputtered metal into compound. This leads to an enhanced cleaning of the sputter target surface and increased metal sputtering, so that the balance is tipped toward the metal mode as seen in Fig. 6.1A (up arrow). The hysteresis is especially severe for oxides because of the large difference in sputter yields between metal and oxide surfaces. Taking the example of Ti, the sputter yield by 500 eV Ar+ ions is about 0.69 for the pure metal, but only about 0.05 for TiO2 (Kubart et al., 2010). The corresponding sputter yield for TiN is 0.42 (Ranjan et al., 2001). It should be noted that several process parameters change simultaneously when increasing/decreasing the reactive gas flow rate. The quantity controlling the process behavior is the partial pressure of the reactive gas, seen in Fig. 6.1C, that determines the reactive gas flux to all surfaces. Direct measurement of partial pressures, however, requires specialized instrumentation, which is not always available. The discharge voltage, seen in Fig. 6.1B, is easily accessible and provides quick information on the working point, because the secondary electron emission usually changes upon compound formation and hence immediately affects the discharge voltage (Depla et al., 2007) (see also Section 6.2.2). However, in HiPIMS discharges the discharge characteristics is less dependent on the secondary electron yield, as described in more detail in Section 7.2.1.2. Monitoring the HiPIMS peak discharge current instead is a better solution in some cases, as we will see in Section 6.4.2. Already the first models of reactive sputtering (Kadlec et al., 1986, Berg et al., 1987) reproduced the basic process characteristics and explained the relation between the sputter yields, gas reactivity, and pumping speed of a deposition system. The pumping speed is one of the factors determining the occurrence of hysteresis for a given set of process parameters. If the excess reactive gas at the metal to compound mode transition may be removed by the pump, then the abrupt transition and thus hysteresis can be completely avoided (Kadlec et al., 1987). The required pumping speeds, however, make this solution impractical for larger depositions system. Modeling also

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suggested other ways of avoiding hysteresis, for instance, by reducing the active area of the sputter target (Nyberg et al., 2005).

6.1.2 Process control An easy way to ensure the deposition of stoichiometric films is to operate in the compound mode. The oversupply of reactive gas ensures stoichiometric deposition albeit at the cost of very low deposition rate, often, an order of magnitude lower than in the metal mode. Although such a low rate may be acceptable in laboratory experiments, the productivity is low. Moreover, for some materials, the excess of reactive gas may deteriorate film properties. For example, the color of nitrides such as TiN is very sensitive to the N2 supply (Mumtaz and Class, 1982, Roquiny et al., 1999) and requires very careful control of the stoichiometry. Increasing the deposition rate while keeping the desired stoichiometry may be possible inside the transition region. As explained earlier, the deposition process is not stable in the transition region when the reactive gas flow is controlled and a suitable feedback control of the process is required (Sproul et al., 2005). Controlling the reactive gas partial pressure offers a more reliable way of process control. The difference between gas flow and partial pressure control is illustrated in Fig. 6.3. When the deposition rate is plotted as a function of the oxygen gas flow, as seen in Fig. 6.3A, the data points form an S-shaped curve characteristic of a process with hysteresis. The slope of the curve inside the transition region is negative, indicating an unstable area. However, the same data plotted as a function of the oxygen partial pressure, seen in Fig. 6.3B, forms a smooth curve demonstrating that the partial pressure is suitable as a control parameter. Although various control techniques are available for reactive sputtering based, for instance, on reactive gas partial pressure or the discharge voltage (Sproul, 1996), they present additional complications for the process implementation. In addition, gradients in the reactive gas pressure may lead to different local conditions across large sputtering targets, and a combination of several sensors and advanced gas distribution systems is required in large deposition systems (Ruske et al., 2006). The reported hysteresis-free reactive HiPIMS operation (Wallin and Helmersson, 2008) has therefore attracted a lot of attention and will be discussed in Section 6.3.1. Control techniques suitable for reactive HiPIMS are summarized in Section 6.4.2.

6.2 Fundamentals of reactive sputtering Here the elementary surface and plasma processes specific for reactive sputtering are discussed. The purpose is to provide a base for the discussion of experimental results. A simple balance model of hysteresis in reactive sputtering, taking into account the surface processes, is also presented.

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Figure 6.3 Reactive sputtering of Ce in an Ar/O2 discharge with oxygen partial pressure control. The mass deposition rate versus the (A) oxygen flow and (B) the oxygen partial pressure. Although the deposition process again exhibited hysteresis (A), the transition region was accessible, and gradual evolution of the deposition rate was achieved through partial pressure control (B). Data from Aiempanakit et al. (2011).

6.2.1 Molecular gas and plasma chemistry In reactive sputtering, a reactive gas (e.g. O2 , N2 , CH4 , etc.) is mixed with the noble working gas to synthesize a compound film. When a molecular gas is added to the noble working gas, the plasma chemistry becomes significantly more complex, and various surface processes need to be taken into account. The molecules dissociate, the atoms and molecules are ionized, and there are attachment processes that form negative ions. Furthermore, as the molecular gas is added to the noble working gas, we would expect that the energy loss for generating electron–ion pairs increases and thus the electron density is decreased. This is due to higher total electron impact excitation cross-sections for molecular gases due to excitation to vibrational and rotational levels in the molecules. Nevertheless, the electron density in the HiPIMS discharge is expected to enhance the dissociation of the molecular gas, which is sometimes considered beneficial for oxide, nitride, or carbide deposition.

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Figure 6.4 The initial sticking probability S0 of the O2 molecule on Al 111, at normal incidence, as a function of translational energy Et . Open and closed symbols represent experiments with ground-state and mixed ground-state vibrationally excited O2 molecules, respectively. Reprinted figure with permission from Österlund et al. (1997). Copyright 1997 by the American Physical Society.

Let us first look at chemisorption of reactive species on the surfaces of the deposition system. There are various processes where atoms and molecules of the reactive gas interact with the surfaces. Each of the discharge species has a sticking coefficient S that depends on the composition of the chamber wall, substrate, or target surfaces. For example, when depositing from a titanium target, the compound formation rates are higher in oxygen as compared to nitrogen. This can be explained by the higher oxygen affinity to titanium compared to nitrogen. The enthalpy of formation of TiO2 and TiN is −944 and −388 kJ/mol, respectively (Haynes et al., 2017). Also, the sticking coefficient of nitrogen on titanium is lower than that of oxygen. Although the oxygen sticking coefficient is close to unity, Mao et al. (2002) reported values for the sticking coefficient for atomic nitrogen on titanium as low as 0.1. Furthermore, dissociation of diatomic molecules on solid surfaces (dissociative sticking) is a process that can influence both the plasma chemistry and the surface properties. Dissociation of molecules and subsequent formation of adsorbate–substrate bonds is an important process in metal oxidation. It has been suggested that the dissociative sticking probability of thermal (300 K) O2 molecules on Al surfaces is very low, (< 10−2 ) (Gartland, 1977). However, as seen in Fig. 6.4, the dissociative sticking probability increases steeply with increased translational energy of the molecule in the range from room temperature up to 0.6 eV and then remains at a constant value of 0.9 up to 2 eV (Österlund et al., 1997). Also the crystal face of the surface can have significant influence as has been demonstrated for Al(111) and Al(100) faces (Gartland, 1977). It is, however, important to point out that in reactive sputtering, there are two pathways for incorporation of reactive gas into the surface. In addition to chemisorption often described by a sticking coefficient (Depla and De Gryse, 2004b), direct implantation of energetic reactive gas ions can occur (Depla and De Gryse, 2004a). A combination of both processes, referred to as ion impact enhanced chemisorption, has also been reported for reactive HiPIMS and is discussed in Section 6.2.4. The atoms or molecules of the reactive gas can also recombine at surfaces. As a reactive neutral species hits the chamber walls or the target surface, it can return as a

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thermal particle, and atoms can recombine to form a thermal molecule. As an example, we can look at the oxygen discharge. The wall recombination coefficient for the neutral atoms in ground state O(3 P) has been suggested to decrease with increasing discharge pressure from about 0.5 at 2 mTorr to roughly 0.1 at 150 mTorr (Gudmundsson and Thorsteinsson, 2007). The atoms then recombine to form the ground state oxygen molecule O2 (X3 g− ), whereas some of the oxygen atoms O(3 P) hitting the chamber walls or target surface are reflected with typically a lower energy. Similarly, the metastable oxygen atoms O(1 D) that hit the chamber walls and either recombine or are reflected or quenched. In the oxygen discharge the singlet metastable molecular states have a significant influence on the discharge properties as they dictate the creation and loss of the negative oxygen ions within the plasma volume (Gudmundsson and Thorsteinsson, 2007). It has been pointed out by Du et al. (2011) that the quenching probability of the singlet metastable O2 (a1 g ) increases with both the duration of the exposure to a surface and the concentration of O2 (a1 g ). The values for the measured wall quenching coefficient, found in the literature, for metastable O2 (a1 g ) and O2 (b1 g+ ) on various surfaces have been summarized by Proto and Gudmundsson (2018). It is noted that the values found in the literature span a few orders of magnitude and depend on the surface material. In fact, the measured values also vary by orders of magnitude for the same materials. The quenching probability for the singlet metastable O2 (b1 g+ ) is in general significantly higher than for O2 (a1 g ). It should be noted that it is not easy to determine an actual value for the surface recombination or quenching coefficients of the various species on the various surfaces either experimentally or theoretically. In general, we expect that the recombination or quenching probability for any species hitting a surface depends not only on the species itself, but also on the surface material, the surface temperature, and the actual surface conditions, such as surface roughness and contamination, which can vary substantially. In addition, negative ions can also form on surfaces, and it is well known that high-energy negative ions such as O− are generated at the target surface and can arrive at the substrate with energies corresponding to the cathode potential (typically 200 – 1000 eV) in absence of collisions (Bowes et al., 2013), which is discussed in Section 6.4.5. These energetic ions, although important for the quality of the deposited films, are assumed to play a negligible role in the discharge physics. The plasma chemistry in reactive HiPIMS has been studied by Gudmundsson et al. (2016) and Lundin et al. (2017) using the IRM code (see Section 5.1.3). In this model, oxygen is added to the argon working gas, and a number of species are added to the discharge model. The model includes oxygen molecules in the ground state O2 (X3 g− ), metastable oxygen molecules O2 (a1 g ) and O2 (b1 g ), oxygen atoms in the ground state O(3 P), metastable oxygen atoms O(1 D), positive ions O+ 2 and O+ , and negative ions O− . The model also takes into account changes in secondary electron emission yield (discussed in Section 6.2.2) and sputter yield (discussed in Section 6.2.3) of the target. This model was applied to explore an Ar/O2 HiPIMS discharge with a Ti target in both metal and poisoned modes. Some of the model results are discussed in Section 6.4.4, in particular, the density evolution of the ionic species involved.

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6.2.2 Secondary electron emission Ions in dcMS discharges are created to a large extent by secondary electrons emitted from the cathode surface by ion bombardment (Thornton, 1978). These electrons are accelerated in the cathode sheath to an energy corresponding to the discharge voltage, and we often denote them as hot electrons eH . The minimum discharge voltage to sustain the plasma was defined by Eq. (1.38), the Thornton equation. From this equation we see that a higher secondary electron emission yield γsee results in a lower discharge voltage. As discussed in Section 1.1.4, the secondary electron emission from clean metal surfaces is dominated by potential emission. However, in the presence of a reactive gas, the secondary electron emission is significantly affected, and the underlying processes are summarized here. The secondary electron emission coefficient γsee can be estimated using the empirical expression given by Eq. (1.15). The condition for secondary electron emission is that the ionization energy Eiz of the projectile has to be sufficiently high compared to the metal work function φ, that is, 0.78Eiz > 2φ. The work function and ionization energy of common metals are listed in Table 1.3. Given that the work function is in the range 4 – 6 eV for most metals, the secondary electron emission coefficient is about 0.07 for Ar+ ions bombarding a clean metal surface. Whereas neutral atoms cannot induce potential emission, metastable process gas atoms are very efficient in doing so (Lieberman and Lichtenberg, 2005, Phelps and Petrovi´c, 1999) due to their relatively high potential energy. Values of γsee determined by Ar+ and Ar beam experiments up to 10 keV were critically reviewed by Phelps and Petrovi´c (1999). The result showing a fit to experimentally determined values for a range of materials bombarded by Ar+ ions, for both clean and dirty surfaces, is shown in Fig. 1.4 and corresponds well to the theory. Up to about 500 eV, the secondary electron emission due to bombardment by Ar+ ions is constant as is characteristic for potential emission predicted by Eq. (1.16). At higher ion bombarding energies, kinetic emission becomes important. Energetic Ar neutrals produce electrons only by kinetic emission, and at high energies, γsee is comparable to that for Ar+ ions. On the other hand, results for “dirty” surfaces covered by adsorbed and chemisorbed atoms, also shown in Fig. 1.4, reveal significantly higher γsee at lower energies. The dirty surfaces are relevant for reactive sputtering, where the sputtering target surface is far from clean. Depending on the operating conditions, the surface may be covered by a layer of physisorbed reactive gas or a compound. The difference in γsee shows that the threshold for kinetic emission is about an order of magnitude lower in the case of dirty metal surfaces. The value of γsee increases from about 0.07 for 500 eV Ar+ ions impinging on a clean metal surface to about 0.2 when the surface is contaminated. An increased electron emission can be explained by a reduced surface barrier for electron removal observed for insulators (Baragiola and Riccardi, 2008). Despite the importance of γsee , the measured values are rather scattered and sometimes contradicting. This is caused both by difficulties in quantifying the surface composition in beam experiments and the complexity of the environment, in particular, in reactive experiments. We will therefore summarize results from dcMS experiments

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and discuss some results from beam measurements. Depla et al. (2007) studied extensively the discharge behavior of reactive dcMS and presented a comprehensive review of the secondary electron emission coefficients for a range of oxides, and the results are shown in Fig. 6.5A. The values were determined from the discharge voltage in dcMS with Ar as the working gas. Two groups of oxides were identified based on the secondary electron emission behavior with the surface oxidation. Compounds that form substoichiometric oxides and are prone to preferential sputtering of oxygen exhibit reduced electron emission upon oxidation. TiO2 is a prominent member of this group. On the other hand, oxides that do not lose oxygen preferentially show an increase in the electron emission with surface oxidation. One such example is Al2 O3 . Fig. 6.5A confirms the contrasting behavior of Ti and Al with a reduced γsee from an oxidized Ti surface and significantly enhanced γsee from oxidized Al. This work demonstrated that the surface stoichiometry is crucial for the secondary emission. The same group carried out an extended study of γsee due to nitride formation (Depla et al., 2009), and the results are presented in Fig. 6.5B. Only wide-band-gap semiconductor nitrides (AlN and Mg2 N3 ) showed a pronounced increase in the value of γsee when a nitride is formed on the surface. Recently, Ar+ beam measurements with controlled flux of O atoms and O2 molecules were carried out for Al and Ti surfaces (Corbella et al., 2016). Unlike the earlier works, the secondary electron emission coefficient was measured directly in this work. For an oxidized Al surface, surprisingly high values of γsee were detected, about 0.4 at 500 eV. Even for Ti, an increase, rather than a decrease, of γsee upon oxidation was observed. These results on high γsee values for oxidized surfaces are indirectly confirmed in an extensive review on the secondary electron emission by Hannesdottir and Gudmundsson (2016), who fitted all the data available in the literature for O+ and O+ 2 ion-induced emission from clean and oxidized surfaces. The fit showed values significantly exceeding the typical values for clean surfaces bombarded by Ar+ ions and essentially independent of the target material. Larger values of γsee were found for oxidized targets. The large spread in reported γsee values can be explained by the strong effect of surface composition. Especially for materials that reduce under ion bombardment due to preferential sputtering, the ratio between reactive gas and ion flux is very important. Moreover, in pulsed processes such as HiPIMS, the surface composition may vary in time and therefore lead to effective γsee values different from those observed during dc sputtering (Kubart and Aijaz, 2017).

6.2.3 Sputter yields for compounds The theory of sputtering was introduced in Section 1.1. Although the basic theory holds for reactive sputtering, determining the sputter yields of compounds is more complex. This is caused by preferential sputtering that leads to changes in the surface composition and by lack of input values for simulations of compound sputtering. Here we discuss some basic aspects of compound sputtering and review the typical values of sputter yields. We also provide a general guidance for sputter yield calculations.

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Figure 6.5 Relative change in the secondary electron emission coefficient of metal surfaces upon (A) oxidation and (B) nitridation under Ar+ ion bombardment in dcMS operation. Reprinted from Depla et al. (2009), with permission from Elsevier.

In compounds, the different constituents have generally different partial sputter yields. TiO2 is a well-known example where preferential sputtering leads to pronounced oxygen losses from the surface and changes in the surface stoichiometry

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(Diebold, 2003). The surface composition changes with the ion fluence until a steady state is reached.1 From Sigmund’s theory (Sigmund, 1981) it is found that the ratio of partial sputter yields Y1 and Y2 for a compound consisting of elements 1 and 2 is given by Y1 c1 = Y2 c2



M2 M1

m 

Esb2 Esb1

(1−2m) ,

(6.1)

where Esb1 and Esb2 are the surface binding energy of elements 1 and 2, respectively, M1 and M2 are the atomic masses of each element, ci is the concentration of element i, and m is a factor typically lower than 0.2. The differences in partial sputter yields are determined mainly by the difference in Esb rather than by the atomic mass ratio M2 /M1 since m is small. The energy Esb is also used in binary collision simulations to describe the surface potential barrier for removal of an atom from the surface. The values of Esb1 and Esb2 are in general difficult to determine for compounds. Dullni (1984) measured the velocity distributions of Ti and Al atoms sputtered in the presence of O2 and N2 and determined Esb using Eq. (1.28). The results showed a significant increase in the surface binding energy upon surface oxidation, up to 16 eV for TiO2 . Kelly (1986) developed a model based on point-defect theory to explain the experimental results on ionic oxides. Very high values of Esb were predicted in reasonable agreement with Dullni’s experiments (Dullni, 1984). Sputter yields are most often calculated using the binary collision models described in Section 1.1.7. Static codes, such as TRIM, however, do not reflect the evolution in the surface composition. Dynamic codes such as SDTrimSP (Mutzke et al., 2011) or TRIDYN (Möller et al., 1988), which take into account surface evolution, provide a better picture. All the codes, however, require the surface binding energy Esb as one of the input parameters. Due to the difficulty determining accurate values of sputter yields for oxides, Kubart et al. (2010) used a combination of deposition rates measured in sputtering experiments, surface composition measured by X-ray photoelectron spectroscopy (XPS) with ion beam sputtering, and dynamic binary collision approximation (BCA) simulations in TRIDYN to determine the values of Esb . Fitting the experimental data resulted in values of the surface binding energies shown in Table 6.1. Note that the values for compounds are in many cases very high as compared to that for pure metals in agreement with the theory presented by Kelly (1986). Using the fitted data, partial sputter yields and the surface evolution may be simulated although the Esb values are, strictly speaking, valid only for TRIDYN. Oxides with an intermediate composition may not fit the model for Esb implemented in TRIDYN, as discussed in more detail by Kubart et al. (2010). As an example, sputter yields for Ti from a Ti target and for Ti and O from a TiO2 target bombarded with Ar+ ions are shown in Fig. 6.6. To simplify the situation, only the extreme cases, either clean Ti or stoichiometric TiO2 surfaces, were considered, and the surface composition was fixed in each simulation. The simulations show that the sputter yield for 1 Ion fluence is defined as the number of ions intersecting a unit area in a specific time interval, i.e. a product of ion flux and time t given in [m−2 ] (Zhang and Weber, 2016).

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metal,oxide Table 6.1 Surface binding energies of metal Esb and oxygen,oxide

oxygen Esb in an oxide determined by fitting data from reactive sputtering experiments (Kubart et al., 2010). metal are also shown Corresponding values for pure metal Esb in the last column. Element Ti Al Ta Nb V

metal,oxide

Esb [eV] 10.0 12.0 8.1 7.6 6.2

oxygen,oxide

Esb [eV] 7 9 8 9 6

metal Esb [eV] 4.86 3.36 8.1 7.6 5.3

Figure 6.6 Ti sputter yield versus ion energy for Ar+ ions bombarding a Ti target and O and Ti sputter yields for Ar+ ions bombarding a TiO2 target, calculated using TRIDYN. Surface binding energies from Table 6.1 were used.

Ti decreases nearly 20 times, from 0.62 to 0.033 for bombardment by Ar+ ions at 500 eV. The sputter yield of oxygen is higher than for the metal in compound mode, 0.21 at 500 eV, indicating pronounced preferential sputtering. The results are in agreement with experiments, which show an order of magnitude drop in the deposition rate upon surface oxidation (Kubart et al., 2008). In reality, an intermediate stoichiometry is established with the exact composition depending on the O2 supply and the extent of preferential sputtering. Extra caution is necessary in the specific case of TiO2 . Ti suboxides have very high sputter yields, and the surface depleted in oxygen may therefore exhibit a Ti sputter yield much higher than expected from a combination of Ti and TiO2 (Kubart et al., 2008).

6.2.4 Reactive gas implantation and thickness of the compound layer We will now discuss the thickness of the compound layer formed on a surface of the sputter target. Chemisorption would lead only to an atomically thin compound layer.

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Experiments, however, have shown that the compound thickness is of the order of a few nm, indicating that an additional mechanism is at play. Abe et al. (2005) measured by ellipsometry the thickness of a TiO2 layer on a Ti target during sputtering in an Ar/O2 mixture. They reported a thickness of the oxide layer up to 7 nm. The oxide thickness increased to as much as 100 nm when the target was only mechanically clamped to a cooling plate, which was attributed to inefficient cooling. The same value of 7 nm was also determined for an Al2 O3 layer on an Al target surface sputtered in pure O2 (Chiba et al., 2008). Güttler et al. (2004) performed in situ ion beam measurements of a titanium magnetron target surface for various Ar/N2 ratios. These experiments showed a nitrogen areal density of 1016 cm−2 corresponding to about 10 monolayers (2.5 nm) of stoichiometric TiN for higher flows of nitrogen. The observed compound thickness beyond a monolayer was explained by Depla et al. (2004) as a result of ion implantation of the reactive gas. Energetic ions of the reactive gas are implanted into the target surface in direct implantation. In addition, chemisorbed reactive atoms from the surface are pushed deeper into the sputter target surface by impinging ions in a knock-on implantation (Möller and Güttler, 2007). Knock-on implantation dominates in reactive systems, whereas direct implantation is more important in material systems with low reactivity. This is because the knock-on (or forward) yield is typically several times higher than the corresponding sputter yield (Kubart et al., 2006), and both Ar+ ions and reactive gas ions contribute to the knockon process. The thickness of the implanted layer is in this scenario related to the ion range, which is typically 1.5 nm for 500 eV Ar+ ions in a Ti target according to TRIM, and therefore the resulting compound thickness is only a few nm in good agreement with the experimental results of 2 – 7 nm. However, when diffusion is taking place at elevated temperatures, the compound thickness may be substantially higher in line with the previously discussed results by Abe et al. (2005).

6.2.5 Balance (Berg) model of hysteresis reactive sputtering Modeling is crucial for understanding the process physics. Various physical mechanisms can be implemented in a model and the simulated results compared to experiments verifying the accuracy of our description. Modeling is also very useful in process optimization and development in order to reduce the time required for trial-and-error testing. There are models of various complexity available to model the HiPIMS process, as described in Chapter 5. In this section a simple balance equation model of reactive sputtering, also known as the Berg model, is presented (Berg et al., 1987, 1988, Berg and Nyberg, 2005). Despite its simplicity, it well reproduces the main features of the hysteresis behavior in dcMS, and it also is useful for understanding the HiPIMS process. One of the main limitations of the Berg model is a complete absence of plasma processes. To address this issue, results on the plasma characteristics is discussed in Sections 6.4.4 and 6.4.5 using a reactive version of the IRM code, introduced in Section 5.1.3. The Berg model approach is to formulate a very simple description that reproduces the experimental behavior of the process characteristics rather than including all possible physical mechanisms. The description is therefore simplified taking into account

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Figure 6.7 A schematic of a reactive magnetron sputtering setup consisting of a sputter target, substrate, gas handling and pumping system.

Figure 6.8 Model representation of the reactive deposition process from Fig. 6.7. Surfaces of the sputter target (top) and substrate (bottom) are shown together with the pathways for molecular and atomic oxygen and for metal atoms. θt denotes the fraction of target surface covered by a compound. The remaining part of the target surface (1 − θt ) consists of pure metal. The same principle is used for the compound fraction on the substrate, θs .

only the most important mechanisms. Despite these simplifications, the basic features of reactive sputtering are well reproduced although the results should be considered as qualitative only. On the other hand, the simplicity of the model facilitates evaluation of the impact of various physical mechanisms. The philosophy behind the model is reviewed in detail by Berg and Nyberg (2005), and models of reactive dcMS are described by Depla and Mahieu (2008). Here a simple model is introduced using some of the physical and chemical mechanisms described earlier. A reactive sputtering system, schematically represented in Fig. 6.7, is described by a set of balance equations. A schematic representation of the system implemented is illustrated in Fig. 6.8, where the compound coverage of the target and substrate are indicated. In the model, the compound coverage of the sputter target, denoted by θt , and of the substrate surface θs , together with the partial pressure pRG of reactive gas, in the deposition system are followed.

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A constant surface density of metal atoms, independent of the reactive gas atom concentration, is assumed. The surface therefore represents a constant density of surface sites, which can be either metallic or covered with compound. Fig. 6.8 shows such an example of the sputter target. Formation of the compound is caused by a flux of reactive gas RG with a sticking coefficient SRG , which is often assumed close to unity although a more detailed evaluation suggests significantly lower values (Strijckmans et al., 2012). The compound formation is described by assuming a stoichiometry of 1:1 such that each reactive gas atom occupies one metal site. The reactive gas flux to the surface is given by the ideal gas equation as RG = 

pRG , 2kB Tg πMRG

(6.2)

where pRG is the reactive gas partial pressure, kB is the Boltzmann constant, Tg is the gas temperature, and MRG is the mass of the reactive gas molecule. The balance for the compound fraction θt on the sputter target surface can be formulated assuming that chemisorption of reactive gas on the target is counteracted by removal through sputtering of the compound. Assuming atomic sputtering, that is, that metal and reactive gas atoms are ejected as individual atoms from the surface, the compound is removed at a rate (Ji /qe )YCC , where YCC is the partial sputter yield of reactive gas atoms from the compound, and Ji /qe is the ion flux to the surface calculated from the discharge current Ji =

ID , At qe (1 + γsee )

(6.3)

where At is the target area. Then the balance equation is dθt Ji = 2SRG RG (1 − θt ) − YCC θt , dt qe

(6.4)

where the first term on the right-hand side accounts for the formation of the compound due to the flux of diatomic molecules of the reactive gas to the metallic part of the target surface, and the second term describes removal of the reactive gas off the surface covered by the compound. The substrate balance is described in an analogous way as dθs Ji At = 2SRG RG (1 − θs ) − (YMM (1 − θt ) + YMC θt ) θs    dt q As e   I II

At Ji + YCC θt (1 − θs ) qe As   

(6.5)

III

with terms I and III representing the formation of compound on the metallic fraction of the substrate surface by thermal flux of reactive gas (term I) and by reactive gas

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atoms sputtered from the target with unity sticking coefficient (term III). Deposition of metal atoms (term II) over the compound part of the substrate provides fresh metallic surface and reduces the compound coverage. The fluxes of sputtered species from the target with an area At are distributed uniformly over the whole receiving substrate area As . The last system variable expresses the amount of reactive gas in the system. It can be expressed either by the partial pressure pRG or by the number of reactive gas molecules NRG : N dNRG = qRG − SRG  (1 − θt )At 2 dt 2πV MRG /(kB T )    I

− SRG  

N 1 Ji YCC θt At θs , (1 − θs )As − Sp + V 2 qe RG /(kB T )       

N 2πV 2 M

II

III

IV

(6.6) where the supplied reactive gas qRG (in molecules/s) is consumed at the sputtering target (term I), substrate (term II), or removed by the pump with a pumping speed Sp (in m3 /s) (term III). In the case of atomic sputtering, additional reactive gas may be supplied by sputtering from reacted parts of the target surface (IV). The equation system (6.4) – (6.6) can be solved analytically for a system in steady state (Berg and Nyberg, 2005). In steady state, all the state variables have constant values, the time derivatives on the left-hand side are zero, and the equation system simplifies to a set of algebraic equations. Fig. 6.9 shows a typical solution for compound coverage of the target and substrate, target erosion rate and the partial pressure of reactive gas as a function of the reactive gas flow. As an example of a reactive system, we use dcMS of a Ti target in an Ar/O2 atmosphere as described by Kubart et al. (2008). The experimental data were fitted using the input data summarized in Table 6.2. The results are characteristic for reactive processes where hysteresis occurs. In the model, the reactive gas partial pressure is used as a system variable to ensure a singlevalued solution in each working point. This way, it is possible to obtain solutions inside the transition region, and instead of a hysteresis loop, an S-shaped curve is obtained. Dashed vertical lines in Fig. 6.9 indicate the corresponding hysteresis loop that can be compared to experimental measurements shown in Fig. 6.1. The modeled S-curve describes an experiment where a feedback process control is used such as in Fig. 6.3. The erosion rate, presented in Fig. 6.9 (middle panel), can be converted to the mass deposition rate by taking into account the substrate surface coverage. The absolute value of the deposition rate, however, is averaged over the whole receiving area As and therefore smaller than the deposition rate on a substrate facing the sputtering target.

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Figure 6.9 Typical dcMS modeling results displayed as a function of the reactive gas supply. The hysteresis loop is indicated by vertical dashed lines as discussed in the text. The input data is summarized in Table 6.2.

Table 6.2 Input parameters used in the Berg model presented in this section. The values are based on a study of reactive dcMS of titanium in Ar/O2 mixture (Kubart et al., 2008). Symbol SRG YMM YMC YCC MRG At As ID Tg Sp

6.3

Value 1 0.4 0.02 6 × YMC 32 8 cm2 400 cm2 160 mA 400 K 16.8 l/s

Explanation Sticking coefficient of O2 on metal Sputter yield of metal from metal surface Sputter yield of metal from compound surface Sputter yield of oxygen from compound surface Atomic mass of the reactive gas molecule Effective area of the sputter target Effective receiving area including the substrate and chamber walls Discharge current Gas temperature Pumping speed

Hysteresis in reactive HiPIMS

In this section, we discuss results from various experiments on the reactive HiPIMS discharge. We start by investigating the hysteresis behavior and attempt to provide an explanation of different observations. The discussion is supported by results from the balance (Berg) model introduced in Section 6.2.5. Then, we focus on the sputter target surface that determines the dynamics of the reactive process and the discharge characteristics. Finally, we summarize the main results obtained from plasma characterization with relevance for reactive processes.

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Figure 6.10 Hysteresis-free deposition of Al2 O3 by reactive HiPIMS. (A) The mass deposition versus the O2 flow rate. The limit for deposition of stoichiometric Al2 O3 is indicated as a shaded region to the right of the dashed line in the top figure. (B) The O2 partial pressure versus the O2 flow rate. Increased O2 partial pressure during HiPIMS operation confirms operation inside the transition region. Pulse on-time was 35 µs at a repetition frequency of 1 kHz, and the peak current density was in the range 0.35 – 1.25 A/cm2 . Reprinted from Wallin and Helmersson (2008), with permission from Elsevier.

6.3.1 Experimental observations The key features of hysteresis in reactive magnetron sputtering were introduced in Section 6.1. Because of the technological importance of the hysteresis behavior, the initial reports on hysteresis-free operation of reactive HiPIMS attracted much attention. Wallin and Helmersson (2008) compared the behavior of dcMS and HiPIMS while depositing Al2 O3 in Ar/O2 mixture from an Al target, and the results are seen in Fig. 6.10. They demonstrated deposition of stoichiometric alumina by reactive HiPIMS without transition to the oxide mode. Although the range of oxygen gas flows was limited during the HiPIMS deposition, the HiPIMS process could be operated beyond the dcMS critical flow, and Al2 O3 was deposited at a deposition rate comparable to the metal mode value without any process control. The authors tentatively attributed the lack of hysteresis to the pulsed nature of HiPIMS, namely strong target cleaning during the pulses and limited oxidation during the off-time. Sarakinos et al. (2007) observed a similar behavior and reported increased deposition rates when sputtering a TiO1.8 target in an Ar/O2 mixture by HiPIMS. The hysteresis-free operation was attributed to a stronger gas rarefaction in HiPIMS (see Section 4.2.2), and thus a reduced target oxidation since less reactive gas is available. The same authors analyzed in detail reactive deposition of ZrOx from a metal target in an Ar/O2 mixture and confirmed a smooth hysteresis-free transition between the metal and oxide modes in contrast to the corresponding dcMS process, where an abrupt transition was observed (Sarakinos et al., 2008), as shown in Fig. 6.11. In this study, relatively high duty cycles of 3 and 10% were used.

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Figure 6.11 The target voltage versus the O2 flow rate showing hysteresis-free HiPIMS of Zr in an Ar/O2 atmosphere. (A) The dcMS process shows an abrupt change in the discharge voltage for an O2 flow rate between 2.25 and 2.5 sccm. In contrast, the discharge voltage evolves continuously with the O2 flow in HiPIMS processes for (B) 50/450 and (C) 50/1450 pulse on/off time. The closed and open symbols correspond to target voltage values recorded for increasing and decreasing oxygen flow, respectively. Reprinted from Sarakinos et al. (2008), with permission from Elsevier.

Figure 6.12 Discharge voltage versus the O2 flow rate in reactive sputtering of a Ce target in Ar/O2 with O2 partial pressure control. The results show a pronounced hysteresis in the dcMS process. The width of the hysteresis loop decreased with increasing pulsing frequency of HiPIMS. The average discharge power was kept constant at 70 W in all experiments resulting in a pulse power density of up to 450 W/cm2 at a frequency of 1 kHz. Reprinted from Aiempanakit et al. (2011), with permission from Elsevier.

The effect of pulsing frequency was further studied by Aiempanakit et al. (2011) for Al and Ce targets sputtered in Ar/O2 atmosphere. Reduction of hysteresis was reported for both material systems, and the Ce case is shown in Fig. 6.12. The hysteresis was minimized for an intermediate frequency of 4 kHz with the hysteresis loop widening both for higher (not shown) and lower values (shown) of the repetition frequency. The behavior was reproduced for larger area Ti targets with the same result (Kubart et al., 2011).

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Figure 6.13 The reactive gas partial pressure versus O2 flow rate showing hysteresis in dual magnetron sputtering experiments. Ti and Al targets were used, and the pulse power density was varied from 16 – 19 W/cm2 to 360 – 405 W/cm2 , corresponding to a peak current density of up to 2 A/cm2 . Reprinted ˇ from Capek and Kadlec (2017), with the permission of AIP Publishing.

A recent study of dual magnetron sputtering using Ti and Al targets in Ar/O2 and Ti ˇ and Kadlec (2017) provided data on hysteresis in reactive targets in Ar/N2 by Capek HiPIMS as a function of the duty cycle and pulsing frequency. The dual magnetron configuration does not suffer from the disappearing anode effect2 and is in general more stable than a single-cathode system. A reduction of hysteresis with increasing peak power is clearly visible for both oxides in Fig. 6.13. The increasing peak power has also an effect on the nitride processes without a clear hysteresis, where the transition from metal to nitride mode becomes more gradual. The authors explained their results by back-attraction of the sputtered metal and developed a model based on the ˇ experimental results (Kadlec and Capek, 2017) (see Section 7.5 for more detail on back-attraction). Interestingly though, there is no minimum of the hysteresis width at an intermediate frequency in contrast to the study by Aiempanakit et al. (2011). However, the two experiments used different pulse configurations. Whereas Aiemˇ panakit et al. (2011) kept the on-time constant and varied the pulsing frequency, Capek and Kadlec (2017) varied both the frequency and the on-time. Therefore, very short on-time of only 5 µs was used at some frequencies in the latter study, which might possibly influence gas rarefaction. 2 Loss of electrical ground when the grounded surfaces facing the plasma are covered by insulating com-

pound.

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Most of the available experimental results come from small laboratory systems with sputtering targets commonly smaller than 80 cm2 . With respect to the influence of the target size, Surpi et al. (2013) confirmed the effect of frequency on the width of the hysteresis loop in reactive HiPIMS with a Ti target using an area of 375 cm2 . At a repetition frequency of 500 Hz, a more narrow hysteresis loop was recorded than at 200 Hz despite the higher deposition rate at 500 Hz. An average power density of 5 W/cm2 was kept constant in both experiments. Assuming the gas refill time proportional to the depleted volume and thus also the target area, increasing the target size would lead to reduction in the optimum pulsing frequency as a result of longer refill times. Although this explanation agrees with the data of Surpi et al. (2013), comparison of different experimental systems is complicated, and more experiments are necessary. It is, however, clear that the effect of the sputtering target size needs to be considered. In summary, there are a number of studies demonstrating a reduction of hysteresis in reactive sputtering with HiPIMS. The effect, however, is best noticeable in laboratory systems with small sputtering targets. Large systems generally show a much wider hysteresis loop due to their limited pumping speed. As a result, even if the hysteresis is somewhat reduced, the final effect may be less pronounced in such large systems. From the technological viewpoint, the most important consequence of hysteresis-free operation using HiPIMS is the possibility of a high deposition rate of a stoichiometric compound in the transition mode or close to the transition from metal mode.

6.3.2 Dynamics of the hysteresis Contrary to the results on reduced hysteresis in HiPIMS, Audronis and BellidoGonzalez (2010, 2011) found the hysteresis comparable or even more pronounced in HiPIMS discharges than in dcMS discharges for a number of target–reactive gas combinations. The authors, however, used a different experimental configuration with an optical emission feedback control system. By changing the setpoint for the control system, the whole process curve could be recorded during a time as short as 180 s. Such a fast experiment, however, is influenced by additional dynamical effects briefly described here. Kubart et al. (2006) adapted a Berg model to study the dynamical behavior of hysteresis in dcMS. The results, shown in Fig. 6.14, suggest that the hysteresis loop widens when the reactive gas flow changes quickly. Therefore, the series of experiments described by Audronis and Bellido-Gonzalez (2010, 2011) probed the dynamic behavior of the reactive process rather than the traditional steady-state hysteresis. The wide hysteresis loop observed by Audronis and Bellido-Gonzalez (2010) can be compared to Fig. 6.14. Note that in the experiments (Audronis and Bellido-Gonzalez, 2010), the oxygen flow was varied very fast, from 0 up to 30 sccm and back to 0 over only 90 s. The rate of gas flow change was therefore 40 sccm/min. Interpretation of such dynamic measurements is challenging and cannot be compared to the process curves measured slowly. Rather, the work highlighted the complexity of reactive HiPIMS processes. Especially for points close to the critical flows, the transition times

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Figure 6.14 Hysteresis curves simulated for several rates of reactive gas flow change. With increasing rate of reactive gas flow change, the apparent hysteresis loop widens. Reprinted from Kubart et al. (2006), with permission from Elsevier.

may be very long, and “steady-state” hysteresis requires very slow rate of change and long measurement time (Kubart et al., 2006).

6.3.3 Models of hysteresis in reactive HiPIMS In the previous sections, several mechanisms have been proposed to explain the observed reduction of hysteresis in reactive HiPIMS. These have been: (i) fast cleaning of the sputtering target surface due to the high current density in a pulse (Wallin and Helmersson, 2008), (ii) rarefaction and thus reduction of the flux of reactive gas to the target surface (Sarakinos et al., 2007), (iii) a change in the sputtering as a result of increased discharge voltage (Sarakinos et al., 2008), or (iv) back-attraction of the ˇ sputtered metal (Kadlec and Capek, 2017). The simple Berg model introduced in Section 6.2.5 is very useful to judge the impact of these mechanisms on the hysteresis in reactive HiPIMS. Here we use the set of parameters listed in Table 6.2 to assess the impact of metal ion return, gas rarefaction, and increased preferential sputtering of the reactive gas on the hysteresis curve. Rather than developing new models, the input data can be adjusted to reflect each mechanism. Specifically, preferential sputtering of oxygen and enhanced target surface cleaning is accommodated by doubling the partial sputter yield of oxygen YCC . The metal return to the target (metal ion back-attraction) leads to a reduced deposition rate and is therefore taken into account by reducing the metal sputter yield YMM to 50% of the reference value. Finally, gas rarefaction that results in a reduced partial pressure of oxygen in the target vicinity is accounted for by reducing the oxygen flux O2 to the target. Results from the simulation, together with the dcMS reference from Fig. 6.9, are shown in Fig. 6.15. Both enhanced surface cleaning (curve (b)) and reduced oxidation due to gas rarefaction (curve (c)) result in reduced oxidation of the sputter target. Both mechanisms also reduce the width of the hysteresis loop, that is, the distance between the critical flows. At the same time, however, a shift of the hysteresis region to higher oxygen flow rates is predicted. The shift toward higher flow rates contradicts experiments. Metal returning to the sputter target (curve (a)), on the other hand, leads

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Figure 6.15 Results from a simple Berg model calculations assessing the impact of (a) metal ions returning to the target, (b) enhanced target cleaning, (c) gas rarefaction, and (d) reference results for a corresponding dcMS system.

to reduced hysteresis and a shift toward lower oxygen flow due to the reduced overall deposition rate. The simulations may be qualitatively compared to the experimental data shown in Fig. 6.13. In the HiPIMS experiments, the hysteresis becomes narrower with increasing peak power, and a shift toward lower oxygen flow is observed. The simulation shows that although the width of the hysteresis loop is reduced in all cases, only the models with metal return reproduce the observed shift of the hysteresis toward lower reactive gas flow. ˇ Kadlec and Capek (2017) extended the analytical model to take into account the return of metal ions to the sputtering target surface. The return probability βt of ionized sputtered material reached up to 60% for the highest peak power. The model showed very good agreement to the experimental data for three different material systems ˇ (TiO2 , Al2 O3 , and TiN) (Capek and Kadlec, 2017). A model taking the return of metal ions into account was developed by Kozák and Vlˇcek (2016). In this case the authors focused on the effect of reactive gas distribution with different configurations of the oxygen gas inlet and operation inside the transition region. In this comprehensive time-dependent model, gas rarefaction was also considered together with time-dependent values of the sticking coefficient. The authors did not study the hysteresis behavior, but rather focused on optimizing process conditions for high deposition rate and showed how to arrange the reactive gas inlet to minimize formation of a compound on the sputtering target surface. Furthermore, they demonstrated that the compound coverage of the target surface changes very little during a single HiPIMS pulse, which we will return to in Section 6.4.3.

6.4

Important aspects of reactive HiPIMS

In addition to the previously described characteristics of the hysteresis behavior, there are several other important process characteristics in reactive HiPIMS, such as changes

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in the discharge current evolution with the addition of a reactive gas, which is connected to changes in the plasma characteristics and target dynamics. We have also seen that the reduced hysteresis can potentially have an impact on the process stability and deposition rate, which will be addressed in this section.

6.4.1 Discharge waveforms The understanding of the shape and amplitude of the discharge current waveform of the nonreactive HiPIMS discharge is now rather well established (Gudmundsson et al., 2012, Lundin et al., 2009, Huo et al., 2012), and the different stages during the pulse current evolution are discussed in detail in Section 7.2.2 when exploring the physics of HiPIMS. For the reactive HiPIMS discharge, the current waveform shows a somewhat different behavior, where the discharge current waveform can change significantly in shape and/or in amplitude (peak value) when the target surface enters the compound mode (Gudmundsson, 2016). The change in the shape of the current waveform depends on the target material, on the state of the target, and on the reactive molecular gas. Experimental findings indicate that the current increase appears to follow one of two paths. On one hand, the current waveform becomes distinctly triangular in shape for Ar/O2 discharges with Al target (Aiempanakit et al., 2013), Ti target (Aiempanakit et al., 2013, Straˇnák et al., 2008, Magnus et al., 2012, Cemin et al., 2018), and V target (Aijaz et al., 2016), and for an Ar/N2 discharge with a Hf target (Shimizu et al., 2015), as the discharge enters the compound mode. Fig. 6.16 shows this behavior when sputtering a Ti target in an Ar/O2 mixture. When operating in the compound mode (higher oxygen flow rate), the current appears triangular as the current is still rising at the time it terminates at the end of the applied voltage pulse. Also, the discharge current peak increases with increased oxygen flow. However, the discharge current waveform does not always become triangular as the target transitions into compound mode. In some cases, on the other hand, the current maintains the shape of the nonreactive waveform as the current increases. This is seen for an Ar/N2 discharge with Ti target (Magnus et al., 2011), an Ar/O2 discharge with Nb target (Hála et al., 2012), and for a Ru target in Ar/O2 mixture in a pre-ionized HiPIMS discharge (Benzeggouta et al., 2009). Note, however, that the pulse discharge current increase when moving from the metal mode to the compound mode can for all these discharges be very high. For example, Hála et al. (2011) report a peak current density for an argon discharge with Cr target of 0.5 A/cm2 (metal mode), whereas for a pure oxygen discharge, it is 6 A/cm2 (compound mode) at the same voltage and pressure. Such a strong discharge current increase is very different from dcMS operation, where the amplitude of the discharge current is governed by the secondary electron emission yield, which in turn depends on the state of the target material (Depla et al., 2009), as discussed in Section 6.2.2. For example, Ti is one of the metals where a decrease in the discharge current is observed in the compound mode when operating dcMS in an Ar/O2 mixture, which is in line with the decreased secondary electron emission yield in the oxide mode reported in Fig. 6.5. This is in stark contrast to the significantly higher peak currents observed in HiPIMS (Magnus et al., 2012) for the same material system.

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Figure 6.16 Discharge current waveforms for reactive HiPIMS of Ti target in Ar/O2 discharge. The pulse repetition frequency was 150 Hz, the pulse length 100 µs, and the target diameter 100 mm. The average power was kept constant at 540 W for all experiments.

Discharge current waveforms in reactive HiPIMS were first analyzed in detail by Benzeggouta et al. (2009) for HiPIMS discharges with a Ru target in an Ar/O2 mixture. The discharge current waveforms exhibited a significant increase in current amplitude as the discharge transitioned to the compound mode. The authors attributed this current increase to a higher ionization cross-section of O2 as compared to Ar and thereby a larger ion production (i.e. increased charge carrier density). In addition, they also noted an initial discharge current decrease when going from the pure Ar discharge to the Ar/O2 mixture, which they ascribed to the loss of low-energy electrons to the excitation of rotational and vibrational levels of the O2 molecules. Magnus et al. (2011) offered another interpretation of the increasing discharge currents in compound mode when studying an Ar/N2 discharge with a Ti target. They attributed this behavior to an increased total secondary electron emission yield of the nitride when the ion flux impinging on the surface contains large fractions of N+ ions compared to mainly metal ions in the metal mode. As shown in Eqs. (1.15) and (1.16), the ionization energy of the impinging ion determines the secondary electron emission in the potential emission regime, which would increase in the case of N+ ions (ionization energy of 13.6 eV for N) compared to Ti+ ions (6.83 eV for Ti). The secondary electron emission may also be increased due to the pulsed nature of HiPIMS. Kubart and Aijaz (2017) argued that the surface would be rich in oxygen at the onset of a HiPIMS pulse. This would lead to an increase of the secondary emission in contrast to the behavior of dcMS. Currently, however, it is believed that the changes in the secondary electron emission play a minor role in HiPIMS discharges (Gudmundsson et al., 2016, Brenning et al., 2017), where only a small fraction of the ionization is due to these hot secondary electrons, which is further explored in Section 7.2.3. Instead, the observed changes in the discharge current shape and amplitude are dominated by changes in the type of ion recycling needed to reach high discharge currents, where we differentiate between ionized sputtered species returning to the target (self-sputter recycling) and the release of working gas from the target followed by ionization and back-attraction to the target (gas recycling) (Brenning et al., 2017). The details of ion recycling are given in Section 7.2.1.1, but we will here summarize the implications of this mechanism on

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the reactive HiPIMS discharges. Applying the previously described ionization region model (Section 5.1.3) to an Ar/O2 HiPIMS discharge with a Ti target in both metal mode and in compound mode, Gudmundsson et al. (2016) found that the composition and the contribution of different ions to the discharge current vary significantly between the metal mode and the compound mode in reactive HiPIMS. In the compound mode the current was dominated by Ar+ ions, of which two thirds were recycled. The considerably higher discharge current and the triangular shape of the current waveform in the poisoned mode can thereby be understood as a consequence of the discharge being dominated by working gas recycling. When this is the case, the discharge current can in principle become very high if the return probability of the working gas from the target is close to unity, which is likely to be the case for noble gases (Anders et al., 2012). In the metal mode the discharge was instead governed by mainly recycling of the titanium ions. However, due to a self-sputter yield significantly below one (YSS = 0.7) at the chosen operating conditions, the resupply of Ti neutrals was limited (limited self-sputter recycling) and hence stabilized the discharge current at a much lower amplitude.

6.4.2 Process stability and deposition rate High-rate deposition of stoichiometric compounds can be achieved in the transition regime. Various control strategies have been employed in reactive HiPIMS to control the working point. In addition to the traditional approaches, such as plasma emission monitoring (Audronis et al., 2010, Wu et al., 2014) or partial pressure control (Sittinger et al., 2008), pulsed reactive gas flow control (Vlˇcek et al., 2013) has been used for process control in reactive HiPIMS. In addition, Shimizu et al. (2015) utilized the relation between the discharge current waveform and the condition of the sputter target surface discussed in Section 6.4.1. In this approach the peak discharge current was kept constant by automatically adjusting the pulsing frequency. In this way, the average discharge power was adjusted to keep a stable working point in a wide range of reactive gas flows as demonstrated in the case of HfN deposition (Shimizu et al., 2015). The peak current control may be useful also to stabilize optimum growth conditions for a desired phase composition. Also Cemin et al. (2018) reported on high deposition rate of anatase TiO2 using this approach. There is also a number of studies reporting high deposition rate of stoichiometric compounds in reactive HiPIMS without process control. Such results are very interesting for applications. Hála et al. (2012, 2014) explored hysteresis-free HiPIMS with Nb and Ta targets. The authors demonstrated stable deposition of stoichiometric optically transparent Nb2 O5 and Ta2 O5 at deposition rates comparable to the pure metal rates. This was not possible in the corresponding dcMS process that exhibited hysteresis. Similarly, Ganesan et al. (2015) investigated the effect of pulse on-time in reactive HiPIMS deposition of HfO2 . By varying the pulse length, the discharge could be stabilized close to the metal mode with a corresponding increase in deposition rate. In this experiment, the discharge voltage was kept constant, and longer on-times led to a higher average power. The studies of Hála et al. (2012, 2014) and Ganesan et al. (2015) were operated in a constant voltage mode. As a result of the increasing

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discharge current upon oxidation in HiPIMS (see also Section 6.4.1), the sputtering power increased with increasing oxygen supply, in contrast to the dcMS case. Therefore, we speculate that complete oxidation of the sputter targets was prevented in this unintentional process control. The experiments were thereby carried out in the transition region with correspondingly high sputter rate. The fact that the deposited films still exhibited full stoichiometry indicates either enhanced incorporation of oxygen or improved stability of the metal mode. In another experiment, Kohout et al. (2016) demonstrated deposition of stoichiometric Al2 O3 films while operating in the metal mode. Although the system used in the study exhibited hysteresis even with HiPIMS, the use of HiPIMS improved the process stability, and a stable operating point could be maintained without any process control. A relatively high duty cycle of 10% and short pulses, 10 and 25 µs long, that is, frequencies of 10 and 4 kHz were used for the depositions. High deposition rates agree with the original study by Wallin and Helmersson (2008), where HiPIMS allowed growth of stoichiometric Al2 O3 at deposition rates close to the metal mode. Recent studies of the dynamics of target poisoning and cleaning demonstrated much longer times required for target poisoning in HiPIMS as compared to dcMS (Kubart and Aijaz, 2017). Such a behavior can explain more stable metal or transition mode operation in HiPIMS and is further discussed in Section 6.4.3. It is interesting that the relative width of the hysteresis loop in the study of Kohout et al. (2016) was smaller at 4 kHz than at 10 kHz, confirming reports by Aiempanakit et al. (2011) discussed earlier.

6.4.3 Dynamics of the sputter target surface The surface of the sputter target plays an important role in the reactive sputter process since it determines the mode of operation (metal-transition-compound). Several possible mechanisms seem to be different in HiPIMS compared to dcMS, where higher compound thickness on the target surface (Audronis et al., 2012), reduced rate of compound formation (Sarakinos et al., 2007), and faster surface cleaning (Wallin et al., 2008) have been suggested. Therefore, here we analyze the compound formation and removal from the target surface while referring to the physical processes introduced in Section 6.2. We also consider the relation between the target surface state and discharge characteristics and discuss the overall impact on the reactive process behavior. The thickness of the compound layer determines the dynamical response of the sputtering process. A thicker compound layer requires more time for removal, which slows down the transition from the compound mode. It is therefore of great interest to determine the layer thickness. To verify the compound thickness, Kubart and Aijaz (2017) carried out a series of target cleaning experiments. A Ti target was first operated in compound mode in Ar/O2 or Ar/N2 mixture to ensure that the target was completely covered by the compound. Subsequently, the time and ion fluence required for complete removal of the surface compound was determined by sputtering in a pure Ar atmosphere. The results showed comparable cleaning times for HiPIMS and dcMS operation and were consistent with an expected compound layer thickness of less than

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10 nm (see also Section 6.2.4). A recent XPS study by Layes et al. (2017) of Cr targets operated in Ar/O2 sputtered by HiPIMS confirmed an oxide layer thickness of about 2.5 nm in good agreement with the ion implantation range discussed in Section 6.2.4. Although the higher discharge voltage in HiPIMS leads to somewhat higher ion energies, the difference between the mean projected ion range at 500 and 1000 eV is rather small. For Ar+ ions impinging on a Ti surface, the predicted ion range is 1.6 and 2.4 nm, respectively. Therefore, even under HiPIMS conditions, only a very thin compound layer is expected, that is, a layer thickness similar to what is found for dcMS conditions. Note, however, that thick layers of for example TiOx may be formed by indiffusion of oxygen into Ti at high temperatures in case of poor target cooling (see Section 6.2.4). Furthermore, Greczynski et al. (2018) observed a layer thickness of about 5 nm, 2.5 times thicker than observed in dcMS when depositing TiN by HiPIMS. The higher thickness was explained by implantation of N+ ions that + dominate over N+ 2 ions in reactive HiPIMS. This is because atomic N ions have + twice the energy per atom compared to molecular N2 ions at the same acceleration (discharge) voltage. In an impact, the N+ 2 ion molecule splits into two atoms that penetrate shallower into the surface as compared to an N+ ion. Considering the target compound thickness in HiPIMS comparable to dcMS, we turn to the effect of sputtering. Because the peak discharge current in HiPIMS is high, a fast target surface cleaning has been proposed (Wallin and Helmersson, 2008). This would obviously result in a higher deposition rate. However, the sputter yields are very low, in particular, for oxides (see Section 6.2.3). As a result, removal of several nm of oxide would require a large ion fluence. Calculations by Kozák and Vlˇcek (2016) show that at most only a fraction of a monolayer is removed during a single HiPIMS pulse, and binary collision modeling (Kubart and Aijaz, 2017) has revealed that an ion fluence on the order of 1017 cm−2 is required to remove a 2 nm-thick layer of TiO2 . For instance, a triangular current pulse with a peak current of 60 A and a pulse length of 100 µs, as shown in Fig. 6.17B, applied to a circular target with a diameter of 50 mm represents an ion fluence of 9 × 1014 cm−2 calculated as T

=

ID 0 qe dt

At

,

(6.7)

where T is the pulse on-time, and At is the target area. Fig. 6.17A shows experimental results from the cleaning experiments by Kubart and Aijaz (2017). Starting with an oxidized sputter target, the peak current is very high initially and reaches a value corresponding to a clean metal target only after about 600 ms. The peak discharge current was used as an indicator of the target surface state because there was a pronounced difference in the peak value and the waveform shape, as seen in Fig. 6.17B in line with our discussion in Section 6.4.1. In this experiment, 343 HiPIMS pulses were required to clean an oxidized titanium target surface. We can therefore conclude that significant changes of the target surface stoichiometry in compound mode do not occur during a single pulse (Kozák and Vlˇcek, 2016).

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Figure 6.17 (A) The peak discharge current vs process time during HiPIMS cleaning of an oxidized titanium target. The discharge current in metal mode is shown as a reference (clean surface). Reprinted from Kubart and Aijaz (2017), with the permission of AIP Publishing. (B) Discharge current waveforms in metal and compound mode of sputtering for continuously operated HiPIMS discharges.

We should also consider the build-up of a compound layer. The rate of the compound formation is strongly influenced by the reactive gas sticking discussed in Section 6.2.1. Although a unity value of the sticking coefficient is usually assumed in simple hysteresis models, Strijckmans et al. (2012) argued that this is incorrect and the true values are much lower. Beam experiments (Kuschel and von Keudell, 2010) confirmed low values of O2 sticking coefficients on Al. On the other hand, the gas reactivity is also influenced by the plasma chemistry, and gas dissociation in the HiPIMS discharge may enhance the otherwise generally low sticking coefficient (Smith, 1995, Nouvellon et al., 2012). Enhanced oxygen reactivity has indeed been demonstrated in a hybrid process combining HiPIMS with a separate microwave plasma source to activate oxygen (Stranak et al., 2017). The results clearly show the influence of enhanced reactivity and demonstrate increased incorporation of oxygen into the growing film. Transparent TiO2 films could thereby be deposited in the metal mode of operation. Interestingly, process hysteresis was broadened by oxygen activation in the study of Stranak et al. (2017). This is most likely a result of enhanced reactivity of the activated gas. Vlˇcek et al. (2015) utilized enhanced reactivity in HiPIMS for deposition of several oxides without a negative impact on the process hysteresis. By carefully placing an oxygen inlet to direct the O2 flow though the plasma region toward the substrate, the oxygen partial pressure required for deposition of a stoichiometric oxide was reduced. In this way, the deposition rate of ZrO2 was increased twofold. Despite the expected higher reactivity of HiPIMS plasmas, Kubart and Aijaz (2017) observed slow target poisoning in reactive HiPIMS, suggesting a slower rate of compound formation than

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in dcMS. The authors tentatively attributed the slow compound formation to either reduced reactive gas flux to the target surface caused by gas rarefaction or to higher preferential sputtering of the oxygen from the target surface. Another possibility can be the increased back-attraction of ionized metallic species discussed in Sections 6.3.1 and 6.3.3. More research, however, is necessary to understand the target surface processes.

6.4.4 Plasma characteristics in the metal and compound mode Metal and compound modes of operation are very different, and a change in the plasma properties is also expected upon the transition between the modes. In Section 3.3.3, we already discussed changes in the electron dynamics, where commonly a higher electron temperature is observed when operating in the compound mode. Also, the ion dynamics in reactive HiPIMS discharges were discussed in Section 4.1.3.3, where high ionized flux fractions could be maintained at least in the oxide mode (Kubart et al., 2014). From the point of view of the film growth, the flux composition and energy of the ions are most important. Mass spectroscopy measurements revealed a significant difference of the ion energy distribution functions (IEDFs) for working gas ions and reactive gas atom ions (Jouan et al., 2010, Schmidt et al., 2012, Aiempanakit et al., 2013), and a detailed description is found in Section 4.1.3.3. Typical results are shown in Fig. 6.18, where the IEDF of the N+ ions shows a high energy tail comparable to that of the metal ions in Ar/N2 mixture with Al target. Similar observations have been made for O+ ions in Ar/O2 mixture with Al and Ti targets (Aiempanakit et al., 2013). Ar+ and molecular ions of the reactive gas, on the other hand, have a rather narrow IEDF, as seen for Ar+ and N+ 2 ions in Fig. 6.18. The results indicate a different origin + of the atomic reactive gas ions compared to Ar+ , N+ 2 , and O2 ions, where these latter species are ionized in the bulk plasma, while the reactive gas atoms are ionized close to the sputter target surface in a similar way as the metal atoms. The exact ratio between the Ar+ ions and reactive gas ions is process dependent. + Al and N+ 2 ions dominated the discharge in a study of AlN sputtering (Jouan et al., 2010), whereas the O+ ion was the main ion species observed in reactive sputtering of TiO2 (Aiempanakit et al., 2013). However, these attempts at estimating the importance of various reactive ionic species were carried out using mass spectrometry, and, as always, we should be very careful when trying to quantify and compare ion densities based on the recorded ion intensities (see Section 4.1.1.1). Instead, Gudmundsson et al. (2016) and Lundin et al. (2017) applied the previously described IRM code (Section 5.1.3) to an Ar/O2 HiPIMS discharge with a Ti target in both metal and compound modes to study the time-evolution of the various species present during a 400 µs long discharge pulse. The temporal variations of the ion densities during the pulse are shown in Fig. 6.19 for the compound mode. Ar+ ions dominate the discharge by typically one order of magnitude higher density than the sum of Ti+ , Ti2+ , and O+ ions, which is in line with our previous discussion on the recycling of large quantities of Ar+ ions to reach high discharge currents (see Section 6.4.1). Ti+ and O+ ions have very similar densities, but the temporal variation is different: the Ti+ ion density

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Figure 6.18 The time-integrated IEDFs of an Ar/N2 HiPIMS discharge with Al target at a pressure of 0.4 Pa, a pulse length of 28 µs, and a repetition rate of 1.6 kHz. Copyright 2010 IEEE. Reprinted, with permission, from Jouan et al. (2010).

Figure 6.19 The temporal variation of the density of ions in a 400 µs Ar/O2 HiPIMS discharge with a Ti target operated in the compound mode. The total discharge pressure was 0.60 Pa, and the peak current density was 1.6 A/cm2 . The shaded area represents a period during the pulse during which the seed electrons may affect the calculated density values. Data from Gudmundsson et al. (2016).

increases more rapidly during the early stage of the pulse. The authors also found that the observed O+ ion density is more than two orders of magnitude larger compared to the metal mode at the same O2 flow rate (different pulse frequencies). In addition, the + O+ 2 ion density is about one order of magnitude lower than the O ion density. The Ti2+ ion density increases fast with time and has a similar density evolution as the O+ ion density. Based on these observations, we conclude that although the O+ ion is not dominating the discharge, it is still very important, and the obvious question is by what mechanism(s) do we generate such large quantities? In a follow-up study, Lundin et al. (2017) observed a strong gas rarefaction of the reactive gas (O2 ) in all modes of operation (see also Section 4.2.2 for more detail on gas rarefaction). For example, the O2

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Figure 6.20 The temporal variation of the most important reaction rates for (A) gain and (B) loss of O(3 P) in a 400 µs Ar/O2 HiPIMS discharge with a Ti target operated in the compound mode. The total discharge pressure was 0.60 Pa, and the peak current density was 1.6 A/cm2 . The shaded area represents a period during the pulse during which the seed electrons may affect the calculated density values. Data from Lundin et al. (2017).

molecule density in compound mode was reduced by 80% at peak discharge current, which is even more than was observed in the metal mode (67% density reduction). This means that gas rarefaction of O2 is not suppressed in reactive HiPIMS. However, the authors report that the loss is compensated by a strong increase of ground state atomic oxygen O(3 P), which is observed at a significantly higher density compared to O2 during the second half of the discharge pulse. The gain and loss rates of O(3 P) are plotted in Fig. 6.20, where we can see that the loss of O2 can to some extent be explained by dissociation to atomic oxygen, although it is not the dominant mechanism (Lundin et al., 2017). The most important gain rate for O(3 P) is instead sputtering of O(3 P) from the oxidized target in the compound mode, which makes up about 88% of the total gain rate. Furthermore, by studying the loss rates in Fig. 6.20 we also see that a significant fraction of the neutral atomic oxygen is ionized and thus explains the high O+ ion density seen in Fig. 6.19.

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6.4.5 Negative ions in R-HiPIMS In reactive sputtering with oxygen, energetic negative oxygen O− ions may have a pronounced effect on the deposited films. O− ions that are created at the surface of the sputter target are accelerated to the full target potential (Mráz and Schneider, 2006). A detailed description of how O− ions are created and their energy range is discussed in Section 4.1.3.3 and will not be repeated here. The impact of such energetic ions on the growing film has detrimental effects on the material structure by defect generation (Seeger et al., 2009) and resputtering. However, in some cases, the additional energy input may be beneficial, since energetic ions promote crystallization of TiO2 at low temperatures (Amin et al., 2010). Transparent conductive oxides are particularly sensitive to O− ion bombardment (Tominaga et al., 1993). Lateral gradients in the conductivity of deposited transparent conductors well correlated with the substrate position relative to the target race track, and degradation of the properties directly in front of the race track were observed (Tominaga et al., 1985). Combining experimental measurements of angle-resolved IEDFs with modeling, Mahieu et al. (2009) demonstrated a connection between the secondary electron emission coefficient γsee and the generation of O− ions and related these parameters to the target work function. Their study provides an estimation of the impact of negative ions depending on the material system and process conditions. Welzel and Ellmer (2012) measured O− from a number of other material systems relevant for transparent conductors and confirmed the importance of γsee . However, there are few investigations on the negative ion density in reactive HiPIMS. Bowes and Bradley (2014) estimated the peak density of volume-created negative oxygen ions to be about 3 × 1016 m−3 , but the contribution from fast O− ions created at the target could not be accounted for. Also, Gudmundsson et al. (2016) estimated rather low densities of volume-created O− , as seen in Fig. 6.19, of less than 1 × 1015 m−3 during the pulse. IEDFs for O− ions in reactive HiPIMS of a Ti target in Ar/O2 mixture measured by Bowes et al. (2013) confirmed sputtering of oxygen from the target surface as the source of energetic O− ions in line with dcMS studies. Recently, the angular distributions of O− and O− 2 ions from the target have been measured by Franz et al. (2016) while sputtering Nb target in an Ar/O2 mixture. They found that all the high-energy ions have angular distributions that are within ±20◦ of the target surface normal. Further attempts at quantifying the total negative ion density are needed, since the contribution of O− ions created at the target may be considerably higher. Because the discharge voltages, and thus the cathode sheath potentials, are higher in HiPIMS than in dcMS, a negative effect of HiPIMS on the properties of sensitive oxide films such as ZnO:Al can be expected. Surprisingly, improvement in optoelectronic properties of HiPIMS-deposited Al-doped ZnO films has been reported by Mickan et al. (2016). The electrical resistivity was lower than that of the corresponding dcMS deposited films, and the uniformity was also improved. In some cases, the nonuniformity in electrical resistivity could be completely avoided. The improvement in ZnO:Al properties has been attributed to better control of the deposition process in HiPIMS. Reduced target surface oxidation limited the generation of O− ions and resulted in

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reduced damage by energetic impacts (Horwat et al., 2016). Also, Vlˇcek et al. (2017) utilized HiPIMS with an optimized gas inlet to reduce target oxidation to limit formation of energetic O− ions. It resulted in an improved quality of thermochromic VO2 films.

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Schmidt, S., Czigány, Z., Greczynski, G., Jensen, J., Hultman, L., 2012. Ion mass spectrometry investigations of the discharge during reactive high power pulsed and direct current magnetron sputtering of carbon in Ar and Ar/N2 . Journal of Applied Physics 112 (1), 013305. Seeger, S., Harbauer, K., Ellmer, K., 2009. Ion-energy distributions at a substrate in reactive magnetron sputtering discharges in Ar/H2 S from copper, indium, and tungsten targets. Journal of Applied Physics 105 (5), 053305. Shimizu, T., Villamayor, M., Lundin, D., Helmersson, U., 2015. Process stabilization by peak current regulation in reactive high-power impulse magnetron sputtering of hafnium nitride. Journal of Physics D: Applied Physics 49 (6), 065202. Sigmund, P., 1981. Sputtering by ion bombardment theoretical concepts. In: Behrisch, R. (Ed.), Sputtering by Particle Bombardment I: Physical Sputtering of Single-Element Solids. In: Topics in Applied Physics, vol. 47. Springer Verlag, Berlin–Heidelberg, Germany, pp. 9–71. Sittinger, V., Ruske, F., Werner, W., Jacobs, C., Szyszka, B., Christie, D.J., 2008. High power pulsed magnetron sputtering of transparent conducting oxides. Thin Solid Films 516 (17), 5847–5859. Smith, D.L., 1995. Thin-Film Deposition: Principles and Practice. McGraw-Hill, New York. Sproul, W.D., 1996. New routes in the preparation of mechanically hard films. Science 273 (5277), 889–892. Sproul, W.D., 1998. High-rate reactive DC magnetron sputtering of oxide and nitride superlattice coatings. Vacuum 51 (4), 641–646. Sproul, W.D., Christie, D.J., Carter, D.C., 2005. Control of reactive sputtering processes. Thin Solid Films 491 (1–2), 1–17. ˇ Stranak, V., Kratochvi, J., Olejnicek, J., Ksirova, P., Sezemsky, P., Cada, M., Hubicka, Z., 2017. Enhanced oxidation of TiO2 films prepared by high power impulse magnetron sputtering running in metallic mode. Journal of Applied Physics 121 (17), 171914. Straˇnák, V., Quaas, M., Wulff, H., Hubiˇcka, Z., Wrehde, S., Tichý, M., Hippler, R., 2008. Formation of TiOx films produced by high-power pulsed magnetron sputtering. Journal of Physics D: Applied Physics 41 (5), 055202. Strijckmans, K., Leroy, W., De Gryse, R., Depla, D., 2012. Modeling reactive magnetron sputtering: fixing the parameter set. Surface and Coatings Technology 206 (17), 3666–3675. Sundgren, J.E., Johansson, B.O., Karlsson, S.E., Hentzell, H.T.G., 1983. Mechanisms of reactive sputtering of titanium nitride and titanium carbide II: morphology and structure. Thin Solid Films 105 (4), 367–384. Surpi, A., Kubart, T., Giordani, D., Tosello, M., Mattei, G., Colasuon, M., 2013. HiPIMS deposition of TiOx in an industrial-scale apparatus: effects of target size and deposition geometry on hysteresis. Surface and Coatings Technology 235, 714–719. Thornton, J.A., 1978. Magnetron sputtering: basic physics and application to cylindrical magnetrons. Journal of Vacuum Science and Technology 15 (2), 171–177. Thornton, J.A., Cornog, D.G., Hall, R.B., Shea, S.P., Meakin, J.D., 1984. Reactive sputtered copper indium diselenide films for photovoltaic applications. Journal of Vacuum Science and Technology A 2 (2), 307–311. Tominaga, K., Sueyoshi, Y., Munfei, C., Shintani, Y., 1993. Energetic O− ions and O atoms in planar magnetron sputtering of ZnO target. Japanese Journal of Applied Physics 32 (9B), 4131–4135. Tominaga, K., Yuasa, T., Kume, M., Tada, O., 1985. Influence of energetic oxygen bombardment on conductive ZnO films. Japanese Journal of Applied Physics 24 (8), 944–949.

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ˇ Vlˇcek, J., Kolenatý, D., Houška, J., Kozák, T., Cerstvý, R., 2017. Controlled reactive HiPIMS-effective technique for low-temperature (300◦ C) synthesis of VO2 films with semiconductor-to-metal transition. Journal of Physics D: Applied Physics 50 (38), 38LT01. Vlˇcek, J., Rezek, J., Houška, J., Kozák, T., Kohout, J., 2015. Benefits of the controlled reactive high-power impulse magnetron sputtering of stoichiometric ZrO2 films. Vacuum 114, 131–141. ˇ Vlˇcek, J., Rezek, J., Houška, J., Cerstvý, R., Bugyi, R., 2013. Process stabilization and a significant enhancement of the deposition rate in reactive high-power impulse magnetron sputtering of ZrO2 and Ta2 O5 films. Surface and Coatings Technology 236, 550–556. Wallin, E., Helmersson, U., 2008. Hysteresis-free reactive high power impulse magnetron sputtering. Thin Solid Films 516 (18), 6398–6401. Wallin, E., Selinder, T.I., Elfwing, M., Helmersson, U., 2008. Synthesis of α-Al2 O3 thin films using reactive high-power impulse magnetron sputtering. Europhysics Letters 82 (3), 36002. Welzel, T., Ellmer, K., 2012. Negative oxygen ion formation in reactive magnetron sputtering processes for transparent conductive oxides. Journal of Vacuum Science and Technology A 30 (6), 061306. Wu, W.-Y., Hsiao, B.-H., Chen, P.-H., Chen, W.-C., Ho, C.-T., Chang, C.-L., 2014. CrNx films prepared using feedback-controlled high power impulse magnetron sputter deposition. Journal of Vacuum Science and Technology A 32 (2), 02B115. Zehnder, T., Patscheider, J., 2000. Nanocomposite TiC/a-C:H hard coatings deposited by reactive PVD. Surface and Coatings Technology 133–134, 138–144. Zhang, Y., Weber, W.J., 2016. Defect accumulation, amorphization and nanostructure modification of ceramics. In: Wesch, W., Wendler, E. (Eds.), Ion Beam Modification of Solids: Ion-Solid Interaction and Radiation Damage. In: Springer Series in Surface Sciences, vol. 61. Springer-Verlag, Cham, Switzerland, pp. 287–318. Österlund, L., Zori´c, I., Kasemo, B., 1997. Dissociative sticking of O2 on Al(111). Physical Review B 55 (23), 15452–15455.

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Daniel Lundina , Ante Hecimovicb , Tiberiu Mineaa , André Andersc , Nils Brenningd , Jon Tomas Gudmundssond,e a Laboratoire de Physique des Gaz et Plasmas - LPGP, UMR 8578 CNRS, Université Paris–Sud, Université Paris–Saclay, Orsay Cedex, France, b Max-Planck-Institut for Plasma Physics, Garching, Germany, c Leibniz Institute of Surface Engineering (IOM), Leipzig, Germany, d Department of Space and Plasma Physics, School of Electrical Engineering and Computer Science, KTH Royal Institute of Technology, Stockholm, Sweden, e Science Institute, University of Iceland, Reykjavik, Iceland

The most striking difference between HiPIMS and other magnetron sputtering discharges, in terms of the plasma process itself, lies in the high-power discharge pulses applied and the large discharge currents generated. We will therefore start this chapter on the physics of HiPIMS by exploring the current composition at the target surface and the physical and chemical mechanisms operating at different stages of the discharge pulse and afterglow, which give rise to large discharge currents. Of particular interest is how internal process features such as gas rarefaction, ionization of the sputtered species, self-sputter recycling, and working gas recycling can be influenced by (as well as influence) the choice of pulse length, repetition frequency, applied power density, magnetic field strength and topology, target material, working gas, and so on. Using our understanding of the physics behind the discharge pulse, we will then turn to discussing several key aspects in non-reactive and reactive HiPIMS, which includes dealing with the much debated issues of deposition rate as well as loss and transport of charged particles. The latter topic will, by necessity, also address plasma instabilities in HiPIMS.

7.1

The discharge current

The discharge currents realized in the HiPIMS discharge are indeed very high. Typical discharge currents are in the range of a few tens to a few hundreds of Amperes depending on the target size. Thus the observed discharge currents are significantly higher than commonly observed in conventional dcMS or asymmetric bipolar magnetron sputtering discharges. In the following sections, we explain why and how the discharge current is composed and how it evolves in time. In the context of magnetron sputtering discharges, we define the term “nominal power density” as the power of the discharge divided by the area of the target. In this way, we define a useful and simple parameter that helps to compare phenomena of different reports. At the same time, High Power Impulse Magnetron Sputtering. https://doi.org/10.1016/B978-0-12-812454-3.00012-7 Copyright © 2020 Elsevier Inc. All rights reserved.

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we stress that the nominal power density (or the similarly defined current density) is a simple parameter, whereas the physics is governed by the actual local power density, which can significantly deviate from the nominal, especially when we observe plasma instabilities. The majority of reports in the literature drop the word “nominal” and report target current density.

7.1.1 The discharge current composition To understand the large discharge currents observed in HiPIMS discharges, we start by reviewing an analysis by Huo et al. (2017) of two distinct HiPIMS discharges using the IRM code introduced in Section 5.1.3. Their study gives an insight into the discharge current composition at the target surface as well as the ionization fractions and electron heating mechanisms. The first set of experimental data analyzed was taken from the work of Anders et al. (2007), who used a planar balanced magnetron sputtering discharge equipped with an Al target. The target was 50 mm in diameter. The discharge was operated with argon as the working gas at a pressure of 1.8 Pa. The pulse length was 400 µs, and the power supply maintained the discharge voltage throughout the entire pulse. The complete set of discharge current characteristics was already shown in Fig. 5.9A. The second set of experiments were performed by Mishra et al. (Mishra et al., 2010, Bradley et al., 2015) using a 150 mm-diameter Ti target. The discharge was operated with argon as the working gas at a pressure of 0.54 Pa. Here the discharge voltage was not maintained constant throughout the entire pulse. Fig. 7.1 shows the discharge current composition at the target surface for the discharge with Al target at discharge voltages of 360 V, 400 V, and 800 V calculated by the IRM. Note that for all discharge voltages, the ions carry almost all the discharge current, and the contribution of secondary electrons ID,se is small. When the discharge is operated at 360 V (Fig. 7.1A), the peak discharge current is in the range of a few hundred mA, and the current density is roughly ∼ 30 mA/cm2 (averaged over the entire target area) or in the middle of the dcMS regime (see Section 1.2.1). We see in Fig. 7.1A that the Ar+ ions contribute to roughly 2/3 of the discharge current whereas Al+ ions contribute roughly 1/3. At 400 V (Fig. 7.1B) the peak discharge current has risen to a few Amperes, and the current density to ∼ 250 mA/cm2 , whereas the power density is now ∼ 100 W/cm2 , just below the HiPIMS limit given in Fig. 1.13. Now the contributions of Al+ and Ar+ ions to the discharge current are very similar, whereas the contributions from Al2+ ions and secondary electrons are much smaller. Note that, however, in the initial current peak the Al+ ions have a slightly higher contribution whereas in the plateau region, Ar+ ions contribute roughly to 2/3 of the current. When operating at 800 V (Fig. 7.1C), the peak discharge current is in tens of Amperes, the current density > 1 A/cm2 , the power density ∼ 1 kW/cm2 , and the discharge is operated well into the HiPIMS regime. Now the Al+ ions dominate the discharge current, whereas the contribution of Ar+ ions is below 10% except at the initiation of the pulse. Al2+ ions and secondary electrons have almost negligible contributions. The small contribution of Al2+ ions is consistent with the findings of Jouan et al. (2010) that while sputtering an Al target in an Ar/N2 mixture, they detected Al2+ ions, but their intensity was orders of magnitude lower than for Al+ ions. Thus, when operating

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Figure 7.1 The temporal variation of the discharge current composition at the target surface for an argon discharge at 1.8 Pa with a 50 mm-diameter Al target for a discharge voltage of (A) 360 V (JD,peak ≈ 0.04 A/cm2 ), (B) 400 V (JD,peak ≈ 0.26 A/cm2 ), and (C) 800 V (JD,peak ≈ 1.32 A/cm2 ). Note the different scales of the y-axes. Reprinted from Huo et al. (2017). ©IOP Publishing. Reproduced with permission. All rights reserved.

a HiPIMS discharge with Al target, the discharge goes into a self-sputter dominated mode as will be discussed in Section 7.2.1. The discharge current composition for the HiPIMS discharge with Ti target is different, as shown in Fig. 7.2, for a peak current density of JD,peak ≈ 3.84 A/cm2 . The largest contribution is here from Ar+ ions (∼ 53%), whereas the contribution of Ti+ ions is somewhat smaller (∼ 28%), and Ti2+ ions have an even smaller contribution (∼ 17%) but still significant. The contribution of Ar+ ions and the sum of the contributions of Ti+ and Ti2+ ions are of similar magnitude. This is consistent with experimental findings that HiPIMS discharges with Ti target can produce significant amounts of multiply charged titanium ions (Bohlmark et al., 2006a, Andersson et al., 2008, Hippler et al., 2019). Bohlmark et al. (2006a) claim that while sputtering a Ti

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Figure 7.2 The temporal variation of the discharge current composition at the target surface for an argon discharge at 0.54 Pa and pulse frequency of 75 Hz with a 150 mm-diameter Ti target (JD,peak ≈ 3.84 A/cm2 ). Reprinted from Huo et al. (2017). ©IOP Publishing. Reproduced with permission. All rights reserved.

target in an argon discharge up to 24% of the ion flux consists of Ti2+ ions. The difference between the presented two discharges with Al and Ti targets will be discussed further within the framework of generalized recycling in Section 7.2.1.1. One way of evaluating the discharge properties is to compare the ionized density fractions Fdensity as given by Eq. (4.4). We will first focus on the argon working gas. For the discharge with Al target, the ionized density fraction for argon is always well below 10% (Huo et al., 2017). For low discharge voltages, the ionized density fraction for argon follows rather well the time-evolution of the discharge current, whereas for higher discharge voltages, it decreases with increased discharge voltage. Huo et al. (2014, 2017) showed that whereas the discharge current increased with increased discharge voltage, the electron temperature Te substantially decreases. This explains how there can be a decreasing ionization efficiency of Ar with increasing discharge voltage. For the modeled discharge with Ti target, the ionized density fraction for argon reaches at most 18% for the highest peak current, which is significantly higher than for the modeled discharge with Al target. The ionized density fraction for the sputtered metal is considerably higher for the singly charged metal ions compared to the argon ions and reaches values of roughly 60% for the highest peak currents for both Al and Ti targets. The temporal behavior of these ion fractions follows rather well the discharge current evolution, as expected, since a large fraction of the discharge current is carried by the singly charged metal ions, as seen in Figs. 7.1 and 7.2. Concerning the twice ionized metal, the situation is quite different between the discharges with Al and Ti targets. In the case of Al, the Al2+ ion never reaches more than about Fdensity ≈ 1%, and Al2+ ions only play a minor role in the discharge operation, which is in line with the contribution of Al2+ ions to the discharge current (as seen in Fig. 7.1). This also means that the secondary electron emission due to aluminum ion bombardment is negligible, since singly charged Al+ ions have a secondary electron emission yield close to zero (see also Section 1.1.4), while very few Al2+ ions are present. However, for the Ar/Ti discharge, Fdensity for Ti2+ is about one third of Fdensity for Ti+ . Note that the second ionization energy of Ti is 13.58 eV, significantly lower than the second ionization en-

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ergy of Al, which is 18.8 eV, whereas the first ionization energy of argon is 15.76 eV. Thus we would expect a much higher density of Ti2+ ions when operating with a Ti target than that of Al2+ ions when operating with an Al target. In summary, there is a significant change in the ion current composition to the target when moving from dcMS-like to HiPIMS discharge currents, which is also reflected in the ion composition in the magnetic trap (ionization region) above the target. The composition also changes in time and gives rise to the observed discharge current variations during the pulse. However, we still need to identify the physical and chemical mechanisms operating at different stages of the discharge pulse and afterglow, which give rise to the observed compositional variations and ultimately the large HiPIMS discharge currents.

7.2 Discharge modes To define and explore the discharge modes in the HiPIMS discharge, we start by considering a schematic of various HiPIMS discharge current shapes presented in Fig. 7.3. These discharge current waveforms are typically observed for both non-reactive and reactive HiPIMS pulses when the applied peak power density is varied from about 0.1 kW/cm2 up to several kW/cm2 , that is, from the middle of the MPPMS range to the higher end of the HiPIMS range, as seen in Fig. 1.13. In the present example, this corresponds to peak current densities of approximately 0.1 – 1.6 A/cm2 averaged over the entire target area. For simplicity, here we assume square-shaped voltage pulses. The schematic discharge current waveforms of Fig. 7.3 are similar to the set of discharge current data presented in Fig. 7.1A – C for an Al discharge operated at various discharge voltages. In Fig. 7.3 the HiPIMS discharge current waveforms have been divided into five different phases during an approximately 300 µs-long pulse. The choice of a relatively long HiPIMS discharge pulse in the present example is based on the need to explore all the types of discharge regimes reported. The discharge current pulses in this example are shown to develop along different pathways generally characterized by an initial peak followed by a more or less stable current plateau (Fig. 7.1B and bottom current curves in Figs. 7.3) or by an initial peak followed by a second increase of the discharge current (Fig. 7.1C and top current curves in Figs. 7.3). Note that, for each of these different pathways, the discharge current amplitude, the point in time for reaching the peak current, current transitions, and so on are likely to change somewhat depending on discharge conditions, such as target material, target dimension, working gas pressure, gas composition, repetition frequency, magnetic field strength, and other factors (Anders et al., 2007, Magnus et al., 2011, ˇ Capek et al., 2012), and should therefore not be taken as exact values. We propose to suitably categorize these current curves according to the composition of the ion current at the target surface, which reflects the amount and type of ion recycling present in the discharge and which we will deal with in detail in Section 7.2.1. This description is followed by a discussion on the time-evolution of the discharge current in the volume in Section 7.2.2, and the physics involved in the various phases displayed in Fig. 7.3.

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Figure 7.3 A schematic illustration of the HiPIMS discharge current density (averaged over the entire target) divided into five different phases: Phase 1 (ignition), Phase 2 (current rise to first maximum), Phase 3 (decay/transition from the first maximum to the next phase), Phase 4 (plateau/runaway), and Phase 5 (afterglow). The bottom two curves display an approximately 300 µs-long current pulse, where the current decays after an initial peak at around 80 µs, mainly due to rarefaction of the working gas, followed by a current plateau. The top two curves illustrate considerable ion recycling (working gas recycling and/or self-sputter recycling), where the current may reach a second maximum before the pulse is switched off. The middle curve displays an intermediate state with moderate ion recycling (sometimes denoted working gas-sustained self-sputtering). After Gudmundsson et al. (2012).

7.2.1 The discharge current amplitude We have already in Sections 6.3.3 and 7.1 seen that the discharge current waveforms ID (t) of the HiPIMS pulses show large variations with target material, pulse length, and applied power (Anders et al., 2007), whether operated in metal mode or poisoned mode (Magnus et al., 2012, Gudmundsson, 2016) and depending on the power supply used (as discussed in Section 2.2). With increasing discharge current amplitude, magnetron sputtering discharges have commonly been described (Gudmundsson et al., 2012) as gradually shifting character from working gas sputtering (Lundin et al., 2009), through working gas-sustained self-sputtering (SS) (Huo et al., 2014), and finally, for the highest currents, enter either self-sustained self-sputtering (Anders et al., 2007) or self-sputter runaway (Anders, 2008). An addition to this description is the concept of a working gas recycling trap proposed by Anders et al. (2012a), where working gas ions bombarding the substrate return during the HiPIMS pulse and are subsequently ionized and drawn back to the target to further amplify the discharge current. Anders et al. (2012a) argued that self-sputter recycling and working gas recycling can sometimes combine and lower the threshold for discharge current runaway, enabling this route to high discharge currents also for target materials with self-sputter yields YSS below unity. Definitions of these important discharge operating modes are summarized in Table 7.1.

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Table 7.1 A summary of the different types of discharge modes of the HiPIMS discharge and how they affect the discharge current. Process Working gas sputtering

Working gas sustained self-sputtering

Self-sustained self-sputtering

Self-sputter runaway

Working gas recycling

Description Atoms and molecules of the working gas, which are ionized and then sputter the target. This assumes no recycling of the working gas ions, i.e., no return of gas atoms from the target. Gas ion current is dominating ID (t). Ionized working gas is required for sputtering enough target atoms that are subsequently ionized and drawn back to the target starting a series of metal (target atom) recycling, which dominates the current. Working gas ion current, however, still provides an important contribution to ID (t). Significant ionization of the sputtered species, where a large fraction of these ions is attracted back to the target to sputter more target atoms, which are subsequently ionized. Through target atom recycling the discharge is maintained with sputtered species only, i.e., the discharge can run without working gas. ID (t) is completely dominated by the ions of the sputtered species. Self-sputtering amplifies itself, and the self-sputter parameter exceeds unity, so that there is a positive feedback, and the self-sputtering accelerates or runs away. Thus the current increases until the power supply reaches its limit. ID (t) is completely dominated by the ions of the sputtered species. Working gas ions are neutralized at the target, but a fraction returns to the discharge during the pulse. These returning gas neutrals are subsequently ionized and drawn back to the target, starting a series of gas-recycling. The working gas ions may carry a large fraction of the (high) discharge current.

Reference (Lundin et al., 2009)

(Huo et al., 2014)

(Anders et al., 2007)

(Anders, 2008)

(Brenning et al., 2017)

To understand the current evolution to high discharge currents, here we will mainly follow the ideas presented by Brenning et al. (2017), which involve analyzing and quantifying the individual contributions of the various ion fluxes to the target (carrying the discharge current), including recycling of ions via self-sputter recycling

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(SS-recycling) and working gas-recycling (sometimes referred to as process gas recycling or gas-recycling). For the analysis of the combined processes of SS-recycling and working gas-recycling, the generalized recycling model (GRM) will be employed. The GRM was developed by Gudmundsson et al. (2016) for the analysis of a reactive (Ar/O2 ) HiPIMS discharge with a Ti target and later on expanded to other target materials (Al, C, Cu, Ti, and TiO2 ) by Brenning et al. (2017) to cover a wide range of current densities from the dcMS range to the HiPIMS range.

7.2.1.1

The generalized recycling model (GRM)

The basic idea of the GRM is focusing on the ion current at the target surface and neglecting the small electron fraction of the discharge current due to an effective secondary electron emission yield, which is commonly below 0.1 for typical voltages applied to the cathode in HiPIMS operation (as can be seen in Fig. 1.4 for argon ions), that is, it assumes that ID (t) ≈ Ii (t). In the GRM, the ions that hit the target are separated into three groups depending on their history: primary ions of the working gas, which are ionized for the first time, recycled ions of the working gas, and ions of the sputtered material. These components are all illustrated in Fig. 7.4 as parts of a causeand-effect chain of events, which goes from left to right in the figure. Note that the widths of all flow arrows in the figure are drawn consistent with the list of parameter values given in the caption, which is explained below and also used for a numerical example.

Figure 7.4 A schematic illustration of the combined processes of working gas recycling and self-sputter recycling to generate high discharge currents. The widths of the flow arrows are drawn to scale with a parameter combination αprim = 1, ξpulse = 1, αg = 0.7, βg = 0.7, Yg = 0.4, αt = 0.8, βt = 0.7, and YSS = 0.5. This combination is arbitrarily chosen as suitable to illustrate combined working gas-recycling and SS-recycling. Reprinted from Brenning et al. (2017). ©IOP Publishing. Reproduced with permission. All rights reserved.

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We start with the primary current Iprim , which is defined by those atoms and molecules of the working gas (index g) that are ionized for the first time with probability αprim (close to 1 in Fig. 7.4), then go to the target, and finally sputter with a sputter yield Yg . Thus Iprim acts as a seed for the entire discharge current. However, Iprim has an upper limit, corresponding to the case where all incoming gas atoms (often Ar gas) from the surrounding gas reservoir are ionized and drawn to the target. This upper limit was used by Huo et al. (2014) to derive a critical current Icrit . They assumed the thermal refill rate of ambient Ar to be given by the perpendicular thermal gas flux toward the active race track area SRT at pressure pg and gas temperature Tg . All incoming working gas atoms were then assumed to become singly ionized and drawn to the target. This gives   k B Tg 1 Icrit = eng SRT = epg SRT , (7.1) 2πMg 2πMg kB Tg where kB is Boltzmann’s constant, ng is the working gas density, and Mg is the mass of the working gas atom. For a gas temperature of 300 K, this gave an estimate of the maximum primary current given in practical units as Icrit = 0.38SRT pg ,

(7.2)

where SRT is the race track area in cm2 , and pg is the working gas pressure in Pa. In magnetron sputtering, it is often easier to use the average current density over the whole target area ST . For typical magnetron sputtering discharge parameters (T = 300 K, SRT = 0.5ST , and argon at pg = 1 Pa), this gives the critical current density Jcrit =

Icrit = 0.2 A/cm2 . ST

(7.3)

Conventional dcMS devices are operated well below this critical current density, and therefore there is no need for ion recycling, whereas for JD ≥ Jcrit , recycling is needed. This is the case for the HiPIMS discharge, where JD is commonly a factor 3 – 20 higher than Jcrit (see also Section 1.4.4). For example, the critical current for the discharge with Al target discussed in Section 7.1.1 is Icrit ≈ 7 A. Fig. 7.1 shows that the experiment with Al target is operated with discharge currents from far below Icrit to high above it, up to 36 A. Also, the discharge with the Ti target discussed in Section 7.1.1 is operated with peak discharge currents far above the critical current (up to 650 A while Icrit ≈ 19 A). So a significant fraction of the discharge current has to be recycled in both cases. From Fig. 7.4 we find that there are two ways to generate more ions going to the target and thereby to increase the discharge current ID (t) beyond Icrit : (i) recycling of working gas atoms from Iprim and (ii) recycling of sputtered target atoms. We start by looking at the possibility of working gas recycling. In this scenario the ions that constitute Iprim are neutralized at the target, and a fraction ξpulse returns to the discharge during the pulses. As discussed by Huo et al. (2014), embedded Ar atoms are most likely to leave the target when it is bombarded by ions. This corresponds to the

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value ξpulse = 1, which will also be used here. The returning working gas atoms are subsequently ionized with probability αg and drawn back to the target with probability βg . The remaining fraction of the working gas ions (1 − βg ) goes to the surrounding volume. These steps constitute a first cycle in the working gas recycling loop (seen in the left-hand side of Fig. 7.4), where a recycled current Iprim πg is added to Iprim , and πg = αg βg ξpulse

(7.4)

is the working gas-sputtering parameter as defined by Gudmundsson et al. (2016). Each subsequent cycle adds yet another contribution to the working gas current by  n multiplying the recycled current with πg . Since ∞ n=1 a = a/(1 − a) for 0 < a < 1, it is possible to express the total current carried by recycled working gas ions in steady state (n → ∞) as a mathematical series of the form Igas-recycle = Iprim

πg . 1 − πg

The total current carried to the target by working gas ions therefore becomes   πg Ig = Iprim + Igas-recycle = Iprim 1 + . 1 − πg

(7.5)

(7.6)

This current can become much larger than Iprim if the denominator in the parenthesis approaches zero, that is, if πg approaches unity. We now turn to the possibility of recycling sputtered target atoms, referred to as self-sputter recycling (seen in the right-hand side of Fig. 7.4). Each ion of the working gas that constitutes Ig (Eq. (7.6)) sputters target atoms with a sputter yield Yg , which are subsequently ionized with probability αt and drawn back to the target with probability βt . This is the start of a self-sputter recycling process. It is almost identical to the working gas recycling, except that it relies on the self-sputter yield YSS , and it is therefore possible to apply the same way of reasoning for expressing the self-sputter current amplification. The total self-sputter current generated by Ig (acting as seed) with the subsequent SS-recycling added becomes (Gudmundsson et al., 2016)   Yg πSS , (7.7) ISS = Ig 1 + YSS 1 − πSS where the self-sputter parameter (Anders, 2008, Gudmundsson et al., 2016) is πSS = αt βt YSS .

(7.8)

Adding the currents given by Eqs. (7.6) and (7.7) gives the total ion current Ii . Thus the total discharge current can now be written as    πg Yg πSS 1+ ID ≈ Ii = Iprim + Igas-recycle + ISS = Iprim 1 + 1 − πg YSS 1 − πSS (7.9)

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Figure 7.5 The recycling map (slightly modified from Brenning et al. (2017)). The ion current mix of Iprim , Igas-recycle , and ISS to the target in a magnetron discharge is defined by a point. For ISS /ID > 0.5, we have the SS-recycle-dominated regime A and, for Igas-recycle /ID > 0.5, the gas-recycle-dominated regime B. As an example (described at the end of Section 7.2.1.1), the parameter combination used for Fig. 7.4 is represented by a filled circle inside the AB regime. Note that the value of Iprim /ID , 39% in this example, is read on the diagonal lines. Iprim /ID ≥ 0.85 defines the dcMS regime, whereas Iprim /ID < 0.5 defines the recycling regime (blue-shaded region (gray in print version)).

or ID ≡ Iprim gas-recycle SS-recycle .

(7.10)

The last step defines the two amplification factors gas-recycle and SS-recycle as the two parentheses in the step before, respectively. Note that there is an asymmetry in Eq. (7.9) between the two types of recycling. This is more clearly seen in Eq. (7.6), where the working gas ion current Ig is completely independent of how large the selfsputter current ISS is. The primary current Iprim , amplified by the first parentheses in Eq. (7.9), is therefore a one-way seed for the self-sputter process, without any feedback in the other direction, that is, from self-sputtering to working gas-recycling. The process can be seen as a food chain: the current Iprim acts as a seed for the working gas-recycling process, which enhances it with the factor gas-recycle . The resulting total current Ig of ionized working gas atoms then acts as the seed for the self-sputter process. If πSS > 1, then the discharge goes into runaway. If not, then the current is further amplified by the factor SS-recycle . Let us now see how the GRM framework, developed above, can be put to use in order to quantify the type and the amplitude of ion recycling. As a suitable tool to illustrate such an analysis, Brenning et al. (2017) proposed the use of a recycling map, similar to that shown in Fig. 7.5, which, for a given discharge, shows the fractions of Igas-recycle and ISS compared to the total discharge current ID on the x- and y-axes, respectively. If the ion mix bombarding the target in a discharge is known, then it can be represented on the recycling map by a point. Above a diagonal line where Iprim /ID < 0.5 in Fig. 7.5 (blue shaded region (gray in print version)), the discharges are dominated by ion recycling. This recycling regime is subdivided into an SS-recycle dominated regime A (ISS /ID > 0.5), a working gas-recycle dominated

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regime B (Igas-recycle /ID > 0.5), and a mixed-recycling regime AB in between. The region where Iprim /ID ≥ 0.85 represents dcMS-like discharge currents, where little ion recycling is needed. As a demonstration of how to use the recycling map, we take as an example the discharge given in Fig. 7.4. By inserting the corresponding values αprim = 1, ξpulse = 1, αg = 0.7, βg = 0.7, Yg = 0.4, αt = 0.8, βt = 0.7, and YSS = 0.5 into Eq. (7.7) along with ID ≈ Ii = Iprim + Igas-recycle + ISS from Eqs. (7.6) and (7.9) and Igas-recycle = αg βg ξpulse Ig we find that Igas-recycle /ID = 0.37 and ISS /ID = 0.24, which is marked by a filled circle in Fig. 7.5. This discharge is found in the mixed-recycling regime AB, as expected, based on the widths of the flow arrows for the recycled currents in Fig. 7.4. In this case, the primary current Iprim is the seed for a considerably higher discharge current ID , since Iprim /ID = 1 − Igas-recycle /ID − ISS /ID = 0.39 by Eq. (7.9).

7.2.1.2

Discharge analysis

Analysis of several discharges using the generalized recycling model shows that the self-sputter yield YSS is the key parameter, which determines the type of ion recycling at high discharge currents. The starting point is the recycling map introduced in the previous section and here shown in Fig. 7.6 displaying discharges with five different targets. The five different discharges are based on TiO2 , C, Ti, Al, and Cu targets with self-sputter yields in the range from 0.1 (TiO2 ) to 2.6 (Cu) (Brenning et al., 2017). These discharges exhibit discharge current densities of JD ≈ 0.6 to 3.1 A/cm2 , averaged over the entire target surface, that is, in all cases well above the typical Jcrit ≈ 0.2 A/cm2 of Eq. (7.3). A summary of the discharge characteristics is provided in Table 7.2 to establish the necessary background for the following discussion on ion recycling. The required fractions of ISS /ID and Igas-recycle /ID needed to pinpoint these discharges on the recycling map in Fig. 7.6 were either extracted directly from modeling using the previously discussed IRM code (see Section 5.1.3) or assessed by analyzing the discharges by other means. The details can be found elsewhere (Brenning et al., 2017). From the combined results on ion recycling from these five different discharges displayed in Fig. 7.6 and described in Table 7.2 we see that a combination of working gas recycling and self-sputter recycling is generally involved at high discharge currents, beyond the critical current of Eq. (7.2) (all the discharges are in the blue-shaded region (gray in print version), in which the recycling current dominates over the primary current). Furthermore, high-YSS target materials result in discharges of type A (dominated by self-sputter recycling), whereas low-YSS materials give discharges either of type B (dominated by working gas recycling) or of mixed case AB. In type A discharges, large amounts of target material atoms are sputtered, which are easily ionized and can thereby achieve effective self-sputter recycling, which ultimately enables high discharge currents. Type A discharges with high YSS and operated with long pulses all saturate at steady-state plateau values (see Table 7.2) that can be gradually increased by increasing the discharge voltage, as earlier exemplified for a discharge with Al target and shown in Fig. 5.9 and discussed by Huo et al. (2014, 2017). The main reason

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Figure 7.6 A recycling map showing five discharges with typical HiPIMS discharge current densities of JD ≈ 0.6 – 3. A/cm2 taken over the whole target, and with self-sputter yields in the range from YSS ≈ 0.1 (TiO2 ) to 2.6 (Cu). Reprinted from Brenning et al. (2017). ©IOP Publishing. Reproduced with permission. All rights reserved.

Table 7.2 Overview of the five HiPIMS discharges investigated displaying the discharge voltage VD , the self-sputter yield YSS , the current density JD , and the pulse current evolution. The discharges are listed in order of decreasing self-sputter yield of the target material. The span in YSS for the TiO2 target is due to the various possible combinations of self-sputtering ions (Ti+ and O+ ) and sputtered atoms (Ti and O). The references point to the original works, where these discharges were first reported. Target

VD [V]

YSS

JD [A/cm2 ]

Cu

600

2.6

1.3

Al

600

1.1

0.6

Ti

630

0.7

0.6

C

1150

0.5

3.1

TiO2

600

0.04 – 0.25

1.6

Current evolution Stable plateau Stable plateau Stable plateau Current jump Triangular rising

Reference (Andersson and Anders, 2009) (Anders et al., 2007) (Magnus et al., 2012) (Anders et al., 2012a) (Magnus et al., 2012)

for such a stable current evolution with increasing discharge voltage was identified by Huo et al. (2014) as an increase in the self-sputter yield with increasing ion bombarding energy. They argued that a simplified relation between the sputter yield and the discharge current can be found from the expression for the total discharge current due to ion recycling, Eq. (7.9), with the assumption that the current above Icrit is mainly due to self-sputter recycling for type A discharges. The discharge current can then be simplified to ID ≈ Iprim

αt βt Yg . 1 − αt βt YSS

(7.11)

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As long as the product αt βt YSS stays below 1 (no self-sputter runaway, described at the end of this section), the current can increase smoothly with increasing discharge voltage because YSS is a smooth function of the ion energy (see Section 1.1.7). The two cases with low YSS , that is, type AB and B discharges, exhibit a more complex current evolution. In one case (TiO2 ), there is no plateau (Magnus et al., 2012). Here the current increases with time during the whole pulse, with no sign of saturation (Gudmundsson et al., 2016). In the other case (carbon target), there are plateau currents, but they jump abruptly with increasing voltage, from a value below Icrit to a current high above Icrit (Anders et al., 2012a) (see also Table 7.2). These discharges do not sputter significant amounts of target material but instead rely on ionization of the working gas, which is mainly Ar. This implies a larger contribution of hot secondary electrons, since the secondary electron emission yield due to bombardment by Ar+ ions is γsee,Ar+ ≈ 0.1, whereas for singly charged metal ions, γsee,M+ ≈ 0. This important difference between type A and type AB/B discharges was quantified by Brenning et al. (2017), who investigated the trends in the fraction of secondary electron density to the total electron density (hot and cold thermal electrons eH and eC , respectively) neH /(neC + neH ), as well as the electron temperature Te . The data was taken from the discharges with TiO2 , Ti, Al, and Cu targets summarized in Table 7.2. In Fig. 7.7, this data is plotted versus self-sputter yield. The carbon case was not included due to lack of data. There is a clear trend with a less energetic electron population (both fewer hot secondary electrons and a lower electron temperature) with increasing self-sputter yield. The trend in hot electron density can be understood as follows: The TiO2 discharge is of type B and thereby dominated by working gas recycling. This discharge has the largest population of hot electrons because essentially all the bombarding ions (mainly Ar+ , but also O+ and Ti2+ toward the end of the pulse) contribute to the secondary electron emission, as verified by Gudmundsson et al. (2016). In the discharge with a pure Ti target, on the boundary between type AB and type A, only half of the ions contribute to the secondary electron emission (Ar+ and Ti2+ ), whereas the other half does not contribute at all (Ti+ with γsee,Ti+ ≈ 0) (Gudmundsson et al., 2016). This trend continues to the extreme type A discharges with Al and Cu targets, which are dominated by self-sputter recycling, and where the singly charged metal ions (Al+ and Cu+ ) carry almost all of the discharge currents (see Fig. 7.6). These ions release no secondary (hot) electrons, which leads to a low fraction of hot electrons in the EEDF of the type A discharges. That these discharges also have a lower electron temperature seems puzzling at a first glance. We might expect the discharge to compensate the lack of hot electrons with more efficient Ohmic heating, which would give a higher Te . However, this seems not to be needed, probably because type A discharges are dominated by the sputtered species, which are relatively easy to ionize. In contrast, type AB/B discharges can also reach high-current operation in HiPIMS, but they require a high-energy EEDF to enable the significant ionization of Ar needed for working gas-recycling (Brenning et al., 2017). In this scenario the sudden current jump with increasing discharge voltage of the investigated carbon discharge is due to working gas-recycling having a threshold behavior related to the requirement that returning Ar atoms from the target need to be ionized during one crossing time across the ionization region. For this to occur, a sufficiently high plasma density has to be

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Figure 7.7 Features of the EEDF versus the self-sputter yield. Black circles: the fraction of the secondary (hot) electron density to the total electron density. Red squares (gray in print version): electron temperature. Reprinted from Brenning et al. (2017). ©IOP Publishing. Reproduced with permission. All rights reserved.

reached at the beginning of the pulse to establish a loop in which a growing working gas-recycled current exceeds Icrit . For type AB/B discharges with low YSS , there is no stable operation at intermediate discharge currents, between Icrit and some much higher current, and hence the sudden current jump (Brenning et al., 2017) which has ˇ been observed experimentally (Anders et al., 2012a, Capek et al., 2012). It remains to discuss the cases with continuously increasing discharge currents during the pulse. In self-sputter dominated (type A) discharges, unlimited runaway, that is, an unlimited current increase at a fixed discharge voltage, is known to be possible (Anders et al., 2007), provided that the condition πSS = αt βt YSS > 1 is fulfilled. Physically, sputtering of new target atoms provides the source of new ions to the recycling loop that is needed for the current to increase in time. When YSS > 1 this is, in principle, an infinite source, and the current can therefore increase without a limit. The current rise limit is only imposed by the pulse cutoff. For a discharge where YSS < 1 (type AB and B), such as the TiO2 discharge, which also may exhibit an increasing current during the pulse, the situation is different. From Eq. (7.10) we see that self-sputter recycling gives a current amplification with a factor SS-recycle . This amplification is generally limited when YSS < 1. Working gas-recycling can give a separate amplification by a factor gas-recycle , but this factor never causes unlimited runaway for the reason that ξpulse ≤ 1, which (since also αg < 1 and βg < 1) gives πg = αg βg ξpulse < 1. In the TiO2 discharge, it was found that the reason for the continuously increasing (high) discharge current was due to a combination of high working gas ionization probability αg and high return probability βg (Gudmundsson et al., 2016). Then the current amplification factor gas-recycle of Eq. (7.10) can become very large. For the TiO2 discharge, the limiting factor in the product πg = αg βg ξpulse was identified as the ionization probability αg (Gudmundsson et al., 2016). At the end of the pulse, this probability was still a bit below 1, αg = 0.75, but had an increasing trend. The discharge was in a positive feedback loop: (higher αg ) → (higher ne ) → (higher ionization rate) → (higher αg ), and so on, and hence a continuously increasing current is observed. This behavior, applicable to type AB and B discharges, is defined as lim-

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ited runaway, because the current increase can be large, but, for any fixed voltage, it still is limited by an upper bound (Brenning et al., 2017). It is also worth noting that the observed change in current shape from the stable plateau current for the pure Ti target to the continuously increasing triangular-shaped current seen with the oxidized Ti target (Magnus et al., 2012) has also been investigated experimentally in more detail by Layes et al. (2018) for a Cr target operated in an Ar/O2 mixture. They used in situ spatially resolved X-ray photoelectron spectroscopy (XPS) to measure the surface composition of the Cr target when operating in the entire range from metal to compound mode. Only when the target race track was completely covered by an oxide layer, they recovered the triangular pulse shape. In all other cases, a plateau current was observed. In fact, they found that if at least 20% of the target area is metallic, then metal atom recycling dominates despite the significant oxidation, and a plateau current is observed.

7.2.2 Temporal evolution of the discharge current We now address the time-evolution of the discharge current waveform, which involves discussing the physical mechanisms operating during the five phases shown in Fig. 7.3. We focus our discussion on experimental and modeling data from the commonly reported high-current pulses, represented by the middle and top curves in Fig. 7.3. However, also the low-current cases will be addressed where appropriate. Phase 1 (ignition) covers approximately the first 10 µs of the discharge pulse, which constitutes the ignition phase during which there is negligible plasma in the bulk volume of the discharge chamber. The discharge will likely ignite as a localized glow discharge at the target surface in the vicinity of the anode ring where the vacuum electric field is strongest. An example is seen in the current transport in Fig. 7.8A, where the initially small discharge current is mainly found being radially transported close to the target surface in the case of a circular magnetron target (Lundin et al., 2011). An obvious question is when can we expect to see the current rise in relation to the applied discharge voltage, as exemplified by the ∼ 10 µs-long delay to the current onset in Fig. 7.3. Experimentally it is known that the delay between the onset of the discharge voltage and the discharge current depends on the working gas pressure (Gudmundsson et al., 2002), working gas composition (Hála et al., 2010), target material (Hecimovic and Ehiasarian, 2011), and applied voltage (Yushkov and Anders, 2010). As was discussed in Section 2.2.5, the delay time increases with decreasing working gas pressure and can be in the range of a few µs to over 100 µs (Gudmundsson et al., 2002, Poolcharuansin et al., 2010). If the pressure is very low and the delay time is significant, then the plasma cannot fully develop within the pulse, and if the delay is longer than the actual pulse width, then the plasma will not ignite at all. To prevent this situation, Poolcharuansin et al. (2010) have demonstrated how a dc preionizer can be used to reduce or eliminate the time lag and thus the ignition delay time in a HiPIMS discharge when operating at pressures below 0.1 Pa (see also Section 2.2.4). By particle-in-cell modeling, the effect of pre-ionization has also been

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Figure 7.8 Analysis of the current transport in a HiPIMS discharge during (A) phase 1 – 2 (ignition and initial current rise), (B) phase 3 (decay/transition), and (C) phase 3 – 4 (decay/transition and plateau/runaway) above a 6” magnetron (7.6 cm radius) based on measured current densities in a Cu discharge with argon as the working gas at 0.53 Pa. The net current flow across the different boundaries of two cylindrical volumes in the discharge, between z coordinates 0 – 4 cm and 4 – 8 cm, respectively, is shown. The areas of the block arrows are drawn proportional to the currents, which are also given as a percentage of the discharge current. The ellipses above the target race track represent cross-sections of the dense plasma torus developing during the discharge pulse. The peak current was 145 A, which corresponds to a peak current density of 0.8 A/cm2 . The race track is centered at approximately r = 4.5 cm, z = 0 cm. The grounded anode ring is shown as a hatched rectangle above the edge of the target surface. Reprinted from Lundin et al. (2011). ©IOP Publishing. Reproduced with permission. All rights reserved.

demonstrated to lead to the rise of the discharge current by two orders of magnitude in ∼ 2 µs (Revel et al., 2018). The discharge characteristics of such a situation is shown in Fig. 5.2. During the ignition phase, time-resolved tunable diode-laser absorption spectroscopy measurements by Vitelaru et al. (2012) show that there is a very strong increase of the density of the metastable working gas atoms (Arm ) before the discharge current increases, as can be seen in Fig. 7.9. These results are consistent with the particle densities previously discussed in Section 4.2 and shown in Fig. 4.13B, where the Arm density starts to increase already within the first 5 µs, although the discharge current ID (t) is still very small (see Fig. 4.3 of Section 4.1.2). The sudden rise in the Arm density is due to the metastable density being built up practically without any losses during phase 1 (Stancu et al., 2015). This behavior is different from the temporal variation of the densities of the charged particles, since these carry the discharge current and therefore are continuously lost, electrons to the surrounding plasma volume and ions both to the target and the surrounding plasma volume. It should also be noted that the increase in the Arm density occurs before we can detect a significant density of sputtered material, since little sputtering can occur due to few ions impinging on the target (see also Section 4.1.2, where the spatio-temporal evolution of Ti+ ions is shown in Fig. 4.4, and Section 4.1.2, where the spatio-temporal evolution of Ti atoms is shown in Fig. 4.13A). As previously described in Section 3.2, Poolcharuansin and Bradley (2010) detected a short burst of hot electrons (70 – 100 eV) within the first 10 µs of the HiPIMS pulse, which would explain the great increase in the number of metastable Arm atoms observed as due to electron impact excitation. Also, a third very hot electron population has been observed during the first two microseconds of

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Figure 7.9 Typical results of time resolved tunable diode-laser absorption spectroscopy in a HiPIMS discharge taken at 1 cm from the target surface at an Ar working gas pressure of 1.3 Pa. The full black curve displays the HiPIMS discharge current waveform ID (t) (corresponding to a peak current density of 0.5 A/cm2 ) during a 200 µs pulse, the red curve with circles (light gray in print version) is the temperature of the metastable working gas atoms Arm and the blue curve with squares (dark gray in print version) represents the Arm density. Reprinted from Vitelaru et al. (2012). ©IOP Publishing. Reproduced with permission. All rights reserved.

the pulse in PIC/MCC simulations and seen in Fig. 5.18 (Revel et al., 2018). Also, the neutral gas temperature starts to increase reaching values around 600 – 800 K, whereas the discharge current is still very low, as seen in Fig. 7.9 (Vitelaru et al., 2012). This is likely due the increasing amount of collisions with energetic sputtered atoms that are taking place. Using optical emission spectrometry, Hála et al. (2010) find that there is an initial strong increase in the emission from the neutral working gas atoms (Ar) before the discharge current starts to increase, as seen in Fig. 7.10. Phase 2 (current rise) displays the strong initial current increase, commonly seen after the bulk plasma breakdown, as seen in Fig. 7.3. Secondary electrons (hot electrons eH ) and electrons created in the ionization region close to the target (cold electrons eC ) are accelerated out along the magnetic field lines into the bulk volume and begin to ionize the neutral working gas resulting in a strong axial ion current (perpendicular to the target surface) (Lundin et al., 2011). The relative importance of eH and eC is of great interest for the energy balance of the discharge and will be discussed in more detail in Section 7.2.3. A dense plasma torus above the target race track is now also developing (Lundin et al., 2011), as indicated by ellipses in Fig. 7.8A. At this stage the metal atom and argon metastable densities build up, whereas working gas rarefaction sets in, mainly due to ionization losses (Huo et al., 2012), as previously discussed in Section 4.2.2. The metastable Arm density, which during phase 2 becomes coupled to the ground state Ar density, peaks and subsequently decreases (Stancu et al., 2015). The reason for this coupling is that Arm loss processes, such as Penning ionization of the sputtered atoms and electron impact ionization of neutral metastable gas atoms, have come into play (Vitelaru et al., 2012, Gudmundsson et al., 2015). However, the role of Penning ionization is small. Stancu et al. (2015)

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Figure 7.10 (A) Discharge current and voltage waveforms, where the discharge current peak corresponds

to a peak current density of approximately 2.5 A/cm2 , (B) optical emission from Cr, Cr+ , and Cr2+ , and + (C) optical emission from N2 , Ar, N+ 2 , and Ar for an HiPIMS discharge operated in an N2 /Ar (1/1) mixture at 1.3 Pa with Cr target. The three phases observed are by these authors denoted as the ignition phase (I), the high-current metal-dominated phase (M), and the transient phase (T). Reprinted from Hála et al. (2010), with the permission of AIP Publishing.

explain the decrease after the peak in the Arm density during this phase, which is seen in Fig. 7.9, as being due to gas rarefaction. At this time, there is a balance between the ongoing production (mainly electron impact excitation e + Ar −→ Arm + e) and loss mechanisms (mainly electron impact ionization e + Arm −→ Ar+ + 2e). Costin et al. (2011) used fast time-resolved 2D imaging to explore short pulses. They followed the emission of Ar and Al lines in an Ar/Al discharge looking at the Al target during a 4 µs pulse. After a 0.5 µs delay, they see a fast rise in the Ar emission lines to a peak at 1.2 µs into the pulse, which coincides with a rapid expansion of the torus. In contrast, the Al emission lines exhibit the same temporal behavior as the discharge current, a slow increase in the intensity to a maximum 2.8 µs into the pulse. Also, the optical emission spectrometry (OES) measurements reported by Hála et al. (2010) using a Cr target confirm these trends, where a fast increase in the Ar emission is detected before the peak in the discharge current is reached as well as a limited, but visible, increase in the density of the sputtered Cr during the same time, as seen in Fig. 7.10. Also, note that a first increase of the metal ion density occurs at this time, as earlier observed for Ti+ ions in Fig. 4.4 of Section 4.1.2. The occurrence of metal ions is slightly de-

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layed vis-á-vis the sputtered neutrals (Hála et al., 2010) due to the time it takes to sputter and then ionize these species, also seen in the results from the time-dependent HiPIMS IRM studies (Gudmundsson et al., 2015) and described in Section 5.1.3. Furthermore, electron impact excitation and ionization of the sputtered target atoms will lower the effective electron temperature as the sputtered particle density grows during this early stage of the HiPIMS pulse, since the ionization potential of most sputtered elements is well below that of Ar. We typically find effective electron temperatures around Teff ≈ 2 – 5 eV, depending on the degree of self-sputter recycling, during the pulse (see Fig. 7.7 and Section 3.2 for more detail on the evolution of the electron temperature). As the peak in the discharge current is approached toward the end of phase 2, there is a strong decrease in the density of the metastable argon atoms, whereas the neutral argon temperature TAr begins to increase; see Fig. 7.9 (note that the authors assume that TAr ∼ TArm since Arm are produced by electron impact excitation from Ar and no great additional heating of the Arm is expected (Vitelaru et al., 2012)). Also, there is reported a strong increase in the emission from neutrals and ions of the sputtered material, which is often (but not always) found to dominate the discharge during phases 2 and 3. These trends are clearly shown in Fig. 7.10, where strong emission from neutral Cr atoms and Cr+ ions are detected by OES at the peak in the discharge current ID,peak when sputtering a Cr target in an Ar/N2 mixture (Hála et al., 2010). The same trends were also observed earlier when visualizing the particle densities in an Ar/Ti discharge shown in Figs. 4.13A and 4.4 for Ti atoms and Ti+ ions, respectively. In that case, short pulses were applied (20 µs), and the peak in the discharge current was reached at the end of the pulse, resulting in high Ti atom and Ti+ ion densities at that point in time. During phase 3 (current decay/transition), the bulk plasma density builds sufficiently to admit current closure across the magnetic field lines (i.e., cross-B electron drift toward the anode/ground): first, at larger distances from the target surface illustrated in Fig. 7.8B, but eventually the plasma density above the target race track is high enough so that this route is the easiest for the electron current to cross the magnetic field lines, which results in a more extended axial current, as shown in Fig. 7.8C (Lundin et al., 2011). The plasma potential has been found to be less negative compared to the ignition phase but might still reach down to −40 V close to the target surface (Mishra et al., 2010) (see also Section 3.3.2). At the time around the current peak, a strong reduction of the working gas atom density occurs, referred to as gas rarefaction and discussed in detail in Section 4.2.2. Gas rarefaction is mainly due to (i) electron impact ionization of the working gas and (ii) gas expansion. Electron impact ionization is dominant in the HiPIMS discharge due to the much higher electron densities during the peak discharge current as compared to, for example, dcMS (Raadu et al., 2011). Gas expansion is a result of heating due to momentum transfer in collisions between the background working gas and the increasing amount of sputter-ejected target atoms as well as reflected working gas atoms (Kadlec, 2007), as discussed in Section 4.2.2. Phase 3 begins with a discharge current decrease, which can sometimes be quite large, as shown in Fig. 7.9. When the discharge current decreases, the refill of argon

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from the surrounding gas reservoir becomes larger than the rarefaction rate, and therefore the Ar density increases again as shown in Fig. 5.13. This has the counterintuitive consequence that the metastable Arm density increases as the current decreases, as shown in Fig. 7.9 (Stancu et al., 2015). Phase 3 does not exhibit a steady state, as can be seen in Fig. 7.3, since it ends when the discharge either goes into the decay phase characterized by a decrease in the discharge current or an ion recycling regime (Brenning et al., 2017) characterized by yet another discharge current increase (or at least a sustained high-current mode), which will be addressed next. Phase 4 (plateau/runaway). This phase can exhibit very different current pathways, as seen in Fig. 7.3. It was discussed in detail in Section 7.2.1 concerning ion recycling to achieve high (or low) currents in long HiPIMS pulses. It is therefore not necessary to repeat the physical arguments as to why we achieve a certain current amplitude during this phase. However, it is worth spending some time looking at the time dynamics involved and connecting it to the general discharge modes presented in Table 7.1. During this phase, a dense plasma torus is now maintained above the target race track in essentially steady state (depending on the current evolution), which leads to considerable ionization in this region (Lundin et al., 2011). As shown in Fig. 7.8C, electrons are now transported across the magnetic field lines B, the entire way from close to the target surface and through the plasma volume until they reach the first grounded magnetic field line, which intersects the grounded anode ring. Axial crossB current transport is now the dominant fraction of the measured total current (88% in the Cu discharge illustrated in Fig. 7.8C), that is, a significant change compared to phases 1 – 2, where most of the discharge current crosses the B-field radially, and close to the target surface (as shown in Fig. 7.8A). Here we can have two scenarios depending on the discharge current amplitude. First, we discuss low discharge currents. In the case of a decaying discharge current (in the sense that the plateau current is lower than the peak current), such as the bottom current density curve in Fig. 7.3, the plasma density is during phase 4 decreased due to working gas rarefaction, which reduces the ionization of the working gas and of sputtered particles and thereby causes a reduced sputtering (i.e. decreasing metal flux) (Lundin et al., 2009). The low-current discharge characterized by Iprim /ID ≥ 0.85 as defined in Fig. 7.5 in Section 7.2.1, is dominated by the neutrals of the working gas and neutral sputtered species as in conventional dcMS. The overall effect on the gas dynamics is a modest gas heating (few collisions) and ultimately a gas rarefaction at the level expected in dcMS operation. Note that at low enough discharge currents the gas rarefaction is replaced by gas refill during this phase, as observed by Huo et al. (2012) and shown in Fig. 5.13. The increase of the working gas density is also consistent with the results of Vitelaru et al. (2012), where they find that the emission from the metastable working gas atoms (Arm ) increases during phases 3 – 4, as seen in Fig. 7.9. The reaction chain involving a replenished supply of Ar followed by an increase of Arm was later verified by Stancu et al. (2015) when modeling the same discharge; see Section 5.2.3.2. For the high-current regimes, the situation is quite different. Let us first consider moderate plateau currents like the middle current curve in Fig. 7.3. As already discussed in Section 7.2.1, this current evolution typically involves a combination of

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working gas recycling and self-sputter recycling, which increases the discharge current ID (t) beyond the critical current Icrit and thereby leads to significantly higher current compared to the dcMS-like case (bottom curve, Fig. 7.3). Note that the discharge at such current amplitudes is neither defined as pure working gas sputtering nor self-sustained self-sputtering, but instead referred to as working gas-sustained selfsputtering (see also Table 7.1), where the working gas ion current acts as a seed for a stronger metal ion current (Huo et al., 2014). Hála et al. (2010) refer to this phase as the high-current metal-dominated phase since intense emission is observed from both neutrals and ions of the sputtered material. This emission dominates the discharge emission as seen in Fig. 7.10B (except in discharges dominated by working gas recycling (see Section 7.2.1.2)). Huo et al. (2014, 2017) studied a set of discharge voltage–current curves for an Al discharge operated in pure Ar using the previously discussed IRM code (see also Section 7.1.1). For high discharge voltage (VD > 750 V), the metal ion current is about one order of magnitude higher than the working gas ion current during phases 3 and 4 (Huo et al., 2014), which is defined as a type A discharge in Section 7.2.1.2. The authors found that there is a faster and stronger rarefaction of the neutral argon gas with increasing peak-current during phase 3, which affects the amplitude of the following plateau-current in phase 4. If the discharge had remained in the working gas-sustained self-sputtering mode throughout the remainder of the pulse, then the total current should not have increased again. Instead, for VD > 750 V, the discharge current ID (t) increased after a narrow minimum (see Fig. 7.1C) and finally settled at a steady-state plateau that, depending on the discharge voltage, could be even higher than the initial discharge current peak (Huo et al., 2014) (see Fig. 5.13). This was clearly a transition away from the working gas-sustained self-sputtering. By artificially turning off the argon working gas supply in the IRM code during phase 4 the authors found that the discharge had now transitioned into the self-sustained self-sputtering mode for the highest discharge voltage (∼ 1000 V), which roughly corresponds to the second top-most current curve in Fig. 7.3. However, this did not occur for the lower discharge voltages investigated, where instead the discharge died out when the working gas supply was turned off. Furthermore, it ˇ should be noted that Capek et al. (2012) have demonstrated stable sputtering operation for a number of target materials and were able to control the current plateau level in the range of 14 – 105 A by varying the magnetic field strength. By decreasing the magnetic field strength the plateau current can be lowered. It remains to investigate the possibility of self-sputter runaway illustrated by the continuously increasing (highest) current curve in Fig. 7.3, which requires that the self-sputter parameter fulfills πSS = αt βt YSS > 1 (Anders, 2008), as already touched upon in Section 7.2.1.2. Since αt and βt are always ≤ 1, self-sputter runaway requires YSS > 1. Self-sputter runaway can indeed occur for copper and other high-yield materials, including silver and zinc, as pointed out by Anders (2011). However, YSS > 1 does not guarantee self-sputter runaway, since the product πSS = αt βt YSS still has to be greater than 1, hence the onset of runaway at a well-defined (high enough) threshold power, which is set by the discharge voltage. Furthermore, in the seminal work of Anders et al. (2007), where the discharge current waveforms are measured for a number of target materials over a wide range of discharge voltages, sudden and irre-

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producible current increases up to 5 A/cm2 for both Ti and Nb targets were reported, which indicate the onset of self-sputter runaway. This behavior was observed for a discharge voltage of 600 V, where the self-sputter yields of both Ti+ and Nb+ ions are roughly 0.7 – 0.8, that is, too low for self-sputter runaway. In the Ti case the amplitude of the current was shown to be directly correlated to the Ti2+ ion count in a mass spectrometer. The physical mechanisms involved can be understood directly from the self-sputter parameter πSS = αt βt YSS . The effect of doubly charged ions on πSS is double. First, their impact energy on the target is twice that of Ti+ ions, giving a higher YSS . Second, in contrast to singly charged ions, they release secondary (hot) electrons that add to the ionization rate and increase αt . At some discharge power, these two effects can combine to make πSS > 1, resulting in a rapid current increase and self-sputter runaway. Phase 5 (afterglow). This stage is reached as the HiPIMS pulse is switched off and is characterized by a sharp drop of the discharge current. During the afterglow, Poolcharuansin and Bradley (2010) detect an initial fast decrease of the electron density with a time constant of about 30 µs followed by a much slower decay rate (3500 µs). The effective electron temperature Teff also quickly decays reaching values around 0.2 eV, which is sustained during several milliseconds (Poolcharuansin and Bradley, 2010). In addition, we see in Fig. 7.9 that the density and temperature of Arm are rapidly decreasing as the sputtered flux disappears and the plasma species are lost through recombination and diffusion toward the chamber walls (Vitelaru et al., 2012). The decay of the Arm density is characterized by an initial fast decrease followed by a more slow decay which is due to diffusion of the metastables out of the ionization region. The reason for the initial fast decay is a rapid disappearance of the most energetic electrons that constitute the EEDF. This reduces the rate of electron-impact population of metastable Arm from the Ar ground state while the loss mechanisms are still active: the sum of electron impact ionization (e + Arm −→ Ar+ + 2e, dominating) and electron impact quenching loss to the ground state (e + Arm −→ Ar + e, a smaller contribution) (Stancu et al., 2015). For discharge current evolutions that are characterized by a current peak ID,peak at the end of the pulse, there is commonly also a peak observed in the density of the ionized sputtered material in the immediate afterglow. For example, we found in Fig. 4.4 that the Ti+ ion density peaked about 5 – 10 µs after pulse-off, which was followed by a rather slow decay. On the other hand, if ID,peak was reached much earlier during the pulse followed by a current decrease, such as seen in Fig. 7.10, then low ion densities are expected during phase 5, which is also in agreement with the results seen in Fig. 7.10B. It is worth bearing in mind that the HiPIMS discharge plasma can survive for a long time during the off-time, where a weak electron density was detected for up to 10 ms after the pulse was switched off (Poolcharuansin and Bradley, 2010). Also Hecimovic and Ehiasarian (2009, 2011) have found that working gas ions and various metal ions are long-lived in the HiPIMS discharge and in some cases present during the entire pulse-off time (up to 10 ms), which is described in more detail in Section 4.1.3.2.

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7.2.3 Ohmic heating versus sheath acceleration As discussed in Section 1.1.1, the dc glow discharge is maintained through secondary electron emission from the cathode surface. These secondary electrons and new electrons created by the onset of electron-impact ionization avalanches within the sheath are accelerated by the electric field within the sheath and gather the energy needed for these (hot) electrons to participate in the ionization processes that maintain the discharge. Sheath acceleration of electrons is important also in the magnetron sputtering discharge but with one important difference: here the ionization mean free path is typically longer than the thickness of the cathode sheath, and electron avalanches cannot begin to develop within the sheath. Therefore, ionization within the sheath is taken into account by multiplying the secondary electron emission coefficient γsee with a factor m that accounts for secondary electrons ionizing in the sheath, as described in Section 1.2.4. Early on, sheath acceleration was believed to be the main source of electron energy also within the magnetron sputtering discharge (Thornton, 1978). However, recently it has been demonstrated that sheath acceleration alone cannot sustain the magnetron sputtering discharge at typical discharge voltages (Huo et al., 2013, 2017, Brenning et al., 2016). As seen in Fig. 1.8, sheath energization, already in dc magnetron sputtering, provides only 30 – 70% of the electron energization. Fig. 1.8 also shows that this fraction depends in a natural way on the secondary electron emission coefficient: a higher γsee gives a larger fraction of sheath energization, and vice versa. In the HiPIMS discharge, sheath energization plays an even smaller role, sometimes almost negligible as recently demonstrated (Huo et al., 2013, 2017). Also, here the general rule holds: a lower secondary electron emission coefficient gives a lower fraction of the total energy spent in sheath acceleration. However, this connection is less strong in the HiPIMS discharges, where the importance of sheath energization is mainly determined by the self-sputter yield YSS of the target. Fig. 7.7 shows an example of this: higher values of YSS are correlated to low densities of hot (i.e. sheathaccelerated) electrons in the discharge. This connection between sheath energization and self-sputter yield can be understood as follows. The value of γsee in a HiPIMS discharge depends mainly on the composition of the ions that hit the target. This, in turn, is determined by the type of ion recycling that dominates in the discharge, which was discussed in Section 7.2.1.1. Fig. 7.6 shows that a HiPIMS discharge with an aluminum target, which is of type A, is dominated (close to 100%) by self-sputter recycled Al+ ions. These have γsee ≈ 0, and therefore the role of sheath energization is practically negligible. In the other extreme, the type B discharge with a TiO2 target is dominated by working-gas recycling. Here 57% of the ion current to the target is due to Ar+ ions with γsee ≈ 0.1 (see Fig. 7.6), which gives significant sheath energization. The “missing electron heating”, the part that is supplied outside the cathode sheath, is commonly called Ohmic heating. This concept was introduced by Huo et al. (2013) and was briefly touched upon in Sections 1.2.4 and 5.1.3. Ohmic heating is a simplified concept based on two time-averaged macroscopic features in the plasma outside the sheath. First, there is an electric field E due to the potential difference across the plasma outside the sheath, in Section 1.2.4 denoted as VIR , which (as discussed in Section 1.2.4) in both dc magnetron sputtering discharges and in HiPIMS discharges is of

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the order of 50 – 100 V, or 10 – 20% of the applied discharge voltage VD . This is also consistent with 2D PIC simulation results reported by Revel et al. (2018). Second, the electrons carry a fraction Je of the discharge current, a fraction which is small close to the target, but which increases with the distance from the target, so that the electron current dominates at the boundary between the ionization region and the diffusive plasma outside the ionization region. The rate of Ohmic heating of electrons is simply defined by the scalar product Je · E, in analogy with the heating by electric energy dissipation when a current is led through a resistive medium. Provided that the electrons can be assumed to carry typically half of the current in the ionization region, this gives the total Ohmic heating power as POhm = 12 ID VIR (see e.g. Huo et al. (2013)). This is used as a standard assumption in the IRM (see Section 5.1.3). It is important to realize that the concept of Ohmic heating implicitly involves two assumptions: first, that the time-averaged values of E and Je give the correct energy dissipation through the product Je · E and, second, that the electron population is collectively heated and therefore retains a thermal (Maxwellian) energy distribution. The strength of the Ohmic heating concept is that it gives a simple first-approximation physical picture of the electron energy gain outside the sheath; for refined results, the specific mechanism(s) that enable the electron transport across B and in the direction of E (a condition that excludes the Hall drift, which is perpendicular to E) need to be considered. We will return to this issue in Section 7.3.1.2. Further evidence of the differences between the discharges with Al and Ti targets introduced in Section 7.1.1 is found when comparing the fraction of the Ohmic heating (Huo et al., 2013, Brenning et al., 2016) for the Al and Ti targets. For the Al target, the fraction of the total electron heating that is attributable to Ohmic heating is found to be of the order of 99% in the HiPIMS operation regime. This particular result has previously been discussed by Huo et al. (2013), who demonstrated that for a HiPIMS discharge with Al target operated at typical high discharge voltages, almost all of the electron heating is of Ohmic nature and located within the ionization region. The energetic secondary electrons accelerated in the cathode sheath, as well as the twice ionized Al2+ , play very small roles in line with our discussion earlier in this section. For the discharge with Ti target, we instead find a mix of Ohmic heating and sheath energization, which is a result both of the presence of more Ar+ ions and of the ionization degree of Ti2+ being at least an order of magnitude larger than the ionization degree of Al2+ . When operating with a Ti target, the fraction of the total electron heating that is attributable to Ohmic heating is about 92% in the HiPIMS operation regime (Huo et al., 2017).

7.3

Transport of charged particles

It is not straightforward to analyze the motion of charged particles in HiPIMS discharges due to a rather complex nature of the plasma. Still, we can try to find various ways to illustrate the plasma dynamics by studying some simple cases of particle motion. One such example was already given in Section 1.2.2, where it was shown

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that the Hall drift and the diamagnetic drift give rise to an azimuthal current flowing above the target race track. However, we need to go further in our studies of transport of charged particles to also understand other phenomena, such as the reported backattraction of ionized sputtered species (Christie, 2005), ion azimuthal rotation along the race track (Lundin et al., 2008b, Poolcharuansin et al., 2012, Yang et al., 2015), fast electron transport across magnetic field lines, which carries the discharge current (Lundin et al., 2008a, 2011), and rotating dense plasma structures often referred to as spokes (Hecimovic and von Keudell, 2018). The motion of charged particles is one of the most challenging problems in the physics of the HiPIMS discharge. As discussed in Section 1.2.2, only the electrons are confined by the magnetic field. The electrons gyrate around the magnetic field lines and recoil at the sheath edge. However, local electric fields may be established and consequently drive instabilities, which weaken the magnetic confinement. The key parameters that determine the macroscopic flow speeds ve and vi of electrons and ions, respectively, in the plasma are: the magnetic field B, the gradient in electron pressure ∇pe , the electric field, which here is split up into a “quasi-dc” part denoted by E (which varies on the time scale of the HiPIMS pulse), and a high frequency Ehf part associated with waves, turbulence, and anomalous resistivity and transport, the classical elastic mean free path λcoll for collisions with charged and neutral working gas particles, and the characteristic length scale c of the device. In magnetron sputtering discharges the inequalities rce c rci generally hold, as discussed in Section 1.2.2, meaning that the electrons are magnetized while the ions are practically unmagnetized. Ion-neutral mean free paths are found in ranges from λcoll c to λcoll > c , depending on apparatus size and working gas pressure. However, for the electron flow and transport, classical collisions are usually less important than “anomalous collisions” mediated by the high frequency Ehf fields, which we will return to in Section 7.3.2. In a fluid description, these can be represented by an anomalous effective ion–electron momentum exchange time constant τeff , which, however, only applies to the cross-B component of the electron–ion relative motion (alternatively expressed as resistivity, a tensor η¯ with a small field-aligned component). Often, τeff is referred to as the effective collision time. Hence both species, the electrons and the ions, exhibit an anomalous transport discussed in Sections 7.3.2.1 and 7.3.2.2, respectively. Strongly related to the anomalous resistivity and the related instabilities is the phenomenon of spokes in the HiPIMS discharges (Hecimovic and von Keudell, 2018), which will be addressed in detail in Section 7.4. One way to look at the spoke structures is that they are large-scale versions of two-stream driven microinstabilities, and like these give anomalous transport and azimuthal electron–ion drag and also are involved in the important mechanism(s) of electron heating outside the sheath. The fundamental difference is that the spokes have scale sizes comparable to the plasma characteristic length scale c . An important common feature of both instabilities and spokes is that if they enable cross-B electron transport needed for the electrons to carry the discharge current, then they will also transmit the macroscopic azimuthal Je × B force, which is associated with that current, from the electrons to the ions. We attempt to introduce the mechanisms involved in such a way that they appear in a natural sequence of increasing complexity. Three types of mechanisms need to be

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considered in HiPIMS discharges: (i) The classical cross-B mobility through collisions between electrons and neutrals, or Coulomb collisions between electrons and ions, (ii) anomalous cross-B mobility through the wave structure in instabilities with length scales c , and (iii) electron cross-B motion in spokes, which have length scales c . In all these scenarios, electrons exchanging momentum with ions or neutrals lead to a shift of the electron guiding centers and a drift across magnetic field lines (recall that the electron is moving in circles around a guiding center in a plane perpendicular to the magnetic field, as discussed in Section 1.2.2). Three types of charged species will be treated: working gas ions, denoted as G+ , ions of the sputtered material, denoted as M+ , and electrons e. For the following discussion, we define z = 0 at the target surface, and the +z-direction is perpendicularly away from the target surface. Also, the most interesting plasma region is above the race track, where B is parallel to the target.

7.3.1 Classical ion and neutral species transport 7.3.1.1

Ion transport

We start by looking at the ions. In Section 7.2.1.2, we saw that a high return probability of the working gas ions βg to the target was beneficial to sustain of the discharge due to a nonzero secondary electron emission. The bombardment of the target by the ions of the working gas provides the discharge with hot secondary electrons for continued ionization. Due to a large cross section for resonant charge exchange collisions, the ion motion of G+ for the simplest case with zero E field (which applies in the afterglow plasma when the pulsed potential is switched off) can, in the first approximation, be treated as diffusion through the background gas. The ion flux is then given by Fick’s law (Lieberman and Lichtenberg, 2005, p. 134) diff = −Ddiff ∇nG+ ,

(7.12)

where Ddiff , for ions, is the ambipolar diffusion coefficient (Chen, 2016). However, both the neutral working gas and the working gas ions are, in addition to the diffusion flux, moving away from the target under the action of the sputter wind (Hoffman, 1985), which also includes fast recombined working gas ions reflected from the target surface (Lundin et al., 2009, Huo et al., 2012), as discussed in Section 4.2.2. This gas flow speed must be added to the diffusion flow speed. Such a situation is, for example, described by the IRM code (Huo et al., 2012) discussed in Section 5.1.3. In the case of significant gas rarefaction, the problem becomes more complicated because the assumption of a collision-dominated regime might no longer be valid. In the zero E field case, the uncollided M+ ion population does not return to the target, whereas the collided population behaves as the G+ ions in the zero E field treated earlier, moving according to the combined mechanisms of diffusion and rarefaction flow. A simple estimate of returning M+ ions in the zero E field can be extracted from the results of Lundin et al. (2013), who used a 3D Monte Carlo code for studying transport of sputtered neutral Ti atoms in Ar gas. From their published velocity distributions of Ti, it is found that about 9% of the sputtered Ti has a velocity directed

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Figure 7.11 A sketch of back-attraction of ionized sputtered species due to a finite E field extending into the plasma and directed toward the target (−Ez ), which is here displayed as a potential drop (E = −∇V ). The figure is inspired by measurements using an emissive probe in dcMS with Ti target by Bradley et al. (2001).

toward the target (−vz ) at a typical working gas pressure of 0.4 Pa when sampling a small volume above the target race track at z = 1 cm. However, Van Aeken et al. (2008) noted a considerable redeposition on a circular planar magnetron target when simulating sputtering of Al at an Ar working gas pressure of 0.3 Pa, that is, when using a lighter target material compared to the process gas. Rossnagel (1988) also reported a similar trend with higher redeposition when using lighter target materials by experimentally trying to estimate the probability of redeposition on the target using either Al or Cu in an Ar atmosphere. For typical working gas pressures around 0.7 – 1.0 Pa, he found that about 5 – 10% of the sputtered neutrals were redeposited. Based on these results, we might think that return of sputtered material to the target is of limited importance. However, as already discussed in Section 3.3.2, there is usually a nonzero (timeaveraged) E field extending into the plasma and directed toward the target, as seen in Fig. 7.11. This finite E field is a key to understanding the high return probability βt of M+ ions to the target, which is crucial when describing the deposition rate loss (discussed in Section 7.5.1) and when modeling the HiPIMS discharge by the material pathway and the ionization region models (discussed in Section 5.2.1), and a key to Ohmic heating (discussed in Section 7.2.3). Consider the following: Each M+ ion has, at the time and place of ionization, the same initial velocity ui0 as the neutral had (we distinguish here between individual particle velocities u and flow velocities v). After ionization and until the next collision, the ions follow ballistic orbits where the particle acceleration dui /dt (i.e. not ui0 ) is determined by the local electric fields E. Notice that a fluid description cannot accurately describe such a motion. However, a few observations can be made. First, let us consider the consequence of a potential uphill in the z direction as seen in the time-averaged measurements. The collided, thermal, part of the M+ ion distribution is expected to return to the target already at potentials of a few volts, as seen in Fig. 7.11. Uncollided M+ ions, on the other hand, start with ui0 directed away from the target and with the energy distribution of sputtered

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material given by Eq. (1.28) (Section 1.1.8). Their point of ionization is furthermore determined by their velocity: those with low initial velocity uz spend more time close to the target and are therefore on average ionized closer to the target. These slow ions have both a lower directed kinetic energy in the +z-direction and a larger average potential hill qi U to climb, which creates a high-energy-pass filtering effect. The average point of ionization also depends on time during the pulse: as the discharge current peaks, the plasma density is higher, and ionization occurs closer to the target as the mean free path for electron impact ionization changes from several centimeters to a very small value. As an example, we consider the situation depicted in Fig. 7.11. Take a sputtered atom and let it be ionized 20 mm from the target (left vertical dashed line in the figure). If it has a directed kinetic energy of 5 eV in the +z (axial) direction, gained in the sputtering process, it will be drawn back after less than 10 mm of further flight due to the potential hill (right vertical dashed line). Only atoms that are ionized beyond 40 mm have a chance to escape. Most ions are created in the ionization region next to the target with a potential slope of VIR = 50 – 100 V (Rauch et al., 2012) (see also Section 3.3.2). This is sufficient to draw most of these ions back to the target, and the back-attraction probability is typically found to be in the range 0.8 ≤ βt ≤ 1 (Huo et al., 2013), which is considerably higher than the ∼10% we found earlier for zero E field. We will return to this topic in Section 7.5.1 when discussing loss of deposition rate in HiPIMS. If we instead look at the working gas ion dynamics in a finite E field, where we consider only the component Ez , then we can identify two simple extreme cases. In the collision-free extreme the G+ ions move in ballistic orbits and will end up on the target if, at their point of ionization, their kinetic energy in the +z direction (away from the target) is lower than the remaining potential hill qi U they have to climb in the +z-direction. In the collision-dominated case the electric mobility drift uz = μi Ez is added to (and directed against) the outward flow speeds from the diffusion and the rarefaction flows treated earlier. The G+ ions will move toward the target if they become ionized in a region where this total drift has a negative sign. Revel et al. (2018) have carried out detailed PIC/MCC simulations on the working gas Ar+ ion dynamics, which reveal two different ion groups coexisting during the HiPIMS pulse. The first population is composed of ions created at the boundary between the cathode sheath and the ionization region (see also Section 5.2.3.4), of which a fraction is accelerated toward the target with a high-energy tail corresponding to the potential drop in the cathode sheath only. The second population contains ions created in the ionization region volume. A fraction of these ions are accelerated toward the target by the combined potential drops in the ionization region and in the cathode sheath. In summary, the ion transport speeds can generally be expected to be very complicated functions of both the local parameters and the time histories of the individual particles. In any case, it is important to emphasize that ions reaching the cathode or the substrate are far from a monokinetic flux of particles. Even if the electric potential profile U (r, t) were known, calculations of the ion transport velocity would require PIC simulations or at least Monte Carlo simulations for longer pulses. As an example, Fig. 5.14 shows the 2D maps of the electric field and the plasma potential in front of the target (Revel et al., 2018).

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7.3.1.2

Classical electron transport

We now turn to the electron motion, starting from the simplest case, the transport along the magnetic field B. The magnetic-field-aligned component ve of the electron drift speed ve is not determined by the local plasma parameters. The reason is that electrons, with their light mass, easily respond by motions along B which minimize departures from the equilibrium state in which the pressure gradient is balanced by the electric volume force ∇pe = ene E .

(7.13)

If there is a loss (or gain) of charge in one part of a flux tube, then electrons are redistributed along it and modify the electric field (through Poisson’s equation) so that Eq. (7.13) is maintained. The component ve is therefore driven by the global cross-B current pattern, which gives the loss (or gain) of charges on different parts of the magnetic field line that drives the redistribution. The collisional parallel resistivity can generally be neglected in this process. In a homogeneous plasma, ∇pe = 0, giving E = 0, and the magnetic field lines are equipotentials. However, in the dynamic and inhomogeneous HiPIMS pulses the full expression given by Eq. (7.13) might be needed, particularly in the region penetrated by high-energy secondary electrons accelerated across the sheath. More interestingly from a magnetron sputtering (HiPIMS) discharge point of view is the component of the electron transport across B, which is in the z-direction above the race track, since this component both carries the discharge current and contributes to Ohmic heating. The cross-B part of ve is split up into two parts depending on the direction with respect to the net cross-B force Fe⊥ = (−∇pe − ene E)⊥ .

(7.14)

Let us consider a circular planar magnetron with azimuthal symmetry, where Fe⊥ lies in the (r, z) plane. In the Fe⊥ × B direction, there is an azimuthal drift speed veφ =

Fe⊥ ωe2 τc2 , ene B 1 + ωe2 τc2

(7.15)

where τc is the classical collision time due to electron–ion (Coulomb) and electron– neutral collisions, and ωe is the electron cyclotron angular frequency (given by Eq. (1.31)). The dimensionless cross-B transport parameter ωe τc is often referred to as the Hall parameter. The Hall parameter is common for electric conductivity, electron diffusion, diamagnetic drift, electron mobility, and the magnetic field diffusion into a plasma (Brenning et al., 2009). In the collision free limit (ωe τc → ∞) the sum of the Hall drift, Eq. (1.33), and the diamagnetic drift, Eq. (1.34), are recovered from Eqs. (7.14) and (7.15). Since the ions are unmagnetized, they have no corresponding drift motion, and the electron drift gives the azimuthal current density Je,φ = −ene veφ .

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In the direction along Fe⊥ the electron drift component is given by ve (r, z) =

Fe⊥ ωe τc . ene B 1 + ωe2 τc2

(7.16)

This is the drift component that carries the discharge current and contributes to Ohmic heating. An important relation, first proposed by Rossnagel and Kaufman (1987a), can be derived for the case where the pressure term in Fe⊥ is negligible. In that case the currents (i.e. the electron drifts in the ion rest frame) across B are given by the classical Hall and Pedersen conductivities, which can be obtained from the generalized Ohm’s law as functions of the Hall parameter ωe τc . In the plasma bulk the electrons have to move across the magnetic field lines to arrive at a magnetic field line that is in contact with the anode. The electric-field-driven part of the cross-B discharge current density and the electric field are related through the generalized Ohm’s law (Chen, 2016), which in this case gives  −1 JD⊥ ω e τc ene = JD⊥ , E⊥ = σP B 1 + (ωe τc )2

(7.17)

where σP is the Pedersen conductivity. In the parts of the plasma where the current is carried mainly by electrons, we can write (Lundin et al., 2008b) ω2 τ 2

ene e c Je,φ E⊥ σH E⊥ B 1+(ωe τc )2 = = = ω e τc , ωe τc e JD⊥ E⊥ σP E⊥ en B 1+(ω τ )2

(7.18)

e c

where Je,φ is the azimuthal current density, JD⊥ is the discharge current density, and σH is the Hall conductivity. Thus the Hall parameter can be obtained from a measurement of the current density ratio Je,φ /JD⊥ . An important consequence of the interaction between electrons, ions, and neutrals is the constant transfer of momentum (or energy). A somewhat simplified picture is that “friction” arises when groups of different species drift with respect to each other. The strength of the friction is quantified by the resistivity tensor η. The cross-B component of the tensor can be expressed using the Hall parameter as η⊥ =

me B = , 2 τc e ne ωe τc ene

(7.19)

where the last step is made using the electron angular gyro frequency ωe = eB/me . We can therefore sum up the results so far by concluding that a low current ratio Je,φ /JD⊥ corresponds to a low Hall parameter ωe τc and a high cross-B resistivity (Eq. (7.19)), and has a high momentum transfer between electrons and ions. Counter-intuitively, a higher cross-B resistivity η⊥ increases the Pedersen conductivity, making it easier to transport electrons across B in the direction of an applied electric fields (Chen, 2016).

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7.3.2 Anomalous transport1 7.3.2.1

Anomalous electron transport

Classical theory of diffusion and electrical conductivity, where collisions move electrons across the magnetic field lines, results in values of cross-B diffusion and mobility that scale as B−2 . Electrons do not always follow this classical picture, but instead work out new ways of diffusing in the plasma. Several plasma experiments on diffusion during the first half of the 20th century were not able to confirm the B−2 dependence expected from classical theory of collisions. Notable is the helium plasma experiment by Hoh and Lehnert (1960), who investigated the cross-B diffusion of electrons when varying the magnetic field strength. They found that the experiments followed the expected classical diffusion closely up to a critical point in the magnetic field strength when suddenly the cross-B diffusion started to depart from the classical prediction with further increasing magnetic field. Soon the first theories of this anomalous transport were presented by Kadomtsev and Nedospasov (1960), who had discovered that a plasma instability developed at high magnetic field strengths. The presence of plasma instabilities in HiPIMS will be dealt with in some detail in the present section, but first we need to look into the widely accepted Bohm diffusion, commonly seen in many magnetron sputtering experiments (Rossnagel and Kaufman, 1987a,b, Bradley, 1998), where the measured cross-B diffusion of plasmas scales as B−1 leading to a faster than classical transport of charged particles. This more rapid or anomalous loss of plasma across magnetic field lines is caused by microinstabilities and is referred to as Bohm diffusion. It was first discovered by Bohm et al. (1949), who suggested the semiempirical formula (Chen, 2016, Section 5.10) DB =

1 k B Te . 16 eB

(7.20)

Bohm diffusion can be formally ascribed to anomalous collisions with an effective collision time τeff . The empirically found constant 16 in Eq. (7.20) is, in this description, the anomalous Hall parameter (ωe τeff )Bohm = 16. This approach has been generalized to include conductivity, mobility, and magnetic field diffusion (Rossnagel and Kaufman, 1987a, Lundin et al., 2008a, Brenning et al., 2009), wherein the relation given by Eq. (7.18) has been shown to apply also for pressure driven (i.e. diamagnetic) currents. Thus, a determination of the ratio Je,φ /JD⊥ , where Je,φ is the azimuthal current density, and JD⊥ is the discharge current density, gives a direct measure of ωe τeff , and thereby all the transport parameters needed for fluid modeling: μ⊥ , η⊥ , σH , σP , D⊥ , and the magnetic field diffusion constant. For definitions and relations to ωe τeff of these parameters, see Brenning et al. (2009). The azimuthal drift currents in dcMS have been measured for a range of discharge parameters. For a dcMS discharge, the values of the Hall parameter were found close to the Bohm value, that is, (ωe τeff )Bohm = 16 within a factor 2 (Rossnagel and Kaufman, 1987a, Bradley et al., 2001). The drift current for any given discharge was found 1 We will here not restrict ourselves only to collisions, since we will see in the next section that we can

transfer momentum in a plasma instability.

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Figure 7.12 Measured values of Je,φ /JD⊥ ≈ ωe τeff above the race track at 30, 60, 85, 100, and 130 µs into the pulse versus the distance from the cathode surface. The curve marked (A) shows the average of the experimental data. For reference, two values of classical Je,φ /JD⊥ are also given: classical electron– neutral collisions (B) and combined electron–neutral and Coulomb collisions (C), as well as the Bohmvalue Je,φ /JD⊥ = 16 (dashed). The Bohm region 8 < Je,φ /JD⊥ < 30 and the faster-than-Bohm region (super-Bohm) 1.5 < Je,φ /JD⊥ < 5.5 appear as shaded areas. Reprinted from Lundin et al. (2011). ©IOP Publishing. Reproduced with permission. All rights reserved.

to vary roughly linearly with the discharge current. None or only a weak dependence on the gas species or the cathode target material was observed in the dcMS case (Rossnagel and Kaufman, 1987a). Surprisingly, it turns out that electron cross-B transport in the HiPIMS discharge is much faster than classically predicted through collisions and also faster than Bohm diffusion given by Eq. (7.20). We will further also see that ωe τeff changes with distance from the target z in the HiPIMS discharge. Brenning et al. (2009) show that the diffusion coefficient is roughly a factor of 5 greater than predicted by the Bohm diffusion, and the empirically found parameter is now in the range 1.5 < Je,φ /JD⊥ < 5.5. Early measurements by Bohlmark et al. (2004) indicated that the ratio between the azimuthal current density Je,φ and the discharge current JD⊥ in that HiPIMS discharge was Je,φ /JD⊥ ∼ 2. More recently the spatial and temporal variation of the internal current densities Je,φ and JD⊥ (z) have been measured by a Rogowski coil (Lundin et al., 2011). These measurements indicate a variation of the transport parameter Je,φ /JD⊥ over time and space. The low values of Je,φ /JD⊥ ≈ 2 are observed at distances 7 – 8 cm from the target surface. Closer to the target, Je,φ /JD⊥ increases with decreasing distance approaching the values expected for Bohm diffusion. There are small variations in Je,φ /JD⊥ with time; however, the values stay within a factor of two from the average value. These results are shown in Fig. 7.12, which shows Je,φ /JD⊥ above the race track at 30, 60, 85, 100, and 130 µs from the pulse initiation (pulse length 200 µs). The low value of Je,φ /JD⊥ observed for a HiPIMS discharge indicates a much more efficient electron transport across the magnetic field lines than for a conventional dcMS, which can be formally described as being the result of increased cross-B resistivity η⊥ and thereby increased cross-B conductivity in the direction of E and increased diffusion of electrons. However, as will be discussed in Section 7.4, it is

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now known that spokes, azimuthally limited electron current channels with enhanced ionization, are involved and complicate this picture.

7.3.2.2

Anomalous ion transport

The high-energy tails observed in the IEDF from the HiPIMS discharge, with measured energies sometimes exceeding 100 eV (see Fig. 4.7), are a desirable feature for film growth, but the acceleration of these ions is at present not entirely understood, and any model for ion transport that does not include this feature must be regarded as incomplete. Lundin et al. (2008b) argued that this ion energization is associated with the anomalous resistivity effect that gives the efficient cross-B electron transport. This claim was supported by Lundin et al. (2008b) by experimental data, where a mass spectrometer showed a much more pronounced high-energy tail in the IEDF in the expected azimuthal direction, as seen in Fig. 7.13, which is indicated as position S1 in Fig. 7.14. The proposed mechanism is also shown in Fig. 7.14 and is based on results from PIC simulations of the wave structure in the modified two-stream instability (MTSI) (Hurtig, 2004, Hurtig et al., 2005). The instability, when driven by an azimuthal current Je,φ , sets up a wave structure with the wave vector kφ , in which the wave electric field Ew and the density perturbations (δne = δni due to quasineutrality) are correlated in such a fashion that there is a net azimuthal force Fei = ± ene Ew  between ions and electrons. The force is directed along Je,φ and gives an anomalous resistivity effect. However, besides the action on the electrons that facilitates the radial transport, there must be an equal and opposite reaction on the ions, that is, a net average drag in the direction of the electron Hall drift, i.e., against the direction of Je,φ . The MTSI is driven by the relative drifts between electrons ve and ions vi in the plasma, that is, vrel = vi − ve , in the presence of a magnetic field component perpendicular to this relative drift. The MTSI can give rise to acceleration of the charged plasma species and thus give a net transport of electrons across the magnetic field lines. This is the case for the circulating azimuthal current in the magnetic field trap of a magnetron sputtering discharge above the target in a HiPIMS discharge (Bohlmark et al., 2004). Because the ion gyro radii in magnetron sputtering discharges are typically larger than the spatial dimension of the plasma, only the electrons are magnetized and take part in this azimuthal drift. Lundin et al. (2008a) estimated the individual contributions of the various drift terms on the total azimuthal current. They found that the Hall drift (Eq. (1.33)) and the diamagnetic drift (Eq. (1.34)) are oriented in the same direction and combine to an azimuthal drift speed exceeding the MTSI threshold. This approach was further developed by Poolcharuansin et al. (2012), who added a drag force term, accounting for the azimuthal anomalous-resistive drag force, to the ion equation of motion, which was solved numerically. It was shown that a fraction of the circulating ion flux, which does not suffer from collisions, can then overcome a radial electric field and leave the discharge volume in the tangential direction. The results obtained for elevated pressures indicate that the sideway transport of ions is increasingly influenced by scattering of ions out of the discharge volume. Previous investigations of the MTSI have shown that the result will be large oscillations in the electric field, which are often correlated with oscillations in the plasma

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Figure 7.13 A comparison between IEDFs of Ti+ ions originating from (mainly) two opposite sides of the target race track and recorded at positions S1 and S2, as indicated in Fig. 7.14. The measurements were carried out at an Ar working gas pressure of 0.80 Pa and z = 0.01 m using 500 V discharge pulses resulting in a peak current density of 5.9 A/cm2 . Reprinted from Lundin et al. (2008b). ©IOP Publishing. Reproduced with permission. All rights reserved.

Figure 7.14 Azimuthal ion acceleration and the mechanism proposed by Lundin et al. (2008b). The dashed arrows show the deflection of ions sideways toward a mass spectrometer placed at either position S1 or S2. Fiφ is the ion force, vi is the ion velocity, and n symbolizes the neutral background gas. Ew is the oscillating electric wave field (oscillations are indicated by gray and white stripes) found in the anomalous transport, and L is the length scale, which is approximately 0.05 m. Reprinted from Lundin et al. (2008b). ©IOP Publishing. Reproduced with permission. All rights reserved.

density, resulting in a net transport of electrons perpendicular to both Je,φ and B, whereas the ions are too heavy to follow this motion (Hurtig, 2004). Measurements and simulations that indicate oscillating electric fields in the MHz range in magnetron sputtering devices (Bultinck et al., 2010, Lundin et al., 2008a) are also consistent with the MTSI as discussed previously. Lundin et al. (2008a) applied electric field probe arrays to explore oscillating electric fields in the megahertz range in a HiPIMS discharge. They demonstrated that the frequency dependence on the ion mass and the magnetic field strength correspond to lower hybrid oscillations when the fraction of the ions of the sputtered material is roughly 80% of the total ion density. Winter et al. (2013) also report on oscillations at around 2.4 MHz detected by a Langmuir probe biased into the ion saturation regime and connect this phenomenon to electron beams ejected from the cathode target radially. In agreement with Lundin et al. (2008a), they relate these oscillations to MTSI. These findings are also in line with the

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numerical time-dependent results by Pseudo-3D PIC/MCC simulation (Revel et al., 2016), which underline the presence of electron instabilities at high frequency (MHz range). Besides the MTSI, also other frequency ranges and instabilities have been observed. Oscillations or instabilities have been observed in dcMS discharges (Martines et al., 2001, 2004) and in HiPIMS discharges (Kouznetsov et al., 1999, DeKoven et al., 2003, Winter et al., 2013) and sometimes are put in the context of fast electron transport (Martines et al., 2004, Sheridan and Goree, 1989). A recent example is the work by Tsikata and Minea (2015), who report on a MHz, mm-scale instability in a HiPIMS discharge identified as the electron cyclotron drift instability (ECDI). The ECDI has some similarities to the previously described MTSI in that it is driven by the difference in electron and ion velocities and also plays a role in enhancing electron current. However, this drift instability is believed to be of smaller scale compared to the larger wavelength MTSI (∼ cm). It is worth noting that reports of MTSI and ECDI in HiPIMS discharges also report on oscillations in the kHz range (Lundin et al., 2008a, Tsikata and Minea, 2015) consistent with observations of larger scale rotating dense plasma structures, spokes, which is the topic of the following section.

7.4

Plasma Instabilities

Plasmas are practically never uniform and steady. They are sustained by adding energy to an open system, which then inherently tends to develop nonuniformities and selforganized patterns. Self-organization implies the evolution of the plasma into more or less ordered structures, which can be dynamic, periodic, or chaotic. Self-organized patterns in the form of the striations of the positive column were observed already in the early investigations of direct current (dc) discharges (de la Rue and Müller, 1878). Since then, plasma structures have been observed in many different discharge configurations (Hayashi et al., 1999). The development of structures and patterns in plasma discharges is generally associated with a feedback mechanism (e.g. stream interaction, wave coupling, etc.). In an active discharge, neighboring charged particles are coupled via the Coulomb force affecting their position and motion. The motion of charged particles, in turn, will change their distances and strengths of coupling. A charged particle in a plasma interacts with many neighboring particles at the same time, causing the ensemble of charged particles to exhibit a common collective behavior. This collective behavior of charged particles is a general plasma phenomenon. A variation of the plasma density, for example, will propagate via the collective coupling. The feedback forces turn a density variation into an oscillation; a propagating oscillation is called a wave. When energy is supplied by a current driven by an applied voltage, a positive (amplifying) feedback can cause the wave amplitude to grow until large macroscopic variations or patterns appear: the wave becomes an instability. The instability is characterized by strong variations of the local plasma quantities including particle density, particle temperature, potential, and pressure. This section focuses on instabilities observed in magnetron sputtering discharges and in particular HiPIMS discharges, since

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instabilities can have a profound effect on particle transport, especially across magnetic field lines, already touched upon in Section 7.3. Magnetron sputtering discharges belong to the group of E × B discharges. The most investigated such devices are Hall thrusters studied for electric propulsion of spacecraft since the 1960s (Janes and Lowder, 1966, Mazouffre, 2016, Boeuf, 2017). In Hall thrusters, instabilities in the form of moving regions of enhanced ionization are generally referred to as spokes (McDonald and Gallimore, 2011, Ellison et al., 2012, Boeuf, 2017). This nomenclature has been adopted by the HiPIMS community and will be used in the following discussion.

7.4.1 Spokes and breathing instabilities in magnetron sputtering discharges Early observations of electrostatic fluctuations in dcMS discharges operated at nominal power densities in the range 0.5 – 6 W/cm2 lead to the discovery of plasma patterns or coherent modes corresponding to waves propagating in the direction of the electron diamagnetic drift (Martines et al., 2001, 2004). Martines et al. (2001, 2004) found that the presence of waves or modes is influenced by the discharge power and by the neutral working gas pressure. By increasing the neutral working gas pressure to several Pa a progressive transition toward a turbulent state was observed, expressed by nonregular amplitude modulation similar to the behavior of coupled oscillators. Such modes have been interpreted as electron drift waves destabilized by the combined effect of density gradient and electric field. Exploring HiPIMS discharges, using fast cameras, Ehiasarian (2008) showed images of HiPIMS plasmas as early as 2008 with nonuniform light emission, which suggested the presence of instabilities in HiPIMS discharges. Confirmation came in 2011 – 12 from three different laboratories, all using fast imaging techniques, which also allowed researchers to quantify properties of “ionization zones” or “spokes” in terms of their number, velocity, and propagation direction (Kozyrev et al., 2011, Anders, 2012, Ehiasarian et al., 2012). Commonly spokes are observed by probes or by fast ICCD cameras. Time-resolved imaging and probe techniques are the main diagnostic techniques to study spokes (Hecimovic and von Keudell, 2018). Typically, two types of spoke shapes are found when HiPIMS discharges are operated in noble gases, as illustrated in Fig. 7.15. On one hand, it is diffuse as observed for Ti and Nb targets, and on the other hand, it is triangular as observed for Al, Cu, Mo, Cr targets (Hecimovic et al., 2014). A more recent study of a discharge with Ti target suggests, however, that the appearance of various spoke shapes depends on the discharge current density, working gas pressure and magnetic field strength rather than the target material (Hnilica et al., 2018). The addition of a reactive gas leads to compound formation on the target surface (poisoned surface) with profound consequences for many parameters of the magnetron sputtering discharge such as the secondary electron emission yield and the plasma composition near the target. Consequently, the fluxes of atoms and ions leaving the target toward a substrate are also changed, together with film composition, microstructure, and deposition rate, as discussed in Chapter 6. Investigation of several target/reactive gas combinations showed that in

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Figure 7.15 Spoke appearance in a HiPIMS discharge at Ar working gas pressure of 0.2 Pa. The pulse power density varied from 1 kW/cm2 (Mo, Cr, Cu) to 45 kW/cm2 (Al and Ti). From Hecimovic et al. (2014). ©IOP Publishing. Reproduced with permission. All rights reserved.

the poisoned mode, the spoke shape becomes more diffuse (Hecimovic et al., 2017b), that is, similar to the Ar/Ti and Ar/Nb discharges shown in Fig. 7.15. For the conditions of these experiments, the discharge voltage decreased, which can be correlated with an increase in the secondary electron emission (Depla and Mahieu, 2008, Marcak et al., 2015). Note that spokes occur on all kinds of magnetron targets, including rectangular or linear magnetron targets, where the race track has not only curved but also straight sections (Preissing, 2016, Anders and Yang, 2017, 2018). In addition to plasma instabilities that propagate along the race track (i.e. spokes), the plasma may also exhibit other instabilities. In particular, the plasma can oscillate in a direction normal to the target surface, which has been termed “breathing instability” (Yang et al., 2016) in analogy to a similar phenomenon in Hall thrusters (Young et al., 2015). Spokes and the breathing instability usually superimpose, which is shown in Fig. 7.16 (Yang et al., 2016). However, it should be mentioned that the breathing instability in Hall thrusters is linked to almost complete ionization of the neutral gas, whereas in the HiPIMS discharge, the neutral species are continuously injected in the ionization region via working gas and metal recycling (discussed in Section 7.2.1.1), and therefore strongly depends on the working gas pressure and the target material.

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Figure 7.16 Floating potential characteristic period contour for Au target (76 mm diameter) at Ar pressures from 0.13 Pa to 2.7 Pa and current from 10 mA to 300 A. Modes are indicated as regions separated by white dashed lines. Reprinted from Yang et al. (2016), with the permission of AIP Publishing.

For some target materials, especially for those with high self-sputter yield, the spoke patterns disappear when the applied power density is above 5 kW/cm2 , as indicated for the highest discharge currents in Fig. 7.16. Then the plasma emission becomes homogeneous along the race track, as shown, for example, for chromium in Fig. 7.17 (Hecimovic et al., 2016) and also for copper (Yang et al., 2015). Such transition can be clearly observed during current rise (Fig. 7.17C) within a single HiPIMS pulse. The triangular spoke shape (seen in Fig. 7.17A, left) is present at low discharge current, and its presence is related to an oscillating plasma potential (Fig. 7.17B shows the recorded floating potential). After increase of the power density above a threshold, the plasma becomes homogeneous (seen in Fig. 7.17A, right) and the floating potential value becomes constant in time, as seen in Fig. 7.17B. For high power, the system exhibits high impedance associated with a high rate of collisions within the discharge, and we can deduce that the collision rate is high enough to eliminate the need of instabilities for charged particle transport. When entering the spoke free regime, we can observe an increased ion flux toward the substrate (de los Arcos et al., 2013, 2014, Andersson and Anders, 2009). So far, the transition to a spoke-free mode has only been observed for a limited number of target/gas combinations (in Ar gas: Cr, Au, Cu, Al, Ta, Mo; in Kr gas: Al; and in gasless environment: Cu) although further combinations may be discovered in the future. The transition to spoke-free plasma in reactive HiPIMS discharges has so far not been observed for any target/gas combinations. The velocity of a spoke along the race track exhibits a dependence on power density, working gas pressure, and target material. Below 25 W/cm2 , spokes move in the retrograde direction (i.e. opposite to the general E × B direction) with a velocity

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Figure 7.17 (A) ICCD images showing the transition from a spoke mode (left image) to a spoke-free mode (right image). (B) Floating potential oscillations corresponding to the images above. (C) Discharge current waveform. The transition to an azimuthally uniform plasma occurs when the nominal power density exceeds 5 kW/cm2 for Cr HiPIMS. Reprinted from Hecimovic et al. (2016). ©IOP Publishing. Reproduced with permission. All rights reserved.

approximately proportional to the power density. They reach, as shown in Fig. 7.18, values of order 103 m/s. Comparison of the spoke velocity for three different target materials (Al, Cr, Ti) shows that, for a given power density, the velocity is independent of the target material and determined by the background working gas, which is not surprising given that the plasma is primarily composed of background working gas. This changes when the power density exceeds about 25 W/cm2 : the spoke velocity becomes dependent on the target material. We could argue that the observed threshold itself is related to the power density needed to change the plasma composition from being dominated by the working gas to become target material dominated. The spoke velocity and even the direction changes with power. At high power, spokes propagate in the E × B direction and can reach velocities up to one order of magnitude faster than in dcMS mode, that is, ∼ 104 m/s. The number of spokes also changes with HiPIMS plasma parameters. Under some conditions of working gas pressure and power, spokes appear well defined: we can observe a specific small number of spokes, which often are more or less regularly spaced from each other. The most regular appearance can be found in dcMS discharges, where we can set discharge conditions such as, for example, to have exactly 1, 2, or 3 spokes. This regularity has been exploited to determine the potential structure of spokes using probes (Panjan and Anders, 2017) (see Section 7.4.2). At higher power, like in HiPIMS operations, the situation is more complicated. Under many conditions, at any given moment, we can usually observe a discrete and finite number of spokes; however, the spokes are not of the same intensity (brightness, plasma density, etc. (Yang et al., 2015)). Even under nominally the same discharge conditions, the number of

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Figure 7.18 Spoke angular velocity for Al, Cr and Ti targets as a function of discharge current at an Ar working gas pressure of 0.5 Pa. The half-filled symbols at the very left stand for spoke velocity for alternating mode at lowest discharge currents. Negative velocities represent retrograde E × B motion. From Hecimovic et al. (2016). ©IOP Publishing. Reproduced with permission. All rights reserved.

spokes can vary. In some cases, an assignment of a distinct number of spokes is not even possible as these regions of enhanced ionization and excitation amplify and decay, and their intensity varies on a more gradual scale. Furthermore, using optical and probe techniques, we can observe spoke splitting (Anders and Yang, 2018) and spoke merging (Hecimovic et al., 2015, Klein et al., 2017). Merging and splitting of spokes can readily be observed in Fig. 7.19. This figure was recorded using a streak camera by aligning the entrance slit of the camera with a linear section of the race track (Anders and Yang, 2017). Also here, the local character of spokes indicates a local character of electron energization, which can be associated with the local structure of the spoke plasma potential, as discussed in Section 7.4.3. The use of bandpass interference filters allows looking at spokes in the light of selected spectral lines associated with plasma species of interest such as ions or neutrals of the working gas or target ions or neutrals. A direct way to analyze the spokes evolution was performed by following the spatial distribution of light emission from the different species in the spoke by using interference bandpass filters in front of an ICCD camera. The results from such an investigation are shown in Fig. 7.20. This technique is even more powerful when using four ICCD cameras, each with a different bandpass filter, triggered simultaneously because one can record the emission from ionic species, both working gas ion species (Ar+ ) and sputtered metal ion species (Al+ ), and show that the atomic species are completely depleted in the spoke. This emphasizes the understanding that a spoke is an ionization zone (Anders et al., 2012b, Hecimovic, 2016) in agreement with the modeling results dis-

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Figure 7.19 Spokes in a HiPIMS discharge with an applied voltage of 547 V (leading to a 900 A peak in the discharge current at the end of the pulse), with a 240 × 120 mm2 Al target in 0.4 Pa Ar with 16 mPa N2 added. We see an example of spoke splitting at about 8 µs into the image. The horizontal brightness modulations correlate with oscillations of discharge current, which often occur near the end of each pulse. Reprinted from Anders and Yang (2017), with the permission of AIP Publishing.

cussed at the end of this section. Also, spectral filters offer to study optical emission from different energy levels. This approach provides an opportunity to learn something about the excitation conditions, that is, about localized electron heating and the presence of energetic electrons. Light emission from increasingly higher energy levels, especially from ions, is concentrated in ionization zones: the higher the energy level from which the optical transition originates, the more spatially localized the optical emission (see Fig. 7.20). This indicates that, in the presence of spokes, the heating or energization of electrons responsible for the excitation and ionization is localized, as opposed to being evenly distributed (Anders, 2014, Hecimovic et al., 2017a). Since the spokes move, the location of the most intense electron heating is moving. The spokes have also been modeled using the Pseudo-3D PIC/MCC simulation approach introduced in Section 5.1.4.2 (Revel et al., 2016). The model shows that the number of spokes increases with increased discharge current for relatively low power density (< 100 W/cm2 ). In addition, the model gives access to the microscopic events occurring in the plasma including the electron motion, as shown in Fig. 7.21. The spoke ionization zone appears to be confined close to the target at the border between the sheath and the IR (z < 1.5 mm), as can be seen in Fig. 7.21C, consistent with OES measurements by Andersson et al. (2013). Moreover, the Pseudo-3D PIC/MCC approach can also reproduce plasma flares that travel in the axial direction (Ni et al., 2012), as shown in Fig. 7.21A (Revel et al., 2016) which is addressed in Section 7.4.3.2.

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Figure 7.20 Spatial distribution of light-emission from different species. The shape of a spoke is determined by the light that is observed, indicative of local electron heating and locally different excitation of the upper levels of optical transitions (the light intensity is in false colors, with the camera image intensifier optimized for the spectral line observed). Reprinted from Andersson et al. (2013), with the permission of AIP Publishing.

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Figure 7.21 2D projection of the electron density (A) and (B) and ionization (C) maps for the dc operation regime of a planar magnetron sputtering discharge, as simulated by Pseudo-3D PIC/MCC. An illustrative trajectory of a trapped electron is shown by the black line. Note that the electron trajectory is obtained in time whereas 2D maps show instant structures. Input parameters: discharge voltage 600 V, mean secondary electron current 0.1 A, discharge current 1 A, and Ar working gas pressure 0.4 Pa. Reproduced from Revel et al. (2016), with the permission of AIP Publishing.

7.4.2 The potential structure Measurements using electrical probes (e.g. Panjan and Anders (2017)), ion energy analyzers (e.g. Yang et al. (2015)), and spectrally selective imaging (e.g. Andersson et al. (2013)) provide ample evidence that ionization zones (spokes) are locations of locally enhanced potential. Such potential structures can explain the disruption of closed electron drift, formation of plasma flares, and formation of energetic ions, especially considering the differences of ion energies in E × B and −E × B directions (Yang et al., 2015). Each spoke represents a potential hump relative to its surroundings. Each is enclosed by an electric double layer, creating a local electric field (denoted Es ) that affects the local direction of electron drift and can give rise to local acceleration of ions. Electrons arriving at a spoke, enter the potential hump, reach a region of higher potential, and are thus energized, enabling them to cause localized excitation and ionization, as illustrated in Fig. 7.20. In that sense, images of spokes are approximate images of the potential distribution (Anders, 2014). For potential measurements, it is highly desirable to utilize conditions that are regular and reproducible. Such conditions have been found at certain power and pressure conditions in dcMS. Using closely spaced cold and hot emissive probes (see Section 3.1.2) has allowed researchers to derive the potential distribution, the local electric fields, and the energy gain of electrons.

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Figure 7.22 Plasma potential (color) and electric field (vector) distributions in the azimuthal-radial (ξ − r) plane for different axial (z) distances from the target surface (z from 2.5 mm to 40 mm). In the right bottom corner: a corresponding fast-camera image of the spoke, correlating the potential distribution to the image as seen in visible light (the light intensity is in false color for better presentation). Reprinted from Panjan and Anders (2017), with the permission of AIP Publishing.

The potential difference between the spoke and its surroundings can reach 70 V, and therefore the energy gain was found to be far in excess of the ionization energies (Panjan and Anders, 2017). Fig. 7.22 illustrates this point. The plasma potential distribution, as recorded by the floating potential of an emitting probe, can be mapped in an elegant way using a stationary probe with exactly one spoke moving along the race track. The spoke passes the probe, and the time dependence of the probe potential can readily be converted to a spatial distribution knowing the position and speed of the spoke. Through axial and radial changes of the probe position, the entire axial (z, distance from target surface), radial (r, distance from target center), and azimuthal (ξ , coordinate along the race track) space is mapped as shown in Fig. 7.22. The measured spoke field was Es = 8 × 103 V/m (Panjan and Anders, 2017), which is slightly below the maximum Es found by Pseudo-3D PIC/MCC modeling (3 × 104 V/m) (Revel et al., 2016), but the discharge used in the experiment was operated in dcMS (lower power), whereas the model results were for a HiPIMS discharge. Modeling provides at least two scenarios to explain the electron movement and their organization in spokes. In the first scenario the electron movement is driven by a combination of at least three drifts, all of the type E×B. In addition to (i) the widely known

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Figure 7.23 A phenomenological depiction of electron motion across spokes based on the Pseudo-3D PIC/MCC simulation results. In (A): the spoke electric field Es is shown with the spoke main azimuthal velocity vs ; v2 is the electron velocity in the azimuthal-axial plane. In (B): v3 is the electron velocity in the azimuthal-radial plane; the trajectory of an isolated electron is shown with a dotted line. The color levels illustrate qualitatively the observation of higher electron densities at the leading edges of the spokes. Input parameters: discharge voltage 600 V, mean secondary electron current of 0.1 A, discharge current of 1 A, and argon working gas pressure of 0.4 Pa. Reproduced from Revel et al. (2016), with the permission of AIP Publishing.

Hall drift v1 = Ez × B /B 2 , (Eq. (1.33)), with Ez being the macroscopic discharge field normal to the target, two other drifts have been identified (Revel et al., 2016): (ii) a drift v2 = Es × B /B 2 involving the locally developed electric field Es due to the spoke itself and the magnetic field component parallel to the target surface, and (iii) a drift v3 = Es × Bz /B2 due to the axial (Bz ) component of the magnetic field, which changes sign when crossing the target surface (the center and edge magnets have opposite polarity). These two latter drifts are represented in Fig. 7.23, where v2 acts in the vertical plane of the race track. It pushes the electrons up and down making them “surf on” the moving spokes because Es always points toward the center of the spoke, whereas B stays unchanged (B = Bx in Fig. 7.23). The third drift v3 does not change sign because both Es and Bz change sign when electrons bounce on each side of the race track (see Fig. 7.23B). In the second modeling scenario, spokes form due to wave coupling (wave coupling model (WCM) introduced in Section 5.1.6.3.2) driven by the Doppler-shifted electron Bernstein (DSEB) wave and the ion sound (IS) wave (Luo et al., 2018). If their respective frequencies are close, then they couple to each other, and the electric field experiences a faster oscillation with the sum frequency (SF) and its amplitude modulated by the difference frequency (DF). Analogous modulations of the electron electric field have been experimentally observed in dcMS and HiPIMS discharges (Tsikata and Minea, 2015), identified as an electron cyclotron drift instability discussed in Section 7.3.2.2. The WCM can explain the spoke split initiated when the local spoke field exceeds the amplitude of the DF wave field, as experimentally recorded by Anders and Yang (2017) (Fig. 7.19). This can explain the lack of coherence observed sometimes in the movement of the spokes. In addition, the WCM predicts the same number

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of spokes as experimentally recorded (Hecimovic, 2016) with increasing pulse discharge current. This model allows a collisionless energy transfer from electrons to ions and thus provides a mechanism for anomalous ion heating (as discussed in Section 7.3.2.2). As the electrons are magnetized, they keep their trajectory close to the race track, whereas the ions are not trapped by the magnetic field. If they gain a tangential velocity component, then they can leave the spoke, as found by Lundin et al. (2008b) (Fig. 7.14). Analogous to this mechanism, the energetic ions could be pushed away, normal to the target, leaving behind only low-energy ions inside the spoke. No azimuthal ion movement has been detected in spokes.

7.4.3 Effect of spokes on charged particle transport The appearance of spokes, as well as other instabilities, is related to the need to close the electrical circuit and provide conditions allowing the electrical current to flow. The magnetron’s E × B configuration is an electron trap. Electrons are confined in a closed drift until they escape through collisions (“classical transport” in Section 7.3.1.2) or via instability-facilitated processes (“anomalous transport” in Section 7.3.2.1). The spoke instability can be seen as a modulation of the high-frequency instabilities discussed in Section 7.3.2. This section summarizes the physics of the cross-B motion of charged particles due to spokes, which has been identified as the third mechanism for electron transport in HiPIMS. Since only electrons are magnetized, we can focus on the issue of how electrons manage to move across the magnetic field line structure.

7.4.3.1

Transport near the target

Using a segmented target, the current densities at the target associated with spokes in a HiPIMS discharge have shown that spokes can be identified as more or less regular perturbations of the local discharge current density with about 25% modulation induced by the traveling spokes. The plasma density at the target between the spokes never decreases to zero (Poolcharuansin et al., 2015, Hecimovic et al., 2017b, Lockwood Estrin et al., 2017). The plasma density within the spokes is of order 1019 m−3 and generally increases approximately linearly with increasing power density (Hecimovic et al., 2017b). Ionized sputtered atoms in the presheath will be accelerated toward the target by the local electric field. Target ions are subplanted (shallow implantation) and thus (re)deposited at the target. Due to the direction of the local electric field and the motion of the spokes, target ions may arrive at the target somewhat displaced relative the location of the origin (Layes et al., 2017a,b). Layes and coworkers investigated the distribution of sputtered material from a small disk embedded in the circular target at the race track position in two configurations, a small Cr disk inserted into an Al target and a small Al disk inserted into a Cr target. The target surface composition was characterized using in vacuo XPS (the target was not exposed to air but analyzed in the same vacuum chamber). The target redeposition of sputtered species was more effective for Cr atoms than for Al atoms at all powers. The region of redeposition of target material was larger than the source region. Deposition did not occur symmetrical

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relative to the source area but somewhat displaced in the E × B direction irrespective of the presence of spokes. When spokes were present, an enhanced transport in the −E × B direction was also observed. This can be explained by the large electric field at the trailing edge of each spoke, affecting the direction of ions after they have been produced.

7.4.3.2

Transport in the bulk plasma

As discussed in Section 7.3.2.1, cross-B transport of electrons is for many systems approximately 5 times greater than Bohm diffusion, an empirical scaling often used to benchmark transport and given by Eq. (7.20). The anomalous cross-B transport in HiPIMS discharges has been correlated to the appearance of spokes. This implies that transport is not just based on diffusion but facilitated by collective processes governed by the local electric fields, which can significantly deviate from the average electric field (e.g. see Fig. 7.22). Our current understanding of spoke dynamics is still incomplete, but it is clear that ions formed in the spoke volume (where a potential hump is observed) are accelerated by the electric field of the double layer surrounding the spoke. This acceleration is displacing ions in all directions (Hecimovic, 2016) and preferentially in the spoke-forward direction (Panjan et al., 2014), suggesting the picture of a propeller acting on ions (Anders et al., 2013). Using a triple probe 15 mm above the target, Lockwood Estrin et al. (2017) determined that each spoke has a dense but relatively “cool” leading edge (ne ∼ 2.0 × 1019 m−3 , Te ∼ 2.1 eV) and a relatively hotter but more rarefied trailing edge (ne ∼ 1 × 1019 m−3 , Te ∼ 3.9 eV). We should keep in mind, though, that the temperature is an expression related to the width of a Maxwellian distribution, whereas there may be hot, non-Maxwellian electrons present that are not well represented by Te . Furthermore, at 15 mm from the target, the potential inside is about 8 V more positive than the potential of the inter-spoke regions, giving rise to an azimuthal electric field of ∼1 kV/m (Lockwood Estrin et al., 2017). Their result is in qualitative agreement with observations made on dcMS discharges (Panjan and Anders, 2017). The reason for the higher electron temperature at the trailing edge can be qualitatively understood keeping in mind that drifting electrons arrive first at the trailing edge, get energized by entering the region of higher potential, keep drifting and produce ion–electron pairs, and thereby loosing energy. This picture also offers a clue why HiPIMS spokes move in the E × B direction. Namely, ions and electrons leave the location of highest plasma density on different time scales: electrons with drift velocity (∼ 105 m/s) and ions much slower, depending on their mass and local electric field. Hence, the location of highest plasma density becomes the location of highest charge imbalance or electric field, which is the trailing edge; the trailing edge shifts to the location of highest ionization. This was qualitatively described in the early spoke reports (Anders et al., 2012b, Anders, 2012) and is now supported by experimental findings. However, much more needs to be done to fully describe spoke formation and displacement processes. Spokes are also the origin of plasma flares, that travel axially out into the plasma volume (Ni et al., 2012, Anders et al., 2012b), which have been illustrated by numerous fast camera images, of both the frame and the streak type (see e.g. Fig. 7.24).

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Figure 7.24 Flares from HiPIMS spokes, operated with an Nb target with argon at 0.27 Pa as the working gas; z is the distance from the target surface. Top: as observed with a fast frame camera, 10 ns exposure time. Bottom: same discharge pulse observed with a streak camera. Reprinted from Anders et al. (2012b), with the permission of AIP Publishing.

Flares have been associated with large changes of local electric field, which can redirect electron drift and produce ionization far from the target. Flares are likely the most effective process disrupting the electron trap of the magnetron E × B configuration. In addition to the observed electric field structures associated with spokes, magnetic fluctuations have also been detected using miniature magnetic pickup-coils (Spagnolo et al., 2016). The magnetic fluctuations are in the frequency range of 100 kHz and correlate well with the electrostatic oscillations detected with probes. Spagnolo et al. (2016) concluded that spokes are not purely electrostatic but of electromagnetic nature, at least when the power level is high and the βkm parameter, the ratio of kinetic to magnetic pressure, reaches a few percent.

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Transport near the substrate

Film growth occurs on the scale of minutes or even hours for thick coatings. Therefore the effects of spokes “smear out” in time and space but are still relevant since particle fluxes and energies change. The most relevant effects of the spokes are in changes induced in the ion energy distribution functions (IEDFs) as measured at the substrate position. In HiPIMS discharges, when the spokes are dominated by sputtered metal or recycled working gas species and the plasma densities in the spoke reach up to 8 × 1019 m−3 (Hecimovic et al., 2017), the IEDF of metal ions comprise a low-energy peak and an additional broad peak at high energies. It is generally assumed that the high-energy ions originate from the potential hump of the spoke, where the ions are accelerated away from the target toward the substrate (Maszl et al., 2014a,b). At high power densities, when metal-dominated spokes are present, an additional peak at energies in the range 15 – 25 eV is observed with the position of the second peak shifting to higher energy when the power density is increased. Additionally, it was found that doubly charged ions have approximately twice the energy of singly charged ions, indicating an electric acceleration mechanism as provided by a potential hump (Panjan et al., 2014, Anders et al., 2013). However, the absolute energy values are somewhat higher than the simple hump argument allows, and future research is needed to clarify and quantify the origin of the energy, for example, by considering the contribution of the breathing instability. An interesting question is what happens to the IEDF when the power density is increased beyond the threshold where the plasma becomes azimuthally homogeneous. Breilmann et al. (2015) determined that the high-energy part of the metal ion IEDF, measured normal to the target, does not change but the low energy peak shifts by several eV to higher energies. Therefore a change of plasma behavior from a spoke mode to the spoke-free mode is not of concern in terms of energy effects on films deposited using the ion flux normal to the target. When looking from the side, however, the situation is different. The low-energy peak is smaller, and the high-energy tail of the distribution is always higher when measured tangentially in the E × B direction than when measuring the flux in the opposite, −E × B direction, as seen in Fig. 7.25 (Panjan et al., 2014, Yang et al., 2015, Franz et al., 2016). Similar results were already shown in Fig. 7.14. The same asymmetry was found under dcMS conditions, suggesting that the same ion acceleration mechanisms may be at work when the discharge is continuously operating, even though the motion of spokes in dcMS is in the −E × B direction. When the HiPIMS power level goes beyond the threshold to an azimuthally homogeneous plasma, the ions going sideways are generally of lower energy, and the pronounced azimuthal asymmetry disappears when ionization zones are absent as seen in Fig. 7.25 (Yang et al., 2015). Estimates of neutral working gas and metal atom flux from the target suggest that a rarefaction of neutrals does not occur, but rather the density of neutrals becomes high enough to enable a collision rate sufficiently high for cross-field transport without the need of instabilities. Measuring sideway IEDFs is one way to determine the presence or absence of spokes (Yang et al., 2015).

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Figure 7.25 Energy distribution functions for argon and copper ions emitted “sideways” from a magnetron sputtering discharge. This experiment was designed to test if the presence of spokes matters for ion acceleration: Spokes are present at 40 A but not at 400 A. Reprinted from Yang et al. (2015), with the permission of AIP Publishing.

7.5

Deposition rate

Before moving on to deposition of thin films by HiPIMS in Chapter 8, we would first like to discuss the much-debated topic of deposition rate. The deposition rate depends on the sputter rate, which was discussed in Section 1.1.7. For dcMS, the deposition rates are practically found to be directly proportional to the power applied to the target (Waits, 1978). The deposition rates are thus determined by the power density, target material, size of the erosion area, target-to-substrate distance, and discharge pressure. In the HiPIMS regime the situation is somewhat more complex due the pulsed nature of the discharge. For example, for certain discharge conditions, the absolute deposition rate can increase almost linearly with increasing (time-averaged) applied power (Ross et al., 2011). However, the applied power can be increased by increasing the amplitude of the voltage and current pulses, but we can equally well maintain the pulse amplitudes and instead increase the pulse frequency (or pulse length), and the resulting deposition rates will not be the same. Samuelsson et al. (2010) compared the deposition rates of various metals (Ti, Cr, Zr, Al, Cu, Ta, Pt, Ag) with pure argon as the working gas for both dcMS and HiPIMS discharges applying the same average power. They observed that the HiPIMS deposition rates are in the range of 30 – 85% of the dcMS deposition rates depending on target material. These results are shown in Fig. 7.26. However, the reduction in the deposition rate was not more pronounced for materials with low sputter yield as had earlier been concluded from measured data (Helmersson et al., 2005). In addition, Konstantinidis et al. (2006a) found that the deposition rate depends on the pulse length

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Figure 7.26 Deposition rates for dcMS and HiPIMS discharges plotted as bars for the different target materials used (left axis). The ratio of the deposition rate of HiPIMS over dcMS deposition rate is shown as a scatter plot (right axis). The average power was kept constant at 125 W for both deposition methods, except in the case of Pt and Ta, where the average power was slightly lower. Reprinted from Samuelsson et al. (2010), with permission from Elsevier.

and increases from 20% to 70% of the dcMS values as the pulse length is decreased from 20 to 5 µs for the same average power of 300 W when sputtering a Ti target with argon as the working gas at 1.33 Pa. Similar trends are also reported by (Leroy et al., 2011) using a rotating cylindrical magnetron, where the deposition rate is found to be up to 75% lower for HiPIMS compared to dcMS when sputtering Ti in Ar at 0.7 Pa, and the decrease in deposition rate becomes more pronounced with increased pulse length (5 – 20 µs were investigated).

7.5.1 Physics of deposition rate loss There have been several suggestions on the cause of the lower deposition rate observed in non-reactive HiPIMS. The most common explanation to the reduction in deposition rate stems from a work by Christie (2005), who argued that back-attraction of the ions of the sputtered material M+ to the target followed by self-sputtering causes a reduction in the amount of sputtered particles reaching the substrate. The idea is as follows. After the sputtering event the target neutrals are transported out into the plasma, where they may undergo an ionizing collision. The probability of an ionizing collision is denoted by αt and depends on the plasma conditions, as discussed in Section 7.2.1.1. In agreement with our discussion on ion transport in Section 7.3.1.1, a fraction of those ions will be close enough to the cathode fall and also have a low enough kinetic energy as to be back-attracted to the target surface, thereby causing a reduction in the amount of sputtered particles reaching the substrate. This means that by using predominantly ions instead of neutrals in the deposition process the electric potential applied to the target and the resulting electrical field Ez (directed toward the target) can reduce the deposition rate significantly if these fields extend outside the cathode sheath and into the dense plasma, where most of the ionization occurs. In Christie-type models (Christie, 2005, Vlˇcek and Burcalová, 2010, Andersson and Anders, 2009) (previously

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discussed in Section 5.1.2) a key variable is the return fraction βt of ionized sputtered target atoms. An electric field Ez in the plasma can turn such ions around, increase βt , and decrease the deposited fraction of ions of the target material M+ . Spatial measurements of the plasma potential in HiPIMS discharges (Sigurjónsson, 2008, Mishra et al., 2010, Rauch et al., 2012, Liebig and Bradley, 2013) have shown that there commonly is a potential uphill, from the cathode sheath edge and reaching far outside the ionization region (several cm), which can vary at least in the range 7 – 100 V, as discussed in Sections 3.3.2 and 7.3.1.1. Stronger Ez and higher potentials VIR across the ionization region are generally observed closer to the target, as well as for stronger magnetic field, for higher applied power, and during the early stage of the HiPIMS pulses (the latter particularly for lower pressure) (Mishra et al., 2010). In Fig. 7.27A, we see one example from Mishra et al. (2010) of how the plasma potential varies with axial distance from the target z when weakening the absolute magnetic field strength |B| at the target by 33%. Profile A corresponds to the weakest |B|, and profile C to the strongest |B|. All the measurements were taken at peak discharge current. Using this data along with a typical energy distribution of sputtered Ti shown in Fig. 7.27B (Lundin et al., 2013) and assuming that ionization of sputtered atoms is distributed with some unknown probability, depending mainly on the plasma density, over the whole range of potential profiles shown in Fig. 7.27A, we can make the following observations (Brenning et al., 2012): Consider ions that are created at a distance of 30 mm from the cathode and for simplicity assume that they have the more or less preserved energy distribution from the sputtering event at the target. From 30 to 90 mm (∼ substrate position), the potential differences in Fig. 7.27A are VA − VA ≈ 1 V, VB − VB ≈ 5 V, and VC − VC ≈ 10 V. With a sputter energy distribution as seen in Fig. 7.27B at z = 30 mm, only a small fraction would be back-attracted in potential profile A (< 10%), about half in B, and the majority in C (∼ 90%). This is consistent with measured variations in deposition rates (Mishra et al., 2010), which for profile A was a factor of 6 higher than for profile C at a typical substrate location (z = 100 mm); see Fig. 7.28. Note also that if the sputtered energy distribution in Fig. 7.27B is taken as typical for HiPIMS, then a high deposition rate is unlikely when the potential drop extending into the plasma is significantly higher than ≈ 10 V; or, conversely expressed, significant escape of ionized sputtered material is quite possible, provided that the potential is well below ≈ 10 V. Therefore, controlling and optimizing the potential profile in the cathode region will greatly affect the number of metal ions incident on the target surface (Poolcharuansin and Bradley, 2010), which so far has not been fully explored. In addition, we note that it is not only the return probability of ionized sputtered species βt that determines the reduction of deposition rate in the described scenario. It is also closely connected to previously discussed discharge modes, where we saw in Section 7.2 a transition from gas-sputtering to self-sputtering as the discharge begins to create and attract M+ ions back to the target. First, the curves for sputter yield versus ion energy for Ar+ ions and self-ion sputtering for various target materials are very similar; however, they are not identical, and the self-sputter yield is typically 10 – 15% lower (Anders, 2010), which will also have a negative influence on the total deposition rate. Second, discharges that are prevented from transiting into significant

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Figure 7.27 (A) The plasma potential versus axial distance z from the cathode measured at current maximum. Results for three different B-field configurations are shown: profiles A (weakest |B|), B, and C (strongest |B|), and with parts marked A-A’, B-B’, and C-C’. The measurements were carried out at an average discharge power of 750 W, an Ar working gas pressure of 1.08 Pa, and above the race track of a planar circular magnetron equipped with a Ti target, 15 cm in diameter. Data from Mishra et al. (2010) and Brenning et al. (2012). (B) Typical sputter energy distribution of Ti calculated using a modified Thompson distribution from Stepanova and Dew (2004) using a cutoff energy of 17 eV. The vertical lines show the threshold energies for escaping back-attraction after ionization at z = 30 mm (at the marks A, B, and C) in the potential profiles in (A). Data from Lundin et al. (2013).

self-sputtering, such as when applying short HiPIMS pulses (t ≤ 50 µs), are dominated by G+ ions for sputtering, which means that the effective sputter rate can be kept high. This latter point is likely one reason for the reported higher deposition rates for shorter pulses discussed earlier. However, the risk with short pulses is that the increase in deposition rate is accompanied by a decrease in ionization fraction (Konstantinidis et al., 2006a). There are also other processes affecting the deposition rate in HiPIMS. In Section 4.2.2, we saw that gas rarefaction leads to lower density of the working gas in front of the target and thus a reduction in the number of ions available for sputtering. This subsequently leads to a reduction in the deposition rate, in particular, for long pulses (t > 100 µs), although we are not aware of any reports quantifying this contribution. In addition, Emmerlich et al. (2008) argue that the nonlinear scaling of

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Figure 7.28 The deposition rate measured using a QCM at different axial positions above the race track for the three different B-field configurations shown in Fig. 7.27A. The measurements were carried out at an average discharge power of 750 W and an Ar gas pressure of 1.08 Pa using a planar circular magnetron equipped with a Ti target, 15 cm in diameter. Data from Mishra et al. (2010).

√ the sputter yield with the applied voltage is not taken into account (often Y ∝ VD ) when comparing dcMS and HiPIMS discharges operated at the same average power. This would reduce the sputter rate since in HiPIMS operation the target voltage is significantly higher than for a conventional dcMS discharge. It is therefore not reasonable to compare the two at the same average power. In the case of Cu sputtering the authors estimated a relative HiPIMS-to-dcMS deposition rate between 43% and 76%, depending on the fraction of Ar+ to Cu+ ions sputtering the target (Emmerlich et al., 2008). These results were benchmarked against experiments, where the relative deposition rate based on thickness measurements was determined to be 32%, and thus the difference in sputter yields cannot fully explain the difference in deposition rates. Also, Alami et al. (2006) address the difference in discharge voltage and current between dcMS and HiPIMS and suggest that the lower deposition rate in HiPIMS is at least partially due to a lower average target current during HiPIMS deposition when the same average power is applied due to higher voltage necessary for HiPIMS operation. They conclude that comparison should be made for the same average discharge current. Another possible reason for the deposition rate loss is linked to the previously discussed anomalous transport of charged particles in Section 7.3.2.2. Lundin et al. (2008b) show that a significant fraction of the sputtered metal species is deposited sideways. This enhanced radial transport (across the magnetic field lines) increases the deposition rates perpendicular to the target surface but decreases the amount of sputtered vapor that reaches a substrate in front of the target. The authors investigated Cr and Ti deposition in Ar on samples located outside the edge of a circular planar magnetron, which were placed perpendicular to the target surface. The measured deposition rates were normalized to a reference sample on the standard substrate holder. By combining results on the sideways deposition rate for various distances z, they found a 25% and 10% higher sideways deposition rate in HiPIMS for Cr and

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Ti, respectively. Leroy et al. (2011) carried out similar investigations using a rotating cylindrical magnetron. However, they did not observe an increase in sideways deposition and suggest that anomalous transport might work differently in these devices or that the sideways deposited material is transported in a different direction compared to the angular range investigated (Leroy et al., 2011).

7.5.2 Increasing the deposition rate There have been some attempts to increase the deposition rate in the HiPIMS discharge. In the previous section, we already identified that a reduction of the magnetic field strength resulted in both a reduction of the back-attracting electric field (reduction of the plasma potential) and an increase in the deposition rate (Mishra et al., 2010). The deposition rate profiles above the target race track are shown in Fig. 7.28 for the three different B-field configurations displayed in Fig. 7.27. As one possible reason for the deposition rate increase, Mishra et al. (2010) proposed a reduced βt due to the weaker electric field, which would increase the ion flux to the substrate in line with our general explanation on ion back-attraction. However, the situation is not quite clear. In a later analysis of the same experimental data (Bradley et al., 2015), it was argued that there was also a lower ionization probability αt at the weaker magnetic fields. This gives an alternative explanation for the increased deposition rate: at lower αt , ions are replaced by neutrals, which are not back-attracted. Whatever the main reason for the increased deposition rate is, however, decreases of the magnetic field strength is a promising way to increase the deposition rate. Furthermore, Raman et al. (2016) modified the magnetic field topology of a HiPIMS discharge, which increased the deposition rate (Raman et al., 2016, McLain et al., 2018). In the cited studies the modified magnet pack had a high magnetic field region over three concentric race track regions but fell off more steeply than for a conventional magnet pack as we move away from the target surface. Such a configuration, with open field lines toward the substrate region, which allows electrons to escape the magnetic trap more easily, is suggested to reduce the effect of self-sputter recycling (lower discharge current) and thus reduce βt . The authors benchmarked the deposition rates to dcMS using the same magnetron configuration and found that the HiPIMS rates were up to 25% higher with a Ti target, about equal with a carbon target, and 25% lower with an Al target compared to the dcMS rates (Raman et al., 2016). Similar trends were found by making the same modifications to a rectangular magnetron, where McLain et al. (2018) report an increased deposition rate in HiPIMS mode compared to a standard magnet pack (commercial magnetron assembly). There are also reports of a deposition rate increase related to guiding the ionized flux using external magnetic fields (Bugaev et al., 1996, Bohlmark et al., 2006b). In conventional magnetron sputtering, we saw in Section 1.2.2 that ions are not magnetized by the relatively weak static magnetic field. However, Bohlmark et al. (2006b) demonstrated that a sufficiently strong B-field (|B| ∼mT) can be created with a current-carrying coil placed in front of the magnetron target. When current was drawn through the coil, it generated a magnetic field opposing the field from the center pole of the magnetron. An increase of 80% in deposition rate was observed for

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the sample placed in the central position (right in front of the target center i.e. typical substrate position), and the deposition rate was strongly decreased on samples placed to the side of the target. The measurements were also performed using dcMS, but no major effect of the magnetic field was observed in that case probably due to the low ionized flux fraction. For another possibility to reduce βt , Butler et al. (2018) investigated the number of Ti+ ions that are in the ionization region at the end of a HiPIMS pulse. Since the back-attracting electric field disappears at pulse end, these ions will experience an abruptly lowered βt . In a 100 µs-long reference pulse the authors found that the time-integrated number of Ti+ ions going from the ionization region and out into the volume plasma is approximately ten times the number of Ti+ ions that are left in the ionization region at pulse end. If these “afterglow ions” retain their directed velocity from the sputtering process, then they are all directed away from the target. For the case of such an effective βt = 0 after the pulse, about 10% of the time-integrated (pulse + afterglow) ion flow to the volume plasma would come from the afterglow. However, if we instead consider a shorter 10 µs-long pulse with the same current at the pulse end, then the number of ions that experience high βt during the pulse would be reduced by a factor of 10 (probably more, keeping in mind that the ion production rate is lower during the beginning of a pulse), whereas the same amount of ions would be released at the end of the pulse with low βt (Butler et al., 2018). The average βt could be shifted down considerably. One scenario built on this approach is chopped HiPIMS (Barker et al., 2013, Antonin et al., 2015) discussed in Section 2.4.3. Butler et al. (2018) also point out that concepts such as modulated pulse power magnetron sputtering (MPPMS) (Liebig et al., 2011) and deep oscillation magnetron sputtering (DOMS) (Ferreira et al., 2014) could have similar effects. Both of these methods are based on a train of micropulses (∼ µs) that constitutes a macropulse (∼ ms). The key parameter is the value of the voltage after the individual micropulses in which the ionization occurs. This voltage has to go down to zero, or at least become very low, to release the produced ions. In another attempt to reduce back-attraction of ionized sputtered species, Konstantinidis et al. (2006b) added a secondary discharge by placing an inductive coil to create an inductively coupled discharge, halfway between the target and the substrate to increase the conductivity of the interelectrode volume plasma. They demonstrated increased ion collection at the substrate with increased rf power to the inductive coil and claim that this effect could be used to minimize the decrease in deposition rate due to self-sputtering as it would make it easier for the metal ions to leave the magnetic trap (reduced βt ). Also, the use of bipolar HiPIMS, where a positive voltage pulse is applied after the conventional negative HiPIMS pulse, have been claimed to increase the deposition rate. Wu et al. (2018) report a rate increase of up to 19% when sputtering Cu target in argon at 1.07 Pa using 100 µs long HiPIMS pulses followed by a 100 µs positive pulse with amplitude of maximum Vreverse ≤ 150 V. The HiPIMS discharge current peaked at about 40 A corresponding to a peak current density of 0.12 A/cm2 , that is, a rather weak HiPIMS discharge. The authors propose that the observed rate increase is due to

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the creation of a positive sheath at the target during the positive pulse, which pushes more positive ions to the substrate. The situation is not clear, however, since other investigations using the same approach do not observe an increase in deposition rate when sputtering Cu (Nakano et al., 2013) or Ti (Britun et al., 2018, Keraudy et al., 2019) with argon as the working gas. Keraudy et al. (2019) state that no deposition rate increase is to be expected, since the positive pulse does not primarily create an ion-reflecting sheath between the plasma and the target, as previously suggested. Instead, the main effect of the reversed pulse is that it raises the plasma potential in the whole magnetic trap (the ionization region), which the authors define as the region where both ends of the magnetic field lines are connected to the target. The reservoir of ions that are inside the magnetic trap at the end of the HiPIMS pulse therefore do not react on the application of the positive pulse. However, the IEDF indicates that as the ions leave the magnetic trap they are uniformly accelerated, and gain an energy qVreverse given by the applied reversed potential. The result is a uniform addition of the same amount of energy to all the ions that leave the cathode plasma during the time of the application of the positive pulse. In addition, Vlˇcek et al. (2009) have demonstrated an increase in the deposition rate (up to 1.9 times) by increasing the target surface temperature (up to 1700◦ C) for a Ti target. It was also shown that the required discharge voltage to maintain the same discharge current was decreased when heating the target, which resulted in an even greater power-normalized deposition rate (deposition rate/time-averaged discharge power) by a factor close to 2.9 at a pulse current density of 0.33 A/cm2 . They point out that the target temperature can be controlled over a wide range in HiPIMS operation. It is likely that at these temperatures the surface of the target, and in particular the race track zone, may be heated to such degree that sublimation (from a solid) or evaporation (from a liquid) takes place. A more detailed study of the target melting, including the spatial and temporal variation of the target surface temperature for various discharge conditions, was reported by Tesaˇr et al. (2011). It should be noted that Anders (2010) carried out a literature survey of hot target effects and argued that the deposition rate increase reported by Bohdansky et al. (1986) under these conditions is related to evaporation rather than to sputtering. This conclusion was supported by Behrisch and Eckstein (1993, 2007), who also acknowledged that the surface binding energy has a nonlinear effect on the sputter yield. Although the heat of sublimation decreases with increasing temperature, evaporation is still dominating at high temperatures by a wide margin (Behrisch and Eckstein, 1993). Indirectly related to the deposition rate is target utilization. Among the early claims about the HiPIMS technique, target utilization was improved (Kouznetsov et al., 1999). Indeed, Liebig et al. (2010) have shown using 2D OES that the sputter distribution of the target is wider for a HiPIMS discharge than for dcMS. Similar findings have been reported by Clarke et al. (2009). This is consistent with empirical observations that show that the width of the ion current density distribution in the target vicinity and thus the erosion width increases with increased discharge current and voltage (Wendt and Lieberman, 1990), both of which are significantly higher for HiPIMS than for dcMS.

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7.5.3 Deposition rates in reactive HiPIMS Last, we address the situation in reactive HiPIMS discussed in Chapter 5. From the discussion on hysteresis in Section 6.3 we conclude that reactive HiPIMS differs significantly from reactive dcMS due to a less abrupt transition to the poisoned (compound) mode and an eliminated, or at least significantly reduced, hysteresis. The combination of these two factors lead to higher deposition rates and the mechanisms were discussed in Section 6.3.1. For example, investigations of the process characteristics during reactive HiPIMS deposition of Al2 O3 (Wallin and Helmersson, 2008, Aiempanakit et al., 2011), ZrO2 (Sarakinos et al., 2008), and CeO2 (Aiempanakit et al., 2011) have shown that these processes can exhibit a hysteresis-free and stable transition zone at deposition conditions, which in the case of dcMS result in hysteresis and an unstable transition zone (see Fig. 6.10 for Al2 O3 ). The stabilization of the transition zone allows for deposition of stoichiometric films at a lower target compound coverage when compared to the compound mode in dcMS (Wallin and Helmersson, 2008, Aiempanakit et al., 2011, Sarakinos et al., 2008). This has been shown to result in deposition rates similar (Wallin and Helmersson, 2008) or up to two times higher (Sarakinos et al., 2008) than those obtained by dcMS.

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Rauch, A., Mendelsberg, R.J., Sanders, J.M., Anders, A., 2012. Plasma potential mapping of high power impulse magnetron sputtering discharges. Journal of Applied Physics 111 (8), 083302. Revel, A., Minea, T., Costin, C., 2018. 2D PIC-MCC simulations of magnetron plasma in HiPIMS regime with external circuit. Plasma Sources Science and Technology 27 (10), 105009. Revel, A., Minea, T., Tsikata, S., 2016. Pseudo-3D PIC modeling of drift-induced spatial inhomogeneities in planar magnetron plasmas. Physics of Plasmas 23 (10), 100701. Ross, A.E., Sanginés, R., Treverrow, B., Bilek, M.M.M., McKenzie, D.R., 2011. Optimizing efficiency of Ti ionized deposition in HIPIMS. Plasma Sources Science and Technology 20 (3), 035021. Rossnagel, S.M., 1988. Deposition and redeposition in magnetrons. Journal of Vacuum Science and Technology A 6 (6), 3049–3054. Rossnagel, S.M., Kaufman, H.R., 1987a. Charge transport in magnetrons. Journal of Vacuum Science and Technology A 5 (4), 2276–2279. Rossnagel, S.M., Kaufman, H.R., 1987b. Induced drift currents in circular planar magnetrons. Journal of Vacuum Science and Technology A 5 (1), 88–91. Samuelsson, M., Lundin, D., Jensen, J., Raadu, M.A., Gudmundsson, J.T., Helmersson, U., 2010. On the film density using high power impulse magnetron sputtering. Surface and Coatings Technology 202 (2), 591–596. Sarakinos, K., Alami, J., Klever, C., Wuttig, M., 2008. Process stabilization and enhancement of deposition rate during reactive high power pulsed magnetron sputtering of zirconium oxide. Surface and Coatings Technology 202 (20), 5033–5035. Sheridan, T.E., Goree, J., 1989. Low-frequency turbulent transport in magnetron plasmas. Journal of Vacuum Science and Technology A 7 (3), 1014–1018. Sigurjónsson, P., 2008. Spatial and Temporal Variation of the Plasma Parameters in a High Power Impulse Magnetron Sputtering (HiPIMS) Discharge. Master’s thesis. University of Iceland, Reykjavik, Iceland. Spagnolo, S., Zuin, M., Cavazzana, R., Martines, E., Patelli, A., Spolaore, M., Colasuonno, M., 2016. Characterization of electromagnetic fluctuations in a HiPIMS plasma. Plasma Sources Science and Technology 25 (6), 065016. Stancu, G.D., Brenning, N., Vitelaru, C., Lundin, D., Minea, T., 2015. Argon metastables in HiPIMS: validation of the ionization region model by direct comparison to time resolved tunable diode-laser diagnostics. Plasma Sources Science and Technology 24 (4), 045011. Stepanova, M., Dew, S.K., 2004. Anisotropic energies of sputtered atoms under oblique ion incidence. Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms 215 (3–4), 357–365. Tesaˇr, J., Martan, J., Rezek, J., 2011. On surface temperatures during high power pulsed magnetron sputtering using a hot target. Surface and Coatings Technology 206 (6), 1155–1159. Thornton, J.A., 1978. Magnetron sputtering: basic physics and application to cylindrical magnetrons. Journal of Vacuum Science and Technology 15 (2), 171–177. Tsikata, S., Minea, T., 2015. Modulated electron cyclotron drift instability in a high-power pulsed magnetron discharge. Physical Review Letters 114 (18), 185001. Van Aeken, K., Mahieu, S., Depla, D., 2008. The metal flux from a rotating cylindrical magnetron: a Monte Carlo simulation. Journal of Physics D: Applied Physics 41 (20), 205307. Vitelaru, C., Lundin, D., Stancu, G.D., Brenning, N., Bretagne, J., Minea, T., 2012. Argon metastables in HiPIMS: time-resolved tunable diode-laser diagnostics. Plasma Sources Science and Technology 21 (2), 025010.

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Vlˇcek, J., Burcalová, K., 2010. A phenomenological equilibrium model applicable to highpower pulsed magnetron sputtering. Plasma Sources Science and Technology 19 (6), 065010. Vlˇcek, J., Zustin, B., Rezek, J., Brucalova, K., Tesar, J., 2009. Pulsed magnetron sputtering of metallic films using a hot target. In: Proceedings of the 52nd Annual Technical Conference Society of Vacuum Coaters. Santa Clara, California, May 9–14, 2009. Society of Vacuum Coaters, Albuquerque, New Mexico, pp. 219–223. Waits, R.K., 1978. Planar magnetron sputtering. Journal of Vacuum Science and Technology 15 (2), 179–187. Wallin, E., Helmersson, U., 2008. Hysteresis-free reactive high power impulse magnetron sputtering. Thin Solid Films 516 (18), 6398–6401. Wendt, A.E., Lieberman, M.A., 1990. Spatial structure of a planar magnetron discharge. Journal of Vacuum Science and Technology A 8 (2), 902–907. Winter, J., Hecimovic, A., de los Arcos, T., Böke, M., Schulz-von der Gathen, V., 2013. Instabilities in high-power impulse magnetron plasmas: from stochasticity to periodicity. Journal of Physics D: Applied Physics 46 (8), 084007. Wu, B., Shchelkanov, I.H.I., McLain, J., Patel, D., Uhlig, J., Jurczyk, B., Leng, Y., Ruzic, D.N., 2018. Cu films prepared by bipolar pulsed high power impulse magnetron sputtering. Vacuum 150, 216–221. Yang, Y., Tanaka, K., Liu, J., Anders, A., 2015. Ion energies in high power impulse magnetron sputtering with and without localized ionization zones. Applied Physics Letters 106 (12), 124102. Yang, Y., Zhou, X., Liu, J.X., Anders, A., 2016. Evidence for breathing modes in direct current, pulsed, and high power impulse magnetron sputtering plasmas. Applied Physics Letters 108 (3), 034101. Young, C.V., Fabris, A.L., Cappelli, M.A., 2015. Ion dynamics in an E × B Hall plasma accelerator. Applied Physics Letters 106 (4), 044102. Yushkov, G.Y., Anders, A., 2010. Origin of the delayed current onset in high power impulse magnetron sputtering. IEEE Transactions on Plasma Science 38 (11), 3028–3034.

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Kostas Sarakinosa , Ludvik Martinub a Nanoscale Engineering Division, Department of Physics, Chemistry and Biology, Linköping University, Linköping, Sweden, b Department of Engineering Physics, Polytechnique Montréal, Montréal, Quebec, Canada

Surface engineering by the addition of thin films and coatings are used in a wide range of technological applications, including surface protection of metal cutting and forming tools, optical devices, and microelectronics. The functionality of thin films and coatings crucially depends on their physical attributes, which are in turn governed by the film morphology and phase composition. By generating ample amounts of ionized film-forming species HiPIMS represents an effective way of controlling film growth and thereby opens the way to tune film material properties, including hardness, refractive index, and residual stress.

8.1 Introduction to the fundamentals of thin film growth The growth of thin films is initiated by atom condensation on the substrate surface, which nucleates into islands and coalesces to form a continuous film. The use of energetic ionized species and pulsed vapor fluxes affects the film-forming processes throughout all growth stages, as explained in the present section.

8.1.1 Thin film growth from an atomistic point of view Thin films, that is, atomic layers with thicknesses ranging from a few Å to several µm, are applied on the surface of a material to control the way by which this material interacts with its ambient. The latter makes thin films a vital part in manufacturing components and devices in a multitude of technological sectors, for example, surface protection, metal cutting and forming, optics, energy storage and generation, data storage, and microelectronics. A large fraction of thin films are today synthesized by vapor condensation on solid surfaces (Ohring, 2002, Martin, 2010), during which relatively large arrival rates of film forming species (typically of the order of 1017 m−2 s−1 or High Power Impulse Magnetron Sputtering. https://doi.org/10.1016/B978-0-12-812454-3.00013-9 Copyright © 2020 Elsevier Inc. All rights reserved.

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Figure 8.1 Schematic illustration of thin film formation stages in polycrystalline films (3D island type). Reproduced with permission of Taylor and Francis, from Pilch and Sarakinos (2016); permission conveyed through Copyright Clearance Center, Inc.

equivalently 10−2 ML/s and above),1 and deposition temperatures corresponding to ∼30% or below of the melting point of the thin film material result in limited atomic assembly kinetics (Petrov et al., 2003). The latter, in combination with extremely large cooling rates (∼1013 K/s) encountered during condensation of the material vapor on the substrate surface (Barbee et al., 1977), lead to far-from-equilibrium growth, which in turn makes it possible to form metastable phases and microstructures with unique physical attributes (Petrov et al., 2003, Münz, 1986, Rovere et al., 2010). Depending on the film and substrate crystallographic structure, as well as on the growth conditions, films that are amorphous (i.e. no defined crystal structure), polycrystalline films (i.e. films that feature grains with different crystallographic orientations), or single crystals may be formed. In the remainder of the present section, we focus on mechanisms that determine growth evolution and microstructure of polycrystalline films, since they represent a substantial part of today’s film synthesis processes and related applications. However, similar mechanisms are also relevant during epitaxial deposition of single-crystalline films. Growth of polycrystalline films can be summarized as follows: it starts with vapor condensation on the substrate surface and formation of spatially separated singlecrystalline islands (nucleation), which grow in size (island growth) and impinge on each other forming new larger islands (coalescence). This process also leads to reduction of the island density on the substrate surface. The coalescence process continues until the boundaries between single-crystalline islands (i.e. grains) become immobile and coalescence stops (formation of polycrystalline islands), which leads to the formation of a continuous film (Petrov et al., 2003). These processes, which typically account for the first hundred angstroms of the film thickness, are schematically depicted in Fig. 8.1. The film morphological evolution, throughout the stages shown in Fig. 8.1, is governed by the effects of thermodynamics and kinetics (as set by the deposition process parameters) on the three fundamental structure forming phenomena: nucleation, crystal growth, and grain growth (Barna and Adamik, 1998). 1 One ML (monolayer) corresponds to the number of atoms required to form a complete layer of a given

material on a substrate of a given crystallographic orientation. Typical values for one ML are of the order 1019 atoms/m2 .

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An atom (or molecule) approaching a substrate is subjected to the attractive potential of the substrate surface, and it is accelerated gaining kinetic energy Ekin , which is of the order of the cohesive energy Ecoh of the substrate lattice.2 Upon impingement on the surface, Ekin is dissipated into vibrations of the surface crystal lattice (phonons). Through this process, the energy Ekin of the impinging atom is reduced, and if it becomes smaller than the surface adsorption energy Ead (a fraction of Ecoh ),3 the atom becomes adsorbed (i.e. becomes an adatom) on the substrate. The probability for the condition Ekin < Ead to be fulfilled is also known as the sticking coefficient. For an atom impinging on a cold substrate (i.e. for temperatures below 50% of the melting point of the thin-film material), the sticking coefficient is typically very close to unity (Michely and Krug, 2004) (see also Section 6.2.1 for more details on sticking coefficients). Once the film forming species have become adatoms, they perform a thermally activated two-dimensional random walk on the substrate, executing jumps between neighboring adsorption sites, as determined by the potential landscape of the surface. The rate of successful jumps and thereby the distance traveled by adatoms during this walk is expressed in terms of their diffusivity: 1 D = 2 ν, 4

(8.1)

where 2 denotes the mean square displacement covered per single jump, and ν is the diffusion rate, which is equal to   −ED ν = ν0 exp , (8.2) kB T where T is the substrate temperature, kB denotes the Boltzmann constant, and ED is the energy barrier that an adatom has to overcome for the jump between adjacent sites to occur. The prefactor ν0 is the attempt frequency and, essentially, represents how often an adatom attempts to escape from an adsorption site; hence the product of this prefactor with the exponential term in Eq. (8.2) describes the number (frequency) of successful escape events. Typical values for ν0 are of the order 1012 – 1013 s−1 , whereas ED can be anywhere in the range 0.05 to 1.0 eV, or even higher (Michely and Krug, 2004). Film-forming species deposited from the vapor phase increase the adatom density on the substrate until adatom–adatom encounters become inevitable and diatomic clusters (i.e. dimers) nucleate. These clusters (islands) may dissociate or grow in size by incorporating more adatoms or species from the vapor phase (Frenkel, 1924, Zinsmeister, 1966). In general, clusters may also be mobile with their mobility depending on their size and chemical nature (see e.g. Sangiovanni et al. (2012) and/or Jamnig et al. (2019)). This process results in an increase of the nuclei density N on the substrate until the nucleation rate becomes equal to the rate at which adatoms get incorporated into existing islands. At this point, during growth, the island saturation density Nsat is 2E coh is the energy required to disperse a solid into its constituent atoms. 3 E is the energy required to remove an adsorbed atom from the surface to the infinity. ad

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reached. In the simplest scenario, clusters are immobile, dimers are stable (referred to as irreversible nucleation), and the sticking coefficient is equal to unity. In that case, Nsat is expressed as (Kryukov and Amar, 2010)  x F . (8.3) Nsat ∝ D In Eq. (8.3) x is a scaling exponent (x < 1) which depends on the dimensionality of growth (i.e. 2D or 3D growth) and the critical nucleus size, (i.e., the size of the smallest stable atomic cluster), and F is the adatom arrival rate (i.e. deposition rate) expressed in ML/s. For 3D island growth on a 2D surface, and for a dimer being the smallest stable atomic island, x = 1/3. Equation (8.3) encodes the dynamic competition among island nucleation and growth during initial growth stages. Increase of D (e.g. caused by increasing T ) leads to a larger adatom mean free path on the substrate surface. This favors adatom incorporation into existing islands at the expense of nucleating new ones and results in a decrease of Nsat . Conversely, increase of F leads to a larger adatom density on the substrate surface. This enhances the probability of adatom–adatom encounters, promotes island nucleation at the expense of island growth, and results in a larger Nsat . As stated before, islands grow in size by incorporating adatoms or species from the vapor phase. Beyond the point of Nsat , island growth becomes the main process that determines film morphology by increasing the fraction of substrate surface covered by the deposit. That is until two or more islands start to impinge on each other and coalesce into a larger single-crystalline island, which reduces the island density and erases morphological features attained during earlier stages of film growth. A simple way to describe the dynamics of coalescence of neighboring atomic clusters is the sintering theory developed by Nichols and Mullins (1965) and Nichols (1966), which assumes that impinging islands are merged together by diffusion of atoms on their surfaces, driven by surface energy minimization. According to this theory, the time from impingement to full shape equilibration of a coalescing island pair is given by τcoal =

R4 , B

(8.4)

where R is the radius of the smaller island, and B is the so-called coalescence strength, a material- and temperature-dependent constant (Nichols and Mullins, 1965, Nichols, 1966). As R increases with time, while B remains constant, τcoal eventually becomes so large that further coalescence events cannot be completed before a third island grows large enough to impinge on a coalescing cluster; this leads to the formation of a polycrystalline island consisting of multiple grains separated by grain boundaries. The shapes of grain boundaries are stabilized by the competition among boundary and surface energies, and depending on the growth temperature, grain boundaries can become mobile (Greene, 2010). This leads to grain growth, which, in combination with the kinetically controlled rate at which adatoms descend from the surface of the films to the grain boundary base (hole filling), determines the final film morphology in terms of grain size and surface roughness.

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8.1.2 Effect of energetic ions on thin film microstructural evolution Physical vapor deposition (PVD) processes in which ions constitute more than 50% of the total flux of the film-forming species are referred to as ionized-PVD (Hopwood, 2000b), often abbreviated IPVD. HiPIMS belongs to this family of techniques (Helmersson et al., 2006), which also includes inductively coupled plasma assisted magnetron sputtering (Hopwood, 2000a), microwave amplified magnetron sputtering (Wendt, 2000, Holber, 2000), pulsed laser ablation (Willmott and Huber, 2000, Eason, 2007), and cathodic arc evaporation (Anders, 2010b). As opposed to neutral species, we have already in Section 4.1.3 seen that ions can easily be manipulated using electric or magnetic fields, which means that ionized-PVD is an ideal technology platform for generating deposition fluxes with controlled energy and direction. The latter has been the main driving force for the initial surge in the development of ionized-PVD processes in the late 1980s (Hopwood, 2000b) to facilitate deposition of uniform metallic contacts and diffusion barrier films into high-aspect-ratio microelectronic devices (Rossnagel and Hopwood, 1994, Hopwood, 1998, Rossnagel, 1999). Control of the ion energy during film growth has, already from the early 1970s, been shown to affect the film microstructure (Mattox and Kominiak, 1972). The way by which this occurs depends on the nature of the interaction between growing film and ions, as determined by the ion energy, that is, whether the energy of impinging ions affects the film surface (typically, a few tens of eV) or is dissipated in the film bulk (typically, above 100 eV) (Ensinger, 1997). The most common effect of ion bombardment with respect to the surface of the film is enhancement of the adatom mobility (Petrov et al., 2003). The enhanced adatom mobility can be achieved by: (i) direct transfer of kinetic energy to single adatoms or clusters by the bombarding species; (ii) bombardment-induced phonons that are coupled to an adatom; and (iii) shallow collision cascades that affect an adatom (Ensinger, 1997). All these mechanisms lead to a decrease of the nucleation density (see Eq. (8.3)), densification, smoothening of film surface, and changes in the film crystallographic orientation (Hultman et al., 1995, Petrov et al., 1993, Adibi et al., 1993, Gall et al., 1998, Shin et al., 2002, Patsalas et al., 2004, Hultman et al., 1991). Further increase of the bombarding energy in the range of 100s of eV yields implantation of energetic species at the subsurface side of the growing film, which gives rise to bulk effects. Implantation often creates lattice defects, such as displacement of lattice atoms to interstitial positions and vacancy formation (Ensinger, 1997). These phenomena lead to densification, but also to generation of residual compressive stress and film failure (Petrov et al., 1989, Windischmann, 1987, Thornton and Hoffman, 1989, Davis, 1993, Petrov et al., 1992, Pauleau, 2001). Stress and densification may also be a pathway for synthesis of metastable phases and structures, as in the case of diamond-like carbon films (Robertson, 2002).

8.1.3 Effect of pulsed vapor fluxes on thin film growth dynamics As discussed in Section 8.7 in greater detail, HiPIMS generates pulsed vapor fluxes, that is, vapor fluxes that arrive at the substrate in concentrated pulses of well-defined

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Figure 8.2 Schematic illustration of diffusivity regimes and scaling relations for island saturation density in pulsed deposition. Reprinted from Sarakinos et al. (2014), with permission from Elsevier.

width ton , frequency f , and instantaneous rate (i.e. amplitude) Fi (see Fig. 8.2 for a schematic illustration). Flux temporal modulation affects the nucleation dynamics depending on the relation between the adatom lifetime τm (i.e. the mean time that an adatom needs to get incorporated into a stable island) and the time scale of the deposition flux as determined by the parameters ton , f , and Fi (Jensen and Niemeyer, 1997). Three different time scale/adatom diffusivity regimes can be defined (Fig. 8.2) (Jensen and Niemeyer, 1997): (i) Slow diffusivity regime (τm  1/f ), in which the adatom density does not vanish between the vapor pulses, i.e., the substrate encounters a continuous deposition flux Fav = Fi × ton × f , and the island density scales according to Eq. (8.3). (ii) Fast diffusivity regime (τm  ton ), in which adatom condensation, adatom diffusion, and island formation occur within a single vapor pulse (nearly zero adatom density during pulse off-time). This means that the adatom density on the substrate surface is determined by the instantaneous rate during the pulse Fi , and the island density scales as  Nsat ∝

Fi D

x .

(8.5)

From Eq. (8.5) it is evident that pulsed fluxes effectively lead to an increase of Nsat , since Fi  Fav . (iii) Intermediate diffusivity regime (ton < τm < 1/f ), in which the adatom diffusion time is longer than the pulse on-time. Thus, during the pulse, there is not enough time for diffusion to become the rate-limiting step for setting the nucleation density (Michely and Krug, 2004), which in this case scales as Nsat ∝ (Fi ton )x/(1−x) .

(8.6)

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From the previous discussion it becomes evident that nucleation can be tailored in pulsed deposition processes by appropriate selection of flux time scales (ton , f , and Fi ), whereas for certain combinations of time scales, growth can be manipulated to achieve a two-dimensional growth morphology (Michely and Krug, 2004). Moreover, the effect of pulsed fluxes on the nucleation may affect later growth stages, as these are determined by the dynamic competition between island growth and coalescence (Lü et al., 2015).

8.2 Deposition on complex-shaped substrates The deposition of homogeneous films on substrates of complex geometry is a requirement for many technological applications, such as metallization of submicrometer patterns in optical and semiconductor devices (Weis et al., 1999, Siemroth and Schülke, 2000, Je et al., 1997, Rossnagel and Hopwood, 1994, Hopwood, 1998, Rossnagel, 1999, Hopwood, 2000b), and deposition of thick protective layers on forming tools and turbine blades (Schuelke et al., 1999, Alami et al., 2009, Bobzin et al., 2008, 2009). In conventional sputtering techniques, such as dcMS, the generated vapor consists largely of neutral species. The trajectory of neutral species is determined by the initial angular distribution of their velocities at the target and the gas-phase scattering (Ohring, 2002, Behrisch and Eckstein, 2007, Gnaser, 2007), which result in a highly anisotropic deposition flux (Hopwood, 2000b) and a faster deposition along the line-of-sight. Thus, substrate sites located along low flux directions, for example, parallel to the deposition flux, are shadowed leading to inhomogeneous deposition, porosity, and poor coverage (Siemroth and Schülke, 2000). As mentioned in Section 8.1.2, the microelectronics industry first recognized that a high degree of ionization of the deposited flux can enable the use of magnetron sputtering for device fabrication. To increase the ionization of the sputtered material, a secondary inductively coupled discharge was added between the magnetron target and the substrate (Rossnagel and Hopwood, 1994, Hopwood, 1998, Rossnagel, 1999). The trajectory of ions can then easily be manipulated through the use of electric and magnetic fields. HiPIMS deposition, being an ionized-PVD process, offers a route for depositing uniform coatings onto complex-shaped substrates and structures. In their seminal work, Kouznetsov et al. (1999) used HiPIMS to generate Cu fluxes with an ionized flux fraction of up to ∼70%, as previously discussed in Section 4.1.4. These fluxes were then directed toward the substrate by applying a bias potential of −80 V, which enabled uniform coverage of micrometer-sized via-holes exhibiting an aspect ratio of ∼1. Besides Cu, Ti is another commonly used metal that can easily be ionized by HiPIMS (Fdensity ≥ 90% was reported by Bohlmark et al. (2005)) and has been demonstrated to cover high-aspect-ratio structures (Chistyakov et al., 2007). Along the same lines, Alami et al. (2005) sputtered Ta using both dcMS and HiPIMS on a silicon substrate clamped on the side of a trench with an area of 1 cm2 and a depth of 2 cm, and

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Figure 8.3 Cross-sectional SEM images of Ta films grown by (A) HiPIMS (here denoted HPPMS) and (B) dcMS on a silicon substrate clamped on the side of a trench with an area of 1 cm2 and a depth of 2 cm. The HiPIMS-deposited film is dense with columns growing perpendicular to the Si/Ta interface. Conversely, dcMS deposited films exhibit a porous morphology with columns tilted from the interface normal, as a result of atomic shadowing. Reprinted with permission from Alami et al. (2005). Copyright 2005, American Vacuum Society.

studied the resulting film morphology on a negatively biased substrate placed parallel to the magnetron target normal (see Fig. 8.3). They found that the dcMS-deposited film exhibits a porous columnar structure with columns tilted from the normal of the film/substrate interface, whereas the HiPIMS deposited film is dense with columns growing perpendicularly to the film/substrate interface, as ions are collimated with the applied electric field in the substrate sheath. These findings are consistent with the notion that dcMS is a line-of-sight deposition method giving rise to underdense films, due to atomic shadowing (Hopwood, 2000b), and suggest that the HiPIMS process can alleviate some of the problems related to covering 3D structures. Seeking to establish the correlation between ion content in the deposition flux and film microstructure during off-normal HiPIMS deposition, Greczynski et al. (2011) and Elofsson et al. (2013) studied the growth of metal films as a function of peak discharge current density JD,peak . They found that a higher JD,peak , and thereby a larger degree of ionization of the sputtered material, leads to a smaller tilt angle of the columnar microstructure (i.e. the columns grow closer to the substrate normal); the latter is, however, the case as long as initial nucleation conditions favor atomic shadowing (Elofsson et al., 2013). Another type of complex shaped substrates, in which uniform coating is a requirement, is metal cutting tools in applications that generate high rates of crater wear at the tool rake side (i.e. the side not facing the deposition flux) (Bobzin et al., 2008, 2009). Using HiPIMS, Bobzin et al. (2008, 2009) have shown that it is possible to deposit Ti–Al–Si–N and Cr–Al–Si–N coatings with comparable deposition rates on both flank (facing the target) and rake side of turning inserts (see Fig. 8.4). On the contrary, this was not possible by using any other sputtering-based technique, that is, dc and mid-frequency magnetron sputtering (Bobzin et al., 2009). HiPIMS has also been used to deposit ceramic Ti–Al–N coatings on the inner walls of submillimeter

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Figure 8.4 Cross-sectional SEM images of TiAlN coatings deposited by HiPIMS on the flank and the rake side of a cutting insert. Reprinted from Bobzin et al. (2009), with permission from Elsevier.

microdies (Shimizu et al., 2014, 2017). Compared to dc magnetron sputtered coatings, which were also deposited for reference, HiPIMS results in a better coverage of the inner wall, denser and smoother coatings with higher hardness, and better adhesion. The practical implication is that the HiPIMS-coated dies exhibit a better microformability, as compared to the dies coated by dcMS. Another case, in which the coating uniformity achieved by HiPIMS was found to be beneficial, is the deposition of γ -Mo2 N on patterned steel surfaces, which led to a substantial decrease of the surface friction coefficient (Sube et al., 2017).

8.3

Interface engineering

The chemistry and crystallographic structure of the film/substrate interface are key factors affecting initial thin film growth stages and, by extension, crystallographic quality in epitaxial films (Michely and Krug, 2004), texture and crystallographic orientation in polycrystalline films (Greene, 2010), and stress generation and adhesion of the film on the substrate (Sander, 2004, Koch, 2010, Consonni et al., 2014, Cemin et al., 2017b). Exposure of a surface to the atmosphere leads to contamination and formation of oxide and organic layers (Ehiasarian et al., 2007). These layers result in weak van-der-Waals forces between the film and the substrate and, subsequently, to poor film adhesion (Ehiasarian et al., 2007). To enhance adhesion, cleaning of the surface via ballistic removal (i.e. sputtering) of contaminants prior to the film deposition is employed using Ar+ ions, a process that is known as ion etching. In the common industrial practice, Ar+ ions are generated from the Ar working gas using external ionization sources (e.g. hollow cathodes and electron guns), which are mounted onto the deposition chamber (Vetter et al., 1999, Bobzin et al., 2009, Alami et al., 2009).

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Figure 8.5 (A) Chemical composition of a steel-CrN interface etched by an Ar–Nb HiPIMS discharge. Nb atoms are subplanted into the substrate over a thickness range of 5 nm. (B) Cross-section TEM micrograph of a Cr+ ion treated steel substrate showing the formation of a sharp interface. Reprinted from Ehiasarian et al. (2007), with the permission of AIP Publishing.

Subsequently, the Ar+ ions are accelerated toward and impinge on negatively biased substrates with energies in the range 300 to 1500 eV and sputter etch organic and inorganic contaminants. Besides Ar+ ions, metal ions can be used to etch the substrate, and create an interfacial layer that promotes local epitaxial growth of the film, and enhance film adhesion (Hovsepian, 1988, Schönjahn et al., 2001, Håkansson et al., 1991). This has been, for instance, demonstrated for steel and WC substrates etched using cathodic arc evaporation (Hovsepian, 1988, Schönjahn et al., 2001), which is a technique that provides a nearly 100% ionized metal discharge. However, cathodic arcs generate macroparticles which can be detrimental for the film/substrate interface. An alternative is to use the highly ionized metal fluxes generated by HiPIMS as a substrate etching tool. This has been demonstrated for a number of monolithic (Ehiasarian et al., 2003, 2004, Lattemann et al., 2006, Bakoglidis et al., 2016) and multilayer (Ehiasarian et al., 2007, Hovsepian et al., 2009, Reinhard et al., 2007) nitride compounds, yielding comparable scratch test critical loads and adhesion with coatings grown on substrates cleaned using Ar+ ions (Vetter et al., 1999). This fact indicates that HiPIMS can serve as a route to engineer film/substrate interfaces without the drawbacks of arc discharges and the technical complexity imposed by external ionization sources. Similar to all other etching approaches that use metal ions, HiPIMS etching leads to metal subplantation at the substrate forming an interfacial region ranging from 5 to 15 nm (Ehiasarian et al., 2004, 2007), which serves as template to promote local epitaxial growth of individual film grains on substrate grains (Ehiasarian et al., 2007) (see Fig. 8.5 for an example of a CrN/NbN coating on a stainless steel substrate pretreated by HiPIMS). Local epitaxial growth is achieved not only after intentional etching using HiPIMS generated ion fluxes, but also during film growth on Si substrates, that is, without plasma etching prior to deposition. This is the case for AlN films grown on Si(100), as

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Figure 8.6 Cross-sectional TEM micrograph of AlN/Si(100) interface during film growth by (A) dcMS deposition and (B) HiPIMS deposition. The amorphous native SiOx layer, observed in dcMS deposition, seen in (A), has been sputtered away by the energetic deposition during HiPIMS deposition of AlN as seen in (B). Reprinted from Ait Aissa et al. (2014), with permission from Elsevier.

reported by Ait Aissa et al. (2014) who showed that HiPIMS deposition yields sharp interfaces between film and substrate without any native SiOx layer oxide, which is presumably sputtered away by the energetic ionized deposition flux, as seen in Fig. 8.6B. This is in contrast to films grown by dcMS (which generates a largely neutral deposition flux), where an amorphous layer associated with the SiOx native oxide is observed at the film/substrate interface (Fig. 8.6A). More recently, global epitaxial growth was reported by Cemin et al. (2017b) for Cu films (up to 150 nm thick) deposited by HiPIMS at room temperature on negatively biased (−130 V) Si(100)/SiOx substrates, without any prior chemical or plasma surface treatment. Although the exact mechanisms leading to this behavior are not yet fully understood, the authors suggest that epitaxial growth is facilitated by the implantation of energetic Cu+ ions below the native SiOx layer during the early stages of film growth, favoring the formation of a copper silicide compound with better lattice match to the Cu layer. In parallel, the ionic flux also interacts with the native SiOx , resulting in sputter etching, which in combination with ion-induced local atomic rearrangement and Cu deposition lead to the formation of a complex mixed interlayer.

8.4 Thin film microstructure and morphology As explained in Section 8.1.1, thin film growth from the vapor phase proceeds far from thermodynamic equilibrium. Thus, microstructure and morphology is primarily determined by growth kinetics, that is, the occurrence rates of thermally activated atomic-scale processes are affected by growth temperature, chemistry, and arrival rate of the film forming species (Petrov et al., 2003). Energetic ions, which are part of the deposition flux, may modify these rates via the pathways described in Section 8.1.2. In the following subsections, we discuss, in detail, the way by which ionized fluxes generated by HiPIMS affect film morphological evolution.

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8.4.1 Film density and surface roughness The effect of ions with energies in the range ∼10 – 20 eV, generated by HiPIMS,4 is most notably exemplified by growth of polycrystalline films, which exhibit mass densities close to the reference values of the corresponding bulk materials and ultrasmooth surfaces, even when deposition is performed at room temperature and on electrically grounded substrates (Helmersson et al., 2006, Sarakinos et al., 2010, Gudmundsson et al., 2012, Anders, 2011, Samuelsson et al., 2010). This is attributed to enhancement of adatom mobility mediated by the energetic bombardment and differs from the morphology obtained when growing films using low-ionization deposition processes (e.g., dcMS) at similar conditions, which lead to surface roughness and extended porosity (Petrov et al., 2003). Despite the qualitative trends with respect to mass density of HiPIMS deposited films reported across the literature over the last 20 years, there is a wide spread of experimental conditions (e.g. growth geometry, arrangement and strength of magnetic field, vacuum quality, materials) at which density data have been obtained. This renders a universal correlation among density, material intrinsic properties, and process conditions a nontrivial task. A study aiming to address this gap in understanding was performed by Samuelsson et al. (2010), who measured the mass density change achieved by HiPIMS deposition over dcMS deposition for eight different metallic materials deposited using the same deposition apparatus. Their analysis showed that the HiPIMS deposition, via its energetic contribution to film growth, leads to a statistically significant increase of film density (in the range ∼5 to 15%) relative to dcMS deposition. They also performed discharge simulations using an early version of the ionization region model (see Section 5.1.3 for model details) to calculate the maximum ionized density fractions (Fdensity ) generated by different target materials. Their results indicate that a larger Fdensity and, by extension, a larger flux of energetic species to the growing surface lead to a more pronounced density increase (see Table 8.1). However, it should be noted that film morphological features (e.g. mass density) are determined not only by the growth conditions, but also by intrinsic material properties; high melting point materials exhibit in general low atomic mobility and hence are more prone to form underdense films when deposited at low temperatures. Thus, energetic ions can have a more pronounced effect on film density, as compared to lowmelting-point materials; see Table 8.1. This indicates that more systematic studies are required to establish a general quantitative understanding on the effect of the HiPIMS process on film density. Besides polycrystalline films, HiPIMS can also affect the density of materials that typically form amorphous structures. A characteristic example is amorphous carbon for which Aijaz et al. (2012) reported density values similar to that of other ionized PVD techniques and up to ∼30% higher as compared to dcMS; which has direct implications on the fraction of sp3 bonds and film hardness. It is important to note that carbon exhibits an intrinsically low ionization probability, even in a highly dense 4 Typical ion energy distributions for ionized sputtered species in HiPIMS extend to ≤ 100 eV with the

peak of the energy distribution found at energies of a few eV and an average energy of about 10 – 20 eV. See Section 4.1.3 for more detail.

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Table 8.1 HiPIMS-to-dcMS mass density ratio ρHiPIMS /ρdcMS and maximum ionized density fraction Fdensity for Al, Ag, Cu, Ti, Pt, Zr, Cr, and Ta films as reported by Samuelsson et al. (2010), along with melting points Tm of the corresponding materials. The substrate holder was grounded. Element

ρHiPIMS ρdcMS [%]

Fdensity [%]

Tm [K]

Al Ag Cu Ti Pt Zr Cr Ta

106 105 98 116 103 100 112 104

49 34 27 56 n/a n/a n/a n/a

933 1234 1357 1941 2041 2128 2180 3290

HiPIMS plasma (Lundin et al., 2015), and hence the ionized flux in Ar–C-based HiPIMS discharges primarily consists of Ar+ ions (DeKoven et al., 2003, Sarakinos et al., 2012). Hence, specially designed strategies for achieving high C+ -to-C ratios are necessary (Aijaz et al., 2012, Anders et al., 2012, Konishi et al., 2016). One such approach, which concerns the generation of very high peak discharge currents in carbon discharges, is discussed in detail in Section 7.2.1.2 (Brenning et al., 2017).

8.4.2 Film texture and morphological evolution Film density is a macroscopic quantity that provides an average representation of film morphology at the mesoscale. Concurrently, polycrystalline films may exhibit a variety of microstructures with respect to size, morphology, and relative orientation of crystallites (Petrov et al., 2003, Barna and Adamik, 1998). These are, in turn, determined by the effect of surface and bulk diffusion processes (as controlled by, for instance, the substrate temperature during deposition, Ts ) and growth chemistry on the three fundamental structure-forming phenomena, namely nucleation, crystal growth, and grain growth (Barna and Adamik, 1998). A convenient way to classify morphology is to apply the structure zone models (SZM), in which the rates of surface and bulk atomic diffusion during growth are qualitatively accounted for using the so-called homologous temperature Ts /Tm (Tm is the melting point of the deposited material in K) (Messier et al., 1984, Thornton, 1977, Grovenor et al., 1984, Anders, 2010a). A commonly used SZM that describes sputter deposition of metallic and compound films is shown schematically in Fig. 8.7. Zones I, T, and II refer to pure metal growth. In Zone I (typically, for Ts /Tm values below 0.2), due to the limited surface diffusion, the lateral size of the grains is determined by the nucleation density. As a consequence, the film consists of uninterrupted fibrous columns, exhibits porous and rough morphologies, and has a random crystal-

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Figure 8.7 Qualitative schematic representation of the structure zone model for sputter deposition of metallic films. Zones I, T, and II refer to impurity-free deposition, whereas zone III describes high temperature growth under the presence of low concentration of impurities. Reprinted from Barna and Adamik (1998), with permission from Elsevier.

lographic texture (Petrov et al., 2003, Barna and Adamik, 1998). In zone T (typically, in the Ts /Tm range 0.2 to 0.4), surface diffusion has considerable influence on morphology. A key feature in this structure zone is competitive growth at the interface (manifested by V-shaped grains), since grains with different crystallographic orientations lead to different diffusion coefficients and, therefore, different residence times for adatoms. At larger film thicknesses, faster-growing grains overtake slower ones, giving rise to a columnar dense morphology, smoother surfaces, and strong texture (Petrov et al., 2003, Barna and Adamik, 1998). At higher temperatures (Ts /Tm > 0.4; Zone II), bulk diffusion becomes significant, yielding a dense columnar microstructure, which is retained from the interface to the film surface (Petrov et al., 2003, Barna and Adamik, 1998). At even larger Ts /Tm values a new microstructure zone may appear (denoted as Zone III), which is characterized by equi-axed three-dimensional (globular) grains. Zone III is the result of impurities,5 which can cause periodic interruption of crystal growth, repeated nucleation, and globular grains (Petrov et al., 2003, Barna and Adamik, 1995, 1998). It is important to note that the temperature onset for Zone III depends on the level of impurities, with higher impurity concentration leading to the appearance of globular morphology at lower Ts /Tm values (Barna and Adamik, 1995). The addition of low flux ion bombardment (as in the case of conventional sputtering processes such as dcMS) allows for the transitions between the structure zones to occur at lower homologous temperatures, whereas the morphological features predicted by the SZMs remain valid (Messier et al., 1984, Thornton, 1977). On the contrary, the HiPIMS discharge is able to provide ample amounts of energetic ions that can significantly modify the growth processes and morphology, as has been shown for a number of elemental and compound films (Ehiasarian et al., 2003, 2004, Lin and Chistyakov, 2017, Mendizabal et al., 2016, Ferreira et al., 2016, Fernandes et al., 2016, Alami et al., 2009b, Del Giudice et al., 2016, Bobzin et al., 2015, Purandare et al., 2008, Kamath et al., 2010, Samuelsson et al., 2012a, Sonderby et al., 2014). An example is given in Fig. 8.8, where cross-sectional TEM images of CrN films grown on electrically floating Si(100) substrates by dcMS and HiPIMS at various ionized flux 5 Here the term “impurity” denotes foreign species that are incorporated in the film during growth both

intentionally and nonintentionally. Hence, this definition covers both growth of elemental films in contaminated environments and growth of compound films (e.g. metal nitrides and oxides).

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Figure 8.8 Cross-sectional TEM micrographs of CrN films deposited on electrically floating Si substrates by (A) dcMS, (B) HiPIMS at JD,peak = 1 A/cm2 , and (C) HiPIMS at JD,peak = 4 A/cm2 . Increase of ionized flux fraction, facilitated by the use of HiPIMS and subsequent increase of JD,peak leads to a transition from an underdense columnar, through dense columnar to featureless morphology. From Alami et al. (2009b). ©IOP Publishing. Reproduced with permission. All rights reserved.

fractions (controlled by the peak target current density JD,peak , as previously described in Section 4.1.4) are shown (Alami et al., 2009b). When using dcMS (i.e. low ionized flux fractions), underdense columnar films are obtained (Fig. 8.8A). Deposition using HiPIMS at JD,peak = 1 A/cm2 (Fig. 8.8B) results in film densification and suppression of the columnar structure, while columns start to grow on existing columns, that is, repeated nucleation occurs; this highlights the use of energetic ions during growth for obtaining globular morphology. This is further emphasized as the peak target current is increased to JD,peak = 4 A/cm2 (Fig. 8.8C), leading to a film with a featureless morphology. From the previous discussion it is evident that the low-energy high-flux ion irradiation during HiPIMS deposition can be used to overcome the characteristically underdense and rough microstructures and obtain morphologies unique for low-temperature deposition. This in turn allows deposition of films with higher hardness (Chistyakov et al., 2007, Paulitsch et al., 2007, Ehiasarian et al., 2004), lower friction coefficient (Ehiasarian et al., 2003, Paulitsch et al., 2007), and improved scratch and wear, and corrosion resistance (Paulitsch et al., 2007, Ehiasarian et al., 2004), as compared to films deposited using conventional low-ionization routes. The effect of large ionized fluxes on film morphology is also present during growth of low-melting-point noble metal films, which typically do not form underdense structures, when deposited at room temperature (see Table 8.1). In this case, metal ions may

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lead to increased adatom mobility, resulting in larger grain sizes (Cemin et al., 2016, Wu et al., 2017) and/or smaller surface corrugation (Sarakinos et al., 2008), which enhances electrical conductivity, compared to dcMS grown films. Besides the changes in the film morphology, the highly ionized fluxes of sputtered material provided by the HiPIMS discharge affect also the film texture, most notably manifested in monolithic and multilayer metal nitrides (Paulitsch et al., 2007, Ehiasarian et al., 2004, Alami et al., 2009b, Del Giudice et al., 2016, Purandare et al., 2008, Ferreira et al., 2016, Greczynski et al., 2010b). A commonly observed trend is that, upon increasing the flux of energetic ions (by adjusting process conditions, such as pulse power and peak discharge current), the preferred crystallographic orientation in metal nitrides that exhibit the B1 NaCl structure changes from (111) to (200). This is consistent with the notion that a more intense energetic bombardment enhances surface diffusion allowing for the adatoms to be accommodated in the (200) planes, which exhibit a lower surface free energy than that of the (111) planes (Patsalas et al., 2004, Hultman et al., 1995). Another class of materials for which HiPIMS deposition can facilitate control of microstructure and texture are transparent conductive oxides, notably Al-doped ZnO (AZO) (Sittinger et al., 2008, Zhang et al., 2016, Mickan et al., 2016). Studies have shown that metal ions generated by the HiPIMS discharge can, in addition to dense and smooth films, lead to a very pronounced c-axis-oriented microstructure (i.e. (0002) crystallographic orientation), which in turn results in an increase of the electrical conductivity (Sittinger et al., 2008, Zhang et al., 2016, Mickan et al., 2016). In this case, the beneficial effect on film texture and structure is not only a result of the ion-induced increased adatom mobility, but also by the ability to stabilize the reactive HiPIMS process in the transition mode (as explained in Section 6.3.1) and, thereby, minimize the impact of negatively charged oxygen ions that are accelerated toward the growing film by the target potential (Mráz and Schneider, 2006, Severin et al., 2007, Tominaga et al., 2006, Ngaruiya et al., 2004) (see also Section 6.4.5 concerning negative ions).

8.4.3 Synthesis of self-organized nanostructures Energetic ions available in HiPIMS also offer a pathway for the synthesis of and microstructure control in self-organized nanocomposite films, that is, films consisting of crystalline phases embedded in an amorphous matrix. Typical material systems that exhibit a strong tendency toward nanocomposite structure formation are transition metal nitrides (e.g. TiN and TiAlN) embedded in an amorphous SiNx matrix (Vepˇrek and Reiprich, 1995, Vepˇrek et al., 1995, Parlinska-Wojtan et al., 2004, Holubar et al., 2000, Fager et al., 2013), which, owing to a combination of high hardness and oxidation resistance, are widely used as wear-resistant coatings in metal cutting applications (Carvalho et al., 2003, Kim et al., 2005). The driving force for the formation of the nanocomposite structure is that transition metal nitride and SiNx phases are immiscible. Hence, in the presence of sufficient atomic mobility, SiNx diffuses and segregates on the transition metal nitride grains, which interrupts the crystal growth process and leads to repeated nucleation and nanocomposite formation (Hultman et al., 2007).

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The required atomic mobility for the segregation process to occur is typically provided by depositing films at elevated temperatures, of the order of 800 K and above (Vepˇrek and Reiprich, 1995, Vepˇrek et al., 1995), but ions can be used as an alternative route to provide the energy required for achieving sufficient atomic mobility during growth. This has been demonstrated by Wu et al. (2015), who used modulated pulsed power magnetron sputtering (MPPMS) to grow TiAlSiN films reactively from a single compound target. They identified process conditions with respect to the content of N2 in the working gas mixture, which allowed formation of a nanocomposite structure at temperature of ∼500 K. They also found that the separation between TiAlN and SiNx phases was complete giving rise to a hardness of ∼33 GPa. Concurrently, Wu et al. (2015) observed that the films exhibited very low residual stress, and hence the high hardness values could be ascribed to the sharp interface between the TiAlN and SiNx phases (Wu et al., 2015). Greczynski et al. (2015) explored this path to deposit TiSiN films reactively from two elemental (i.e. Ti and Si) sources using a hybrid method comprising both HiPIMS and dcMS. In a first set of experiments, they operated the Ti cathode in HiPIMS mode and the Si cathode in dcMS mode, while the opposite configuration was selected in a second set of experiments. This allowed them to generate and study the effect of preferential/selective bombardment of Ti+ and Si+ ions on the growth of TiSiN. They showed that growth under the presence of Ti+ ions leads to a nanocomposite structure, whereas Si+ ions favor the formation of a Ti–Si–N solid solution (see Fig. 8.9). Greczynski et al. (2015) explained their findings in light of differences in momentum transfer. Ti+ ions transfer momentum to the film forming species more efficiently, due to their higher mass (MTi = 47.9 amu, MSi = 28.1 amu), and thereby increase the adatom migration length, which promotes nanocomposite structure formation. On the contrary, Si+ ions are less effective in momentum transfer, causing only rearrangement at the surface and solid solution formation. Another example of a material system that has a tendency for phase segregation and nanocomposite formation is the binary Ti–C system. Samuelsson et al. (2012b) showed that the energetic deposition flux provided by the HiPIMS process, in combination with the ability to stabilize the reactive process in the transition mode, allows us to better control incorporation of C and suppress the tendency for amorphous C matrix formation. This in turn offers a pathway to effectively tune growth evolution and navigate between nanocomposite and solid–solution structure.

8.5 Stress generation and evolution Mechanical stress is crucial for thin film functionality, since it largely determines film adhesion on the underlying substrate (Koch, 1994, Janssen, 2007, Koch, 2010). Stress also affects the physical properties of films and can, for example, be used to tailor the band structure in semiconductors (Koch, 2010), and to modify anisotropic response in magnetic films (Sander, 1999). In the following sections, we briefly review the mechanisms responsible for stress generation and evolution and the way by which these mechanisms are modified by the highly ionized fluxes of the HiPIMS process.

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Figure 8.9 (Left hand side) Plan-view STEM micrograph and EDX/STEM maps of Ti-HiPIMS/SidcMS of Ti–Si–N coatings, showing segregation and formation of a nanocomposite structure. (Right hand side) Cross-section STEM micrograph and elemental EDX/STEM maps of Ti-dcMS/Si-HiPIMS Ti–Si–N coatings showing the formation of a solid solution microstructure. Reprinted from Greczynski et al. (2015), with permission from Elsevier.

8.5.1 Atomistic view on stress generation and evolution A common cause of stress in thin films is differences in thermal expansion between film and substrate materials. This may cause excessive forces at the film/substrate interface, as well as film cracking delamination when the film is deposited at elevated temperatures or is subject to thermal cycling (Doerner and Nix, 1988). Thermal stress is of extrinsic origin, whereas another, often larger, contribution to the total film stress is intrinsic and is generated during film deposition. Intrinsic stress emerges when growth conditions lead to a film volume that deviates from equilibrium, whereas the lateral film dimensions are constrained by the substrate. In particular, a smaller-thanequilibrium volume yields compressive stress, whereas tensile stress develops when growth conditions yield a larger-than-equilibrium film volume. By convention a tensile stress is positive, and compressive stress is negative. In general, stress generation differs between epitaxial and polycrystalline films. In heteroepitaxial film/substrate systems, the deviation from equilibrium volume emanates from film/substrate lattice mismatch. If the lattice spacing of the film is smaller than that of the substrate, then the film will be subjected to tensile strain and hence the film develops tensile stress state. In the opposite case (i.e. film lattice spacing is larger than that of the substrate) compressive stress develops. As the film grows thicker, the strain energy increases up to a point where the film/substrate system relieves strain and lowers its total energy either by nucleation of misfit dislocations at the film/substrate interface or by undergoing strain-induced roughening (also referred to as Stranski–Krastanov growth mode) (Greene, 2010). In polycrystalline thin films deposited from the vapor phase, the origin of intrinsic stress is different, as compared to the case of epitaxially grown films. Moreover, intrinsic stress exhibits a complex dependency on film thickness, closely related with the various stages of morphological evolution, which are described in Section 8.1.1. Typically, a compressive-tensile-compressive stress evolution is observed with increasing thickness, when the mobility of the film forming species (i.e. atoms) is high

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(Koch, 2010, 1994, Abermann et al., 1978, Shull and Spaepen, 1996). Under deposition conditions resulting in low atomic mobility, the final stress state of the film is tensile, that is, a compressive-tensile stress evolution is observed (Koch, 1994, 2010, Doljack and Hoffman, 1972). Irrespective of the atomic mobility during growth, there is a general agreement in the literature that the initial compressive stress results from surface stress, which generates Laplace pressure in small islands leading to a smaller-than-bulk lattice spacing being frozen during island growth (Cammarata et al., 2000). Also, it is widely accepted that the subsequent tensile stress is due to elastic deformation of islands during the coalescence stage (Nix and Clemens, 1999, Freund and Chason, 2001, Rajamani et al., 2002). Finally, in the postcoalescence stage, at conditions of limited atomic assembly kinetics (such as during thermal evaporation of refractory metals), the steady-state tensile stress is caused by attractive forces between grains over grain boundaries (Doljack and Hoffman, 1972, Hoffman, 1976, Janssen et al., 2003), whereas the bombardmentinduced compressive stress is associated with point defects that cause a hydrostatic lattice expansion in the grains (Janssen and Kamminga, 2004, Kamminga et al., 1998, Debelle et al., 2007). This stress contribution is additive with the tensile stress generated in the grain boundaries (Janssen and Kamminga, 2004). The physical origins of the steady-state compressive stress in the postcoalescence regime for high mobility conditions are still under debate. Among the various mechanisms proposed (González-González et al., 2011, 2013, Koch et al., 2005, Spaepen, 2000), the theory that compressive stress is caused by densification of grain boundaries, due to adatom incorporation, has been gaining acceptance (Chason, 2012, Chason et al., 2002, Shin and Chason, 2009, Leib et al., 2009, Pao et al., 2007, Chason et al., 2012, 2014, 2013).

8.5.2 Effect of highly ionized fluxes on stress generation evolution By generating a discharge containing a large number of ionized species with various energies and compositions, HiPIMS offers a route to affect, and potentially even control, the mechanisms responsible for stress generation and evolution in polycrystalline films. Early studies by Ehiasarian et al. (2003, 2004) on the growth of CrN by HiPIMS showed that the films deposited on floating substrates exhibit compressive stress on the order of 2 – 4 GPa. Later studies on other transition metal nitrides (Sáfrán et al., 2009, Machunze et al., 2009, Greczynski et al., 2010a) confirmed the above trends and also showed that, by applying negative voltage potentials on the substrate and thereby increasing the energy of the energetic ionic species impinging on the growing film, compressive stress values as high as ∼11 GPa can be reached (Hovsepian et al., 2014). Systematic scanning of the HiPIMS process parameter space (e.g. pulsing frequency, working pressure, target peak power) showed that growth conditions that lead to an increase of the ion energy and flux to the substrate trigger a transition from tensile to compressive stress in a number of refractory metals and compounds (Magnfält et al., 2013a, Ait Aissa et al., 2014, Lin and Chistyakov, 2017, Samuelsson et al., 2012, Nedfors et al., 2016).

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Figure 8.10 (A) Intrinsic stress σ , (B) stress-free lattice parameter a0 , and (C) mass density ρm of Mo films deposited by HiPIMS on Si(100) substrates at different values of peak target power. The target size was 75 mm in diameter. Reprinted from Magnfält et al. (2013a), with the permission of AIP Publishing.

A widely accepted explanation is that high stress in HiPIMS is the result of ioninduced generation of point defects, which lead to hydrostatic lattice expansion. However, data by Magnfält et al. (2013a) on Mo films showed that hydrostatic lattice expansion is not the reason for stress generation, as the stress-free lattice parameter remains constant at all growth conditions, irrespective of the stress stage in the film as seen in Fig. 8.10A,B. Instead, stress is the result of densification of grain boundaries via adatom insertion, manifested by increase of the film mass density (Fig. 8.10C) and elimination of intercolumnar porosity, which is in line with the microstructure evolution data discussed in Section 8.4.2. The effect of grain boundaries on the stress generation was corroborated by growing Mo films by HiPIMS on various Mo–Si template layers to control the grain size and by extension of the total grain boundary length (Magnfält et al., 2016), showing that the magnitude of the compressive stress

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scales with the inverse of the grain size. Further support to this notion was provided in the study by Cemin et al. (2017a), where polycrystalline and epitaxial Cu films were deposited by HiPIMS at different negative bias voltages applied to Si(001) substrates. Contrarily to common expectations, the compressive stress magnitude was significantly reduced despite the energy increase of the bombarding particles when using HiPIMS and biased substrates (from 0 V to −100 V). This is primarily due to a significant increase of the film lateral grain size (due to increased adatom mobility) and, thereby a reduction of the grain boundary number density, resulting in lower incorporation of excess atoms into grain boundaries and lower compressive stress. As a final note, an alternative route for tuning stress in HiPIMS deposition was presented by Greczynski et al. (2015, 2014) by controlling the type of ionic species and thereby the momentum transfer efficiency during film growth, as explained in Section 8.4. Less efficient momentum transfer, for example, by using Al+ and Si+ ions for growth of TiAlN and TiSiN films, leads to a lower rate of point defect generation and smaller compressive stress, as compared to growth at conditions of efficient momentum transfer using Ti+ ions.

8.5.3 Tailoring of stress in optical coatings by HiPIMS The prospects of HiPIMS, namely synthesis of dense thin films due to high fluxes of energetic particles possibly leading to materials with tailored microstructure and high packing density and hence high environmental stability, have also stimulated research on HiPIMS-deposited optical coatings (OC). Of particular interest is the possibility of enhancing their optical, mechanical, and other functional properties, especially the residual stress that appears to be critical with respect to coating performance and durability including adhesion, curvature of the optical substrate, and other characteristics (Abadias et al., 2018). The relevance of HiPIMS as an appropriate tool for residual stress control is well illustrated in Fig. 8.11. The figure shows the results of an earlier study by KlembergSapieha et al. (2004) of selected low (nL ) and high (nH ) refractive index coatings, namely SiO2 and Ta2 O5 . They performed a systematic comparison of these nH and nL materials fabricated by different complementary OC deposition techniques, namely Ion Beam Assisted Evaporation (IBAD), dcMS, Dual Ion Beam Sputtering (DIBS), Filtered Cathodic Arc Deposition (FCAD), and Plasma Enhanced Chemical Vapor Deposition (PECVD). In comparison, the HiPIMS-deposited films clearly exhibit a lower compressive stress σ compared to the other techniques. In addition, multilayer optical interference filters (OIFs), fully fabricated by HiPIMS, were also found to exhibit significantly lower residual stress levels compared to single layers and other deposition techniques, an effect accompanied by a substantially increased scratch resistance and by a high environmental and long-term stability (Hála et al., 2014). The ability of HiPIMS to facilitate control of stress magnitude in metal oxide films used in OC can be understood in light of studies on the effect of ion energy Ei on OC materials such as Nb2 O5 and Ta2 O5 films prepared by DIBS (Çetinörgü et al., 2009), where energy and flux of film-forming species can be controlled independently. The

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Figure 8.11 Comparison of (optimized) residual stress in low-index (SiO2 ) and high-index (Ta2 O5 ) films prepared by different complementary methods including IBAD, pulsed dcMS, DIBS, and PECVD (see text). The original values for films prepared by HiPIMS are taken from Hála et al. (2014), and for other techniques, from Klemberg-Sapieha et al. (2004). Reprinted from Abadias et al. (2018), with the permission of AIP Publishing.

residual stress σ of DIBS-deposited oxide films was generally found to be compressive, but partial stress relaxation was observed for Ei above about 250 eV. This is in line with Davis’ model (Davis, 1993) for stress generation, according to which energetic species cause compressive stress due to implantation followed by point-defect generation. However, above a certain material-dependent energy threshold, the incoming energetic ions cause annihilation of point defects, resulting in stress relaxation (also known as the “thermal spike” effect). In the case of HiPIMS, energetic species responsible for such a thermal spike can be found among negatively charged O− ions that are accelerated by the large cathode potential toward the growing film (see also Section 6.4.5).

8.6

Phase composition

Materials may form a multitude of crystallographic phases, which exhibit distinctly different physical attributes. One example is the phase formation within the binary Ti–O, system for which the general chemical composition TiO2 may be found in two tetragonal polymorphs, the rutile and the anatase (Wiggins et al., 1996). The rutile phase is characterized by a high refractive index in the visible range of the electromagnetic spectrum, whereas the anatase phase is a UV light photocatalyst. Another example is the Al–O system, which exhibits a number of Al2 O3 polymorphs (Gitzen, 1970), among which corundum (α-Al2 O3 ) is the only thermodynamically stable phase that can retain high hardness, chemical inertness, and transparency at elevated temperatures (Aguilar-Frutis et al., 1998, Lin et al., 1996, Kelly and Arnell, 1999, Dingemans et al., 2010, Benick et al., 2009). From these two examples it becomes evident that control of phase formation and composition is paramount for designing materials tailored to specific applications. Thin film synthesis via vapor condensation proceeds far from thermodynamic equilibrium, as has been highlighted in Sections 8.1 and 8.4. Hence,

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phase formation is governed by a complex interplay between atomic assembly kinetics and composition of the film forming flux. HiPIMS offers a platform for accessing thermodynamically stable phases at lower synthesis temperatures and/or expanding the synthesis window of metastable phases for a wide range of elemental and compound material systems by: (i) providing energetic species that can trigger surface and bulk diffusion processes and cause local densification and intrinsic stress generation; and (ii) using electric fields for controlling the ionized sputtered species and thereby the composition of the film forming flux beyond what is achievable in conventional sputtering-based synthesis techniques. A number of case studies, where these pathways are relevant for controlling phase formation, are highlighted further.

8.6.1 Phase composition tailoring in elemental thin film materials: the Ta case Ta is a material that has been studied repeatedly by HiPIMS over the years. In bulk form, Ta forms a hard material that presents low-electrical-resistivity and forms in bcc crystal structure, also known as the α phase (Clevenger et al., 1992, Face and Prober, 1987). However, in thin films grown via vapor condensation at relatively low temperatures (e.g. room temperature and slightly above), a metastable high resistivity tetragonal phase (β-Ta) is commonly obtained (Clevenger et al., 1992, Face and Prober, 1987). Colin et al. (2017) have shown that phase formation in magnetron sputtered Ta films grown on amorphous or polycrystalline substrates, which do not impose any epitaxial registry upon the film, is governed predominantly by the energetics of nucleation of the two Ta polymorphs. At temperatures below 450 K, nucleation of the metastable β-Ta is favored over the stable α-Ta, whereas the opposite energetic balance prevails above 450 K. They also found that increasing the energy of the film forming species (by an increase of the substrate bias voltage) in discharges characterized by low ionized flux fractions (e.g. dc and rf magnetron sputtering discharges) does not affect phase formation and evolution. This is not the case for HiPIMS deposition, for which studies by Alami et al. (2007) and Lin et al. (2010) have shown that increasing the substrate bias voltage can lead to formation of the thermodynamically stable α-Ta phase. The X-ray diffraction patterns are seen in Fig. 8.12. Although unintentional increase of the substrate temperature during growth due to the intense energetic bombardment cannot be ruled out as contributing reason for the observed phase evolution (Myers et al., 2013). HiPIMS can generate ionized fluxes consisting of up to ∼70% of Ta+ ions (Helmersson et al., 2006), which transfer momentum in a more efficient manner to the growing surface and hence increase adatom mobility without the need for excessive growth temperatures (Dalla Torre et al., 2003), as compared to Ar+ ions, which prevail in conventional sputtering techniques.

8.6.2 Phase composition tailoring in functional oxide films The possibility for HiPIMS to achieve tailored microstructure and crystallinity due to high-energy impact during growth has also led to considerable efforts to fabricate ac-

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Figure 8.12 X-ray diffraction patterns of Ta films deposited by HiPIMS at different values of negative substrate bias voltage. An increasing bias voltage promotes the formation of the thermodynamically stable α-Ta phase up to a critical value upon which the β-Ta phases re-appears. Reprinted from Alami et al. (2007), with permission from Elsevier.

tive optical coatings at low substrate temperature. One example is VO2 films suitable for thermochromic windows having the potential of managing radiative heat transfer in an efficient way. The challenge with thermochromic VO2 is related with a need to apply high deposition temperatures (above ∼700 K), which limits more widespread applicability. Fortier et al. (2014) have demonstrated that by using HiPIMS dense stoichiometric crystalline thermochromic VO2 films can be obtained at lower substrate temperatures (∼600 K) compared to other techniques. These films exhibit a high infrared modulation T , low surface roughness, and lower coloration transition temperatures than the bulk material. The advantage of HiPIMS is illustrated in Fig. 8.13, which displays the T values of a series of as-deposited HiPIMS VO2 films as a function of temperature, and it compares them with the T available in the literature where conventional magnetron sputtering was used for the film growth on glass without a seed layer (Mlyuka et al., 2009, Jin et al., 1997, Sobhan et al., 1996, Granqvist, 2007). The feasibility to fabricate active thermochromic films at low temperatures below 300◦ C stimulates further applications such as deposition of durable VO2 onto plastic substrates (e.g. suitable for retrofitting existing windows) (Loquai et al., 2016, 2017) or the fabrication of thermochromic low-emissivity windows that combine HiPIMS deposited VO2 with silver layers surrounded by SiN1.3 to ensure an antireflective effect (Baloukas et al., 2018). Further studies in this category of materials include a detailed analysis of the HiPIMS effects to deposit VO2 films at low temperature (Aijaz et al., 2016), the use of a gas injection device that ensures cleanliness of the target in the reactive HiPIMS environment to achieve high deposition rate (Houska et al., 2017) and durable HiPIMS indium tin oxide (ITO) transparent conductive films with enhanced flexibility (Sittinger et al., 2008).

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Figure 8.13 Infrared modulation between the hot and the cold state, T2500 nm , for HiPIMS-deposited thermochromic VO2 films as a function of temperature. For comparison, results from the available literature are also included for cases where no seed layer has been used. Reprinted from Fortier et al. (2014), with permission from Elsevier.

Other materials for which ion-induced adatom mobility and subplantion allow for phase composition tailoring include oxides such as Al2 O3 (Wallin et al., 2008) and TiO2 (Alami et al., 2009a, Konstantinidis et al., 2006, Agnarsson et al., 2013). The experimental conditions for anatase TiO2 preferential growth are poorly explored (rutile TiO2 is commonly obtained by standard HiPIMS); however, they were investigated in a recent paper by Cemin et al. (2018). They showed that sputtered Ti ions do not need to be accelerated to high energies to allow anatase growth, that is, no substrate bias is required, although small target-to-substrate distance and moderate working gas pressure are needed to preserve the kinetic energy of these ions at ∼20 eV. Moreover, the pulse peak current density on the Ti target should be maintained at moderate levels to limit the intensity of the ion bombardment at the substrate. At such conditions, grain renucleation is less likely during film growth, whereas adatom mobility is enough to allow grain growth in some cases. These results show the complex interplay of process parameters and film structural properties in reactive HiPIMS and highlight the importance of process optimization especially when using low-to-medium energy ion bombardment.

8.6.3 Phase composition tailoring in metastable ternary ceramic films The benefit of metal–ion bombardment as opposed to bombardment by working gas ions has also been demonstrated for more complex systems, that is, compounds consisting of transition metal nitrides and AlN (Greczynski et al., 2012, 2017). These ternary compounds form a metastable solid solution in the NaCl crystal structure, which is characterized by high hardness (typically above 30 GPa) (Rovere et al., 2010). However, there is a maximum limit in the solubility of AlN in the NaCl crystal structure, above which the equilibrium wurtzite-AlN phase precipitates leading to deterioration of the mechanical properties. Greczynski et al. (2012, 2017) deposited these compounds reactively from two spatially separated metal targets (transition metal and Al) using the hybrid approach described in Section 8.4; one of the targets was pow-

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Figure 8.14 Hardness of Ti–Al–N coatings grown using Al-HiPIMS/Ti-dcMS (black squares) and TiHiPIMS/Al-dcMS (hollow circles) configurations. Reprinted from Greczynski et al. (2012), with permission from Elsevier.

ered by HiPIMS pulses, whereas the other was fed by dc power. A negative bias was applied to the substrate synchronized with the HiPIMS pulse to selectively collect and accelerate metal ions, instead of Ar+ ions, toward the growing film (see Section 2.3.2 for further discussion on synchronized bias). One material system studied is Ti–Al–N (Greczynski et al., 2012), for which it was found that Al+ ions (generated by operating the Al cathode in HiPIMS mode) with energy of the order of ∼70 eV allow growing films with the NaCl crystal structure containing up to ∼65 at.% Al. On the other hand, the maximum Al solubility in the NaCl TiAlN phase when the Ti target was operated by HiPIMS was found to be ∼40 at.%. This is because a HiPIMS-fed Ti cathode generates not only singly, but also doubly ionized Ti species and sometimes even higher charge states (Andersson et al., 2008). These then impinge with twice the energy (as compared to singly charged Al+ ions) on the growing film, providing an excess energy that drives the segregation of the wurtzite AlN phase (see also Section 4.1.3.3 for more detail on the ion fluxes for these systems). The effect of the differences in the solubility limit of AlN is illustrated in Fig. 8.14, where higher hardness values over a larger AlN composition range are obtained for films grown using Al+ ions, as opposed to their counterparts grown in the presence of Ti+ /Ti2+ ions. Another example is the VAlN system (Greczynski et al., 2017). In this case, generation of periodic high fluxes of Al+ ions (HiPIMS operating cathode) accelerated by a negative substrate potential of 300 V toward the growing film, together with a continuous flux of V neutrals (cathode fed by dc power), leads to Al subplantation into a VN-rich phase, which drives incorporation of up to ∼75 mol% of AlN in the NaCl-type VAlN lattice. This is to be compared to the case where AlN and VN are dc co-sputtered, which reduces the Al solubility limit to ∼52 at.%.

8.6.4 Phase formation tailoring via control of chemical composition In HiPIMS discharges, part of the ions moves along the off-normal axis with respect to the target, as explained in Section 4.1.2, when studying radial ion transport above a cylindrical target. This abnormal ion transport results in differences in the flux, en-

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Figure 8.15 X-ray diffraction patterns of Ti–Si–C films deposited on MgO(111) substrates by HiPIMS on substrates oriented (A) parallel and (B) perpendicular with respect to the target surface. The hollow circles and the filled squares indicate the position of the peaks in bulk TiCx and Ti5 Si3 Cx phases, respectively. Reprinted from Alami et al. (2006), with permission from Elsevier.

ergy, and composition of the deposited and bombarding species as function of the deposition angle (Lundin et al., 2008, 2009). Substrates placed perpendicularly to the target surface are subjected to deposition fluxes with ion-to-neutral ratios higher than those on parallel oriented substrates (Alami et al., 2005). In addition, the total energy flux due to all species (electrons, ions, neutrals) impinging on perpendicularly oriented substrates are, on average, lower than those along the target normal (Lundin et al., 2009). Another implication of the high ion-to-neutral ratios is that, in the case of compound targets, the composition of the material flux along off-normal directions is largely determined by the ionization fraction of the target’s constituent elements (Alami et al., 2006). This composition is different from that along directions close to the target normal, which is also influenced by the angular distribution of the neutral species (see Sections 4.1 and 4.2 for visualization of the ion and sputtered neutral fluxes, respectively). The effect of the deposition angle on the phase composition has been studied for the ternary system Ti–Si–C (Alami et al., 2006). This combination of elements is technologically interesting, since it can allow for the formation of the socalled MAX phases, which exhibit an attractive combination of metallic and ceramic properties (Eklund et al., 2010). Regarding the composition of the deposited material, sputtering of light elements, like C, along the target normal is favored at the expense of heavier elements, such as Ti and Si, whereas lighter elements scatter far more effectively to off-normal directions (larger scattering angles) in collisions with the process gas (Neidhardt et al., 2008). Compositional changes, when simultaneously depositing both light and heavy elements, are therefore dependent on both pressure and distance, where typically films deficit of heavy elements, such as Ti, are found at low pressures and short distances when depositing along the target normal (Neidhardt et al., 2008). On the other hand, substrates placed at an angle of 90◦ with respect to the target generally experience a lower flux of C due to limited gas scattering at low pressure in combination with a lower ionization probability of C compared to Ti and Si (i.e. reduced attraction of C+ ions using a substrate bias) (Alami et al., 2006), leading to the formation of the Nowotny’s Ti5 Si3 Cx MAX phase as seen in Fig. 8.15.

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Figure 8.16 Time evolution of Ag+ flux in a HiPIMS Ar–Ag discharge. The temporal profile of the flux is consistent with the discharge pulsing frequency. From Magnfält et al. (2013b). ©IOP Publishing. Reproduced with permission. All rights reserved.

8.7 Time-domain effect of HiPIMS on film growth The pulsed character of the HiPIMS processes provides a pathway for generating temporally modulated deposition fluxes. This feature of HiPIMS was first studied by Mitschker et al. (2012), who developed a method that comprises the use of a shutter with an opening of 200 µm rotating synchronously with the HiPIMS pulse in front of the substrate. Such an arrangement generated a thickness profile on the substrate from which the temporal profile of the deposition flux during Ti and TiN growth could be extracted (Mitschker et al., 2013a,b). It was found that the deposition flux reaches its maximum during the pulse and rapidly decays after the pulse with a time constant of ∼100 µs. This behavior was later confirmed by Magnfält et al. (2013b) in Ar– Ag HiPIMS discharges by means of time-resolved mass spectrometry measurements and Monte-Carlo particle-transport simulations. They also showed that the temporal profile of the deposition flux can be controlled by the HiPIMS pulse energy and pulsing frequency, as shown in Fig. 8.16. Hence vapor fluxes characterized by deposition rates up to three orders of magnitude larger as compared to the average deposition rate could be generated while independently controlling the relaxation time between material pulses. These features of HiPIMS were leveraged by Lattemann et al. (2010), who synthesized fully dense, (111)-textured, and nonfaceted TiN films in the absence of external heating and without applying a negative substrate bias potential. The high instantaneous rate during the HiPIMS pulse leads to a high island density (small islands) and, as the deposition continues, to rapid coalescence of islands (as explained in Section 8.1.3). This results in a spatially limited region in which (111)-oriented grains overgrow their (100) counterparts. Concurrently, the presence of moderate-

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energy/high-flux ion bombardment by Ti+ ion and N+ ion species, and the long relaxation times between vapor pulses drive the elimination of intercolumnar porosity and film densification. The effect of the time-domain of the pulsed deposition flux on the growth dynamics of Ag films was studied by Elofsson et al. (2014). By combining in situ monitoring of film growth, by means of spectroscopic ellipsometry, growth simulations, and ex situ real-space imaging, they found that the temporal profile of the pulse flux controls the competition between island growth and coalescence rate and thereby final film morphology. Another aspect related to the pulsed character of HiPIMS is the ability to generate multiatomic fluxes from spatially separated sources as discussed in Section 2.4. Elofsson et al. (2016, 2018) and Magnfält et al. (2017) showed that such pulses enable control over atomic arrangements across multiple length scales in multinary metal–metal and metal–ceramic systems, highlighting a new path for the synthesis of functional multicomponent films.

8.8 Summary The ionized fluxes generated by HiPIMS can easily be manipulated using electric fields and, thereby, deposit uniform films on nonflat substrates. Electric fields can also be used to tune the energy of ions and treat the film/substrate interface, which in turn can enhance film adhesion and improve the crystallographic quality of epitaxially grown films. Ion irradiation by means of HiPIMS can also be applied during film growth. When this happens, the atomic-scale processes that govern film formation are affected in a way that yields film densification, deposition of smoother films, and suppression of columnar microstructure. The results of these changes are films with better functional properties, including improved hardness and higher electrical conductivity. Growth under conditions of intense energetic bombardment is typically associated with generation of high compressive stress. HiPIMS deposited films are not an exception, even when no substrate bias is applied during deposition. This stress is predominantly generated by bombardment-induced densification of grain boundaries. This is contrary to conventional deposition methods, in which working gas ions prevail, whereby stress is generated in the grains due to bombardment-induced point defects. Hence stress in HiPIMS films may be reduced, relative to films deposited by dcMS, if growth conditions that lead to increase of grain size and elimination of grain boundaries prevail. Another possibility that HiPIMS offers is control of phase composition, where energetic metal ions promote nucleation and growth of thermodynamically stable and/or metastable phases in elemental and compound systems. Besides high ion densities, HiPIMS generates a pulsed deposition flux characterized by large instantaneous deposition rates during the pulse on-times. This provides an additional handle for controlling nucleation dynamics and thereby film morphology and texture. Finally, the time-domain character of HiPIMS offers the possibility to generate multicomponent

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fluxes with submonolayer modulation, which opens a new dimension for the synthesis of compositionally complex materials.

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Index

A Abnormal glow discharge, 4 Accelerated plasma electrons, 112 Advanced HiPIMS configurations, 69 Afterglow, 98, 121, 135, 291, 321 AlN sputtering, 253 Aluminum target, 17, 177, 288 Anode, 2, 5, 6, 10, 14, 22–25, 52, 55, 59, 69, 70, 72, 82, 103, 284, 295 cold, 10 dark, 6 glow, 6 grounded, 285 magnetron, 62 ring, 280 shields, 25 side, 5 surface, 24 zone, 22 Anomalous collisions, 290 Argon dc discharge, 6 discharge, 50, 134, 135, 247, 268 ionization, 208 ions, 12, 167, 169, 173, 177, 268, 272 neutrals, 12 Atomic absorption spectroscopy (AAS), 121 Atomic ions, 127 Atomic sputtering, 18, 238, 239 Automotive applications, 32 Azimuthal plasma structures, 160 B Beamlike electrons, 94 Biased substrates, 353 Binary collision, 150, 187 Binary collision approximation (BCA), 234 Bipolar HiPIMS, 321 Bipolar pulsed discharges, 33 Bulk plasma, 25, 99, 127, 148, 166, 169, 171, 282, 284, 312

C Capacitive plasma load, 66 Carbon target, 278, 320 Cathode current densities, 50 cylindrical, 64 dark, 5, 6, 22, 23 fall, 6, 23, 131, 182, 188, 316 glow, 2, 5 magnetron, 52, 55, 56, 58, 59, 62, 72 sheath, 2, 4–6, 10, 23, 35, 99, 173, 182, 189, 198, 200, 204, 211, 213, 231, 256, 288, 289, 293, 316, 317 sheath edge, 26 spots, 4 surface, 4, 5, 13, 17, 22, 24, 189, 288 target, 1, 2, 11, 18, 23, 25, 26, 30, 31, 34, 97, 126, 168, 299 target material, 297 voltage, 14, 52, 56, 61, 82, 96, 112, 134, 135, 138, 201, 212 Chemical ionization, 113 Chopped HiPIMS, 74 Circular magnetron target, 280 planar magnetron, 292, 294, 319 Clean metal target, 251 Cold anode, 10 argon neutrals, 169 electron, 93, 172, 175, 282 substrate, 335 Collective plasma effects, 123 Collisional radiative model (CRM), 190, 208 Collisionless plasma, 84, 85 Compositional variations, 269 Compound mode, 117, 137, 225–227, 235, 247–250, 253, 255, 280, 323 mode transition, 226

376

sputtering, 232 targets, 18, 349, 359 Computer simulations, 170 Conductive targets, 34 Configurations, 26, 30, 100, 101, 178 discharge, 300 hybrid, 38 magnetron sputtering, 30 Continuous IEDF, 211 Continuous sputtering, 32 Conventional dcMS, 25, 51, 63, 92, 164, 208, 265, 273, 285, 297, 319 dual HiPIMS, 104 HiPIMS process, 98 planar magnetrons, 27 sputtering processes, 346 sputtering techniques, 339, 355 Copper ions, 139 Crystallographic orientations, 334, 346 Cylindrical cathode, 64 hollow cathode, 24 magnetron, 30 target, 31, 51, 358 D dc discharge, 2–4, 8, 23, 72, 179 argon, 6 glow discharge, 2, 4–6, 10, 11, 22, 23, 288 magnetron discharge, 73 magnetron sputtering, 25, 160, 162, 288 sputtering, 2, 23, 34, 232 dcMS conditions, 29, 251, 314 conventional, 51, 164, 208, 265, 273, 285, 297 critical, 241 deposition, 256, 315, 320, 344 discharges, 30, 56, 124, 142, 147, 177–179, 186, 189, 212, 244, 296, 300, 304, 312 experiments, 231 grown films, 348 levels, 38 limit, 39 mode, 212, 304, 349

Index

operation, 51, 247, 250, 285 pulsed, 39 range, 39, 51, 272 reactive, 129, 232, 237, 323 regime, 213, 266 studies, 256 Deep oscillation magnetron sputtering (DOMS), 51, 321 Density discharge current, 23, 33, 96, 106, 276, 295, 296, 311 distributions, 141, 144 HiPIMS plasma, 207 neutrals, 183 perturbations, 298 Deposition, 250 conditions, 149, 323, 351 dcMS, 344 HiPIMS, 103, 241, 344 reactive HiPIMS, 249 sputter, 2, 22, 23 Difference frequency (DF), 310 Diffusion region (DR), 161, 180 Diode sputter sources, 22 Direct simulation Monte Carlo (DSMC), 146, 184, 186 Discharge argon, 50, 134, 135, 247, 268 axis, 8 capacitor, 52 characteristics, 198, 201, 226, 240, 250, 276 conditions, 94, 98, 133, 192, 212, 269, 304 configurations, 300 current density, 23, 33, 96, 106, 276, 295, 296, 311 evolutions, 287 peak, 133, 134, 286 pulse, 96, 150 waveforms, 38, 58, 96, 160, 195, 198, 247–249, 269, 270, 280, 286 dc, 2–4, 8, 72, 179 dc glow, 2, 4–6, 10, 11, 22, 23, 288 dc voltage, 28 emission, 286 gap, 6 gas, 2 hollow cathode, 166

Index

ignition, 203 kinetics, 141 magnetron, 25, 32, 52, 54, 58, 62, 73, 166, 189 model, 165, 230 operation, 268 parameters, 28, 163, 165, 187, 193, 196, 296 physics, 2, 4, 8, 11, 20, 230 plasma, 71 power, 103, 124, 126, 136, 196, 287, 301 pre-ionized, 50, 204 pressure, 230, 315 process, 28, 173 properties, 230, 268 pulse, 65, 69, 91, 93, 96, 99, 102, 119, 121, 127, 130, 131, 136, 195, 198, 253, 255, 269, 280 regimes, 50, 162, 179, 212, 269 species experience, 118 stability, 104, 135 target, 37 volume, 63, 104, 121, 144, 145, 166, 170, 205, 298 Doubly charged ions, 13, 114, 287, 314 Dual ion beam sputtering (DIBS), 353 Durable HiPIMS, 356 E ECWR-HiPIMS hybrid, 137 Electrical discharge, 187, 189 Electrically grounded substrates, 344 Electron cyclotron drift instability (ECDI), 300 Electron cyclotron wave resonance (ECWR), 98, 103, 105, 106, 137 Electron distribution function (EDF), 14 Electron energy distribution function (EEDF), 14, 15, 84–86, 88, 90, 91, 95, 98, 116, 173, 184, 189, 190, 199, 208, 278, 287 Electron energy probability function (EEPF), 15 Electrons cold, 93, 172, 175 collisions, 20, 85 energetic, 26, 190, 287, 306 energy distributions, 202

377

ionization, 19, 20, 25, 35–38, 121, 127, 134, 136, 138, 142, 147, 174, 175, 177, 186, 191, 192, 208, 282–284, 287, 293 Ohmic heating, 289 plasma, 16, 81, 86, 103, 105, 106, 112, 116, 117, 134, 172, 209, 213 populations, 14, 98, 172, 173, 208, 209, 211 sheath acceleration, 288 Energetic electrons, 26, 190, 287, 306 ions, 211, 230, 236, 256, 308, 311, 337, 343, 344, 346–348, 354 neutrals, 126 sputtered atoms, 282 Energy balance equations, 160, 165 Energy resolutions, 113 Enhanced ionization, 24, 298, 301, 305 F Field equations, 178 Filtered cathodic arc deposition (FCAD), 353 Floating substrates, 99, 351 Flowing plasmas, 86, 87 Fractions, 117, 135, 139, 160, 253, 275, 276, 347, 355 G Gas ions, 167, 357, 361 neutrals, 141 rarefaction, 96, 125, 146, 147, 149, 150, 165, 169, 172, 177, 179, 183, 187, 241, 243, 245, 246, 253–255, 283, 284, 291, 318 Generalized recycling model (GRM), 272 Glow discharge, 1, 4, 5, 14, 15, 19, 20, 22, 24, 50, 280 Gradual discharge, 66 Graphite target, 98, 170 Grounded anode, 23, 285 substrates, 99 Growth conditions, 224, 334, 344, 350–352, 361 H Heat sensitive substrates, 31 Helium plasma, 296

378

High power pulsed magnetron sputtering (HPPMS), 37, 39 HiPIMS afterglow, 98 applications, 51 conditions, 141, 251 deposition, 103, 241, 344 rates, 315 device, 203 discharge, 126, 252 current, 101, 102, 269, 321 voltage, 68, 73 effects, 356 etching, 342 experiments, 246 hardware, 64 hybrid, 104, 137 IRM, 284 limit, 39, 266 mode, 212, 349, 358 operation, 51, 57, 73, 97, 289, 304, 319, 322 peak discharge, 96 period, 179 phenomenon, 188 PIC simulations, 179 plasma, 73, 84, 91, 202, 252, 287, 301 density, 207 dynamics, 160 parameters, 304 pulse, 98, 106, 123 power, 71, 314 pre-ionized, 38 process, 66, 137, 146, 236, 241, 340, 344, 349, 351, 360 pulse duration, 95 pulse energy, 360 pulser, 61, 68, 75 range, 39, 51, 269, 272 rates, 74, 320 reactive, 74, 102, 106, 127, 129, 130, 143, 227, 229, 230, 240, 241, 243–246, 249, 255, 256, 323, 348, 356, 357 regime, 177, 201, 212, 213, 266, 289, 315 repetition frequency, 140, 179 sources, 55, 137 substrate bias voltage pulse, 68 system, 133

Index

technique, 56, 322 units, 103 Hollow cathode, 24 cylindrical, 24 discharge, 166 lamp, 121 magnetron, 30, 50 Homogeneous plasma, 26, 294 Hybrid configurations, 38 ECWR-HiPIMS, 137 HiPIMS, 104, 137 sources, 98, 103, 106 technologies, 103 sputtering system, 138 I Impinging ions, 114, 236, 337 Indium tin oxide (ITO), 356 Inductively coupled plasma (ICP), 103, 132 Industrial applications, 30 Industrial HiPIMS sources, 55 Inelastic collisions, 20, 22, 172, 174, 175, 190 Instantaneous deposition rates, 361 discharge power, 126 HiPIMS power, 212 Interstitial positions, 337 Inverted magnetron, 30 Ion argon, 12, 169, 173, 268, 272 energetic, 230, 236, 256, 308, 311, 337, 343, 344, 346–348, 354 gas, 357 incident, 112 metal, 13, 127, 129, 132, 133, 135, 167, 173, 175, 192, 246, 248, 253, 268, 278, 283, 287, 305, 317, 321, 342, 347, 348, 358, 361 plasma, 111, 112, 116, 211 plasma frequency, 85 reactive gas, 229, 236, 253 target, 160, 161, 163–165, 192, 193, 305, 311 titanium, 249, 267 Ion energy distribution function (IEDF), 112, 115, 123, 124, 126, 127, 129–132, 211, 253, 298, 314

Index

metal ions, 131, 314 Ion sound (IS), 192, 310 Ionization argon, 208 avalanches, 6 cage, 114 chamber, 113 coefficient, 8 degree, 172, 212, 289 efficiency, 268 electrons, 192 energy, 13, 22, 140, 208, 268, 269, 309 flux fraction, 133, 138, 140 fraction, 23, 139, 141, 194, 202, 266, 318 frequency, 174, 186 losses, 148, 149, 282 mechanisms, 160 metal, 186, 206 methods, 113 neutrals, 188 peak value, 209 potential, 12, 134, 175, 177, 284 probability, 35, 136–138, 195, 206, 320 processes, 6, 9, 288 rate, 174, 287 rate coefficients, 173 sputtered metal, 184 target material, 193 threshold, 22, 194 zones, 30, 122, 126, 301, 305, 306, 308, 314 Ionization region (IR), 26, 160, 166, 196 Ionization region model (IRM), 147, 165 Ionized density fractions, 268, 344 sputtered atoms, 311 material, 35, 112, 246, 287, 317 metal, 193 species, 123, 126, 127, 248, 290, 317, 321 species target, 192, 317 target material, 193 Ionized physical vapor deposition (IPVD), 37, 64 Ionizing collisions, 6 Ionizing electrons, 24 IRM predictions, 196

379

L Lighter ions, 113 Lighter target materials, 292 Limitations, 81, 165, 179 Local plasma, 300 Local plasma perturbations, 82 Luminous torus shaped plasma, 24 M Macroscopic discharge field, 310 Magnetic fluctuations, 313 presheath, 99 trap, 99, 118, 121, 142, 160, 163, 179, 182, 202, 204, 212, 213, 269, 320–322 Magnetron, 28, 37, 50, 59, 62, 71–73, 99, 103, 106, 168, 311, 320 anode, 62 assembly, 106 cathode, 32, 52, 55, 56, 58, 59, 62, 72, 73 configuration, 320 damage, 37 discharge, 25, 32, 52, 54, 58, 62, 73, 166, 189 discharge currents, 55 hollow cathode, 30, 50 plasma, 59, 132 pulsed, 37, 50, 53 rotatable, 27 sources, 68 sputter, 24, 170 target, 25, 38, 51, 55, 57, 61, 64, 70, 73, 94, 95, 104, 112, 118, 121, 123, 130, 142, 144, 302, 320 Maxwellian EEDF, 175 MCC simulations, 183, 204, 211, 282, 293 Metal cathode, 5, 33 deposition rate, 34, 35 ion, 13, 127, 132, 133, 135, 167, 173, 175, 192, 246, 248, 253, 268, 278, 283, 287, 317, 321, 342, 347, 348, 358, 361 ion IEDF, 314 ionization, 186, 206 neutrals, 167, 185 sputtered, 190, 191, 202, 208, 225, 226, 243, 245, 268, 314 target, 13, 34, 223, 241, 357 Metallic ions, 165

380

Metastable, 141, 167, 281, 282, 285, 287 Microwave surfatron discharge, 106 Model calculations, 192 Modulated pulse power magnetron sputtering (MPPMS), 38, 51, 321 Momentum exchange collisions, 169 Monoenergetic ions, 111 Monte Carlo algorithm, 184 Monte Carlo collision (MCC), 184 Monte Carlo simulations, 141, 160, 184, 187, 293 Multicathode configurations, 69 Multiple target, 103 Mutual collisions, 186 N Negative ions, 22, 129, 130, 228, 230, 256, 348 Neutrals, 14, 23, 37, 114, 116, 117, 133, 140, 141, 169, 170, 178, 183, 184, 186, 191, 195, 206, 284–286, 291, 295, 305, 314, 316, 320, 358, 359 argon, 12 bombarding, 11 density, 183 energetic, 126 gas, 141 ionization, 188 metal, 167, 185 plasma, 141 populations, 168 sputtered, 19, 35, 121, 124, 141, 285, 291, 292 sputtered Ti, 141 target, 316 Nitrogen discharge, 50 Non-reactive HiPIMS, 102, 247, 316 Nonflat substrates, 361 O Ohmic heating, 28–30, 165, 173, 198, 278, 288, 289, 292, 294, 295 Operation HiPIMS, 97 Optical coatings (OC), 353 Optical interference filters (OIF), 353 Optimized deposition conditions, 102 Optimum growth conditions, 249 Oscillations, 192, 298–300 Oxidized sputter target, 251

Index

Oxidized targets, 232, 255 Oxygen discharge, 230 Oxygen ions, 230, 256, 348 P Parallel oriented substrates, 359 Partial sputter, 233, 234 Particle collisions, 185 Peak power density, 38, 269 pulse discharge currents, 96 target power density, 51 Penning ionization, 25, 141, 143, 172, 174, 175, 191, 282 Perturbations, 298, 311 Photo ionization, 113 Physical vapor deposition (PVD), 1, 337 PIC simulations, 186, 293, 298 PIC simulations HiPIMS, 179 Plasma afterglow, 121 anisotropy, 105 behavior, 165, 183, 314 boundaries, 15 breakdown, 9, 55 buildup, 106 bulk, 7, 15, 28, 90, 99, 126, 127, 129, 130, 162, 164, 295 cathode, 322 characteristics, 69, 202 chemistry, 130, 166, 167, 175 composition, 301, 304 conditions, 66, 90, 102, 185, 316 deconfinement, 212 diffusion, 74 dynamics, 289 electrons, 16, 81, 86, 103, 105, 106, 112, 116, 117, 134, 172, 209, 213 emission, 123, 303 evolution, 131 expansion, 94, 95 generation, 4, 73 ignition, 58 impedance, 53, 56, 72, 73, 75 instabilities, 14, 86, 90, 122, 123, 160, 183, 191, 192, 266, 296, 300, 302 ions, 111, 112, 116, 211 kinetics, 207 magnetron, 59, 132 mixture, 124

Index

modeling, 184 neutrals, 141 parameters, 6, 15, 82, 85, 86, 88, 90, 91, 93–95, 106, 178, 179, 196, 202, 204, 294 penetration, 112 perturbed potential, 191 phase, 184 phenomenon, 300 physics, 2, 184 potential distribution, 309 oscillating, 303 pre-ionized, 204 processing applications, 23 properties, 14, 66 pulse, 91, 92, 94, 95, 98, 99, 101, 102, 117–119, 121, 122, 136, 141, 143 pulse afterglow, 121 pulse initiation, 98 quasineutrality, 15 region, 291 scales, 296 sheaths, 15 species, 118, 160, 199, 287, 305 structures, 300 volume, 112, 118, 121, 160, 181, 182, 184, 209, 285, 321 wave, 191 zone, 32 Plasma enhanced chemical vapor deposition (PECVD), 353 Plastic substrates, 356 Poisoned magnetron target, 55 Polycrystalline substrates, 355 Populations electrons, 14, 98, 172, 173, 208, 209, 211 Populations neutrals, 168 Power density, 37, 39, 50, 51, 164, 193, 266, 303, 304, 306, 311, 314, 315 Power density peak, 38, 269 Power density target, 25, 160, 193 Pre-ionization, 63, 71, 121, 179, 201, 204, 280 Pre-ionized discharge, 50, 204 HiPIMS, 38, 50, 247 Predominantly ions, 316

381

Preferential sputtering, 34, 232, 233, 235, 245, 253 Process conditions, 344, 349 Pulsed HiPIMS bias, 130 hollow cathodes, 50 magnetron, 32–34, 37, 39, 50, 52, 53, 166, 179 substrate bias, 64 Q Quadrupole mass spectrometer (QMS), 114 Quartz crystal microbalance (QCM), 112, 116 Quasineutral plasma, 5, 188 R Race track target, 26, 92, 121, 122, 146, 256, 280, 282, 284, 285, 290, 292, 320 Reactive atomic gas ions, 127 dcMS, 129, 232, 237, 323 gas atoms, 224, 238, 253 flow, 224–227, 239, 244, 246, 249 inlet, 246 ions, 229, 236, 253 molecules, 238, 239 pressure, 227 sticking, 252 magnetron sputter deposition, 223, 224 magnetron sputtering, 241 plasmas, 102 sputter process, 250 sputtering, 32–34, 36, 106, 117, 127, 137, 223, 226–229, 231, 232, 236, 237, 244, 253, 256 Rectangular magnetron, 320 Recycling, 272, 274 Region of interest (ROI), 118 Remnant plasma, 103 Repel plasma electrons, 117 Resonant plasma excitation, 105 Retarding field energy analyzer (RFEA), 112, 115 Rotatable cylindrical magnetron target, 32 magnetron, 27 targets, 32

382

S Segmented target, 311 Sheath, 10, 23, 27, 28, 84, 85, 88, 90, 93, 94, 163, 171, 173, 175, 209, 211, 288–290, 294, 306, 322 acceleration, 198, 288 cathode, 2, 4–6, 10, 23, 35, 99, 173, 182, 189, 198, 200, 204, 211, 213, 231, 256, 288, 289, 293, 316, 317 edge, 90, 93, 171, 290 electron energization, 15 energization, 165, 173, 288, 289 potential, 10, 173 region, 6, 7 space charge, 82, 88 thickness, 2, 6, 10, 11, 88, 90 voltage drop, 2, 11 Sideways deposition rate, 319 Sideways IEDFs, 314 Silicon substrate, 339 Single magnetron mode, 71 Spokes, 126 evolution, 305 ionization zone, 306 Sputter, 17, 33, 34, 161, 166, 168, 226, 232, 234, 235, 251, 273, 278, 284, 319 activity, 24 applications, 20, 22 deposition, 2, 22, 23 distribution, 322 energy distribution, 317 magnetron, 24 power efficiency, 23 process, 18, 225 pulsed magnetron, 52 rate, 18, 224, 315, 319 source, 22 surface, 24 target, 11, 18, 23, 37, 127, 223, 225, 227, 235, 237, 238, 245, 250, 256 target atoms, 274 target surface, 224–226, 238, 240, 249, 250, 253 wind, 168, 183, 291 Sputtered atoms, 2, 18, 19, 23, 25, 132, 142, 187, 188, 282, 293 atoms ionization, 317

Index

atoms ionization rate, 138 atoms ions, 138 elements, 284 energy distribution, 317 flux, 287 material, 13, 19, 25, 36, 37, 64, 71, 125, 138, 160, 163, 188, 189, 272, 281, 284, 286, 291–293, 299, 311, 316, 340, 348 metal, 190, 191, 202, 208, 225, 226, 243, 245, 268, 314 atoms, 25, 38, 185, 186, 207, 212 ionization, 184 ions, 129, 305 species, 319 neutrals, 19, 35, 121, 124, 291, 292 particle, 25, 169, 285, 316 particle density, 284 precursor, 223 region, 168 species, 124, 141, 145, 146, 148, 160, 169, 170, 179, 185, 239, 278, 311 species ionization, 121 target atoms, 164, 273, 284 atoms ionization, 163 material, 161, 162 species, 162 titanium, 168, 186, 291, 317 ionization, 35 ions, 357 neutrals, 141 neutrals density distributions, 141 vapor, 37, 319 Sputtering compound, 232 event, 25, 317 experiments, 234 gas atoms, 146 metal, 226 metal ions, 13 process, 18, 131, 250, 293, 321 pulsed magnetron, 33, 34, 37 reactive, 32–34, 36, 106, 117, 127, 137, 223, 226–229, 231, 232, 236, 237, 244, 253, 256 system, 23, 103, 104 target, 34, 239, 244 target surface, 231, 236, 245, 246

Index

Stable discharge, 104 sputtering operation, 286 weakly ionized discharge, 51 Stepwise ionization, 165, 208 Striations, 5, 300 Structure zone models (SZM), 345 Substrate bias, 31, 64, 66, 68, 130, 357, 359, 361 current, 36 potential, 360 cold, 335 current, 65 etching tool, 342 holder, 23, 319 interface, 340–343, 350, 361 lattice, 335 materials, 224, 350 normal, 340 position, 91, 92, 94, 314, 317 potential, 358 region, 320 surface, 237, 238, 333–336, 338 surface coverage, 239 system, 350 temperature, 224, 335, 345, 356 vicinity, 25, 31, 91, 92 Sum frequency (SF), 310 Superimpose dual HiPIMS, 73 Superthermal electrons, 93 Surfatron discharge, 106 Synchronized pulsed HiPIMS bias, 68 T Target area, 198, 238, 244, 251, 266, 269, 273, 280 atoms, 17, 168, 279 cathode, 1, 2, 11, 18, 23, 25, 26, 30, 31, 34, 97, 126, 168, 299 center, 121, 138, 309, 321 changes, 224 cleaning, 241 compound coverage, 323 cooling, 251 current, 160, 319, 347 discharge, 37 dynamics, 247 fractions neutrals, 164

383

ions, 163, 305, 311 magnetron, 25, 38, 51, 55, 57, 61, 64, 70, 94, 95, 112, 118, 121, 123, 130, 142, 144, 302 magnetron sputtering, 13, 160 material dependent, 17 ionization, 193 ions, 160, 161, 164, 165, 192–194 metal, 13, 34, 223, 241, 357 neutrals, 316 normal, 16, 359 oxidation, 241 poisoning, 18, 23, 34, 250, 252 potential, 11, 14, 130, 256, 348 power density, 25, 160, 193 race track, 26, 92, 121, 122, 146, 256, 280, 282, 284, 285, 290, 292, 320 region, 31 size, 97, 244, 265 species, 166 sputter, 11, 18, 23, 37, 127, 223, 225, 227, 235, 237, 238, 245, 250, 256, 280 sputtering, 34, 239, 244 surface, 280 cleaning, 245, 251 composition, 311 normal, 256 oxidation, 256 temperature, 322 temperature, 322 transitions, 247 utilization, 26, 27, 32, 322 vicinity, 23, 26, 27, 84, 146, 245, 322 voltage, 62, 63, 164, 193, 319 Technological plasmas, 14, 82 Temporal evolutions, 91 Temporal variations, 91, 253 Thermal ionization, 113 Thermalized energy distributions, 124 Titanium cathode, 103, 104 discharge, 194, 198 ionization, 141, 142 ionization mechanism, 142 ions, 249, 267 magnetron target surface, 236 neutrals, 140, 142–144 neutrals depleted density regions, 145

384

plasma, 103 sputtered, 168, 186, 291, 317 target, 17, 165, 192, 229 target surface, 98 Townsend discharge, 3 Traveling spokes, 311 U Unbalanced magnetron, 31, 99 Unipolar HiPIMS discharge, 69

Index

V Velocity distribution, 185, 234, 291 Vibrations, 335 Virtual anode, 25 W Warm neutral population, 170 Wave coupling model (WCM), 310 Z Zirconium ions, 126