The World Scientific Reference of Amorphous Materials: Structure, Properties, Modeling and Main Applications (Volume 3) 9789811215551, 9789811215568, 9789811215582, 9789811215605

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Materials and Energy Print ISSN: 2335-6596 Online ISSN: 2335-660X Series Editors: Leonard C. Feldman (Rutgers University) Jean-Luc Brédas (King Abdullah University of Science & Technology, Saudi Arabia) Richard A. Haight (IBM Thomas J. Watson Research Ctr, USA) Angus Alexander Rockett (University of Illinois at Urbana-Champaign, USA) Eugene A. Fitzgerald (MIT, USA, Cornell, USA & The Innovation Interface, USA) Gary Brudvig (Yale University, USA) Michael R. Wasielewski (Northwestern University, USA) Energy and sustainability are keywords driving current science and technology. Concerns about the environment and the supply of fossil fuel have driven researchers to explore technological solutions seeking alternative means of energy supply and storage. New materials and material structures are at the very core of this research endeavor. The search for cleaner, cheaper, smaller and more efficient energy technologies is intimately connected to the discovery and the development of new materials. This collection focuses onmaterials-based solutions to the energy problem through a series of case studies illustrating advances in energy-related materials research. The research studies employ creativity, discovery, rationale design and improvement of the physical and chemical properties of materials leading to new paradigms for competitive energy-production. The challenge tests both our fundamental understanding of material and our ability to manipulate and reconfigure materials into practical and useful configurations. Invariably these materials issues arise at the nano-scale! For electricity generation, dramatic breakthroughs are taking place in the fields of solar cells and fuel cells, the former giving rise to entirely new classes of semiconductors; the latter testing our knowledge of the behavior of ionic transport through a solid medium. Inenergy-storage exciting developments are emerging from the fields of rechargeable batteries and hydrogen storage. On the horizon are breakthroughs in thermoelectrics, high temperature superconductivity, and power generation. Still to emerge are the harnessing of systems that mimic nature, ranging from fusion, as in the sun, to photosynthesis, nature's photovoltaic. All of these approaches represent a body of materials–based research employing the most sophisticated experimental and theoretical techniques dedicated to a commongoal. The aim of this series is to capture these advances, through a collection of volumes authored by leading physicists, chemists, biologists and engineers that represent the forefront of energy-related materials research.

Published Vol. 15

The World Scientific Reference of Amorphous Materials Structure, Properties, Modeling and Main Applications (In 3 Volumes) edited by Alexander V. Kolobov (Herzen State Pedagogical University of Russia, Russia), Koichi Shimakawa (Gifu University, Japan), Ivar E. Reimanis (Colorado School of Mines, USA), Nikolas J. Podraza (University of Toledo, USA) and Robert W. Collins (University of Toledo, USA)

For further details, please visit: http://www.worldscientific.com/series/mae (Continued at the end of the book)

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Published by World Scientific Publishing Co. Pte. Ltd. 5 Toh Tuck Link, Singapore 596224 USA office: 27 Warren Street, Suite 401-402, Hackensack, NJ 07601 UK office: 57 Shelton Street, Covent Garden, London WC2H 9HE

British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library. Materials and Energy — Vol. 15 THE WORLD SCIENTIFIC REFERENCE OF AMORPHOUS MATERIALS Structure, Properties, Modeling and Main Applications (In 3 Volumes) Volume 1: Structure, Properties, Modeling and Applications of Amorphous Chalcogenides Volume 2: Structure, Properties and Applications of Oxide Glasses Volume 3: Structure, Properties, and Applications of Tetrahedrally Bonded Thin-Film Amorphous Semiconductors Copyright © 2021 by World Scientific Publishing Co. Pte. Ltd. All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means, electronic or mechanical, including photocopying, recording or any information storage and retrieval system now known or to be invented, without written permission from the publisher.

For photocopying of material in this volume, please pay a copying fee through the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, USA. In this case permission to photocopy is not required from the publisher. ISBN 978-981-121-555-1 (set_hardcover) ISBN 978-981-121-593-3 (set_ebook for institutions) ISBN 978-981-121-594-0 (set_ebook for individuals) ISBN 978-981-121-556-8 (vol. 1_hardcover) ISBN 978-981-121-557-5 (vol. 1_ebook for institutions) ISBN 978-981-121-558-2 (vol. 2_hardcover) ISBN 978-981-121-559-9 (vol. 2_ebook for institutions) ISBN 978-981-121-560-5 (vol. 3_hardcover) ISBN 978-981-121-561-2 (vol. 3_ebook for institutions) For any available supplementary material, please visit https://www.worldscientific.com/worldscibooks/10.1142/11697#t=suppl Desk Editor: Rhaimie Wahap Typeset by Stallion Press Email: [email protected] Printed in Singapore

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Preface by Editor-in-Chief

Amorphous solids (including glassy and non-crystalline solids) are ubiquitous since the vast majority of solids naturally occurring in our world are amorphous.∗,1 Although this field is diverse and complex, the attached three volume set covers the vast majority of the important concepts needed to understand these materials and their principal practical applications. One volume discusses the most important subset of amorphous insulators, namely oxide glasses; the next two volumes discuss the most important subsets of amorphous semiconductors, namely tetrahedrally coordinated amorphous semiconductors and amorphous and glassy chalcogenides. Together these three volumes provide advanced graduate students, postdoctoral research associates, and researchers wishing to change fields or sub-fields a comprehensive set of theoretical concepts and practical information needed to become conversant in the field of amorphous materials.

∗

The term amorphous does not have a universally accepted scientific definition. In the oxide glass community amorphous materials are defined as those disordered materials not undergoing a glass transition. In this case glasses are a class of materials distinct from amorphous materials. Other scientific communities, including the semiconducting glass community, define amorphous materials as those disordered materials that lack long range periodic order. In this case glasses are a subset of amorphous materials. These discrepancies notwithstanding, the distinction is purely semantic. v

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The topics covered in these three volumes include: • concepts for understanding the structures of amorphous materials, • techniques to characterize the structural, electronic, and optical properties of amorphous materials, • the roles of defects in affecting the electronic and optical properties of amorphous materials, and • the concepts for understanding practical devices and other applications of amorphous materials. Applications discussed in these volumes include transistors, solar cells, displays, bolometers, fibers, non-volatile memories, vidicons, photoresists, and optical disks. The editors of these volumes and the authors of each chapter are internationally-recognized experts in their respective fields. Taken together, these experts cover all the essential aspects needed for researchers entering the field of amorphous materials to succeed. As the editor of this three-volume set, I am indebted to them without whom this endeavor would not have been possible. Reference 1. Michael Pollak, European Phys. J. 227, 2221–2240 (2019).

P. Craig Taylor Colorado School of Mines 1 March 2020

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Preface by Volume Editors

In a series of ten chapters by leading experts, this volume reviews the well-established foundations as well as recent advances that define the current status of applied science and engineering in the field of hydrogenated silicon (Si:H) based thin film semiconductors. The field of amorphous and nanocrystalline Si:H (a-Si:H and nc-Si:H) has reached maturity with the seminal work having been published more than 40 years ago on the topics of plasma enhanced chemical vapor deposition (PEVCD) and sputtering, silicon-hydrogen bonding analysis, bandgap determination, doping, and transistor and solar cell fabrication. Tens of thousands of papers have been published since then that apply and expand on this work and, thus, comprise the progress of the science and engineering in numerous aspects of the field. In fact, even today, progress continues to be made in materials fabrication and metrology, including analysis of structural, optical, electronic, and magnetic properties, as well as in device applications. As a result, students and newcomers to the field may find it daunting to accumulate and assimilate the vast literature and identify the state of the art in experimental fabrication and measurement techniques, data interpretation methodologies, and overall scientific understanding. The purpose of this text is to serve as a valuable resource for the knowledge base and to provide an upto-date status for practitioners new to the field. The editors of this volume acknowledge Professor Craig Taylor who, in the capacity of series editor, initiated this project in vii

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recognition of a critical need for such a volume to assist a new generation of students and researchers. Professor Taylor has provided many helpful suggestions and encouragement along the way. The editors also express their appreciation to the many authors and coauthors for their considerable efforts on the volume chapters and also for their significant contributions to the field of thin film Si:H. In some cases, chapters serve as retrospectives, as authors have moved on to other endeavors; the time taken to document the status of the field for the new generation is truly appreciated. The editors also note with sadness the passing of Christopher Wronski, Professor Emeritus of The Pennsylvania State University, during the initial planning of this volume. Professor Wronski’s contributions appear in many places throughout the volume (as can be realized through the chapter citation lists); we are sure that he would be pleased to see his impact on the field as reflected in these contents. Not only has he contributed significantly to the foundations of the field early in his career, but he also has impacted the current state of the art more recently through the key research contributions of his group at Penn State including many students, post-doctors, and collaborators worldwide.

Nikolas Podraza and Robert Collins Department of Physics and Astronomy and Wright Center for Photovoltaics Innovation and Commercialization (PVIC), University of Toledo

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Contents

Preface by Editor-in-Chief

v

Preface by Volume Editors

vii

Introduction

xi

Robert W. Collins and Nikolas J. Podraza

Chapter 1.

Film Growth Evolution and Structure

1

Nikolas J. Podraza and Robert W. Collins Chapter 2.

Structure, Defects and Hydrogen in Tetrahedral Amorphous Materials: a-Si and nc-Si

35

Kristin Kiriluk Rabosky Chapter 3.

Infrared Optical Properties: Hydrogen Bonding and Stability Jimmy Melskens, Nikolas J. Podraza, and Michael E. Stuckelberger

ix

85

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Chapter 4.

Near-Infrared to Ultraviolet Optical Response and the Absorption Onset: Parametric Representations

129

Robert W. Collins, Prakash Koirala, and Nikolas J. Podraza Chapter 5.

Structure, Bonding, and Temperature Effects on the Dielectric Function and Bandgap

167

Dipendra Adhikari, Maxwell M. Junda, Balaji Ramanujam, Prakash Koirala, Nikolas J. Podraza, and Robert W. Collins Chapter 6.

Optoelectronic Properties: Carrier Transport, Recombination, and Stability

207

Lihong (Heidi) Jiao and Joshua M. Pearce Chapter 7.

Growth and Properties of Tetrahedrally-Bonded Thin-Film Amorphous Silicon Alloys

247

Nikolas J. Podraza and Robert W. Collins Chapter 8.

Materials and Device Characterization by Optical Probes

279

Prakash Koirala, Jason A. Stoke, Nikolas J. Podraza, and Robert W. Collins Chapter 9.

Application of Amorphous and Nanocrystalline Silicon in Solar Cells

329

Baojie Yan Chapter 10. Amorphous Silicon Microbolometers for IR Imaging

409

Athanasios J. Syllaios, Vincent C. Lopes, Chris L. Littler, and Kiran Shrestha Index

441

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Introduction Robert W. Collins and Nikolas J. Podraza University of Toledo

Mature traditional applications and new uses for hydrogenated silicon (Si:H) based materials continue to be explored, building on the extensive knowledge base that serves as the foundation of the technology. In terms of fabrication, the plasma-enhanced chemical vapor deposition (PECVD) capabilities developed for Si:H and related materials are compatible with integrated circuit (IC) systems, and so this deposition technology may provide advantages over other methods. In terms of materials properties, Si:H in amorphous and nanocrystalline phases can be readily adapted to given applications through tailoring the degree of order, crystallinity and grain size, mechanical properties and stress, surface and interface passivation, optical properties and bandgap, and transport, electrical, and optoelectronic characteristics. Traditional applications in areas such as thin film transistors, solar cells, and detectors continue to draw, if not commercial, at least scientific and engineering interest. In some cases, such as in photovoltaics (PV) applications, the materials have found long-term commercial uses, not as originally intended in the role of a solar cell absorber, but rather as the passivation layers in state-of-the-art crystalline silicon (c-Si) PV technology. Also, the ability to coat nanostructured and nanopatterned substrates xi

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uniformly and the ability to control the nanostructure of the Si:H itself through the PECVD process enables exploration of various concepts in third generation PV. Emerging applications of a-Si:H include coatings for precision interferometry for which the high index of refraction, low thermal noise, and low mechanical losses of the material provide unique advantages over other thin films. The application of nc-Si:H in optomechanical cavities that couple light and mechanical vibrations is also emerging due to the controllability of the nc-Si:H structure, mechanical properties and stress, and optical properties. This application relies on the ability to tailor the films for the specific application, enabling flexibility in the design of the cavities. This volume addresses specific issues and questions that have arisen over the years since the seminal publications and prior extensive literature contributions that are summarized in published collections of topical reviews and monographs [1–22]. Before giving detailed summaries of the chapter contents, some of the key issues that each chapter addresses will be highlighted. The first six chapters focus on the growth and properties of Si:H thin films whereas the last four chapters focus on bandgap and electronic property control through alloying as well as fabrication and characterization of optoelectronic devices including solar cells and infrared sensing array detectors. Chapter 1 focuses on the growth of a-Si:H and nc-Si:H by PECVD and sputtering and presents growth evolution diagrams that enable one to evaluate relationships between process parameters and film properties. Deposition of optimized materials is a difficult challenge due to the substrate and accumulated thickness dependence of the film structure, and such diagrams assist fabrication specialists in overcoming this challenge. Chapter 2 addresses the challenge of understanding the hydrogen bonding, structure, and stability of Si:H films with an emphasis on magnetic resonance methods. Given the interest in nc-Si:H applications in devices due to its high stability against light induced defect formation, Chapter 2 also focuses on the nature of grain boundaries and internal interfaces of nc-Si:H films using a variety of powerful characterization tools. The focus of Chapter 3 is similar, but with an emphasis on the insights into

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Introduction

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a-Si:H film structure provided by infrared absorption spectra. Relationships between the silicon-hydrogen bonding configurations and the optoelectronic performance are identified. The goal of Chapter 4 is to resolve the issue of bandgap determination for amorphous semiconductors through simultaneous analysis of both the real and imaginary parts of the optical response in the form of complex dielectric function spectra. The methodology presented in Chapter 4 is then applied in Chapter 5 to identify the effects of voids and hydrogen bonding configurations on the optical properties. Chapter 6 describes the application of the spectral and irradiance dependence of photoconductivity for characterization of defect states, recombination, and light-induced degradation and subsequent annealing of a-Si:H. Observations on optimized materials prepared with H2 dilution on the amorphous side of the amorphous/nanocrystalline boundary of the growth evolution diagram are found to be inconsistent with standard models incorporating only dangling bond defects. As a result, additional yet to be identified defects, proposed to be charged, are detected through these observations. Chapter 7 describes application of the methodologies of Chapters 1 and 4 to alloys of a-Si1−x Cx :H and a-Si1−x Gex :H. Alloying is used to control the bandgap of these films over a wider range than is possible with H-incorporation alone but results in poorer electronic properties than pure Si:H films. As a result, accurate optical property and bandgap determinations are important as are methods for optimizing the electronic properties. In fact, a library of accuratelydetermined optical properties for alloys and other components of optoelectronic devices enable optical analysis of complete devices and prediction of device performance as described in Chapter 8. From this analysis, the external quantum efficiency of a PV device can be predicted, and the spectral dependence of the experimentally observed deviations from the prediction can indicate the fraction and location of photogenerated carrier recombination within the device. Chapter 9 provides an extensive review of the research and development activities that have led to triple junction solar cells in the nc-Si:H/a-Si1−x Gex /a-Si:H deposition sequence with a maximum stabilized efficiency of 14%. In this chapter, the focus also includes

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application of the PECVD knowledge base to the development of passivating layers in the highest efficiency c-Si PV technology. Some of the same characteristics that have led to the selection of a-Si:H as a passivation layer and doped a-Si:H as the emitter and back field contact layers in c-Si PV technology also serve well in a second optoelectronic application, uncooled microbolometer arrays for infrared imaging. These characteristics include the wellestablished PECVD method for fabrication and its compatibility with IC processing, the quality of a-Si:H interfaces with a variety of materials, the mechanical robustness with the ability to control stress, and finally, the non-toxicity of Si:H layers. Chapter 10 provides a tutorial that introduces the electronic properties of a-Si:H including the temperature coefficient of resistivity and thermal noise with regards to their impact on bolometric detection. The following paragraphs include more detailed summaries of each of the ten chapters. Chapter 1 by Podraza and Collins provides guidance for controlling the fabrication of a-Si:H and nc-Si:H primarily by PECVD with the goal being to achieve the desired properties for device applications. In this chapter, it is emphasized that the film properties depend not only on the set of deposition parameters, e.g. substrate temperature, gas composition and pressure, plasma power and polarity, but also on the nature of the substrate and the accumulated thickness (or the depth into the final film). The substrate and accumulated thickness dependence of the Si:H film properties are stronger under the PECVD conditions used for optimum device performance and stability, typically low temperature (∼200◦ C), low plasma power for low rate deposition ( 0 Si:H, which remains in the amorphous growth regime and no further roughening is observed except with R sufficiently high for crystallites to nucleate from the amorphous phase, the a → (a + nc) transition [24, 48]. For the films on R = 0 a-Si:H relative to those on native oxide covered c-Si, crystallites are observed to appear [a → (a + nc)] and coalesce [(a + nc) → nc] at higher values of R due to substrate-induced persistence of the amorphous growth regime from the underlying R = 0 a-Si:H. Substantially greater R is required for immediate nucleation of crystallites on R = 0 a-Si:H relative to on native oxide covered c-Si. In those cases, the persistence of amorphous growth in the overdeposited Si:H film may be prevented as the greater amount of atomic hydrogen in the plasma may alter the underlying R = 0 amorphous network. Exposure to hydrogen rich plasmas has been previously determined to narrow the broadening of the primary visible range absorption feature, which is indicative of an increase in the mean free path of electrons and

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improved film order [63]. Overdeposition of p-type doped a-Si:H layers with a 10–20 nm intermediate R undoped a-Si:H layer prior to 380 nm of lower R a-Si:H completing the intrinsic layer in p-i-n solar cells resulted in better open circuit voltage, fill factor, and stability under illumination [3, 42]. These improvements in photovoltaic device performance with increased hydrogen in the plasma of overdeposited a-Si:H layers indicate that electronic quality is improved and the amorphous network has been altered. Next consider intrinsic Si:H growth in single-junction a-Si:H and nc-Si:H n-i-p solar cell device configurations. Both device structures are similar, with an underlying supportive substrate made from a metal foil or glass, a metallic back reflector overcoated with a transparent conducting oxide, a n-type doped Si:H layer, an intrinsic Si:H absorber layer, a p-type doped Si:H layer, and a transparent conducting oxide front contact. Further details of the use of a-Si:H in solar cells can be found in Chapter 9. For devices with a-Si:H absorbers, the n-type doped layer is amorphous [22]. For devices with nc-Si:H absorbers, the n-type doped layer is either nanocrystalline or mixed phase [21, 23]. The structure of the n-type layer either prevents or promotes nucleation of crystallites in the a-Si:H or nc-Si:H absorber layer–based devices, respectively. For films deposited on a-Si:H n-layers, the same amorphous, mixed-phase, and nanocrystalline growth regimes are observed via the a → (a + nc) and (a + nc) → nc transitions as for films on R = 0 a-Si:H, albeit at different R due to different deposition conditions (Fig. 1.11) [23]. Even in this device structure, films prepared at low R remain amorphous throughout the deposited thickness while those at higher R nucleate crystallites at decreasing accumulated thickness with increasing R. Similar research has been performed for the growth of p-layers on intrinsic layers and n-layers on the back reflector in the n-i-p configuration [20, 65] as well as for p-layers on front transparent conducting oxides [66], intrinsic layers on p-layers [48], and n-layers on intrinsic layers [61] in p-i-n configuration devices. Returning to intrinsic layer deposition on n-layers in the n-i-p configuration, different behavior is observed in the growing intrinsic films when the underlying n-layer is nc-Si:H, even with identical

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Film Growth Evolution and Structure

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(a)

(b)

Fig. 1.11. Growth evolution diagrams for intrinsic VHF PECVD Si:H prepared under the same conditions but deposited on (a) a-Si:H [22] and (b) nc-Si:H [23] n-layers as functions of R = [H2 ]/[Si2 H6 ]. Reprinted from [22], J. A. Stoke, N. J. Podraza, J. Li, X. Cao, X. Deng, and R. W. Collins “Advanced deposition phase diagrams guiding Si:H-based multijunction solar cells,” Journal of NonCrystalline Solids 354, 2435, Copyright (2008), with permission from Elsevier. c 2008 IEEE. Reprinted, with permission, from [23], J. A. Stoke, L. R. Dahal,  J. Li, N. J. Podraza, X. Cao, X. Deng, and R. W. Collins, “Optimization of Si:H multijunction n-i-p solar cells through development of deposition phase diagrams,” 33rd IEEE Photovoltaic Specialists Conference, 762 (2008).

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intrinsic layer PECVD process parameters (Fig. 1.11) [23]. In the early stages of growth for films at all R, the deposited material is (a + nc)-Si:H due to local epitaxy imposed by the underlying nc-Si:H n-layer. At low R, the crystallite fraction decreases with increasing accumulated thickness and the film eventually becomes amorphous, an (a + nc) → a transition. The appearance of the amorphous phase is delayed to greater accumulated film thickness as R is increased. At intermediate R, however, the mixed-phase growth regime persists throughout the accumulated thickness measured. At greater R, the nanocrystalline phase is favored over the amorphous phase, and a single-phase nanocrystalline growth regime is reached at decreasing accumulated thickness with increasing R. The particular underlying material will dictate the appropriate deposition conditions, R here, needed to produce the desired structure material best suited to the particular device application. The highest electronic quality a-Si:H and nc-Si:H films used as absorbers in the respective type of photovoltaics technology are produced at intermediate R [21–23, 42]. For a-Si:H absorber layers in solar cells, the highest R is chosen prior to the nucleation of crystallites to promote the most order in the amorphous network and the highest degree of electronic quality. In this case the underlying layer is either n-type or p-type doped a-Si:H, depending on the n-i-p or p-i-n solar cell configuration, and this underlying amorphous layer prevents crystallite nucleation. For nc-Si:H absorbers, the lowest R is chosen so that nucleating crystallites are well passivated by hydrogen and a-Si:H. Here the underlying doped layer is nc-Si:H or (a + nc)Si:H, either of which will help promote crystallite nucleation. An advantage of using the lowest R possible for nc-Si:H is that deposition rate decreases with increasing R — so higher quality nanocrystallite material may also grow faster. In both cases with Si:H absorber layers, the underlying doped layer already has similar structure to that desired for the overdeposited layer. However, when passivating c-Si with a-Si:H such as in HIT devices, deposition conditions must be chosen such that local epitaxy is avoided at the film/c-Si interface [29, 30, 44, 45]. The structures of the underlying and overlying materials in this case are

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Film Growth Evolution and Structure

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desired to be vastly different. Conditions are therefore chosen so that a-Si:H provides conformal coverage of the c-Si by 0.9 was exposed to the lowest optical excitation energy of 1.2 eV as crystalline silicon’s bandgap is approximately 1.1 eV. The sample with an increased crystalline volume fraction, Xc = 0.5, was exposed to three different excitation energies. Comparing these spectra to the mostly crystalline sample, the lineshape is very similar indicating again that the mixed-phase material LESR spectrum is due to the c-Si phase of the material [79].

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Fig. 2.20. Light-induced ESR (LESR) lineshape for hydrogenated amorphous silicon (a-Si:H) and hydrogenated nanocrystalline silicon (nc-Si:H) with varying crystalline fraction and varying optical energy. The resonance for nc-Si:H is shifted to a larger value of the field. Reproduced with permission from [79].

The presence of carriers that are trapped in localized states at the crystalline grain boundaries is supported by optical absorption spectra measured by photothermal deflection spectroscopy [79]. Figure 2.21 shows the optical absorption spectra at 300 K for a-Si:H (shown as the black curve, blue curve online), nc-Si:H with a 50% volume fraction as measured by Raman spectroscopy and transmission electron microscopy (TEM) (shown as the gray curve, red curve online), and bulk c-Si (shown as the squares). In the 1.1–1.75 eV energy range, the nc-Si:H absorption spectra most closely resembles the c-Si absorption spectrum. The excitation in this energy range is probably from the crystallites or from the crystallite interfaces. Above this energy range, the nc-Si:H absorption spectra most closely resembles the a-Si:H absorption spectrum. The excitation at higher energies is from the a-Si:H phase of the material. The absorption spectrum indicates that carriers can be preferentially excited depending on the optical wavelength applied [79].

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Structure, Defects and Hydrogen in Tetrahedral Amorphous Materials

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Fig. 2.21. Optical absorption spectra for hydrogenated amorphous silicon (a-Si:H) (black curve, blue curve online), hydrogenated nanocrystalline silicon (nc-Si:H) (gray curve, red curve online), and c-Si (squares). Reproduced with permission from [79].

Additionally, PL data also corroborate that carriers recombine while trapped at defect states at the crystalline grain boundaries. Figure 2.22(a) shows the PL spectra taken at low temperature using an excitation energy of 2.4 eV for a-Si:H (squares) and ncSi:H with Xc of 0.10 (circles), 0.40 (triangles), 0.75 (diamonds) [79]. The a-Si:H spectrum has a peak around 1.4 eV, which comes from recombination of electrons trapped in localized CB tail states with holes trapped in localized valence band tail states [80]. As the crystalline volume fraction grows in the nc-Si:H material, another peak appears in the PL spectra around 0.9 eV, which does not appear in a-Si:H. The peak at 0.9 eV is attributed to recombination between carriers trapped within defect states located at the crystalline grain boundaries [81]. Figure 2.22(b) shows the relative intensity of the amorphous PL peak to the total PL spectra plotted with respect to crystalline volume fraction. The inset of Fig. 2.22(b) shows the same data on a semilog plot. The amorphous PL peak quenches compared

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(a)

(b)

Fig. 2.22. Quenching of photoluminescence (PL) spectra as a function of crystalline volume fraction (Xc ) for hydrogenated nanocrystalline silicon (nc-Si:H) films. (a) Normalized PL spectra for hydrogenated amorphous silicon (a-Si:H), Xc = 0.10, Xc = 0.4, and Xc = 0.75 (b) Relative intensity of the a-Si:H PL to ncSi:H PL as a function of crystalline volume fraction. Inset shows data on semilog plot. Reproduced with permission from [79].

with the peak from crystalline grain boundaries as the crystalline volume fraction increases. The quenching of the amorphous PL peak is attributed to the migration of carriers created in the amorphous phase of the material to the crystalline grain boundaries or grain interior where they recombine [82]. The results from Fig. 2.20, showing that the mixed-phase Xc = 0.5 material produces an LESR signal attributed to the crystalline phase of the material, support the PL quenching results. The carrier relaxation behavior seen in PL and LESR results is depicted in Fig. 2.23. The band structure for the crystalline silicon region, with CB and VB and amorphous silicon region, with the CB and VB mobility edges, is shown. Localized states resulting from defects and disorder in the material are shown inside the band edges. Arrow (1) depicts the excitation of carriers in the crystalline region of the film. Arrows (2) and (3) depict two pathways for carrier excitation in the amorphous region of the film with transfer to the crystalline grain boundaries. Arrow (2) depicts carrier transfer through the localized band tail states of the amorphous region to the crystalline grain boundaries. Arrow (3) depicts the excitation of the

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Fig. 2.23. Schematic of the potential relaxation pathways, shown by arrows (1), (2), and (3), in hydrogenated nanocrystalline silicon (nc-Si:H). Reproduced with permission from [79].

carriers, which then reach the crystalline grain boundary before fully thermalizing [79]. Time-resolved terahertz spectroscopy (TRTS) experiments have directly observed the electron transfer from the amorphous phase of nc-Si:H to the crystalline phase [83]. TRTS is sensitive to carriers in the extended states of the CB and VB. The carrier absorption cross sections in these states are directly proportional to carrier mobility when measured at THz frequencies. TRTS is a pumpprobe technique that measures a photomodulated THz electric field. Carriers thermalize to the band tail states in approximately 1 ps [84–86] and the resolution of these experiments is in the sub-ps to ns range making it sensitive enough for these measurements [83]. TRTS measurements have been reported in a-Si:H and several ncSi:H films with varying crystalline fraction [83]. Figure 2.24 shows a model of the fraction of carriers in each state. The green lines represent Xc = 0.5, the blue lines represent Xc = 0.7, and the red lines represent Xc = 0.3. To model the TRTS data, three states have been taken into account: an a-Si extended state (fa ), an interface trap state (ft ), and a c-Si extended state (fc ). The carrier dynamics at very early times can be seen in the inset of Fig. 2.24. At very early times, the carriers reside in either the amorphous or crystalline states. The carriers originating in the a-Si quickly transfer to interface states

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Fig. 2.24. Model of time resolved terahertz spectroscopy results for amorphous silicon (a-Si) extended states (fa ), crystalline interface trap states (ft ), and crystal silicon (c-Si) extended states (fc ). fc and ft increase with increasing Xc for three samples shown with Xc = 0.3, 0.5, and 0.7. The inset is focused on the early time behavior of the charge carriers. In the inset, fa decreases with increasing Xc for three samples shown with Xc = 0.3, 0.5, and 0.7. Reproduced with permission from [83].

then to the interior of the c-Si grain. The fraction of carriers that were initially excited in the a-Si:H phase and transfer to the crystalline interface was greatest for the nc-Si:H sample with Xc = 0.7. 2.7. Increased Stability of µc-Si:H and nc-Si:H Films over a-Si:H Theoretical calcuations support the experimental evidence in μcSi:H or nc-Si:H materials showing that charge carriers are able to diffuse to the crystalline interfaces before recombining. If charge carriers diffuse to the crystalline grain boundaries by tunneling through localized band tail states (pathway [2] in Fig. 2.23), then the theoretically calculated distance that carriers diffuse is 4 nm before recombining [79]. If charge carriers diffuse directly from the a-Si extended states to the crystalline interface before thermalizing (pathway [3] in Fig. 2.23), then electrons 1 eV above the a-Si

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mobility edge will diffuse approximately 10 nm or more and slightly less for holes [79]. The diffusion of carriers before thermalization is plausible as experiments show that thermalization is slower in amorphous materials than crystalline materials [86–88]. The evidence that charge carriers are able to diffuse to the crystalline interfaces before recombining may explain the absence of degradation in μcSi:H and nc-Si:H films with optical excitation, behavior unlike their amorphous counterpart. If the carriers do not recombine in the amorphous phase of the material, they will not create Staebler– Wronski defects. 2.8. Impact on Applications The crystalline structure and nature of defects in both a-Si and nc-Si can be both advantageous and detrimental to their potential applications. Historically, a-Si:H and nc-Si:H thin films have been used as the active layer in photovoltaic devices. Crystalline Si has been used in photovoltaic devices for many decades but its efficiency is limited by its indirect bandgap of 1.1 eV. A more optimal bandgap for a solar material tuned to the solar spectrum is 1.3–1.4 eV [89]. Thin-film a-Si:H exhibits stronger absorption than crystalline Si, but has struggled to overcome its light-induced degradation discussed previously. Groups have been successful in engineering around the Staebler–Wronski effect. Since nc-Si:H is more stable under light exposure than a-Si:H, as shown previously in the chapter, it too has been explored as an active layer for a single-junction solar cell. Currently, the highest efficiency stabilized a-Si:H-based solar cell has been produced by the Research Center for Photovoltaics, National Institute for Advanced Industrial Science and Technology in Japan in 2016 [90]. This solar cell is 14% efficient and is a triple-junction cell utilizing an a-Si:H/μc-Si:H/μc-Si:H stack. 2.8.1. Third-Generation Solar Cells Since crystalline Si single-junction solar cells have world record maximum efficiencies of 26%, much higher efficiencies are needed in active layer materials. Researchers have been integrating Si

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(b)

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Fig. 2.25. Transmission electron microscopy (TEM) analysis from a range of SiNP growths with (a) lowest gas flow to (b) highest gas flow. Scale bar is 5 nm in all images [91].

nanoparticle or quantum dots into amorphous matrices to tailor ncSi:H material. The advantages are two-fold: an increase in stability under light exposure and tunability of the material’s opto-electronic properties. Figure 2.25 shows the TEM images of SiNPs made through PECVD in an a-Si:H matrix [91]. Through the adjustment of gas flow rate and chamber pressure, nanoparticles of 3–8 nm have been achieved with associated bandgaps of 1.6–1.3 eV. These nanostructured materials, once optimized, could produce a lower quality crystalline material to produce efficiencies on par with crystalline silicon solar cells [92]. Additionally, the higher bandgap opens the possibility for a Si-based material that can be used in a tandem solar cell with crystalline Si or as a superlattice structure with graded bandgap [93, 94].

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2.8.2. Precision Interferometry Precision interferometry is used to measure optical path changes in a variety of applications. Recently, gravitational wave detectors using precision interferometry are being explored with the potential of a-Si serving as a high-index coating material for low thermal noise. These detectors use mirrors, which can be deflected by a passing gravitational wave. a-Si films have low mechanical losses when heat treated after deposition compared to more conventional mirror coatings. Hydrogenated a-Si films have even lower mechanical losses compared with non-hydrogenated films. As thermal noise from coatings of the mirrors is expected to limit performance of the detectors, a-Si is a good candidate for a coating material [95]. 2.8.3. Optomechanical Cavities Since the speeds of sound and light in a solid are drastically different, optomechanical cavities are being implemented to enhance the interaction between waves. nc-Si is being explored for use in these optomechanical cavities because of the tunability of its grain size, stress, and optoelectronic and mechanical properties [96]. This tunability allows for multilayer optomechanical cavities providing the ability to tailor the structure to the necessary experiment, allowing more flexibility in design. Additionally, nc-Si is lower in cost than conventional silicon on insulator materials that are mostly used [96]. 2.8.4. Thin-Film Transistors a-Si:H is being used in TFTs that act as switches in active-matrix liquid crystal displays. These TFTs are used in a variety of industries including mobile and personal computer (PC) applications [97]. a-Si:H is ideal because of its ability to be deposited on glass substrates, its long-range deposition uniformity, and its scalable manufacturing process [98]. Defect states in the a-Si:H strongly influence the threshold voltage for these devices and are integral to the lifetime and overall stability of the device [99].

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66. Yonezawa, F. (1982). In: Amorphous Semiconductor Technologies and Devices, Hamakawa, Y., Ed. (Amsterdam, North-Holland Publ.), pp. 9–31. 67. Rieger, P. H. (2007). Electron Spin Resonance Analysis and Interpretation (RSC Publishing). 68. Biegelsen, D. K., and Stutzmann, M. (1986). Microscopic nature of coordination defects in amorphous silicon, Physical Review B, 33, p. 3006, doi:10.1103/PhysRevB.40.9834, https://journals.aps.org/prb /abstract/10.1103/PhysRevB.40.9834. 69. de Lima, M. M., et al. (2002). ESR observations of paramagnetic centers in intrinsic hydrogenated microcrystalline silicon, Physical Review B, 65, p. 235324, doi:10.1103/PhysRevB.65.235324, https:// journals.aps.org/prb/abstract/10.1103/PhysRevB.65.235324. 70. Dersch, H., Stuke, J., and Beichler, J. (1981). Light induced dangling bonds in hydrogenated amorphous silicon, Applied Physics Letters, 38, p. 456, doi:10.1063/1.92402, https://aip.scitation.org/doi/abs/10. 1063/1.92402. 71. Branz, H. (1998). Hydrogen collision model of light-induced metastability in hydrogenated amorphous silicon, Solid State Communications, 105, p. 387, doi:10.1016/S0038-1098(97)10142-9, https://www.science direct.com/science/article/pii/S0038109897101429. 72. Zou, X., et al. (2000). Photoinduced dehydrogenation of defects in undoped a-Si:H using positron annihilation spectroscopy, Physical Review Letters, 84, p. 769, doi:10.1103/PhysRevLett.84.769, https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.84.769. 73. Schultz, N., and Taylor, P. C. (2002). Temperature dependence of the optically induced production and annealing of silicon dangling bonds in hydrogenated amorphous silicon, Physical Review B, 65, p. 235207, doi:10.1103/PhysRevB.65.235207, https://journals.aps.org/prb/abstr act/10.1103/PhysRevB.65.235207. 74. Su, T., Taylor, P. C., Ganguly, G., and Carlson, D. E. (2002). Direct role of hydrogen in the Staebler–Wronski effect in hydrogenated amorphous silicon, Physical Review Letters, 89, p. 015502, doi:10.1103/ PhysRevLett.89.015502, https://journals.aps.org/prl/abstract/10.110 3/PhysRevLett.89.015502. 75. Beyer, W., and Wagner, H. (1982). Determination of the hydrogen diffusion coefficient in hydrogenated amorphous silicon from hydrogen effusion experiments, Journal of Applied Physics, 53, pp. 8745–8750, doi:10.1063/1.330474, https://aip.scitation.org/doi/abs/10.1063/1.33 0474. 76. Zafar, S., and Schiff, H. A. (1989). Hydrogen-mediated model for defect metastability in hydrogenated amorphous silicon, Physical Review B,

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86. White, J. O., Cuzeau, S., Hulin, D., and Vanderhaghen, R. (1998). Subpicosecond hot carrier cooling in amorphous silicon, Journal of Applied Physics, 84, pp. 4984–4991, doi:10.1063/1.368744, https://ai p.scitation.org/doi/10.1063/1.368744. 87. Vardeny, Z., and Tauc, J. (1981). Hot-carrier thermalization in amorphous silicon, Physical Review Letters, 46, pp. 1223–1226, doi: 10.1103/PhysRevLett.46.1223, https://journals.aps.org/prl/abstract/ 10.1103/PhysRevLett.46.1223. 88. Wraback, M., and Tauc, J. (1992). Direct measurement of the hot carrier cooling rate in a-Si:H using femtosecond 4 eV pulses, Physical Review Letters, 69, pp. 3682–3685, doi:10.1103/PhysRevLett.69.3682, https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.69.3682. 89. Shockley, W., and Queisser, H. (1961). Detailed balance limit of efficiency of p-n junction solar cells, Journal of Applied Physics, 32, p. 510, doi:10.1063/1.1736034, https://aip.scitation.org/doi/abs/10.10 63/1.1736034. 90. Sai, H., Matsui, T., and Matsubara, K. (2016). Stabilized 14.0%efficient triple-junction thin-film silicon solar cell, Applied Physics Letters, 109, p. 183506, doi:10.1063/1.4966996, https://aip.scitation. org/doi/abs/10.1063/1.4966996. 91. Kendrick, C., et al. (2014). Controlled growth of SiNPs by plasma synthesis, Solar Energy Materials & Solar Cells, 124, pp. 1–9, doi:10. 1016/j.solmat.2014.01.026, https://www.sciencedirect.com/science/ar ticle/pii/S0927024814000427?via%3Dihub. 92. Kayes, B., Atwater, H., and Lewis, N. (2014). Comparison of the device physics principles of planar and radial p-n junction nanorod solar cells, Journal of Applied Physics, 97, p. 114302, doi:10.1063/1.1901835, https ://aip.scitation.org/doi/abs/10.1063/1.1901835?journalCode=jap. 93. Conibeer, G., et al. (2006). Silicon nanostructures for third generation photovoltaic solar cells, Thin Solid Films, 511, p. 654, doi:10.1016/j. tsf.2005.12.119, https://www.sciencedirect.com/science/article/pii/S0 040609005024703. 94. Ma, J., et al. (2016). Size-controlled nc-Si:H/a-SiC:H quantum dots superlattice and its application to hydrogenated amorphous silicon solar cells, Solar Energy Materials and Solar Cells, 157, pp. 923–929, doi:110.1016/j.solmat.2016.08.001, https://www.sciencedirect.com/sci ence/article/pii/S0927024816302860. 95. Murray, P. G., et al. (2015). Ion-beam sputtered amorphous silicon films for cryogenic precision measurement systems, Physical Review D, 92, p. 062001, doi:10.1103/PhysRevD.92.062001, https://journals.aps. org/prd/abstract/10.1103/PhysRevD.92.062001.

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96. Navarro-Urrios, D., et al. (2018). Nanocrystalline silicon optomechanical cavities, Optics Express, 26, pp. 9829–9839 doi:10.1364/OE.26. 009829, https://www.osapublishing.org/oe/abstract.cfm?uri=oe-26-8 -9829. 97. Choi, J. W., Kim, J. I., Kim, S. H., and Jang, J. (2010). Highly reliable amorphous silicon gate driver using stable center-offset thinfilm transistors, IEEE Transactions on Electron Devices, 57, pp. 2330– 2334, doi:10.1109/TED.2010.2054453, https://ieeexplore.ieee.org/doc ument/5523929/. 98. Lin, C.-L., et al. (2017). Gate driver based on a-Si:H thin film transistors with two-step-bootstrapping structure for high-resolution and high-frame-rate displays, IEEE Transactions on Electron Devices, 64(8), pp. 3494–3497, doi:10.1109/TED.2017.2710180, https://ieeexpl ore.ieee.org/document/7947093/. 99. Powell, M. J., van Berkel, C., and Hughes, J. R. (1989). Time and temperature dependence of instability mechanisms in amorphous silicon thin-film transistors, Applied Physics Letters, 54, pp. 1323–1325, doi:10.1063/1.100704, https://aip.scitation.org/doi/10.1063/1.100704.

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CHAPTER 3

Infrared Optical Properties: Hydrogen Bonding and Stability Jimmy Melskens∗ , Nikolas J. Podraza† and Michael E. Stuckelberger‡ ∗

Eindhoven University of Technology, The Netherlands University of Toledo, USA ‡ Deutsches Elektronen-Synchrotron DESY, Germany †

3.1. Motivation Hydrogen incorporation into the amorphous silicon (a-Si) network yields hydrogenated amorphous silicon (a-Si:H). The primary means of introducing hydrogen bonded to silicon in a-Si:H is through chemical vapor deposition (CVD) involving silane (SiH4 ), disilane (Si2 H6 ), hydrogen (H2 ), and other source gases dissociated by a plasma or through reactive physical vapor deposition (PVD) of a solid source in H2 as described in Chapter 1. Hydrogen present during deposition controls the growth evolution of hydrogenated silicon (Si:H) thin films. An increased concentration of hydrogen present during the a-Si:H growth can improve the order within the amorphous network via enhanced diffusion of precursors and hydrogen etching of weakly bound material on the growing surface. With sufficiently mobile atoms during growth, nanocrystallites nucleate from the amorphous 85

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phase and grow preferentially over the less energetically favorable a-Si:H. Hydrogen is incorporated within these Si:H thin films as part of the amorphous network in a-Si:H and as grain boundary passivation in the nanocrystalline phase. Here we will focus on hydrogen incorporated into a-Si:H, presenting some interpretations of its nature [1–17]. The incorporation and role of hydrogen in a-Si:H is a complicated process, which is for instance illustrated by the absence of a direct correlation between the amount of hydrogen source gas that is present during the deposition and the atomic hydrogen content in the deposited film. In general, the incorporation of hydrogen and its configuration in the amorphous network depends on all process parameters during film growth. Nevertheless, already in early a-Si:H research and its application toward devices, the importance of hydrogen to passivate defects in a-Si was established. By incorporating hydrogen into the a-Si network, the number of dangling bond defects decreased by four orders of magnitude from 1020 to 1016 cm−3 , enabling fabrication of sufficiently high-quality material suitable for electronic devices [1, 18–20]. In addition to substantially improving the electrical properties by the passivation of Si dangling bonds, hydrogen bonded into the film can alter the material density and optical response [16, 17, 21, 22]. The impact on material density and opto-electronic response depends on the amount of hydrogen present but also on the bonding configuration within the amorphous network (Fig. 3.1). A variety of bonding configurations between silicon and hydrogen and a range of hydrogen contents in films are possible and are dictated by deposition and post-deposition processing conditions. An obvious means of manipulating hydrogen content in films is during growth, as the silicon-hydrogen bonds in the source gases and hydrogenhydrogen bonds in H2 during plasma-based CVD may be easily dissociated and hydrogen atoms can become incorporated into the film. However, hydrogen bound in films may effuse during growth or post-deposition annealing at temperatures greater than 200–250◦ C [16, 23–25]. The bonding configurations which result from the growth process or annealing directly impact the functionality of the deposited material for different applications. Not all “device quality”

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Fig. 3.1. (a) Three-dimensional structure of crystalline silicon and (b) its twodimensional representation with substitutional boron and phosphorus doping. (c) Two-dimensional representation of hydrogenated amorphous silicon (a-Si:H) with silicon atoms (solid circles), hydrogen atoms passivating dangling bonds (empty circles), a paired and unpaired dangling bond, and fully hydrogen-passivated nanovoids due to a monovacancy and a divacancy. Reprinted with permission from M. Stuckelberger, R. Biron, N. Wyrsch, F.-J. Haug, and C. Ballif, Review: Progress in solar cells from hydrogenated amorphous silicon, Renewable and c 2017 Elsevier Ltd. Sustainable Energy Reviews, 76, 1497 (2017). Copyright  All rights reserved.

a-Si:H has the same hydrogen bonding configuration and associated characteristics [6–17, 26–28]. Furthermore, the term “device quality” has been widely used to refer to a type of a-Si:H that is dense and has a relatively low density of nanosized voids (NV; see section 3.4) that suffers less from light-induced degradation (see Section 3.5), although this all refers exclusively to the intended application of aSi:H as a light absorber in solar cells. However, for various kinds of device applications, different types of a-Si:H may be preferred so the term “device quality” has to be used with caution. When doped with trivalent or pentavalent atoms such as boron and phosphorus, respectively, the electrical response of doped a-Si:H depends on the concentration of dopant atoms or free charge carriers. However, these dopant atoms can form complexes with hydrogen in the amorphous network which reduce the doping efficiency. This illustrates that an improper inclusion of hydrogen in the doped amorphous network can be detrimental [29]. a-Si:H materials with different densities and optical responses as manipulated by hydrogen content and bonding configurations are used for distinct roles in photovoltaic (PV) devices. In thinfilm a-Si:H based solar cells, dense material that is relatively stable

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against the Staebler-Wronski effect [30] and associated light-induced degradation is typically used as the absorber layer [6–15, 17, 31]. For crystalline silicon wafer-based heterojunction (heterojunction with intrinsic thin, HIT) solar cells, low-density a-Si:H can be used to passivate dangling bonds present on the silicon crystal surface [16, 26, 27]. In both device configurations, doped a-Si:H may be used as p- and n-type contacts. In other applications outside PV, even other types of a-Si:H may be preferred. For instance, in the context of programmable photonics where the optical instead of the electrical properties are the relevant indicator of quality, it is desirable to use a type of a-Si:H with a density that is optimized for refractive index change upon light soaking and annealing [28, 32]. Note that these changes in refractive index are a relatively unknown aspect of the Staebler-Wronski effect, which through the Kramers-Kronig relations are characterized by changes not only in the extinction coefficient (or photoconductivity) but also in the refractive index, although the latter plays a negligible role in the context of PV. This chapter will discuss manifestations of silicon-hydrogen bonding in the infrared (IR) optical response of a-Si:H films and its measurement; IR absorption peaks associated with cumulative hydrogen content and particular silicon-hydrogen bonding configurations [1–5]; utilization of silicon-hydrogen bonding to identify the nanostructure of a-Si:H including vacancies and voids [6, 7, 33]; and the impact of these characteristics in a-Si:H applied in optoelectronic devices such as solar cells [6–17, 26, 27, 31] and photonics [28, 32, 34, 35].

3.2. Infrared Optical Properties of a-Si:H The bandgap of a-Si:H typically ranges from 1.5 to 1.8 eV and can be narrowed or widened by alloying with germanium (a-Si1-x Gex :H) or carbon (a-Si1-x Cx :H) and oxygen (a-Si1-x Ox :H), respectively, as discussed in Chapter 7 and Ref. [17], but can also be manipulated by inclusion of hydrogen and by the nanostructure of the material [9, 10, 36], as discussed in Chapters 4 and 5. The optical properties are expressed in terms of the complex dielectric function (ε = ε1 + iε2 = N 2 ), complex index of refraction (N = n + ik), and absorption coefficient (α = 4πk/λ) spectra as functions of photon

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energy, wavenumber (ω), or wavelength (λ). At photon energies less than the bandgap energy, contributions to absorption as noted in the imaginary part of complex ε (ε2 ), extinction coefficient (k), or α spectra in a-Si:H arise from free carriers, defect states, and IR vibrational modes. Free carriers manifest as Drude tails increasing in magnitude with decreasing photon energy or wavenumber and increasing wavelength. Even for heavily doped a-Si:H, this contribution is negligible in the near- to mid-IR spectral range. Sub-bandgap absorption due to defects is detectable, but it is relatively small as it depends on the generally low density of those defect states and is spectrally confined due to the nature of these electronic transitions between discrete gap states and band states. Note, however, that defect states enhance charge carrier recombination, which is far more harmful for the device performance than the absorption. IR vibrational modes are due to silicon-hydrogen bonding and localized to a relatively narrow spectral range for each mode. However, the amplitudes of these features are detectably large and scale with the amount of silicon-hydrogen bonds. Often measurements of silicon-hydrogen bonding using IR spectroscopy are combined with sub-bandgap absorption measurements of defect states in order to elucidate the atomistic origin of those defect states based on characteristics of the amorphous network [8–12]. The origin of silicon-hydrogen IR vibrational modes is the same as any molecular absorption feature, in that a chemical bond with an associated binding energy exists between the constituent atoms. Electromagnetic waves with a frequency or photon energy corresponding to the resonance frequency or energy of that bond perturb the atoms from equilibrium positions leading to absorption of electromagnetic radiation at those frequencies. These absorption features are typically described as Lorentzian or Gaussian broadened line shapes represented by an amplitude corresponding to the concentration of these bonds, a resonance frequency or energy associated with the bond and its constituent atoms, and a broadening due to scattering during the excitation. Typically, Gaussian broadened line shapes are used to describe vibrational mode absorption manifested in α, k, or ε2 for a-Si:H. Visually, each bonding mode appears in these spectra as a relatively sharp peak centered about the resonance

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Fig. 3.2. Infrared (IR) complex dielectric function, ε = ε1 + iε2 , spectra for a-Si:H. The inset shows low and high stretching modes (LSM, HSM) around 2000 and 2090 cm−1 , respectively. Reprinted with permission from D. Adhikari, M. M. Junda, S. X. Marsillac, R. W. Collins, and N. J. Podraza, Nanostructure evolution of magnetron sputtered hydrogenated silicon thin films, Journal of c 2017 AIP Publishing. All Applied Physics, 122, 076302 (2017). Copyright  rights reserved.

frequency or energy and decaying rapidly beyond its full width half maximum. Perturbations in the real part of the complex optical response (ε1 or n) correspond to these features due to KramersKronig consistency (Fig. 3.2) [21, 37]. Silicon-hydrogen IR vibrational modes in a-Si:H are commonly measured using Fourier transform IR (FTIR) unpolarized

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Fig. 3.3. Absorption coefficient (α) spectra for a-Si:H made with hydrogen (-H) and deuterium (-D). Reprinted with permission from M. H. Brodsky, M. Cardona, and J. J. Cuomo, Infrared and Raman spectra of the silicon-hydrogen bonds in amorphous silicon prepared by glow discharge and sputtering, Physical Review c 1977 The American Physical Society. All B, 16, 3556–3571 (1977). Copyright  rights reserved.

transmittance and reflectance spectroscopy to deduce the absorptance spectra from which the individual bonding modes are characterized (Fig. 3.3). These measurements require IR transparent substrates, typically undoped or high resistivity crystalline silicon wafers, onto which the a-Si:H films are deposited. After obtaining these measured spectra, optical models assuming coherent multiple reflections between the thin a-Si:H film, substrate, and any other layers in the sample stack should be used to reliably extract a-Si:H property spectra [38]. Not accounting for multiple reflections in samples can result in erroneous optical properties and resulting derived values. Reflection mode FTIR spectroscopic ellipsometry has also been used recently to characterize the complex optical response of a-Si:H in the IR and can be performed for films deposited on any substrate which is specularly reflecting in the IR including layers in thin-film a-Si:H based solar cell configurations [21, 31, 39, 40]. Both spectroscopic ellipsometry and unpolarized transmittance & reflectance spectroscopy are mostly used for ex-situ measurements of samples after a-Si:H film fabrication [16], although in-situ ellipsometry

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measurements have been performed as well [37, 41]. Attenuated total reflectance (ATR) spectroscopy relies on depositing the a-Si:H film onto an undoped silicon crystal in which an evanescent wave is generated from the interaction of incident IR light with the crystal substrate and deposited film sample [26, 27, 42]. The enhanced sensitivity to absorptance in the a-Si:H layer due to the substrate requirement enables ATR measurements to be made in situ during a-Si:H film growth or processing. When combined with in situ thickness information for a growing film, such as obtained from in situ real time spectroscopic ellipsometry (RTSE), the evolution of the silicon-hydrogen vibrational modes can be tracked (Fig. 3.4) [26, 27].

(a)

(b)

(c)

Fig. 3.4. (a) Si-H2 content, (b) Si-H content, and (c) instantaneous growth rate as a function of accumulated thickness for a-Si:H deposited on crystalline silicon for heterojunction with intrinsic thin layer (HIT) solar cell structure as determined by ATR (a, b) and real time spectroscopic ellipsometry (c). Reprinted with permission from H. Fujiwara and M. Kondo, Effects of a-Si:H layer thicknesses on the performance of a-Si:H/c-Si heterojunction solar cells, Journal c 2007 AIP Publishing. All of Applied Physics, 101, 054516 (2007). Copyright  rights reserved.

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ATR spectroscopy has also been applied to determine a-Si:H surface hydrogen bonding during isotope exchange between hydrogen and deuterium [42]. 3.3. Silicon-Hydrogen Bonding and Related Modes Classically, the nanostructure of a-Si:H is described as a glassy structure that has become known as the continuous random network (CRN) [43, 44]. Despite the appealing simplicity of the CRN, the view that the a-Si:H network is not continuously random has gained significant popularity since the 1980s when it was considered that vacancies and voids also likely play a role in an accurate description of the nanostructure [45, 46]. According to this view which can be labeled as a disordered network with hydrogenated vacancies (DNHV), there is some short range order and medium range order in the nanostructure to a given extent depending upon the sample, while the disordered silicon sits in between regions that are dominated by vacancies and voids [6–9, 11–13, 15, 47]. A schematic representation of each of these nanostructure models is shown in Figure 3.5. As will be discussed in the next section, the nanostructure has a significant impact on the amount of hydrogen that can be present in the film and how it is incorporated into the network. Silicon is tetravalent leaving the opportunity for up to three of its bonds to form a covalent bond with hydrogen when incorporated in the film; at least one bond must be to another polyvalent atom to attach it to the amorphous network. These silicon-hydrogen (Si-Hn ; n = 1, 2, 3) bonds are manifested in the IR absorptance spectrum as peaks associated with particular bonding modes [1–5, 48, 49]. The general types of bonding modes are stretching, bending, rocking, and wagging. Stretching modes are due to changes in the bond length between atoms, bending modes are due to changes in the bond angle, rocking modes are due to changes in the bond angle between groups of atoms, and wagging modes are due to changes in the bond angle between the plane of a group of atoms. A schematic of these modes and the vibrational frequencies associated with these Si-Hn modes is shown in Fig. 3.6 [1]. Si-Hn peaks related most closely to the order and structure of the a-Si:H network are the wagging mode peaks at 640 cm−1 , the

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(b)

Fig. 3.5. (a) Schematic representation of the models that have been used to describe the a-Si:H nanostructure. In the continuous random network (CRN), isolated dangling bonds are the dominant defects. (b) In the disordered network with hydrogenated vacancies (DNHV), however, the dominant defects in the DNHV are associated with not fully passivated vacancies and nanosized voids (NV) which are embedded in regions of disordered silicon. Note that defect configurations in divacancies (DV) and larger open volumes can occur in many different configurations involving both clustered and non-clustered dangling bonds. Adapted with permission from J. Melskens, Hydrogenated amorphous silicon: nanostructure and defects, PhD thesis, Delft University of Technology, c 2015 J. Melskens. All rights reserved. the Netherlands, 2015. Copyright 

stretching mode at 2000 cm−1 also referred to as the low stretching mode (LSM), and the stretching mode at 2090 cm−1 also referred to as the high stretching mode (HSM). As the Si-H, Si-H2 , and Si-H3 wagging modes are all concurrent at 640 cm−1 , this IR mode is commonly used to determine the total hydrogen content within the a-Si:H layer. To determine the cumulative silicon-hydrogen bond density, the 640 cm−1 mode observed is fit to a Gaussian, α(ω)/ω integrated with respect to frequency (ω), and the result is scaled based on Eq. 3.1 [6].  19 −2 (3.1) ω −1 α(ω)dω NSi-H,640 cm−1 = 1.6 × 10 cm

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Fig. 3.6. Schematic of silicon-hydrogen (Si-Hn , n = 1, 2, 3) bond stretching (S, top row), bond bending (B, middle row), and bond wagging (W) and rocking (R) (bottom row) in a-Si:H. Reprinted with permission from M. H. Brodsky, M. Cardona, and J. J. Cuomo, Infrared and Raman spectra of the silicon-hydrogen bonds in amorphous silicon prepared by glow discharge and sputtering, Physical c 1977 The American Physical Review B, 16, 3556–3571 (1977). Copyright  Society. All rights reserved.

The atomic concentration of hydrogen (cH ) from the 640 cm−1 wagging mode associated with Si-H, Si-H2 , and Si-H3 bonding is determined by normalizing the result of Eq. 3.1 to the number density of silicon, 5 × 1022 cm−3 [4]. The LSM and HSM peaks can be treated similarly to obtain the concentrations of hydrogen bound in siliconhydrogen bonds as cH,LSM and cH,HSM assuming the appropriate

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scaling based on Eq. 3.2 [6]. NSi-H, LSM

or HSM

19

= 9.1 × 10 cm

−2



ω −1 α(ω)dω

(3.2)

Note here that while Si-H2 contributes exclusively to the HSM peak, Si-H bonds contribute to both the LSM and HSM peaks, so the classical direct assignment of Si-H bonds to the 2000 cm −1 mode and Si-H2 to the 2090 cm−1 mode does not hold exactly. The relative absorption strengths of the HSM and LSM have been correlated to material quality. Films with a higher magnitude LSM peak have been correlated to dense material which exhibits only a limited amount of light-induced degradation; a popular experimental route to fabricate this type of a-Si:H is by using H2 dilution of the SiH4 gas during the plasma deposition [50]. Those films with a higher magnitude HSM peak have been correlated to lower density films that are typically less stable against light-induced degradation [51]. It should be noted, however, that predominant LSM or HSM bonding characteristics do not immediately imply “good” or “bad” electronic quality a-Si:H, as materials with a dominant LSM contribution can still have varying degrees of sub-bandgap absorption indicating significant differences in defect densities, while also generally certain bonding characteristics are preferred for different types of devices. Beyond bonding between silicon and hydrogen, the IR absorptance spectrum of a-Si:H based films may have other absorption peaks associated with different component species. In the case of a-Si1-x Gex :H and a-Si1-x Cx :H alloys, carbon-hydrogen and germanium-hydrogen bonds are also expected and will manifest in the optical response (Fig. 3.7). For a-Si1-x Cx :H, peaks related to C-H2 and C-H3 stretching will appear in the 2870 to 2960 cm−1 frequency range and those related to bonding complexes involving silicon, carbon, and hydrogen appear in the ∼600 to 1500 cm−1 frequency range [52–54]. The frequency of the silicon-hydrogen HSM at 2090 cm −1 also now coincides with a stretching mode where one or two carbon atoms are attached to silicon in the Si-H mode, making deconvolution of the different bonding configurations associated with the 2090 cm−1 peak in a-Si1-x Cx :H alloys complicated [53]. The

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Fig. 3.7. IR absorption in (top) a-Si1-x Cx :H and (bottom) a-Si1-x Gex :H alloy thin films. (top) Reprinted from Y. Tawada, K. Tsuge, M. Kondo, H. Okamoto, and Y. Hamakawa, Properties and structure of a-SiC:H for high-efficiency aSi solar cell, Journal of Applied Physics, 53, pp. 5273–5281 (1982), with the permission of AIP Publishing. (bottom) Reprinted with permission from K. W. Jobson, J.-P. R. Wells, R. E. I. Schropp, N. Q. Vinh, J. I. Dijkhuis, Infrared transient grating measurements of the dynamics of hydrogen local mode vibrations in amorphous silicon-germanium, Journal of Applied Physics, 103, 013106 (2008), with the permission of AIP Publishing.

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smaller size and mass of carbon generally blue-shift absorption features associated with carbon-hydrogen bonds relative to those associated with silicon-hydrogen bonds. For a-Si1-x Gex :H alloys, GeH and GeH2 modes are observed near the silicon HSM and LSM but are red-shifted [55–59]. In this case, the Ge-H2 mode overlaps with the silicon LSM, similarly convoluting the nature of that absorption feature to be a combination of Ge-H2 and Si-H bonding. The wagging mode attributed to Ge-H, Ge-H2 , and Ge-H3 is also red-shifted to a lower frequency relative to that of Si-H, Si-H2 , and Si-H3 observed at 640 cm−1 . These red shifts are associated with the larger size and mass of germanium relative to silicon. Other elements are often incorporated into the a-Si:H network either intentionally via choices of source gases during CVD or unintentionally due to contamination. Oxygen falls into both of those categories as it may be purposely incorporated into a-Si:H passivation and doped layers in order to reduce parasitic absorption, to shape the band structure, and to foster favorable growth conditions of subsequent layers in the respective device [60, 61], but may also appear as a result of leaks in vacuum chambers for deposition [40]. In either case, oxygen bound into the a-Si:H network adopts its own vibrational modes including those at 500, 650, and 940 cm−1 due to oxygen bonding between two silicon atoms (Si-O-Si) and at 630, 650, 750, 980, and 2090 cm−1 when one of those silicon atoms is bound to hydrogen (Si-O-Si-H) (Fig. 3.8) [62]. Other atoms intentionally added to the a-Si:H network may be dopant atoms such as phosphorus and boron making the material n-type and p-type, respectively [63, 64]. In the case of boron doping, boron-hydrogen bonding modes are observed at 2475, 2370, and 720 cm−1 with a mode at 840 cm−1 due to boron-silicon bonding. Modes associated with phosphorus bound in the a-Si:H network may be weaker in magnitude and more difficult to measure. Fluorine incorporation into the a-Si:H network may also occur due to the use of fluorine-based silicon carrying source gas (SiF4 ) [65–67] or dopant gases (BF3 ) [40]. In these cases, fluorine is bound into the a-Si:H network manifesting as silicon-fluorine wagging at 300 cm−1 , bending at 380 cm−1 , and stretching at 828, 930, and 1010 cm−1 .

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(a)

(b) (c)

(d)

Fig. 3.8. Transmittance spectra for a-Si:H films prepared with different oxygen contents. Additional peaks associated with silicon-oxygen bonding are observed. Reprinted with permission from G. Lucovsky, J. Yang, S. S. Chao, J. E. Tyler, and W. Czubatyj, Oxygen-bonding environments in glow-discharge-deposited amorphous silicon-hydrogen alloy films, Physical Review B, 28, 3225–3233 (1983). c 1983 The American Physical Society. All rights reserved. Copyright 

Replacement of hydrogen with deuterium and tritium isotopes has also been applied in deducing the characteristics of surface hydrogen bonding and bonding in the bulk [42, 68]. The modes associated with isotope inclusion are red-shifted with wagging modes for deuterium- and tritium-silicon bonding at 515 and 373 cm −1 ; bending modes for deuterium- and tritium-silicon bonding at 650 and 490 cm−1 ; and stretching mode clusters for deuterium- and tritiumsilicon bonding near 1500-1600 and 1200-1300 cm −1 , respectively (Figs. 3.3 and 3.9). Additional bending modes associated with replacement of hydrogen with deuterium or tritium are found at 782 and 755 cm−1 , respectively.

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Fig. 3.9. Absorption coefficient for a-Si:H fabricated with hydrogen (H1), deuterium (D1), and tritium (T1). Curves are shifted with respect to the vertical axes. Reprinted from L. S. Sidhu, T. Kosteski, and S. Zukotynski, Infrared vibration spectra of hydrogenated, deuterated, and tritiated amorphous silicon, c 1999 AIP Publishing. Journal of Applied Physics, 85, 2574 (1999). Copyright  All rights reserved.

3.4. The a-Si:H Nanostructure Silicon-hydrogen bonds can be embedded in different structural parts of the material, namely at the inner surfaces of vacancy and void complexes (Fig. 3.10) or in the disordered silicon surrounding these regions that are dominated by open volumes [6–9, 11–13, 15, 16, 33]. The interpretation of the IR silicon-hydrogen modes and the ratios of the integrated absorption strengths of those modes elucidate the details of the a-Si:H nanostructure. Start by considering the absence of any tetrahedrally bonded silicon atom as a vacancy, as it would be defined in a crystal. This monovacancy would leave four bonds which could be passivated by hydrogen. Two adjacent vacancies, a divacancy, would generate six bonds passivated by hydrogen forming a more energetically stable configuration than two isolated monovacancies, which are in fact not stable at room temperature.

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(b)

(c)

(d)

(e)

(f)

(g)

Fig. 3.10. Schematic illustration of silicon-hydrogen bonding configurations in a-Si:H including monovacancy, divacancy, trivacancy, and nanosized void configurations with associated structure parameter K. Reprinted with permission from A. H. M. Smets and M. C. M. van de Sanden, Relation of the Si-H stretching frequency to the nanostructural Si-H bulk environment, Physical Review B, 76, c 2007 The American Physical Society. All rights 073202 (2007). Copyright  reserved.

In a divacancy, the bonds passivated by hydrogen would be in the Si-H configuration and contribute to the LSM. A larger LSM relative to the HSM is considered to indicate vacancy-dominated a-Si:H with a film density that is decreased only with increasing hydrogen content

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while the extent of this decrease depends on the particular vacancy configuration [6]. With the absence of a larger number of silicon atoms, nanosized voids ∼ 2–8 nm in diameter appear [6, 7]. Hydrogen may be bound in Si-H2 and Si-H configurations on the interior surface of these voids and contribute to the HSM. In this case, film density decreases at a greater rate with increasing hydrogen content and the material becomes void-dominated. The transition between vacancyand void-dominated a-Si:H occurs when the contributions to the total hydrogen content from the LSM and HSM are equal. Structure parameters are a convenient way to express differences between different types of a-Si:H. One of them, the nanostructure parameter K, is defined as the number of monohydrides (Si-H) per unit volume of a missing silicon atom in the a-Si:H network [7]. Monovacancies and divacancies have K = 4 and K = 3, respectively, while larger nanosized voids have K < 1. The monohydride stretching mode frequency has been experimentally demonstrated to depend linearly on the nanostructure parameter K, as shown in Fig. 3.11. Another commonly used structure parameter is R∗ , defined as the relative contribution of the HSM to the total sum of stretching modes [13, 16]: R∗ =

IHSM IHSM + ILSM

(3.3)

Here, IHSM and ILSM denote the integrals of the HSM and LSM absorptance peaks, respectively. Hence, vacancy-dominated a-Si:H has low R∗ values and void-dominated a-Si:H has higher values of R∗ approaching 1. As vacancy-dominated a-Si:H has a density that decreases gradually with increasing hydrogen content and voiddominated a-Si:H has a density that decreases more rapidly with increasing hydrogen content, the associated structure parameters are related to material density. These structure parameters are indicative of the optical response of a material and may indicate the preferred use of that material in different optoelectronic devices like solar cells. For example, low R∗ and a large K parameter (divacancy-dominated) indicate dense a-Si:H that can be useful for absorber layers in thin-film solar cells

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Fig. 3.11. Relation between the frequency positions (ωSM ) of silicon-hydrogen stretching modes of Si-H monohydrides incorporated in different Si:H networks and the nanostructure parameter K that is defined as the number of Si-H monohydrides per unit volume of a missing Si atom from the network. Reprinted with permission from A. H. M. Smets, C. R. Wronski, M. Zeman, and M. C. M. van de Sanden, The Staebler-Wronski effect: new physical approaches and insights as a route to reveal its origin, Materials Research Society Proceedings, c 2010 Materials Research Society. All rights 1245, A-14-02 (2010). Copyright  reserved.

due to the limited light-induced degradation [8–12, 14, 15, 17], while higher R∗ and a smaller K parameter (void-dominated) indicate less dense a-Si:H that is suitable for use in heterojunction silicon solar cells as is evident from the high minority carrier lifetimes that have been reached when using this type of a-Si:H for the passivation of crystalline silicon surfaces [16]. The nanostructure may also be more complicated due to the formation of open volumes intermediate to divacancies and nanosized voids. A middle stretching mode (MSM) is sometimes observed at frequencies of 2030–2040 cm −1 in a-Si:H [69, 70] namely in grain boundary material in nanocrystalline Si:H (nc-Si:H) and highpressure processed amorphous material [13, 71] (Figs. 3.12 and 3.13). R∗ is once again defined as the contribution of the HSM to the cumulative stretching modes, in this case the sum of those from the HSM, LSM, and MSM. Contributions from the MSM will

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(b)

(c)

Fig. 3.12. IR absorptance showing low, middle, and high stretching modes (LSM, MSM, HSM) for high pressure deposited a-Si:H. Reprinted with permission from M. Fischer, H. Tan, J. Melskens, R. Vasudevan, M. Zeman, and A. H. M. Smets, High pressure processing of hydrogenated amorphous silicon solar cells: relation between nanostructure and high open-circuit voltage, Applied Physics c 2015 AIP Publishing. All rights Letters, 106, 043905 (2015). Copyright  reserved.

decrease R∗ . With the presence of the MSM, the number of absent silicon atoms in a vacancy is expressed as F = 2+3IMSM /ILSM [13]. For only divacancies, trivacancies, tetravacancies, and pentavacancies, F equals 2, 3, 4, and 5, respectively. Intermediate values correspond to the presence of multiple vacancy types in the material. a-Si:H with 2 < F < 3 indicates the presence of trivacancies. However, in combination with sufficiently low R∗ the amount of nanosized voids in the material is small enough for a suitable electronic quality for use as absorber layer in solar cells. This type of a-Si:H enables a reasonably high fill factor which is attributed to the low R∗ value, while a high open-circuit voltage can be obtained thanks to increased bandgap energies due to the distributed presence of divacancies and

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Fig. 3.13. LSM, MSM, HSM, extreme LSM (ELSM), and narrow high stretching modes (NHSM) in the IR absorption for nc-Si:H. Reprinted with permission from A. H. M. Smets, T. Matsui, and M. Kondo, Infrared analysis of the bulk silicon-hydrogen bonds as an optimization tool for high-rate deposition of microcrystalline silicon solar cells, Applied Physics Letters, 92, 033506 (2008). c 2008 AIP Publishing. All rights reserved. Copyright 

trivacancies and the associated elevated hydrogen concentration in the material [13]. The a-Si:H network contains silicon-hydrogen bonds in different configurations and associated vacancy and nanosized void structures. Within nc-Si:H thin films, hydrogen may be incorporated to passivate defects within crystalline grains but also on grain boundary surfaces directly and as part of a-Si:H passivating grain boundaries. In addition to the LSM, MSM, and HSM, stretching modes have been observed in nc-Si:H including extreme low stretching modes (ELSM) and narrow high stretching modes (NHSM) (Fig. 3.13) [70]. NHSM are relatively sharp features and are observed at 2083, 2103, and 2137 cm−1 corresponding to Si-H, Si-H2 , and Si-H3 bound on crystalline surfaces such as grain boundaries in the nc-Si:H film. ELSM observed near 1895, 1929, and 1950 cm−1 may be due to high local hydrogen bonding densities in combination with hydride

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dipole-dipole interactions. nc-Si:H with low NHSMs but high integrated other stretching modes is correlated with high performance and stability within solar cell devices [70], illustrating that the characteristics of the embedded a-Si:H material that passivates the ncSi:H grain boundaries also plays a crucial role in the functionality of these devices. Note that this is very similar to a-Si:H absorber layers in thin-film silicon solar cells as well as the a-Si:H passivation layers on crystalline silicon surfaces that are part of typical heterojunction solar cells. The a-Si:H material at the interface between a-Si:H and a-Si:H/nc-Si:H mixed phase material, as shown in Fig. 3.14, yields unique properties [37]. In [51], this transition has been approached in H2 + SiH4 plasma-enhanced CVD at different excitation frequencies, pressures, and temperatures. While the bandgap of a-Si:H may be tuned by the deposition temperature (Fig. 3.15), an even wider bandgap range is accessible by varying the H2 /SiH4 ratio in combination with the deposition temperature [10, 51]. In general, the bandgap increases slightly with increasing H2 /SiH4 ratio for a-Si:H far from the transition to nc-Si:H. Close to the transition,

Fig. 3.14. Schematic structure of the structural growth of different kinds of Si:H films as a function of film thickness (db ) and H2 /SiH4 dilution ratio R. The dashed and dotted lines indicate the transitions from amorphous to mixed-phase material and finally to nanocrystalline material for increasing db and R. Adapted from R. W. Collins, A. S. Ferlauto, G. M. Ferreira, C. Chen, J. Koh, R. J. Koval, Y. Lee, J. M. Pearce, and C. R. Wronski, Evolution of microstructure and phase in amorphous, protocrystalline, and microcrystalline silicon studied by real time spectroscopic ellipsometry, Solar Energy Materials & Solar Cells 78, 143 (2003). c 2003 Elsevier Ltd. All rights reserved. Copyright 

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(b)

Fig. 3.15. (a): Deposition temperature dependence of the bandgap for two series of a-Si:H materials deposited at 13.56 MHz (RF) and 40.68 MHz (VHF) and the lowest power allowing stable plasma conditions without H2 dilution of the SiH4 source gas. The lines are linear fits. (b): Bandgap measurements for three H2 dilution series deposited at different temperatures. The lines are guides to the eye. Reprinted with permission from M. E. Stuckelberger, Hydrogenated amorphous silicon: Impact of process conditions on material properties and solar cell efficiency, PhD thesis, Ecole Polytechnique F´ed´erale de Lausanne, c 2014 M. E. Stuckelberger. All rights reserved. Switzerland, 2014. Copyright 

the bandgap sharply increases and peaks before the transition to a mixed-phase amorphous + nanocrystalline (a + nc)-Si:H material (Fig. 3.16), whereas the description of the absorption spectra by a single-bandgap material is not appropriate for the mixed-phase region [37, 51]. Along with increases in bandgap, compressive stress in a-Si:H layers also increases substantially towards the amorphous to nanocrystalline Si:H transition [72]. Experimentally, this is noted by the difficulties in growing a-Si:H near this transition at useful thicknesses as films delaminate from smooth substrates even with adhesion layers. Furthermore, the stress at the transition leads to plateletshaped voids above the peaks of the substrate (Fig. 3.17) [17]. During the deposition of these layers with constant deposition conditions, nanocrystalline phase Si:H grows on top of underlying a-Si:H as a result of increasing order of the substrate as seen by the adatoms during growth. At such high H2 /SiH4 ratios at the transition from a-Si:H to nc-Si:H, the bandgap of a-Si:H can be maximized as long as the nucleation of nc-Si:H material is avoided, e.g. by keeping the

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(a)

(b)

Fig. 3.16. Bandgap as a function of the H2 dilution for ten series deposited in different pressure regimes at 13.56 MHz (RF) (a) and 40.68 MHz (VHF) (b). Reprinted with permission from M. E. Stuckelberger, Hydrogenated amorphous silicon: Impact of process conditions on material properties and solar cell efficiency, PhD thesis, Ecole Polytechnique F´ed´erale de Lausanne, Switzerland, c 2014 M. E. Stuckelberger. All rights reserved. 2014. Copyright 

(a)

(b)

(c)

Fig. 3.17. Transmission electron microscope images of a solar cell with a 1-μm-thick absorber layer deposited at the transition from a-Si:H to nc-Si:H. (a): Overview of the cell cross section with arrows indicating peaks of the ZnOcovered substrate, above which chains of voids are located. (b-c): High-resolution images of a co-processed solar cell show that the nanovoids are platelet-shaped. Images courtesy of Dr. D. T. L. Alexander, EPFL, and Dr. M. Duchamp, FZ J¨ ulich. Reprinted with permission from M. Stuckelberger, R. Biron, N. Wyrsch, F.-J. Haug, and C. Ballif, Review: Progress in solar cells from hydrogenated amorphous silicon, Renewable and Sustainable Energy Reviews, 76, 1497 (2017). c 2017 Elsevier Ltd. All rights reserved. Copyright 

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(a)

(b)

(c) ∗

Fig. 3.18. Microstructure factor R as a function of the hydrogen/silane flow ratio during deposition of the intrinsic absorber layers, varying pressure for 40.68 MHz (VHF) (a) and 13.56 MHz (RF) (b), and temperature for 13.56 MHz (c). For each series, the power was just high enough to enable stable plasma conditions except for the series with open symbols, where the power was slightly higher. Reprinted with permission from M. Stuckelberger, R. Biron, N. Wyrsch, F.-J. Haug, and C. Ballif, Review: Progress in solar cells from hydrogenated amorphous silicon, Renewable and Sustainable Energy Reviews, 76, 1497 (2017). c 2017 Elsevier Ltd. All rights reserved. Copyright 

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layers thin enough. This enables the fabrication of single-junction a-Si:H solar cells with > 1 V open-circuit voltage [13, 14, 51]. Even though the large voids are inhomogeneously distributed, they lead to a dramatic increase of the average number of siliconhydrogen bonds per missing Si atom (i.e., lower K), which corresponds to higher HSM and higher R∗ , which in turn results in a reduced stability against light-induced defect formation (Fig. 3.18) [14, 51]. On the other hand, the porous nature and high average hydrogen concentration at low hydrogen/silane flow ratios result in high IHSM , (high R∗ ) as well. Note that this trend is stronger for lower plasma excitation frequencies. The dependence of R∗ on the deposition temperature is weak around 200◦ C. For high-quality a-Si:H material, the lower temperature limit is given by “freezing in” defects, while the upper temperature limit is given by hydrogen effusion. Between the porous a-Si:H at low hydrogen dilutions and the stressed a-Si:H with voids at high hydrogen dilution, there is a minimum R∗ yielding dense a-Si:H with little hydrogen incorporated that is predominantly contributing to the LSM. 3.5. Stability and Device Functionality In order to probe the stability and functionality of different a-Si:H layers in devices, the layers characterized in Figs. 3.13 and 3.16 have been included as 220 nm thick absorber layers in optimized singlejunction solar cells, mapping out the three-dimensional deposition parameter space of hydrogen/silane ratio, excitation frequency, and pressure [10, 17, 51]. After measurements of the as-deposited state, the solar cells were light soaked under standard conditions and re-measured afterwards to evaluate the performance after light-induced degradation (Fig. 3.19) and quantify the relative losses (Fig. 3.20). This resulted in a consistent picture of the stability for a variety of a-Si:H materials with the following key observations: • Increasing the H2 to SiH4 gas flow ratio leads to an increase of the open-circuit voltage (Voc ), as expected from the wider bandgap (Fig. 3.16).

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(c)

(d)

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Fig. 3.19. Solar cell performance in terms of open-circuit voltage (a), fill factor (b), short-circuit current density (c), and conversion efficiency (d) after 1000 h light soaking (50◦ C, 1000 W/m2 , AM1.5g), as a function of the hydrogen/silane flow ratio during the deposition of the 220-nm-thick absorber layer at 13.56 MHz. Empty symbols and dashed lines indicate a significant crystalline fraction in the absorber layer. Reprinted with permission from M. Stuckelberger, R. Biron, N. Wyrsch, F.-J. Haug, and C. Ballif, Review: Progress in solar cells from hydrogenated amorphous silicon, Renewable and Sustainable Energy Reviews, 76, c 2017 Elsevier Ltd. All rights reserved. 1497 (2017). Copyright 

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(a)

(b)

(c)

(d)

Fig. 3.20. Relative light-induced degradation (1000 h light soaking at 50◦ C, 1000 W/m2 , AM1.5g) of the solar cell performance in terms of open-circuit voltage (a), fill factor (b), short-circuit current density (c), and conversion efficiency (d), as a function of the hydrogen/silane flow ratio during the deposition of the 220nm-thick absorber layer at 13.56 MHz. Empty symbols and dashed lines indicate a significant crystalline fraction in the absorber layer. Reprinted with permission from M. Stuckelberger, R. Biron, N. Wyrsch, F.-J. Haug, and C. Ballif, Review: Progress in solar cells from hydrogenated amorphous silicon, Renewable and c 2017 Elsevier Ltd. Sustainable Energy Reviews, 76, 1497 (2017). Copyright  All rights reserved.

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• Consistent with the bandgap widening and Voc increase, the current density (Jsc ) decreases with increasing H2 to SiH4 gas flow ratio. • The fill factor (F F ) increases with the H2 to SiH4 gas flow ratio towards a maximum that corresponds to the minimum R∗ (Fig. 3.17). Particularly the combination of low H2 to SiH4 gas flow ratio and high pressure leads to highly porous material consisting of clusters (“powder”) that is synthesized in the plasma, which results in high defect densities and corresponding high recombination rates in the a-Si:H absorber. • The trends observed in the conversion efficiency are dominated by the trends observed for F F . This behavior occurs because the trends of Voc and Jsc partially compensate each other and the relative variation of the FF is larger. • At the amorphous to nanocrystalline transition, all solar cell parameters degrade substantially due to high recombination at ncSi:H/a-Si:H interfaces, band alignment issues, and low absorptance of the nc-Si:H phase. In the initial state (all parameters are shown in Ref. [51]), the external parameters of the solar cells are comparable apart from intrinsic bandgap effects. Therefore, the performance after light soaking is governed by the relative light-induced degradation (Fig. 3.20), with the degradation being minimal for cells with aSi:H absorbers that are characterized by a relatively small HSM contribution. One aspect may be surprising: under certain conditions that depend on the details of the p-i interface, the open-circuit voltage systematically increases upon light soaking [73]. Obviously, the solar cell performance of a-Si:H solar cells is not uniquely determined by the properties of the absorber layer. Nevertheless, it is remarkable how strong the fill factor after light soaking is correlated to the microstructure factor R∗ , even across deposition series with three independent parameters varied (Fig. 3.21). At first view, this suggests that the minimization of R∗ for the absorber layer would be an appropriate way to maximize the fill factor after light soaking. This is clearly valid for a-Si:H with microstructure

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Fig. 3.21. Microstructure factor R∗ measured on layers deposited on glass, correlated with the fill factor of solar cells with these layers incorporated as absorbers for H2 dilution series at different pressures, frequencies, and temperatures. Lines connect H2 dilution series with all other deposition parameters kept constant. Reprinted with permission from M. E. Stuckelberger, Hydrogenated amorphous silicon: Impact of process conditions on material properties and solar cell efficiency, PhD thesis, Ecole Polytechnique F´ed´erale de c 2014 M. E. Stuckelberger. All rights Lausanne, Switzerland, 2014. Copyright  reserved.

factors above 20% that yield poor fill factors, making these types of a-Si:H not ideal as a solar cell absorber layer. Below 20%, R∗ is not sufficiently sensitive, among other reasons due to uncertainties in the quantification of R∗ , to find a strong correlation with the solar cell performance. Yet, it has been consistently established across laboratories that the absorber layers of high-efficiency solar cells always satisfy R∗ < 20% [74]. Since FTIR spectroscopy is sensitive to large scale changes in the a-Si:H nanostructure, while changes in Si-H bonds at the ppm level already have an impact on the photoconductivity and recombination activity, it is not surprising that the sensitivity of this technique to directly study the StaeblerWronski effect is limited. Other characterization techniques which

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are directly sensitive to changes in the electrical properties of a-Si:H, such as the ubiquitous current-voltage (IV) and external quantum efficiency (EQE) measurements, are generally more fitting for this purpose. More advanced techniques can quantify the sub-bandgap absorption that is associated with the formation of electrical defects such as the constant photocurrent method (CPM) [75], dual beam photoconductivity (DBP) [76], and Fourier transform photocurrent spectroscopy (FTPS) [77–79] that is often paired with photothermal deflection spectroscopy (PDS) [80]. Furthermore, electron paramagnetic resonance (EPR) spectroscopy has been instrumental in gaining a better understanding of the Staebler-Wronski effect thanks to its strength in the detection of unpaired spins, i.e. silicon dangling bonds, in the material [12, 81, 82]. Combining these techniques with FTIR analyses has proven to be a rigorous and powerful approach in attacking this four decades old problem. Apart from the well-known application of a-Si:H in the context of solar cells, it is also possible to use this material in other types of devices, such as transistors and sensors [44]. Recently, it has become clear that a-Si:H can also be used in programmable photonic integrated circuits [28, 32]. Interestingly, the programmable aspect in these devices relies on a careful control of the refractive index between two different values, which is achievable through cycles of light soaking and annealing. While similar changes in the extinction coefficient (or photoconductivity) are commonly known as the Staebler-Wronski effect in solar cells, the Kramers-Kronig relations dictate that analogous, yet small, changes in refractive index should occur as part of this effect as well. Consequently, this adverse material characteristic in solar cells can be used in a beneficial way for programmable photonics. When using this principle in the IR part of the spectrum on a thin-film interferometric device consisting of an a-Si:H/SiO2 stack deposited on a crystalline silicon wafer substrate, the wavelength at which the reflectance minimum occurs can be shifted to lower and higher values by cycles of annealing and light soaking, respectively (see Fig. 3.22). Based on analysis of FTIR spectra corresponding to this type of a-Si:H, as shown in Fig. 3.23, an atomic hydrogen concentration

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(a)

(b)

Fig. 3.22. Effects of subsequent cycles of annealing and light soaking on the wavelength at which a reflectance minimum occurs for a thin-film interferometric device consisting of an a-Si:H/SiO2 stack deposited on a crystalline silicon wafer substrate. After an initial decrease in the reflectance minimum wavelength, a reversibility of 0.4 nm is observed (a), which is associated with reversible changes in the refractive index that amount to 0.001 (0.3% relative) after an initial irreversible decrease (b). Reprinted from M. A. Mohammed, J. Melskens, R. Stabile, F. Pagliano, C. Li, W. M. M. Kessels, and O. Raz, Metastable refractive index manipulation in hydrogenated amorphous silicon for reconfigurable photonics, Advanced Optical Materials, 1901680 (2020). Open access (CC BY-NC-ND 4.0).

of 20.5% and a microstructure parameter R∗ value of 21% could be derived. This rather void-rich material, at least in comparison to the high-quality materials discussed above in the context of thin-film silicon solar cells, is prone to some initial oxidation effects that do, however, saturate after a few cycles of annealing and light soaking. While oxidation in air is a natural effect for a-Si:H, especially for the materials with an elevated R∗ , these materials are also prone to a more pronounced Staebler-Wronski effect than low R∗ materials, which is not preferred in a PV context (see Fig. 3.21), but which is in fact desirable in the context of programmable photonics. The merits of this elevated R∗ type of a-Si:H also become clear when applying it in a micro-ring resonator, in which the changes in refractive index due to annealing and light soaking are exploited in terms of changes in the resonance wavelength of the device, as depicted in Fig. 3.24. Here it is shown that after three cycles of annealing and light soaking, two very well-defined resonance wavelengths that are spaced 0.3 nm

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(b)

(c)

Fig. 3.23. Effects of subsequent cycles of annealing and light soaking on the Si-H (a) and Si-O (b) stretching modes, as well as the extracted Si-H stretching mode peak absorbance at 2000 cm−1 and the Si-O stretching mode at 1075 cm−1 (c), for a thin-film interferometric device consisting of an a-Si:H/SiO2 stack deposited on a crystalline silicon wafer substrate. Reprinted from M. A. Mohammed, J. Melskens, R. Stabile, F. Pagliano, C. Li, W. M. M. Kessels, and O. Raz, Metastable refractive index manipulation in hydrogenated amorphous silicon for reconfigurable photonics, Advanced Optical Materials, 1901680 (2020). Open access (CC BY-NC-ND 4.0).

apart can be achieved after subsequent cycles of annealing and light soaking. Although an extinction ratio in excess of 20 dB between the two switchable states has already been realized, investigations into fine tuning of the reversibility and long-term stability of these two programmed states are still desired to make further steps towards a-Si:H based reconfigurable photonics and integrated circuits [32].

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(a)

(b)

(c)

(d)

Fig. 3.24. Effects of subsequent cycles of annealing and light soaking on an a-Si:H based photonic micro-ring resonator, visualized schematically (a) and in an SEM image (b). The resonance wavelength can be shifted by using annealing and light soaking treatments (c) with good reversibility between two switchable states after the first few cycles of annealing and light soaking (d). Reprinted from M. A. Mohammed, J. Melskens, R. Stabile, F. Pagliano, C. Li, W. M. M. Kessels, and O. Raz, Metastable refractive index manipulation in hydrogenated amorphous silicon for reconfigurable photonics, Advanced Optical Materials, 1901680 (2020). Open access (CC BY-NC-ND 4.0).

3.6. Summary FTIR spectroscopy is a versatile and non-destructive optical characterization method for many materials, including a-Si:H and nc-Si:H, and structural material properties can be derived with relative ease. The ratio of the FTIR absorption in the hydrogen-silicon stretching modes at 2090 and 2000 cm−1 was correlated early in the history of aSi:H solar cells to light-induced degradation. However, the stretching modes were predominantly attributed to the number of hydrogen atoms bonded to a silicon atom and only recently a more adequate

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model based on the a-Si:H nanostructure has been established, which accounts for the influence that vacancies and voids have on the material properties. Hydrogenated amorphous silicon stands out from other semiconductors by great tunability in a wide deposition parameter space. This allows for the synthesis of different layers with unique properties, and the IR absorptance spectra have proven to be useful as a tool to select the right materials for the right application: • For the archetypical application as a PV absorber layer, a-Si:H material is optimized for high mass density, low defect density, and a low microstructure factor. The combination of a moderately narrow bandgap with minimized light-induced degradation yields high-efficiency devices [10, 51, 83–87]. • Narrow-bandgap a-Si:H can be used as bottom-cell absorber in multi-junction solar cells, yielding high currents [14]. Alloying with Ge reduces the bandgap further. • Wide-bandgap a-Si:H can be used as top-cell absorber, yielding high voltages [14, 88–93]. Alloying with C or O widens the bandgap further. • Few nanometer thick a-Si:H layers are optimized for the surface passivation of crystalline silicon in heterojunction solar cells, in which case not only low microstructure material performs well, but also more porous a-Si:H can be suitable [16]. • Stress-controlled a-Si:H is required to grow thick a-Si:H for detector applications [94]. • For optical applications, a-Si:H can be used in waveguides [34, 35] and is also useful for programmable applications due to the tunability of the complex optical response [28, 32]. For the latter application, a-Si:H with a somewhat elevated microstructure factor seems to be preferred to realize a larger difference between two switchable values of the refractive index, owing to the more pronounced Staebler-Wronski effect in such a-Si:H material in comparison to the type of a-Si:H that is typically preferred as a PV absorber layer. • Porous a-Si:H can serve as solid matrix or reservoir to embed other materials such as lithium for battery applications [95].

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When a-Si:H is utilized in each of these applications, the particular nanostructure, hydrogen content, and the way hydrogen is configured in the material all impact the final material and device functionality.

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silicon monitored by advanced application of Fourier transform photocurrent spectroscopy, Solar Energy Materials & Solar Cells, 129, pp. 70–81. Holovsk´ y, J., Schmid, M., Stuckelberger, M., Despeisse, M., Ballif, C., Poruba, A., and Vanˇeˇcek, M. (2012). Surface defect states in hydrogenated amorphous silicon studied by photothermal and photocurrent spectroscopy and optical simulation, Journal of Non-Crystalline Solids, 358, pp. 2035–2038. Fehr, M., Schnegg, A., Rech, B., Lips, K., Astakhov, O., Finger, F., Pfanner, G., Freysoldt, C. Neugebauer, J., Bittl, R., and Teutloff, C. (2011). Combined multifrequency EPR and DFT study of dangling bonds in a-Si:H, Physical Review B, 84, 245203. Fehr, M., Schnegg, A., Rech, B., Astakhov, O., Finger, F., Bittl, R., Teutloff, C., and Lips, K. (2014). Metastable defect formation at microvoids identified as a source of light-induced degradation in a-Si:H, Physical Review Letters, 112, 066403. Matsui, T., Maejima, K., Bidiville, A., Sai, H., Koida, T., Suezaki, T., Matsumoto, M., Saito, K., Yoshida, I., and Kondo, M. (2015), High-efficiency thin-film silicon solar cells realized by integrating stable a-Si:H absorbers into improved device design, Japanese Journal of Applied Physics, 54, 08KB10. Matsui, T., Bidiville, A., Maejima, K., Sai, H., Koida, T., Suezaki, T., Matsumoto, M., Saito, K., Yoshida, I., and Kondo, M. (2015). Highefficiency amorphous silicon solar cells: Impact of deposition rate on metastability, Applied Physics Letters, 106, 053901. Sai, H., Matsui, T., and Matsubara, K. (2016). Stabilized 14.0% — efficient triple-junction thin-film silicon solar cell, Applied Physics Letters, 109, 183506. Salaba¸s, E. L., Salaba¸s, A., Mereu, B., Caglar, O., Kupich, M., Cashmore, J. S., and Sinicco, I. (2016). Record amorphous silicon single-junction photovoltaic module with 9.1% stabilized conversion efficiency on 1.43 m2 , Progress in Photovoltaics: Research and Applications, 24(8), pp. 1068–1074. Cashmore, J. S., Apolloni, M., Braga, A., Caglar, O., Cervetto, V., Fenner, Y., Goldbach-Aschemann, S., Goury, C., H¨ otzel, J. E., Iwahashi, T., Kalas, J., Kitamura, M., Klindworth, M., Kupich, M., Leu, G.-F., Lin, J., Lindic, M.-H., Losio, P. A., Mates, T., Matsunaga, D., Mereu, B., Nguyen, X.-V., Psimoulis, I., Ristau, S., Roschek, T., Salabas, A., Salabas, E. L., and Sinicco, I. (2016). Improved conversion efficiencies of thin-film silicon tandem (MICROMORPHTM ) photovoltaic modules, Solar Energy Materials & Solar Cells, 144, pp. 84–95.

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88. Sch¨ uttauf, J.-W., Bugnon, G., Stuckelberger, M., H¨ anni, S., Boccard, M., Despeisse, M., Haug, F.-J., Meillaud, F., and Ballif, C. (2014). Thin-film silicon triple-junction solar cells on highly transparent front electrodes with stabilized efficiencies up to 12.8%. IEEE Journal of Photovoltaics, 4(3), pp. 757–762. 89. Sch¨ uttauf, J.-W., Niesen, B., L¨ ofgren, L., Bonnet-Eymard, M., Stuckelberger, M., H¨ anni, S., Boccard, M., Bugnon, G., Despeisse, M., Haug, F.-J., Meillaud, F., and Ballif, C. (2015). Amorphous silicongermanium for triple and quadruple junction thin-film silicon based solar cells, Solar Energy Materials & Solar Cells, 133, pp. 163–169. 90. Kirner, S., Neubert, S., Schultz, C., Gabriel, O., Stannowski, B., Rech, B., and Schlatmann, R. (2015). Quadruple-junction solar cells and modules based on amorphous and microcrystalline silicon with high stable efficiencies, Japanese Journal of Applied Physics, 54(8S1), 08KB03. 91. Urbain, F., Smirnov, V., Becker, J.-P., Lambertz, A., Rau, U., and Finger, F. (2016). Light-induced degradation of adapted quadruple junction thin film silicon solar cells for photoelectrochemical water splitting, Solar Energy Materials & Solar Cells, 145, pp. 142–147. 92. Multone, X., Fesquet, L., Borrello, D., Romang, D., Choong, G., VallatSauvain, E., Charri`ere, M., Billet, A., Boucher, J.-F., Steinhauser, J., Orhan, J.-B., Monnard, R., Cardoso, J.-P., Charitat, G., Dehbozorgi, B., Guillot, N., Monteduro, G., Marmelo, M., Semenzi, R., Benagli, S., and Meier, J. (2015). Triple-junction amorphous/microcrystalline silicon solar cells: Towards industrially viable thin film solar technology, Solar Energy Materials & Solar Cells, 140, pp. 388–395. 93. Banerjee, A., Su, T., Beglau, D., Pietka, G., Liu, F. S., Almutawalli, S., Yang, J., and Guha, S. (2012). High-efficiency, multijunction nc-Si:H-based solar cells at high deposition rate, IEEE Journal of Photovoltaics, 2, pp. 99–103. 94. Franco, A., Geissb¨ uhler, J., Wyrsch, N., and Ballif, C. (2014). Fabrication and characterization of monolithically integrated microchannel plates based on amorphous silicon, Scientific Reports, 4, 4597. 95. He, Y., Yu, X., Wang, Y., Li, H., and Huang, X. (2011). Aluminacoated patterned amorphous silicon as the anode for a lithiumion battery with high coulombic efficiency, Advanced Materials, 23, pp. 4938–4941.

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CHAPTER 4

Near-Infrared to Ultraviolet Optical Response and the Absorption Onset: Parametric Representations Robert W. Collins, Prakash Koirala, and Nikolas J. Podraza University of Toledo, USA

4.1. Introduction The spectra that define the linear optical response as a function of photon energy E for a semiconductor embody key characteristics that determine its performance in a variety of optoelectronic applications [1–6]. The optical response of any isotropic medium is defined in terms of the complex index of refraction N = n + ik with the real and imaginary parts being the real index of refraction n and the extinction coefficient k. The real index of refraction describes the phase speed v of a light wave within the material according to v = c/n, where c is the speed in vacuum. For a semiconductor over the range in E of greatest interest, that is, near the bandgap, n controls the reflection and refraction of the wave at interfaces and its interference behavior within thin films. The extinction coefficient describes the absorption of the light wave as it passes through the semiconductor; in essence, the exponential decay of the optical 129

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→ − → − electric field vector according to E (z) = E (0) exp(−αz/2), where z is the distance traveled along the light ray, α is the absorption coefficient, α = 4πk/λ, and λ = hc/E is the wavelength with h as Planck’s constant. An alternative description of the optical response of an isotropic material is based on the real and imaginary parts of the complex relative permittivity (more commonly referred to as the complex dielectric function) ε = ε1 + iε2 , which relates the → − polarization P or dipole moment per unit volume of the material to → − → − the optical electric field. In fact, P = ε0 (ε − 1) E in the International System of Units (SI units), where ε0 is the absolute permittivity of free space. The pair of optical responses (n, k) and (ε1 , ε2 ) are related by ε1 = n2 −k2 and ε2 = 2nk, and each pair is referred to as a version of the optical constants, based on the understanding that they are constants at a fixed optical frequency or photon energy for a given single crystal material. Alternatively, they are referred to as optical functions based on the fact that they are functions of the photon energy. For structures and devices in some technologies, knowledge of the optical functions is required as a direct predictor of their functionality. Example structures include optical coatings in which the derived transmittance and reflectance (T & R) spectra define their functionality [7, 8]; example devices include light detectors, imagers, and photovoltaic cells in which the derived spectral absorbance of the active layer, leading to electron–hole pair generation, is the initial event in simulations of device performance [9–11]. As a result, for the associated technologies, measurement of the optical functions is critically important as it provides the fundamental material properties from which one can simulate the operational characteristics of the structures and devices, including spectra in the transmittance, reflectance, and individual layer absorbances. In other technologies, the measured optical functions are not directly applicable, but can be further analyzed to extract useful information on the nature of the electronic band structure of the materials [1–6]. For example, in all semiconductor devices, each component material’s bandgap energy is a critical operational parameter, the bandgap being the energy difference between the minimum energy of the

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conduction band and the maximum energy of the valence band. Although the optical functions may not be of critical interest on their own in these cases, they can be analyzed to extract the bandgap using an appropriate theory for the optical transitions at the onset of absorption. Thus, the single optical parameter of greatest interest that can be extracted from the optical functions of a semiconductor is its bandgap. The bandgap and its nature, whether direct or indirect and allowed or forbidden, control many of the key semiconductor optoelectronic properties [9, 11]. For a crystalline semiconductor, the absorption onset is typically quite sharp and the bandgap is well defined. As a result, it is straightforward to extract the bandgap from the spectra in the optical functions, either from the absorption coefficient α, applying the theory of optical absorption, or from both (ε1 , ε2 ), applying more general theories of optical transitions at the lowest band structure critical point [1–4]. In order to extract the bandgap Eg from α for a crystalline semiconductor, the expression (αE)μ = C(E − Eg ) is traditionally applied to data from T&R or photoconductive spectroscopies. In this expression, the exponent μ depends on the nature of the transition: μ = 2 or 2/3 for allowed or forbidden direct transitions, respectively, and μ = 1/2 or 1/3 for allowed or forbidden indirect transitions, respectively. Thus, if (αE)μ is plotted versus E, the photon energy at the zero ordinate extrapolation provides the bandgap. The (αE)μ extrapolation method of bandgap determination is based on the assumption of parabolic functions En (k); n = c, v, describing the valence (v) and conduction (c) band energies versus electron momentum k, as well as the assumptions that the momentum matrix element is constant and, furthermore, that the index of refraction is also constant [3, 4]. Since the theory of the absorption onset is framed in terms of ε2 , which is given in terms of α by ε2 = αnhc/2πE, a more rigorous approach would be to use an extrapolation of (αnE)μ in these bandgap plots. For a crystalline semiconductor, the absorption onset is sufficiently sharp, however, such that one can neglect the variation in the index of refraction over the photon energy range of the onset. Then n−μ can be absorbed into the slope constant C. To incorporate the alternative possibility

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of a constant dipole (CD) matrix element, one would instead plot (α/E)μ or (αn/E)μ , but given that the range of energy of these plots is narrow, the effect of this alternative approach on the deduced bandgap is small. In order to extract the bandgap from the optical functions more rigorously and accurately, both spectra (ε1 , ε2 ) from T & R spectroscopy or spectroscopic ellipsometry (SE) can be analyzed. In fact, in the neighborhood of the absorption onset, one can fit the complex dielectric function to a Lorentzian lineshape expression of the form ε = CΓ−μ exp(iφ) (E − Eg − iΓ)μ , where the phase φ and exponent μ depend on the nature of the band structure critical point [12, 13]. The second derivative of ε is generally fit using this equation to eliminate the smoothly varying background in ε and to achieve enhanced sensitivity and accuracy in Eg determination. This second derivative approach, so-called critical point analysis, also provides the bandgap broadening parameter Γ, which can describe absorption above and below the bandgap energy due to the limitation on the excited state lifetime. The lifetime of an electronic transition in a single crystalline semiconductor at room temperature is typically controlled by electron–phonon interactions. More generally, however, Γ can account for various broadening mechanisms, in addition to thermal site disorder, contributing to the steep Urbach tail at the absorption onset of a crystalline semiconductor [14–16]. The methods for extracting the bandgaps of crystalline semiconductors are straightforward due to the sharpness of the transitions, which make the bandgap values relatively insensitive to the various assumptions. In fact, exceedingly accurate values are possible through critical point analysis of the lowest energy optical transitions [12, 13]. In contrast, the corresponding approaches for amorphous semiconductors lead to considerable challenges due to the observed broadening of the absorption spectra, which suppresses critical point structure. The broadening of the absorption onset arises from the short lifetimes of optical transitions, as well as the static site disorder which generates electronic states below the bandgap and a broad Urbach absorption tail [17–20]. When the absorption onset is broad, the detailed methods and assumptions

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underlying the absorption coefficient plots — to which single crystal bandgap determinations are relatively insensitive — become critically important in amorphous material bandgap determination. These include (i) the contribution to the plot from the photon energy dependence of the index of refraction, (ii) the assumptions concerning the matrix element of the band edge transitions and the density of states distribution, (iii) the effect of sub-gap absorption due to the broadening of above bandgap transitions and to static disorder, and (iv) transitions well above the bandgap and a broad Urbach absorption tail whose presence leads to deviations of the absorption onset behavior from the standard assumptions. After application of many different approaches to address the problem of bandgap determination from the standpoint of the optical absorption plots versus photon energy, the method of zero-ordinate 1/2 extrapolation of (αn/E)1/2 ∝ ε2 versus E has provided the most reliable linear relations for silicon-based amorphous semiconductors [3, 21]. This plot is derived assuming densities of states that increase from the band edges in accordance with a square root dependence on photon energy along with a CD matrix element. The index of refraction is included since its variation with photon energy over the broad range of the absorption onset cannot be neglected. In contrast, the traditional Tauc plot [22, 23] of (αnE)1/2 versus E relying on the same assumptions with the exception of a constant momentum (CM) matrix element (and in most cases a constant index of refraction [19, 20]) shows clear curvature, resulting in a bandgap that varies according to the range used in linear extrapolation. With the development of SE as a more widely used tool for determination of (ε1 , ε2 ) spectra in place of (or in addition to) T&R spectroscopies [24, 25], efforts have been directed toward a comprehensive description of the optical properties of amorphous semiconductors similar to that used in accurate critical point analysis for crystalline semiconductors. The first highly successful effort in this direction was made by Jellison and Modine who proposed a single broad Lorentz oscillator to describe the ε2 spectrum of an amorphous semiconductor modified with a bandgap function that serves to reproduce the Tauc plot at absorption onset energies [26].

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Then the ε1 spectrum could be generated by an analytical Kramers– Kronig integration of ε2 . The resulting expressions included only five parameters, three being the amplitude A0 , resonance energy E0 , and broadening Γ of the Lorentz oscillator, the fourth being the bandgap Eg , and the final one being a constant contribution ε0s to the real part of the dielectric function. An enhancement of the overall approach was applied by Ferlauto et al. who modified the bandgap function component of ε2 for consistency with a CD matrix element and also included the capability of an Urbach tail addition [27]. The resulting expression for ε2 could be integrated analytically as well to extract ε1 . The corresponding expressions for the (ε1 , ε2 ) spectra without the Urbach tail included six parameters, having one additional parameter compared to those of the Jellison and Modine model. The additional parameter has been found to be critical, providing an adjustable transition energy EP between the band edge function and the Lorentz oscillator. In most cases, the six parameter expressions of Ferlauto et al. could be reduced to five parameter ones by fixing ε0s to unity or at least to a constant (> 1) in analyses of groups of samples. With the addition of the Urbach tail with its slope and transition energy, the expressions for the (ε1 , ε2 ) spectra include either eight or seven parameters and are suitable for fitting experimental spectra from below the amorphous semiconductor bandgap to well above, where the Lorentz oscillator behavior is observed to dominate. In this chapter, the development of parametric expressions for the (ε1 , ε2 ) spectra of amorphous semiconductors will be reviewed starting from a discussion of the general expression for the photon energy dependence of ε2 for a single crystal semiconductor. The emphasis will be on motivating the underlying origins of the parametric expressions, which include the Urbach tail, band edge, and Lorentz oscillator components. Two limiting forms of the ε2 spectra for an amorphous semiconductor will be elaborated here. The first arises by neglecting the broadening of individual transitions and working within a joint density of states framework for the band-to-band transitions [21, 28]. This form gives rise to the band edge functions appropriate for CM and CD matrix element

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formulations and predicts the absorption behavior that enables bandgap determination via linear extrapolation of functions of α, n, and E. The second suppresses the joint density of states distribution and considers broadening as dominant in controlling the photon energy dependence of ε2 . This form generates the Lorentz oscillator component with an amplitude that reflects the combined density of states and a broadening parameter that reflects the excited state lifetime for band-to-band transitions, which is controlled by the static disorder and by defects in the network [3, 26, 27]. The latter limiting form arises from a comparison of the broadening parameters of the dielectric function critical points for single crystal and hydrogenated nanocrystalline silicon (nc-Si:H), with a natural extension of the observed trend to hydrogenated amorphous silicon (a-Si:H). The results of this second set of manipulations for ε2 are two parametric forms based on the three components: sub-gap, band edge, and above gap, which are sufficiently simple in form that Kramers–Kronig integration can be performed. The partial fraction method of integration is described that provides the desired analytical expressions for ε1 . 4.2. Theory of the Optical Response of Amorphous Semiconductors 4.2.1. Background The starting point for a discussion of the theory of semiconductor optical properties is the following equation for the complex relative permittivity or complex dielectric function [3, 13]:     |e · pcv (E  )|2 2e2 2  J ε(E) = 1 + cv E ε0 m2 c,v E 2   1 1 × + (4.1) dE  , E  − E − iΓ E  + E + iΓ given in SI units. This expression requires elaboration before further manipulation for comparison with experimental data. In the prefactor of the summation, e and m are the electron charge and mass,  is Planck’s constant ( = h/2π), and ε0 is the permittivity of

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free space. The summation and indices represent pairs of occupied valence band states (v) and unoccupied conduction band states (c) separated by an energy E  , and Jcv (E  ) is the number of such single spin states (i.e., not including the factor of two for spin) per → − → e and p cv (E  ) describe volume per energy interval. The vectors − the polarization direction and the momentum matrix element for the optical transition between the states v and c. In general, the matrix element depends not only on the energy separation between the initial and final states, but also on the states v and c themselves. As a result of a limited lifetime of the excited state, that is, the hole in state v and the electron in state c, transitions may occur between states separated by an energy E  when the photon energy E differs from E  . The factor consisting of two terms in parentheses under the integral describes a Lorentzian lineshape function for photon energy E, which accounts for the broadening of the optical transitions between states separated by energy E  . The quantity Γ approximates the half width of the imaginary part of the lineshape function, and so can be used to describe the excited state lifetime τ according to τ = /2Γ . Because the primary interest is in optical absorption by the semiconductor, the imaginary part of the complex dielectric function ε2 (E) is extracted from Eq. (4.1). The result is given by: ε2 (E) =

     |e · pcv (E  )|2  2πe2 2  Im L E, E  , Γ dE  , Jcv E  2 2 ε0 m c,v E (4.2)

where L(E, E  , Γ ) describes the normalized lineshape function of Eq. (4.1): 



L E, E , Γ





1 = π



1 1 + E  − E − iΓ E  + E + iΓ

 .

(4.3)

The factor 1/π is for normalization based on the assumption that Γ  E  ; otherwise a more complicated factor is required.

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Im [L(E, E  , Γ )] is the imaginary part of the lineshape function: Im[L(E, E  , Γ )] =

1

π

2E  ΓE .  Γ  2 2 2 2 2 2 +Γ E E −E + 2

(4.4)

The relationship between Γ on the right side and Γ on the left side of Eq. (4.4) is simply Γ = 2Γ , that is, Γ approximates the full width at half-maximum of the ε2 (E) lineshape. This redefinition must be made to reconcile the standard definition of the critical point lineshape used widely in crystalline semiconductor physics as in Eq. (4.3) [12, 13] with the Lorentz oscillator lineshape used widely in amorphous semiconductor analysis [26, 27]. Equation (4.2) can be considered in two separate limits as will be described in the following paragraphs, motivated by the results shown in Fig. 4.1, which will be discussed first. Figure 4.1 depicts comparisons of the complex dielectric functions for representative thin films of hydrogenated amorphous silicon (a-Si:H) and hydrogenated nanocrystalline silicon (nc-Si:H) [3, 30] with that for bulk single crystal Si (c-Si) [29]. For c-Si, ε2 (E) is clearly representative of the joint density of states function Jcv (E  ) with → − → − sharp features at the van Hove singularities where ∇Ecv (k) = 0 , at the so-called critical point energies in the band structure E(k) [1–4]. Broadening of the features does occur, but Γ is small relative to the critical point energies indicated in Fig. 4.1 and the differences between the energies of the two dominant critical points. In contrast, for a-Si:H, ε2 (E) is clearly representative of the imaginary part of the lineshape function Im [L(E, E  , Γ )], as it exhibits the features of a single Lorentz oscillator. In fact, the characteristic broadening parameter of this oscillator is larger than the lowest bandgap energy and the energy difference between the two dominant critical points in c-Si. The observed behavior is intuitively reasonable given estimates of the electron mean free path as λ = υth τ ∼ υth /Γ. Taking the thermal velocity of an electron in silicon as υth ∼ 2 × 105 m/s, a broadening value of Γ ∼ 2 eV yields λ ∼ 1 ˚ A, on the order of an atomic spacing. This behavior is characteristic of electron scattering associated with the static disorder of the amorphous network [17–20].

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Fig. 4.1. Complex dielectric functions (ε1 , ε2 ) of representative thin-film hydrogenated amorphous silicon (a-Si:H) (upper panel) and hydrogenated nanocrystalline silicon (nc-Si:H) (center panel) along with that of bulk crystal silicon

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The longer mean free path predicted for the single crystal Si based on Γ ∼ 0.2 eV is characteristic of phonon interactions [31]. 4.2.2. The Absorption Onset Formalism First, the limiting form whereby ε2 (E) directly reflects Jcv (E  ) rather than L(E, E  , Γ ) will be considered. Thus, one can write: lim {Im[L(E, E  , Γ )]} = δ(E  − E)

Γ→0

(4.5)

where δ(E  − E) represents the delta function. This assumption leads to the standard expression for ε2 (E), which is a common starting point for general discussions of the optical absorption onset for semiconductors [1, 3, 32]: ε2 (E) =

 2πe2 2 [P (E)]2 Jcv (E), 2 2 ε0 m E c,v

(4.6)

where [P (E)]2 describes an average value of the momentum matrix element squared, where the average is taken over all transitions occurring at photon energy E. This average can be given explicitly as [32]: e · pcv (E)|2 c,v Jcv (E)| 2 (4.7) [P (E)] = c,v Jcv (E) In addition, the summation over the joint density of states function can be written in terms of the valence and conduction band densities of states Nv (E) and Nc (E) as well as the semiconductor bandgap Eg ←−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−− Fig. 4.1. (Continued ) (c-Si) (lower panel) in the near-infrared to near-ultraviolet range. The vertical lines indicate the energy positions for the critical points as obtained by second derivative analysis of the data for c-Si. An approximate value is given for the broadening parameter Γ of the resonance feature in the (ε1 , ε2 ) spectra of a-Si:H. Values of Γ for the lowest energy E0 + E1 critical point of nc-Si:H and bulk c-Si are also provided. This plot has been composed from data in [3] and graphics in [29] Thin Solid Films, Vol. 313–314, Leng, J., et al. Analytic representations of the dielectric functions of materials for device and structural modeling, pp. 132–136, Copyright (1998), with permission from Elsevier.

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according to [28, 32–35]:       Ω 0 Jcv (E) = Nv E  Nc E  + E dE  ; 4 Eg −E c,v

E ≥ Eg ,

(4.8)

where Ω is the semiconductor volume, E is the photon energy, E  is the integration variable, which ranges from an energy E below the conduction band edge to the top of the valence band, defined here as the energy zero. The factor of four arises since the summation at left is over single spin states, whereas Nv (E) and Nc (E) are the total density of states including both spin orientations. Assuming densities of states that increase away from the band edges as square roots of the energy, Nv (E) = Nv0 (Ev − E)1/2 ; E < Ev , and Nc (E) = Nc0 (E − Ec )1/2 ; E > Ec , then ε2 (E) can be expressed as: ε2 (E) =

π 2 e2 2 Ω [P (E)]2 N N (E − Eg )2 ; c0 v0 16ε0 m2 E2

E ≥ Eg ,

(4.9)

with ε2 (E) = 0 for E < Eg . An alternative derivation starts with the dipole matrix element given in terms of the momentum matrix element by:  2 

  

e · rcv E  2 = (4.10) |e · pcv (E  )|2 m2 E 2 as derived from operator commutation relations, for example, [px , x] = −i [1]. This leads to the alternative expression: ε2 (E) =

π 2 e2 Ω Nc0 Nv0 [R(E)]2 (E − Eg )2 ; 16ε0

E ≥ Eg ,

(4.11)

again with ε2 (E) = 0 for E < Eg . Thus, Eq. (4.11) is given in terms of an average dipole matrix element, where the averaging is performed as in Eq. (4.7) [32]. Before comparisons of experimental data to Eqs. (4.9) and (4.11) are made, comments on validity of these equations are appropriate. First, the assumption of square root densities of valence and conduction band states may be valid over only a narrow range of photon energies immediately above Eg . In

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addition, the lack of any assumed broadening of band edge optical transitions or static disorder–induced valence and conduction band states with energy differences less than Eg implies that Eqs. (4.9) and (4.11) will not be valid below Eg where the theory predicts ε2 (E) should vanish. In fitting experimental data, in which case the absorption coefficient α(E) is measured most often — typically by T & R spectroscopy, the relation ε2 (E) = cn(E)α(E)/E is applied. In this expression, c is the speed of light and n(E) is the real index of refraction. In addition, one considers two possible choices: either the average momentum matrix element P (E) in Eq. (4.9) or the average dipole matrix element R(E) is independent of photon energy [3, 32, 36]. As a result, Eq. (4.9) for constant P 2 becomes:  α(E)n(E)E = C  (E − Eg ); E ≥ Eg , (4.12) where C  = (Nv0 Nc0 Ω/ε0 c)1/2 (πeP/4m). For constant R2 , Eq. (4.11) becomes:  α(E)n(E) = C (E − Eg ) ; E ≥ Eg , (4.13) E where C = (Nv0 Nc0 Ω/ε0 c)1/2 (πeR/4). By plotting experimental data for the left side of the equation and evaluating the linearity of the resulting plot, one can assess the validity of the assumptions on the densities of states, the matrix elements, and the role of broadening and disorder. Figure 4.2 shows such data for a representative a-Si:H thin film, uniquely generated for assessing Eqs. (4.12) and (4.13) [3]. These data are plotted over a 2.5 eV range of E approximately centered on the deduced bandgap. The data include α(E) from a combination of dual beam photoconductivity (DBPC), transmittance spectroscopy, and SE, and n(E) from a Kramers–Kronig consistent analysis of SE results [3, 27, 36]. The unique aspects of the data set presented here include (i) evaluation of the thickness dependence of the optical properties to ensure uniformity with depth throughout the film, (ii) incorporation of n(E) in the bandgap plots as required by the

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theoretical development, and (iii) correction of the effects of surface roughness for both n(E) and α(E) in the SE analysis of the optical properties using the Bruggeman effective medium theory and a 50– 50 volume % (vol.%) mixture of underlying material and void [37–39]. In most studies of amorphous semiconductors, n(E) is not included in the analysis [19, 20], a simplification appropriate for crystalline semiconductors in which case the absorption onset is sharp and the energy range of linear extrapolation is very narrow, typically on the order of ∼ 0.1 eV. In fact, for crystalline semiconductors, there is little or no distinction between CD and CM matrix elements in bandgap determinations since the factors of E and E −1 on the left sides of Eqs. (4.12) and (4.13), respectively, can be considered constant over a very narrow extrapolation range. In contrast, for amorphous semiconductors with a range of extrapolation on the order of 1 eV, the variations in n(E) and even more importantly in the factors of E and E −1 cause significant differences in the bandgap determinations [36, 40]. The latter differences are clear in Fig. 4.2. From the figure it is clear that the assumptions of a CD matrix element, square root densities of states just above the band onset, and negligible optical transition broadening are consistent with the measurements and that a well-defined value of the bandgap can be obtained in an extrapolation of a linear fit that extends from ∼0.1 to ∼1.4 eV above the deduced bandgap. In contrast, the assumption of a CM matrix element (while retaining the two other assumptions) is not supported by the measurements that show a consistent upward curvature when (αnE)1/2 is plotted versus E. This in turn leads to a bandgap determination that incorrectly depends on the accessible range of α [36, 40]. The typical range of α accessible to transmittance measurements is a factor of ∼ 1/20 below and a factor of 20 above the value of α = 0.2/d, where d is the thickness of the film. Thus, based on the curvature in Fig. 4.2, the deduced bandgap can range from ∼1.6 eV, lower than that obtained from (αn/E)1/2 plots, for a thickness of ∼ 3 μm to 1.8 eV, higher than that obtained from (αn/E)1/2 plots, for a thickness of ∼3 nm, even though the above bandgap optical properties of the film are essentially independent

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Fig. 4.2. Optical spectra at the absorption onset for hydrogenated amorphous silicon (a-Si:H) plotted as (αn/E)1/2 (left) and as (αnE)1/2 versus photon energy, where α is the absorption coefficient spectrum and n is the index of refraction spectrum. A linear plot at left would be expected based on the assumption of a CD matrix element, whereas a linear plot at right would be expected for a CM matrix element. Linearity on either plot would reflect square root densities of states versus E and negligible effects of transition broadening and disorderinduced states. The solid lines represent best fits of the data between 2.3 and 3.0 eV, which are extrapolated to zero ordinate to identify the bandgaps Eg . These plots have been reproduced from [3] Handbook of Ellipsometry, Collins, R. W., and Ferlauto, A. S., Optical physics of materials, pp. 93–235, Copyright (2005), with permission from Elsevier.

of thickness over this range (see Chapter 5) [36, 41]. It must be concluded that bandgap determinations from (αnE)1/2 or (αE)1/2 plots are only meaningful on a relative scale and only if films of the same thickness are compared. For the (αn/E)1/2 plot at the left in Fig. 4.2, deviations from linearity are found for photon energies >1.5 eV above the bandgap and within 0.1 eV of the bandgap. These deviations are likely due to the breakdown of assumptions of square root densities of states for the high-energy deviations and to the neglect of disorder-induced states and broadening effects for the low-energy deviations. The next sub-section addresses these issues with new expressions for ε2 (E) that will be subjected to analytical Kramers–Kronig integrations, developed and assessed for a wide variety of applications [26, 27].

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4.2.3. The Modified Lorentz Oscillator Formalism Returning to Eq. (4.2), the opposite limit from a delta function lineshape can be considered. In this opposite limit, the lineshape associated with the transition at E  is broader than the density of states function Jcv (E  ). Specifically, for a given photon energy E, the lineshape is then sufficiently broad that the density of states function is then dominated by a specific transition at an energy of E  = E0 , such that: Jcv (E  ) = Ncv,tot (E)δ(E  − E0 ),

(4.14)

where Ncv,tot (E) is the number of states per volume associated with the transition for photon energy E. Ordinarily under these conditions, E0 and Ncv,tot will not depend on photon energy E; however, in this derivation, Ncv,tot is allowed to depend on E, an ansatz to account for the observed bandgap and shape of the absorption onset. One may argue that the broadening of transitions with E just above Eg is reduced by the localization of electrons excited below the mobility gap or by excitonic or electron–phonon interactions. Following through a similar derivation yielding Eq. (4.6) and applying the assumption of Eq. (4.14) the following expression can be derived: ε2 (E) =

π 2 e2 2 Ω U Nc0 Nv0 Im[L(E, E0 , Γ)] 16ε0 m2 [P (E)]2 (E − Eg )2 ; E ≥ Eg × E2

(4.15)

with ε2 (E) = 0 for E < Eg . Here U is an assumed constant energy that depends on upper cut-off and average transition energies and is determined so that ε2 satisfies a sum rule [1]. The revised lineshape function is now given by the standard form of the Lorentz oscillator: Im[L(E, E0 , Γ)] =

A E0 ΓE . (E02 − E 2 )2 + Γ2 E 2

(4.16)

In Eq. (4.15) and in this revised function Γ = 2Γ , E0 = [(E0 )2 + (Γ2 /4)]1/2 , and A is the unitless quantity given by A = 2E0 /πE0 . Assuming a constant average momentum matrix element, the final

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result of this derivation suitable for comparison with experiment and subsequent Kramers–Kronig integration is given by [26]: ⎫ ⎧ ⎪ ; E < Eg ⎪ ⎬ ⎨0 2 , (4.17) ε2 (E) = (E − Eg ) A0 E0 ΓE ⎪ ⎪ ; E ≥ E g ⎭ ⎩ 2 E2 (E0 − E 2 )2 + Γ2 E 2 where

  2 1/2 πe2 2 ΩP 2 Γ U A0 = Nc0 Nv0 . E02 − 2 8ε0 m E0 2

(4.18)

Equation (4.17) exhibits the very convenient form ε2 (E) = L0 (E)GCM (E) for E ≥ Eg , where L0 (E) is the standard description of the Lorentz oscillator, and GCM (E) given by: (E − Eg )2 (4.19) E2 is an absorption onset function, in this case consistent with a CM matrix element [26]. The expression for ε2 (E) is qualitatively consistent with the shape of the measured imaginary part of the dielectric function in Fig. 4.1 (top) in that for E Eg , GCM (E) → 1, and ε2 (E) → L0 (E), yielding the Lorentz oscillator at high energies. In addition, for E ≈ Eg (with E ≥ Eg ), then ε2 (E) ∝ [(E − Eg )/E]2 , in consistency with the Tauc plot of Eq. (4.9), as evaluated in Fig. 4.2 (right). Above the absorption onset region, GCM (E) increases from 0 to ∼1/2, as E increases from Eg to 3.4 Eg . For a typical value of Eg = 1.6 eV, GCM (E) ∼ 1/2 at 5.5 eV, which is well above the value of E0 ∼ 3.8 eV. This implies that above the absorption onset region, GCM (E) varies relatively slowly with E, and ε2 (E) retains the characteristics of the Lorentz oscillator as shown in Fig. 4.1 (top). One advantage of an expression such as that of Eq. (4.17) is its simplicity, which enables a straightforward analytical Kramers–Kronig integration for the determination of ε1 (E) [26]. With an appropriate analytical expression for ε(E), combining both real and imaginary parts, bandgap determination in amorphous semiconductors from one or more SE measurements can be definitive as will be shown in the next sub-section. GCM (E) =

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4.2.4. Parametric Expressions via Kramers–Kronig Integration The Lorentz oscillator modified by the absorption onset function GCM (E) given in Eqs. (4.17) and (4.18) is expected to have limitations in its ability to describe ε2 (E) over the complete spectral range. First, it is assumed that ε2 (E) = 0 below Eg , whereas real materials exhibit an Urbach tail, that is, an absorption coefficient increasing exponentially versus E for photon energies below Eg [3, 15, 16] Second, as indicated in Fig. 4.2 at the right, the CM matrix element expression GCM (E) does not provide a suitable description of the absorption onset, and an onset function that simulates Eq. (4.11) is needed. Finally, the onset function GCM (E) has no free parameters other than Eg and flexibility in modifying the Lorentz oscillator component is lacking. The first limitation can be overcome with an ε2 (E) spectrum in two segments [3, 27]: ⎧E ⎫   1 t) ⎪ ⎪ exp (E−E ; E < E ⎨ ⎬ t Eu E , (4.20) ε2 (E) = A E ΓE ⎪ ⎪ ⎩ 2 0 0 ⎭ G(E) ; E ≥ E t (E0 − E 2 )2 + Γ2 E 2 where Et represents a transition energy between the Urbach tail and the absorption onset functions, the former with an absorption coefficient that increases exponentially with the increase in energy below Et . Eu describes the slope of this exponential increase. The energy E1 is selected for continuity of ε2 (E) at E = Et ; thus, E1 = Et L0 (Et )G(Et ). Although Et (> Eg ), Eu , and Eg are considered independent, Et can be selected so that the derivative of ε2 (E) is continuous at Et , giving a value of Et in accordance with the approximate equation Et ≈ Eg + 2Eu . For a-Si:H with Eu ≈ 0.05 eV, this places Et at the mobility gap as deduced by internal photoemission [36]. Although the addition of the Urbach absorption addresses the first of the three limitations described earlier, other changes to Eqs. (4.17), (4.18), and (4.19) are needed. Next, incorporation of a more general, empirically determined, lineshape function G(E) into Eq. (4.20) can be applied to address the second and third limitations.

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A function G(E) that has been used successfully for this purpose is given by [3, 27]: G(E) = GCD (E) =

(E − Eg )2 , (E − Eg )2 + EP2

(4.21)

which is sufficiently simple so that ε2 (E) = L0 (E)G(E) can subjected to an analytical Kramers–Kronig integration. This expression has the following additional advantages. First, in the region just above Et ≈ Eg + 2Eu , the denominator is dominated by the constant EP2 and GCD (E) ∝ (E − Eg )2 , which is consistent with Eq. (4.11) based on the assumption of a CD matrix element. Furthermore, the incorporation of the variable EP provides additional flexibility in modifying the shape of the Lorentz oscillator. In fact, above the absorption onset region, GCD (E) increases from 0 to 1/2, as E increases from Eg to Eg + EP . Thus, by varying EP , one can vary the transition energy between the absorption onset region and the Lorentz oscillator region. Finally, the expression in Eq. (4.21) approaches unity as E becomes large and the form of the Lorentz oscillator is regained in this limit. In order to develop an expression for the complex dielectric function ε(E) = ε1 (E) + iε2 (E), a Kramers–Kronig integration of Eq. (4.20) can be performed, which requires the following integration over photon energy E  [1]:  ∞  2 E ε2 (E  )  P dE , ε1 (E) − 1 = π E 2 − E 2 0

(4.22)

where P denotes the principal value of the integral. Applying the integration to the two segments of Eq. (4.20) gives [3, 27]: ε1 (E) = ε0s + IU (E) + IL (E)  Et 2E1 exp[(E  − Et )/Eu ]  P dE = ε0s + π E 2 − E 2 0  ∞  2 E G(E  )L0 (E  )  + P dE , π E 2 − E 2 Et

(4.23)

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where the term of unity on the left side of Eq. (4.22) has been replaced by ε0s to account for possible transitions outside the spectral range accessible in the measurement. It should be noted that the weak discontinuity in the first derivative and the discontinuous higher derivatives of ε2 (E) at Et lead to a divergence in ε1 (E) at Et . This divergence is restricted to a very narrow range of E, however, and can be easily excluded from simulations and fitting procedures. The first focus is on the integral IL (E) for the two cases of G(E) = GCM (E) and G(E) = GCD (E), denoted IT L (E) and ICL (E), respectively [26, 27]. Integration with G(E) = GCM (E) is easier [26] and the results for that integration can be used to evaluate the integral with G(E) = GCD (E) [27]. Applying the method of partial fractions to the second integrand of Eq. (4.23) gives:  3   ∞  2A0 E0 Γ (E  )n  dE anT (E) IT L (E) = π L0d (E  ) E t n=0   ∞  ∞ 1 1   dE dE + d (E) + c0T (E) P 0T   Et E − E Et E + E (4.24) where L0d (E) = (E02 − E 2 )2 + Γ2 E 2 is the denominator of L0 (E), and {anT (E); n = 0, . . . , 3; [cnT (E), dnT (E)]; n = 0} are the photon energy–dependent nth order coefficients for each of the three integrals, as determined by the method of partial fractions. Performing the six integrals leads to the following expression: IT L ([anT (E); n = 0, . . . , 3]; [cnT (E), dnT (E); n = 0])  2A0 E0 Γ a3T (E)[ζ 2 I1T (E0 , Et , Γ) − ln[L0d (Et )]1/4 ] = π + a2T (E)[I0AT (E0 , Et , Γ) + I0BT (E0 , Et , Γ)] + a1T (E)I1T (E0 , Et , Γ) a0T (E) [I0AT (E0 , Et , Γ) − I0BT (E0 , Et , Γ)] E02  − c0T (E) ln |E − Et | − d0T (E) ln |E + Et | , +

(4.25)

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where ζ = [E02 − (Γ2 /2)]1/2 , and I0AT , I0BT , and I1T represent three integrals that depend on the energies (E0 , Et , Γ). The integral expressions are given by:    1 2Et + χ π − arctan I0AT (E0 , Et , Γ) = 2Γ Γ   −2Et + χ , (4.26) + arctan Γ  2  Et + E02 + χEt 1 ln , (4.27) I0BT (E0 , Et , Γ) = 4χ Et2 + E02 − χEt   2 1/2 Et − ζ 2 1 π − 2 arctan 2 , (4.28) I1T (E0 , Et , Γ) = 2χΓ χΓ where χ = (4E02 − Γ2 )1/2 . The set of six coefficients {anT (E); n = 0, . . . , 3; [cnT (E), dnT (E)]; n = 0} are easily obtained by solving a linear system of equations. For the case of G(E) = GCM (E) in Eqs. (4.24)–(4.28), these equations will be solved in an analogous manner to the more difficult set of equations encountered when G(E) = GCD (E). First, the highest order coefficients in the first integral of Eq. (4.24), a3T (E) and a2T (E), are determined in terms of the coefficients c0T (E) and d0T (E) according to a2T (E) = −E[c0T (E) − d0T (E)],

(4.29)

a3T (E) = −[c0T (E) + d0T (E)].

(4.30)

The remaining coefficients are derived by solving the 4 × 4 matrix equation ⎤⎛ ⎞ ⎛ ⎞ ⎡ a0T (E) 0 E 2 − 2ζ 2 0 1 E 2 − 2ζ 2 ⎢ −1 0 −E(E 2 − 2ζ 2 ) E(E 2 − 2ζ 2 ) ⎥ ⎜ a1T (E) ⎟ ⎜ −1 ⎟ ⎥⎜ ⎟ ⎜ ⎟ ⎢ ⎦ ⎝ c0T (E) ⎠ = ⎝ 2Eg ⎠ ⎣ 0 E2 −E04 −E04 −Eg2 E2 0 −E04 E E04 E d0T (E) (4.31) The final results for this solution are as follows [27]: a0T (E) = 1 − E(E 2 − 2ζ 2 )[c0T (E) − d0T (E)],

(4.32)

a1T (E) = −(E 2 − 2ζ 2 )[c0T (E) + d0T (E)],

(4.33)

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c0T (E) =

EGCM (E) , 2L0d (E)

(4.34)

d0T (E) =

−(E + Eg )2 . 2EL0d (E)

(4.35)

Equations (4.25)–(4.35) complete the derivation of IT L (E) for use in Eq. (4.23) with G(E) = GCM (E). In the following paragraphs IL (E) Eq. (4.23) will be evaluated for G(E) = GCD (E) [3, 27]. Compared to Eq. (4.24), this evaluation requires a different set of eight coefficients from the partial fraction decomposition, designated {anC (E); n = 0, . . . , 3; bnC (E); n = 0, 1; [cnC (E), dnC (E)]; n = 0}. The equation corresponding to Eq. (4.24) for G(E) = GCD (E) is:  3   ∞  2A0 E0 Γ (E  )n dE  anC (E) ICL (E) = ) π L (E 0d E t n=0   1  ∞  (E  )n bnC (E) dE  +  − E )2 + E 2 (E g Et P n=0  ∞ 1 dE  + c0C (E) P  E − E Et   ∞ 1  dE +d0C (E) (4.36)  Et E + E whereby the second integral has been added to Eq. (4.24) and the new set of coefficients has been incorporated. Although a new set of coefficients is required in Eq. (4.36), three of the four integrations remain the same as in the evaluation of Eq. (4.24). As a result, Eq. (4.36) can be evaluated using Eqs. (4.25), (4.26), (4.27), and (4.28) as components of the solution according to: ICL ([anC ; n = 0, . . . , 3]; [bnC ; n = 0, 1]; [cnC , dnC ; n = 0]) = IT L ([anC ; n = 0, . . . , 3]; [cnC , dnC ; n = 0]) +

2A0 E0 Γ {b1C (E)[Eg I0C (Eg , Et , EP ) π

− ln[(Et − Eg )2 + EP2 ]1/2 ] + b0C (E)I0C (Eg , Et , EP )}

(4.37)

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It must be emphasized that in the first term on the right a new set of partial fraction coefficients must be used. The second integral term in Eq. (4.36) leads to the integral I0C in Eq.(4.37), which depends on Eg , Et , and EP . This integral is given by:   Et − Eg 1 π − arctan . (4.38) I0C (Eg , Et , EP ) = EP 2 EP It remains to determine the eight coefficients arising from the partial fraction decomposition, designated {anC (E); n = 0, . . . , 3; bnC (E); n = 0, 1; [cnC (E), dnC (E)]; n = 0}. Guidance in solving the eight equations in eight unknowns comes from the simpler problem with G(E) = GCM (E). First, the two highest order coefficients of the first term of Eq. (4.36) can be easily obtained as: a3C (E) = −[b1C (E) + c0C (E) + d0C (E)],

(4.39)

a2C (E) = −{b0C (E) + 2Eg b1C (E) +E[c0C (E) − d0C (E)]}

(4.40)

With these expressions, the remaining equations can be determined by solving a 6 × 6 matrix equation: 0

0 B 1 B B −2Eg B B −(E 2 − F 2 ) B @ 2Eg E 2 −F 2 E 2

1 −2Eg −(E 2 − F 2 ) 2Eg E 2 −F 2 E 2 0

2Eg −(F 2 + 2ζ 2 ) −2Eg E 2 2 (F + 2ζ 2 )E 2 + E04 0 −E04 E 2

E 2 − 2ζ 2 (E − 2ζ 2 )(E − 2Eg ) 2 (E − 2ζ 2 )(F 2 − 2Eg E) + E04 F 2 E(E 2 − 2ζ 2 ) + E04 (E − 2Eg ) E04 (F 2 − 2Eg E) E04 F 2 E 2

−(K 2 − F 2 ) −2Eg F 2 2 (K − F 2 )E 2 + E04 2Eg F 2 E 2 −E04 E 2 0

1 E 2 − 2ζ 2 2 C −(E − 2ζ )(E + 2Eg ) C 2 2 2 4 (E − 2ζ )(F + 2Eg E) + E0 C C 2 2 2 4 −[F E(E − 2ζ ) + E0 (E + 2Eg )] C C A E04 (F 2 + 2Eg E) −E04 F 2 E 2

0

1 1 0 a0 0 B a1 C B 1 C B C B C B b0 C B −2Eg C B B C C ×B C = B 2 C B b1 C B E g C @ c0 A @ 0 A d0 0

(4.41)

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where F 2 = EP2 + Eg2 and K 2 = 2F 2 + 2ζ 2 − 4Eg2 . The solution to this problem is given by: a0C = 1 + (K 2 − F 2 )b0C + 2Eg K 2 b1C − E(E 2 − 2ζ 2 )(c0C − d0C ), (4.42) a1C = −[2Eg b0C − (K 2 − F 2 )b1C + (E 2 − 2ζ 2 )(c0C + d0C )] (4.43) b0C =

Y 4 F 2 {L0d (E)[E −1 (c0C − d0C ) + 2Eg K 2 Y −4 (c0C + d0C )]−1} (K 2 − F 2 )F 2 Y 4 + E04 Y 4 + 4Eg2 F 2 K 4 (4.44) b1C =

2Eg K 2 b0C − L0d (E)(c0C + d0C ) Y4

(4.45)

and EGCD (E) 2L0d (E) −E(E + Eg )2 , = 2L0d (E)[(E + Eg )2 + Ep2 ]

c0C =

(4.46)

d0C

(4.47)

where   Y 4 = E04 + F 2 K 2 − F 2 − 4Eg2 K 2 .

(4.48)

To complete the integrations for ε1 (E) in Eq. (4.23) and arrive at a parametric form for the complex dielectric function appropriate for both absorption onset functions G(E), the Kramers–Kronig integral IU (E) of the Urbach tail must be performed [3, 27]. The final result of this integration is:        E − Et E1 Et − E −E exp Ei − Ei IU (E) = πE Eu Eu Eu       Et + E E −(E + Et ) Ei − Ei . − exp Eu Eu Eu (4.49)

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where Ei(x) designates the exponential integral given by:  x exp(t) dt. Ei(x) ≡ t −∞

153

(4.50)

The incorporation of the Urbach tail in the parametric form for ε(E) introduces difficulties in the evaluation of the two integrals in Eq. (4.23) as noted earlier [27]. These arise due to the discontinuity in the first derivative of ε2 (E) at Et , which is weak, and those of the higher derivatives, which may be large. In fact, Ei(x) diverges when x → 0 suggesting divergences when E → 0 or E → Et . The divergences in the two integrals at Et cancel for the most part, and the residual feature at Et that results is so narrow and weak as to be easily avoided in simulations and in fitting experimental data. As an example of these approaches, Fig. 4.3 shows two fiveparameter fits to the measured real and imaginary parts (ε1 , ε2 ) of

Fig. 4.3. Complex dielectric function spectra measured in situ at room temperature (points) for an a-Si1−x Gex :H alloy thin film with x = 0.34 (points). Best fits (lines) employ five parameter expressions assuming constant dipole (CD) and constant momentum (CM) matrix element factors to describe the absorption onset function G(E). The Urbach tail component could be neglected in this case by setting Et = Eg and ε2 = 0 for E ≤ Eg . For the CD fitting expression, ε0s in Eq. (4.23) was fixed at unity. The best fit parameters in the overall expression for ε(E) are given in Table 4.1. This figure has been adapted with permission from Springer Nature: Spectroscopic Ellipsometry for Photovoltaics; Volume 1: Fundamental Principles and Solar Cell Characterization, Fujiwara, H., and Collins, R. W., eds. (2018) [42] using data from the studies of [43, 44].

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the complex dielectric function for an a-Si1−x Gex : H alloy with x = 0.34, comparing results for the CM matrix element analytical form of Eqs. (4.24)–(4.35) with the CD matrix element form of Eqs. (4.36)– (4.48). The (ε1 , ε2 ) spectra in this figure were measured in situ under vacuum after growth by plasma-enhanced chemical vapor deposition (PECVD) and after cooling to room temperature [43, 44]. A c-Si substrate was used and real-time SE was performed during growth in order to establish accurate values of bulk and surface roughness layer thicknesses in a structural analysis of the substrate/film. These thicknesses were then used to extract the (ε1 , ε2 ) spectra, performing numerical inversion on the spectra in the ellipsometry angles (ψ, Δ). The insets in the figure show an improvement in the fit quality achieved with the CD analytical expression. Table 4.1 shows the best fit parameters for (ε1 , ε2 ) as described by the CM and CD analytical forms obtained for the alloy of Fig. 4.3 along with those for a second a-Si1−x Gex :H alloy film having Table 4.1. Best fit parameters obtained in analyses of the complex dielectric function spectra (ε1 , ε2 ) for two a-Si1−x Gex :H alloy thin films with x = 0.17 and 0.34 as measured in situ at room temperature after deposition as shown in Fig. 4.3. Five free parameters were employed in both expressions for ε(E), one using the constant momentum (CM) matrix element factor GCM and the other using the constant dipole (CD) matrix element factor GCD . In the latter expression, the constant contribution to the real part of the dielectric function ε0s in Eq. (4.23) was fixed at unity. The fit quality σ describes the root mean square deviation between the measured and best fit (ε1 , ε2 ) spectra. The results demonstrate the consistent improvement in fit made possible by the CD matrix element expression for the absorption onset factor G(E) [42]. x 0.17

Model

A0 (eV)

Γ (eV)

E0 (eV) Eg (eV) EP (eV)

CM

197.4 ± 3.6 93.7 ± 1.6

2.848 ± 0.019 3.037 ± 0.012

3.599 ± 0.009 3.787 ± 0.010

1.47 ± 0.01 1.49 ± 0.02

171.1 ± 3.5 82.3 ± 1.0

3.012 ± 0.021 3.051 ± 0.012

3.458 ± 0.009 3.691 ± 0.009

1.18 ± 0.02 1.29 ± 0.02

CD 0.34

CM CD

— 1.20 ± 0.05 — 0.82 ± 0.04

ε0s

σ

0.35 ± 0.21 0.08 1 0.15 0.04 ± 0.23 0.09 1 0.16

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composition x = 0.17. Because the low energy limit of the data is above the bandgap, no Urbach tail is required in the expression; as a result, Et = Eg in Eq. (4.20) and ε2 = 0 for E ≤ Eg . For the CM expression, the five parameters include (ε0s , A0 , E0 , Γ, Eg ), that is, a constant ε1 component, three Lorentz oscillator parameters, and the bandgap Eg that defines GCM (E). By fixing the constant term in ε1 for the CD expression to ε0s = 1, five parameters can be used as well for the fit applying the CD expression. These include (A0 , E0 , Γ, Eg , EP ), where now two parameters Eg and EP describe the absorption onset function GCD (E). The value of σ in Table 4.1 is a measure of the quality of the fit, and demonstrates the improvement possible through the five-parameter CD expression as described by Eqs. (4.36)–(4.48). It is also noted that for the CM expression, ε0s is less than unity and decreases with increasing Ge content in the alloy film. This would erroneously suggest a large negative contribution from resonances outside the spectral range [3], and the resulting unphysical conclusion is avoided by using the CD expression. For the absorption onset function GCM , Eg is established by the absorption onset; however, once Eg is fixed, there is no further control over the effect of GCM on the Lorentz oscillator shape. Apparently, the appropriate function GCM required to fit ε2 leads to an overestimation of ε1 , and a negative contribution to ε0s ≥ 1 must be incorporated to compensate. In contrast, for the absorption onset function GCD , the magnitude of the additional free parameter EP can be used to control the behavior of the function independently of Eg , and in this case, ε0s can be fixed at the physically reasonable value of unity. Finally, it should be noted that the complete six- and eightparameter versions (the latter including Eu and Et ) of the CD expression as described by Eqs. (4.36)–(4.50) have been incorporated into commercial software, making the fitting process straightforward [45]. The method has been highly successful in modeling a wide variety of amorphous semiconductors, not only additional group IV alloys [46] but also chalcogenides [47, 48], ferroelectric materials [49], high-k dielectrics [50, 51], and other oxide thin films [52–59].

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4.3. Alternative Approaches To conclude this chapter, consideration will be given to the possibility of densities of states functions for the conduction and valence bands that differ from the square root relationships assumed in the derivations of Eqs. (4.9) and (4.11). In fact, previous studies have considered linear densities of states functions in evaluating the conformance of experimental data to linearity on plots such as those of Fig. 4.2 [17] with support coming from experimental results [60, 61]. Table 4.2 summarizes the dependence of ε2 on photon energy near the bandgap for the three cases whereupon (i) both the conduction and valence band densities of states exhibit square root dependences on photon energy as treated in detail in this Table 4.2. Optical absorption onset functions used in this work (first row) and possible alternatives based on two alternative functional forms for the valence and conduction band densities of states (second and third rows). The final row shows a generalized function designed to show the desired behavior for an absorption onset function, including the proper behavior near the bandgap with E slightly above Eg and G(E) → 1 as E  Eg + EP . Densities of States

CD Absorption Onset Behavior

CM Absorption Onset Behavior (E−Eg )2 E2

Square root Nv (E) ∝ (Ev − E)1/2 Nc (E) ∝ (E − Ec )1/2

2 (E) ∝ (E − Eg )2 ⇒

Square root/linear Nv (E) ∝ (Ev − E) Nc (E) ∝ (E − Ec )1/2

2 (E) ∝ (E − Eg )5/2

2 (E) ∝

(E−Eg )5/2 E2

Linear Nv (E) ∝ (Ev − E) Nc (E) ∝ (E − Ec )

2 (E) ∝ (E − Eg )3

2 (E) ∝

(E−Eg )3 E2

General expression

2 (E) ∝ (E − Eg )n ⇒

2 (E) ∝

GCD (E) = n≥2

(E−Eg )n ⇒ E2 (E−Eg )n

n>2

GCD (E) =

2

2 (E) ∝ GCM (E) =

(E−Eg ) 2 (E−Eg )2 +EP

Square root/linear Nv (E) ∝ (Ev − E)1/2 Nc (E) ∝ (E − Ec )

n

(E−Eg ) n (E−Eg )n +EP

GCM (E) =

n−2 2 (E−Eg )n +EP E

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section, (ii) one band has a square root dependence and the other a linear dependence, and (iii) both bands exhibit linear dependences. In order to generate an absorption onset function G(E) that approaches unity well above the bandgap, only the expression derived assuming square root densities of states with CM matrix element requires no modification. Each onset function based on alternative assumptions about the photon energy dependences of the densities of states and matrix element requires modification with a denominator whose photon energy dependence is designed to match that of the numerator at high energy so that G(E) → 1. An example of such a modification was shown in Eq. (4.21) based on the assumptions of square root densities of states and CD matrix element. Similar modifications are presented in the last row of Table 4.2. For the alternative functions for G(E), it seems possible that analytical Kramers–Kronig integrations can be performed when linear densities of states are assumed; however, in fitting using the most general expressions in the last row of the table, including obtaining best fit exponents n, numerical integrations would be required.

4.4. Summary Starting from a general theoretical formalism that describes the imaginary part of the dielectric function ε2 of a crystalline semiconductor, two expressions have been proposed and developed specifically to solve the more challenging problem of bandgap determination for an amorphous semiconductor. The expressions provide a complete parametric representation of the linear optical response of the semiconductor that can be applied from ∼0.5 eV below the bandgap to as much as ∼ 5 eV above the bandgap. The most general form of the expressions includes three components of ε2 : (i) a sub-gap Urbach tail with two photon energy–independent parameters — essentially a slope and a transition energy; (ii) a band-to-band absorption onset with either one or two parameters, one being the bandgap; and (iii) an above-gap Lorentz oscillator with three parameters, an amplitude, resonance energy, and broadening. Two models for ε2 explored in detail are sufficiently simple mathematically

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so that analytical Kramers–Kronig integrations can be applied, leading to companion expressions for the real part of the dielectric function ε1 . The integration requires the inclusion of another free parameter, namely a photon energy–independent contribution to ε1 . The resulting seven or eight parameters in the three components of the most general expression for the (ε1 , ε2 ) spectra appear to be the minimum number for describing the optical response of a-Si:H and related materials from sub-gap in the near infrared to well into the ultraviolet. This range can span several orders of magnitude in the absorption coefficient α = Eε2 /cn and is of greatest interest for understanding and modeling optoelectronic device operation. The two analytical expressions for the (ε1 , ε2 ) spectra differ based on the form of the component describing the band-to-band absorption onset. The traditional form is based on the assumption of square root densities of states distributions in energy at the valence and conduction band edges and a constant momentum (CM) matrix element for the band-to-band transitions, whereas the alternative uses the same densities of states distributions but a constant dipole (CD) matrix element. Both expressions are designed to enable analytical Kramers–Kronig integrations that provide ε1 from ε2 . Although other functional forms for the densities of states and matrix elements are certainly possible and have been described here, however, analytical Kramers–Kronig integrations of ε2 are unlikely for these alternatives. In such cases, a numerical approach would be required. The band-to-band component expression based on the assumption of a CD matrix element has been widely recognized as providing an improved description of α as a function of energy as deduced by T&R spectroscopy for a-Si:H at its absorption onset. For completeness and accuracy, the description also incorporates n, the index of refraction determined from either T & R spectroscopy or SE. As a result, a plot of (αn/E)1/2 versus E based on the assumption of a CD matrix element is more closely linear compared to the CM version of (αnE)1/2 versus E. In fact, one finds that when the traditional plot of (αnE)1/2 versus E is extrapolated to zero ordinate, the apparent

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bandgap extrapolation depends spuriously on film thickness because the center of the accessible range of α increases as the film thickness decreases. In contrast, for the more closely linear plots of (αn/E)1/2 , the extrapolated bandgap is less dependent on the ordinate range used for extrapolation. Although the use of the CD matrix element formalism can significantly improve bandgap determination from T&R spectroscopy, the best possible solution is analogous to critical point analysis for crystalline semiconductors, specifically fitting both optical spectra (ε1 , ε2 ). It is also desirable to span a wide range of α combining results from multiple experimental methods. Results to be presented in Chapters 5 and 8 include not only T&R but also the photoconductive response via DBPC, which spans the sub-gap range, and SE, which spans the high α side of the absorption onset. The improved linearity of the (αn/E)1/2 data from T&R spectroscopy is also consistent with the improved mean square error obtained when fitting (ε1 , ε2 ) spectra from in situ SE of a-Si1−x Gex :H samples using a simpler five-parameter version of the dielectric function expression based on the CD matrix element. The importance of combined real-time and in situ SE in this application is that it provides data sufficient to characterize surface roughness and ultimately correct for it in data analysis. Furthermore, an in situ measurement at the end of deposition avoids surface oxidation and contamination which, along with roughness, exert significant influence on the (ε1 , ε2 ) spectra if unrecognized or left uncorrected. In the comparison of the two expressions based on the different assumptions for the matrix element, five-parameter models for analysis of in situ SE are often used for high electronic quality materials. These models neglect the Urbach tail range, since the low α values of the Urbach tail cannot be determined to the required accuracy by SE methods. In such studies, the CD matrix element formulation not only gives a better five-parameter fit to SE data, but the values of the parameters are physically reasonable for a wider variety of materials compared to those deduced from the CM matrix element formulation. To obtain a five-parameter CD matrix element expression, the following are used: (i) two band edge parameters including the bandgap Eg and a band edge to oscillator transition energy EP

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and (ii) three Lorentz oscillator parameters of amplitude A0 , energy E0 , and width Γ. In this case, the constant contribution to ε1 can be fixed typically at physically acceptable values of ε0s ≥ 1. To obtain the CM matrix element expression, no band edge to oscillator transition energy is used; however, it is not possible to fix ε0s at unity in this case. For these latter fits, ε0s has been observed to depend sensitively on bandgap, with best fit values above unity for a-Si1−x Cx :H, dropping below unity for a-Si:H, and decreasing with decreasing H-content as will be indicated in Chapter 5. In fact, ε0s passes through zero, becoming negative for the lowest bandgap a-Si1−x Gex :H alloys investigated. Given the similarity of the single Lorentz oscillator nature of the band-to-band optical response of all these materials, such an unexpected variation in ε0s with bandgap or alloy content is not physically interpretable and so is a limitation of the CM matrix element expression for the dielectric function.

References 1. Wooten, F. (1972). Optical Properties of Solids (New York, NY, Academic), Chapter 5, pp. 108–172. 2. Cohen, M. L., and Chelikowsky, J. R. (1988). Electronic Structure and Optical Properties of Semiconductors (Berlin, Germany, Springer), Chapter 6, pp. 51–72. 3. Collins, R. W., and Ferlauto, A. S. (2005). Optical physics of materials. In: Handbook of Ellipsometry, edited by Tompkins, H. G., and Irene, E. A. (Norwich, NY, William Andrew), Chapter 2, pp. 93–235. 4. Yu, P., and Cardona, M. (2010). Fundamentals of Semiconductors: Physics and Materials Properties, 4th Ed. (Berlin, Germany, Springer), Chapter 6, pp. 243–344. 5. Fox, M. (2010). Optical Properties of Solids, 2nd Ed. (Oxford, UK, Oxford University Press), Chapter 3, pp. 49–75. 6. Alonso, M. I., and Garriga, M. (2018). Optical properties of semiconductors. In: Spectroscopic Ellipsometry for Photovoltaics; Volume 1: Fundamental Principles and Solar Cell Characterization, edited by Fujiwara, H., and Collins, R. W. (Cham, Switzerland, Springer), Chapter 4, pp. 89–113. 7. Macleod, H. A. (2010). Thin Film Optical Filters, 4th Ed. (Boca Raton, FL, CRC), Chapter 2, pp. 13–72.

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8. Stenzel, O. (2015). The Physics of Thin Film Optical Spectra: An Introduction, 2nd Ed. (Berlin, Germany, Springer), Chapters 6–7, pp. 97–162. 9. Pankove, J. I. (1975). Optical Processes in Semiconductors (New York, NY, Dover), Chapter 14, pp. 303–336. 10. Krˇc, J., and Topiˇc, M. (2013). Optical Modeling and Simulation of Thin-Film Photovoltaic Devices (Boca Raton, FL, CRC), Chapter 1, pp. 3–34. 11. Sze, S. M., and Ng, K. K. (2007). Physics of Semiconductor Devices, 3rd Ed. (Hoboken, NJ, John Wiley & Sons), Chapter 1, pp. 7–78. 12. Cardona, M. (1969). Solid State Physics: Modulation Spectroscopy, edited by Seitz, F., Turnbull, D., and Ehrenreich, H. (New York, NY, Academic), Suppl. 11, pp. 9–87. 13. Aspnes, D. E. (1980). Modulation spectroscopy: Electric field effects on the dielectric function of semiconductors. In: Handbook of Semiconductors, Vol. 2; Optical Properties of Solids, edited by Balkanski, M. (North-Holland, Amsterdam), Chapter 4A, pp. 109–154. 14. Urbach, F. (1953). The long-wavelength edge of photographic sensitivity and of the electronic absorption of solids, Physical Review, 92, p. 1324. 15. Fagen, E. A., and Fritzsche, H. (1970). Optical properties of amorphous chalcogenide alloy films, Journal of Non-Crystalline Solids, 2, pp. 180–191. 16. Cody, G. D. (1992). Urbach edge of crystalline and amorphous silicon: A personal review, Journal of Non-Crystalline Solids, 141, pp. 3–15. 17. Mott, N. F., and Davis, E. A. (2012). Electronic Processes in NonCrystalline Materials (Oxford, UK, Oxford University Press), Chapter 2, pp. 7–64. 18. Zallen, R. (1983). The Physics of Amorphous Solids (Weinheim, Germany, Wiley-VCH), Chapter 6, pp. 252–296. 19. Morigaki, K. (1999). Physics of Amorphous Semiconductors (Singapore, World Scientific), Chapter 8, pp. 137–152. 20. Singh, J., and Shimakawa, K. (2003). Advances in Amorphous Semiconductors (London, Taylor & Francis), Chapter 4, pp. 57–95. 21. Cody, G. D. (1984). The optical absorption edge of a-Si:H. In: Semiconductors and Semimetals: Hydrogenated Amorphous Silicon, Part B, Optical Properties, edited by Pankove, J. I. (Orlando, FL, Academic), Chapter 2, pp. 11–82. 22. Tauc, J., Grigorovici, R., and Vancu, A. (1966). Optical properties and electronic structure of amorphous germanium, Physica Status Solidi, 15, pp. 627–637.

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23. Tauc, J. (1968). Optical properties and electronic structure of amorphous Ge and Si, Materials Research Bulletin, 3, pp. 37–46. 24. Aspnes, D. E. (1976). Spectroscopic ellipsometry. In: Optical Properties of Solids: New Developments, edited by Seraphin, B. O. (NorthHolland, Amsterdam), Chapter 15, pp. 799–846. 25. Fujiwara, H. (2007). Spectroscopic Ellipsometry: Principles and Applications (New York, NY, John Wiley & Sons), Chapter 4, pp. 81–140. 26. Jellison, G. E. Jr., and Modine, F. A. (1996). Parameterization of the optical functions of amorphous materials in the interband region, Applied Physics Letters, 69, pp. 371–373; Erratum, Applied Physics Letters, 69, p. 2137. 27. Ferlauto, A. S., et al. (2002). Analytical model for the optical functions of amorphous semiconductors from the near-infrared to ultraviolet: Applications in thin film photovoltaics, Journal of Applied Physics, 92, pp. 2424–2436. 28. O’Leary, S. K., and Malik, S. M. (2002). A simplified joint density of states analysis of hydrogenated amorphous silicon, Journal of Applied Physics, 92, pp. 4276–4282. 29. Leng, J., et al. (1998). Analytic representations of the dielectric functions of materials for device and structural modeling, Thin Solid Films, 313–314, pp. 132–136. 30. Ferlauto, A. S., et al. (2002). Thickness evolution of the microstructural and optical properties of Si:H films in the amorphous-tomicrocrystalline phase transition region. In: Conference Record of the 29th IEEE Photovoltaics Specialists Conference, 20–24 May 2002, New Orleans, LA, (New York, NY, IEEE), pp. 1076–1081. 31. Lautenschlager, P., Garriga, M., Vi˜ na, L., and Cardona, M. (1987). Temperature dependence of the dielectric function and interband critical points of silicon, Physical Review B, 36, pp. 4821–4830. 32. Jackson, W. B., et al. (1985). Energy dependence of the optical matrix element in hydrogenated amorphous and crystalline silicon, Physical Review B, 31, pp. 5187–5198. 33. O’Leary, S. K., Johnson, S. R., and Lim, P. K. (1997). The relationship between the distribution of electronic states and the optical absorption spectrum of an amorphous semiconductor: An empirical analysis, Journal of Applied Physics, 82, pp. 3334–3340. 34. Jiao, L., Chen, I. S., Collins, R. W., and Wronski, C. R. (1998). An improved analysis for band edge optical absorption spectra in hydrogenated amorphous silicon from optical and photoconductivity measurements, Applied Physics Letters, 72, pp. 1057–1059.

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35. O’Leary, S. K. (2004). An empirical density of states and joint density of states analysis of hydrogenated amorphous silicon: A review, Journal of Materials Science: Materials in Electronics, 15, pp. 401–404. 36. Dawson, R. M., et al. (1992). Optical properties of hydrogenated amorphous silicon, silicon-germanium, and silicon-carbon alloy thin films. In: Materials Research Society Symposium Proceedings; Amorphous Silicon Technology — 1992, Vol. 258, edited by Thompson, M. J., Hamakawa, Y., Lecomber, P. G., Madan, A., and Schiff, E. (Pittsburgh, PA, MRS), pp. 595–600. 37. Aspnes, D. E. (1982). Optical properties of thin films, Thin Solid Films, 89, pp. 249–262. 38. Fujiwara, H., Koh, J., Rovira, P. I., and Collins, R. W. (2000). Assessment of effective-medium theories in the analysis of nucleation and microscopic surface roughness evolution for semiconductor thin films, Physical Review B, 61, pp. 10832–10844. 39. Fujiwara, H. (2018). Effect of roughness on ellipsometry analysis. In: Spectroscopic Ellipsometry for Photovoltaics; Volume 1: Fundamental Principles and Solar Cell Characterization, edited by Fujiwara, H., and Collins, R. W. (Cham, Switzerland, Springer), Chapter 6, pp. 155–172. 40. Mok, T. M., and O’Leary, S. K. (2007). The dependence of the Tauc and Cody optical gaps associated with hydrogenated amorphous silicon on the film thickness: αl experimental limitations and the impact of curvature in the Tauc and Cody plots, Journal of Applied Physics, 102, pp. 113525: 1–9. 41. Collins, R. W., et al. (2003). Evolution of microstructure and phase in amorphous, protocrystalline, and microcrystalline silicon studied by real time spectroscopic ellipsometry, Solar Energy Materials and Solar Cells, 78, pp. 143–180. 42. Huang, Z., et al. (2018). Ex situ analysis of multijunction solar cells based on hydrogenated amorphous silicon. In: Spectroscopic Ellipsometry for Photovoltaics; Volume 1: Fundamental Principles and Solar Cell Characterization, edited by Fujiwara, H., and Collins, R. W. (Cham, Switzerland, Springer), Chapter 7, pp. 175–200. 43. Podraza, N. J., Wronski, C. R., Horn, M. W., and Collins, R. W. (2006). Dielectric functions of a-Si1−x Gex :H versus Ge content, temperature, and processing: Advances in optical function parameterization. In: Materials Research Society Symposium Proceedings; Amorphous and Polycrystalline Thin-Film Silicon Science and Technology — 2006, Vol. 910, edited by Wagner, S., Chu, V., Atwater, H. A., Yamamoto, K., and Zan, H.-W. (Warrendale, PA, MRS), pp. 259–264.

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44. Podraza, N. J. (2008). Real Time Spectroscopic Ellipsometry of the Growth and Phase Evolution of Thin Film Si1−x Gex :H, Ph.D. Dissertation (Toledo, OH, University of Toledo). 45. Hilfiker, J. N., and Tiwald, T. (2018). Dielectric function modeling. In: Spectroscopic Ellipsometry for Photovoltaics; Volume 1: Fundamental Principles and Solar Cell Characterization, edited by Fujiwara, H., and Collins, R. W. (Cham, Switzerland, Springer), Chapter 5, pp. 115–153. 46. D’Costa, V. R., Wang, W., Schmidt, D., and Yeo, Y.-C. (2015). Parametrized dielectric functions of amorphous GeSn alloys, Journal of Applied Physics, 118, pp. 123102: 1–5. 47. Ohl´ıdal, I., et al. (2006). Comparison of dispersion models in the optical characterization of As–S chalcogenide thin films, Journal of Non-Crystalline Solids, 352, pp. 5633–5641. 48. Orava, J., et al. (2008). Optical properties and phase change transition in Ge2 Sb2 Te5 flash evaporated thin films studied by temperature dependent spectroscopic ellipsometry, Journal of Applied Physics, 104, pp. 043523: 1–10. ˇ 49. Chvostov´a, D., Pajasov´ a, L., and Zelezn´ y, V. (2008). Optical properties of PZT thin films by spectroscopic ellipsometry and optical reflectivity, Physica Status Solidi (c) — Proceedings, 5, pp. 1362–1365. 50. Price, J., et al. (2004). Spectroscopic ellipsometry characterization of Hf x Siy Oz films using the Cody–Lorentz parameterized model, Applied Physics Letters, 85, pp. 1701–1703. 51. Diebold, A. C. (2009). Advanced metrology for next generation transistors. In: Advances in Solid State Physics, Vol. 48, edited by Haug, R. (Berlin, Germany, Springer), pp. 371–383. 52. Prato, M., Chincarini, A., Gemme, G., and Canepa, M. (2011). Gravitational waves detector mirrors: Spectroscopic ellipsometry study of Ta2 O5 films on SiO2 substrates, Thin Solid Films, 519, pp. 2877–2880. 53. Afshar, A., and Cadien, K. C. (2013). Growth mechanism of atomic layer deposition of zinc oxide: A density functional theory approach, Applied Physics Letters, 103, pp. 251906: 1–5. 54. Schmidt-Grund, R., et al. (2013). Temperature dependent dielectric function in the near-infrared to vacuum-ultraviolet ultraviolet spectral range of alumina and yttria stabilized zirconia thin films, Journal of Applied Physics, 114, pp. 223509: 1–8. 55. Delegan, N., Daghrir, R., Drogui, P., and El Khakani, M. A. (2014). Bandgap tailoring of in-situ nitrogen-doped TiO2 sputtered films intended for electrophotocatalytic applications under solar light, Journal of Applied Physics, 116, pp. 153510: 1–8.

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56. Awasthi, V., et al. (2016). Plasmon generation in sputtered Gadoped MgZnO thin films for solar cell applications, Journal of Applied Physics, 119, pp. 233101: 1–13. 57. Deligiannis, D., et al. (2017). Passivation mechanism in silicon heterojunction solar cells with intrinsic hydrogenated amorphous silicon oxide layers, Journal of Applied Physics, 121, pp. 085306: 1–7. 58. Magnozzi, M., et al. (2018). Optical properties of amorphous SiO2 -TiO2 multi-nanolayered coatings for 1064-nm mirror technology, Optical Materials, 75, pp. 94–101. 59. Hilfiker, J. N., et al. (2019). Spectroscopic ellipsometry characterization of multilayer optical coatings, Surface and Coatings Technology, 357, pp. 114–121. 60. Vorl´ıˇcek, V., Z´avˇetov´a, M., Pavlov, S. K., and Pajasov´ a, L. (1981). On the optical gap of amorphous silicon, Journal of Non-Crystalline Solids, 45, pp. 289–292. 61. Klazes, R. H., Van den Broek, M. H. L. M., Bezemer, J., and Radelaar, S. (1982). Determination of the optical bandgap of amorphous silicon, Philosophical Magazine B, 45, pp. 377–383.

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CHAPTER 5

Structure, Bonding, and Temperature Effects on the Dielectric Function and Bandgap Dipendra Adhikari, Maxwell M. Junda, Balaji Ramanujam, Prakash Koirala, Nikolas J. Podraza, and Robert W. Collins University of Toledo, USA

5.1. Introduction The complete parametric expressions developed to characterize the (ε1 , ε2 ) spectra of amorphous semiconductors as described in Chapter 4 have a wide variety of applications in amorphous silicon materials research and device development [1, 2]. The effects of structure and bonding, crystalline inclusions, alloying of Si with Ge and C, and measurement temperature on the (ε1 , ε2 ) spectra can be quantified using a relatively small number of photon energy independent parameters [3, 4]. In addition to such effects, the influence of substrate on the evolution of order in the amorphous network with layer thickness can be quantified based on optical measurements performed in real time during deposition and processing [5, 6]. Such information can provide insights into mechanisms of film growth and post-deposition modification. In situ and real-time measurements of amorphous silicon-based materials result in photon energy independent (ε1 , ε2 ) parameters at elevated temperature, 167

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and adjustments are needed for direct comparison with parameters obtained from ex situ measurements at room temperature. Thus, sets of temperature coefficients are determined to enable parameter adjustment from the elevated measurement temperature to room temperature [7, 8]. In this chapter, such applications will be presented in detail including the effects on the thin-film (ε1 , ε2 ) spectra and their parameters arising from void structures in a-Si [9, 10], H-bonding in hydrogenated amorphous silicon (a-Si:H) in Si–H and Si–H2 configurations [11–16], and nanocrystalline Si:H phases that nucleate from a-Si:H during growth, typically at high H2 dilution [5, 17]. Results will be described that identify with high sensitivity the interrelated roles of substrate and thickness on the (ε1 , ε2 ) spectra and associated parameters, based on insights from in situ and real-time spectroscopic ellipsometry (SE) experiments and accompanying advanced modeling methodologies [5, 6, 18]. The fundamental concepts underlying the modeling of these material characteristics include effective medium theories [9, 19] and the virtual interface (VI) approximation [6, 20, 21], which will be introduced next. The various effective medium theories are based on the assumption that the scale of the structures within the plane of the film must be smaller than the wavelength of the probe light inside the material [9, 19, 22]. Also dielectric functions of the components used in the effective medium theory should be appropriate for the size scale of the microstructures in the thin film. In other words, size effects on the optical properties of the components should be taken into account [23]. Effective medium theories can be complemented with multi-layer models for out-of-plane variations in film structure of various scales, for example, due to the evolution of void or crystalline volume fraction with film thickness [5, 9, 17–19]. Because the complexity of such multi-layer models accumulates very rapidly as the film increases in thickness, a VI approximation can be used in conjunction with real-time SE for characterization [5, 6, 20, 21]. This approach replaces an optically graded thin-film structure with a two-layer outer-layer/roughness model. Thus, the structure underlying the outer-layer/roughness is approximated as a semi-infinite

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substrate, referred to as the pseudo-substrate, defined by a single pair of (ε1 , ε2 ) spectra. The VI is positioned between the pseudosubstrate and the outer-layer and tracks the outer-layer/roughness interface, maintaining a constant outer-layer deposition time (or approximately the same thickness) as the film grows. This model is a suitable approximation for generating depth profiles in structure from real-time SE data as long as (i) the bulk layer of the film and the associated pseudo-substrate are strongly absorbing, (ii) the light does not penetrate to the true substrate, and (iii) the optical properties evolve gradually with thickness. As a result, interference fringes must not be observable in the real-time SE data set. Often these requirements can be met by proper selection of the outer-layer thickness and the spectral range [6].

5.2. Relation to Structure and Bonding The complex dielectric function models based on the constant momentum matrix element (CM) analytical form of Chapter 4, Eqs. (4.19)–(4.20) and (4.22), and the constant dipole matrix element (CD) form of Eqs. (4.20)–(4.21) and (4.22) treat the amorphous semiconductor as a homogeneous continuous random network of tetrahedrally-bonded group IV atoms [1, 2]. It is widely recognized, however, that heterogeneities exist in thin-film amorphous silicon and its alloys [8–19], and extensive research has focused on characterizing these heterogeneities and understanding their effects on fundamental material properties. Considering first pure a-Si film without hydrogen as prototypical, heterogeneities may include isolated dangling bond defects, localized regions of various sizes with density near or even greater than that of the crystal, as well as extended void structures. As a result, spatial non-uniformities in the Si atom concentration exist on a wide range of scales from voids that are sub-nanometer in size to columnar structures that extend throughout the thickness of the film [24]. These non-uniformities depend sensitively on the deposition process and conditions. Within the dielectric function modeling approaches of Chapter 4, Eqs. (4.19)–(4.22), it is expected that the nature of the heterogeneity is reflected in the eight fitting

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parameters that describe (ε1 , ε2 ). These include the Urbach and absorption onset parameters, Eu , Et , Eg , and EP ; the Lorentz oscillator parameters, A0 , E0 , and Γ; and the constant contribution to ε1 , ε0s . The parameter that is expected to depend most strongly on the structural heterogeneity is the oscillator amplitude A0 , through its dependence on the density of states pre-factors Nv0 and Nc0 . These pre-factors describe the numbers of electronic states per unit volume at 1 eV below and above the valence and conduction band edges, respectively, which decrease as the concentration of Si atoms in the network decrease. Weaker effects may be expected on the Urbach tail slope Eu , and along with it, Et ≈ Eg + 2Eu , as well as the bandgap Eg and Lorentz oscillator energy E0 and width Γ. These four parameters are most closely related to the electronic structure and degree of short-range order of the amorphous network. One possible approach for extracting physical information on the structural heterogeneity of a-Si, as characterized by the film density, is to measure and fit the (ε1 , ε2 ) spectra for a set of films of known density, for example, measured by direct weighing or by the flotation method using delaminated material [25]. Fitting (ε1 , ε2 ) spectra with CM or CD parametric expressions will provide as many as the eight parameters or as few as five, that is, if sub-gap absorption data are unavailable and ε0s is set to unity in the CD expression. The fitting parameters are then plotted versus the density, and if clear trends are observed, these trends can be fit with polynomial functions. As a result for any film of unknown density, the polynomial functions would permit direct fitting of the (ε1 , ε2 ) spectra using density as a single parameter to be determined non-destructively. Conversely, ε can be simulated for hypothetical films of any specified density. Because of the challenge of measuring density directly and accurately, a theoretical approach for determining the density directly from the (ε1 , ε2 ) spectra can be applied based on the concept of an effective medium theory. The general expression for effective medium theories appropriate for a two-component composite is [9, 19, 22, 26]: ε=

εa ευ + κεh (fa εa + fυ ευ ) , κεh + (fa ευ + fυ εa )

(5.1)

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where ε is the complex dielectric function of the composite, εh is a host dielectric function within which it is assumed a-Si and void inclusions are embedded, εa and fa are the dielectric function and volume fraction of a hypothetical fully dense a-Si network, and ευ and fυ are the dielectric function and volume fraction of void, given by ευ = 1 and fυ = 1 − fa . In addition, in Eq. (5.1), κ = (1/q) − 1, where q (0 ≤ q ≤ 1) is the screening parameter associated with the phase boundaries. Assuming spherical inclusions leads to a screening parameter of q = 1/3, and applying the Bruggeman approximation, εh (E) = ε(E), meaning that the dielectric function of the host is that of the composite, a simpler expression results: fa

εa (E) − ε(E) ευ − ε(E) + fυ = 0, εa (E) + 2ε(E) ευ + 2ε(E)

(5.2)

where ευ = 1 for a composite of dense a-Si and void components. This equation is solved for ε(E), the dielectric function of the composite. By identifying a dielectric function associated with a film of the highest density, that is, the largest Lorentz oscillator amplitude A0 in a parametric fit of ε(E), then any other dielectric function can be fit using Eq. (5.2) with fυ as a single free parameter. Thus, the Bruggeman approximation uses a single parameter to describe variations in the structure, with little or no information provided on the sizes or shapes of the voids (assumed spherical). In fact, the resulting value of fυ should be interpreted as a bond packing density deficit, as the polarizability of the a-Si network over the spectral range above the bandgap and up to the high photon energy limit of the instrumentation describes transitions between bonding and anti-bonding sp3 states of the Si–Si bonds [27]. The approach based on Eq. (5.2) has been applied successfully to model the dielectric functions of the bulk and overlying surface roughness layers that describe the microstructure of a-Si thin films of low H-content fabricated at high temperature by chemical vapor deposition (CVD) [9, 26]. Information on the geometry of the surface roughness could be deduced through a step-wise depth profile in the parameter fυ . Figure 5.1 (left) shows results in which the dielectric function of sputtered a-Si measured in situ is scaled to the

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(a)

(b)

Fig. 5.1. (Left) Room temperature dielectric functions derived from that of sputtered amorphous silicon (a-Si) measured in situ immediately after deposition. For fv = 0 vol.%, the measured dielectric function is scaled to a reference maximum ε2 of 29.5, applying the effective medium theory of Eq. (5.2). Increasing volume percentages of void are then added to this scaled result. (Right) Results of fitting the dielectric functions of a-Si at the left as a function of void content by applying the five parameter constant dipole matrix element formalism of Eqs. (4.20)–(4.22). Plots depict unpublished data [28].

maximum ε2 value observed near 3.75 eV for CVD a-Si according to Eq. (5.2) [28]. This is done by analytically removing void volume fraction to generate a hypothetical dense reference material. Then increasing void volume fractions are added to this material to generate the series of dielectric functions that reflect the influence of void content. This series of dielectric functions is fit using the five parameter CD expression [2], which is obtained by setting Et = Eg (with ε2 = 0 for E ≤ Eg ), thus removing the Urbach tail from the model, and fixing ε0s = 1.25, a value that gives the best overall fit. Figure 5.1 (right) shows the five parameters, Eg and EP associated with the absorption onset and A0 , E0 , and Γ associated with the Lorentz oscillator component, each plotted as a function of the void

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content used in the effective medium theory of Eq. (5.2). These best fit results are consistent with expectations in that the dominant influence of void is on the oscillator amplitude A0 , which decreases by an average of 1.5 eV per volume % (vol.%) increase in void content. The three energies Eg , Γ, and E0 are not strongly affected by void content, varying in magnitude by 3μm when smooth substrates such as native oxide covered c-Si and fused silica are used. More generally, however, depending on the deposition conditions and substrate, subtle changes in the Lorentz oscillator width can be detected from real-time SE measurements analyzed with the VI approximation. These changes appear to reflect changes in the network order and defect density of the a-Si:H that influence the band-to-band excited state lifetime. For depositions on smooth c-Si surfaces under conditions for which the a-Si:H is not fully optimized (e.g., no H2 dilution), a slight increase in broadening of the Lorentz oscillator can occur with increasing thickness as substrate-induced order gradually relaxes with thickness and the film reaches an equilibrium degree of network order determined by the growth conditions. For depositions on rough transparent conducting oxide surfaces, the opposite behavior is observed, namely a decrease in broadening with thickness as substrate-induced disorder is reduced as the thickness increases. Surface smoothening is observed simultaneously, which may also reflect improved network order with thickness. For these informative real-time SE studies of film properties and structure, the photon energy independent parameters deduced in the optical analysis are characteristic of the deposition temperature. As a result, temperature adjustments of the parameters are needed if comparisons are to be made with the results of ex situ measurements at room temperature. For a series of a-Si1−x Gex :H alloys, the five parameters in the CD expression are found to be either constant or vary linearly with temperature over the 20◦ C to 200◦ C range [8]. The resulting temperature coefficients facilitate adjustment of the (ε1 , ε2 ) spectra measured at elevated temperatures to results applicable

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for comparisons at room temperature. The temperature coefficient of the a-Si:H band gap is equal within experimental error to the temperature coefficient of the lowest direct bandgap of c-Si at the E0 -E1 transitions; however, the temperature coefficients of the Lorentz oscillator broadening parameters are larger than any associated with the two dominant critical points of c-Si, suggesting stronger electron–phonon interactions for excitations of a-Si:H well above the bandgap.

References 1. Jellison, G. E. Jr., and Modine, F. A. (1996). Parameterization of the optical functions of amorphous materials in the interband region, Applied Physics Letters, 69, pp. 371–373; Erratum, Applied Physics Letters, 69, p. 2137. 2. Ferlauto, A. S., et al. (2002). Analytical model for the optical functions of amorphous semiconductors from the near-infrared to ultraviolet: Applications in thin film photovoltaics, Journal of Applied Physics, 92, pp. 2424–2436. 3. Fujiwara, H., and Collins, R. W. editors. (2018). Spectroscopic Ellipsometry for Photovoltaics; Volume 1: Fundamental Principles and Solar Cell Characterization (Cham, Switzerland, Springer). 4. Fujiwara, H., and Collins, R. W. editors. (2018). Spectroscopic Ellipsometry for Photovoltaics; Volume 2: Applications and Optical Data of Solar Cell Materials (Cham, Switzerland, Springer). 5. Collins, R. W., et al. (2003). Evolution of microstructure and phase in amorphous, protocrystalline, and microcrystalline silicon studied by real time spectroscopic ellipsometry, Solar Energy Materials and Solar Cells, 78, pp. 143–180. 6. Junda, M. M., Gautam, L. K., Collins, R. W., and Podraza, N. J. (2018). Optical gradients in a-Si:H thin films detected using realtime spectroscopic ellipsometry with virtual interface analysis, Applied Surface Science, 436, pp. 779–784. 7. Collins, R. W., and Ferlauto, A. S. (2005). Optical physics of materials. In: Handbook of Ellipsometry, edited by Tompkins, H. G., and Irene, E. A. (Norwich, NY, William Andrew), Chapter 2, pp. 93–235. 8. Podraza, N. J., Wronski, C. R., Horn, M. W., and Collins, R. W. (2006). Dielectric functions of a Si1−x Gex :H versus Ge content, temperature, and processing: Advances in optical function parameterization, MRS Proceedings, 910, p. A10.01.

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9. Aspnes, D. E., Theeten, J. B., and Hottier, F. (1979). Investigation of effective-medium models of microscopic surface roughness by spectroscopic ellipsometry, Physical Review B, 20, pp. 3292–3302. 10. Collins, R. W., Biter, W. J., Clark, A. H., and Windischmann, H. (1985). A study of the microstructure of a-Si:H using spectroscopic ellipsometry measurements, Thin Solid Films, 129, pp. 127–138. 11. Ewald, D., Milleville, M., and Weiser, G. (1979). Optical spectra of glow-discharge-deposited silicon, Philosophical Magazine B, 40, pp. 291–303. 12. Windischmann, H., Collins, R. W., and Cavese, J. M. (1986). Effect of hydrogen on the intrinsic stress in ion beam sputtered amorphous silicon films, Journal of Non-Crystalline Solids, 85, pp. 261–271. 13. An, I., Li, Y. M., Wronski, C. R., and Collins, R. W. (1992). Modification of a-Si(:H) by thermally-generated atomic hydrogen: A real time spectroscopic ellipsometry study of Si bond breaking, MRS Proceedings, 258, pp. 27–32. 14. Feng, G. F., Katiyar, M., Abelson, J. R., and Maley, N. (1992). Dielectric functions and electronic band states of a-Si and a-Si:H, Physical Review B, 45, pp. 9103–9107. 15. An, I., Li, Y. M., Wronski, C. R., and Collins, R. W. (1993). Chemical equilibration of plasma-deposited amorphous silicon with thermally generated atomic hydrogen, Physical Review B, 48, pp. 4464–4472. 16. Kageyama, S., Akagawa, M., and Fujiwara, H. (2011). Dielectric function of a-Si:H based on local network structures, Physical Review B, 83, pp. 195205: 1–11. 17. Ferlauto, A. S., et al. (2004). Evaluation of compositional depth profiles in mixed-phase (amorphous + crystalline) silicon films from real time spectroscopic ellipsometry, Thin Solid Films, 455–456, pp. 665–669. 18. Koh, J., et al. (1999). Evolutionary phase diagrams for plasmaenhanced chemical vapor deposition of silicon thin films from hydrogendiluted silane, Applied Physics Letters, 75, pp. 2286–2288. 19. Fujiwara, H., Koh, J., Rovira, P. I., and Collins, R. W. (2000). Assessment of effective-medium theories in the analysis of nucleation and microscopic surface roughness evolution for semiconductor thin films, Physical Review B, 61, pp. 10832–10844. 20. Aspnes, D. E. (1993). Minimal-data approaches for determining outerlayer dielectric responses of films from kinetic reflectometric and ellipsometric measurements, Journal of the Optical Society of America, 10, pp. 974–983. 21. Kim, S., and Collins, R. W. (1995). Optical characterization of continuous compositional gradients in thin films by real time spectroscopic ellipsometry, Applied Physics Letters, 67, pp. 3010–3012.

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22. Niklasson, G. A., Granqvist, C. G., and Hunderi, O. (1981). Effective medium models for the optical properties of inhomogeneous materials, Applied Optics, 20, pp. 26–30. 23. Nguyen, H. V., and Collins, R. W. (1993). Finite-size effects on the optical properties of Si microcrystallites: A real-time spectroscopic ellipsometry study, Physical Review B, 47, pp. 1911–1917. 24. Paul, W., and Anderson, D. A. (1981). Properties of amorphous hydrogenated silicon, with special emphasis on preparation by sputtering, Solar Energy Materials, 5, pp. 229–316. 25. Moss, S. C., and Graczyk, J. F. (1969). Evidence of voids within the as-deposited structure of glassy silicon, Physical Review Letters, 23, pp. 1167–1171. 26. Aspnes, D. E. (1982). Optical properties of thin films, Thin Solid Films, 89, pp. 249–262. 27. Zallen, R. (1983). The Physics of Amorphous Solids (Weinheim, Germany, Wiley-VCH), Chapter 6, pp. 252–296. 28. Adhikari, D., Collins, R. W., and Podraza, N. J. (2019). Unpublished work (Toledo, OH, University of Toledo). 29. Stradins, P., Teplin, C. W., and Branz, H. M. (2009). Phase evolution in nanocrystalline silicon films: Hydrogen dilution and the cone kinetics model, Philosophical Magazine A, 89, pp. 2461–2468. 30. Dahal, L. R., et al. (2014). Applications of real-time and mapping spectroscopic ellipsometry for process development and optimization in hydrogenated silicon thin-film photovoltaics technology, Solar Energy Materials and Solar Cells, 129, pp. 32–56. 31. Yuguchi, T., Kanie, Y., Matsuki, N., and Fujiwara, H. (2012). Complete parameterization of the dielectric function of microcrystalline silicon fabricated by plasma-enhanced chemical vapor deposition, Journal of Applied Physics, 111, p. 083509: 1–8. 32. An, I., et al. (1991). In situ determination of dielectric functions and optical gap of ultrathin a-Si:H by real time spectroscopic ellipsometry, Applied Physics Letters, 59, pp. 2543–2545. 33. Dawson, R. M., et al. (1992). Optical properties of hydrogenated amorphous silicon, silicon-germanium, and silicon-carbon alloy thin films, MRS Proceedings, 258, pp. 595–600. 34. Fujiwara, H. (2018). Amorphous/crystalline Si heterojunction solar cells. In: Spectroscopic Ellipsometry for Photovoltaics; Volume 1: Fundamental Principles and Solar Cell Characterization, edited by Fujiwara, H., and Collins, R. W. (Cham, Switzerland, Springer), Chapter 9, pp. 227–252.

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35. Chen, J., et al. (2006). Multilayer analysis of the CdTe solar cell structure by spectroscopic ellipsometry, IEEE 4th World Conference on Photovoltaic Energy Conversion, pp. 475–478. 36. Collins, R. W. (1989). Dielectric functions of thin interface layers in a-Si:H-based device structures by spectroscopic ellipsometry, Journal of Non-Crystalline Solids, 114, pp. 160–162. 37. Junda, M. M., et al. (2014). Spectroscopic ellipsometry applied in the full pin a-Si:H solar cell device configuration, IEEE Journal of Photovoltaics, 5, pp. 307–312. 38. Podraza, N. J. (2008). Real Time Spectroscopic Ellipsometry of the Growth and Phase Evolution of Thin Film Si1−x Gex :H, Ph.D. Dissertation (Toledo, OH, University of Toledo). 39. Kasap, S. O. (2006). Principles of Electronic Materials and Devices, 3rd Ed. (New York, NY, McGraw-Hill), Chapter 2, pp. 136–138. 40. Lautenschlager, P., Garriga, M., Vi˜ na, L., and Cardona, M. (1987). Temperature dependence of the dielectric function and interband critical points of silicon, Physical Review B, 36, pp. 4821–4830.

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CHAPTER 6

Optoelectronic Properties: Carrier Transport, Recombination, and Stability Lihong (Heidi) Jiao∗ and Joshua M. Pearce† ∗ †

Grand Valley State University, USA Michigan Technological University, USA

6.1. Introduction A continuous distribution of localized states within the energy bandgap is inherent to hydrogenated amorphous silicon (a-Si:H), a material that exhibits unique optoelectronic properties such as high optical absorption and high initial photoconductivity. Although aSi:H has outstanding optoelectronic properties for an amorphous material, a serious problem exists in its stability to extended illumination such as sunlight. This is perhaps most important for the amorphous silicon solar photovoltaic (PV) cell invented by David Carlson and Christopher Wronski in 1976 [1]. Only a year after the seminal discovery of a-Si:H PV, Staebler and Wronski [2] found that the electronic properties of a-Si:H undergo metastable 207

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changes upon light exposure due to the creation of defect states within the energy bandgap. Defect creation is completely reversible with annealing at temperatures above about 150◦ C. Despite extensive studies on the origin and nature of the light-induced defect states, these characteristics are still not well understood. As the development of a-Si:H-based device physics continues, however, it becomes more and more important to understand the nature and distribution of the defect states within the energy bandgap of intrinsic a-Si:H in the annealed state as well as after light-induced degradation. Extensive work has been carried out on improving the performance of a-Si:H-based solar cells fabricated over a wide range of deposition conditions. The different conditions of growth for these materials can cause significant differences in microstructure and hydrogen incorporation, which lead to differences in the defect states. Such differences are found not only in states associated with neutral dangling bonds, but in other gap states as well [3]. Despite this, little attention has been given to the gap states other than the neutral dangling-bond states. In addition, the different materials of interest are still characterized with very limited measurements of photoconductivity and sub-bandgap absorption, generally by the constant photocurrent method (CPM), and results are routinely analyzed with a very simple gap state model [3]. This has seriously limited the ability to obtain insights into the nature of the intrinsic and light-induced gap states in a-Si:H. Furthermore, such a simple approach to addressing the issues related to the gap states in a-Si:Hbased materials also appears to be an important factor for the lack of reliable correlations between the properties of thin film materials and the performance of the corresponding solar cells [4, 5]. In some studies, however, the importance of charged defect states in determining the properties of a-Si:H materials has been recognized and attempts have been made to characterize them and evaluate their contributions to the optoelectronic properties and stability of a-Si:H [6–10]. Subsequently, extensive evidence has accumulated for distributions of gap states associated with charged defects, which consist of donor-like D+ states with positive charge located above the

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Fermi level and acceptor-like D− states with negative charge located below the middle of the gap (mid-gap) [11–14]. Consequently, it is necessary to carry out detailed measurements and establish reliable analysis of results on a-Si:H materials in both the annealed and lightdegraded states, which are then used to characterize the charged defect states. The effects of charged defect states were first identified in the simpler Schottky barrier solar cell structures [15, 16], which clearly demonstrated that self-consistent analysis of the results can only be achieved if charged defect states are included. Later work on full p-i-n and n-i-p solar cells confirmed these results [17, 18]. The “operational” parameters obtained from such characterization of the gap states have important consequences for realistic modeling of the performance and stability of a-Si:H-based solar cells. 6.2. Carrier Transport in a-Si:H When a-Si:H materials are exposed to light, free electrons and holes can be generated. Three different types of electronic transitions exist depending on the incoming light frequency: (i) valence band to conduction band transitions, (ii) valence band tail to conduction band transitions, (iii) deep gap state to conduction band transitions. Under steady-state illumination, the concentrations of free electrons and holes can be expressed as: nph = Gτn ;

(6.1)

pph = Gτp ,

(6.2)

where G is the carrier generation rate; τn and τp are the recombination lifetimes of electrons and holes, respectively. These photogenerated carriers undergo drift and recombination with the assumption of uniformly distributed gap energy states in the material. The photocurrent density is given by: Jph = q(nph vdn + pph vdp ),

(6.3)

where vdn and vdp are the drift velocities of electrons and holes, respectively. At low and medium electric fields, carrier drift velocity

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is linearly proportional to the electric field, ε. As a result, vdn = μn ε;

(6.4)

vdp = μp ε,

(6.5)

where μn and μp are the drift mobilities of electrons and holes, respectively. The photocurrent density can then be written as: Jph = q(μn nph + μp pph )ε.

(6.6)

The photocurrent density is also related to the photoconductivity by the following equation: Jph = σph ε.

(6.7)

The above two equations result in the formula for the photoconductivity as follows: σph = q (μn nph + μp pph ) = qG(μn τn + μp τp ).

(6.8)

Equation (6.8) shows that photoconductivity is governed by both carrier transport and recombination processes. 6.2.1. Photoconductivity in a-Si:H As shown in the previous section, the steady-state photoconductivity can be expressed as: σph = qG(μn τn + μp τp ). Since a-Si:H is a slightly n-type material, μn τn  μp τp . Hence, the steady-state photoconductivity becomes: σph = qGμn τn .

(6.9)

Photoconductivity is one of the important optoelectronic properties of amorphous silicon materials. It reflects the electron lifetime determined by the nature and distribution of the recombination centers within the energy gap. Since the generation rate changes the position of the quasi-Fermi levels for both the electron and the hole, hence the nature of the gap energy states, the relationship between

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Light Source (ENH Lamp)

Filters (Color and Neutral)

Sample Box

Voltage Source

Current Meter

Fig. 6.1. The block diagram of photoconductivity measurement.

the photoconductivity and the generation rate can be used to derive the nature and distribution of the gap defect states. Equation (6.9) shows that the photoconductivity is linearly proportional to the generation rate if the product of electron mobility and lifetime is constant. This can be evaluated by the photoconductivity measurement shown in Fig. 6.1. Recent advances in open source hardware and additive manufacturing enable labs to digitally replicate major components of this system such as the automated filter wheel changer [19, 20]. The band-pass filter can be used as a color filter to pass the red light to the sample and the neutral filters can be used to change the generation rate, which can be determined by the incident photon flux F (hν), the generation efficiency η(hν), the reflectance R, the absorption coefficient α(hν), and the film thickness d [21]: G=

η (hν) F (hν)(1 − R)(1 − e−α(hν)d ) . d

(6.10)

The absorption coefficient α(hν) at a specific wavelength (687 nm) and the thickness d can be obtained from transmission and reflection (T&R) measurements. Since the incident photon flux F (hν) can be measured using a crystalline Si solar cell, the generation rates for different neutral filters can be calculated. An example of steady-state photoconductivity versus the generation rate ranging from 1015 to 1020 cm−3 s−1 is shown in Fig. 6.2

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Fig. 6.2. Steady state photoconductivity as a function of generation rate for hydrogen-diluted and undiluted hydrogenated amorphous silicon (a-Si:H) films deposited at 170◦ C and 200◦ C.

plotted on logarithmic scales for two different a-Si:H materials deposited by the plasma-enhanced chemical vapor deposition (PECVD) method at substrate temperatures of 170◦ C and 200◦ C. The undiluted material was deposited with pure SiH4 and the diluted material was deposited with SiH4 diluted by hydrogen (R = [H2 ] [SiH4 ] = 10) [22]. It can be easily seen that photoconductivity is not linearly dependent on the generation rate. Rose [23] proposed that in many cases, the carrier recombination lifetime is dependent on the generation rate so that photoconductivity has a power dependence on the generation rate. This dependence can be expressed as σph ∝ Gγ , where γ is a constant having a value between 0.5 and 1 [16, 23]. This is due to the increased number of recombination centers as the splitting between electron and hole quasi-Fermi levels (EF n and EF p ) widens when the generation rate is increased [23], which

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effectively reduces the electron lifetime. However, Fig. 6.2 shows that the photoconductivity at higher generation rates does not follow a straight line on the logarithmic plot, implying that a single γ cannot be used to express the relationship between the photoconductivity and the generation rate over such a wide range of generation rate. Equation (6.9) shows that given a generation rate, photoconductivity can be used to determine the product of electron mobility and lifetime, μn τn . The changes in the μn τn product directly reflect the changes in the free electron lifetime since the carrier mobility is assumed to be constant in these a-Si:H materials. Figure 6.3 shows the μn τn product as a function of generation rate G for the materials of Fig. 6.2. The μn τn product decreases as the generation rate increases due to the introduction of different gap states as recombination centers, which change the

Fig. 6.3. Mobility-lifetime product as a function of generation rate for hydrogendiluted and undiluted hydrogenated amorphous silicon (a-Si:H) films deposited at 170◦ C and 200◦ C.

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recombination kinetics. The dependence of the μn τn product on G is a much more sensitive probe of the recombination kinetics than the corresponding dependence of the photoconductivity. The latter changes by five orders of magnitude rather than the one or so in the μn τn product results. Figure 6.3 shows not only that the μn τn product does not change linearly with G, but also that both the magnitudes of the μn τn product as well as the functional dependence on G are different in different films. This indicates that there are significant differences in recombination kinetics in the films. 6.2.2. Sub-bandgap Photoconductivity In high quality intrinsic a-Si:H materials, the gap state densities are on the order of 1015 –1016 cm−3 and their sub-bandgap optical absorption coefficients are on the order of 10−2 cm−1 , which cannot be measured using direct optical transmission techniques on ∼1 μm thick films. Hence, different techniques have been developed to measure the weak optical absorption associated with these gap states. Sub-bandgap absorption, obtained from photoconductivity measurements, is associated with gap states occupied by electrons. These gap states are emptied by the absorbed photons with the excited electrons contributing to the photocurrent. Such weak absorption can be measured by photocurrent spectroscopies, such as CPM [7, 24] and dual-beam photoconductivity (DBP) [25, 26]. From Eqs. (6.9) and (6.10), photoconductivity can be expressed as: σph = qμn τn

η (hν) F (hν)(1 − R)(1 − e−α(hν)d ) . d

(6.11)

For a-Si:H films less than 1 μm thick, αd  1; therefore 1 − e−αd ≈ αd. The generation efficiency η is unity in most cases. Then the photoconductivity can be rewritten as: σph = qμn τn F (hν)(1 − R)α(hν).

(6.12)

If μn τn is constant at all generation rates, the photoconductivity is proportional to F (hν) and α(hν), hence α(hν) ∝ σph /F (hν).

(6.13)

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Since the lifetimes of photogenerated carriers are dependent on the generation rate, which is directly related to the optical absorption, the magnitude changes of generation rate in the sub-bandgap region must be compensated. In CPM, in order to keep μn τn constant, the photocurrent is kept constant while varying F . In DBP, however, a constant volume absorbed bias light, whose carrier generation rate is much larger than that of the probing monochromatic beam, is employed to keep μn τn constant. Since the photoconductivity spectra do not give absolute magnitudes of the optical absorption coefficient, the absorption spectra obtained from T&R measurements are often used to calibrate these photoconductivity spectra. One of the differences between CPM and DBP is the volume absorbed light employed in DBP. The generation rate of the bias light in DBP is much larger than that of the monochromatic light. As a result, the steady-state condition is maintained; thus the lifetime is kept constant throughout the entire photon energy range. When the intensity of the bias light increases, the electron and hole quasiFermi levels move toward the band edges and the states above the dark Fermi level become occupied. Therefore, by changing the intensity of the bias light, gap states at different energies below as well as above the dark Fermi level can be probed. The absorption coefficients obtained from DBP measurements at low generation rates (∼1015 cm−3 s−1 ) are equivalent to those obtained from CPM. A schematic diagram of a DBP measurement system is illustrated in Fig. 6.4. A 150 watt halogen lamp and monochromator are used Power Supply

Light Source

Chopper

Ge Calibration

Computer

Monochromator

Sample

Lock-in Amp.

Fig. 6.4. The block diagram of the dual beam photoconductivity (DBP) measurement system.

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as the light source, which is chopped at a frequency of 13 Hz and calibrated by a Ge photodiode. Sub-bandgap photoconductivities are generated by the monochromatic light over the energy range of 0.8 eV to 2.0 eV and are detected by the lock-in amplifier, which uses the frequency of the chopper as the reference frequency. Due to the optics of the thin film, there exist interference fringes in the output of the DBP measurement. These interference fringes can be removed by performing a fast Fourier transform (FFT) developed by Wiedeman et al. [27]. Typical sub-bandgap absorption spectra at two generation rates are illustrated in Fig. 6.5 for the diluted and undiluted a-Si:H materials deposited at a substrate temperature of 200◦ C. Subsequent work has shown that by normalizing the lightinduced absorption profile to that of the annealed state, the light-induced density of states can be visualized [13]. This method

Fig. 6.5. The absorption coefficients obtained from dual beam photoconductivity (DBP) at two different generation rates for diluted and undiluted hydrogenated amorphous silicon (a-Si:H) materials deposited at 200◦ C.

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makes it clear that there are states not only at mid-gap but also at approximately 1.2 eV from the conduction band that have a greater effect on the degradation of the material and concomitant PV device. 6.3. Recombination in a-Si:H 6.3.1. Statistics of Recombination Shockley–Read–Hall (SRH) [28] statistics have been successful in describing the non-equilibrium steady-state recombination process in crystalline semiconductors in which case the process occurs only through a single discrete trapping level. When the SRH approach was extended to more than one distinct trapping level, however, the extension resulted in extremely complex equations. Furthermore, in the case of amorphous materials, the SRH approach is inherently more complicated due to the continuous distribution of gap states. Rose addressed, the problem of different distributions of recombination centers in a semi-quantitative approach with emphasis on the physical insights and successfully introduced complex mathematics [23]. However, Rose’s approach is limited in that only selected trap configurations can be addressed, and it is difficult to obtain highly quantitative information about the gap states themselves. Simmons and Taylor [29] generalized SRH and formulated the generation and recombination statistics applicable to an arbitrary distribution of traps, which is relevant to the case of amorphous silicon. In a-Si:H, the densities of gap states are typically much higher than the concentrations of free carriers. In theory, Simmons and Taylor statistics cannot be applied directly to a-Si:H since the dangling bond defect states in a-Si:H are not single-electron states but are amphoteric in nature. Okamoto addressed this problem by simulating trivalent dangling-bond states with correlated bivalent defect states [30]. However, Simmons and Taylor statistics can still provide useful insights in the recombination process. 6.3.2. Simmons and Taylor Statistics In the case of different energy distributions of gap states, each one may have different carrier capture cross-sections for electrons and

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holes. Such gap states can be classified into different species by R, the ratio of the capture cross-section of the electron Sn to that of the hole Sp as follows: R(S) = Sn /Sp .

(6.14)

Thus, the gap states having the same R can be described by the same statistics and treated as one species. The occupation function f (E, S), which depends on the energy location E of the gap states, describes the probability of the gap states being occupied by electrons. The probability of the gap states being occupied by holes can be described as 1 − f (E, S). f (E, S) for a certain type of gap state at energy location E can be derived by balancing the generation-recombination processes through this particular type of state. Four basic processes must be considered: (i) electron capture from the conduction band by the gap state; (ii) electron emission from the electron occupied state; (iii) hole capture from the valence band by the gap state; and (iv) hole emission to the valence band. By assuming the rate equations of the basic processes under non-equilibrium steady-state illumination conditions, the occupation function of a certain type of gap state at an energy E was derived as: f (E) =

vnSn (E) + ep (E) . en (E) + vnSn (E) + vpSp (E) + ep (E)

(6.15)

Here n is the concentration of free electrons in the conduction band; p is the concentration of free holes in the valence band; Sn is the capture cross-section for electrons; Sp is the capture cross-section for holes; en is the electron thermal emission probability; ep is the hole thermal emission probability; and v is the thermal velocity. The function f (E) is the same as that in SRH statistics for a single discrete level in the distribution of states and is independent of the energy distribution of gap states. f (E) depends on the free carrier concentrations for a specific species, hence on the illumination conditions. In this single-electron approach, the charge state of the gap states of energy E is not important as it is reflected in the respective capture cross-sections. For example, the positively charged

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defect states have a capture cross-section for electrons larger than that for holes. Under steady-state illumination, quasi-Fermi levels for trapped electrons and holes can be defined as:   Rn + p , (6.16) Efnt = EC + kT ln RNC   Rn + p p . (6.17) Ef t = EV − kT ln RNV Gap states, located above Efnt , are occupied by electrons according to the Boltzmann distribution: n

f (E) =

Rn − E−Ef t e kT . Rn + p

(6.18)

Gap states, located below Efnt , are occupied by electrons to a constant level given by: f (E) =

Rn . Rn + p

(6.19)

The quasi-Fermi level Ef n for free electrons in the conduction band is different from that for the trapped electrons and can be described as:   n . (6.20) Ef n = EC + kT ln NC Equations (6.16) and (6.20) show that Efnt > EF n at all times under steady-state conditions. That is, the quasi-Fermi level for trapped electrons is always positioned above the quasi-Fermi level for free electrons as illustrated in Fig. 6.6, which depicts a typical occupation function for an arbitrary distribution of traps [29]. The above description shows that the occupation of each type of defect state within the gap is governed by the quasi-Fermi levels for the trapped electrons and trapped holes. The quasi-Fermi levels for free carriers, Ef n and Ef p , are independent of the type of gap state. In the non-equilibrium steady state, the charge neutrality condition is maintained at all times. The number of trapped electrons in the states above the dark Fermi level EF 0 is equal to the number of trapped holes in the states below EF 0 , providing that

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Fig. 6.6. A typical occupation function for an arbitrary distribution of traps. n1 is the free-electron concentration; p1 is the free-hole concentration; Edn is the demarcation level for an electron trap; Edp is the demarcation level for a hole trap [29].

the concentration of free carriers is far less than that of the trapped carriers, which is the case for a-Si:H under normal illumination conditions. The charge neutrality condition can be expressed as follows:  ns  s=1



Ec

fs (E)Ns (E)dE Ef

=

n s   s=1

Ef

 (1 − fs (E))Ns (E)dE ,

Ev

(6.21)

n s

where s=1 denotes all different types of defect states. In the steady state, the carrier generation rate G is balanced by the total recombination rate U , and can be written as: G=U =

n s   s=1

+

en (E)fs (E)Ns (E)dE

Ev

ns   s=1



Ec

Ec

Ev

 vSn (E)n(1 − fs (E))Ns (E)dE , (6.22)

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where the first term is the rate of electron emission from the gap states to the conduction band and the second term is the rate of electron capture by the gap states. A similar formula can also be written for holes. Considering the gap states located between the quasi-Fermi level for trapped electrons and the bottom of the conduction band, the role of these states in the recombination process decreases exponentially as their energy moves toward the conduction band. A free electron that falls into one of these states has a very high probability of being re-emitted to the conduction band. These gap states are called shallow traps. Similarly, a free hole that falls into one of the gap states located between the quasi-Fermi level for trapped holes and the top of the valence band would likely be re-emitted to the valence band. These gap states are also called shallow traps. In contrast, the gap states positioned between the quasi-Fermi levels of trapped electrons and trapped holes are effective recombination centers.

6.3.3. Density of States in a-Si:H It can be seen from the previous section that the energy states located within the energy bandgap of a-Si:H are very important due to their effects on the material properties such as optical absorption and photoconductivity. For many years, the gap states in a-Si:H materials have been considered to consist of exponential band tails due to disorder and defect states near the middle of the gap, associated with dangling bonds as shown in Fig. 6.7. The nature and distribution of the defect states within the bandgap have been studied with photoconductivity and sub-bandgap absorption such as measured by CPM or DBP. The sub-bandgap absorption coefficients obtained from either CPM or DBP are due to the electronic transitions between the initial electron occupied states and the final delocalized extended states. The quantitative relationship between the optical absorption coefficient and the density of gap states can be obtained through the imaginary part of the dielectric function, 2 . The relation between 2

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Ev

Energy

Ec

Fig. 6.7. A plot of the density of states versus energy for hydrogenated amorphous silicon (a-Si:H) illustrating the continuous distribution of the localized states.

and the density of gap states can be expressed as [31]:  2 (hν) = 0.43 × 10−44 R2 NI (E) f (E) Nf (E + hν) × (1 − f (E + hν)) dE,

(6.23)

where R is the average dipole matrix element found to be constant with a value of 3.2 ˚ A between 0.6 and 3.0 eV, NI (E) is the density of initial states, and Nf (E + hν) is the density of the final states in the conduction band. The occupation function f (E), is determined by Eq. (6.15). The absorption coefficient can be obtained from the following equation: α(hν) =

2πν 2 (hν), nc

(6.24)

where c is the speed of light and n is the refractive index of a-Si:H. As seen in Fig. 6.5, the regions of α greater than 103 cm−1 correspond to the electronic transitions between the valence and conduction bands. The regions of α between about 103 and 10 cm−1 , which are exponential in nature, arise from the absorption by electrons in valence band-tail states, which are introduced by the disorder

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in these amorphous materials [32]. The densities of the valence band-tail states are significantly higher than those of the conduction band-tail states [33] even in the more recently developed materials with highly ordered networks [34]. The shoulders in the absorption spectra at photon energies less than ∼1.4 eV, with values of α below ∼10 cm−1 , are due to the electronic transitions originating from defect states near and around the middle of the gap where the absorption is determined by the densities and nature of these states [35, 36]. The DBP technique involves two photon beams, a steady-state volume absorbed bias light beam with energy greater than the bandgap energy and a monochromatic chopped probe beam with energies in the range of 0.5 eV to 2.2 eV. The first beam is used to establish a steady-state photoconductivity in the sample. This results in a constant response time for the probe beam and electron occupation of gap states acting as recombination centers, which keeps the electron lifetime constant. The monochromatic beam is used to probe the effects of transferring electrons from the gap states to the extended states by measuring perturbations of the steady-state photoconductivity induced by this probe beam. When the bias light intensity is varied, the generation rate is modified accordingly. As a result the occupation function at a given energy will change, meaning that the density of occupied states will change. This change in the occupancy function can be reflected in the differences in sub-bandgap absorption coefficient α(hν) at two different generation rates as observed in Fig. 6.5. Figure 6.5 shows that the sub-bandgap absorption coefficients at low generation rates are smaller than those at high generation rates. At low generation rates, electron and hole quasi-Fermi levels are close to the mid-gap (similar to the dark Fermi level) and only states below the Fermi level are occupied by electrons. At high generation rates, electron and hole quasi-Fermi levels move toward the band edges so that more states become occupied by electrons, and in particular those states that are above the dark Fermi level. Consequently, there is a difference in the absorption spectra in the sub-bandgap region for

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the two generation rates where the different “splits” reflect differences in occupancies of the corresponding gap states. Figure 6.5 also shows that both the magnitude as well as the shape of the sub-bandgap absorption spectra are different for the two films. Equations (6.23) and (6.24) show that a complex process is required in order to obtain gap state information from the subbandgap absorption spectra. The most commonly used procedures include (i) using the value of sub-bandgap absorption coefficient at a specific energy such as 1.2 eV; (ii) detailed numerical modeling of CPM or DBP sub-bandgap absorption spectra. 6.3.3.1. Sub-bandgap Absorption at a Single Photon Energy The sub-bandgap absorption coefficient at a given photon energy, hν, is an integration of electronic transitions from electron occupied states located at E to the extended states located at E + hν. Consequently α(hν) measured at a single energy had been used extensively to relate α(hν) to the density of mid-gap states: Nmidgap ∼ = (Constant)α(1.2 eV ),

(6.25)

Most studies have been carried out for a photon energy of 1.2 eV, but this selection is somewhat arbitrary. The constant is determined by the density of dangling bond defect states D 0 measured from ESR with the assumption that the density of gap states probed by either CPM or DBP is the same as that measured by ESR. Wyrsch et al. [37] used CPM and ESR measurements in the light degraded states of several a-Si:H films and obtained the constant of (2.5 – 5) × 1016 cm−3 . Gunes correlated densities of ESR spins with the sub-bandgap absorption measured by DBP on various intrinsic aSi:H films and obtained the constant of 3.0 × 1016 cm−3 [38]. This approach does not take into account the presence of other defects and their changes in density in different films. Charged defect states contribute to the sub-bandgap absorption but have no ESR signal. Thus, very large uncertainties could be introduced using such a “calibration” constant. For the undiluted film in Fig. 6.5, there is a much-pronounced shoulder in α(hν) for the energy region between 1.0 and 1.3 eV. This points out that the single value of α is not a

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valid representation of the nature and densities of gap defect states in a-Si:H materials. 6.3.3.2. Analytical Treatment of Sub-bandgap Absorption It can be seen that there are fundamental problems with the procedures used to derive densities of gap states from sub-bandgap absorption spectra using the α(hν) value at a single energy. The inherent complexity associated with the existence of multiple gap states limits the ability to reliably correlate ESR with the sub-bandgap absorption. In order to obtain more quantitative information about the gap state properties, numerical modeling of the sub-bandgap absorption coefficient spectra is carried out such as that done at Pennsylvania State University using the SAM program [38, 39]. The recombination kinetics used in this modeling program apply a distribution consisting of single-electron states and Simmons and Taylor statistics [29]. To reflect the experimentally observed continuous distributions of mid-gap states, Gaussian distributions are used with no interacting recombination among these gap states. Along with the requirement of charge neutrality, the occupation of the individual energy state and carrier concentrations in the extended energy states are calculated for a given carrier generation rate. The sub-bandgap absorption is then calculated from the transitions of electrons from occupied energy states to the extended energy states assuming a constant optical transition matrix element for all gap states. Simulations of the experimental data are then carried out with locations, densities, and capture cross-sections of Gaussian distributions as fitting parameters. The information on gap states is obtained from these fitting parameters. This approach has been successful in providing insights into the nature of gap states. Since many of the gap state parameters have not been measured, a number of these parameters must be assumed. Consequently, the results are treated as “operational parameters” to distinguish them from parameters that could be actually measured. The results obtained may not be unique since in some cases the same experimental results could be modeled with different sets of operational parameters.

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6.4. Stability in a-Si:H 6.4.1. The Staebler–Wronski Effect The light-induced changes in a-Si:H-based materials, known as the Staebler–Wronski effect (SWE), are not only of great scientific interest, but also of great technological importance because of their effects on the long-term stability of a-Si:H-based solar cells. The SWE was first observed as changes due to sunlight in the carrier transport of thin films, and was also found to be completely reversible after annealing the materials for a few hours at temperatures of 150◦ C [2]. These changes result from the introduction of metastable defects whose rate of creation and densities depend on both the intensity of illumination and temperature. The reversible changes that occur between an annealed initial state A and a “light soaked” state B have become one of the most investigated phenomena in a-Si:H-based materials and solar cells [13, 40–44]. However, progress has been relatively slow in obtaining a definitive understanding and control of the SWE. This is in large part due to the complex nature of the defects as well as differences in microstructure that exist in the a-Si:H materials that are prepared under a wide range of growth conditions. An example of changes observed for a-Si:H films upon illumination with 100 mW/cm2 of white light (AM1.5 or 1 sun) is illustrated in Fig. 6.8. Figure 6.8 shows the well-known decrease in photoconductivity, which is generated here by white light, as well as the many orders of magnitude decrease in the dark conductivity. Although advances have been made in the understanding of SWE, as of yet there is still no general consensus on the exact nature of the light-induced defects or the mechanism responsible for their creation. Stutzmann [45] introduced the weak-bond/dangling-bond conversion model, whereas on the other hand, Adler [46] suggested that charged defects (D+ and D− ) capture photogenerated electrons and holes and reconfigure into metastable neutral dangling bonds (D0 ). Branz and Silver [6] have described the charged defect model proposing that charged defect states are introduced by the short range of potential fluctuations due to the material inhomogeneity. There is general consensus, however, that hydrogen, which plays a key role

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Fig. 6.8. Dark conductivity and photoconductivity of a hydrogenated amorphous silicon (a-Si:H) thin film shown as a function of the illumination time under sunlight [2].

in eliminating defects in a-Si:H alloys, also plays a key role in their light-induced creation [22]. For a long time, the widely held view was that the only light-induced defect states were those associated with the neutral dangling bond, D0 . However, there is extensive evidence now indicating that the light-induced changes in charged defect states are just as important, if not more so, in comparison to changes in the D0 states [13, 36, 47]. Significant progress has been made over the years not only in improving the initial properties of a-Si:H-based materials but also in reducing their SWE. This has been achieved by optimizing the growth conditions to improve the microstructure of the materials through enhanced incorporation of hydrogen into the network. As a

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result, it is possible to obtain solar cells with not only higher initial efficiencies, but more importantly, better steady-state performance. In addition, these optimized materials and their solar cells require dramatically shorter times to reach a degraded steady state (DSS) under sunlight such that it occurs in less than 100 hr for these materials, as compared to thousands of hours for standard materials [22, 48]. This makes fundamental studies of SWE, as well as those on solar cell improvements, possible through detailed analyses that have in the past been limited by the long-time constraints. 6.4.2. Rapid Light-induced Changes in a-Si:H It has been found that a-Si:H materials exhibit large changes in photoconductivity and electron μτ products in the first few minutes of AM1.5 illumination. However, there are no corresponding increases in sub-bandgap absorption [49]. These characteristics are clearly inconsistent with the conventional model proposed by Stutzmann et al. [3], which is based on recombination kinetics dominated by the neutral dangling bonds, D0 , and predicts that the electron μτ product is inversely proportional to the densities of these bonds and hence the sub-bandgap absorption. In addition, the model predicts that the μτ product is insensitive to the generation rate. Examples of large, rapid initial light-induced changes obtained during the first 5 min of AM1.5 illumination are illustrated in Fig. 6.9, where the photoconductivities are shown for the diluted and undiluted films deposited at a substrate temperature of 200◦ C. Both of these films exhibit about an order of magnitude decrease in their photoconductivities within the first 5 min of AM1.5 illumination. Similar results are observed for a variety of diluted and undiluted a-Si:H films as well as Schottky barrier cell structures [50]. These rapid changes in photoconductivity consist not only of large decreases in the electron lifetime, but also of significant changes in the carrier recombination kinetics reflected in the functional dependence of the electron μτ product on the carrier generation rate, G. For the diluted film of Fig. 6.9, the changes in electron μτ product occurring between the annealed state and after a halfminute and 5 min of AM1.5 illumination are depicted in Fig. 6.10

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Fig. 6.9. AM1.5 light-induced changes of photoconductivity within the first 5 min for diluted and undiluted films deposited at a substrate temperature of 200◦ C.

Fig. 6.10. μτ (G) of the diluted hydrogenated amorphous silicon (a-Si:H) in the annealed state and after 0.5 and 5 mins of AM1.5 illumination.

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Fig. 6.11. Sub-bandgap absorption of the diluted hydrogenated amorphous silicon (a-Si:H) in the annealed state and after 0.5 and 5 min of AM1.5 illumination.

for generation rates ranging from 6 × 1014 to 1020 cm−3 s−1 . It can be seen in Figs. 6.9 and 6.10 that a decrease of up to a factor of approximately five in the μτ product occurs after only a halfminute of illumination. In contrast, there are no detectable changes in the sub-bandgap absorption as indicated by results in Fig. 6.11 obtained with a generation rate of 6 × 1014 cm−3 s−1 after a halfminute of AM1.5 illumination. Furthermore, there is only a very small increase in the sub-gap absorption after 5 min of illumination. These results clearly indicate that as the generation rate increases the electron lifetime and corresponding recombination kinetics change in a way that can only be explained by the presence of gap states different from those of D0 [51]. This is also true of the annealing kinetics [52, 53].

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6.4.3. Light-induced Changes in a-Si:H after Extended Light Illumination The extensively studied decreases in photoconductivity and increases in sub-bandgap absorption during prolonged illumination do reflect the changes in μτ products and the density of neutral dangling bonds, N (D0 ), respectively, but detailed measurements also clearly indicate contributions from light-induced charged defect states [5]. The lightinduced changes in both the magnitude of μτ and its dependence on G are inconsistent with carrier recombination determined solely by N (D0 ) as are the light-induced degradation kinetics, which do not in most cases proceed according to a t−0.33 dependence [3]. Degradation kinetics with time dependences similar to this are found in undiluted a-Si:H films and only at high generation rates whereas other a-Si:H materials exhibit distinctly different degradation kinetics. This is illustrated in Fig. 6.12 where the μτ products

Fig. 6.12. The μτ products at a generation rate of 1 × 1019 cm−3 s−1 for four hydrogenated amorphous silicon (a-Si:H) films plotted versus AM1.5 illumination time at room temperature.

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at G = 1019 cm−3 s−1 are shown as functions of 1 sun illumination time for two undiluted and two diluted films together with lines indicating t−0.3 and t−0.2 as guides to the eye [54]. Although in undiluted materials degradation kinetics can be interpreted in terms of the well-known t−1/3 dependence, such a dependence is found only in undiluted materials and at high generation rates such as the value of 1 × 1019 cm−3 s−1 in Fig. 6.12, which is close to that of 1 sun. The diluted materials clearly show degradation kinetics that are significantly slower, indicating a distinctly different evolution of lightinduced recombination centers compared to that for the undiluted materials. The creation of defects other than dangling bonds is further indicated by differences in the time dependence observed with changes in generation rates used to measure the μτ products (from the photoconductivities). This is illustrated in Fig. 6.13 where the μτ products for the undiluted material of Fig. 6.12 are shown for generation rates of 1×1016 cm−3 s−1 as well as 1×1019 cm−3 s−1 . The wide range of kinetics such as shown in Figs. 6.12 and 6.13 cannot

Fig. 6.13. Kinetics of light-induced changes at two generation rates for R = 0 materials prepared at Pennsylvania State University.

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be explained with the creation of only neutral dangling-bond states in the middle of the gap, but also require a contribution from defect states located closer to the band edges [43]. It is very important to note here that the absence of a universal t−0.33 time dependence for light-induced changes clearly points out the inconsistencies in the common practice of using arbitrary exposure times to characterize the stability of different a-Si:H materials. A striking difference can be found in the kinetics of light-induced changes under AM1.5 illumination between undiluted (R = 0) and diluted (R = 10) materials. Whereas in undiluted films, there is no evidence of a DSS in photoconductivities even after 500 hr of illumination, there is a clearly defined steady state present in R = 10 materials. Such a distinct difference in the kinetics between diluted and undiluted materials (which is also reflected in the corresponding solar cells) offers a means for improving the understanding of the mechanisms responsible for the SWE as well as its effect on solar cell degradation. The observation that hydrogen diluted materials saturate within 100 hr whereas undiluted materials do not saturate even after 500 hr indicates that there is a difference of the microstructure of these materials. Lower steady-state values of the electron μτ product under 10 AM1.5 illumination compared to those under 1 AM1.5 illumination as shown in Fig. 6.14 clearly indicate that the densities of light-induced defects depend on the intensity of the illumination. These results are in contrast to previously reported observations that such densities are independent of the illumination level [55]. In addition, it was found that the 1 sun light-induced changes, even between 25◦ C and 75◦ C, have distinctly different degradation rates as well as values of the μτ products in their respective DSSs [56]. Because of such dependences of the light-induced changes on both temperature and light intensity, the arbitrarily chosen high intensity tests commonly used are irrelevant unless quantified with 1 sun DSS results. The contribution of the charged defect states to sub-bandgap absorption is subtler because, with prolonged illumination, the magnitude of α(hν) becomes increasingly dominated by the large densities of D0 states [57]. However, the differences in the shapes of

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Fig. 6.14. Kinetics of light-induced changes of diluted materials at two light intensities.

α(hν), which are not as large as in the case of the annealed state, do indicate differences in defect densities at energies displaced from the middle of the gap. As a consequence, materials after AM1.5 degradation can have virtually the same densities of D0 defects, as measured with ESR and indicated by the α(1.2 eV) values, and yet have distinctly different photoconductivity and μτ product characteristics. This is illustrated in Fig. 6.15 with results of the sub-bandgap absorption for diluted films and undiluted films after exposure for 100 hr to AM1.5 illumination. It can be seen in Fig. 6.15 that the two films have virtually the same absorption coefficient at the energy of 1.2 eV, which is consistent with their neutral dangling-bond densities of 8 × 1016 for diluted films and 9 × 1016 for undiluted films as obtained from ESR measurements. However, even though the values of α(1.2 eV) and N (D0 ) are the same, there are differences in the shapes of the α(hν) spectra, which indicate differences in gap states closer to the band edges that affect both the μτ products in the films and the fill factors in the corresponding cells. In the case presented here, the μτ products of diluted films are 4–5 times higher than those of undiluted films, whereas in corresponding 0.5 μm Schottky barrier cell structures the fill factors are 0.52 and 0.40, respectively.

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Fig. 6.15. The subgap absorption of diluted (R = 10) and undiluted (R = 0) films after 100 hr of AM1.5 illumination.

6.4.4. Numerical Modeling of the Gap States in a-Si:H In the past, analysis of a-Si:H thin film and solar cell results has been based on a model of two Gaussian distributions of gap states associated with the neutral, D0 , and negatively charged, D− , dangling bonds, which is considered the conventional model of gap states [58, 59]. As a consequence, the analysis of many results for the properties of both films and devices were carried out focusing only on the role of D0 , which could be clearly identified by its ESR signal [60] and the sub-bandgap absorption such as measured by CPM [61]. Although it was claimed that such a gap state distribution was consistent with results on a-Si:H-based materials, it appears that this was satisfied only to a limited extent. Various experimental results have

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been obtained that cannot be explained by this conventional model such as: (i) the different characteristics of the functional dependence of μτ products on generation rates and the different shapes of the subbandgap absorption spectra for a wide variety of a-Si:H films; (ii) the initial rapid light-induced changes in photoconductivity and slight changes in sub-bandgap absorption; and (iii) the different shapes and dependences of sub-bandgap absorption on the bias light illumination. As a result of wide-ranging studies on materials and devices, extensive evidence has accumulated for significantly different distributions than those in the conventional model. In order to analyze results of both photoconductivity and sub-bandgap absorption self-consistently for the wide variety of materials, it was necessary to take into account the effect of charged defect states: the donor-like, D+ , states located above the Fermi level with positive charge, and acceptor-like, D− , states located below the mid-gap with negative charge under thermal equilibrium [8, 10, 11, 18, 62]. A similar distribution has been proposed by Branz and Silver [6] resulting from the short range of potential fluctuations due to the inhomogeneity of the material. To take into account the amphoteric nature of the defect states, an improved distribution of one-electron density of states was proposed [39], which is illustrated in Fig. 6.16. In Fig. 6.16, the densities of extended states have parabolic distributions, which merge with the exponential tails as derived from the self-consistent analysis of DBP, PDS, and T&R measurements. The neutral dangling-bond states are represented by a single Gaussian distribution and the distributions of charged states were expanded to include the (+/0) transitions for the negatively charged defect states D−∗ , and the (0/−) transitions for the positively charged defect states D+∗ , where these new states are closer to the valence and conduction bands, respectively. The Gaussian distribution closest to the conduction band has a smaller electron capture cross-section as it represents the D+ states associated with the (0/−) transition.

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Fig. 6.16. Distribution of gap states used in self-consistent analysis of hydrogenated amorphous silicon (a-Si:H) materials and devices. D0 are the neutral dangling bonds; D+ , D+∗ are the positively charged states; and D− , D−∗ are the negatively charged states.

The Gaussian distribution that is the closest to the valence band has a smaller hole capture cross-section since it represents the D− states associated with the (+/0) transition. The three Gaussian distributions of states closer to the mid-gap are similar to those used in the previous analysis by Gunes et al. [11]. In the dark, the states closest to the energy band edges are neutral. However, under illumination, as concentrations of free carriers increase, the Fermi level of electrons and holes is split, introducing electron and hole quasi-Fermi levels, EF n and EF p , respectively. As the quasiFermi levels sweep through the gap and move toward the band edges, trapping of free carriers occurs in these new states and more and more of the states become recombination centers. The energies, capture cross-sections, and densities of all the energy states affect the electron μτ products, and the concurrent changes in the occupation of these states by electrons affect the magnitude and shape of the sub-bandgap absorption spectra.

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Because of the large number of adjustable parameters associated with the energy locations, densities, and carrier capture crosssections of different gap states, an iterative procedure is necessary for the self-consistent fitting of all the results on thin films and the corresponding Schottky barrier solar cells using the same values for the parameters [36]. The characteristics of the a-Si:H thin film materials can be fit using the distributions of gap states shown in Fig. 6.16 and their associated parameters. The same parameters can be used to fit the results for the corresponding Schottky barrier solar cells. For diluted a-Si:H thin film material, the gap state parameters used to fit the electron μτ (G) and the sub-bandgap absorption for two generation rates are shown in Tables 6.1 and 6.2 in the annealed state and after 100 hr of 1 sun illumination, respectively. These results clearly indicate that after prolonged illumination there is not only an increase in D0 states but also an increase in the charged defect states. The contribution of the charged defect states, when large densities of D0 states are Table 6.1. Gap state parameters for the diluted film in the annealed state.

Density (cm−3 ) Energy (eV) from V.B. Half-width (eV)

D0

D+

D−

D+∗

D−∗

5.20 × 1015

9.50 × 1015

1.05 × 1016

8.00 × 1015

8.00 × 1015

0.9

1.34

0.67

1.37

0.50

0.080

0.067

0.042

0.060

0.060

Table 6.2. Gap state parameters for the diluted film after 100 hr 1 sun illumination.

Density (cm−3 ) Energy (eV) from V.B. Half-width (eV)

D0

D+

D−

D+∗

D−∗

1.20 × 1017

4.50 × 1016

4.80 × 1016

1.00 × 1017

1.00 × 1016

0.9

1.2

0.72

1.31

0.50

0.080

0.050

0.070

0.045

0.060

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present after prolonged illumination, cannot be readily identified unless the sensitivities of both the μτ products and the sub-bandgap absorption are characterized in detail. The densities of charged defect states could only be obtained by the self-consistent fitting of such results. Fits to the electron μτ product and the sub-bandgap absorption with two generation rates for the diluted a-Si:H thin film material after 100 hr 1 sun illumination are shown in Fig. 6.17, where the symbols are experimental results and lines are the fits. It may be pointed out that the value of the μτ product at each generation rate corresponds to an individual result. The good fits of both the μτ product and the sub-bandgap absorption using the same “operational” gap state parameters clearly support the importance of including charged defects in any realistic characterization of gap

Fig. 6.17. Sub-bandgap absorption characteristics of the diluted materials in the degraded steady state (DSS). Symbols are experimental results and solid lines are fits. Also shown are fits to mobility-lifetime product results in their DSSs.

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states and their effects on cell performance. However, the distribution of states chosen to represent the charged defects is not unique but rather a possibility; nevertheless, the “operational” parameters such as derived here offer a more realistic and reliable approach for modeling of p-i-n and n-i-p solar cell characteristics in their DSSs. This is useful not only for conventional a-Si:H-based PV, but also solar photovoltaic thermal (PVT) systems that take advantage of solar thermal energy to anneal SWE defects from a-Si:H to boost electrical performance [63–66].

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45. Stutzmann, M. (1987). Weak bond-dangling bond conversion in amorphous silicon, Philosophical Magazine B, 56, pp. 63–70. 46. Adler, D. (1981). Defects in amorphous chalcogenides and silicon, Journal of Physics, 42, pp. C4-3–C4-14. 47. Lu, Z., et al. (1999). Characteristics of different thickness a-Si:H/metal Schottky barrier cell structures — results and analysis, Materials Research Society Symposium Proceedings, 557, pp. 785–790. 48. Yang, L., and Chen, L. F. (1994). The effect of H2 dilution on the stability of a-Si:H based solar cells, Materials Research Society Symposium Proceedings, 336, pp. 669–674. 49. Jiao, L., et al. (1996). Importance of charge defects in a-Si:H materials and solar cell structures. In: Proceedings of 25th IEEE Photovoltaic Specialists Conference (PVSC) (New York, NY, IEEE), pp. 1073–1076. 50. Wronski, C. R., Jiao, L., and Collins, R. W. (1998). Effects of charged defects on light induced changes in a-Si:H materials and solar cells. In: 11th “Sunshine” Workshop on Thin Film Solar Cells; Technical Digest (Tokyo, MITI-NEDO), p. 67. 51. Deng, J., et al. (2004). Characterization of the bulk recombination in hydrogenated amorphous silicon solar cells, Materials Research Society Symposium Proceedings, 808, p. A8.8. 52. Albert, M. L., et al. (2005). The creation and annealing kinetics of fast light induced defect states created by 1 sun illumination in a-Si:H, Materials Research Society Symposium Proceedings, 862, pp. 1536– 1539. 53. Pearce, J. M., et al. (2005). Room temperature annealing of fast state from 1 sun illumination in protocrystalline Si:H materials and solar cells. In: Conference Record of the Thirty-first IEEE Photovoltaic Specialists Conference (PVSC) (New York, NY, IEEE), pp. 1536–1539. 54. Jiao, L., et al. (2001). New perspective on the characterization of materials for a-Si:H solar cells, Solar Energy Materials and Solar Cells, 66, pp. 231–237. 55. Isomura, M. (1993). Effect of Material Properties on Light-induced Degradation of Amorphous Silicon Solar Cells, Ph.D. Thesis (Osaka, Japan, Osaka University). 56. Wronski, C. R., Jiao, L., Niu, X., and Collins, R. W. (1999). Characterization of amorphous silicon materials for solar cell applications. In: 12th “Sunshine” Workshop on Thin Film Solar Cells; Technical Digest (Tokyo, MITI-NEDO), p. 10. 57. Wyrsch, N., et al. (1996). Correlation between transport properties of a-Si:H layers and cell performances incorporating these layers, Journal of Non-Crystalline Solids, 198–200, pp. 238–241.

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58. Davis, E. A., and Mott, N. F. (1970). Conduction in non-crystalline systems V. Conductivity, optical absorption and photoconductivity in amorphous semiconductors, Philosophical Magazine, 22, pp. 903–922. 59. Vasanth, K., Wagner, S., Caputo, D., and Bennett, M. (1994). The role of interfaces in the end-of-life performance of a-Si:H solar cells. In: Proceedings of 1994 IEEE 1st World Conference on Photovoltaic Energy Conversion — WCPEC: Conference Record of the 24th IEEE Photovoltaic Specialists Conference (PVSC), Vol. 1 (New York, NY, IEEE), pp. 488–491. 60. Dersch, H., Stuke, J., and Beichler, J. (1981). Electron spin resonance of doped glow-discharge amorphous silicon, Physica Status Solidi (b), 105, pp. 265–274. 61. Schauer, F., and Kocka, J. (1985). Study of light-induced metastable defects by means of temperature-modulated space-charge-limited currents, Philosophical Magazine B, 52, pp. L25–L30. 62. Powell, M. J., and Dean, S. C. (1993). Improved defect pool model for charged defects in amorphous silicon, Physical Review B, 48, pp. 10815– 10827. 63. Pathak, M. J. M., Pearce, J. M., and Harrison, S. J. (2012). Effects on amorphous silicon photovoltaic performance from high-temperature annealing pulses in photovoltaic thermal hybrid devices, Solar Energy Materials and Solar Cells, 100, pp. 199–203. 64. Pathak, M. J. M., Girotra, K., Harrison, S. J., and Pearce, J. M. (2012). The effect of hybrid photovoltaic thermal device operating conditions on intrinsic layer thickness optimization of hydrogenated amorphous silicon solar cells, Solar Energy, 86, pp. 2673–2677. 65. Rozario, J., et al. (2014). The effects of dispatch strategy on electrical performance of amorphous silicon-based solar photovoltaic-thermal systems, Renewable Energy, 68, pp. 459–465. 66. Rozario, J., and Pearce, J. M. (2015). Optimization of annealing cycles for electric output in outdoor conditions for amorphous silicon photovoltaic–thermal systems, Applied Energy, 148, pp. 134–141.

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CHAPTER 7

Growth and Properties of Tetrahedrally-Bonded Thin-Film Amorphous Silicon Alloys Nikolas J. Podraza and Robert W. Collins University of Toledo, USA

7.1. Motivation In addition to its direct use in device applications, hydrogenated amorphous silicon (a-Si:H) films are also used in modified forms by alloying with other group IV elements such as carbon, germanium, and tin. Alloys with carbon (a-Si1−x Cx :H) and germanium (aSi1−x Gex :H), have found the most use in applications ranging from undoped absorber layers in thin-film solar cells, n-type and p-type doped semiconductor films, light-emitting diodes, infrared sensors, and others [1–20]. In both alloys, the carbon or germanium atoms substitute for a portion of the silicon atoms in the amorphous network, and the desired diamond-like bonding configuration is maintained in most cases. The carbon in a-Si1−x Cx :H sometimes also exhibits graphite-like bonding occurring at high carbon contents 247

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[21, 22]; however, the materials discussed in this chapter have predominate diamond-like bonding. The amorphous networks of alloys have increased disorder relative to a-Si:H, similar to configuration entropy induced when a foreign atom occupies a lattice site in a crystal. In this case, however, additional disorder may be introduced by changes in the local bonding configuration by the presence of the alloying atoms and in how hydrogen is incorporated into the amorphous network. The presence of the alloying atoms and the changes induced in the amorphous network impact the resultant opto-electronic properties of the materials and their performance within devices. Changes to the deposition process, such as replacing some of the silicon-carrying source gas with carbon- or germaniumcarrying gases not only change the amorphous material properties, but also the structural evolution of the material described in detail for hydrogenated silicon (Si:H) in Chapter 1. Specific device application relevant topics discussed here include band gap widening and narrowing by introduction of carbon and germanium, respectively, the impact of these band gap variations on solar cells, and electrical transport properties relevant to solar cells and infrared sensors.

7.2. Growth Evolution and Microstructural Transitions Alloy films with carbon (Si1−x Cx :H) and germanium (Si1−x Gex :H) can be made using the same chemical and physical vapor deposition processes as for Si:H. Plasma-enhanced chemical vapor deposition (PECVD) is discussed for these as it is the most widespread technique adopted in research and industrial settings. Like with PECVD of Si:H, process parameters include substrate temperature, total gas pressure, gas composition, plasma excitation frequency, and plasma power. The structure, chemistry, and relative order of the underlying substrate material influence alloy films in the same way as for Si:H as described in Chapter 1, namely that the alloy material may be amorphous, nanocrystalline, or mixed phase [12, 15, 19, 23–31]. New parameters for alloys arise from replacing a fraction of the silicon-carrying source gas (commonly SiH4 ) with carbon-carrying

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(CH4 ) or germanium-carrying (GeH4 ) source gases [19, 23–34]. Here, the relative fractions of the alloying gases are described as Z = [CH4 ]/{[CH4 ] + [SiH4 ]} and G = [GeH4 ]/{[GeH4 ] + [SiH4 ]}. The hydrogen to reactive gas flow ratios are now defined as R = [H2 ]/{[GeH 4 ] + [SiH4 ]} and R = [H2 ]/ {[CH4 ] + [SiH4 ]}. Other notations may be found in the literature. Growth rates for films prepared under otherwise identical conditions decrease with increasing CH4 content and increase with increasing GeH4 content during respective depositions due to different dissociation rates of these source gases relative to SiH4 [26, 28, 32] and incorporation rates of carbon and germanium relative to silicon [32, 33, 35]. For a-Si1−x Cx :H, the source gas composition ratio Z is greater than x, the mole fraction of carbon actually incorporated into the films. Conversely for Si1−x Gex :H, the source gas composition ratio G is less than x, here the amount of germanium incorporated into the films. Other gas combinations result in different relationships between alloying gas content and film incorporation. For example, replacing SiH4 with Si2 H6 and mixing with GeH4 result in closer alloy gas flow ratios and elemental film incorporation fractions [12, 28]. As a function of accumulated film thickness and R, alloy films will grow in the same amorphous, mixed-phase, and nanocrystalline regimes as for Si:H. The amorphous to mixed-phase amorphous + nanocrystalline [a → (a + nc)] and mixed-phase to single-phase nanocrystalline [(a + nc) → nc] transitions are still observed, as is the amorphous to amorphous roughening [a → a] transition when films are prepared on sufficiently smooth substrates [12, 23, 24, 26, 27, 31]. For both types of alloys, crystallite nucleation is suppressed due to the increased disorder induced in the amorphous or protocrystalline network as a result of the mixed group IV element incorporation. The initial appearance of crystallites is shifted to increasing values of R for both Si1−x Cx :H and Si1−x Gex :H relative to Si:H [24, 26]. The R values at which crystallites first nucleate track with the amount of alloying gas present during PECVD. When G is varied and R remains fixed at conditions showing both crystallite nucleation and coalescence transitions for Si:H, crystallite

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Fig. 7.1. Growth evolution diagram for PECVD R = 40 Si1−x Gex :H films as a function of GeH4 flow ratio G. Crystallinity is suppressed with alloying. Thicknesses of the amorphous roughening transition [a → a] (solid line and square points), and the amorphous to (mixed-phase amorphous + nanocrystalline) transition [a → (a + nc)] (dashed line and circles), and the (mixed-phase)-to-(single-phase) nanocrystalline transition [(a + nc) → nc] (dotted line and triangles) are depicted. Up-arrows indicate that the transitions occur at the thickness above the indicated value. Reprinted from [27], Journal of Non-Crystalline Solids, vol. 352, N. J. Podraza, C. R. Wronski, and R. W. Collins, Deposition phase diagrams for Si1−x Gex :H from real time spectroscopic ellipsometry, 1263–1267, Copyright (2006), with permission from Elsevier.

nucleation is suppressed to greater thickness, and at sufficiently large values of G, no crystallite nucleation is observed at all (Fig. 7.1). In fact, for some deposition conditions, nanocrystalline Si1−x Cx :H (nc-Si1−x Cx :H) is not observed to form at all. When crystallites do nucleate in the alloys, the a → (a + nc) transition thickness typically decreases as R increases. After the crystallites have grown preferentially over the amorphous phase at sufficient accumulation of material thickness, the (a + nc) → nc transition is observed with the thickness also decreasing with increasing R. In the case of crystallite nucleation for Si1−x Gex :H, the energetic incentive to form nc-Si1−x Gex :H over a-Si1−x Gex :H depends upon the germanium content. Crystallites in nc-Si:H evolve as inverted cone

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shapes and can be described with a geometrical cone growth model [29, 31, 36]. In this model, the a → (a + nc) transition occurs with the initial nucleation of crystallites, which occurs at a given area density on the surface. Comparable nucleation densities can be observed for silicon, silicon–germanium alloy, and germanium crystallites, although these values will occur under different combinations of PECVD process parameters [31]. A higher crystallite nucleation density implies less accumulated thickness in the mixed-phase growth regime prior to crystallite coalescence. Another parameter controlling the thickness of the mixed-phase regime is the cone half angle. After nucleation, each crystallite grows as an inverted cone, whereby the cone half angle is related to how much surface area the crystallite occupies over the surrounding amorphous phase (Fig. 7.2). If the crystalline phase is energetically favored over the amorphous phase,

Fig. 7.2. (left) Cross sectional transmission electron micrograph of a R = 400 Ge:H thin film showing crystallites growing as inverted cones. (right) Average nucleation density and cone half angle ascertained from the cone growth model [36] for Si1−x Gex :H prepared at different G but with similar a → (a+nc) transition thicknesses. Cone half angle decreases monotonically with increasing G, indicating a reduction in the energetic difference between amorphous and nanocrystalline c 2010 IEEE. Reprinted, with permission from [31], N. J. Podraza, D. B. phases.  Saint John, J. Li, C. R. Wronski, E. C. Dickey, and R. W. Collins, Microstructural evolution in Si1−x Gex :H thin films for photovoltaics applications, 35th IEEE Photovoltaic Specialists Conference, pp. 158–163, 2010.

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the cone half angle is non-zero, crystallites will eventually cover the full surface, and a single-phase nanocrystalline film will form. If there is no energetic incentive to form crystallites, then the amorphous phase persists. In the case of Si1−x Gex :H prepared at different reactive gas compositions, G, films prepared under identical conditions show a systematic reduction in the cone half angle with increasing G or germanium content in the film (Fig. 7.2). This reduction in cone half angle implies that for increasing germanium content, the energetic difference between the amorphous and nanocrystallite phases decreases. Given the same nucleation densities, a longer mixed-phase regime will persist in increasingly germanium-rich films due to this reduction in the cone half angle. Within the amorphous growth regime for the alloys, reductions in order are observed through the a → a roughening transition thicknesses, material density, and width of the characteristic visible wavelength range absorption feature. From the complex optical response, as discussed in Section 7.4, both a-Si1−x Cx :H and aSi1−x Gex :H alloys show an increase in broadening with increasing alloy atom content [33, 35, 37]. This increase implies a reduction in mean free path of excited electrons in the material with the increased scattering frequency due to disorder and defects within the amorphous network. For both a-Si1−x Cx :H and a-Si1−x Gex :H alloys, material made under unoptimized conditions exhibits a lower relative density as assessed from the optical response as well, indicating the presence of nano-/micro-scale voids [23, 24, 35]. Porous a-Si:H with these voids typically results in reduced performance of solar cells incorporating these materials as absorber layers [38]. As mentioned in Section 1.3, the a → a transition thickness is correlated with the diffusion length of precursors on the surface [39, 40]. Longer diffusion lengths of precursors occur with greater a → a transition thicknesses indicative of higher electronic quality when those materials are incorporated into devices. Under PECVD conditions producing optimum a-Si:H, a-Si1−x Gex :H alloy films show a → a transitions at more than an order of magnitude lower accumulated material thickness (Fig. 7.3) [26]. Even when process conditions are altered to optimize a-Si1−x Gex :H, the same maximum a → a transition

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Fig. 7.3. Growth evolution diagrams as a function of R for Si:H (squares) and G = 0.167 Si1−x Gex :H (circles). The (up, down) arrows indicate that the transition occurs (above, below) the designated value. Increased R is required for crystallite nucleation and coalescence for Si1−x Gex :H relative to Si:H as a result of increased configurational disorder due to alloying. N. J. Podraza, G. M. Ferreira, C. R. Wronski, and R. W. Collins, Development of deposition phase diagrams for thin film Si:H and Si1−x Gex :H using real time spectroscopic ellipsometry, MRS Proceedings, 862, A16.3, 2005, [26] reproduced with permission.

thicknesses observed for a-Si:H cannot be reached. For material optimized at different G, decreasing values of the a → a transition thickness are observed with increasing G (Fig. 7.4) [28]. Overall, these kinds of observations are somewhat expected for the alloys as ordering is reduced simply by the presence of germanium or carbon as an addition to the predominately a-Si:H network. Another consideration is how hydrogen is incorporated into the alloy films and how hydrogen in the plasma during deposition interacts with the growing film surface (Fig. 7.5) [30]. In a purely hydrogen plasma, a R = 0 a-Si:H film will be modified and ultimately etched by atomic hydrogen present. For a R = 0 a-Ge:H film, this etching occurs at a rate about two orders of magnitude slower.

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Fig. 7.4. Growth evolution diagram depicting the a → a transition for R = 10 a-Si1−x Gex :H as a function of G. The dotted arrows show an increase in the a → a transition thickness possible with increased R up to the a → (a + nc) transition R value for a thick film. Addition of germanium reduces film electronic quality at fixed R and is not fully recoverable by increasing R further. N. J. Podraza, C. R. Wronski, M. W. Horn, and R. W. Collins, Surface roughening transition in Si1−x Gex :H thin films, MRS Proceedings, 910, A3.2, 2006, [28] reproduced with permission.

This reduced etching implies that in the plasma germanium and hydrogen interact differently than silicon and hydrogen, impacting the order within the amorphous network. Interestingly, for R = 0 a-Si1−x Gex :H, etching rates are initially higher upon first exposure followed by a reduction at later time. This behavior indicates that silicon is etched preferentially by hydrogen over the germanium present. The stronger interaction between silicon and hydrogen than germanium and hydrogen means that hydrogen may be less effectively incorporated into the amorphous germanium network, resulting in less passivation of defects by hydrogen in the films and a reduction in order.

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Fig. 7.5. Effective material thickness for a-Si:H and G = 0.167 a-Si1−x Gex :H as a function of hydrogen plasma etching time. Higher etching rates for aSi:H and for a-Si1−x Gex :H at early times indicate that silicon is selectively etched by hydrogen over germanium and that hydrogen interacts more strongly with silicon than germanium. The etching rate of a-Ge:H is 0.002 ˚ A/s. N. J. Podraza, J. Li, C. R. Wronski, M. W. Horn, E. C. Dickey, and R. W. Collins, Analysis of compositionally graded Si:H and Si1−x Gex :H thin films by real time spectroscopic ellipsometry, MRS Proceedings, 1066, A10.1, 2006, [30] reproduced with permission.

7.3. Optimization of a-Si1−x Gex :H Growth In optimizing PECVD process parameters for a-Si1−x Gex :H, those producing optimized a-Si:H were logically used as a starting point albeit with G = 0.167 to produce material with a ∼1.4 eV band gap suitable for the bottom junction of a triple-junction solar cell [3, 26, 35]. Comparing the growth evolution diagrams tracking the a → a and a → (a + nc) transition thicknesses as functions of R for Si:H and Si1−x Gex :H shows a shift in crystallite nucleation to much higher R for Si1−x Gex :H and a reduction of the highest a → a transition thickness to a value well below the highest thickness observed for a-Si:H (Figs. 7.3 and 7.6). Optimization of a-Si1−x Gex :H has been challenging [2, 6, 10–12]. Two examples here include variations in substrate temperature and also in electrode configuration for optimization [26]. When the substrate temperature is increased for Si1−x Gex :H, the a → a transition thickness shifts to higher values and the initial appearance of crystallites shifts to lower R (Fig. 7.7). These shifts imply that order has been improved in the amorphous network and

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Fig. 7.6. Growth evolution diagrams at different G as functions of R. The (up, down) arrows indicate that the transition occurs (above, below) the designated value. With increasing germanium content, the onset of crystallinity is delayed to higher R and the maximal a → a transition thickness decreases indicating a reduction in material electronic quality. Reprinted from [27], Journal of Non-Crystalline Solids, vol. 352, N. J. Podraza, C. R. Wronski, and R. W. Collins, Deposition phase diagrams for Si1−x Gex :H from real time spectroscopic ellipsometry, 1263–1267, Copyright (2006), with permission from Elsevier.

that hydrogen-induced crystallinity is occurring more efficiently, both of which are positive signs for optimization. These characteristics improve from 200◦ C to 290◦ C. However, at temperatures greater than 290◦ C, hydrogen-induced crystallinity is suppressed due to hydrogen effusion from the material (Fig. 7.8) [41]. a → a transition thicknesses do not increase substantially, indicating that only limited improvement in the alloy amorphous network is achieved at elevated temperatures due to competing thermal and hydrogen-induced effects. Higher temperature leads to greater diffusion of surface precursors, but less incorporation of hydrogen into the amorphous network to improve order and passivate defects. An alternative for optimization is based on implementing ion bombardment to promote removal of weakly bound material on the surface and suppress crystallinity at high R. Consider a comparison of material prepared on the powered electrode, the cathode, with

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Fig. 7.7. Growth evolution diagrams for G = 0.167 Si1−x Gex :H at different substrate temperatures. The up arrows indicate that the transition occurs above the designated value. Increased substrate temperature improves hydrogen induced crystallinity at lower R and improves the quality of the a-Si1−x Gex :H at maximal R before crystallite nucleation. N. J. Podraza, G. M. Ferreira, C. R. Wronski, and R. W. Collins, Development of deposition phase diagrams for thin film Si:H and Si1−x Gex :H using real time spectroscopic ellipsometry, MRS Proceedings, 862, A16.3, 2005, [26] reproduced with permission.

that more commonly deposited on the unpowered electrode, the anode [26, 27]. For Si:H, material prepared on the anode exhibits a higher a → a transition thicknesses at the optimized value of R = 10 while the extra ion bombardment expected for material on the cathode reduces this thickness (Fig. 7.9). For this a-Si:H, the complex optical property broadening is greater for material deposited on the cathode, indicating a reduction in order within the amorphous network (Fig. 7.10). This increased ion bombardment also suppresses crystallinity. For Si1−x Gex :H, ion bombardment shifts crystallinity to sufficiently high R such that the greater amount of hydrogen present is more effective in improving the order within the amorphous network, as evidenced by the increase in a → a transition thickness at maximal R prior to crystallite nucleation (Fig. 7.11). In this case,

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Fig. 7.8. Growth evolution diagram for G = 0.167 and R = 60 Si1−x Gex :H as a function of substrate temperature. The up arrow indicates that the transition occurs above the designated value. Increased substrate temperature up to 290◦ C improves amorphous material quality and promotes hydrogen induced crystallinity. At higher temperatures, hydrogen effusion occurs leading to less hydrogen incorporation and the delay of crystallinity to higher thickness.

the absorption feature broadening is reduced indicating improvement in the order within the amorphous network for a-Si1−x Gex :H alloys deposited on the cathode. The a-Si1−x Gex :H network has greater disorder than a-Si:H due to the presence of alloying atoms, and, the effectiveness of hydrogen in the etching of weakly bound surface material and in improving the diffusion length of surface precursors is reduced. Some enhanced low-energy ion bombardment is beneficial to the alloy amorphous network in that it provides the extra energy to increase the diffusion lengths of those precursors and etch weakly bound material while preventing nucleation of crystallites that would dominate growth. Such ion bombardment can be accomplished by a variety of means including other electrode configurations [42], addition of non-reactive noble gases like helium to the chamber during PECVD [28], and use of other deposition processes.

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Fig. 7.9. Comparison of Si:H growth evolution for films deposited on the unpowered anode and powered cathode. The (up, down) arrows indicate that the transition occurs (above, below) the designated value. Crystallinity is suppressed and the maximum a → a transition thickness is reduced at R = 10 due to increased ion bombardment for material deposited on the cathode. N. J. Podraza, G. M. Ferreira, C. R. Wronski, and R. W. Collins, Development of deposition phase diagrams for thin film Si:H and Si1−x Gex :H using real time spectroscopic ellipsometry, MRS Proceedings, 862, A16.3, 2005, [26] reproduced with permission.

7.4. Optical Response of Amorphous Group IV Alloys A primary motivation for alloying a-Si:H with carbon or germanium has been to change the optical response, typically characterized by the band gap [33, 35, 37]. For thin-film Si:H-based solar cells, as described in more detail in other chapters, there have been two general initiatives. In multi-junction solar cells, a sub-cell with a wide band gap absorber is partnered with one or more sub-cells having narrower band gap absorbers [3, 6, 11, 14, 18]. Light is initially incident in the widest band gap junction. Light that is absorbed generates current and light that is not passes through for possible absorption in the successively narrower gap junctions. In this way, more of the solar irradiance spectrum can be absorbed by functional layers and converted into current to improve overall device efficiency. Alloying

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Fig. 7.10. (left) Complex dielectric function, ε = ε1 + iε2 , spectra for representative a-Si:H and G = 0.167 a-Si0.6 Ge0.4 :H. (right) Cody–Lorentz model parameters describing spectra in ε as a function of germanium content, x, for material deposited on the cathode and for material deposited on the anode for x = 0 and 0.4. Ion bombardment on the cathode reduces order in a-Si:H and increases order in a-Si0.6 Ge0.4 :H as reflected in the increase and decrease in the Cody–Lorentz broadening, Γ, respectively. N. J. Podraza, C. R. Wronski, M. W. Horn, and R. W. Collins, Dielectric functions of a-Si1−x Gex :H versus Ge content, temperature, and processing: advances in optical function parameterization, MRS Proceedings, 910, A10.1, 2006, [35] reproduced with permission.

with carbon widens the band gap relative to a-Si:H [33, 37, 43], and those absorber layer materials have been studied for top junctions in multi-junction devices or as other device layers with minimal parasitic absorption [4, 14, 15, 17, 18, 23, 24, 32–34]. Alloying with germanium does the opposite by narrowing the band gap [35, 43], and those materials have been studied as bottom or middle junction absorbers [2, 3, 6, 8, 10–12, 26–31]. Another consideration is that Si:H-based solar cells are made in n-i-p or p-i-n structures such that the intrinsic absorber layer is sandwiched between p-type and n-type doped layers. Any light absorbed in these doped layers, or really in any layer but the intrinsic absorber, does not generate current. Wide

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Fig. 7.11. Comparison of Si1−x Gex :H growth evolution for films deposited on the unpowered anode and powered cathode. The (up, down) arrows indicate that the transition occurs (above, below) the designated value. Crystallinity is suppressed, but the maximum a → a transition thickness is higher indicating improvements to electronic quality of amorphous alloy material deposited at maximal R on the cathode. N. J. Podraza, G. M. Ferreira, C. R. Wronski, and R. W. Collins, Development of deposition phase diagrams for thin film Si:H and Si1−x Gex :H using real time spectroscopic ellipsometry, MRS Proceedings, 862, A16.3, 2005, [26] reproduced with permission.

band gap doped layers, produced by alloying with carbon, provide an opportunity to produce a doped material with the desired electrical properties but with less parasitic absorption. More of the incident solar irradiance spectrum can then be absorbed in the intrinsic layer, increasing the current generated and overall device performance. Toward that end, the complex optical response, in the form of the complex dielectric function spectra, has been studied as a function of processing conditions yielding different carbon and germanium contents in a-Si1−x Cx :H and a-Si1−x Gex :H. The models describing the complex dielectric function spectra are elaborated upon in Chapter 4. Here we consider how these alloying contents impact that optical response; however, it should be noted that a variety of other characteristics of a-Si:H-based films also have an impact, including

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hydrogen content, hydrogen bonding configurations, presence of nano-/micro-scale voids, and film stress. Even without alloying, there are many considerations; however, when present, group IV element alloying is the most predominate contributor to the general shape of the optical properties and the value of the band gap. The complex dielectric function spectra for amorphous alloy films can be obtained from spectroscopic ellipsometry measurements performed ex situ [43], from in situ real-time spectroscopic ellipsometry (RTSE) data collected during film growth [23, 24, 26–35], or though transmittance + reflectance spectroscopy measurements. Results from analysis of RTSE data at the deposition temperature are described here. In this procedure, the complex dielectric function spectra are obtained by simultaneously analyzing multiple sets of ellipsometric spectra collected such that the real and imaginary parts are obtained at each spectral point individually along with the film thickness and surface roughness values. As a result, there is not bias toward a particular dielectric function model in the acquisition of the complex dielectric function spectra. These numerically obtained dielectric function spectra can then be modeled using Tauc–Lorentz, Cody–Lorentz, or other parametric expressions similar to those used in analysis of ex situ optical spectra. In literature, the Tauc–Lorentz [43, 44] and Cody–Lorentz [43] models have become the most commonly applied toward describing the optical response of a-Si1−x Cx :H and a-Si1−x Gex :H. The Tauc–Lorentz model is derived assuming square root densities of states in the valence and conduction bands versus energy and a constant momentum matrix element, with parameters including a constant additive term to the real part of the complex dielectric function spectra, a band gap energy, and amplitude, broadening, and resonance energy associated with a Lorentz-like feature. The Cody– Lorentz model is derived assuming square root densities of states and a constant dipole matrix element and shares the same parameters as the Tauc–Lorentz model plus a parameter defining the transition from “gap-like” to “Lorentz-like” behavior. Regardless of the model, trends in these parameters with sample composition are used to generate databases in the complex dielectric function spectra. Using these databases the complex dielectric function spectra is obtained

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here from a single parameter, the group IV element composition [33, 35, 37, 45]. These databases can also be expanded to include other factors such as measurement temperature [35] and hydrogen content [45]. For PECVD a-Si1−x Cx :H films prepared as a function of Z under otherwise fixed conditions, the complex dielectric function spectra obtained from RTSE changes substantially as x increases from 0 to 0.23 in Ref. [33] (Fig. 7.12). The maxima of the imaginary part of

Fig. 7.12. Spectra in ε for a-Si1−x Cx :H prepared at different methane flow ratios Z and carbon contents x. Reprinted from [33], Thin Solid Films, vol. 313– 314, H. Fujiwara, J. Koh, and R. W. Collins, Depth-profiles in compositionallygraded amorphous silicon alloy thin films analyzed by real time spectroscopic ellipsometry, 474–478, Copyright (1998), with permission from Elsevier.

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the complex dielectric function spectra decreases in magnitude and blue shifts to higher photon energies with increasing carbon content. Similarly, the band gap widens and shifts to higher photon energies with increasing carbon content, as expected. The shapes of these optical properties have been modeled with a Tauc–Lorentz oscillator parameterization where each parameter is deemed physically realistic (Fig. 7.13). The parameterization of optical response shows a decrease in the dielectric function amplitude A with increasing carbon content in agreement with the visual decrease in the maxima

Fig. 7.13. Variation in carbon content-dependent Tauc–Lorentz parameters describing spectra in ε for a-Si1−x Cx :H. Reprinted from [33], Thin Solid Films, vol. 313–314, H. Fujiwara, J. Koh, and R. W. Collins, Depth-profiles in compositionally-graded amorphous silicon alloy thin films analyzed by real time spectroscopic ellipsometry, 474–478, Copyright (1998), with permission from Elsevier.

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in the imaginary part of the dielectric function. This is indicative of a reduction in the probability of electronic transitions occurring due to light of these incident photon energies or possibly a reduction in material density due to the formation of nano-/micro-scale voids. The dielectric function broadening C in Fig. 7.13 increases with increasing carbon content, which is reflective of reduced order in the amorphous network due to substitution of some silicon atoms with carbon. Due to that same substitution, the band gap ET in Fig. 7.13 shifts from near 1.7 eV for the a-Si:H endpoint to greater than 2.2 eV with a carbon content approaching x = 0.25. The absorption feature resonance energy remained relatively stable in this parameterization as did the constant additive term to the real part of the dielectric function, which should be close to unity. PECVD a-Si1−x Gex :H prepared as a function of G under otherwise fixed conditions show some variations in the complex dielectric function spectra obtained from RTSE with changing germanium content similar to that observed for a-Si1−x Cx :H, but other variations differ [35] (Fig. 7.10). The maxima of the imaginary part of the complex dielectric function spectra and the band gap red shift to lower photon energies with increasing germanium content. The magnitudes of the maxima remain close. Although the shape is qualitatively similar between the two sets of alloys, the complex dielectric function spectra for a-Si1−x Gex :H necessitated the use of the Cody–Lorentz parameterization, as unphysical parameters resulted from the Tauc–Lorentz parameterization (Fig. 7.11). Although an additional parameter demarcating the transition energy from gaplike to Lorentz-like behavior Ep is present in the Cody–Lorentz parameterization, the constant additive term to the real part of the dielectric function is fixed at unity without sacrificing the quality of fit to the numerically inverted complex dielectric function spectra. Within the parameterization, the amplitude parameter decreases with increasing germanium content, although integration of the imaginary part of the dielectric function over the measured spectral range appears similar. This behavior implies that the probability of electronic transitions has remained about the same, the material remains dense without nano-/micro-scale void variations in this film

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series, and that the electronic transitions have shifted to lower photon energies as expected by incorporation of germanium atoms. Once again, with increasing alloying by germanium here, the broadening increases although not to the extent seen in a-Si1−x Cx :H for the same alloy contents. This implies that the electronic quality of a-Si1−x Gex :H prepared under these conditions is not reduced as much as that for a-Si1−x Cx :H. For a-Si1−x Gex :H the band gap shifts from near 1.7 eV for a-Si:H to about 1.3 eV for germanium content x = 0.4. The transition energy between gap-like and Lorentz-like behavior decreases with increasing germanium content, as does the band gap. The optical responses of both alloy series described here are obtained from RTSE with data collected at the 200◦ C deposition temperature. Other RTSE studies have identified the temperature dependence of the dielectric function parameters so that room temperature optical response can be predicted from measured hightemperature data and known relationships [35]. In this way, an optical response database dependent on germanium or carbon composition and measurement temperature is obtained. Applications of this kind of database involve identifying the composition optically for new samples without resorting to other techniques such as x-ray photoelectron spectroscopy [46, 47], Rutherford backscattering spectroscopy [48, 49], or secondary ion mass spectrometry [49], which can be destructive to the sample. Optical measurements like spectroscopic ellipsometry are non-destructive and can be performed on either test films on substrates or on layers within the full device structure. More complicated non-destructive measurements are performed using RTSE along with a virtual interface analysis procedure for compositionally graded a-Si1−x Cx :H and a-Si1−x Gex :H films whereby Z or G is varied during the course of the deposition. a-Si1−x Cx :H layers with relatively sharp maxima in composition with thickness have been of interest for insertion at the interface between the intrinsic and p-type doped layers in solar cells [32–34] (Fig. 7.14). Compositionally graded a-Si1−x Gex :H films with relatively broad maxima have been considered as the absorber layer in multi-junction

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Fig. 7.14. Carbon content profile of a graded composition alloy structure determined optically from RTSE using a database of spectra in ε as a function of carbon content for a-Si1−x Cx :H and from secondary ion mass spectrometry (SIMS). Results from RTSE are Gaussian broadened yielding improved agreement with SIMS which has limited resolution compared to RTSE. Reprinted from [34], H. Fujiwara, J. Koh, C. R. Wronski, R. W. Collins, and J. S. Burnham, Optical depth profiling of band gap engineered interfaces in amorphous silicon solar cells at monolayers resolution, Applied Physics Letters, 72, 2993–2995, Copyright (1998), with the permission of AIP Publishing.

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Fig. 7.15. Germanium content profile of a graded composition alloy structure determined optically from RTSE using a database of spectra in ε for a-Si1−x Gex :H as a function of germanium content and from SIMS. Gas profile G, surface roughness, and band gap profiles are also determined, the latter two from analysis of RTSE. Reprinted from [29], N. J. Podraza, J. Li, C. R. Wronski, E. C. Dickey, M. W. Horn, and R. W. Collins, Analysis of Si1−x Gex :H thin flms with graded composition and structure by real time spectroscopic ellipsometry, Physica Status Solidi A, 205, 892–895, Copyright (2008), with the permission of John Wiley and Sons.

devices with minimum germanium content near the interfaces with both doped layers to engineer the band gap profile [29, 50] (Fig. 7.15). In both cases, the idealized prediction of the composition and the experimental results obtained optically or by destructive methods are close; however, subtle differences between these results may indicate the occurrence of sub-surface modification and/or the presence of residual alloying gas during changes in Z or G. In these scenarios, the compositional dependence of the optical response database enables

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depth-resolved composition to be obtained quickly and in a nondestructive way.

7.5. Electrical and Device Properties of Amorphous Group IV Alloys The purpose of studying these alloys is for their ultimate implementation in devices when the properties of a-Si:H are insufficient. As already mentioned, Si:H-based solar cell device structures can be improved by utilizing band gap widening in a-Si1−x Cx :H and narrowing in a-Si1−x Gex :H relative to a-Si:H. However, in addition to differences in the optical response, variations in electrical transport properties and the electrical performance of the final devices are also expected. Both a-Si1−x Cx :H and a-Si1−x Gex :H can be n-type or p-type doped by including a group V atom, typically phosphorous by adding PH3 to PECVD, or a group III atom, typically boron by adding B2 H6 , B(CH3 )3 , or BF3 to PECVD, allowing for manipulation of both carrier type and concentration. For alloys as for a-Si:H, both electron and hole mobilities can be affected by processing conditions. In general, some trends have appeared such as a decrease in electron mobility with increasing carbon content in a-Si1−x Cx :H and increasing germanium content in a-Si1−x Gex :H [51]. Hole mobility has been reported to be similarly low but without much variation depending on the alloy type or degree of alloying. There have been some reports of a reduction in hole mobility for small carbon contents in a-Si1−x Cx :H followed by a stabilization for larger amounts of carbon, these amounts deduced from the band gap shifts [52]. Alloying in both cases introduces additional disorder in the network with a reduction in the mobility of both charge carriers. For doped amorphous alloy materials, as for doped a-Si:H and other semiconductors, increases in the carrier concentration will also reduce the mobility further such that a minimum in resistivity is found. Considering the room temperature resistivity of representative doped or undoped a-Si:H, resistivity will increase with the addition of carbon in a-Si1−x Cx :H and decrease with the

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Fig. 7.16. Resistivity, TCR, and 1/f noise quantified in terms of the normalized Hooge parameter for n-type a-Si:H as a function of doping gas flow D and ntype a-Si1−x Cx :H as a function of methane flow ratio Z. Reprinted from [19], H.-B. Shin, D. Saint John, M. Y. Lee, N. J. Podraza, and T. N. Jackson, Electrical properties of plasma enhanced chemical vapor deposition a-Si:H and a-Si1−x Cx :H for microbolometer applications, Journal of Applied Physics, 114, 183705, Copyright (2013), with the permission of AIP Publishing.

addition of germanium in a-Si1−x Gex :H [19, 53] (Fig. 7.16). These changes are linked to the widening and narrowing of the band gaps in a-Si1−x Cx :H and a-Si1−x Gex :H, respectively. Temperature dependent resistance measurements provide the thermal activation energy which generally scales with room temperature resistivity

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in these materials in that higher thermal activation energies are obtained for the more resistive samples [16, 19, 53]. However, there are some variations among the parameters, which may be linked to order within the amorphous network. The related temperature coefficient of resistance (TCR) is of interest for uncooled infrared sensing microbolometers [5, 9, 13, 16, 19, 20, 53, 54] as discussed in Chapter 10. a-Si:H-based semiconductors exhibit a negative TCR, with the magnitude of TCR dependent upon the thermal activation energy for charge carriers. For comparable resistivity, the thermal activation energy and resultant TCR vary with amorphous network composition. The addition of carbon decreases the value of TCR when compared to a-Si:H films of similar resistivity [19] (Fig. 7.16). Typically, a-Si1−x Gex :H alloys and a-Ge:H have higher TCR for similar resistivity a-Si:H films [16, 53]. Another property of merit for these films in microbolometers applications is the 1/f noise, reflected in the Hooge parameter. Generally speaking, lower 1/f noise and Hooge parameter are linked to better signal to noise ratio in these imaging devices. For a-Si1−x Cx :H alloys even though TCR is worse than that of a-Si:H films of similar resistivity, the noise is lower (Fig. 7.17). Additionally for a-Si1−x Gex :H and a-Ge:H, lower noise can be obtained as well [16, 53]. Decreases in noise are expected with an increase in the number of conducting pathways present in the sample. As a comparison, consider comparable resistivity doped a-Si:H and a-Si1−x Cx :H. Lower mobility and high resistivity are expected for a-Si1−x Cx :H due to the presence of carbon. To reach resistivity comparable to doped a-Si:H, the carrier concentration must be higher. Disruptions in the order of the amorphous network from the higher dopant atom concentration and presence of carbon may increase the number of equivalent conducting pathways, in turn lowering noise. When a-Si1−x Cx :H and a-Si1−x Gex :H alloys are applied as absorber layers in single junction solar cells, expected changes in device performance occur as discussed in Chapter 9. Namely, for wider band gap a-Si1−x Cx :H and narrower band gap a-Si1−x Gex :H, short circuit current density decreases and increases respectively [2, 3, 6–8, 10–12, 14, 18, 55]. A wider spectrum of light can be

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Fig. 7.17. TCR as a function of resistivity and noise in the form of the normalized Hooge parameter for n-type a-Si:H and a-Si1−x Cx :H. For comparable resistivity material, the addition of carbon reduces TCR; however, for materials with similar TCR, addition of carbon also reduces noise. Reprinted from [19], H.-B. Shin, D. Saint John, M. Y. Lee, N. J. Podraza, and T. N. Jackson, Electrical properties of plasma enhanced chemical vapor deposition a-Si:H and a-Si1−x Cx :H for microbolometer applications, Journal of Applied Physics, 114, 183705, Copyright (2013), with the permission of AIP Publishing.

absorbed in narrow band gap a-Si1−x Gex :H compared to wider band gap a-Si1−x Cx :H. The open circuit voltage is lower for a-Si1−x Gex :H due to the lower potential energy to be overcome in transiting the gap [12]. Overall device efficiency depends on both short circuit current density and open circuit voltage, as well as on the ratio of the power generated at the point of maximum power to the product of open circuit voltage and short circuit current density, known as the fill factor. The product of short circuit current density, open circuit voltage, and fill factor yields device efficiency. Highest stable efficiency single junction devices are obtained with a-Si:H absorbers as electronic quality is degraded in a-Si1−x Cx :H and a-Si1−x Gex :H [55]. Initial efficiency of a-Si1−x Gex :H single junction devices can be greater than a-Si:H; however, these devices may be less stable due to the Staebler–Wronski effect [10, 11]. As discussed in Chapter 9, alloy absorber layers still serve a purpose in multijunction solar cells whereby an a-Si:H absorber–based sub-cell is paired with wider and narrower band gap absorber sub-cells to

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absorb more of the solar irradiance spectrum with the combined open circuit voltage being additive and overall device performance increased [3, 6–8, 11, 14, 18]. 7.6. Summary a-Si1−x Cx :H and a-Si1−x Gex :H alloys exhibit similar growth evolution and microstructural transitions as a-Si:H; however, the processing conditions needed to produce optimized material are shifted to higher amounts of hydrogen dilution of reactive gases during PECVD. The initial appearance of crystallites from the amorphous network for the alloys also requires more hydrogen to be present in the plasma and to interact with the growing film. Hydrogen-induced crystallization and hydrogen incorporation in the amorphous network are simply less effective for alloys. The amorphous network for alloys itself differs from a-Si:H in that addition of other group IV elements results in reduced order or increased configurational entropy. This reduction in order is observed with carbon or germanium alloying in the growth evolution of thin films via lower maximum a → a transition thickness for alloys relative to a-Si:H, in the broadening of the absorption feature of the complex dielectric function upon alloying with either element, and in the reduction of carrier mobility, all under respective optimization conditions. Alloying itself, however, is a valuable tool in that the band gaps of a-Si1−x Cx :H and a-Si1−x Gex :H are wider and narrower, respectively, with increasing carbon and germanium contents. These variations are exploited in opto-electronic devices such as multi-junction solar cells where the band gap is designed to absorb particular regions of the solar irradiance spectrum. Changes in the order of the amorphous network upon alloying also provide means for manipulating electrical response in other devices including microbolometers. References 1. Chen, Z., Sun, G., and Pu, H. (1991). Amorphous thin film whiteLED and its light-emitting mechanism, Conference Record of the 1991 International Display Research Conference, pp. 122–125.

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2. Terakawa, A., et al. (1995). Optimization of a-SiGe:H alloy composition for stable solar cells, Japanese Journal of Applied Physics, 34, p. 1741. 3. Yang, J., Banerjee, A., and Guha, S. (1997). Triple-junction amorphous silicon alloy solar cells with 14.6% initial and 13.0% stable conversion efficiencies, Applied Physics Letters, 70, pp. 2975–2977. 4. van Cleef, M. W. M., et al. (1998). Amorphous silicon carbide/ crystalline silicon heterojunction solar cells: A comprehensive study of the photocarrier collection, Japanese Journal of Applied Physics, 37, p. 3926. 5. Syllaios, A. J., et al. (2000). Amorphous silicon microbolometer technology, MRS Proceedings, 609, p. A14.4. 6. Guha, S., Yang, J., and Banerjee, A. (2000). Amorphous silicon alloy photovoltaic research-present and future, Progress in Photovoltaics: Research Applications, 8, pp. 141–150. 7. Deng, X., and Schiff, E. A. (2003). Amorphous silicon-based solar cells. In: Handbook of Photovoltaic Science and Engineering, edited by. Luque, A., and Hegedus, S. (John Wiley), Chapter 12, pp. 505– 565. 8. Guha, S., et al. (2003). High quality amorphous silicon materials and cells grown with hydrogen dilution, Solar Energy Materials & Solar Cells, 78, pp. 329–374. 9. Garcia, M., Ambrosio, R., Torres, A., and Kosarev, A. (2004). IR bolometers based on amorphous silicon germanium alloys, Journal of Non-Crystalline Solids, 338–340, pp. 744–748. 10. Liao, X., et al. (2005). High efficiency amorphous silicon germanium solar cells, 31st IEEE Photovoltaic Specialists Conference, pp. 1444– 1447. 11. Fan, Q. H., et al. (2010). High efficiency silicon-germanium thin film solar cells using graded absorber layer, Solar Energy Materials & Solar Cells, 94, pp. 1300–1302. 12. Stoke, J. A., et al. (2008). Advanced deposition phase diagrams guiding Si:H-based multijunction solar cells, Journal of Non-Crystalline Solids, 354, pp. 2435–2439. 13. Torres, A., Moreno, M., Kosarev, A., and Heredia, A. (2008). Thermo-sensing silicon-germanium-boron films prepared by plasma for un-cooled micro-bolometers, Journal of Non-Crystalline Solids, 354, pp. 2556–2560. 14. Yunaz, I. A., et al. (2009). Fabrication of amorphous silicon carbide films using VHF-PECVD for triple-junction thin-film solar cell applications, Solar Energy Materials & Solar Cells, 93, pp. 1056–1061. 15. Hamashita, D., Kurokawa, Y., and Konagai, M. (2011). Preparation of p-type hydrogenated nanocrystalline cubic silicon carbide/n-type

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crystalline silicon heterojunction solar cells by VHF-PECVD, Energy Procedia, 10, pp. 14–19. Saint John, D. B., et al. (2011). Thin film silicon and germanium for uncooled microbolometer applications, SPIE Proceedings, 8012, p. 80123U-1-10. Chang, T.-H., Chu, Y.-H., Lee, C.-C., and Chang, J.-Y. (2012). Crystalline silicon interface passivation improvement with a-Si1−x Cx :H and its application in hetero-junction solar cells with intrinsic layer, Applied Physics Letters, 101, p. 241601. Kim, S., et al. (2013). Remarkable progress in thin-film silicon solar cells using high-efficiency triple-junction technology, Solar Energy Materials & Solar Cells, 119, pp. 26–35. Shin, H.-B., et al. (2013). Electrical properties of plasma enhanced chemical vapor deposition a-Si:H and a-Si1−x Cx :H for microbolometer applications, Journal of Applied Physics, 114, p. 183705. Moreno, M., Jimenez, R., Torres, A., and Ambrosio, R. (2015). Microbolometers based on amorphous silicon-germanium films with embedded nanocrystals, IEEE Transactions on Electron Devices, 62, pp. 2120–2127. Clark, S. J., Crain, J., and Ackland, G. J. (1997). Comparison of bonding in amorphous silicon and carbon, Physical Review B, 55, pp. 14059–14062. Pereyra, I., et al. (2000). Highly ordered amorphous silicon-carbon alloys obtained by RF PECVD, Brazilian Journal of Physics, 30, pp. 533–540. Lu., Y., et al. (1993). Nucleation and growth of hydrogenated amorphous silicon-carbon alloys: Effect of hydrogen dilution in plasmaenhanced chemical vapor deposition, Applied Physics Letters, 63, pp. 2228–2230. Lu, Y., et al. (1994). Process-property relationships for a-Si1−x Cx :H deposition: Excursions in parameter space guided by real time spectroellipsometry, MRS Proceedings, 336, pp. 595–600. Rajagopalan, T., et al. (2003). Low temperature deposition of nanocrystalline silicon carbide films by plasma enhanced chemical vapor deposition and their structural and optical characterization, Journal of Applied Physics, 94, pp. 5252–5260. Podraza. N. J., Ferreira, G. M., Wronski, C. R., and Collins, R. W. (2005). Development of deposition phase diagrams for thin film Si:H and Si1−x Gex :H using real time spectroscopic ellipsometry, MRS Proceedings, 862, p. A16.3. Podraza, N. J., Wronski, C. R., and Collins, R. W. (2006). Deposition phase diagrams for Si1−x Gex :H from real time spectroscopic ellipsometry, Journal of Non-Crystalline Solids, 352, pp. 1263–1267.

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28. Podraza, N. J., Wronski, C. R., Horn, M. W., and Collins, R. W. (2006). Surface roughening transition in Si1−x Gex :H thin films, MRS Proceedings, 910, p. A03.02. 29. Podraza, N. J., et al. (2008). Analysis of Si1−x Gex :H thin films with graded composition and structure by real time spectroscopic ellipsometry, Physica Status Solidi A, 205, pp. 892–895. 30. Podraza, N. J., et al. (2008). Analysis of compositionally and structurally graded Si:H and Si1−x Gex :H thin films by real time spectroscopic ellipsometry, MRS Proceedings, 1066, p. A10-01. 31. Podraza, N. J., et al. (2010). Microstructural evolution in Si1−x Gex :H thin films for photovoltaic applications, 35th IEEE Photovoltaic Specialists Conference, pp. 158–163. 32. Fujiwara, H., Koh, J., Wronski, C. R., and Collins, R. W. (1997). Application of real time spectroscopic ellipsometry for high resolution depth profiling of compositionally graded amorphous silicon alloy thin films, Applied Physics Letters, 70, pp. 2150–2152. 33. Fujiwara, H., Koh, J., and Collins, R. W. (1998). Depth-profiles in compositionally-graded amorphous silicon alloy thin films analyzed by real time spectroscopic ellipsometry, Thin Solid Films, 313–314, pp. 474–478. 34. Fujiwara, H., et al. (1998). Optical depth profiling of band gap engineered interfaces in amorphous silicon solar cells at monolayer resolution, Applied Physics Letters, 72, pp. 2993–2995. 35. Podraza, N. J., Wronski, C. R., Horn, M. W., and Collins, R. W. (2006). Dielectric functions of a-Si1−x Gex :H versus Ge content, temperature, and processing: Advances in optical function parameterization, MRS Proceedings, 910, p. A10.01. 36. Ferlauto, A. S., et al. (2004). Evaluation of compositional depth profiles in mixed-phase (amorphous + crystalline) silicon films from real time spectroscopic ellipsometry, Thin Solid Films, 455–456, pp. 665–669. 37. Basa, D. K., et al. (2010). Spectroscopic ellipsometry study of hydrogenated amorphous silicon carbon alloy films deposited by plasma enhanced chemical vapor deposition, Journal of Applied Physics, 107, p. 023502. 38. Smets, A. H. M., and van de Sanded, M. C. M. (2003). Vacancies and voids in hydrogenated amorphous silicon, Applied Physics Letters, 82, pp. 1547–1549. 39. Podraza, N. J., Wronski, C. R., and Collins, R. W. (2006). Model for the amorphous roughening transition in amorphous semiconductor deposition, Journal of Non-Crystalline Solids, 352, pp. 950–954. 40. Kryukov, Y. A., Podraza, N. J., Collins, R. W., and Amar, J. G. (2009). Experimental and theoretical study of the evolution of surface

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roughness in amorphous silicon films grown by low-temperature plasma-enhanced chemical vapor deposition, 80, p. 085403. Matsuda, A. (1983). Formation kinetics and control of microcrystallite in µc-Si:H from glow discharge plasma, Journal of Non-Crystalline Solids, 59–60, pp. 767–774. Matsuda, A., et al. (1985). Preparation of highly photosensitive amorphous Si-Ge alloys using a triode plasma reactor, Applied Physics Letters, 47, pp. 1061–1063. Ferlauto, A. S., et al. (2002). Analytical model for the optical functions of amorphous semiconductors from near-infrared to ultraviolet: Applications in thin film photovoltaics, Journal of Applied Physics, 92, pp. 2424–2436. Jellison, G. E., and Modine, F. A. (1996). Parameterization of the optical functions of amorphous materials in the interband region, Applied Physics Letters, 69, pp. 371–373. Summonte, C., et al. (2019). A ternary-3D analysis of the optical properties of amorphous hydrogenated silicon-rich carbide, Materials Chemistry and Physics, 221, pp. 301–310. Lucovsky, G. (1982). An XPS study of sputtered a-Si,Ge alloys, Journal of Vacuum Science & Technology, 21, pp. 838–844. Tabata, A., et al. (1990). X-ray photoelectron spectroscopy (XPS) of hydrogenated amorphous silicon carbide (a-Six C1−x :H) prepared by the plasma CVD method, Journal of Physics D: Applied Physics, 23, p. 316. Shimada, T., Katayama, Y., and Komatsubara, K. F. (1979). Compositional and structural properties of amorphous Six C1−x :H alloys prepared by reactive sputtering, Journal of Applied Physics, 50, pp. 5530–5532. Nelson, B. P., et al. (2000). Techniques for measuring the composition of hydrogenated silicon-germanium alloys, Journal of Non-Crystalline Solids, 266–269, pp. 680–684. Pieters, B. E., Zeman, M., van Swaaij R. A. C. M. M., and Metselaar, W. J. (2004). Optimization of a-SiGe:H solar cells with graded intrinsic layers using integrated optical and electrical modeling, Thin Solid Films, 451–452, pp. 294–297. Schiff, E. A. (2004). Drift-mobility measurements and mobility edges in disordered silicons, Journal of Physics: Condensed Matter, 16, pp. S5265–5275. Schmidt, J. A., Hundhausen, M., and Ley, L. (2000). Transport properties of a-Si1−x Cx :H films investigated by the moving photocarrier grating technique, Physical Review B, 62, pp. 13010–13015.

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53. Saint John, D. B. (2012). Optical and Electrical Characterization of High Resistivity Semiconductors for Constant-Bias Microbolometers (The Pennsylvania State University). 54. Saint John, D. B., et al. (2011). Influence of microstructure and composition on hydrogenated thin film properties for uncooled microbolometer applications, Journal of Applied Physics, 110, p. 033714. 55. Green, M. A., et al. (2019). Solar cell efficiency tables (version 53), 27, pp. 3–12.

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CHAPTER 8

Materials and Device Characterization by Optical Probes Prakash Koirala, Jason A. Stoke, Nikolas J. Podraza, and Robert W. Collins University of Toledo, USA

8.1. Introduction Measurements and analyses that provide spectra in the real and imaginary parts of the dielectric function (ε1 , ε2 ) from the nearinfrared to ultraviolet, along with associated derived parameters such as the bandgap and Urbach tail slope, are valuable components of basic characterization for hydrogenated amorphous silicon (a-Si:H) and related materials [1–5]. The results of such analyses assist in developing process–property relationships for these materials and process–performance relationships for device structures. In plasmaenhanced chemical vapor deposition (PECVD), the key deposition variables include substrate temperature, plasma frequency, and power, as well as gas pressure, composition, and flows [6–8]. These 279

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can be adjusted to achieve the desired deposition rates and thickness, composition and bandgap, and optoelectronic properties. Plasma power and frequency allow deposition of films at suitable rates, and the concept of maximum H2 dilution of SiH4 can be applied to optimize the electronic quality and enhance the stability of the materials [9–12]. This concept involves fabricating the film at the highest possible H2 dilution level without crossing into the amorphous + nanocrystalline mixed-phase deposition regime for the desired thickness. In order to vary the bandgap under conditions of maximum dilution, the H-content in the film can be adjusted through substrate temperature variation. For pure a-Si:H, a bandgap range of ∼0.10–0.20 eV centered on ∼1.7 eV can be achieved, depending on the substrate temperature capability. For a larger bandgap variation, alloys can be fabricated using mixtures of SiH4 or Si2 H6 and GeH4 or mixtures of SiH4 and CH4 . These gas mixtures provide narrower and wider bandgap materials, respectively, spanning the bandgap range of 1.3–1.9 eV, while retaining electronic quality via the maximum H2 dilution condition [4]. In order to characterize these processes reliably, accurate models of the (ε1 , ε2 ) spectra are desired that provide bandgap and material quality indicators irrespective of the thickness of the film, its substrate, or the device structure within which the film is incorporated [1–5, 13, 14]. In some circumstances, sufficient data can be collected to determine accurate (ε1 , ε2 ) spectra as continuous functions of photon energy, data point by point. Considering the methods of in situ realtime spectroscopic ellipsometry (SE), data collected at multiple times during deposition enable determination of layer thicknesses, both bulk film and surface roughness, required to obtain such continuous (ε1 , ε2 ) spectra [15, 16]. Furthermore, in situ measurements avoid oxidation and surface contamination that can influence the accuracy of optical analysis. An approach alternative to real-time SE is to combine multiple ex situ measurements with differing sensitivities to surface characteristics, for example, combining photoconductive measurements and transmittance and reflectance (T & R) spectroscopy, along with ex situ SE in order to correct data for overlayers [4, 17]. In many studies of complicated substrate or even graded film structures,

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however, continuous spectra in (ε1 , ε2 ) cannot be obtained point by point. In such studies it is useful first to express these spectra in terms of a relatively small number of photon energy-independent parameters, in particular through the parametric expressions of Chapter 4, and then to fit the measured optical data in terms of these parameters [18, 19]. If good fits are possible, the resulting parameters allow generation of the spectra in (ε1 , ε2 ) as analytical functions that can be used in optoelectronic simulations. For continuously graded layer structures, for example, it becomes necessary to express the (ε1 , ε2 ) spectra in terms of a single parameter such as the bandgap or composition, and this requires developing not only a multi-parametric representation of the spectra, but also a database that relates all the parameters to a single one [4, 20, 21]. In this chapter, illustrative examples of these methods will be presented for electronic quality materials including a-Si:H and its alloys with Ge and C fabricated with both variable and maximum H2 dilution. Here it is demonstrated how photon energy-independent parameters that describe the (ε1 , ε2 ) spectra can be obtained from a combination of photoconductive measurements in the sub-gap region, T & R measurements at the absorption onset, and SE measurements above the absorption onset [4, 13]. The clear trends in the parameters observed with the T & R measured bandgap provide insights into the nature of these parameters, along with assessments of relative materials quality, and various frameworks for calculating the (ε1 , ε2 ) spectra for materials of any specified bandgap. The latter capability is extremely valuable for applications in optoelectronic simulations. For a-Si1−x Gex :H and a-Si1−x Cx :H, databases will be described that reduce the number of free parameters in the expressions for the (ε1 , ε2 ) spectra to a single value and enable determination of the bandgap and compositional profiles of bandgap-engineered structures of potential interest in a variety of applications [20–22]. Also in this chapter, the application of least squares regression analysis to multiple angle of incidence and film/glass-side SE data will be demonstrated in studies of complex multi-layer structures incorporating amorphous semiconductor components [18, 19]. This powerful capability provides parameters important in optoelectronic

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device characterization for materials in the actual device configuration, including not only the parameters that describe (ε1 , ε2 ) spectra but also bulk, interface, and surface roughness thicknesses. Once the (ε1 , ε2 ) spectra and the thicknesses of all component layers of an optoelectronic device such as a solar cell or detector are determined by SE, additional useful information can be obtained on the performance of the device. First, one can calculate the maximum external quantum efficiency (EQE) possible for the analyzed device structure based on the assignment of the active layer or layers of the device as well as on the assumption of specular reflection and transmission at optical interfaces [19, 23, 24]. By simulating the EQE for variations from the analyzed structure, one can optimize the current output from the device based on predictions, thus avoiding trial and error. Second, the reflectance spectrum from the device can be predicted, and this result is helpful in determining the need for an anti-reflection coating (ARC) stack as well as in designing the optimum ARC. The EQE simulations presented in this chapter start by assuming that all carriers generated by photons absorbed within the assigned active layers are collected without recombination losses. As a result, a comparison between the simulated and measured EQE for a completed solar cell can provide information on losses via carrier recombination and how these vary with the photon energy. Moreover, when the scattering of light at rough surfaces and interfaces is not taken into account in the simulation, the measured EQE can exceed the simulated EQE in some regions of the spectrum due to light-trapping effects. The excess EQE can then provide a quantitative measure of light trapping caused by scattering at rough surfaces and interfaces. This overall approach for optical analysis of devices can be implemented in a wide variety of optoelectronic applications.

8.2. Role of Hydrogen Dilution in Film Growth Hydrogen dilution of Si-containing gases is an effective method for fabricating high-quality a-Si:H for devices, particularly at low temperatures, and for tailoring the bandgap and network order

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of the material [9–12, 25]. Low-temperature PECVD is desirable, for example, in the fabrication of a-Si:H passivating layers on c-Si surfaces, suppressing epitaxial growth, and in the formation of highquality, wide bandgap interface layers in amorphous semiconductor device structures. Figures 8.1 and 8.2 (left panels) show examples of dielectric functions from two series of PECVD thin films including a-Si:H and a-Si1−x Gex :H, respectively, deposited with varying H2 dilution ratios R on c-Si/native-oxide substrates coated with n-type a-Si:H [26]. These PECVD processes simulate intrinsic layer growth

Fig. 8.1. (Left) Dielectric function (points) determined from a real-time spectroscopic ellipsometry (SE) measurement of a hydrogenated amorphous silicon (a-Si:H) film prepared by plasma-enhanced chemical vapor deposition (PECVD) on a crystal silicon (c-Si)/native-oxide/(n-type a-Si:H) structure at a substrate temperature of 107◦ C using H2 dilution of Si2 H6 with a gas flow ratio of R = [H2 ]/[Si2 H6 ] = 60. Also shown at left is a five-parameter fit (lines) applying a constant dipole (CD) matrix element expression. (Right) The dependence of the bandgap on the H2 dilution ratio R is shown for a collection of samples as obtained from fits (squares) such as those at the left and from extrapolations of (αn/E)1/2 (open circles) both at the deposition temperature. Linear trend lines for the bandgap are shown (broken lines) along with the prediction for room temperature (solid lines) applying the temperature coefficient of the bandgap for a-Si:H in Fig. 5.16. These figures have been adapted from [26] with permission.

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Fig. 8.2. (Left) Dielectric function (points) from a real-time spectroscopic ellipsometry (SE) measurement of an a-Si1−x Gex :H film prepared by plasmaenhanced chemical vapor deposition (PECVD) on a crystal silicon (c-Si)/nativeoxide/(n-type a-Si:H) structure at a substrate temperature of 170◦ C using gas flow ratios of G = [GeH4 ]/{[Si2 H6 ] + [GeH4 ]} = 0.268 and R = [H2 ]/{[Si2 H6 ] + [GeH4 ]} = 45. Also shown at left is a five-parameter fit (lines) applying a constant dipole (CD) matrix element expression. (Right) The dependence of the bandgap on the H2 dilution ratio R is shown for a collection of samples at the deposition temperature as obtained from fits (squares) such as those at the left. A linear trend line is shown (broken line) along with results predicted for room temperature (solid line) applying the temperature coefficient of the bandgap for a-Si1−x Gex :H with x = 0.3 in Fig. 5.16. These figures have been adapted from [26] with permission.

in n-i-p sequence devices. The results in both figures were obtained by real-time SE near bulk layer thicknesses of 200 ˚ A. The a-Si:H film of Fig. 8.1 (left) was deposited from disilane (Si2 H6 ) diluted in H2 with a gas flow ratio of R = [H2 ]/[Si2 H6 ] = 60 at a low substrate temperature of 107◦ C. The a-Si1−x Gex :H film of Fig. 8.2 (left) was deposited using gas flow ratios of G = [GeH4 ]/{[Si2 H6 ] + [GeH4 ]} = 0.268 and R = [H2 ]/{[Si2 H6 ]+[GeH4 ]} = 45 at a substrate temperature of 170◦ C. These dielectric functions measured in situ and in real time extend over a wider spectral range, from 1 eV up to 6 eV, compared to those depicted previously (see, e.g., Chapter 5,

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Figs. 5.4 and 5.14). The best fitting models using five free parameters in the constant dipole (CD) matrix element expression of Chapter 4 with ε0s = 1 show excellent agreement with the experimental data over this widest spectral range. The right sides of Figs. 8.1 and 8.2 show the bandgaps deduced from fits such as those on the left sides of the figures for the full sets of samples [26]. The bandgaps are plotted as functions of the H2 dilution ratio R, the only variable parameter in each deposition process. For the a-Si:H data set in Fig. 8.1, bandgaps are also included as obtained by linear extrapolation of the CD result (αn/E)1/2 over the range of linearity of the SE data for selected samples. For both a-Si:H and a-Si1−x Gex :H data sets, the bandgap is an increasing function of the dilution ratio at least up to R = 120. For a-Si:H, the bandgap shows a trend toward saturation above R = 120. The broken lines in Figs. 8.1 and 8.2 are the best fitting trends in the bandgap values obtained in the five-parameter CD fit of the (ε1 , ε2 ) spectra. Because the bandgaps in Figs. 8.1 and 8.2 are obtained at the deposition temperature, these values must be corrected in order to compare the results with the room temperature bandgaps of Fig. 5.3 and those in additional studies to be discussed in this chapter. For this purpose, the temperature coefficients can be used from Fig. 5.16 with x = 0 and x = 0.30, the estimated Ge content for the films in Fig. 8.2 [21]. These coefficients are −4.2 × 10−4 and −4.6 × 10−4 eV/◦ C, respectively, and the solid lines in the figures indicate the results of the corrections, which give the predicted bandgaps at room temperature. A second well-known effect of increasing H2 dilution is an increase of the order of the amorphous network [12, 25, 27]. Figure 8.3 illustrates this effect for 150 to 300 ˚ A thick a-Si:H and a-Si1−x Gex :H alloys fabricated with three different gas flow ratios G = [GeH4 ]/{[SiH4 ] + [GeH4 ]} = 0, 0.083, and 0.167 [28]. For a fixed H2 dilution level of R = 10, the Lorentz oscillator broadening parameter is observed to increase with increasing G, as was also shown versus x in Fig. 5.15 (left). The broadening parameter decreases for all three values of G = 0, 0.083, and 0.167 as a result of increases in H2 dilution flow ratio from R = 10 to the maximum values of R = 15, 40, and 90, respectively, just before the amorphous to nanocrystalline

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Fig. 8.3. Width of the Lorentz oscillator resonance in the dielectric function A for cathodic plasmameasured at T = 200◦ C and at a thickness of 150–300 ˚ enhanced chemical vapor deposition (PECVD) a-Si1−x Gex :H as a function of G = [GeH4 ]/{[SiH4 ] + [GeH4 ]} for R = [H2 ]/{[SiH4 ] + [GeH4 ]} = 10 (squares) and for the maximal R value (circles) before the thick-film (0.5 μm) transition to nanocrystallinity is crossed. Thus, the arrows indicate improvements in network order possible by increasing R from 10 right up to, but not crossing, the amorphous to nanocrystalline transition. This figure has been reproduced from [28] with permission.

transitions appropriate for an extended deposition approximately 0.5 μm thick. Figures 8.1–8.3 illustrate the important role of H2 dilution in controlling the structure and electronic properties of a-Si:H-based materials at processing temperatures that may be limited to low values due to the nature of the substrate or to the process itself. 8.3. Electronic Materials: Alloys with Germanium and Carbon A large collection of optical property data that forms the most rigorous basis for support of the CD expression of Eqs. (4.36)– (4.50) was acquired from measurements of a-Si1−x Gex :H alloys, unalloyed a-Si:H, and a-Si1−x Cx :H alloys [4, 13]. The bandgaps determined from T & R spectroscopy analysis of these samples

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range from 1.3 to 1.95 eV, obtained using the CD expression by extrapolation of (αn/E)1/2 to zero ordinate. All thin films were grown by PECVD to thicknesses of 0.5–1 μm under conditions that optimize material performance at a given bandgap for applications in electronic devices. The samples were obtained as a collaborative effort among three laboratories that fabricated high-efficiency solar cells (BP Solar, The Pennsylvania State University, and University of Toledo) and were measured by dual-beam photoconductivity (DBPC), T & R spectroscopy, and SE over ranges of increasing photon energy. The result of this combination of three measurements is the absorption coefficient over five orders of magnitude, ranging from ∼10 to 106 cm−1 , as depicted in Fig. 8.4 (points). The solid

(a)

(b)

(c)

Fig. 8.4. Optical properties of 0.5 to 1 μm thick films of (left) hydrogenated amorphous silicon (a-Si:H), (center) a-Si1−x Gex :H, and (right) a-Si1−x Cx :H, expressed in the form of (top) (ε1 , ε2 ) and (bottom) (n, α). These results were obtained ex situ at room temperature by combining data sets from dual-beam photoconductivity, transmittance and reflectance (T & R) spectroscopy, and spectroscopic ellipsometry measurements. The materials are identified based on their bandgaps Eg , extracted from T & R spectroscopy alone, which is the most commonly applied method for determination of Eg . The value of Eg for each sample obtained from T & R data derives from linear extrapolation based on an expression assuming a constant dipole (CD) matrix element as in Fig. 4.2. The solid lines in the figures are fits to the data applying the seven-parameter CD expression of Eqs. (4.36)–(4.50) with ε0s = 1. This figure has been reprinted from [4] Ferlauto, A. S., et al. (2002). Analytical model for the optical functions of amorphous semiconductors from the near-infrared to ultraviolet: Applications in thin film photovoltaics, Journal of Applied Physics, 92, 2424–2436, with the permission of AIP Publishing.

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lines in Fig. 8.4 are seven-parameter fits based on the CD expression derived in Eqs. (4.36)–(4.50) that include the Urbach tail, the band edge function with CD matrix element, and the Lorentz oscillator component [4]. In general in accumulating the data set for fitting, the absorption coefficient from the DBPC measurement must be normalized to that from T & R over the photon energy range of overlap. When overlap does not occur, however, one can extract Eu from the slope of the DBPC data and then Et from the T &R bandgap according to the expression Et = Eg + 2Eu in order to maintain continuity of the best fit and its derivative in the models of the absorption coefficient. In addition, for semitransparent films, it can be a challenge to eliminate interference-related artifacts in the ex situ SE spectra in the lowenergy range [29]. As a result, there may exist spectral ranges where only the absorption coefficient is available, extracted via the T & R spectra. Examples of these limitations are presented in Fig. 8.4 for an a-Si1−x Gex :H sample in which case the DBPC and T & R data do not overlap versus photon energy, and for a-Si1−x Cx :H in which case ε1 is unavailable for the lower photon energies. The best fits show the abilities to interpolate within the gaps between data sets and to extrapolate beyond the range of available data owing to the Kramers–Kronig consistency of the model for the real and imaginary parts of the optical response. For the full set of a-Si:H-based thin-film samples, Fig. 8.5 shows the seven parameters describing the complete CD expression for the optical properties obtained from DBPC, T & R, and SE analysis. The results are plotted as a function of the bandgap deduced from extrapolation of (αn/E)1/2 where the absorption coefficient is obtained by T & R spectroscopy alone and the index of refraction is obtained from SE data or its fitting. For all analyses, suitable seven-parameter fits as in Fig. 8.4 could be obtained with ε0s = 1, in contrast to the best fits using the corresponding constant momentum (CM) matrix element expression, which requires values less than unity for a-Si:H and even negative in the case of the lowest bandgap a-Si1−x Gex :H [13]. Although deposition process–related

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(a)

(d)

(b)

(e)

(c)

(f)

(g)

Fig. 8.5. The best fitting parameters in the expression of Eqs. (4.36)–(4.50) deduced from data acquired on a collection of plasma-enhanced chemical vapor deposition (PECVD) hydrogenated amorphous silicon (a-Si:H)-based thin films plotted versus the bandgap obtained from transmission and reflectance spectroscopy (T & R). Shown in (a–c) are the three Lorentz oscillator parameters of A0 , E0 , and Γ and in (d–g) the four absorption onset–related energies of Et , Eu , EP , and Eg . Both the seven-parameter expression and the linear extrapolation of the T & R data are based on the assumption of a constant dipole matrix element. The solid lines are linear trends for the data sets spanning (i) the lowenergy range of a-Si1−x Gex :H alloys and unalloyed a-Si:H and (ii) the high-energy range of widest bandgap a-Si:H and a-Si1−x Cx :H alloys with H2 dilution. This figure has been adapted from [13] Handbook of Ellipsometry, Collins, R. W., and Ferlauto, A. S., Optical physics of materials, pp. 93–235, Copyright (2005), with permission from Elsevier.

scatter does exist within the data set, given that the materials were fabricated in different laboratories, clear trends are observed that can quantified with linear functions. As expected, the Urbach to band edge transition energy Et , the full CD expression bandgap, indicated in Fig. 8.5 as Eg ,fit , and the bandgap to Lorentz oscillator transition energy EP are all linearly or stepwise linearly increasing

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functions of the bandgap determined from the CD extrapolation of T & R data. Ideally, one would expect an equality between Eg from T & R and that from a fit of the complete data set, Eg,fit . For T & R bandgaps of 1.30 eV for a-Si1−x Gex :H, 1.65 eV for a-Si:H at an elevated substrate temperature of ∼300◦ C (or low H2 dilution of SiH4 ), 1.80 eV for a-Si:H with lower substrate temperature ∼200◦ C and high H2 dilution, and 1.95 eV for a-Si1−x Cx :H, the more accurately determined bandgaps from the complete data set of DBPC, T & R, and SE are 1.34, 1.61, 1.73, and 1.85 eV, according to the linear trends. This suggests that for 0.5 to 1.0 μm thick films where the accessible range of α is 5 × 103 to 1 × 105 cm−1 , extrapolation of the (αn/E)1/2 data from T & R results in a bandgap underestimate for the materials with bandgaps 1.5 eV. The reason lies in the nature of the curvature in the T & R data due to the Lorentz oscillator contribution that is not taken into account in the linear extrapolation of (αn/E)1/2 . Apparently, this curvature is downward for the lower bandgap materials and upward for the higher bandgap materials. For a-Si:H, the observed range in bandgap Eg,fit of 1.61–1.73 eV in Fig. 8.5 is consistent with the room temperature bandgap range of the a-Si:H samples of Fig. 8.1, 1.66–1.84 eV, given the lower deposition temperature of the latter (107◦ C vs. ∼ 200◦ C– 350◦ C), which allows not only a wider bandgap but also a wider range of bandgaps. For the a-Si1−x Gex :H alloys, the range of bandgaps in Fig. 8.5 is 1.34–1.50 eV as compared to 1.41–1.57 eV in Fig. 8.2, the former obtained at maximum H2 dilution but with a higher Ge content (x ∼ 0.35) over a range of substrate temperatures of 200◦ C–400◦ C. Further discussion of the trends in the energies and broadening parameter of Fig. 8.5 is informative. First, it is of interest to evaluate how the values of the different energy parameters scale with the most accurate measure of the bandgap, Eg,fit . The linear trends in Fig. 8.5 when converted to trends in Eg,fit show that, as expected, Et is most closely linked to the bandgap, increasing by

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1.10 eV per 1 eV increase in bandgap. EP increases more sharply and E0 increases more slowly with corresponding slopes of 1.40 and 0.36, respectively, considering the range Eg,fit < 1.75 eV. It is also found that the linear relations for both Et and Eg,fit + 2Eu give values of Eg,fit + (0.10 ± 0.03 eV), as would be expected given the approximate equality of the two functions in the model [4]. Second, it should be noted that the broadening parameter of the Lorentz oscillator and the Urbach energy follow similar trends in Fig. 8.5 given by Eu ∼ 29 meV + (9 meV/eV) Γ for Eg,fit < 1.75 eV and a sharper increase of Eu = − 6 meV + (25 meV/eV)Γ for Eg,fit > 1.75 eV. Such positive correlations reflect the fact that both Eu and Γ are measures of the disorder of the amorphous network, in the former case through the density of states due to static disorder, that is, bond length and bond angle variations [30], and in the latter case through the lifetime of the excited state in band-to-band transitions [31, 32]. The minimum disorder among all samples is obtained for a-Si:H deposited at relatively low temperatures with maximum H2 dilution, corresponding to the a-Si:H with the widest bandgap. A comparison of the trends in Et and EP suggests that Et is most closely linked to the bandgap with a small contribution from the variation in Eu , whereas EP is more strongly affected by Γ, increasing as Γ increases, necessitating the two segment linear fit of EP in Fig. 8.5. Finally, the linear expressions in Fig. 8.5 in conjunction with the full CD expressions of Eqs. (4.36)–(4.50) enable simulation of the optical properties of an a-Si:H-based material based on a single specification of the T & R-determined optical bandgap, the most commonly applied method for bandgap estimation. Examples of such results are presented in Fig. 8.6 for bandgaps of 1.4, 1.6, and 1.8 eV using the lower segment of the linear trends for those parameters that are described by two segments. Such a simulation capability has a wide variety of potential applications in optoelectronic device performance modeling and analysis, from solar cells exploiting thinfilm a-Si:H and c-Si/a-Si:H heterojunctions to detectors and sensors [33–42].

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(a)

(b)

Fig. 8.6. Room temperature optical properties including (a) (ε1 , ε2 ) spectra and (b) (n, α) spectra predicted for hydrogenated amorphous silicon (a-Si:H)-based alloy samples computed on the basis of a single specification of the bandgap determined from transmittance and reflectance (T & R) spectroscopy applying the constant dipole (CD) matrix element extrapolation of (αn/E)1/2 . The results were deduced from Eqs. (4.36)–(4.50) using parameters defined by the trend lines in Fig. 8.5, which provide a realistic method of optical property simulation for device quality a-Si:H-based materials. This figure has been reprinted from [13] Handbook of Ellipsometry, Collins, R. W., and Ferlauto, A. S., Optical physics of materials, pp. 93–235, Copyright (2005), with permission from Elsevier.

8.4. Bandgap Engineering with Compositional Gradients By utilizing a database consisting of photon energy-independent optical parameters versus composition such as those of Fig. 5.15 (left) [21], together with the two-layer virtual interface analysis [43], realtime SE can be applied for bandgap engineering and compositional

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profiling of a-Si:H-related alloy materials during their growth. The model used in virtual interface analysis consists of an outer-layer and a surface roughness layer; these two layers are separated from the pseudo-substrate by the virtual interface. The outer-layer and its component within the surface roughness layer characterize the most recently deposited material and the pseudo-substrate incorporates the past history of the deposition. The optical properties of the pseudo-substrate are derived from the experimental data measured prior to the formation of the outer-layer and are subjected to an appropriate correction for the surface roughness layer thickness. For bandgap profiling of alloys, the information extracted from the analysis as a function of deposition time includes the alloy composition x of the outer-layer, the thickness of the surface roughness ds on the outerlayer, and the deposition rate r of the outer-layer. By integrating over r, a plot of x as a function of accumulated thickness can be obtained. From such a profile in x, profiles in the optical parameters such as bandgap and broadening parameter can be determined from the database, as these are typically of greater interest than composition. Figure 8.7(a) shows the Ge content x in a compositionally graded a-Si1−x Gex :H film as a function of accumulated bulk layer thickness, the latter determined by integration of the deposition rate versus time [22, 28]. The derived parameters are also shown, including in Fig. 8.7(b) the bandgap Eg from the five-parameter CD expression at the deposition temperature of T = 200◦ C and adjusted to T = 20◦ C, as well as in Fig. 8.7(c) the Lorentz oscillator broadening parameter Γ at T = 200◦ C and adjusted to T = 20◦ C. The adjustments were made using the dependences of the temperature coefficients on x in Figure 5.16. The solid line in Fig. 8.7(a) is the predicted result based on the flow meter outputs and the relationship between G = [GeH4 ]/{[SiH4 ] + [GeH4 ]} and x, assuming that the film surface responds instantaneously to the changes in the flow meter output. The difference between the prediction and experimental results is attributed to the residence time of the gas mixture in the deposition chamber. It can be concluded that any specified bandgap profile can be engineered into the sample structure given a gas flow model for

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Fig. 8.7. Depth profiles for a graded a-Si1−x Gex :H thin film fabricated on native oxide covered crystal silicon (c-Si) at a substrate temperature of 200◦ C and R = 10 with the following incrementally stepwise variations in G = [GeH4 ]/{[SiH4 ] + [GeH4 ]}:G = 0.042 → 0.15 → 0. Profiles include (a) the Ge content x from virtual interface analysis (open circles) and a theoretical prediction based on the flow meter output (solid line), (b) bandgap Eg at the deposition temperature T = 200◦ C and at room temperature T = 20◦ C, and (c) Lorentz oscillator broadening parameter Γ at the deposition temperature T = 200◦ C and room temperature T = 20◦ C. This figure has been reproduced from [28] with permission.

the deposition system. Another example will be illustrated through the analysis results to be presented next. A second example of compositional profiling has been demonstrated, consisting of a series of bandgap-engineered a-Si1−x Cx :H interface layer structures fabricated by varying C, the ratio of

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methane gas flow to the sum of silane and methane flows C = [CH4 ]/ {[SiH4 ] + [CH4 ]} in PECVD [20, 44, 45]. The gas flow ratio C was varied according to a triangular ramp in order to form an interface layer on top of the intrinsic a-Si:H layer of an n-i-p solar cell. The ratio C was stabilized at 0.2 before interface layer deposition, and during deposition C was first increased linearly from 0.2 to 0.8 and then decreased linearly back to 0.4. In this way, the carbon content of the graded layer at the i/p interface matched the value used for the top-most a-Si1−x Cx :H p-type layer with x ∼0.05. For a series of device structures, the graded layer deposition time including both flow meter ramps was varied from 38 to 205 s. The virtual interface analyses for these samples require the database shown in Fig. 8.8 (left), which provides the parameters in the CM expression as quadratic functions of composition x, determined by Xray photoelectron spectroscopy. Two of the five parameters could be fixed in this model, the Lorentz oscillator resonance energy at E0 = 3.70 eV and the ε1 constant at ε0s = 1.058. The coefficients of these quadratic functions allow one to calculate the dielectric function of a-Si1−x Cx :H for any value of x spanned by the available samples used in the database development. Figure 8.8 (right) shows the depth profiles for the a-Si1−x Cx :H structures obtained from virtual interface analyses (points) [20]. The solid lines in this figure indicate the depth profiles estimated from the dependence of the composition x on flow ratio C for individually deposited films, assuming that the response of the surface to the variations in gas flow ratio C is instantaneous. The intended thicknesses of the graded layers in Fig. 8.8 were (from top to bottom): 25, 45, 90, and 135 ˚ A, and these values agree with the measured thicknesses to within ∼5 ˚ A. The small profile shifts with depth in the calculated C content in comparison with the measurements are caused at least in part by the ∼5 s residence time of the source gases in the deposition chamber. For the thinnest graded structure, the depth profile in the C content generated during the second ramp deviates significantly from the results calculated for an ideal response and remains near x = 0.16 at the i/p interface likely due to the 5 s gas residence time. For this thinnest structure, the depth resolution appears to be ∼2.5 ˚ A at the peak in the C content

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Fig. 8.8. (Left) Photon energy-independent parameters of A0 , Γ, Eg in the fiveparameter constant momentum (CM) matrix element expression obtained from best fits of (ε1 , ε2 ) spectra for a series of a-Si1−x Cx :H thin films, plotted as functions of the carbon content determined by X-ray photoelectron spectroscopy. In the parametric expression, the Lorentz oscillator resonance energy E0 and the constant ε0s were fixed at 3.70 eV and 1.058, respectively. The solid lines are second-order polynomials given as functions of x in each panel. (Right) Depth profiles in the carbon content of graded a-Si1−x Cx :H layers incorporated in the intrinsic layers adjacent to the i/p interfaces of substrate/n-i-p solar cell structures. The depth is measured from the i/p interface into the intrinsic layer of the device. The solid lines in each case are the depth profiles calculated from the gas flow ratio C = [CH4 ]/{[SiH4 ] + [CH4 ]} assuming instantaneous deposition response to the flow meter signals. These figures have been adapted from [20] Thin Solid Films, Vol. 313–314, Fujiwara, H., Koh, J., and Collins, R. W., Depthprofiles in compositionally-graded amorphous silicon alloy thin films analyzed by real time spectroscopic ellipsometry, pp. 474–478, Copyright (1998), with permission from Elsevier.

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at x = 0.21, suggesting monolayer-level resolution has been achieved in the overall measurement and analysis.

8.5. Novel Substrates Normal incidence transmittance spectroscopy, in some cases supplemented by reflectance spectroscopy, is the most widely applied method for extracting spectra in the absorption coefficient α for amorphous semiconductors at the absorption onset. From these spectra, the bandgap is then estimated from various functions of α (and possibly n) linearly extrapolated to α = 0 [46, 47]. In some cases, for example, in thin films deposited on roll-to-roll stainless steel or in any device configuration with planar metallic back contacts, the underlying substrate structure is opaque and this method is not possible. Although approaches based on reflectance spectroscopy alone are certainly possible, accuracy is limited by the challenge of absolute irradiance calibration of the reflectance. For this reason, SE is a more powerful and accurate method [48, 49]. By exploiting the polarization dependence of the reflection coefficients and determining the ratio of the reflection coefficients for the orthogonal p and s linear polarization states, absolute irradiance calibration is avoided. In addition, because both the p/s ratio of relative reflected electric field amplitudes tanψ ≡ (Epr /Epi )/(Esr /Esi ) and the p–s difference in phase shifts upon reflection Δ ≡ (δpr − δpi ) − (δsr − δsi ) can be determined (r: reflected; i: incident), the method derives information on both the real and imaginary parts of the optical response. Finally, because this measurement is performed at oblique incidence where the p and s reflection coefficients differ, measurements at multiple angles can be performed to reduce uncertainty in least squares regression analysis [50, 51]. This analysis approach uses a set of photon energy independent parameters including thicknesses, void fractions, and the parameters that describe the optical properties of one or more of the layer or material components. As an example of the multiple angle of incidence SE methodology, Fig. 8.9 depicts the outcome of a study performed on ∼0.6 μm thick a-Si:H fabricated by PECVD on an opaque sample of stainless steel

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Fig. 8.9. Ex situ spectroscopic ellipsometry data (ψ, Δ) at room temperature for a sample consisting of hydrogenated amorphous silicon (a-Si:H) fabricated by roll-to-roll plasma-enhanced chemical vapor deposition (PECVD) on a stainless steel substrate. Measurements at angles of incidence of 55◦ , 65◦ , and 75◦ (points) are shown in the three panels. The lines represent the best 10-parameter fit of the complete data set. This figure has been reprinted by permission from Springer Nature: Spectroscopic Ellipsometry for Photovoltaics; Volume 1: Fundamental Principles and Solar Cell Characterization, Fujiwara, H., and Collins, R. W., eds. (2018) [18].

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foil. This substrate is used for roll-to-roll deposition of multi-junction solar cells with a-Si1−x Gex :H bottom and a-Si:H top devices [18, 52]. SE data were collected at multiple angles of incidence using a rotating compensator multichannel ellipsometer, which facilitates high-speed collection of the spectra [53]. This figure includes measured (ψ, Δ) spectra at three angles of incidence for a steel/a-Si:H sample deposited by PECVD for the purpose of evaluating its general structure including thickness as well as bandgap. In a model for data analysis, the sample is assumed to consist of three layers on the steel substrate, that is, steel/(interface roughness)/a-Si:H/(surface roughness). The interface roughness arises from the surface roughness on the steel, and the surface roughness on the a-Si:H consists of substrate-induced and film-growth-derived components. The resulting model incorporates five structural parameters, including the three thicknesses and the interface and surface roughness layer compositions in the Bruggeman effective medium approximation (EMA) [54]. As a result of prior measurements of the uncoated steel substrate, only one unknown dielectric function is required in the modeling, that of the a-Si:H, which is assumed to follow the fiveparameter CD expression [4, 13]. Thus, the six spectra spanning from 0.75 to 5.5 eV for the three angles are fit with a total of ten parameters in all. A stepwise data analysis procedure is used to identify the parameters most critical to achieving an acceptable fit as shown in Table 8.1 and Fig. 8.10 [18]. In stepwise analysis, modeling begins with fixed values for all parameters, and each is allowed to vary in an effort to identify the model with a single variable parameter that provides the lowest mean square error (MSE). In the second step, the remaining variables are evaluated one by one to determine the second variable parameter that provides the best fit. Such steps are continued until all 10 free parameters are incorporated as variables in the model. The parameter values assigned at the start of the procedure include a nominal bulk layer thickness db , a nominal bandgap Eg , and zero interface and surface roughness layer thicknesses, di = ds = 0. Unless varied independently, the five parameters in the CD expression are linked to the fitted value of Eg

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Table 8.1. Parameters added stepwise for in-depth analysis of the ex situ SE data acquired at multiple angles of incidence for a hydrogenated amorphous silicon (a-Si:H) thin film on roll-to-roll stainless steel. In the analyses of these data presented in Fig. 8.10, the p-parameter best fit with p = 1, 2, . . . , 11 is obtained. Each additional parameter in the stepwise procedure is selected based on its ability to generate, from among the available parameters, the largest reduction in the mean square error (MSE) between the experimental data and the best fit as given in the third column [18]. Number of Fitting Parameters 1 2 3 4 5 6 7 8 9 10 11

Parameter Added to Improve MSE Bulk layer thickness db Bandgap in CD expression Eg Surface roughness layer thickness ds Interface roughness layer thickness di Oscillator broadening parameter Γ Oscillator resonance energy E0 Interface roughness layer a-Si:H content fmi Surface roughness layer void content fvs Bulk layer void content fvb Band edge to oscillator transition energyEP Oscillator resonance amplitude A0

MSE (10−2 ) 11.14 7.229 3.529 3.116 3.074 2.481 2.469 2.465 2.467 2.468 2.465

by applying the relationships with Eg = Eg,fit in Fig. 8.5. Once an interface or surface roughness layer thickness is introduced as a free parameter, the volume fraction fmi of a-Si:H in the interface layer or the volume fraction of void fvs in the surface layer becomes an allowable parameter in the EMA to evaluate along with the other structural and optical variables [54]. Once introduced, the starting values of these roughness layer components are 0.50. In addition, the possible presence of bulk layer voids can be evaluated by applying the EMA, and so the void content fvb in the bulk layer can serve as an additional 11th possible parameter if needed. Table 8.1 and Fig. 8.10 summarize the stepwise analysis procedure, indicating that the a-Si:H bulk layer thickness db serves as the single parameter generating the lowest MSE [18]. The resulting MSE value is indicated in Fig. 8.10 as the circular point with a line connecting the MSE values for the best p-parameter models of increasing p. The variables of surface roughness layer thickness

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Fig. 8.10. Stepwise reduction in the mean square error (MSE) performed by assessing fitting parameters one at a time. Starting with the thickness of the intrinsic layer as the variable providing the best single parameter fit, each additional parameter was incorporated into the model for evaluation of the improvement in the MSE. Addition of Eg as a second fitting parameter provided the greatest reduction in the MSE among all available second parameters. The remaining nine parameters were evaluated similarly. The MSE values providing the best fit for p = 1, 2, . . . , 11 free parameters are highlighted as the circles connected by a line. This figure has been reprinted by permission from Springer Nature: Spectroscopic Ellipsometry for Photovoltaics; Volume 1: Fundamental Principles and Solar Cell Characterization, Fujiwara, H., and Collins, R. W., eds. (2018) [18].

ds and bandgap Eg , together with db , generate the three-parameter model yielding the best fit to the data. Four and higher numbers of parameters generate models with smaller improvements in the MSE. As a result, one can conclude that the analysis is less sensitive to the steel/a-Si:H interface roughness layer (as expected), and furthermore that the relationships between Eg,fit and the remaining four parameters Γ, E0 , EP , and A0 are reasonably well defined by the expressions in Fig. 8.5, given the value of Eg,fit . The results in Table 8.1 also suggest that the amplitude A0 can be used as a parameter linked to Eg , and that the bulk layer void percentage fvb is not needed to reduce the oscillator amplitude relative to the linked value A0 . This suggests that the a-Si:H on steel has a similar density

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Fig. 8.11. Real and imaginary parts of the dielectric function spectra (ε1 , ε2 ) for intrinsic hydrogenated amorphous silicon (a-Si:H) of Figs. 8.9 and 8.10, along with p- and n-type a-Si:H, obtained using the stepwise mean square error (MSE) reduction method from ellipsometry spectra (ψ, Δ) measured at room temperature. A constant dipole (CD) matrix element expression for the (ε1 , ε2 ) spectra was assumed with five free parameters in each case. This figure has been adapted by permission from Springer Nature: Spectroscopic Ellipsometry for Photovoltaics; Volume 1: Fundamental Principles and Solar Cell Characterization, Fujiwara, H., and Collins, R. W., eds. (2018) [18].

as the samples of the series in Fig. 8.5. The final 10-parameter best fit with fvb fixed at zero is presented as the solid lines in Fig. 8.9. In fact, the six simulated spectra are indistinguishable from the experimental data on the scales of Fig. 8.9. Figure 8.11 shows a plot of the best fitting analytical expression for the dielectric function of the a-Si:H film of Fig. 8.9 obtained using the values of Eg , Γ, E0 , EP , and A0 as variables in the fiveparameter model for the (ε1 , ε2 ) spectra [18]. Figure 8.12 identifies the location of the latter four parameters (circular points) on a plot versus Eg , shown relative to the linear relationships in Fig. 8.5 for high electronic quality materials. These relationships have been modified such that Eg,fit is the independent variable [4, 13]. The results indicate that best fitting values of E0 , EP , and A0 are close to the piecewise linear relations appropriate for a-Si:H and its alloys with C. The broadening parameter Γ for the a-Si:H on steel substrates is larger than that obtained for the sample set with high electronic quality. This is an indication that the excited carriers in the a-Si:H are more rapidly scattered due to the greater disorder and/or a higher defect concentration in the material. This may be anticipated

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Fig. 8.12. Dielectric function parameters Γ, E0 , EP , and A0 determined at room temperature and plotted versus the bandgap energy Eg from the final best fitting results for undoped and doped samples of hydrogenated amorphous silicon (a-Si:H) deposited on stainless steel substrates. In the (ψ, Δ) data analysis, all five parameters were varied in the constant dipole (CD) matrix element expression for the (ε1 , ε2 ) spectra. The solid lines are the results for the sample set of electronic quality a-Si1−x Gex :H (left line) and a-Si1−x Cx :H (right line) materials given in the study of Fig. 8.5 using Eg = Eg,fit as the independent variable. This plot has been adapted by permission from Springer Nature: Spectroscopic Ellipsometry for Photovoltaics; Volume 1: Fundamental Principles and Solar Cell Characterization, Fujiwara, H., and Collins, R. W., eds. (2018) [18].

due to the direct deposition on a rough steel substrate, which is likely to result not only in roughness-induced disorder, but also in diffusion of metallic and other contaminants into the a-Si:H. This broadening behavior is similar to that observed for thinner a-Si:H

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Table 8.2. The best fitting 10 parameters along with their confidence limits that describe the structure and the constant dipole (CD) matrix element expression at room temperature for i-, p-, and n-type layers deposited on stainless steel, as determined by stepwise mean square error (MSE) reduction. All five CD expression parameters were varied in the analysis [18]. Model with all Five CD Parameters Varied i Surface roughness layer thickness (˚ A) Void volume percentage in surface layer Bulk layer thickness (˚ A) Effective medium approximation (EMA) interface [stainless-steel/ a-Si:H] roughness layer thickness (˚ A) Stainless steel volume percentage in interface layer A0 (eV) Γ (eV) E0 (eV) Eg (eV) EP (eV) Bulk layer void volume percentage

p

n

51.2 ± 2.2

59.5 ± 1.9

39.9 ± 1.5

50.7 ± 2.6 vol.% 5816 ± 16 137.3 ± 59.1

75.2 ± 1.7 vol.% 779.2 ± 3.5 41.5 ± 16.2

48.1 ± 2.4 vol.% 1338 ± 2 80.7 ± 8.8

67.8 ± 17.6 vol.%

71.4 ± 12.5 vol.%

59.6 ± 6.9 vol.%

85.91 ± 0.27 2.608 ± 0.025 3.843 ± 0.009 1.729 ± 0.003 1.177 ± 0.012 0 vol.% (fixed)

76.07 ± 1.38 2.712 ± 0.036 4.160 ± 0.013 1.761 ± 0.007 1.441 ± 0.037 0 vol.% (fixed)

72.61 ± 1.75 2.812 ± 0.039 3.990 ± 0.022 1.747 ± 0.006 1.247 ± 0.046 0 vol.% (fixed)

films deposited using H2 dilution of SiH4 on transparent conducting oxide-coated glass characterized by Sn diffusion due to the reduction of SnO2 :F [55]. The best fitting values of all ten variable parameters, including structural and optical property characteristics, are given in Table 8.2 along with their confidence limits [18]. Very high sensitivity to the value of the bandgap is evident from the confidence limits in this table, indicating that the CD expression is working well for accurate determination of the bandgap in challenging roll-toroll substrate configurations. Corresponding results are shown in Figs. 8.11 and 8.12, and Table 8.2 for thinner ∼800 ˚ A p- and

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∼1300 ˚ A n-type a-Si:H samples, each also deposited on a roll-toroll steel foil substrate. Consistent with expectations is the wider bandgap of the p-type layer, as it has been deposited with higher H2 dilution in a successful attempt to improve its functionality as a window layer. Also consistent are the larger broadening parameters attributed to dopant-induced disorder and defects for the two doped a-Si:H samples compared with the undoped a-Si:H. 8.6. Modeling Solar Cell Structures and EQE The optical modeling capabilities described in Section 8.3 have been utilized to characterize two complete a-Si:H p-i-n solar cells by ex situ SE methods [19, 56]. The deduced structural and optical information was applied in simulations of the EQE spectra of the solar cells for comparison with the measured EQE spectra. The two solar cells were deposited on SnO2 /SiO2 /SnO2 :F-coated glass substrates at 200◦ C in a multi-chamber PECVD cluster tool without vacuum breaks between the sequentially deposited p-, i-, and n-type a-Si:H-based layers. The p-type layers of both cells were hydrogenated amorphous silicon-carbon (a-Si1−x Cx :H) alloys doped using B2 H6 gas in the PECVD process and deposited to intended thicknesses of ∼150 ˚ A. The intrinsic a-Si:H absorber layer for the first cell of this study was deposited in a single PECVD step to a thickness of ∼4000 ˚ A using a hydrogen-to-silane gas flow ratio of R = [H2 ]/[SiH4 ] = 0.5. The second solar cell was fabricated under identical conditions as the first, but with the exception of a two-step intrinsic a-Si:H absorber layer with a total thickness of ∼3300 ˚ A. In the first step of this two-step process, an intended 300 ˚ A thick layer of protocrystalline Si:H was deposited on the p-type a-Si1−x Cx :H using the concept of maximum H2 dilution. For this interface layer, a hydrogen-tosilane gas flow ratio of R = 50 was used in the PECVD process. This was the maximum possible R value without nucleating silicon nanocrystals throughout the 300 ˚ A deposition. The intrinsic a-Si:H component of the second step, located adjacent to the n-type back contact layer in the final solar cell, was deposited under identical conditions as the one-step intrinsic layer of the first cell but with

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Table 8.3. Comparison of the performance parameters of open-circuit voltage VOC , short-circuit current density JSC , fill factor FF, efficiency η, shunt resistance RSH , and series resistance RS measured under air mass 1.5 (AM 1.5) illumination for two solar cells fabricated with intrinsic a-Si:H absorber layers. For the two cells, the absorbers were deposited in one- and two-step processes to thicknesses of ∼4000 and 3300 ˚ A, respectively. For the two-step absorber, the first step consisted of an intended 300 ˚ A thick intrinsic layer of protocrystalline Si:H deposited onto the p-type layer at a high H2 dilution flow ratio of R = 50 prior to deposition of the remainder of the intrinsic layer using the same conditions as the one-step absorber (R = 0.5) [19].

Cell #1 One-step absorber #2 Two-step absorber

VOC (V)

JSC (mA/cm2 )

FF

η (%)

RSH (kΩ)

RS (Ω)

0.734

10.1

0.687

5.10

32.9

119

0.886

14.5

0.733

9.43

6.9

18.1

a reduced thickness of 3000 ˚ A. Finally, the n-type layer for both ˚ cells was ∼300 A thick unalloyed a-Si:H doped during deposition using PH3 . The initial efficiencies of the a-Si:H solar cells incorporating the one- and two-step intrinsic a-Si:H absorber layers are given in Table 8.3 [19]. The solar cell with the one-step absorber layer exhibited a low initial efficiency of ∼5.1%, and as a result, the second cell with a two-step layer was fabricated. It is well documented that a two-step intrinsic a-Si:H absorber layer with a thin high H2 dilution protocrystalline layer at the interface to the p-type aSi1−x Cx :H produces improvements in both the initial performance and stability of the a-Si:H solar cells [57]. This is exemplified by the solar cell performance parameters given in Table 8.3, where it is demonstrated that each of the parameters was improved, with the largest improvement being ∼40% in the short-circuit current density (JSC ). The result for the solar cell with the two-step absorber layer is an initial efficiency of 9.4%. Because these two solar cells exhibit widely differing abilities to collect current, interesting distinctions can be drawn from the EQE measurements and the optical simulations for the two solar cells.

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SE measurements of the two solar cells in the glass/SnO2 / SiO2 /SnO2 :F/(p-i-n a-Si:H) structure were performed ex situ both from the glass side and from the film side, and simultaneous analysis was performed on the two data sets [19]. In glass-side SE measurements, a focusing probe was used along with an aperture in a configuration designed to block the reflection from the ambient/glass interface [58]. In this configuration, higher order reflections making more than two passes through the glass were blocked as well. In film-side SE measurements, an aperture was also used to block any reflection from this same ambient/glass interface. Thus, overlap of incoherent beams that would mix with the beam of interest from the film stack is avoided in both measurements. In glass-side SE, the multi-layer solar cell structure backed by the silver layer serving as the rear contact electrode was probed for higher sensitivity, whereas in film-side SE, a spot on the n-type a-Si:H surface slightly displaced from the same electrode was probed. Thus, in the simultaneous analysis of the two data sets, the multi-layer model differed; the back contact was present for glass-side SE, but not for film-side SE. The model used for analysis of the SE data, including the free parameters varied in the fit as well as the coupled and fixed parameters, is shown in Table 8.4. Before presenting the analysis results, the structural/optical model for the a-Si:H p-i-n solar cell of Table 8.4 will be elaborated in greater detail starting from the soda lime glass at the front. First, a thin optically distinct, tin-modified region is present on the ambient side of the glass resulting from the in-diffusion of tin from the molten bath used in the float glass manufacturing process [58, 59]. In addition, a correction of the ellipsometry angle Δ is incorporated to account for the stress-induced birefringence in the glass and its dispersion with photon energy [60]. The thicknesses and (ε1 , ε2 ) spectra of the thin SnO2 and SiO2 layers on the glass were fixed based on separate analyses of typical structures without over-deposited solar cells [56]. For the SnO2 :F layer, the (ε1 , ε2 ) spectra were fixed in the solar cell analyses, but the bulk layer thickness was allowed to vary. From separate SE analyses of typical glass/SnO2 /SiO2 /SnO2 :F solar cell substrate structures, the thickness of the surface roughness

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Table 8.4. Multi-layer optical model applied in the analysis of film-side spectroscopic ellipsometry (SE) data collected for hydrogenated amorphous silicon (a-Si:H)-based p-i-n solar cells in the superstrate configuration for which sunlight enters from the glass side. The thicknesses and structural/optical parameters that were fixed, fitted, or coupled in the data analysis procedure are shown. Coupled parameters apply the relationships given in Fig. 8.5 between each parameter (A0 , E0 , Γ, EP ) and Eg,fit in the five-parameter constant dipole (CD) expression. Thus, the bandgaps reported here are to be compared with those of Eg,fit obtained in an analysis of the full (ε1 , ε2 ) spectra. For the model to describe the glass-side SE data, opaque Ag was added as a semi-infinite medium at the back of the n-type a-Si:H layer. In this case, Ag was assumed to fill the voids in the roughness on the n-type a-Si:H layer in order to generate an a-Si:H:P/Ag interface roughness layer [19]. (n-type a-Si:H)/void layer Surface roughness thickness: n-type a-Si:H volume fraction:

Fit Fixed (0.5)

n-type a-Si:H layer bulk thickness: CD An : CD E0n : CD Γn : CD Egn : CD EP n :

Fit Coupled to Egn Coupled to Egn Fit Fit Coupled to Egn

i-type a-Si:H layer bulk thickness: CD Ai : CD E0i : CD Γi : CD Egi : CD EP i :

Fit Coupled Coupled Coupled Fit Coupled

SnO2 :F/(p-type a-Si1−x Cx :H)/(i-type a-Si:H) layer Interface layer thickness: SnO2 :F/p-type/i-type volume fractions:

Fit Fixed (0.25/0.25/0.50)

SnO2 :F/(p-type a-Si1−x Cx :H)/(i-type a-Si:H) layer Interface layer thickness: SnO2 :F/p-type/i-type volume fractions:

Fit Fixed (0.50/0.25/0.25)

SnO2 :F layer Thickness:

Fit

to Egi to Egi to Egi to Egi

(Continued )

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Table 8.4. (Continued ) SiO2 layer Thickness:

Fixed (232 ˚ A)

SnO2 layer Thickness:

Fixed (294 ˚ A)

Soda lime glass substrate Phase shift due to strain:

Fit

Sn side layer Thickness:

Fixed (610 ˚ A)

on the SnO2 :F layer was found to be ∼300 ˚ A [61]. Because the thickness of the p-type a-Si1−x Cx :H layer in an a-Si:H solar cell is ∼100 ˚ A, this layer is strongly modulated by the surface roughness on the underlying SnO2 :F. As a result, the p-type a-Si1−x Cx :H layer was considered as a component of the ∼300 ˚ A thick rough interface region between the bulk layers of the SnO2 :F and the intrinsic a-Si:H. This roughness region was modeled by applying the Bruggeman EMA to determine the composite dielectric functions of two three-component interface layers with different sets of fixed volume fractions for the three components of SnO2 :F, p-type a-Si1−x Cx :H, and intrinsic a-Si:H [54]. For the interface layer adjacent to the SnO2 :F layer, ratios of 2:1:1 were used for the three components, respectively, and for the interface layer adjacent to the intrinsic a-Si:H layer, ratios of 1:1:2 were used, respectively. Finally, the roughness layer on the n-type a-Si:H surface in the film-side measurement, which affects the filmside analysis sensitively, and the interface roughness layer between the n-type a-Si:H and Ag, which affects the glass-side measurement, were also modeled using the EMA. Figure 8.13 shows the film- and glass-side (ψ, Δ) data obtained from the SE measurements of the solar cell with a one-step intrinsic a-Si:H layer [19]. Also shown are the best fitting results to the data applying multi-sample analysis. Figure 8.14 presents a comparison of the structural and dielectric function parameters obtained in the best fits of the two pairs of (ψ, Δ) spectra for both solar cells. For the cell with the two-step absorber, the small stress birefringence

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(a)

(b)

Fig. 8.13. (a) Film-side and (b) glass-side spectroscopic ellipsometry (SE) (ψ, Δ) data (points) and their best fits (lines) applying a multi-sample analysis for the a-Si:H-based solar cell in the superstrate configuration fabricated with a singlestep intrinsic hydrogenated amorphous silicon (a-Si:H) absorber. The glass-side data in (b) were collected at a location that lies on top of the silver back contact layer, whereas the film-side data were collected at a nearby location without the silver layer. This figure has been reprinted by permission from Springer Nature: Spectroscopic Ellipsometry for Photovoltaics; Volume 2: Applications and Optical Data of Solar Cell Materials, Fujiwara, H., and Collins, R. W., eds. (2018) [19].

correction for the glass was fixed at the value found for the simpler cell with the one-step absorber. The effective thicknesses or values of the volumes per area for the SnO2 :F, accounting for the bulk and two interface roughness layers, are 3420 and 3150 ˚ A for the cells

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Fig. 8.14. Parameters with confidence limits deduced in the best fitting analysis of the spectroscopic ellipsometry (SE) (ψ, Δ) data collected for hydrogenated amorphous silicon (a-Si:H) solar cells with one-step (left) and two-step (right) intrinsic absorber layers. The values of the parameters that were fixed in the analysis are also shown. Both film- and glass-side SE data were analyzed simultaneously for each sample set. For the cell with the two-step a-Si:H absorber layer, the correction for stress birefringence was fixed in the final best fitting analysis. This graphic has been adapted with permission from Springer Nature: Spectroscopic Ellipsometry for Photovoltaics; Volume 2: Applications and Optical Data of Solar Cell Materials, Fujiwara, H., and Collins, R. W., eds. (2018) [19].

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with one- and two-step absorbers, respectively. These values deviate by no more than 5% from the nominal value of 3300 ˚ A. The effective thicknesses of the p-type a-Si1−x Cx :H layers are in the narrow range of 80 ± 4 ˚ A, which is considerably thinner than the intended value ˚ of 150 A based on the deposition rate measured for thicker films. This comparison suggests a time-dependent deposition rate for the p-type a-Si1−x Cx :H or a substrate-dependent initial rate. In contrast, the n-type layer effective thicknesses of 330 ± 4 ˚ A were consistently ˚ larger than the intended value of 300 A. The one- and two-step total effective thicknesses for the absorber layers were 3960 and 3320 ˚ A, respectively, differing by no more 1% from the intended values due to a more accurate deposition rate calibration. Next, the optical parameters that define the (ε1 , ε2 ) spectra of the a-Si:H-based layers of the solar cells will be described. A comparison of these optical parameters in Fig. 8.14 yields insights into the a-Si:H-based material components of the solar cell [19]. First, the bandgap and Lorentz oscillator broadening parameter for the p-type a-Si1−x Cx :H (1.865 and 2.667 eV, respectively) deduced from an analysis of a film deposited on a smooth substrate are both significantly wider than those of the one-step intrinsic a-Si:H absorber layer (1.632 and 2.273 eV, respectively). This is consistent with the results of Fig. 8.5, given that the p-type layer is an a-Si1−x Cx :H alloy [4]. The role of alloying is to increase JSC by reducing the absorption of solar irradiance in the inactive p-type window layer of the cell and to increase the open-circuit voltage of the cell by widening the p-type layer bandgap. Both alloying and doping broaden the Lorentz oscillator component of the (ε1 , ε2 ) spectra as observed in Fig. 8.5 and Table 8.2, respectively, due to the increased disorder and to the introduction of charged defects and potential fluctuations that readily scatter excited carriers [18]. In contrast to the p-type window layer, the n-type layer at the back of the cell is not alloyed and shows a slightly narrower bandgap (1.611 eV) compared to the one-step absorber layer (1.632 eV). The larger Lorentz oscillator broadening parameter for the n-type a-Si:H layer (2.79 eV) compared to that of the intrinsic layer (2.27 eV) is consistent with Table 8.2 and the corresponding observation for the

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p-type layer. The two-step a-Si:H absorber is modeled as a single layer due to the similarity of the (ε1 , ε2 ) spectra deposited in the two steps. Furthermore, hydrogen incorporated in the interface absorber layer can diffuse into the bulk absorber layer during subsequent processing and modify its (ε1 , ε2 ) spectra [62]. Consequently, the bandgap deduced for the two-step absorber layer (1.671 eV) is wider than that of the one-step absorber (1.632 eV) as a result of the additional hydrogen incorporation due to the high H2 dilution level of the interface absorber layer and the accompanying H diffusion. The simulations of the EQE spectra for both solar cells are based on the assumptions that all interfaces are specularly reflecting/ transmitting, and that the EMA mixtures at interfaces account for their non-ideality relative to abrupt dielectric discontinuities [19]. As presented in Fig. 8.14, the structural models and the (ε1 , ε2 ) spectra of the components from the ex situ SE measurements are used in these simulations with no free parameters. The results of the EQE simulation for the lower performance solar cell with the onestep absorber are shown in Fig. 8.15(a) along with the experimental spectrum, both plotted by convention versus wavelength. In the simulation of this cell, 100% collection is assumed from the bulk absorber layer, whereas 0% collection is assumed from the absorber layer components of the two p/i interface layers. The inset of Fig. 8.15(a) shows the difference between the simulated and measured spectra. The largest difference is found to be positive, reaching as high as +0.12 over the narrow 550–650 nm wavelength range, suggesting a reduction from 100% collection within this range. A negative trending feature is also observed in the inset, reaching almost to ∼−0.05 over the broad 350–750 nm range. A negative difference, implying a measured EQE value in excess of that simulated, suggests a possible role of light scattering and trapping in the solar cell optics. Thus, the broad feature in the simulated — measured EQE difference spectrum may be attributable to the beneficial effects of light scattering. In order to better understand the positive feature over the narrow range of 550–650 nm in the inset of Fig. 8.15(a), additional simulations were performed assuming that various thicknesses of the a-Si:H absorber layer adjacent to the i/n interface at the back of solar

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(b)

Fig. 8.15. (a) Measured external quantum efficiency (EQE) spectrum for the hydrogenated amorphous silicon (a-Si:H) p-i-n solar cell with a one-step intrinsic absorber together with the results of a simulation established on the basis of the spectroscopic ellipsometry (SE) analysis shown in Fig. 8.14 (left) with no free parameters. For the simulation, it is assumed that the entire absorber layer contributes to carrier collection but no p/i interface components contribute. (b) Measured EQE spectrum from (a) along with the results of simulations based on the assumption of inactive absorber layer regions of different thicknesses adjoining the i/n interface. The insets in both panels show ΔEQE, the difference between the simulated and measured EQE spectra. For ΔEQE in the lower panel inset, the thickness of the inactive absorber layer is taken as 600 ˚ A. The negative ΔEQE background in the insets can be attributed to EQE gains due to light trapping not included in the simulation. This figure has been reprinted with permission from Springer Nature: Spectroscopic Ellipsometry for Photovoltaics; Volume 2: Applications and Optical Data of Solar Cell Materials, Fujiwara, H., and Collins, R. W., eds. (2018) [19].

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cell are inactive, meaning 0% collection from this layer [19]. The goal is to reduce the discrepancy between the simulation and experiment through proper choice of the inactive layer thickness. It should be emphasized that an abrupt transition from 100% collection to 0% near the back of the absorber is an over-simplification. Although a carrier collection profile is expected, the over-simplified model provides insights into the origin of the discrepancy between the simulated and measured EQE spectra. The additional simulations for different inactive absorber layer thicknesses adjacent to the n-type a-Si:H layer are shown in Figs. 8.15(b) and 8.16, the latter on an expanded scale. Improved agreement is evident between the simulated and measured EQE for a thickness of 600 ˚ A. By including this inactive absorber component in the simulation, its maximum difference from the measured EQE spectrum decreases by a factor of two. Since the bulk layer thickness of the intrinsic a-Si:H absorber as

Fig. 8.16. Measured external quantum efficiency (EQE) spectrum (broken line) and five simulated spectra (solid lines) from Fig. 8.15 plotted on expanded scales. The simulations were computed by incorporating inactive absorber layer regions of different thicknesses adjoining the i/n interface. The goal is to achieve improved agreement between the simulated and measured spectra through the addition of the inactive layer. This figure has been reprinted with permission from Springer Nature: Spectroscopic Ellipsometry for Photovoltaics; Volume 2: Applications and Optical Data of Solar Cell Materials, Fujiwara, H., and Collins, R. W., eds. (2018) [19].

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determined from SE is 3833 ± 11 ˚ A, the simulations of Fig. 8.15(b) suggest that carrier collection is most efficient within an absorber layer depth of ∼3200 ˚ A from the p/i interface region. This result demonstrates that ∼3200 ˚ A is expected as the optimum absorber layer thickness for carrier collection in the single-junction a-Si:H solar cell fabricated in this one-step absorber layer deposition process. Any further increase in the absorber layer thickness fails to increase carrier collection due to a limitation on the hole diffusion length and to a reduction in the built-in electric field, the latter reduction leading to a lower fill factor [63, 64]. The simulated and measured EQE spectra for the higher performance a-Si:H p-i-n solar cell deposited with the two-step absorber layer are shown in Fig. 8.17(a). For longer wavelengths, improved agreement between the simulated and measured spectra is observed, as compared to the solar cell with the one-step absorber, which was deposited with a thicker intrinsic a-Si:H layer (∼3800 ˚ A) [19]. This supports the concept that the larger difference between the simulated and measured EQE in the 550–650 nm spectral range for the lower performance solar cell is due to an absorber layer thickness greater than the hole diffusion length. Also for the high-efficiency cell, as presented in Fig. 8.17(b), it is necessary to assume 50% collection from the SnO2 :F/p/i interface layer adjacent to the absorber layer in order for the simulation to match the experimental results over the shorter wavelength range (400–550 nm). This additional collection beyond that in the bulk layer of the absorber is likely to originate from the 50 vol.% intrinsic a-Si:H material component in the adjoining interface layer. This result indicates that, in a highquality a-Si:H p-i-n solar cell fabricated with a two-step absorber, the a-Si:H absorber material in the adjoining p/i interface layer also contributes to collection, in contrast to the observations for the cell with the one-step absorber layer. The enhanced collection by the p/i interface layer is attributed to reduced recombination, a beneficial effect when protocrystalline Si:H is incorporated adjacent to the p-type layer in the solar cell with the two-step absorber [57]. In addition, the exposure of the p-type

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(a)

(b)

Fig. 8.17. Simulated and measured external quantum efficiency (EQE) spectra for the hydrogenated amorphous silicon (a-Si:H) p-i-n solar cell in the superstrate configuration fabricated with a two-step absorber layer. The simulations are based on the ex situ spectroscopic ellipsometry (SE) analysis results shown in Fig. 8.14 (right). In (a), it is assumed that 100% carrier collection occurs from the bulk absorber layer whereas the p/i interface components do not contribute; no free parameters are used. In (b), it is assumed that 100% carrier collection occurs from the bulk absorber layer and 50% from the p/i interface layer adjacent to the bulk absorber layer. The insets show ΔEQE, the difference between the simulated and measured spectra. This figure has been reprinted with permission from Springer Nature: Spectroscopic Ellipsometry for Photovoltaics; Volume 2: Applications and Optical Data of Solar Cell Materials, Fujiwara, H., and Collins, R. W., eds. (2018) [19].

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a-Si1−x Cx :H layer to atomic H during initial growth of the a-Si:H absorber at high H2 dilution is likely to lead to a wider bandgap and reduced defect density, thereby improving the properties of the a-Si1−x Cx :H as a p-type window layer [65]. Finally, the wider bandgap of the two-step absorber layer as noted in Fig. 8.14 suggests that additional H incorporated in the layer deposited in the first step diffuses into the overlying bulk absorber and may also serve to improve the performance of the solar cell.

8.7. Summary Several applications of the parametric expressions for the spectra in the real and imaginary parts of the dielectric function (ε1 , ε2 ) of a-Si:H-based materials have been demonstrated in this chapter. The emphasis is on the utility of these expressions for materials and device performance simulations, as well as for controlled materials fabrication and characterization. Both CD and CM matrix element expressions with either five or seven photon energy-independent parameters, depending on the available optical measurements, have been applied in these illustrative applications from a-Si:H-based thinfilm and device fabrication technology [2, 4]. The first application presented in this chapter addressed realtime SE determination of bandgap for a-Si:H and a-Si1−x Gex :H thinfilm materials prepared by PECVD at low temperatures versus the H2 dilution gas flow ratio [26]. Hydrogen dilution at low substrate temperatures is found to provide significant bandgap adjustability, typically over a range of ∼0.15 eV for materials of fixed alloy composition, as determined using a five-parameter CD expression, which neglects the Urbach tail contribution. In addition to bandgap modification, H2 dilution of hydride gases has been developed extensively for optimization of the electronic properties of a-Si:H-based materials. It has been found that optimum properties are obtained under conditions of maximum H2 dilution of hydride gases, but without exceeding the dilution level at which crystallites nucleate from the growing film over the desired thickness. Applying this concept, a series of electronic quality a-Si1−x Gex :H and a-Si1−x Cx :H

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alloy thin films has been prepared by PECVD in different laboratories and has been studied in detail by a combination of DBPC, T & R spectroscopy, and SE performed ex situ [4, 13]. The resulting (ε1 , ε2 ) spectra have been fit using a seven-parameter version of the CD expression including the Urbach tail slope Eu and the Urbach to band edge transition energy Et . The seven parameters show clear trends with the bandgap determined over the range of 1.30 to 1.95 eV from an extrapolation of the CD form (αn/E)1/2 using α from traditional T & R spectroscopy alone. For some parameters, the trends followed by both the a-Si:H and the a-Si1−x Gex :H group of alloys spanning the T & R bandgap range 1.30–1.80 eV differ from those followed by the a-Si1−x Cx :H group of alloys spanning the range 1.80–1.95 eV. The overall trends demonstrate that for such high electronic quality materials prepared with maximum H2 dilution, the complete optical response from the Urbach region in the near-infrared to the Lorentz oscillator region in the ultraviolet can be simulated based on the specification of a single variable, the T & R-deduced bandgap. The trend quantified by the relationship between the true bandgap from a complete analysis and the bandgap determined from T & R alone shows that the latter underestimates the overall best fitting bandgap for values 1.5 eV [13]. This behavior is due to residual curvature in (αn/E)1/2 over the range of bandgap extrapolation accessible to 0.5–1.0 μm films. From the observed trends, the energy difference between the Urbach tail transition energy Et and the true bandgap is found to be nearly constant at ∼+0.10 eV, whereas the corresponding difference for the Lorentz oscillator transition energy increases with increasing bandgap. Thus, a single energy scaling is not sufficient to describe the bandgap dependence of the absorption onset for this set of materials. A correlation is also observed between the Urbach tail slope Eu and the Lorentz oscillator broadening parameter Γ. This suggests that Γ, as a measure of the band-to-band excited state lifetime, is affected by static disorder, that is, the bond length and bond angle distortions that are also reflected in Eu . Finally, the ability to obtain excellent fits while fixing the constant contribution to ε1 at ε0s = 1 for the full set of samples supports the validity of the

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full CD expressions, whereas for the CM expressions, the best fitting ε0s shows a systematic increase with increasing bandgap from values −1 < ε0s < 0 at the lowest bandgap to values 1 < ε0s < 2 at the highest. The origin of this problem is that the CM expression lacks an adjustable transition energy between the band onset region and the Lorentz oscillator [2]. In fact, the photon energy at which the band edge factor modifying the Lorentz oscillator is one-half its maximum is linked to the bandgap according to E = 3.4 Eg , which is typically well above the Lorentz oscillator resonance energy. In contrast, for the CD expression, the corresponding energy is E = Eg + EP , which can enhance the adjustability in the shape of the absorption onset and the Lorentz oscillator. Characterization of device-relevant structures has been facilitated by the parametric representations of the (ε1 , ε2 ) spectra [20, 21]. For bandgap engineering of structures over wider photon energy ranges, by as much as 0.5 eV, continuous variations with thickness in alloy content have been demonstrated. Real-time SE in conjunction with a virtual interface approximation provides the ability to measure bandgap profiles associated with these variations at monolayer resolution in a single sample structure [22, 44, 45]. The deduced temperature coefficients of the bandgap presented in Chapter 5 versus the bandgap itself can provide the adjustments needed to deduce the profiles relevant to room temperature. These bandgap profiles can be compared to those intended and a model for the deposition process can be then developed that enables flow meter control for generation of desired profiles. Such bandgap-engineered structures have applications in a variety of optoelectronic devices. In addition, the CD matrix element expressions have been applied in analyses of multiple angle of incidence SE data obtained from ex situ measurements of thin films on opaque substrates for which T & R spectroscopy is not possible [18]. Excellent fits to the spectra at the multiple angles provide accurate determinations of the bandgap and Lorentz oscillator broadening parameter, the latter as a measure of the disorder and defects. Finally, the parametric CD matrix element expressions have been extended to various applications in ex situ SE analysis of complete

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solar cells incorporating multiple a-Si:H-based semiconductor layers [19]. The results of such analyses, given in terms of parametric (ε1 , ε2 ) spectra along with bulk, interface, and surface roughness layer thicknesses, enable EQE simulations of devices for comparisons with measurements. From these comparisons, it becomes possible to understand in greater depth the nature of photocurrent collection and the origins of optical losses in the devices. In the studies of aSi:H-based p-i-n solar cells reported in this chapter, sensitivity is demonstrated to electronic losses due to recombination of carriers photogenerated near the i/n interface. Losses are attributed to a thickness of the intrinsic a-Si:H absorber layer that is greater than the collection length for holes, as a result of limitations on their mobility. Enhanced collection of carriers near the p/i interface is demonstrated upon incorporation of a protocrystalline Si:H interface layer adjacent to the p-type layer in the SnO2 :F/(p-type a-Si1−x Cx :H)/(intrinsic a-Si:H) structure. These techniques, which employ specular optical models, can be applied as well to quantify light-trapping enhancements for near-bandgap photon energies. The overall optical and electronic analysis capabilities described in Section 8.6 of this chapter can be applied in a wide variety of thin-film optoelectronics technologies.

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36. Albooyeh, M., and Simovski, C. R. (2012). Huge local field enhancement in perfect plasmonic absorbers, Optics Express, 20, pp. 21888– 21895. 37. Solano, M., et al. (2013). Optimization of the absorption efficiency of an amorphous-silicon thin-film tandem solar cell backed by a metallic surface-relief grating, Applied Optics, 52, pp. 966–979. 38. Simovski, C. R., Shalin, A. S., Voroshilov, P. M., and Belov, P. A. (2013). Photovoltaic absorption enhancement in thin-film solar cells by nonresonant beam collimation by submicron dielectric particles, Journal of Applied Physics, 114, pp. 103104: 1–6. 39. Atalla, M. R. M. (2014). Multiple excitations of surface-plasmonpolariton waves in an amorphous silicon p-i-n solar cell using Fourier harmonics and compound gratings, Journal of the Optical Society of America B, 31, pp. 1906–1914. 40. Voroshilov, P. M., Simovski, C. R., Belov, P., and Shalin, A. S. (2015). Light-trapping and antireflective coatings for amorphous Si-based thin film solar cells, Journal of Applied Physics, 117, pp. 203101: 1–7. 41. Molet, P., et al. (2018). Ultrathin semiconductor superabsorbers from the visible to the near-infrared, Advanced Materials, 30, pp. 1705876: 1–6. 42. Fantoni, A., et al. (2018). A simulation study of surface plasmons in metallic nanoparticles: Dependence on the properties of an embedding a-Si:H matrix, Physica Status Solidi A — Applications and Materials Science, 215, pp. 1700487: 1–7. 43. Kim, S., and Collins, R. W. (1995). Optical characterization of continuous compositional gradients in thin films by real time spectroscopic ellipsometry, Applied Physics Letters, 67, pp. 3010–3012. 44. Fujiwara, H., Koh, J., Wronski, C. R., and Collins, R. W. (1997). Application of real time spectroscopic ellipsometry for high resolution depth profiling of compositionally graded amorphous silicon alloy thin films, Applied Physics Letters, 70, pp. 2150–2152. 45. Fujiwara, H., et al. (1998). Optical depth profiling of band gap engineered interfaces in amorphous silicon solar cells at monolayer resolution, Applied Physics Letters, 72, pp. 2993–2995. 46. Morigaki, K. (1999). Physics of Amorphous Semiconductors (Singapore, World Scientific), Chapter 8, pp. 137–152. 47. Singh, J., and Shimakawa, K. (2003). Advances in Amorphous Semiconductors (London, UK, Taylor & Francis), Chapter 4, pp. 57–95. 48. Fujiwara, H. (2007). Spectroscopic Ellipsometry: Principles and Applications (New York, NY, John Wiley & Sons), Chapter 4, pp. 81–140. 49. Collins, R. W. (2018). Measurement technique of ellipsometry. In: Spectroscopic Ellipsometry for Photovoltaics; Volume 1: Fundamental

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Principles and Solar Cell Characterization, edited by Fujiwara, H., and Collins, R. W. (Cham, Switzerland, Springer), Chapter 2, pp. 19–57. Woollam, J. A., et al. (1999). Overview of variable angle spectroscopic ellipsometry (VASE), part I: Basic theory and typical applications. In: SPIE Proceedings; Optical Metrology, CR 72, edited by Al-Jumaily, G. A. (Bellingham, WA, SPIE), pp. 3–28. Johs, B., et al. (1999). Overview of variable angle spectroscopic ellipsometry (VASE), part II: Advanced applications. In: SPIE Proceedings; Optical Metrology, CR 72, edited by Al-Jumaily, G. A. (Bellingham, WA, SPIE), pp. 29–58. Huang, Z. (2016). Spectroscopic Ellipsometry Studies of Thin Film a-Si:H/nc-Si:H Micromorph Solar Cell Fabrication in the p-i-n Superstrate Configuration, Ph.D. Dissertation (Toledo, OH, University of Toledo). Collins, R. W., An, I., Lee, J., and Zapien, J. A. (2005). Multichannel ellipsometry. In: Handbook of Ellipsometry, edited by Tompkins, H. G., and Irene, E. A. (Norwich, NY, William Andrew), Chapter 7, pp. 481–566. Fujiwara, H., Koh, J., Rovira, P. I., and Collins, R. W. (2000). Assessment of effective-medium theories in the analysis of nucleation and microscopic surface roughness evolution for semiconductor thin films, Physical Review B, 61, pp. 10832–10844. Junda, M. M., Gautam, L. K., Collins, R. W., and Podraza, N. J. (2018). Optical gradients in a-Si:H thin films detected using realtime spectroscopic ellipsometry with virtual interface analysis, Applied Surface Science, 436, pp. 779–784. Aryal, P., et al. (2015). Quantum efficiency simulations with inputs from spectroscopic ellipsometry for evaluation of carrier collection in a-Si:H solar cells. In: Conference Record of the 42nd IEEE Photovoltaic Specialists Conference, 14–19 June 2015, New Orleans, LA, (New York, NY, IEEE), Paper 735–6311: pp. 1–4. Koh, J., et al. (1998). Optimization of hydrogenated amorphous silicon p-i-n solar cells with two-step i-layers guided by real time spectroscopic ellipsometry, Applied Physics Letters, 73, pp. 1526–1528. Chen, J., et al. (2011). Through-the-glass spectroscopic ellipsometry of superstrate solar cells and large area panels. In: Conference Record of the 37th IEEE Photovoltaics Specialists Conference, 19–24 June 2011, Seattle, WA, (New York, NY, IEEE), pp. 3486–3491. Synowicki, R. A., Johs, B. D., and Martin, A. C. (2011). Optical properties of soda-lime float glass from spectroscopic ellipsometry, Thin Solid Films, 519, pp. 2907–2913.

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60. Li, J., et al. (2015). Through-the-glass spectroscopic ellipsometry for simultaneous mapping of coating properties and stress in the glass. In: Conference Record of the 42nd IEEE Photovoltaic Specialists Conference, 14–19 June 2015, New Orleans, LA, (New York, NY, IEEE), Paper 735–5642, pp. 1–4. 61. Chen, J., et al. (2006). Multilayer analysis of the CdTe solar cell structure by spectroscopic ellipsometry. In: Conference Record of the IEEE 4th World Conference on Photovoltaic Energy Conversion, 7–12 May 2006, Waikoloa, HI, (New York, NY, IEEE), pp. 475–478. 62. An, I., Li, Y. M., Wronski, C. R., and Collins, R. W. (1993). Chemical equilibration of plasma-deposited amorphous silicon with thermally generated atomic hydrogen, Physical Review B, 48, pp. 4464–4472. 63. Schiff, E. A. (2009). Carrier drift-mobilities and solar cell models for amorphous and nanocrystalline silicon. In: Materials Research Society Symposium Proceedings; Amorphous and Polycrystalline Thin Film Silicon Science and Technology — 2009, Vol. 1153, edited by Flewitt, A., Wang, Q., Hou, J., Uchikoga, S., and Nathan, A. (Warrendale, PA, MRS), Paper A15–01, pp. 1–12. 64. Liang, J., et al. (2006). Hole-mobility limit of amorphous silicon solar cells, Applied Physics Letters, 88, pp. 063512: 1–3. 65. Fujiwara, H., Koh, J., Wronski, C. R., and Collins, R. W. (1999). Analysis of contamination, hydrogen emission, and surface temperature variations using real time spectroscopic ellipsometry during p/i interface formation in amorphous silicon p-i-n solar cells, Applied Physics Letters, 74, pp. 3687–3689.

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CHAPTER 9

Application of Amorphous and Nanocrystalline Silicon in Solar Cells Baojie Yan Ningbo Institute of Materials Technology and Engineering Chinese Academy of Science, P. R. China

9.1. Introduction Amorphous silicon fabricated in a glow discharge of silane (SiH4 ) gas was identified as an electronically useful material by Spear and LeComber in the 70s of the last century [1]. This fabrication method resulted in hydrogen incorporation within the amorphous silicon, although the role of hydrogen was not fully recognized at that time. In the research of Spear and LeComber, glow discharges were used to decompose SiH4 and H2 gas mixtures and deposit thin films of amorphous silicon, within which about 10–20 atomic % (at.%) hydrogen passivates the silicon dangling bonds, reduces the defect density to the 1016 cm−3 level, and makes doping possible. Because the hydrogen incorporation plays an important role in determining the material quality, the material is referred to as hydrogenated 329

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amorphous silicon (a-Si:H). The two major applications of a-Si:H are for thin-film transistors (TFTs) in liquid crystal displays (LCDs) and for thin-film photovoltaic (PV) solar cells. During the same period of time, Carlson and Wronski invented the a-Si:H solar cell at RCA Laboratories, and demonstrated an efficiency of 2.6% [2]. Their invention attracted significant attention, and a massive effort of research and development on a-Si:H solar cells has taken place worldwide since then. As a result of these intensive studies, the a-Si:H solar cell efficiency increased steadily during the period from the 70s of last century to the end of last decade [3–6]. Early in the development of a-Si:H solar cells, the important observation of cell instability was reported. The efficiency of the a-Si:H solar cell was found to degrade with time under light illumination. This was attributed to the so-called Staebler–Wronski effect [7] in which light soaking induces metastable defect generation and reduces the photoconductivity of a-Si:H. The Staebler–Wronski effect has been a topic of great interest in the a-Si:H research community over the years and several microscopic mechanisms have been proposed, including the weak bond breaking model [8], the hydrogen collision model [9], among others. All such models include the motion of hydrogen [10], and it has been observed that light-induced defect generation is associated with a significant structural change and even a volume change in the silicon network, as well [10, 11]. Although the light-induced defect generation and the recovery after thermal annealing have served as ideal topics for the study of metastable physics in material structures, and a great number of papers have been published on the subject, a unified explanation has not yet been accepted by the community. From an applications perspective, improvements of material quality and stability, namely reduction of the initial defect density and suppression of the light-induced defect generation, are the two major tasks for thin-film silicon solar cell optimization. These tasks relate to the improvement of the initial energy conversion efficiency and the reduction of the light-induced degradation in efficiency. For improving the efficiency, a high material quality is essential, which results mainly from the optimization of the deposition process. The

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process is characterized for example by the plasma-enhanced chemical vapor deposition (PECVD) parameters, including the substrate temperature, pressure, excitation power, and flow rates of all the process gases. One important parameter is the hydrogen dilution ratio (H2 /SiH4 ), as it is found that a proper hydrogen dilution ratio not only improves the a-Si:H quality but also reduces the lightinduced degradation [12]. In addition, new alloy and nanocrystalline materials, both with different bandgaps, were developed to match the solar spectrum using multi-junction cell structures. These materials include hydrogenated amorphous silicon–carbon (a-SiC:H) [13], hydrogenated amorphous silicon–germanium (a-SiGe:H) [14], and hydrogenated nanocrystalline silicon (nc-Si:H) [15]. Furthermore, new deposition methods have been invented to improve the thinfilm silicon material quality and device performance, including hot wire chemical deposition [16], very high frequency (VHF) PECVD [17], microwave PECVD [18], among others. High material quality is a required but not sufficient condition for high-efficiency solar cells. The device design and structure also determine the device performance. The major difference in structure between the a-Si:H-based thin-film solar cell and the crystal silicon (c-Si) wafer solar cell is that the a-Si:H cell uses a p-i-n or n-i-p structure [19], whereas the c-Si cell uses a p-n or n-p structure. Here p, i, and n represent the p-type, intrinsic, and n-type materials, respectively. The two major reasons for the different device structures are (i) the much lower carrier mobility in a-Si:H than in c-Si and (ii) the much higher defect density in doped a-Si:H than in intrinsic a-Si:H. When a p-type a-Si:H layer is deposited directly on an n-type a-Si:H layer, they do not form a good diode and cannot perform well as a solar cell. When intrinsic a-Si:H with the proper thickness is inserted between the n and p layers, however, a built-in potential forms due to the difference of the Fermi levels between the two doped layers. As a result, a built-in electric field is created across the i-layer, and the electrons and holes photogenerated there are separated by the built-in field to form a photocurrent through the device. In addition, multi-junction p-i-n or n-i-p solar cell structures can also increase the solar cell efficiency remarkably by utilizing the

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solar spectrum properly and incorporating thinner absorber layers to reduce the light-induced degradation [3, 4, 20, 21]. The initial applications of a-Si:H solar cells were in consumer electronics such as watches, calculators, and various chargers. With the improvement of cell efficiency and the development of largearea deposition systems with low materials usage, it was expected that a-Si:H-based thin-film solar cells would be established as one of the important technologies among those of the so-called secondgeneration solar cells. As a result, many large volume a-Si:H-based thin-film silicon solar panel manufacturing lines were built in the 1990s and 2000s [22–24]. These lines produced a large quantity of thin-film silicon solar panels for PV solar power stations and distributed individual solar power installations, especially building integrated photovoltaic (BIPV) systems. However, with the dramatic drop in the prices of c-Si solar modules and the continued technology improvement of c-Si solar panel manufacturing, c-Si solar modules have become much less expensive than the a-Si:H solar panels. As a result, the a-Si:H-based thin-film solar business has contracted significantly and few, if any, a-Si:H PV companies have survived to this date. Although a-Si:H thin-film PV technology has the disadvantages of lower cell efficiency and higher manufacturing cost than c-Si solar cell technology and a-Si:H solar panels are no longer competitive with their c-Si counterparts, a-Si:H has found several new applications as one or more of the components in c-Si solar cells. Two major advanced c-Si solar cell technologies have both used a-Si:H components. The c-Si heterojunction solar cells with intrinsic thin (HIT) a-Si:H passivation layers have demonstrated significant advantages of higher efficiency with higher open-circuit voltage (Voc ), lower temperature coefficient, and higher bifacial rate than conventional c-Si solar cells [25, 26]. Another high-efficiency c-Si cell structure uses a tunnel oxide passivation contact (TOPCon) to passivate the rear surface. This TOPCon structure is formed by an ultrathin silicon oxide (SiOx ) and a highly doped polysilicon (poly-Si) layer, whereby the doped poly-Si is normally formed by the crystallization of an a-Si:H layer [27, 28]. The TOPCon solar cells not only have

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high-efficiency potential in solar modules, but also can be made using standard c-Si solar cell production lines with minimum retrofit. Therefore, TOPCon technology has been proposed as the next generation c-Si solar cell technology in large-scale manufacturing beyond the current mainstream passivated emitter rear cell (PERC) technology. This chapter first presents the operational principle of thin-film silicon solar cells with an emphasis on the differences from c-Si solar cells, then describes various technical approaches for improving the cell efficiency, and finally provides a perspective on a-Si:H applications in high-efficiency c-Si solar cells. As noted previously, although the thin-film silicon absorber as a PV technology sector has become part of the history of the a-Si:H field, the knowledge gained during the development of this technology remains valuable. Because I had been involved in thin-film silicon solar cell optimization over a long period of time, I would like very much to share my learning and experiences in an easily understood way, and as a result hope they are helpful to the readers, especially graduate students and young researchers.

9.2. Principle and Characteristics of the Thin-Film Silicon Solar Cell In general, a solar cell is a device converting the energy of sunlight into electrical energy. The device is normally made from a semiconductor p–n junction or so-called photodiode as shown in Fig. 9.1(a). For a c-Si solar cell with a p-type c-Si wafer and a thin n-type emitter, the sunlight illuminates the solar cell through the n-layer, penetrating well into the bulk of the p-layer, and is absorbed there to generate electron–hole pairs. The p–n junction forms a potential in the junction region, which drives electrons toward the n-layer and repels holes back to the p layer. Under continued illumination, the photogenerated electrons diffuse into the junction region and are driven to the n-layer and holes diffuse to the back contact. When the solar cell top contact on the n-layer and the back contact on the p-layer are connected to one another by an external

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(a)

(b)

Fig. 9.1. (a) The band diagram of a p-type crystalline silicon (c-Si) solar cell and (b) a schematic of the I-V characteristic to illustrate the definition of the solar cell performance parameters.

conductor, the electrons and holes form a current, which is called the short circuit current (Isc ) and the current density is called the short circuit current density (Jsc ). When no connection is made between the front and back contacts, separated photogenerated electrons and holes accumulate on the front and back contacts, respectively, and a voltage and electric field are generated. The photogenerated electric field across the device is in the direction opposite to the built-in electric field formed by the p–n junction, opposing further flow of photoelectrons toward the n-layer and photoholes toward the p-layer. Consequently, the photocurrent is reduced. When a steady state is reached, no net current flows in the device and a fixed voltage has built up between the front and back contacts, which is called the open-circuit voltage (Voc ). When the front and back contacts are connected through a load resistor, the photocurrent flows through the load and dissipates power within it. In this case, the voltage (V ) between the front and back electrodes is smaller than Voc and the current (I) through the load is smaller than Isc . The power dropped on the load is IV . It is clear that the output power is zero under the open- and short-circuit conditions, varies as the load changes, and reaches a maximum at a given load as shown in Fig. 9.1(b). The solar cell efficiency is defined as the ratio of maximum output power (Pmax ) to the input light power (PLight ), and the corresponding voltage and current at the maximum power are denoted as Vmax and Imax (or Jmax for the current density). With these definitions, the

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efficiency (Eff) is defined as follows: Eff =

Vmax × Jmax Jsc × Voc × FF Pmax = = . PLight PLight PLight

(9.1)

Another characteristic parameter for a solar cell is the ratio of Pmax to the product of Jsc and Voc , which is defined as the fill factor (FF) given by FF =

Jmax × Vmax Pmax = , Jsc × Voc Jsc × Voc

(9.2)

and geometrically defined by the rectangle in Fig. 9.1(b). The solar cell efficiency depends on the illumination conditions such as the light intensity and spectrum as well as on the measurement environment such as the temperature. Normally, without specification, solar cell efficiency is characterized under the so-called standard test condition (STC), which uses the AM1.5 solar spectrum and 100 mW/cm2 at 25◦ C. Under the STC, Eff has the same value as Pmax in mW/cm2 and can be written as Eff = Jsc × Voc × FF. Therefore, Jsc , Voc , and FF are the three factors determining solar cell efficiency. Another two parameters as shown in Fig. 9.1(b) are the slopes of the J-V curve under the short-circuit and open-circuit conditions, which are defined as the shunt (Rsh ) and series (Rs ) resistances, respectively. Rsh and Rs directly affect the solar cell efficiency through their influences on the FF. A high-efficiency solar cell should have a high Rsh and a low Rs , and correspondingly a high FF. The values of Rsh and Rs are determined by the material quality and device structure as well as by the external elements such as metal contacts (grids and bus-bar) and measurement circuits. 9.2.1. Drift versus Diffusion Transport In comparison with the conventional c-Si solar cell, the thin-film silicon solar cell has a very different structure. Figure 9.2 shows schematic band diagrams of an a-Si:H solar cell [29]. As shown in Fig. 9.1, a c-Si solar cell is normally fabricated with a p-type c-Si wafer, although an n-type wafer has become popular for higher

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(a)

(b)

Fig. 9.2. Band diagram of the hydrogenated amorphous silicon (a-Si:H) solar cell (a) under short-circuit and near-dark conditions and (b) under illumination and open-circuit conditions [29].

efficiency in recent years. The working principle of the c-Si solar cell has been described above. The main physical properties of c-Si that ensure an efficient solar cell are the high carrier mobility and long lifetime, which leads to a long diffusion length. For a high quality c-Si wafer, the diffusion length is normally much greater than the thickness of the wafer, which allows most of the photogenerated electrons to diffuse into the junction region and be collected by the external circuit. In contrast, the carrier mobility and lifetime are much lower in a-Si:H than in c-Si. For example, the electron mobility and hole mobility in high quality a-Si:H are normally on the order of 1 cm2 /V.s and 10−2 cm2 /V.s [19, 29], respectively, and their values decrease significantly with an increase of the doping level. Consequently, the diffusion length in doped a-Si:H is much shorter than the thickness required to absorb the sunlight effectively. Therefore, directly depositing an a-Si:H n-layer on an a-Si:H p-layer cannot result in a working solar cell. To overcome this issue, an intrinsic a-Si:H layer is normally inserted between the n-layer and the p-layer as shown in Fig. 9.2(a). The working principle of the a-Si:H solar cell is well described by Deng and Schiff [29]. First, the n and p layers are normally very thin

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because the light absorbed in the doped layers does not contribute to the photocurrent. The optimized doped layers should be thick enough to ensure formation of a high built-in potential but as thin as possible to reduce their light absorption. To satisfy these two conditions, the doped layers are deposited in the range of 10–30 nm, depending on the junction structure such as p-i-n or n-i-p. Second, the intrinsic a-Si:H is the main absorber layer across which the built-in electric field forms. The light absorbed in this layer generates electron–hole pairs, and due to the built-in electric field, the electrons drift to the n-layer and holes to the p-layer resulting in a photocurrent. Therefore, the carrier transport in such a p-i-n structure is different from that of a conventional p–n junction. The carrier transport in the conventional p–n junction is through diffusion, whereas it is through drift under the electric field in the p-i-n structure of a thin-film silicon solar cell. The principle for optimizing the i-layer thickness is by considering the two factors of absorption and recombination. In order to ensure sufficient absorption to generate a high photocurrent density, a thick i-layer is needed. On the other hand, a thick i-layer leads to a long distance for carriers to travel before reaching the doped layers and a thick i-layer also reduces the built-in electric field and the speed of carrier transport. A detailed theoretical analysis of the thickness dependence of a-Si:H solar cell performance was given by Schiff [19]. His calculations showed that Voc has very little thickness dependence, Jsc increases with the thickness initially and then saturates near 300 nm, but the FF decreases with thickness continuously. Combining all three factors together, the efficiency initially increases with i-layer thickness and saturates at a specific thickness, whereas it may subsequently decrease with a further increase in i-layer thickness particularly when the density of defect states is high such as in the stable degraded state. In consideration of the two opposing effects of thickness on Jsc and FF, an optimization of the i-layer thickness should be carried out experimentally. This is accomplished by varying the i-layer thickness in order to achieve the highest efficiency, especially the highest stable efficiency for real world applications. As a guideline for such optimization, a parameter called the drift length (Ld ) is defined as

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follows: Ld =

μd τr Vb , d

(9.3)

where μd is the carrier (presumably hole) drift mobility, τr the recombination lifetime, Vb the built-in potential, and d the thickness of the i-layer. The product μd τr is a measure of the i-layer quality, and the ratio Vb /d is the built-in electric field, the driving force for photogenerated carriers to drift toward the respective contacts. Crandall [30, 31] has made a simple analysis to estimate the photocurrent as a function of the i-layer thickness with the following equation:    d , (9.4) Jphoto = qGLd 1 − exp − Ld where q is the unit charge and G is the assumed uniform generation rate. It is clear that a higher μd τr is a characteristic of an improved quality i-layer material for higher solar cell efficiency. It implies that for a high quality i-layer, a larger thickness could be used for high photocurrent density without noticeable losses in Voc and FF. Because electrons and holes have very different mobility values as given previously, the low hole mobility is the limiting factor for a-Si:H solar cells, rather than the electron mobility which is much higher. As described in previous chapters, the hole mobility depends on the valence band tails. A narrow valence band tail distribution gives a high hole drift mobility, hence a high solar cell efficiency. The second material quality parameter is the recombination lifetime, which is inversely proportional to the deep defect density. Therefore, a low deep defect density is another factor that contributes to a high solar cell efficiency. 9.2.2. p-i-n versus n-i-p Structures in a-Si:H-Based Solar Cells Depending on the deposition sequence, two structures have been used in a-Si:H-based solar cells, namely the p-i-n and n-i-p structures as shown in Fig. 9.3. They are named according to the sequence

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Fig. 9.3. Schematic cross sectional diagrams of (a) p-i-n and (b) n-i-p thin-film silicon solar cells.

of silicon layer deposition. As discussed previously, the hole drift mobility is much lower than the electron drift mobility, and as a result, the photogenerated holes travel much more slowly than photogenerated electrons. Therefore, the solar cell design should ensure that the photogenerated electron–hole pairs are closest to the p-layer rather than the n-layer, such that the holes travel a shorter distance than the electrons. For this purpose, the a-Si:Hbased solar cell should always be designed with the light incident on the p-layer first with the n-layer at the back contact. This results in an absorption profile in the i-layer with the maximum at the p/i interface and decreasing with distance from the p/i interface toward the bulk of the i-layer. This is another critical principle for a-Si:H solar cell design, in addition to the incorporation of the i-layer to form p-i-n or n-i-p structures. The p-i-n structured a-Si:H solar cells are deposited on transparent substrates (also called superstrates to contrast them to the

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substrates of the n-i-p structure). The substrates can be glass or a transparent polymer. In order to generate a front electrode for collecting the photocurrent, a transparent conductive oxide (TCO) is coated on the substrate. The commonly used TCOs include fluorine doped tin oxide (FTO), aluminum doped zinc oxide (AZO), boron doped zinc oxide (BZO), and indium tin oxide (ITO). ITO was used in the early days of the field, but it was soon found that indium could undergo a deoxidization reaction. Atomic hydrogen generated in the plasma leads to an ITO change from colorless to yellowish and consequently results in a reduction of the photocurrent density. Therefore, if one uses ITO as the substrate coating for p-i-n solar cells, one must avoid a high hydrogen dilution p-layer deposition, or instead cap the ITO with a hydrogen plasma resistant layer such as AZO or BZO. The first semiconductor layer on the TCO is the p-layer. The simplest form of p-layer is B-doped a-Si:H (denoted as p-a-Si:H), which can be made by adding a B-containing gas to the plasma such as B2 H6 , BF3 , or B(CH3 )3 (the latter called TMB). B2 H6 gas was widely used in the early days, but it was found to be unstable over time. Therefore, BF3 and TMB have been used in later more advanced a-Si:H solar cells, especially in large volume production lines. Because the p-layer is the first semiconductor layer encountered by the light passing into the cell and the absorption in the p-layer does not contribute to the photocurrent, reducing the absorption in the p-layer is an effective approach for improving the solar cell efficiency. For this purpose, wide bandgap or low short wavelength absorption materials are used, such as B-doped a-SiC:H [32, 33], hydrogenated nanocrystalline silicon carbide (p-ncSiCx :H) [34], silicon rich hydrogenated nanocrystalline silicon oxide (p-nc-SiOx :H) [35], and even hydrogenated nanocrystalline silicon (p-nc-Si:H) [36]. Note that the bandgaps of nc-Si:H, nc-SiOx :H, and nc-SiCx :H are complicated parameters because of the two-phase nature of the material structure. Even though the electronic bandgap in the crystalline phase may be similar to that in c-Si, the indirect nature of the bandgap transitions in the crystalline phase ensures low absorption in nc-Si:H in the short wavelength region [37].

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On top of the p-layer, an intrinsic layer (undoped layer or socalled i-layer) is deposited. Depending on the application, the i-layer may be a-Si:H, nc-Si:H, or an alloy of Si with C, O, or Ge. The thickness of the i-layer is a critical parameter for optimizing solar cell efficiency as discussed above [30, 31]. A thin i-layer may not absorb sufficient sunlight for a high Jsc , but an overly thick i-layer could cause poor carrier collection and consequently a poor FF. The n-layer is deposited on the i-layer to form the complete p-i-n structure. The principle for optimizing the n-layer is the same as that for the p-layer. The n-layer thickness should be small enough for low absorption but large enough to form a high built-in potential. Because the back metal contact is directly deposited on the n-layer, the n-layer is normally slightly thicker than the p-layer in order to prevent metal diffusion and avoid a non-Ohmic contact between the n-layer and metal layer, which affects the cell performance. The simple back electrode is a metal layer, which performs the two functions of collecting photogenerated electrons to form a current and reflecting the light reaching the back electrode for possible multiple path absorption. Therefore, the back electrode is also called a back reflector (BR). The BR is a critical element for light trapping. The ideal metal for the back contact is Ag because of its highest conductivity and highest reflectivity. However, Ag is an expensive metal and exhibits some degree of migration in silicon. As a result, it is used primarily in research laboratories whereas Al is used in thin-film solar module production. The back electrode could also consist of a thick TCO, a TCO/white-paint structure, or a TCO/metal bilayer. One could make semitransparent bifacial thin-film solar cells by using a TCO back contact, or one could cover the rear TCO with white paint to form the BR for high Jsc . A TCO/metal BR has the additional function of shifting the plasmonic resonance absorption to short wavelengths and increasing Jsc . Details about the light-trapping mechanisms will be discussed later. In contrast to the p-i-n structured thin-film solar cells, the n-i-p structured cells are normally made on non-transparent substrates such as stainless steel (SS) foil, aluminum foil, or polymer for

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flexible solar panels [3, 4]. In this configuration, a bilayer structure of metal/dielectric is first deposited on to the substrate to form a BR. The commonly used metals are Ag and Al, and once again Ag is used in research laboratories for high efficiency, and Al in solar panel manufacturing for low cost and high reliability. The commonly used dielectric layer is ZnO, which performs the two functions of blocking metal migration into the silicon layer and shifting the plasmonic resonance absorption to short wavelengths. Both the metal and dielectric layers should be fabricated with specific textures for effective light trapping. The deposition sequence of the n-i-p solar cell is just opposite to that of the p-i-n cell, with the n-layer deposited first and the p-layer last. The top TCO needs a highly conductive layer because the current flows horizontally to the metal grids and the thickness of the TCO must be designed for an anti-reflection effect to increase the light coupling into the solar cell. Since the peak output of the solar spectrum appears near 550–600 nm, the designed minimum in reflection due to the destructive interference of the incoming and outgoing waves should be located near these wavelengths. Normally the wavelength of 550 nm is selected in the expression for the top TCO thickness (d), which is given by d = λ/4n with n as the refractive index of the TCO. For most TCOs, n ≈ 2, and therefore the optimized TCO thickness is designed as ∼70 nm. With such a thin layer, high conductivity of the TCO is critical for high solar cell efficiency. For satisfying this requirement, ITO is normally selected as the top TCO layer in n-i-p structured solar cells. Although FZO, AZO, and BZO are used in p-i-n structured solar cells, where the TCO thickness is much larger than that used in n-i-p solar cells, these materials have not been successfully used to date as the top TCO in n-i-p structured solar cells. Even with ITO as the top transparent contact, metal grids are still needed for high-efficiency solar cells. Grids of Ag evaporated through a shadow mask are widely used in research laboratories for high efficiency, but carbon coated Cu wires are thermally attached to the ITO on commercial flexible thin-film solar cell products as will be described later.

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9.3. Optimization of High-Efficiency Thin-Film Silicon Solar Cells The optimization of solar cell efficiency is a complicated systematic process, involving aspects of the material quality of each layer and the overall cell structure. Specifically for thin-film silicon solar cells, not only are the intrinsic and doped silicon layers important for optimization of the cell efficiency, but the contact layers are important as well. In addition, the interfaces between the layers, such as the p/i and i/n interfaces, also play an important role. The non-silicon contact layers must provide low contact resistivity for low electrical losses, and low absorption for low optical losses, especially for the TCO top contact. Below I will discuss some aspects of the thin-film silicon solar cell optimization. 9.3.1. a-Si:H Solar Cells The basic structure of thin-film silicon solar cells is exemplified by the single-junction a-Si:H solar cell whose i-layer is made with an undoped a-Si:H layer. Although all elements of the structure must be optimized for high-efficiency solar cells, the a-Si:H i-layer quality is the dominant factor controlling cell performance. The a-Si:H quality depends on the deposition process such as the substrate temperature, excitation power (RF, VHF, or microwave), pressure, and ratio of H2 to SiH4 (dilution ratio). I will use this simple cell structure to discuss various principles of the deposition process and cell structure optimizations. First, the discussion will focus on the optimization of substrate temperature. Fundamentally, two factors should be considered for substrate temperature optimization: the kinetic energy of diffusing radicals on the film growth surface and the hydrogen incorporation into the film material. On the one hand, a higher substrate temperature increases the diffusion length of reactive species on the growth surface allowing the species to find lower energy sites, forming a compact structure, and reducing the disorder in the material; on the other hand, a higher substrate temperature reduces the amount of hydrogen incorporated in the material, which is a key

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parameter for optimization of silicon dangling bond passivation and generation of a low defect density. The balance of the two competing processes leads to the optimized substrate temperature, which has been experimentally determined to be in the range from 200◦ C to 300◦ C, depending on the other process parameters. Logically, a lower deposition rate allows a lower optimized substrate temperature because the radicals on the growth surface have a longer time to diffuse and relax before being buried within the growing film. The growth rate depends on other parameters, especially the excitation power and the hydrogen dilution ratio. The excitation power should be optimized based on the requirements of deposition rate. Generally speaking, a lower deposition rate with a lower excitation power gives a higher film quality because of the longer relaxation time of incoming species on the growth surface and the weaker bombardment of the surface. Of course, the lowest excitation power used in the thin-film silicon film deposition should be higher than the threshold for maintaining a stable plasma under the given conditions. Experimentally, the best a-Si:H solar cells using RF PECVD are deposited at a deposition rate at or lower than 0.1 nm/s, whereas a-Si:H solar cells from production lines are normally made at a deposition rate higher than 0.3 nm/s because of manufacturing efficiency and cost-effectiveness considerations. Plasma physics shows that the ion bombardment energy can be reduced and the ion flux can be increased by increasing the excitation frequency. Therefore, increasing the excitation frequency allows use of a high excitation power for increasing the deposition rate without a noticeable increase in the defect density and decrease in solar cell efficiency. For this advantage, VHF (65 MHz) PECVD has been used for high rate a-Si:H solar cells with high efficiency at ∼1.0 nm/s [38], and microwave (2.4 GHz) PECVD has been used at ∼3.0 nm/s [18, 39]. The process pressure also must be optimized. The guidelines for pressure optimization are (i) maintaining a stable plasma under low excitation power, (ii) ensuring a reasonable deposition rate, and (iii) minimizing powder formation in the plasma. The minimum power (Pmin ) to maintain a stable plasma follows Paschen’s law

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Fig. 9.4. Schematic of the deposition rate as a function of pressure in plasmaenhanced chemical vapor deposition (PECVD) processes.

(Pmin ∝ pd, where p is the pressure and d the distance between the cathode and anode) [40]. This law shows that a low pressure is needed for a parallel plate PECVD system with a wide gap between the two electrodes, whereas a high pressure is possible with a narrow gap. Conventional PECVD systems are normally designed with a gap of a few centimeters for a deposition pressure in the range of 1–2 Torr. The deposition rate depends on the process pressure as sketched in Fig. 9.4. This figure shows that the deposition rate is very low in the low pressure regime (the γ regime), increases sharply with the increase of pressure at medium range pressures (the transition regime), and saturates with a slight decrease in the high pressure regime (the α regime). In the γ regime, the low deposition rate results from the low density plasma, in which the mean free path of the ionized species is comparable or longer than the gap width. As a result, these species have a low probability of collision with one another and so do not form large particles. Therefore, the process in this regime is clean. However, the low collision probability leads to ionized species that are accelerated fully by the electric field in the plasma sheath, gain high energies, bombard the growth surface, and as a result cause a high defect density in the film. Therefore, the materials deposited in the γ regime normally have a compact structure but with an elevated level of defect states. In contrast, in the α regime, the deposition

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rate is high because of the high density of the plasma. As a result, the mean free path is reduced to a value shorter than the width of the gap or even the plasma sheath, within which the ionized species have a high probability for collision. The charged species collide with one another in the plasma and form large particles, which have two negative effects on the film quality and system reproducibility. First, the incorporation of large particles within the film leads to a less compact structure with more di-hydrides or multi-hydrides, which degrade the material quality and stability; and second, the accumulation of large particles in the plasma results in powders and leads to the requirement of frequent system cleaning, which reduces the uptime of production lines. From this discussion, it appears that optimization of pressure is a process involving a balance between the extremes of low deposition rate with ion bombardment at the low pressure and high deposition rate with powder formation at the high pressure. With this understanding in mind, use of a narrow gap between the cathode and anode has been proposed, which reduces the travel distance of ionized species before reaching the substrate, or allows use of a relatively high pressure and high excitation power to increase the deposition rate but without a significant increase of ion bombardment and powder formation [41, 42]. This technique is very important in nc-Si:H (or μc-Si:H) solar cell deposition, whereby the i-layer is much thicker than the i-layer in a-Si:H solar cells [17, 43]. The hydrogen dilution level is another very important process parameter determining the quality of deposited films and the solar cell performance. Hydrogen dilution affects the film microstructure. From a plasma physics point of view, hydrogen dilution has two major effects. First, a high hydrogen dilution ratio reduces the collision probability of Si containing radicals such as SiH3 and SiH2 , suppressing large particle formation, and allows use of a high process pressure to reduce high energy ion bombardment; second, the ionized atomic hydrogen impinges on the growth surface and transfers energy to this surface. As a consequence, the network of the resulting film is heated and the diffusion coefficient of Si containing radicals on the growth surface is enhanced. Reduced bombardment and enhanced

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diffusion are both beneficial for improving the microscopic ordering (both short and medium range) of the deposited film. Therefore, the ordering is improved with the increase of hydrogen dilution in the a-Si:H deposition regime, and a high hydrogen dilution ratio is the most influential factor that drives the transition from a-Si:H to nc-Si:H deposition. It has been found that the best a-Si:H films are deposited just on the edge of the transition from a-Si:H to nc-Si:H but on the a-Si:H side; therefore, this type of a-Si:H is called “edge material” [44]. Raman spectroscopy studies have shown that the TO mode of the Si Raman peak shifts to the high energy side and a small shoulder appears on the high energy side as well [44]. Additional changes in other modes are also observed with the increase in structural ordering, but finally disappear when the material becomes fully crystalline because of the momentum selection rules in the crystalline phase. High resolution transmission electron microscopy images reveal isolated nanometer size grains embedded in the a-Si:H matrix; therefore, this type of material is also named “proto-crystalline” silicon or pc-Si:H [45, 46]. Solar cells made with the high hydrogen dilution a-Si:H exhibit much better performance with higher Voc and FF than those with zero or low hydrogen dilution a-Si:H. Above, the guidelines for a-Si:H solar cell optimization have been presented from a plasma process point of view. As discussed previously, the cell structure such as the thicknesses of all layers is also very important for solar cell performance optimization. Next, two additional factors will be discussed, the composition and microstructure of the doped layers and the interface between the doped layers and the intrinsic layer. The Fermi level difference between the doped layers (p- and n-layers) provides the upper limit of the built-in potential, hence the Voc . In addition, the bandgap of the doped layers affects not only Voc but also Jsc because the charge carriers generated by absorption in the doped layers do not contribute to the photocurrent. Therefore, the guidelines in the search for doped layer materials include a wide bandgap and a high effective doping level. In early solar cell development, B-doped and P-doped a-Si:H layers were used

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as the p- and n-layers, respectively. Two major limiting factors exist for B- and P-doped a-Si:H for high-efficiency solar cells. First, the doping efficiency is proportional to the square-root of the atomic concentration in the materials and is very low in a-Si:H, and second, the Fermi levels cannot move very close to the conduction band and valence band edges. For the P-doped a-Si:H, the activation energy is normally near 0.2 eV and for B-doping it is near 0.5 eV, values limited by the band tails below the conduction band edge and above the valence band edge, respectively. Therefore, the maximum built-in potential is limited to approximately 1.0–1.1 eV. In addition, the incorporation of B in a-Si:H narrows the bandgap, which reduces the built-in potential further. Because the sunlight illuminates the solar cell through the p-layer, the properties of the p-layer are dominating factors for solar cell efficiency. In order to resolve the bandgap issue, wide bandgap amorphous silicon alloys have been developed. The well-studied one is B-doped a-SiC:H, for which the bandgap increases with the C content in the material. Using B-doped a-SiC:H [32, 33], Voc and Jsc are indeed increased noticeably. In addition, B- and P-doped nc-Si:H alloyed layers are also widely used in advanced a-Si:H solar cells [34]. In these layers, the band tail distribution is very narrow and the doping efficiency is significantly improved in the crystalline phase, and therefore, Voc is improved remarkably. Furthermore, the high hydrogen incorporation in the amorphous phase and the indirect bandgap nature in the crystalline phase of nc-Si:H result in only very low short wavelength absorption in B-doped nc-Si:H. Effectively, B-doped nc-Si:H can be used as a wide bandgap window layer, which improves Jsc as well. One can also alloy the doped nc-Si:H with C and O to reduce the short wavelength absorption further and improve the cell efficiency [34, 35]. Therefore, the modern advanced a-Si:H solar cells are fabricated with nc-Si:H alloy-based doped layers. When a doped layer is in contact with the intrinsic layer, the interface is very important in consideration of the following aspects: (i) the bandgap continuity, (ii) the interface defect states, and (iii) the dopant distribution. Here, two examples are given. First, B-doped a-SiCx :H is used as the p-layer in a-Si:H solar cells because the

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bandgap of a-SiCx :H is normally wider than that of a-Si:H. For this player, an intrinsic a-SiCx :H buffer layer with a graded C concentration improves the solar cell performance. The desired a-SiCx :H buffer layer has a high C content near the p-layer and low C content near the i-layer. This graded C concentration results in bandgap grading, which avoids a sharp bandgap discontinuity and reduces the density of interface defect states [32, 33]. Second, when doped nc-Si:H layers are used, special care concerning the interface is also needed. An example is the p-type nc-Si:H layer used in solar cells of the n-i-p configuration, in which case the p-layer is deposited directly on the a-Si:H i-layer. It has been found that the crystalline phase formation depends on the nature of the underlying layer, and an amorphous incubation layer is formed before crystalline phase formation. The amorphous incubation layer usually has a poor quality and affects the cell performance. To avoid this layer, a hydrogen plasma treatment is used, which may result in small crystalline seeds for promotion of crystallite nucleation in the following doped layer deposition. A proper hydrogen treatment improves the solar cell performance effectively. In a summary of the strategies applied for a-Si:H solar cell optimization, I would conclude that the material quality must be optimized by tuning the plasma conditions based on the guidelines from plasma physics and chemistry with special attention to ion bombardment and powder formation under the requirement of a given deposition rate. High quality a-Si:H materials are normally made at 200◦ C–250◦ C substrate temperature, under 1.0–2.0 Torr process pressure, low RF power while keeping a stable plasma, and high hydrogen dilution to keep the material near the amorphous/nanocrystalline transition but on the amorphous side. Wide bandgap doped layers with a high doping efficiency are critical with a proper buffer or hydrogen plasma treatment between the doped and intrinsic layers. 9.3.2. a-SiGe:H Solar Cells The optical bandgap of a-Si:H is in the range of 1.70–1.85 eV, depending on the hydrogen content. With a higher hydrogen content,

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the bandgap widens slightly; however, a narrower bandgap is desired for two reasons. First of all, the bandgap of a-Si:H is much wider than the ideal bandgap for high-efficiency solar cells, which is near 1.35 eV. Second, because a-Si:H materials are relatively defective with low carrier mobility–lifetime product, it is difficult to use a thick absorber for sufficient light absorption and high current. One of the solutions to these issues is to alloy silicon with germanium (Ge) resulting in a-SiGe:H. Alloying with Ge is used because Ge is the element just below Si in the same column of the periodical table, forms the same tetrahedral crystalline structure as c-Si, and has a narrower bandgap than c-Si in the crystalline phase. The bandgap of a-SiGe:H can be tuned over a wide range by varying the Ge/Si ratio through adjustment of the GeH4 and SiH4 flow rates in the PECVD process [47]. However, because the Ge–H chemical bond is much weaker than the Si–H bond, incorporating Ge in a-Si:H increases the density of dangling bond defects and also the band tail width. Especially the conduction band tail width increases, which degrades the material quality [48, 49]. Therefore, one can only use low Ge content a-SiGe:H materials in solar cells. The main application of a-SiGe:H is as the bottom and middle cells in a-SiGe:H/a-Si:H double-junction and a-SiGe:H/a-SiGe:H/ a-Si:H triple-junction solar cells [3, 50]. In these cell structure designations, the deposition sequence progresses from left to right. Thus, these designations represent n-i-p structured solar cells, as an example. For both n-i-p and p-i-n structures, the light illuminates the a-Si:H cell first, which is designated as the “top cell.” The a-SiGe:H bottom cell absorber in the a-SiGe:H/a-Si:H double-junction and the a-SiGe:H middle cell absorber in the a-SiGe:H/a-SiGe:H/a-Si:H triple-junction solar cells are both designed with bandgaps near 1.65 eV, and the a-SiGe:H bottom cell absorber in the triple-junction cell is designed with ∼1.55 eV. The corresponding Ge contents in these two types of solar cells are approximately 15%–20% and 25%– 30%, respectively. The optimization of a-SiGe:H solar cells involves all the aspects discussed for a-Si:H above, but additional attention must be paid to the large bandgap offset at the interface between the a-Si:H doped

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(b)

(c)

(d)

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Fig. 9.5. Schematics of bandgap profiles investigated in hydrogenated amorphous silicon–germanium (a-SiGe:H) solar cells.

layer and the a-SiGe:H intrinsic layer. To avoid the sharp band discontinuity and reduce the defect density, an a-Si:H buffer layer and a bandgap profile by grading the a-SiGe:H are used for improving the cell performance. The function of the a-Si:H buffer layer is to separate the doped layer and the more defective a-SiGe:H to reduce the interface defect density. The design of the bandgap profile in the a-SiGe:H involves a form of scientific art, in consideration of material properties and device physics. Figure 9.5 plots four types of bandgap profiles, where (a) is a flat bandgap across the entire a-SiGe:H i-layer, (b) has a wider bandgap near the front i/p interface and narrower near the back n/i interface, (c) is opposite to (b) being narrower near the i/p interface and wider near the n/i interface, and (d) is a “V” shaped profile with a combination of (b) and (c) but with the decreasing region from the front being much thinner than the increasing region to the back [51, 52]. Note that the interface designations n/i and i/p are again given in order of the n-i-p deposition sequence. From the optical absorption point of view, the profile (b) is the best choice. For this profile, the wider bandgap near the i/p interface absorbs the short wavelength light, and due to the decrease of the

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bandgap with depth, more of the long wavelength light is absorbed deep within the i-layer. As in the case of a-Si:H, however, the hole mobility–lifetime product for a-SiGe:H is also much smaller than the electron mobility–lifetime product, and so the holes have a much shorter collection length. Therefore, from a carrier transport point of view, profile (c) has advantages because the narrower bandgap region near the i/p interface absorbs much more light than the region near the n/i interface. As a result, a high density of photogenerated electron–hole pairs appears near the i/p interface, such that the collected holes are traveling a shorter distance to the p-layer than the electrons are traveling to the n-layer. In addition, the negative slope of the valence band edge produces an extra effective electric field to accelerate the hole transport whereas the positive slope of the conduction band edge decelerates the electron transport. The shorter travel distance for holes and the effective electric field from the bandgap profile partially compensate for the lower mobility–lifetime product of holes and in principle improve the solar cell performance. However, the narrower bandgap near the p/i interface increases the bandgap discontinuity and may lead to a high interface defect density. To resolve this issue, a thin layer of decreasing bandgap with depth is added as shown in (d) that takes advantage of the transport benefits of profile (c). This forms the asymmetric “V” shaped profile with the component adjacent to the p-layer designed to be much thinner than that adjacent to the n-layer. Using this bandgap profiling technique, the a-SiGe:H solar cell efficiency has been improved remarkably as shown in Fig. 9.6, where the left and right plots are the J-V characteristics of the middle bandgap and low bandgap a-SiGe:H solar cells, respectively, used as the middle and bottom cells in the n-i-p structured a-SiGe:H/a-SiGe:H/a-Si:H triple-junction solar cells [3]. 9.3.3. nc-Si:H Solar Cells Hydrogenated nanocrystalline silicon (nc-Si:H), also called microcrystalline silicon (μc-Si:H), was initially used for doped layers in a-Si:H solar cells because of its higher doping efficiency compared to a-Si:H. Thin-film nc-Si:H was not suitable for use as the absorber

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(b)

Fig. 9.6. J-V characteristics of hydrogenated amorphous silicon–germanium (a-SiGe:H) n-i-p solar cells on SS/Ag/ZnO substrates. The left and right plots are the middle and bottom cells, respectively, used in hydrogenated amorphous silicon (a-Si:H) based a-SiGe:H/a-SiGe:H/a-Si:H triple-junction solar cells.

layer because of unintentional doping, which resulted in a high dark conductivity and low photoconductivity. Normally, the as-deposited nc-Si:H even without intentional doping shows n-type transport, which arises from the impurities of oxygen and nitrogen incorporated during deposition. The impurities could be incorporated from the process gases, residual contamination, and air due to vacuum system leakage. Both oxygen and nitrogen form shallow donors in nc-Si:H. The pioneering work of using nc-Si:H as the absorber layer in solar cells was made by the Neuchatel group in the mid-1990s [15, 53]. They used gas purifiers to remove the impurities from the process gases in order to reduce their concentrations in the deposited nc-Si:H. They also used microdoping, that is, adding a small amount of B to compensate the unintentional n-type doping, and as a result made nc-Si:H solar cells with respectable efficiencies. This work sparked great interest in the thin-film solar cell community, and a significant amount of research and development has been undertaken to improve the performance of the nc-Si:H solar cell, especially as the bottom cell in multi-junction solar cells [4–6]. In this section, I will present a few critical aspects required for the optimization of nc-Si:H solar cells. First of all, the i-layer impurity level is the most critical issue for nc-Si:H solar cells. The tolerance for oxygen in nc-Si:H solar cells is

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Fig. 9.7. External quantum efficiency (EQE) comparison of microcrystalline silicon (µc-Si:H) solar cells made with and without a gas purifier in the deposition system [53].

much lower than that in a-Si:H solar cells. Normally, 2−3×1019 cm−3 oxygen is allowed within the i-layer of an a-Si:H solar cell without a noticeable effect on the solar cell performance. This amount results in a significant reduction in the long wavelength response of a nc-Si:H solar cell, however. Figure 9.7 shows an external quantum efficiency (EQE) comparison of nc-Si:H solar cells fabricated with and without the gas purifier. The cell fabricated without the gas purifier has a high oxygen content and shows a collapsed EQE curve at long wavelengths whereas the cell fabricated with the gas purifier shows an enhanced long wavelength response. The reason for a reduced long wavelength response is the n-type doping by the O and N impurities that results in a wide region near the n/i interface having a very weak or even no electric field. Therefore, the photocarriers generated there have a low probability for collection before recombination. In fact, the collapsed EQE curve is an indication of impurity contamination in the i-layer of nc-Si:H solar cells, behavior that could then be used as a monitor for contamination. To resolve the impurity issue, a leak tight vacuum chamber is essential. A careful leak-check of both the deposition chambers and the gas lines should be performed after

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each venting of the system. In addition, a thorough thermal baking is helpful to remove the adsorbed moisture from the chamber walls. Furthermore, high purity gases (6N), especially hydrogen, should be used; otherwise gas purifiers are needed. Experimentally, it has been found that the oxygen tolerance level for nc-Si:H solar cells is approximately 5×1018 cm−3 , which is much lower than that of a-Si:H solar cells [54]. The tolerance for nitrogen is much lower than that for oxygen, and on the order of 1017 cm−3 nitrogen could cause a noticeable reduction in the long wavelength EQE of a nc-Si:H solar cells. Another critical issue in nc-Si:H solar cells is porosity. Microvoids and microcracks occur widely in a-Si:H and nc-Si:H materials, and these have been systematically studied by Williamson using small angle X-ray scattering and small angle neutron scattering [55]. It was found that the microvoid density in nc-Si:H could be much higher than in a-Si:H if the nc-Si:H materials are deposited under conditions that are not optimized. The porosity in nc-Si:H provides channels for the penetration of ambient impurities, presumably moisture and oxygen, into the materials and causing a severe degradation in the cell performance. The result is a collapsed long wavelength EQE, similar to the nc-Si:H cells with high concentrations of oxygen impurities. Figure 9.8 depicts the degradation in the EQE of a nc-Si:H solar cell

(a)

(b)

Fig. 9.8. J-V characteristics and quantum efficiency (EQE) of an unoptimized hydrogenated nanocrystalline silicon (nc-Si:H) solar cell in the initial state and after 30 days exposure to the ambient without intentional light soaking [56].

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stored in the ambient for 30 days without intentional light soaking during this period [56]. This phenomenon was called “ambient degradation,” and the solution required for suppressing it involves optimization of the plasma deposition process. It was found that ncSi:H materials deposited under the high pressure and high power conditions usually have a compact structure with no noticeable ambient degradation [43]. The physics underlying this observation is not clear at least to this author. As presented in Chapter 1, the nc-Si:H structure changes dynamically along the growth direction when the deposition is performed under steady-state conditions. An initial a-Si:H incubation layer forms in the early stage of deposition before individual crystal seeds appear on the surface of the incubation layer. These crystallites grow both vertically and horizontally, forming cone-shaped structures that eventually collide with one another. Without space for continued horizontal growth, finally the crystallites grow only vertically to form large “trunks” of crystallites (i.e., large clusters of smaller nanometer sized grains). This process leads to an increase in crystallinity with the increase in thickness of the film as shown in Fig. 9.9, where

(a)

(b)

Fig. 9.9. (Left) Raman spectrum of a hydrogenated nanocrystalline silicon (nc-Si:H) film with a three component fit after a linear baseline correction; (right) crystalline volume fraction as a function of film thickness.

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the Raman crystalline volume fraction is presented for samples of different thicknesses. The overall phenomenon is called crystalline evolution [57], which has two negative effects on nc-Si:H solar cell performance. First, the initial a-Si:H incubation layer adds an additional series resistance, and the transition zone from amorphous to nanocrystalline phases produces a defective material, which results in a poor FF in the solar cell. Second, high porosity is observed within the crystalline boundaries of the top layer having high crystallinity, especially in the range of thickness after the crystallite trunks have collided with one another (herein called crystalline collision). This porosity allows impurities to diffuse into the layer and causes the ambient degradation as described above. For nc-Si:H solar cell optimization, one must control the crystalline evolution. Hydrogen dilution is the most important parameter determining the material structure, either amorphous or nanocrystalline in nature. In fact, a-Si:H forms with low hydrogen dilution and nc-Si:H with high hydrogen dilution, and thus the crystallinity increases with an increase of hydrogen dilution ratio. As a result, one may logically expect a dynamic adjustment of the hydrogen dilution ratio could effectively control the crystalline evolution. Experimentally, a very high hydrogen dilution ratio could be used in the early stage to deposit an incubation-free initial nc-Si:H layer, usually called a seed layer, and then the hydrogen dilution ratio could be adjusted so that it decreases with time. This would compensate for the crystalline evolution that reflects the nature of steady-state deposition. Using this method, a uniform crystalline structure could be made as shown in Fig. 9.10, where the cross sectional transmission electron microscopy (TEM) image reveals the crystalline structure made under dynamically reduced hydrogen dilution. A uniform crystalline structure is observed in contrast with the conically structured crystalline evolution as shown in Fig. 1.1. The technique of dynamically reducing the hydrogen dilution to control the crystalline evolution is called “hydrogen dilution profiling,” which has been proven to be an effective method for improving nc-Si:H solar cell performance [57, 58]. Table 9.1 lists the performance parameters of a set of nc-Si:H solar cells and shows the

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Fig. 9.10. A cross sectional transmission electron microscopy (TEM) image of a hydrogenated nanocrystalline silicon (nc-Si:H) film deposited with a hydrogen dilution profile, showing a uniform crystalline structure.

Table 9.1. Performance parameters of hydrogenated nanocrystalline silicon (nc-Si:H) solar cells made with various i-layer hydrogen dilution levels, thicknesses, and dilution profiles. Sample # 14554 14568 14596 14559 14562 14578 14580 14612 14619 14642 14660

Fill Factor (FF)

Jsc (mA/cm2 )

Voc (V)

AM1.5

Blue

Red

Efficiency (%)

22.58 22.15 22.05 21.48 21.57 23.22 22.58 24.41 24.63 23.42 25.15

0.495 0.488 0.482 0.482 0.484 0.482 0.484 0.485 0.492 0.502 0.502

0.603 0.599 0.622 0.632 0.652 0.594 0.644 0.616 0.645 0.681 0.663

0.652 0.648 0.656 0.678 0.692 0.646 0.688 0.659 0.683 0.706 0.679

0.615 0.599 0.605 0.637 0.651 0.631 0.662 0.647 0.641 0.700 0.693

6.74 6.48 6.61 6.54 6.81 6.63 7.04 7.29 7.81 8.01 8.37

Comments Flat Baseline

20% thicker than baseline Profiling 1 Profiling 2 Profiling 3 Profiling 4 Profiling 5 Profiling 6

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effectiveness of the hydrogen dilution profile. The cells with constant hydrogen dilution had an average initial active-area efficiency of 6.6%. Increasing the i-layer thickness did not increase Jsc ; instead, it decreased. It was speculated that the additional thickness may lead to top layer porosity that caused ambient degradation. By using the hydrogen dilution profiling method, the cell performance was improved gradually and an efficiency of 8.37% was obtained, which was a respectable result at that time. The hydrogen dilution profiling technique has been widely used in the community for improving μc-Si:H solar cell performance. 9.3.4. Light Management in Thin-Film Silicon Solar Cells Thin-film silicon solar cells are much thinner than c-Si solar cells for the reasons that (i) a-Si:H has a much lower carrier mobility–lifetime product than c-Si and the photocarriers cannot travel long distances in order to be collected; (ii) the light-induced degradation is more pronounced in thicker cells than in thinner ones; and (iii) fabrication of thick a-Si:H solar cells is not cost-effective in manufacturing. A thin a-Si:H intrinsic layer is not able to absorb sufficient photons to generate a high photocurrent density, especially for the long wavelengths where the absorption coefficient is low. To resolve this issue, techniques of light management, also called light trapping, have been widely used. Light trapping generates multiple paths and an increase in the photocurrent density equivalent to light propagation in a thicker absorber. The objective of light trapping is to maximize the effectiveness of light coupling and scattering inside the absorber. The first consideration is to reduce the reflection with various anti-reflection coatings and/or nano/microstructures, and the second is to enhance the scattering at both the front and rear surfaces of the solar cell structure. Depending on the cell structure, different light-trapping approaches have been extensively studied. Below, I will discuss a few light management techniques applied to both p-i-n and n-i-p structured solar cells.

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As presented previously, the p-i-n structured thin-film solar cells are deposited on TCO coated glass substrates. The light first strikes the glass substrate, where a portion (∼4%) of light reflects back due to the refractive index difference between the glass substrate (n ∼ 1.5) and air (n ∼ 1). In order to reduce this reflection loss, a thin dielectric layer with a proper thickness can be coated on the front side of glass, which acts as an anti-reflection coating (ARC). The refractive index of the coating layer should be between the glass and air, which is ideally ∼1.25. The selection of low index materials is very limited. MgF2 is one of the low index materials, and could be used as an ARC, but it has not been widely applied in solar cell production because of cost and reliability issues. One can also use nano/microstructures on the glass substrate, for example, etching the glass to make the top layer with a specific porosity or fabricating a coating layer with nanoparticles such as SiO2 . When the feature sizes of the textured surface layer are similar to or smaller than the range of light wavelengths, the porous layer acts as an index gradient layer whose optical behavior can be described by an effective medium theory. Such a layer is more effective than a single layer ARC. However, textures on glass have two negative effects: they could reduce the strength of the glass, which affects the reliability of the product, and they could trap dust and contaminants, which result in difficulties when cleaning the surface. All such effects must be considered before a technology is used in any solar panel product. Light trapping requires scattering, which is normally accomplished by texturing the TCO coating, including FTO, AZO, or BZO. FTO has been widely used in the early stage of a-Si:H solar cell fabrication in both research laboratories and industrial production of a-Si:H solar panels. Later, AZO and BZO have been developed, especially for the fabrication of nc-Si:H solar cells, since these materials are much more stable than FTO in the hydrogen plasma environment. The AZO can be made using sputtering and the textures can be created either during the deposition at elevated substrate temperatures such as 300◦ C–350◦ C, or during chemical etching by acids such as diluted HCl or HF [59, 60]. The BZO is normally deposited using low pressure chemical vapor deposition

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(b)

Fig. 9.11. A tilt-view scanning electron microscopy (SEM) image and experimentally determined total transmittance and haze spectra of magnetronsputtered and texture-etched aluminum doped zinc oxide (AZO) [59].

(LP-CVD), and the textures form during the deposition. Figure 9.11 shows surface morphologies of sputter deposited AZO after chemical etching as well as the transmittance and haze. The scanning electron microscopy (SEM) image shows crater-like structures, which result in high haze for light trapping. Additional light scattering could also come from the rear side electrode, which is made with a dielectric layer such as ZnO and a metal layer such as Ag. The dielectric layer has two functions, namely reducing the plasmonic absorption of the long wavelength light and blocking metal migration into the semiconductor layers. The light management in n-i-p solar cells is different from that in p-i-n solar cells. As previously discussed, the top TCO is a 75–80 nm thick ITO layer selected for its high conductivity and quarter wavelength ARC effect, but such a thin ITO layer is not suitable for texturing. Therefore, light scattering in n-i-p solar cells mainly relies on the rear electrode, which is the BR with a dielectric layer and a metal layer [61–63]. Light trapping in nc-Si:H is more critical than in a-Si:H and a-SiGe:H because the nc-Si:H is usually used as the bottom cell in multi-junction solar cells. In comparison with a-Si:H, nc-Si:H has a much broader absorption spectrum, extending up to 1100 nm. The absorption coefficient of nc-Si:H remains low in the long wavelength region; however, because of its indirect bandgap nature. Therefore,

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the required nc-Si:H intrinsic layer for absorbing sunlight effectively is much thicker than that of a-Si:H. Even though the carrier mobility in nc-Si:H is higher than in a-Si:H, the absorber layer thickness in the nc-Si:H solar cell still cannot be increased excessively without suffering significant losses in FF and Voc . Considering all performance parameters, the optimized nc-Si:H intrinsic layer thickness has been determined to be in the range of 3–5 μm. In consideration of production efficiency and current matching, the nc-Si:H intrinsic layer should be limited to 2–3 μm for double-junction cells and 3–5 μm for triple-junction solar cells. These thicknesses are still not sufficient to absorb the sunlight needed to generate matching current. As discussed above, light trapping in the n-i-p structured solar cells relies on the BR, which is normally made with an Al/ZnO or Ag/ZnO bilayer. The principle of light trapping in the n-i-p solar cell is shown in Fig. 9.12 (left), and an example of the effectiveness of the Al/ZnO and Ag/ZnO bilayers is shown in Fig. 9.12 (right). Here a comparison of EQE curves is presented for three nc-Si:H solar cells deposited with the same recipe but on different substrates. It is observed that a significant enhancement of the long wavelength response is achieved by light trapping. The nc-Si:H solar cell on the

(a)

(b)

Fig. 9.12. A schematic of light trapping in an n-i-p solar cell and the external quantum efficiency (EQE) curves of three hydrogenated nanocrystalline silicon (nc-Si:H) solar cells deposited with the same recipe but on different substrates [61].

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bare SS has a total photocurrent density of 15.56 mA/cm2 ; the ones on the Al/ZnO and Ag/ZnO BRs have values of 20.48 mA/cm2 and 24.48 mA/cm2 , and their gains are 31.6% and 57.3%, respectively. Figure 9.12 demonstrates that the Al/ZnO and Ag/ZnO are very effective for light trapping in nc-Si:H solar cells. As a result, an effective light-trapping technique has been shown to be a required component of both high-efficiency nc-Si:H solar cells and multijunctions with nc-Si:H as the bottom cell. The design of the BR is a form of technical art. The textures can be made on the metal surface, or on the dielectric layer, or on both. Theoretically, scattering is more effective by textures on the metal layer than by those on the dielectric layer. For the metal layer such as Ag, however, plasmonic absorption in the long wavelength region (800–1000 nm) may occur that could reduce the reflectivity. Although the insertion of ZnO between the Ag and Si layers shifts the plasmonic resonance to the short wavelength region, textured metal remains a concern for reaching a high photocurrent density. Thus, the textures on the dielectric layer are desirable in certain cases. Based on this argument, it has been suggested that flat Ag and highly textured ZnO should be used as a BR. The flat Ag provides the highest reflectivity whereas the large textures on the ZnO scatter the light effectively. This structure has proven to serve as the optimized design for a-SiGe:H solar cells, but it does not work properly for nc-Si:H. In fact, the large textures, especially with sharp peaks and valleys, generate microcracks in the nc-Si:H layers and reduce the nc-Si:H material quality noticeably [64]. Therefore, for nc-Si:H solar cells, the design and optimization of the Ag/ZnO BR must be a compromise between the textures of ZnO and Ag. Experimentally, it was found that textured Ag with a thin ZnO layer (100 nm) is a good choice for the Ag/ZnO BR of nc-Si:H solar cells [61–63]. The textures on the Ag surface are much more effective in scattering light than those on ZnO, and therefore moderate textures on Ag are sufficient to provide the scattering required for favorable light trapping. On the other hand, the thin ZnO layer shifts the plasmonic resonance frequency to the short wavelength region. In this region, the light is absorbed before reaching the back contact.

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(a)

(b)

(c)

Fig. 9.13. Atomic force microscopy (AFM) images of three Ag/ZnO BRs with different Ag textures, (left) low texture with root mean square (RMS) = 17 nm, (center) medium texture with RMS = 40 nm, and (right) high texture with RMS = 118 nm.

(a)

(b)

Fig. 9.14. The (a) total and (b) diffuse reflection spectra of Ag/ZnO back reflectors with various textures as measured by the root mean square (RMS) value from atomic force microscopy (AFM) images [62].

Figure 9.13 shows the surface morphologies of three Ag/ZnO BRs, for which the textures arise mainly from the Ag layer. The ZnO layers are deposited under the same conditions for all samples of Fig. 9.13 with thicknesses of 100 nm [63]. Figure 9.14 includes plots of the total and diffuse reflection spectra of the BRs. The figure shows that the total reflectance spectrum decreases slightly with the increase in Ag texture, which could result from the absorption at the Ag/ZnO interface and light trapping in the ZnO layer because the refractive indices of ZnO are larger than that of air. However, the diffuse reflectance spectra are very different with different Ag

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textures. A significant increase in the diffuse reflectance is observed with the increase in Ag texture, implying a potential enhancement of light trapping. The same recipe nc-Si:H solar cells with 1 μm thick nc-Si:H intrinsic layers were deposited on Ag/ZnO BR coated SS substrates of this type but with different textures for the Ag layers. The EQE curves of four selected nc-Si:H solar cells are plotted in Fig. 9.15 and the cell performance parameters are listed in Table 9.2. It can be noted that the solar cells on the Ag/ZnO BR have a significantly higher response in the long wavelength region than that on the bare SS, and these results again demonstrate the effectiveness of the light trapping. The solar cell on the BR with RMS = 17 nm shows strong interference fringes, indicating significant direct reflection, whereas the interference fringes are reduced with the increase of the texture, indicating enhancement of scattering. The solar cell on the SS has a Jsc value of only 15.12 mA/cm2 , whereas the one on the Ag/ZnO BR with RMS = 40 nm has a Jsc value of 25.03 mA/cm2 ; a gain of 66% is observed. It is also found that increasing the texture further (with RMS > 40 nm) does not continue to increase the spectral response even though the diffuse reflection is enhanced. Instead, the

Fig. 9.15. External quantum efficiency (EQE) spectra of hydrogenated nanocrystalline silicon (nc-Si:H) solar cells made with the same recipe but on different Ag/ZnO BRs. The nc-Si:H intrinsic layer is 1 µm.

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Fill factor (FF)

A 17.0

Color >610 nm AM1.5

0.515 0.530

0.738 0.723

B 40.0

Color >610 nm AM1.5

0.522 0.541

0.726 0.711

C 91.7

Color >610 nm AM1.5

0.519 0.537

0.717 0.702

FFb

FFr

0.722

0.720

0.716

0.703

Pmax (mW/cm2 ) ΔQE (%)

QE(0V) (mA/cm2 )

QE(−3V) (mA/cm2 )

11.61 22.43

11.69 22.55

4.41 8.59

0.7 0.5

13.86 24.62

14.16 25.03

5.25 9.47

2.1 1.6

13.59 24.30

14.06 24.98

5.06 9.16

3.3 2.7

0.72

0.704

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Table 9.2. The J-V characteristics of hydrogenated nanocrystalline silicon (nc-Si:H) solar cells made with the same recipe but on different Ag/ZnO BRs. The nc-Si:H intrinsic layer is 1 µm in thickness.

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photocurrent density decreases slightly. Furthermore, the FF also decreases and the EQE loss (ΔQE) increases with the increase of substrate texture, a phenomenon that is often observed in nc-Si:H solar cells relating to the structural defect formation caused by highly textured substrates. By fabricating a thicker nc-Si:H solar cell (3.1 μm) on the optimized Ag/ZnO BR, a high photocurrent density of 30.5 mA/cm2 was obtained; the J-V curve and EQE spectrum for this device are plotted in Fig. 9.16. From the above results, we conclude that the optimized Ag/ZnO BRs are very effective for increasing the spectral response of nc-Si:H solar cells. A current gain of over 60% compared to nc-Si:H solar cells on bare flat SS substrates can be obtained. The best Ag/ZnO BRs are made by incorporating a textured Ag layer and a thin ZnO layer (100 nm) with a proper Ag texture having a root mean square (RMS) texture value of approximately 40 nm. For the RMS textures above this value, no additional gain in the photoresponse is observed. Furthermore, the FF of the solar cells decreases with the increase of the surface roughness. With the optimized Ag/ZnO BR, a shortcircuit current density more than 30 mA/cm2 has been obtained with the cell thickness of 3 μm. As described above, the largest textures can cause microvoids and/or microcracks in nc-Si:H layers. To solve this problem, an

(a)

(b)

Fig. 9.16. J-V characteristics and external quantum efficiency (EQE) spectra of a hydrogenated nanocrystalline silicon (nc-Si:H) solar cell with total photocurrent density >30 mA/cm2 .

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innovative BR was proposed with the concept of optical texture but electrical flatness [65, 66]. The Neuchatel group [65] optimized nc-Si:H n-i-p solar cells on highly textured Ag/ZnO BRs with a “dummy” a-Si:H n-layer deposition to fill the valleys. In this process, the dummy layer is polished to form a flat surface. The interface of ZnO/(dummy a-Si:H) provides the texture for light scattering, and the polished dummy layer serves as a flat surface for nc-Si:H deposition and avoids microvoid formation in the nc-Si:H. The nc-Si:H solar cells on this BR showed a significantly improved performance by taking advantage of optical textures for light trapping and electrical flatness for better nc-Si:H quality. A similar approach was taken by the Advanced Industrial Science and Technology (AIST) group [66]. This group reported fabrication of an electrically flat but optically textured back reflector as shown in Fig. 9.17 [66]. The block structured BR shown in Fig. 9.17 (right) is made from two materials with different dielectric functions and forms a flat surface. Similarly, the flat surface of this BR ensures microcrack-free deposition of nc-Si:H layers, and the array made with two optically distinct materials scatters the light for effective trapping. In reality, the AIST group used n-type a-Si:H and ZnO to form such a BR and made a significant improvement in nc-Si:H solar cell performance, as listed in Table 9.3 [66].

(a)

(b)

Fig. 9.17. Scanning electron microscopy (SEM) images of (a) the conventional hydrogenated amorphous silicon (a-Si:H) and ZnO grating and (b) the flattened a-Si:H and ZnO grating [66].

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Table 9.3. J-V characteristics of hydrogenated nanocrystalline silicon (nc-Si:H) solar cells deposited on different textured substrates [66].

Substrate Flat Texture Grating Polished grating

Voc (V)

Jsc (mA/cm2 )

Fill Factor (FF)

Efficiency (%)

0.538 0.526 0.445 0.539

17.8 20.8 18.8 19.3

0.764 0.729 0.655 0.757

7.3 8.0 5.5 7.9

Compared to the baseline cell on the flat substrate in Table 9.3, the nc-Si:H solar cell deposited on the normal textured BR has a significant gain in the current due to the effective light trapping. Some losses in Voc and FF are caused by the degradation of nc-Si:H material quality by deposition on texture. Such detrimental effects become more serious for the cells on a conventional grating substrate as in Fig. 9.17 (left) because of the highly structured texture. In contrast, a solar cell on the flattened grating substrate of Fig. 9.17 (right) exhibits essentially the same Voc and FF as the cell on the flat substrate, indicating the same high quality nc-Si:H as that on the flat substrate. Although Jsc for the cell on the flattened grating substrate is higher than that for the cell on the conventional grating substrate, however, it is not as high as those for cells on randomly textured reference substrates. Two issues may cause lower effectiveness of light trapping for the grating substrate. First, the grating substrate may be effective for a given wavelength, but less effective for the overall broad spectrum of sunlight; second, the n-type a-Si:H in the flattened BR may absorb some of the light that reaches it. In fact for this specific structure, the grating substrate does not have a high response in the central wavelength region of the spectral response, and this was attributed to absorption in the n-type a-Si:H layer of the back reflector. Such losses can be minimized when the nc-Si:H solar cell is used as the bottom cell in multi-junction solar cells. In addition, the anti-reflection effect of the ITO layer on the flat solar cell is found to be less effective compared to that on the textured solar cell. Other so-called advanced light management concepts have been proposed such as plasmonic light trapping using metal nanoparticles,

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nanopillars, nanorods, and so on. However, no clear and convincing evidence exists that these advanced light management concepts can provide more effective light trapping than that achieved using the optimized Ag/ZnO BRs with randomly distributed textures.

9.4. High-Efficiency Multi-Junction Thin-Film Silicon Solar Cells Because the solar spectrum is very broad, from the ultraviolet to infrared, it is obvious that a semiconductor with a given bandgap cannot effectively use all of the energy in the spectrum. For photons with energies smaller than the bandgap, the photons cannot be absorbed, whereas for photons with energies higher than the bandgap, only that portion of the energy equal to the bandgap is available. The portion of the photon energy larger than the bandgap is lost by thermal relaxation. Multi-junction solar cells with different bandgaps in the component cells can overcome this limitation to a certain extent with the wide bandgap top cell used for absorbing the short wavelength photons, the middle cell for the intermediate wavelength photons, and the bottom cell for the long wavelength ones. From among the possible a-Si:H alloy-based multi-junction solar cells, the most widely studied structures are shown in Fig. 9.18, including a-Si:H/a-Si:H double-junction structures, a-SiGe:H/a-Si:H double junctions, and a-SiGe:H/a-SiGe:H/a-Si:H triple junctions [52], where the n-i-p configurations are used as examples. After the invention of the nc-Si:H solar cell, multi-junction solar cells with nc-Si:H as the bottom cell have been developed with the most widely studied structures shown in Fig. 9.19. Compared with a-Si:H single-junction solar cells, multi-junction cells have not only higher efficiencies but also improved stability against light soaking. Basically, a multi-junction solar cell is constructed with the component cells stacked on top of one another. We use the a-SiGe:H/a-Si:H double-junction cell as an example in the following discussion of the operational principles of multi-junction solar cells. The example cell consists of n-i-p structures including an a-Si:H top cell on an a-SiGe:H bottom cell. Under ideal conditions with no losses

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Fig. 9.18. Schematics of all hydrogenated amorphous silicon (a-Si:H) alloy-based multi-junction solar cell structures investigated at United Solar.

Fig. 9.19. Schematics of n-i-p multi-junction solar cells with hydrogenated nanocrystalline silicon (nc-Si:H) as the bottom cell.

at the contact between the top cell and the bottom cell, the voltage of the double-junction cell equals to the sum of the voltages of the top and bottom cells. The photocurrent takes on the smallest value, and the FFs is determined by the current mismatch between the

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top and bottom cells and by the FFs of the component cells [67]. One principle for the design of the multi-junction solar cell is to ensure that the component cell with the highest FF and the lowest light-induced degradation is the limiting cell (i.e., the cell with the smallest current density). This strategy leads not only to a high initial efficiency but also to an improved stability. An important feature of multi-junction solar cells is the connection between adjacent component solar cells. Considering the doublejunction cell as an example, the n-layer of the top cell is deposited directly on the p-layer of the bottom cell, which results in a p/n junction, inverted with respect to the primary n-i-p junctions. The photoelectrons from the top cell must recombine with the photoholes from the bottom cell to form a continuous current. Because each electron and hole must tunnel a certain distance through a potential barrier to meet one another, the n/p junction connecting the top and bottom cells is also called a recombination tunnel junction (RTJ). If the carriers cannot tunnel to the opposite side, they accumulate in the p/n junction, generate a photovoltage opposite to the main photovoltage, and reduce the cell performance. One effective way to optimize the RTJ is to use nc-Si:H p- and/or n-layers, for which the carrier mobility is much higher than for a-Si:H p- and n-layers. This results in a greater tunneling length; in this case an Ohmic contact with a low resistance forms. 9.4.1. Thin-Film Silicon Double-Junction Solar Cells The simplest multi-junction solar cell is the a-Si:H/a-Si:H doublejunction structure. Although this cell is constructed with two a-Si:H solar cells having the same or similar bandgaps and so does not take advantage of expanding the spectral range of absorption, it usually has a higher FF, hence a higher efficiency, and greater stability than a-Si:H single-junction solar cells. As described previously, the two component cells must have similar photocurrent densities. Because the top cell acts as a filter for the bottom cell, the bottom cell must be much thicker than the top cell, and an optimized BR is additionally required for matching the current. For example, in a high-efficiency n-i-p structured a-Si:H/a-Si:H double-junction solar

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Table 9.4. Hydrogenated amorphous silicon double-junction (a-Si:H/a-Si:H) solar cell characteristics [52]. TunnelJunction Standard Optimized

Jsc (mA/cm2 ) 7.97 8.06

Voc (V)

Fill QE QE QE Factor Efficiency (top) (bottom) (total) Rs (FF) (%) (mA/cm2 ) (mA/cm2 ) (mA/cm2 ) (Ωcm2 )

1.901 0.752 1.919 0.766

11.15 11.85

7.97 8.06

7.80 8.28

15.77 16.34

15.0 14.3

Note: The short-circuit current densities are obtained from the integrals of measured external quantum efficiency (EQE) and the AM1.5 solar spectrum.

cell on Ag/ZnO coated SS substrates, the top cell and bottom cell thicknesses are approximately 100 nm and 300 nm, respectively. In addition, the RTJ must be optimized in order to reduce the optical and electric losses there. Table 9.4 lists the J-V characteristics of two a-Si:H/a-Si:H double-junction solar cells, selected such that the first one incorporates a conventional RTJ and the second one has an improved RTJ leading to an optimized cell [52]. The improved RTJ results in all three performance parameters exceeding those of the baseline; hence a higher cell efficiency is obtained. In order to utilize the solar spectrum effectively, a narrow bandgap bottom cell is needed. For amorphous alloy-based multijunction solar cells, a-SiGe:H is normally used as the i-layer of the bottom cell. The bandgap of the a-SiGe:H layer can be adjusted by varying the Ge content. Reducing the bandgap usually increases the photocurrent density if the material quality does not decrease dramatically, but at a cost; this bandgap reduction also reduces Voc and the FF as expected. The quality of a-SiGe:H degrades with increasing Ge content, however, and the drops in Voc and FF may occur more rapidly than the rise in Jsc . Thus, one cannot use a very low bandgap a-SiGe:H in high-efficiency solar cells. In reality, a systematic optimization is needed to find the best a-SiGe:H intrinsic layer by considering both the long wavelength response and the overall cell performance. For the a-SiGe:H/a-Si:H doublejunction solar cells, the best a-SiGe:H used by United Solar has a bandgap near 1.6 eV and is made with a Ge content of 15%–20%. The a-SiGe:H single-junction solar cell on a SS/Ag/ZnO substrate

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made using an i-layer deposited under such conditions shows Voc in the range of 0.75–0.80 V and Jsc in the range 22–23 mA/cm2 . Using the a-SiGe:H/a-Si:H double-junction structure, initial and stable efficiencies of 14.4% and 12.4% were achieved, respectively [52]. In general, the nc-Si:H solar cell has a higher long wavelength response than the a-SiGe:H solar cell. Thus, it is obvious that by replacing the a-SiGe:H bottom cell with a nc-Si:H cell, one may be able to improve the double-junction solar cell. Several groups have developed p-i-n structured a-Si:H/nc-Si:H double-junction solar cells [35, 68, 69]. Because the nc-Si:H solar cell has a high total photocurrent density, it needs an a-Si:H top cell with a high photocurrent density as well for proper current matching in the double-junction device. Normally, it is difficult to generate a very high current in the a-Si:H top cell. To resolve the current matching issue, an interreflection layer is inserted between the top and bottom cells to reflect some portion of light back into the top cell [68]. An effective interreflection layer is nc-SiOx :H, which performs two functions: (i) as the n-layer of the a-Si:H top cell to form the tunnel junction and (ii) as an inter-reflection layer designed to reflect some light back to the top cell [5, 68]. With a great effort by the research community, the p-i-n structured a-Si:H/nc-Si:H double-junction cell efficiency has been increased rapidly to the maximum initial and stable efficiencies of 14.8% [35] and 12.7% [6], respectively. These values are slightly higher than those achieved with the a-SiGe:H/a-Si:H double-junction solar cells. 9.4.2. Thin-Film Silicon Triple-Junction Solar Cells In order to improve the efficiency further, the n-i-p structured a-SiGe:H/a-SiGe:H/a-Si:H triple-junction solar cell has been studied since the 1980s at Energy Conversion Devices (ECD). Similar to the double-junction solar cell structure, the a-SiGe:H/a-SiGe:H/ a-Si:H triple-junction structure is deposited on a Ag/ZnO coated SS substrate. In 1986, Yang et al. achieved an initial conversion efficiency of 13%, and later in 1997, they advanced the initial and stable efficiencies to 14.6% and 13.0%, respectively [3]. Figure 9.20 shows the J-V characteristics and EQE curves of the record efficiency solar

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(b)

Fig. 9.20. J-V characteristics and external quantum efficiency (EQE) curves of a triple-junction solar cell made from hydrogenated amorphous silicon–germanium and hydrogenated amorphous silicon (a-SiGe:H/a-SiGe:H/a-Si:H) with initial and stable efficiencies of 14.6% and 13.0%, respectively [3].

cell. First, the triple-junction solar cell is capable of using the broad solar spectrum effectively as shown in Fig. 9.20(b), which covers the wide wavelength range of 300–950 nm. Second, the FF of the triplejunction solar cell is much higher than those of single-junction and double-junction solar cells because the current mismatch improves the FF. Because the a-Si:H top cell has a lower defect density than the a-SiGe:H middle and bottom cells, an optimized triplejunction cell structure achieving a high FF should be designed with a thin top cell serving as the current limiting cell. The a-SiGe:H/ a-SiGe:H/a-Si:H triple-junction solar cell structure not only yields the highest efficiency, but also has the best stability. As a result, United Solar used the a-SiGe:H/a-SiGe:H/a-Si:H triple-junction structure for manufacturing flexible solar laminates and established a manufacturing capability of 180 MW/year [22]. As shown previously, the nc-Si:H solar cell has a better long wavelength response than the a-SiGe:H solar cell, the former extending the long wavelength response to 1100 nm. Therefore, it is logical to use a nc-Si:H cell to replace the a-SiGe:H bottom cell in the multi-junction structures. Over the years, significant efforts have been made to

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(a)

(b)

Fig. 9.21. (a) J-V characteristics and (b) external quantum efficiency (EQE) spectra of a triple-junction solar cell made with hydrogenated nanocrystalline silicon, hydrogenated amophous silicon germanium, and hydrogenated amorphous silicon (nc-Si:H/a-SiGe:H/a-Si:H) having an initial efficiency of 16.3% [4].

increase the multi-junction solar cell efficiency using nc-Si:H as a bottom cell. The highest initial efficiency for thin-film silicon solar cells is 16.3%, achieved by United Solar using a nc-Si:H/ a-SiGe:H/a-Si:H triple-junction structure with the J-V characteristics and EQE curves shown in Fig. 9.21 [4]. From the EQE curves for this cell shown in Fig. 9.21(b), one can see that the long wavelength response is indeed much broader than that of the a-SiGe:H/a-SiGe:H/a-Si:H triple-junction solar cell shown in Fig. 9.20(b). Over the years, several institutes have been involved in the development of high-efficiency triple-junction solar cells. LG Solar also achieved an initial triplejunction cell efficiency of 16.1% [24]. One can also use nc-Si:H to replace the a-SiGe:H middle cell for improving the stability. The AIST group optimized the a-Si:H/nc-Si:H/nc-Si:H triple-junction solar cell and achieved a record high stable efficiency of 14.0% with Jsc = 9.94 mA/cm2 , Voc = 1.922 V, and FF = 0.734. The nc-Si:H layers of this cell were made using a triple-electrode PECVD system with reduced ion bombardment [6]. Over the long history of thin-film solar cell research and development, the efficiencies of various solar cell structures have been

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improved gradually. The record initial and stable efficiencies are 16.3% and 14.0% achieved by United Solar and AIST, respectively, using nc-Si:H/a-SiGe:H/a-Si:H and nc-Si:H/nc-Si:H/a-Si:H triplejunction structures. 9.4.3. Thin-Film Silicon Quadruple-Junction Solar Cells From the above results, it appears that the cell efficiency increases with the junction number in thin-film silicon-based multi-junction solar cell structures. For III–V semiconductor solar cells, it has also been demonstrated that the cell efficiency increases with the junction number, and a high efficiency has been achieved with a six-junction solar cell. Therefore, out of curiosity, one would wonder whether the efficiency of the thin-film silicon-based multi-junction solar cell would increase further, stabilize, or decline if the junction number were to be increased beyond three. For this purpose, thinfilm silicon-based quadruple-junction solar cells have been studied experimentally and by simulation. Isabella et al. [70] has simulated the performance of quadruple-junction solar cells and demonstrated that the cell efficiency approaches 20% if the bandgaps and RTJs are properly optimized. Experimentally, several experienced groups have worked on quadruple-junction solar cells. The Neuchatel group has made quadruple-junction solar cells in the p-i-n configuration using an a-Si:H/a-SiGe:H/nc-Si:H/nc-Si:H structure and achieved an efficiency of 10.1% with a high Voc of 2.57 V and FF of 0.804 [71]. The efficiency was limited by the low Jsc resulting from the low total photocurrent density and large current mismatch. The group in J¨ ulich also used an a-Si:H/a-Si:H/nc-Si:H/nc-Si:H p-i-n quadruplejunction structure, tuned the current mismatching, and increased the initial and stable cell efficiencies to 13.2% and 12.2%, respectively, with a high Voc of 2.8 V [72]. The group at Nankai University has made great progress on the improvement of cell efficiency using an a-SiC:H/a-Si:H/a-SiGe:H/ nc-Si:H p-i-n quadruple-junction cell structure. For this structure, the four intrinsic absorbers have different bandgaps, which increase

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the initial efficiency to 15.03% with a high Voc of over 3.0 V [20]. A comparison with the highest efficiency of 16.3% achieved using the n-i-p structured nc-Si:H/a-SiGe:H/a-Si:H triple-junction solar cell [4], however, shows that the efficiency of the quadruple-junction solar cell is still low. Although a quadruple-junction solar cell structure with a higher efficiency compared to that of the triple-junction structure may be predicted theoretically, it is very difficult to realize experimentally for the following reasons. (i) The complexity increases with the number of junctions. (ii) Different bandgap materials are needed for achieving a high Voc and proper current matching; however, the alloys such as a-SiC:H and a-SiGe:H inevitably have more defects than a-Si:H and nc-Si:H, which leads to a poorer FF. (iii) Adding junctions adds more RTJs, where both electrical and optical losses exist, which results in a loss in the cell efficiency. Because no efficiency higher than the best triple-junction solar cells has been achieved to date, quadruple-junction thin-film silicon solar cells are not a suitable option for manufacturing in my opinion unless specialized requirements must be satisfied such as a high Voc for water splitting applications [72].

9.5. Thin-Film Silicon Module Fabrication and Applications Thin-film silicon PV technology has progressed through the entire sequence of steps from academic laboratory research, through industrial research and development, and into mass production. However, the largest production volume reached by United Solar using the roll-to-roll processes on flexible SS substrates was only 180 MW, which is significantly smaller than almost any state-of-the-art c-Si PV production line. Although the thin-film silicon PV industry was not able to survive the intense competition with c-Si solar modules in terms of price and performance, the knowledge acquired in the production of thin-film silicon PV modules remains valuable to various PV technologies, especially other thin-film technologies. Below I summarize some key techniques relevant to thin-film PV module fabrication in general.

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9.5.1. Glass-Based Thin-Film Silicon Solar Modules Thin-film silicon PV module fabrication can be traced back to the 1980s, and a reasonable volume was established in the period from the late 1990s to the 2010s. A manufacturing facility with an initial production line (TF1) having an annual capacity of 10 MW [73] was built at BP Solar. Later the line capacity was increased to 100 MW. BP Solar applied a-Si:H/a-SiGe:H p-i-n double-junction structures made using a DC-PECVD method on TCO coated glass substrates. To make operational modules, the solar cells in this structure must be scribed into small strips and interconnected serially, then encapsulated into modules with a back plate. Schematics of the module layer structure and the scheme for monolithic interconnection are presented in Fig. 9.22 using a triple-junction solar cell as an example. The interconnection needs three laser scribing processes. Before the thin-film silicon deposition, the TCO is scribed into strips with a well-defined width using a UV laser such as a higher harmonic

(a)

(b)

Fig. 9.22. (a) The layer structure of a photovoltaic (PV) module with a triplejunction solar cell made from hydrogenated amorphous silicon and hydrogenated nanocrystalline silicon (a-Si:H/nc-Si:H/nc-Si:H) in the p-i-n configuration and (b) the monolithic interconnection scheme.

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of the Nd:YAG laser (266, 355 nm). The second laser scribing process is performed after the thin-film silicon layer deposition and is used to cut the silicon layer using a green laser such as a frequencydoubled Nd:YAG laser (532 nm). The third scribe is made after the Al electrode deposition. This is the final laser scribing process and is used to cut both the silicon and the back Al contact to isolate the back electrode of each strip. After the three laser scribes, the Al back electrode of a given strip contacts with the front TCO of the adjacent strip to finish the interconnection as shown on the right in Fig. 9.22. After these processes, the strips are connected in series, the current is determined by the photocurrent density and the area of each strip, and the voltage is added for the number of serially connected strips. The interconnected cell is encapsulated with ethylene-vinyl acetate (EVA) and a back sheet, which could be another plate of glass. Since thin-film silicon PV was shown to be a very promising technology for renewable energy, several companies developed large volume production lines to fabricate modules on glass substrates, including Applied Materials in the United States, Oerlikon Solar/TEL Solar in Switzerland, and ULVAC in Japan. These companies not only commercialized thin-film silicon PV production systems, but also developed the cell and module fabrication process. For example, Oerlikon Solar/TEL Solar optimized the recipes and achieved a stable module efficiency of over 12% using the so-called MicroMorphTM solar cell with the a-Si:H/nc-Si:H/nc-Si:H p-i-n triple-junction structure. Their record module characteristics and efficiency are shown in Fig. 9.23 [21, 74]. 9.5.2. Flexible Thin-Film Silicon Solar Laminates The thin-film silicon-based n-i-p structured solar cells are used for making flexible PV modules. The production line most representative of this technology was developed by ECD and United Solar [22]. They used roll-to-roll PECVD and sputtering systems to fabricate flexible thin-film solar cells on thin SS foils and reached 180 MW/year capacity. Figure 9.24 shows a photograph of United Solar’s roll-to-roll PECVD system and a schematic drawing of the deposition process.

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Fig. 9.23. The stable performance of a large-area (1.43 m2 ) thin-film silicon module with the triple-junction structure using hydrogenated amorphous silicon and hydrogenated nanocrystalline silicon (a-Si:H/nc-Si:H/nc-Si:H) in the p-i-n configuration [21].

The PECVD machine is approximately 90 meters long and 6 meters tall. SS foils 36 cm wide and 0.127 mm thick from six rolls each 2.6 km long travel through the machine simultaneously. A significant set of technologies has been developed to realize these large volume roll-toroll deposition systems, including gas gates to isolate dopant gases from the intrinsic deposition chambers, magnetic rollers, and other technologies to allow web transport with no front facing rollers, and a large-area cathode design for uniform fabrication. In flexible solar module production, each roll of SS is cleaned before the Ag/ZnO BR deposition in the first roll-to-roll sputtering machine. Six cleaned rolls with the BR are then loaded into the PECVD system at the same time for deposition of the nine layers of the triple-junction structure. Finally, each roll is coated in the second roll-to-roll sputtering machine for ITO deposition to form the front transparent contact. The rolls with the finished coatings are cut into small pieces for module fabrication. Thin-film silicon deposition inevitably results in pinholes through which shunt paths form that affect the solar cell performance. In order to remove the shunts, an electrochemical passivation process is performed. Next

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Fig. 9.24. (Top) A photograph of United Solar’s 30 MW roll-to-roll plasmaenhanced chemical vapor deposition (PECVD) system, and (bottom) a drawing of the process principle for the roll-to-roll fabrication.

carbon coated metal wires are thermally pressed onto the ITO and adhesively contacted to form grids for current collection. Metal bus bars are attached to the two edges to make contact with the grids as the electrodes for current flow. Finally, a number of cells are

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serially connected and then encapsulated with two layers of polymer with EVA on both sides of the cell array. The number of cells in one array depends on the application. A special requirement for the front polymer is anti-aging, that is, optical stability during prolonged illumination under sunlight; during the product lifetime no changes in the polymer color should occur. Figure 9.25 (left) shows an example of the flexible thin-film silicon PV product, which is adaptable to a variety of applications and has a pleasing appearance. This type of product is a perfect choice for BIPV applications, especially on curved surfaces. Large volumes of these Uni-SolarTM flexible PV modules have been installed worldwide. An example of such a BIPV application is illustrated in the right photograph of Fig. 9.25. The flexible thin-film silicon solar cells have been fabricated on polymer substrates as well, serving as an ultralight PV product [50] for space applications such as unmanned aircraft and high altitude airships. As a source of solar power generation, thin-film silicon PV products have been withdrawn from the market; however, the technology continues to have many other applications such as chargers for various electronics and remote applications. Business opportunities for thin-film silicon PV remain, and the demand for such flexible products has been increasing recently.

Fig. 9.25. (Left) A photograph of the United SolarTM flexible photovoltaic (PV) product and (right) an example of a United SolarTM flexible PV installation on a curved roof.

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9.6. Thin-Film Silicon Applications in c-Si Solar Cells In recent years, the price of crystalline silicon material has dropped significantly, and poly-Si and c-Si solar cell technologies have advanced remarkably as well. These changes have led to a significant manufacturing cost reduction for crystalline silicon solar modules. On the one hand, this technology has made great progress toward grid parity for PV as a provider of clean and green energy for society. On the other hand, it has resulted in loss of market advantage for the so-called second-generation thin-film solar cell technology. Most (if not all) thin-film silicon PV manufacturing companies have left the business. Even so, a-Si and a-Si:H have each found a new life as a surface passivation layer, and have been used widely for highefficiency c-Si solar cells. In fact, two technologies are currently using thin-film silicon in c-Si solar cells. The first one combines a-Si:H and c-Si to make the c-Si/a-Si:H heterojunction solar cell, which has become an advanced high-efficiency silicon PV technology. Because this solar cell uses a very thin (∼5 nm) intrinsic a-Si:H layer to passivate the c-Si interface, it is often called the HIT (Heterojunction with Intrinsic Thin layer) cell. In addition to the intrinsic a-Si:H passivation layer, the HIT solar cell also uses doped p-a-Si:H to form the emitter and doped n-a-Si:H to form the back field junction. The second emerging high-efficiency c-Si solar cell technology applies a-Si:H as the precursor for making a polycrystalline silicon (poly-Si) passivation/contact layer. This cell structure uses a TOPCon layer and, therefore, is referred to as the TOPCon solar cell. For this cell, the key elements are the ultrathin SiOx and doped poly-Si contact layers. 9.6.1. c-Si/a-Si:H Heterojunction (HIT) Solar Cells The HIT solar cell was initially invented by Sanyo (now Panasonic) in Japan in the 1990s [25]. With the expiration of the initial intellectual property of Sanyo, many research institutes and companies have joint research and development projects on HIT solar cells that support the production of these cells. The cell and module efficiencies have steadily improved as a result. For example, the small-area cell

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efficiency reached 25.1% as reported by Kaneka in 2015 [75], and the large area cell efficiency with a 6-inch wafer reached 25.11% by Hanergy. By combining the HIT layer structure and an interdigitated back contact (IBC), Panasonic improved the cell efficiency to 25.6% in 2014 [76], and Kaneka set a new record with 26.6% in 2016 [26]. In recent years, HIT solar module manufacturing has been gradually expanding within the c-Si PV industry. Schematics of HIT cell structures are shown in Fig. 9.26 [77]. In each of these structures, an n-type wafer is usually used for high minority carrier mobility and reduced sensitivity to metal impurities such as Fe. Both sides of the wafer are normally textured for improved light coupling and light trapping. A thin intrinsic a-Si:H (i-a-Si:H) layer of ∼5 nm in thickness is deposited on both sides of the wafer to passivate the interface states, and then B-doped a-Si:H (p-a-Si:H) and P-doped a-Si:H (n-a-Si:H) layers are separately deposited on

(a)

(b)

(c)

(d)

Fig. 9.26. Device architectures for heterojunction solar cells with intrinsic thin layer (HIT); (a) front junction mono-facial, (b) front junction bifacial, (c) rear junction bifacial, and (d) HIT with interdigitated back contact (IBC) [77].

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the front and rear sides, respectively. The p-a-Si:H forms the front junction (or emitter) and the n-a-Si:H forms the back field contact. One can also deposit the n-a-Si:H on the front surface to form the front field contact and p-a-Si:H on the back side to form the rear junction or so-called rear-emitter. Depending on the rear electrode, the cell can be made as a mono-facial structure or as a bifacial structure. For the highest efficiency cells in the IBC configuration, the p-a-Si:H and n-a-Si:H are both on the rear side alternating spatially, and the front surface is passivated with thin a-Si:H and SiNx , the latter as an ARC. The n-a-Si:H shown in the schematics of Fig. 9.26 has a higher quality than the p-a-Si:H because doping with B also leads to a reduction in the bandgap of the a-Si:H. Similarly, if nc-SiOx :H is desired as the window layer of the cell structure, the p-type nanocrystalline films are usually more difficult to fabricate than the n-type films and result in a poorer quality. Because the conductivity of the doped a-Si:H layers is not high enough for effective lateral collection of carriers, highly conductive TCO and metal grids are needed on the top surface. The same structure is required for the rear surface if bifacial cells are made; otherwise, a full area TCO/metal coating on the back is used for mono-facial solar cells. As is the case for all other solar cell configurations, a proper design and an optimized fabrication process are needed for highefficiency HIT devices. First, the wafer cleaning and texturing are critical. Any surface contamination must be properly removed, especially metal ions. Then an optimized texturing process must be performed to create micron-sized pyramids for effective light coupling and light trapping. The deposition of the thin i-a-Si:H passivation layer is the most critical step, however, both for ensuring high quality passivation, which reduces interface defects, and for maintaining a minimum barrier to carrier transport. For this purpose, three major aspects should be taken into consideration. First, the thickness of the i-a-Si:H must be controlled precisely because, if the i-a-Si:H is too thin, it does not provide suitable passivation. If it is too thick, photocarriers cannot easily pass through it, resulting in a high series resistance and a poor FF. Experimentally,

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it has been found that the optimum i-a-Si:H passivation layer is approximately 5 nm in thickness. Second, the quality of the i-a-Si:H passivation layer is also critical. One of the technical difficulties for ensuring high quality passivation is to minimize ion bombardment during the i-a-Si:H deposition. It is well known that a high excitation power (RF or VHF) produces high energy ion bombardment and consequently generates a high defect density at the c-Si/a-Si:H interface. Therefore a low power deposition is preferred, but if the power is too low, the plasma cannot be ignited. A possible solution is the application of an initial high power to ignite the plasma and then a dynamic reduction in the power during the deposition. This dynamic control with a change in the excitation power has been widely used in second-generation thin-film silicon solar cell deposition. This approach has a significant negative impact on HIT solar cell performance, however, because the i-a-Si:H is very thin and the initial high power may damage the interface. Additionally a large portion of the i-a-Si:H layer is deposited under the initial high power condition. To solve this problem, a specially designed tuning network and power control system should be used. From the point of view of ion bombardment, hot wire chemical vapor deposition (hot-wire-CVD) or so-called catalytic chemical vapor deposition (cat-CVD) has a significant advantage [78]. In this method, the reactive radicals are generated thermally from gas molecules by the high temperature wire and no ion bombardment takes place. Third, any interfacial epitaxial growth must be avoided. It has been found that the epitaxial layer deposited in the HIT process normally consists of a mixture of both amorphous and crystalline phases, and thus has a higher defect density than a purely amorphous layer at the interface. Furthermore, the deposition of thin-film silicon depends on the nature of substrate, which implies that the material structures could be different on different substrates even with the same deposition conditions. For example, under a given set of conditions, the deposited material may exhibit a purely amorphous structure when a glass substrate is used, but evolves to a nanocrystalline structure starting from a thin epitaxial layer

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when a clean c-Si surface is used as the substrate. Based on this argument, the deposition conditions must be carefully optimized and controlled, especially so for the hydrogen dilution level, in the case of the HIT cell to avoid epitaxial growth. From a-Si:H studies, it has been recognized that the best a-Si:H for thin-film silicon solar cells is deposited with a hydrogen dilution level near the transition from amorphous to nanocrystalline phases while remaining on the amorphous side. In addition, the material structure changes with the thickness of the film, and so can deviate from the optimum structure during growth. In order to maintain the same material structure, a hydrogen dilution profile is used for nc-Si:H deposition [57, 58]. The same guidance is also valid for HIT cell optimization. Therefore, to maintain the material structure in the optimum amorphous regime, a hydrogen dilution profile with a low or zero hydrogen dilution level is used at the beginning of the deposition to avoid epitaxial growth, and then an increasing hydrogen dilution is applied to maintain high quality material structure throughout the deposition. Here, the guidance is given, but the detailed optimization must be performed on each type of deposition system. The reason is that the deposition system characteristics such as the gap distance and the gas distribution have a sensitive effect on the material quality. The doped layers (both the n and p layers) are also important for HIT cell performance. First, the doped layers should have a high doping efficiency in order to obtain a large Fermi level splitting and to ensure a high built-in potential. These layers should also exhibit a low optical absorption coefficient in order to reduce the parasitic absorption. At first thought, one could propose using nc-Si:H, nc-SiOx :H, or nc-SiCx :H as the doped layers. Logically, this seems the correct choice because the nanocrystalline materials have a much higher doping efficiency and lower parasitic absorption than amorphous materials. However, to incorporate such materials successfully in high-efficiency HIT solar cells additional technical art is required. First, the deposition of nanocrystalline materials entails high hydrogen dilution with a high concentration of atomic hydrogen in the plasma. A flux of atomic hydrogen onto the thin i-a-Si:H

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layer may affect the quality of passivation by etching or modifying the i-a-Si:H material. The hydrogen may also penetrate through the i-a-Si:H and modify the c-Si/i-a-Si:H interface. Although the exact microscopic mechanism is not clear, a simple application of a doped nc-Si:H deposition recipe usually does not produce high-efficiency HIT solar cells. Instead one may need a double-layer structure of a-Si:H/nc-Si:H. In such a structure, the doped a-Si:H layer protects the i-a-Si:H layer from the atomic hydrogen damage, and the nc-Si:H provides the improved doping efficiency and high conductivity for low series resistance. Because the top TCO provides for photocurrent collection and acts as the ARC layer, its thickness is fixed at approximately 75–80 nm to satisfy the quarter wavelength ARC requirement at the wavelength of the solar spectrum with the maximum energy flux. Therefore, a high conductivity is the basic requirement. The commonly used TCO is ITO, which has a higher conductivity than AZO and BZO; however, ITO usually has a high free carrier density, which generates long wavelength absorption due to free carriers. In order to increase the photocurrent density, TCO films with a higher carrier mobility but a slightly lower carrier concentration are desired. For this purpose, tungsten doped indium oxide (IWO) and hydrogendoped indium oxide (IHO) layers [79] have been developed and used in HIT solar cells with an improved Jsc without losses in FF. Several characteristics of the HIT solar cell are improved over the conventional homo-junction c-Si solar cells. First, the HIT cell uses an n-type c-Si wafer, which has higher minority carrier lifetime than the p-type wafer even with the same impurity level. Second, because no boron–oxygen complexes exist in n-type c-Si, the HIT solar cell shows much less or even no potential light-induced degradation compared to the conventional c-Si solar cell based on a p-type wafer. In fact, a light-induced increase in efficiency is observed in some HIT solar cells [80]. Third, because the a-Si:H passivation layer and a-Si:H doped layer have wider bandgaps than c-Si, HIT solar cells have much higher Voc and a smaller temperature coefficient than the homo-junction c-Si solar cell. This leads to a higher energy yield than conventional polySi and c-Si PV modules in real world applications, especially in hot

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climates and during times of low light intensity such as on cloudy days or in morning and evening times. 9.6.2. Precursors for Poly-Si Contacts in TOPCon c-Si Solar Cells Another new emerging high-efficiency c-Si solar cell technology is based on the TOPCon solar cell, so named as an abbreviation of Tunnel Oxide Passivation Contact. The rear contact of this solar cell is made with an ultrathin (∼1.5 nm) SiOx layer and a highly doped poly-Si layer. The SiOx /poly-Si passivation technique is well developed for use in semiconductor devices. The group at Fraunhofer introduced this concept into c-Si solar cells and reported reasonable performance in 2014 [27, 81]. Since then, it has attracted great attention within the PV community, and as a result, the TOPCon cell efficiency has improved rapidly, reaching 25.7% for a small-area (4 cm2 ) cell structure [28] and 24.6% for a 6-inch wafer without the IBC structure. The efficiencies of both the small-area laboratory cells and the large-area industrial cells have matched those of HIT solar cells. Many leading PV companies have been exploring the TOPCon solar cell technology for a number of reasons. First, the TOPCon solar cells are made using a high temperature solar cell fabrication process similar to that of the PERC (Passivated Emitter Rear Contact) or PERL (Passivated Emitter and Rear Localized contact) devices. As a result, the capital equipment cost (Capex) for a TOPCon production line is much lower than that of a HIT production line with the same production capability. In addition such a line can even be made by retrofitting an existing PERC or PERL line. Jolywood Solar is already operating in a large volume production mode of 2.4 GW, and other companies such as JinKo Solar and Trina Solar are in pilot pre-manufacturing mode. It is believed that the TOPCon solar cell manufacturing technology will be widely introduced to the PV community within the next few years, and this introduction will occur before expansion of the HIT technology. As examples with n-type c-Si wafers, the mono-facial and bifacial TOPCon cell structures are presented in Fig. 9.27. The front surfaces shown here are the same as the n-type c-Si PERL cell

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Fig. 9.27. Schematic drawings of (left) a mono-facial tunnel oxide passivation contact (TOPCon) solar cell with a full area rear metal contact and (right) a bifacial TOPCon solar cell with rear grids.

with a B-diffused emitter passivated by Al2 O3 /SiNx :H and with metal grids for current collection. A selective emitter with a high doping concentration underneath the grids may be used for high efficiency. The rear side of the wafer differs from the PERL cell, however, by application of the TOPCon structure. Instead of using localized contacts fabricated by laser opening, the ultrathin SiOx layer passivates the c-Si surface and allows electrons to pass through by tunneling. Transport by tunneling was originally proposed, but it was found that transport through pinholes is another major contributor [82, 83]. Highly P-doped poly-Si then forms a contact layer for the metal electrode and provides an additional passivation effect via the electric field. Similarly, one can also fabricate a TOPCon solar cell using a p-type c-Si wafer by forming a P-doped front emitter by diffusion and incorporating a p-TOPCon consisting of highly B-doped poly-Si as the rear field contact layer. This structure serves as an alternative

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to a B-doped front field contact by diffusion and a rear n-TOPCon emitter. In addition, a double-sided TOPCon structure has also been proposed and systematically studied. The double-sided TOPCon solar cell is similar to the HIT cell except that the thin i-a-Si:H passivation layer is replaced by the ultrathin SiOx , and the p-a-Si:H and n-a-Si:H layers by the p-poly-Si and n-poly-Si, respectively. Generally, the front doped poly-Si contact layer should have the proper thickness, large enough to provide good field passivation and to protect the ultrathin SiOx but not so large as to add extra parasitic absorption. With these two considerations, the optimized front doped poly-Si layer thickness is approximately 20–30 nm. For a poly-Si layer of this thickness, the sheet resistance is not sufficiently low for lateral photocurrent flow, and therefore a TCO layer is needed for the double-sided TOPCon solar cells. The key elements of TOPCon solar cells are the ultrathin SiOx and the doped poly-Si layers. The SiOx layer can be formed with various methods such as acidic oxidization with hot nitric acid or mixed nitric and sulfuric acids at relatively low temperature [84], as well as ozone oxidization, thermal oxidization, or plasma-enhanced oxidization. The poly-Si layer is fabricated by thermal annealing of a P-doped a-Si, a-Si:H, or a-SiCx :H precursor layer which crystallizes as n-poly-Si or n-poly-SiC. The amorphous silicon precursor layer is normally made by LP-CVD or by PECVD. Recently, some reports also demonstrated the feasibility of using sputtering [85] and e-beam evaporation. Each of these deposition methods has its advantages and disadvantages as discussed next. In considering the advantages and disadvantages of LP-CVD, two issues related to annealing and deposition rate of the precursor layer are important. First, the amorphous precursor layer, irrespective of the deposition process, must be annealed at a high temperature above 800◦ C. Therefore, it is logical to assume that the passivation quality is not noticeably affected by whether or not hydrogen is incorporated into the precursor layer as long as no blistering occurs. For this reason, unhydrogenated a-Si made by LP-CVD at substrate temperatures near 500◦ C–600◦ C has been successfully used in TOPCon solar cell fabrication. The advantages of LP-CVD include

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the following. (i) It is a proven viable technology already being used in the mass production of TOPCon solar cells; (ii) its Capex for the deposition machine is low, especially for large volume production lines; and (iii) it is a deposition process with low powder formation, and therefore a long uptime. The most critical disadvantage is the wraparound deposition on the reverse side of the wafer. As a result, additional processes are required for adding a protective layer before LP-CVD and then removing the protective and wraparound layers. Although these processes would seem to be easily incorporated steps in the overall solar cell fabrication, they result in an extra cost and reduce the production yield. The second issue is the trade-off between in-situ doping and deposition rate in LP-CVD. Adding doping gas in the LP-CVD process significantly reduces the deposition rate, and therefore, reduces the production efficiency. To avoid this problem, undoped a-Si is normally deposited by LP-CVD first, and then exsitu doping is performed by ion implantation or diffusion. Once again, the ex-situ doping process adds an extra cost and may lead to yield issues as well. PECVD is a very mature thin-film deposition technology and has been widely used for a-Si:H and nc-Si:H depositions in thinfilm silicon solar cells and in HIT solar cells as discussed above, as well as for TFTs in display applications. Therefore, PECVD could undoubtedly be applied for TOPCon solar cells. In fact, the early TOPCon solar cells were made using PECVD for the a-Si:H precursor layer [27], and the champion efficiency of 25.7% was achieved by using PECVD as well [28]. The advantages of PECVD for TOPCon solar cells include (i) in-situ doping for both n-type and p-type without sacrificing the deposition rate, (ii) very little or no wraparound deposition on the reverse side of the wafer, and (iii) high deposition rates achievable by tuning the plasma process parameters especially using VHF as the excitation source. The disadvantages of this technique include (i) hydrogen incorporation that is a potential cause of blistering or bubbling during the annealing process for crystallization, (ii) powder formation during the deposition that reduces the uptime and necessitates extra maintenance, and (iii) higher deposition system Capex than the LP-CVD system.

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A number of approaches can be adopted to address these disadvantages. The blistering issue can be avoided by tuning the plasma conditions, such as changing the hydrogen dilution during the deposition [86, 87], which involves using a low hydrogen content nc-Si:H seed layer, or by alloying with carbon to make a-SiC:H as the precursor [88]. The group at EPFL has used B-doped a-SiC:H as the precursor for p-TOPCon on p-type wafers and made TOPCon solar cells with respectable performance [88]. This technique has been investigated by Meyer Burger for incorporation in mass production. The powder formation in PECVD can be minimized by tuning the plasma conditions and/or by adding an in-situ cleaning process using a NF3 or CF4 plasma after the deposition of the a-Si:H layer. The Capex of the PECVD machine could be reduced by simplifying the machine structure. This is possible because the requirements for the a-Si:H precursor of polySi in TOPCon solar cells are much less stringent, for example than the a-Si:H layers for the HIT solar cells, for the following reasons. (i) It is a single-sided deposition with no need for inverting the substrate. (ii) There is no need to control the thickness as precisely as that of the i-a-Si:H passivation layer in HIT solar cells. (iii) A much wider tolerance for impurities in the doped a-Si:H precursor layer exists for TOPCon than for the i-a-Si:H and doped a-Si:H layers used in HIT solar cells. (iv) Finally, a high deposition rate can be used such as with VHF excitation, which increases the production volume for a given machine and equivalently reduces the Capex. The combination of the advantages and the range of solutions to address the disadvantages has led to the consensus that PECVD is a viable and cost-effective technology for TOPCon solar cells. For the last few years, Meyer Burger has collaborated with the Solar Energy Research Institute of Singapore (SERIS) [89, 90] to develop a PECVD platform for TOPCon solar cells (so-called monoPOLYTM ). Manufacturing and demonstration lines are expected to be installed soon in some PV manufacturing companies. Another breakthrough toward the reduction in costs of the PECVD process is made possible through the tube-PECVD system.

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A tube-PECVD system has been used in PERC solar cell fabrication for the deposition of SiNx :H and AlOx :H passivation layers. It has a low Capex and large volume production and has been widely deployed in most solar cell manufacturing companies. Conventional tube-PECVD machines use a 40-kHz pulse voltage as the excitation source, which is much lower in frequency than the standard RF (13.56 MHz) excitation. It is widely known that a low frequency plasma is normally associated with high energy ion bombardment, which was a concern when using the 40 kHz tube-PECVD method for a-Si:H deposition. The high energy ion bombardment could damage the ultrathin SiOx passivation layer and produce low quality a-Si:H as well. As a result, the passivation quality may be lower than that obtained using an a-Si:H precursor made by RF PECVD. However, a recent experimental study has shown that high quality passivation has been achieved using a tube-PECVD deposited Pdoped a-Si:H precursor for the poly-Si fabrication in the TOPCon structure [91]. Uniform deposition and high passivation quality have also been achieved over large areas. This study has focused attention on a great opportunity of using the low cost tube-PECVD method for TOPCon solar cells. Furthermore, it has been demonstrated that the passivation quality of the TOPCon structure has a weak correlation with the initial a-Si:H quality, and so has opened up the possibility of using other deposition techniques that are even lower in cost. Similarly, sputtering was also used to deposit a-Si as the precursor of poly-Si in TOPCon solar cells. Before the development of PECVD a-Si:H by Spear and LeComber [1], sputtering had been used to make a-Si. In contrast to PECVD a-Si:H, the sputter-deposited a-Si was found to exhibit a very high defect density, leading to no doping effect at all. Thus sputter-deposited a-Si was not deemed useful from an electronic perspective. However, a different outcome is found for the Si-based layer of TOPCon solar cells. Yan et al. [85] deposited B-doped a-Si using a co-sputtering technique and employed it as the precursor of p-poly-Si in TOPCon solar cells. They achieved 23.0% cell efficiency using a p-type c-Si wafer, which is one of the highest efficiencies reported for such p-TOPCon solar cells.

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From the above discussions, one may conclude that the a-Si or a-Si:H precursor materials for the TOPCon solar cell can be deposited using various methods including CVD and PVD techniques. This implies that the requirements for the initial material quality are not very strict. It does not matter whether hydrogen is incorporated in the materials or not and whether the defect density of states in the as-deposited state is low or high. Therefore, from a solar cell manufacturing point of view, one has more options in selecting the deposition technique. Considerations can then be made on the basis of cost-effectiveness, capability/feasibility of integration with other manufacturing machines, and production efficiency such as the uptime and simplicity of maintenance, and so on. One must keep in mind, however, that TOPCon solar cell efficiency optimization also involves a remarkable amount of scientific and technical art in the form of know-how and tricks. This includes methods for control of the chemical composition and bonding configuration of the SiOx layer as well as its thickness, which all need to be optimized properly. The dopant diffusion and distribution in the poly-Si, SiOx , and c-Si wafer should be controlled in consideration of the need to reduce interface defects and to enhance the effective field passivation, but without the introduction of significant additional Auger recombination. Most of these aspects are beyond the scope of this chapter and I refer readers to the references [27, 28, 81–92].

9.7. Summary and Future Perspective Since the invention of the a-Si:H solar cell in 1976 by Carlson and Wronski, research and development of thin-film silicon solar cells has been the focus of one of the longest lasting materials and devicerelated scientific fields. The Materials Research Society (MRS) has conducted Symposium A on thin-film silicon related topics at their Spring Meeting every year starting in 1983 and continuing for more than 30 years. Over these years, several generations of scientists and engineers have focused their careers in the field working to improve the material quality and device design, and to advance the technology into mass production. As a result, thin-film silicon PV had become

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an important segment of the PV industry, and in fact, was one of the well-attended sessions of the international PV conferences such as the IEEE PVSC, EU-PVSEC, and the Asian/Pacific PVSEC. As a veteran of the field, I have witnessed the rapid growth, vitality, and subsequent maturity of the field. Although thin-film silicon solar cell technology as a segment of the PV industry has declined and very little industrial activity remains, the knowledge base accumulated during the previous more than 30 years is still a valuable asset in the technology field, especially for newcomers in PV research and development. Therefore, in spite of the decline of the industry, I still feel that writing this chapter is my responsibility and a great honor to share this key knowledge and my experiences. Below I have tried to summarize the key points of this chapter on thin-film silicon solar cell technology and hope these points are useful to young scientists and engineers. First, because of the unique property of low mobility–lifetime products for the charge carriers in the absorber of thin-film silicon solar cells, the conventional p-n junction structure cannot be applied. Instead, p-i-n and n-i-p structures are used, and the Fermi level difference between the p- and n-layers forms the built-in potential. This potential is dropped across the i-layer and establishes the built-in electric field. The i-layer is the primary absorber where the photogenerated electron–hole pairs are separated by the builtin electric field. Electrons and holes drift toward the n- and p-layers, respectively, to generate the photocurrent that flows through the external load. Because the mobility–lifetime product of holes is much smaller than that of electrons, the cell should be designed such that the sunlight illuminates the p-layer side first. Then holes travel a shorter average distance than electrons, balancing the electron and hole currents. A thin-film silicon solar cell structure obviously different from that of the c-Si cell determines the different approaches required for thin-film silicon cell optimization. As in the case of all other types of devices, the material quality of the building blocks such as the absorber layer, doped layers, and contacts all must be optimized. In addition, the cell structure such as the layer thicknesses and the

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design of the interfaces is also critical for efficiency optimization. Specifically, from the semiconductor quality point of view, the i-layer should be optimized for low defect density and high photosensitivity (the conductivity ratio of photo/dark), and the doped layers should have a high dark conductivity with a low activation energy and low optical absorption. From the cell structure point of view, the intrinsic layer should be thick enough to absorb sufficient sunlight for a high Jsc but thin enough to avoid a low electric field or even a field free region. The latter requirement is needed for high Voc and FF, as well as better stability against light-induced degradation. In reality, an a-Si:H intrinsic layer thickness of approximately 200–300 nm is used for the state-of-the-art a-Si:H solar cells. The doped layers also should be thick enough to form a large built-in potential but thin enough to avoid parasitic absorption. It has been found experimentally that the n-layer thickness should be in the range of 20–30 nm and the p-layer in the range of 10–20 nm. The non-semiconductor layers also affect the cell such as the TCO and BRs, which should not only serve as the electrodes for current collection, but also improve the light coupling and light trapping. From this perspective, a properly textured TCO on the glass superstrate and a textured BR on the substrate are required for p-i-n and n-i-p solar cells, respectively. In addition, multi-junction structures have been widely developed incorporating multiple thin-film silicon solar cells to utilize the solar spectrum efficiently. For these multi-junction solar cells, optimization of the plasma deposition process parameters to improve the building blocks is critical. For multi-junctions, this involves optimizing alloying with other elements and/or applying nanocrystalline structured materials as the absorbers with different bandgaps. Using a range of bandgaps is the most effective approach for achieving a high efficiency. Following this approach, a-SiGe:H and nc-Si:H have been well studied and used in double-, triple-, and quadruple-junction solar cells. The record initial and stable efficiencies of 14.6% and 13.0% were achieved by United Solar in 1997 using all a-Si:H-based materials. Thin-film nc-Si:H was introduced as a narrow bandgap absorber in the middle of the 1990s and was successfully used as the

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bottom cell absorber in multi-junction solar cells. With a nc-Si:H bottom cell, a record initial efficiency of 16.3% was achieved by United Solar and a stable efficiency of 14.0% by AIST. With respect to manufacturing, several large lines for this purpose were built in the late 1990s and 2000s. Oerlikon and Applied Materials built large PECVD, LP-CVD, and PVD systems for a-Si:H p-i-n solar cell modules on glass substrates, and United Solar/ECD built several very large roll-to-roll PECVD and PVD lines for producing n-i-p structured flexible thin-film silicon PV laminates. However, the disordered nature of thin-film silicon is the ultimate reason for the lower efficiency of these solar cells compared to their c-Si counterparts. Most thin-film silicon solar modules have an average stable efficiency below 10%, which results in reduced competitiveness in the market. As a result, thin-film Si:H solar cell technology as a PV sector for power generation over large areas has gradually disappeared. Nevertheless, the accumulated knowledge and know-how maintained by the thin-film Si:H community have identified new applications of this material in c-Si solar cell technology. Currently the so-called high-efficiency c-Si solar cells are fabricated using thin-film silicon technology. The HIT cell was invented in the 1990s and uses thin i-a-Si:H as the passivation layers and doped a-Si:H as the emitter and back field contact layers. In 30 years of sustained efforts, the HIT solar cell efficiency has surpassed that of the PERC cells, and the HIT technology has reached the threshold for mass production. The key efforts for improving the HIT solar cell efficiency focus on the optimization of the thin (∼5 nm) i-a-Si:H using various approaches for eliminating epitaxial growth, lowering the ion bombardment, and covering the c-Si uniformly. In addition, the doped layers must also be optimized with the goal of high doping efficiency and low parasitic absorption losses. The top TCO layer is critical for reducing series resistance losses by ensuring high conductivity, and for reducing reflection losses by using a quarter wavelength thickness for an antireflection effect. The commonly used TCOs are ITO, IWO, and IHO. The HIT solar cell has several advantages over conventional c-Si

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solar cells such as high Voc , low temperature coefficient, and good bifaciality. Therefore, it has been anticipated that the HIT design would form the basis of one of the high-efficiency c-Si solar cell technologies beyond the current mainstream PERC technology. Another high-efficiency c-Si technology is based on the TOPCon solar cell, which uses an ultrathin SiOx layer to passivate the c-Si interface and a heavily doped poly-Si layer to form the contact and to provide additional electric field passivation. The poly-Si layer is made by crystallization of an a-Si or a-Si:H layer, which can be deposited by LP-CVD, PECVD, or PVD methods. Experimental results have shown that the TOPCon passivation quality has only a weak dependence on the method used for the initial a-Si or a-Si:H precursor deposition and so has a wide tolerance for the precursor quality. Therefore, the TOPCon solar cell allows for a variety of possibilities when selecting a deposition method for the contact precursor. Currently LP-CVD has been well developed, whereas PECVD is coming on line soon. The PECVD method may be able to overcome difficult issues in LP-CVD such as the wraparound deposition and the need for ex-situ doping. Although the TOPCon technology was introduced to the field much later than the HIT technology, the efficiency of the TOPCon cell has matched that of the HIT cell. Furthermore, TOPCon cells are fabricated using the so-called high temperature process, which is compatible with the current PERC or PERL technology. In fact, manufacturing lines for cells in the TOPCon configuration could be established by upgrading the lines currently used for cells in the PERT (Passivated Emitter Rear Totally diffused) configuration with a few pieces of additional equipment. The estimated Capex of the TOPCon production line is lower than that of the HIT line with the same production capability, and therefore, it is believed that TOPCon may become a viable mass production technology even in advance of the HIT technology. In the end, I would emphasize that thin-film silicon solar cell technology has become a milestone in the history of PVs development, and the knowledge accumulated during the research and development of thin-film silicon solar cells has become valuable for the new highefficiency HIT and TOPCon solar cells.

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Acknowledgments I sincerely thank all of the colleagues in the thin-film silicon PV community, especially Professors W. Xu of Nankai University, K. Takahashi and M. Konagai of Tokyo Institute of Technology, L. Ley of Erlangen University, G. Adriaenssens of KU Leuven, P. C. Taylor of Colorado School of Mines, D. Cohen of University of Oregon, E. A. Schiff of Syracuse University, R. Collins of University of Toledo, and H. Fritzsche of University of Chicago for teaching me the fundamental physics of thin-film semiconductors and devices. I greatly appreciate all of my colleagues at United Solar for their help, collaboration, and friendship, especially S. R. Ovshinsky, S. Guha, J. Yang, X. Xu, F. Liu, T. Su, G. Yue, K. Lord, K. Beernink, G. Peikta, L. Sivec, G. DeMaggio, and S. Jones. I enjoyed the memorable life in Michigan, where we developed the triple-junction thin-film solar cells, built the great roll-to-roll technology, and produced the wonderful flexible thin-film silicon solar laminate product, at the same time as we enjoyed the life and raised our family. I also learned a lot from the colleagues of the groups in NREL, Neuchatel, J¨ ulich, Delft, ECN, IMEC, and AIST through the conferences of MRS, IEEE PVSC, EU-PVSEC, and the World PV Conference, and the visits from time to time. References 1. Spear, W. E., and Le Comber, P. G. (1975). Substitutional doping of amorphous silicon, Solid State Communications, 17, pp. 1193–1196. 2. Carlson, D. E., and Wronski, C. R. (1976). Amorphous silicon solar cell, Applied Physics Letters, 28, pp. 671–673. 3. Yang, J., Banerjee, A., and Guha, S. (1997). Triple-junction amorphous silicon alloy solar cell with 14.6% initial and 13.0% stable conversion efficiencies, Applied Physics Letters, 70, pp. 2975–2977. 4. Yan, B., et al. (2011). Innovative dual function nc-SiOx :H layer leading to a >16% efficient multi-junction thin-film silicon solar cell, Applied Physics Letters, 99, pp. 113512-1-3. 5. Stuckelberger, M., et al. (2017). Review: Progress in solar cells from hydrogenated amorphous silicon, Renewable and Sustainable Energy Reviews, 76, pp. 1497–1523. 6. Matsui, T., et al. (2018). Progress and limitations of thin-film silicon solar cells, Solar Energy, 170, pp. 486–498.

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7. Staebler, D. L., and Wronski, C. R. (1977). Reversible conductivity changes in discharge-produced amorphous Si, Applied Physics Letters, 31, pp. 292–294. 8. Stutzmann, M., Jackson, W. B., and Tsai, C. C. (1984). Kinetics of the Staebler-Wronski effect in hydrogenated amorphous silicon, Applied Physics Letters, 45, pp. 1075–1077. 9. Branz, H. M. (2003). The hydrogen collision model of metastability after 5 years: Experimental tests and theoretical extensions, Solar Energy Materials and Solar Cells, 78, pp. 425–445. 10. Su, T., and Taylor, P. C. (2002). Direct role of hydrogen in the StaeblerWronski effect in hydrogenated amorphous silicon, Physical Review Letters, 89, pp. 015502-1-4. 11. Tzanetakis, P. (2003). Metastable volume changes of hydrogenated amorphous silicon and silicon–germanium alloys produced by exposure to light, Solar Energy Materials and Solar Cells, 78, pp. 369–389. 12. Guha, S., Narasimhan, K. L., and Pietruszko, S. M. (1981). On lightinduced effect in amorphous hydrogenated silicon, Journal of Applied Physics, 52, pp. 859–860. 13. Tawada, Y., Okamoto, H., and Hamakawa, Y. (1981). a-SiC:H/a-Si:H heterojunction solar cell having more than 7.1 % conversion efficiency, Applied Physics Letters, 37, pp. 237–239. 14. Huang, C.-Y., Guha, S., and Hudgens, S. J. (1983). Gap state distribution of amorphous hydrogenated Si and Si:Ge alloys, Journal of Non-Crystalline Solids, 59–60, pp. 545–548. 15. Meier, J., Fluckiger, R., Keppner, H., and Shah, A. (1994). Complete microcrystalline p-i-n solar cell — Crystalline or amorphous cell behavior? Applied Physics Letters, 65, pp. 860–862. 16. Mahan, A. H. (2003). Hot wire chemical vapor deposition of Si containing materials for solar cells, Solar Energy Materials and Solar Cells, 78, pp. 299–327. 17. Shah, A. V., et al. (2003). Material and solar cell research in microcrystalline silicon, Solar Energy Materials and Solar Cells, 78, pp. 469–491. 18. Guha, S., Xu, X., Yang, J., and Banerjee, A. (1995). High deposition rate amorphous silicon-based multijunction solar cell, Applied Physics Letters, 66, pp. 595–597. 19. Schiff, E. A. (2003). Low-mobility solar cells: A device physics primer with application to amorphous silicon, Solar Energy Materials and Solar Cells, 78, pp. 567–595. 20. Liu, B., et al. (2017). High efficiency and high open-circuit voltage quadruple-junction silicon thin film solar cells for future electronic applications, Energy & Environment Science, 10, pp. 1134–1141. 21. Cashmore, J. S., et al. (2015). Record 12.34% stabilized conversion efficiency in a large area thin-film silicon tandem (MICROMORPHTM )

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layers in n-i-p microcrystalline silicon solar cells, Applied Physics Letters, 90, pp. 203502-1-3. Tan, H., Babal, P., Zeman, M., and Smets, A. H. M. (2015). Wide bandgap p-type nanocrystalline silicon oxide as window layer for high performance thin-film silicon multi-junction solar cells, Solar Energy Materials and Solar Cells, 132, pp. 597–605. Guha, S., Yang, J., Nath, P., and Hack, M. (1986). Enhancement of open circuit voltage in high efficiency amorphous silicon alloy solar cells, Applied Physics Letters, 49, pp. 218–219. Yan, B., Yue, G., Yang, J., and Guha, S. (2013). On the bandgap of hydrogenated nanocrystalline silicon intrinsic materials used in thin film silicon solar cells, Solar Energy Materials and Solar Cells, 111, pp. 90–96. Yan, B., Yang, J., Guha, S., and Gallagher, A. (1999). Analysis of plasma properties and deposition of amorphous silicon alloy solar cells using very high frequency glow discharge, Material Research Society Symposium Proceedings, 557, pp. 115–121. Jia, H., Saha, J. K., and Shirai, H. (2006). Plasma parameters for fast deposition of highly crystallized microcrystalline silicon films using high-density microwave plasma, Japanese Journal of Applied Physics, 45, pp. 666–673. Chapman, B. (1980). Glow Discharge Processes: Sputtering and Plasma Etching (New York, John Wiley & Sons), Chapter 4. Guo, L., et al. (1998). High rate deposition of microcrystalline silicon using conventional plasma-enhanced chemical vapor deposition, Japanese Journal of Applied Physics, 37, pp. L1116–L1118. Isomura, M., Kondo, M., and Matsuda, A. (2001). High-pressure plasma CVD for high-quality amorphous silicon, Solar Energy Materials and Solar Cells, 66, pp. 217–380. Kondo, M. (2003). Microcrystalline materials and cells deposited by RF glow discharge, Solar Energy Materials and Solar Cells, 78, pp. 543–566. Tsu, D. V., et al. (1997). Effect of hydrogen dilution on the structure of amorphous silicon alloys, Applied Physics Letters, 71, pp. 1317– 1319. Koh, J. H., et al. (1998). Optimization of hydrogenated amorphous silicon p–i–n solar cells with two-step i layers guided by real-time spectroscopic ellipsometry, Applied Physics Letters, 73, pp. 1526–1528. Ferlauto, A. S., Koval, R. J., Wronski, C. R., and Collins, R. W. (2002). Extended phase diagrams for guiding plasma-enhanced chemical vapor deposition of silicon thin films for photovoltaics applications, Applied Physics Letters, 80, pp. 2666–2668.

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47. Chevallier, J., Wieder, H., Onton, A., and Guarnieri, C. (1997). Optical properties of amorphous Six Ge1−x (H) alloys prepared by R.F. glow discharge, Solid State Communications, 24, pp. 867–869. 48. Cohen, J. D. (2003). Light-induced defects in hydrogenated amorphous silicon germanium alloys, Solar Energy Materials and Solar Cells, 78, pp. 399–424. 49. Gu, Q., et al. (1994). Hole drift mobility measurements in amorphous silicon-carbon alloys, Journal of Applied Physics, 76, pp. 2310–2315. 50. Yang, J., Banerjee, A., and Guha, S. (2003). Amorphous silicon based photovoltaics — From earth to the “final frontier,” Solar Energy Materials and Solar Cells, 78, pp. 597–612. 51. Guha, S., et al. (1989). Band-gap profiling for improving the efficiency of amorphous silicon alloy solar cells, Applied Physics Letters, 54, pp. 2330–2332. 52. Yang, J., et al. (1994). Progress in triple-junction amorphous siliconbased alloy solar cells and modules using hydrogen dilution, Proceedings of the 1st World Conference on Photovoltaic Energy Conversion (IEEE, New York), pp. 380–385. 53. Torres, P., et al. (1996). Device grade microcrystalline silicon owing to reduced oxygen contamination, Applied Physics Letters, 69, pp. 1373– 1375. 54. Merdzhanova, T., et al. (2012). Impurities in thin-film silicon: Influence on material properties and solar cell performance, Journal of Non-Crystalline Solids, 358, pp. 2171–2178. 55. Williamson, D. L. (2003). Microstructure of amorphous and microcrystalline Si and SiGe alloys using X-rays and neutrons, Solar Energy Materials and Solar Cells, 78, pp. 41–84. 56. Yan, B., et al. (2002). Hydrogenated microcrystalline silicon solar cells made with modified very-high-frequency glow discharge, Material Research Society Symposium Proceedings, 715, pp. 629–635. 57. Yan, B., et al. (2004). Microstructure evolution with thickness and hydrogen dilution profile in microcrystalline silicon solar cells, Material Research Society Symposium Proceedings, 808, pp. 575–580. 58. Yan, B., et al. (2004). Hydrogen dilution profiling for hydrogenated microcrystalline silicon solar cells, Applied Physics Letters, 85, pp. 1955–1957. 59. M¨ uller, J., et al. (2003). State-of-the-art mid-frequency sputtered ZnO films for thin film silicon solar cells and modules, Thin Solid Films, 442, pp. 158–162. 60. H¨ upkes, J., et al. (2012). Instabilities in reactive sputtering of ZnO:Al and reliable texture-etching solution for light trapping in silicon thin film solar cells, Thin Solid Films, 520, pp. 1913–1917.

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61. Yan, B., et al. (2005). Improved back reflector for high efficiency hydrogenated amorphous and nanocrystalline silicon based solar cells, Material Research Society Symposium Proceedings, 862, pp. 603–608. 62. Yue, G., et al. (2009). Optimization of back reflector for high efficiency hydrogenated nanocrystalline silicon solar cells, Applied Physics Letters, 95, pp. 263501-1–3. 63. Yan, B., et al. (2012). Correlation of texture of Ag/ZnO back reflector and photocurrent in hydrogenated nanocrystalline silicon solar cells, Solar Energy Materials and Solar Cells, 104, pp. 13–17. 64. Python, M., et al. (2009). Influence of the substrate geometrical parameters on microcrystalline silicon growth for thin-film solar cells, Solar Energy Materials and Solar Cells, 93, pp. 1714–1720. 65. S¨ oderstr¨ om, K., et al. (2012). Experimental study of flat lightscattering substrates in thin-film silicon solar cells, Solar Energy Materials and Solar Cells, 101, pp. 193–199. 66. Sai, H., Kanamori, K., and Kondo, M. (2011). Flattened lightscattering substrate in thin film silicon solar cells for improved infrared response, Applied Physics Letters, 98, pp. 113502-1-3. 67. Yan, B., Yue, G., Yang, J., and Guha, S. (2008). Correlation of current mismatch and fill factor in amorphous and nanocrystalline silicon based high efficiency multi-junction solar cells, Proceedings of the 33rd IEEE Photovoltaic Specialists Conference (San Diego, California), paper no. 257. 68. Boccard, M., et al. (2014). High-stable-efficiency tandem thin-film silicon solar cell with low-refractive-index silicon-oxide interlayer, IEEE Journal of Photovoltaics, 4, pp. 1368–1373. 69. Matsui, T., Sai, H., Saito, K., and Kondo, M. (2013). Highefficiency thin-film silicon solar cells with improved light-soaking stability, Progress in Photovoltaics: Research and Applications, 21, pp. 1363–1369. 70. Isabella, O., Smets, A. H. M., and Zeman, M. (2014). Thin-film siliconbased quadruple junction solar cells approaching 20% conversion efficiency, Solar Energy Materials and Solar Cells, 129, pp. 82–89. 71. Sch¨ uttauf, J.-W., et al. (2015). Amorphous silicon–germanium for triple and quadruple junction thin-film silicon based solar cells, Solar Energy Materials and Solar Cells, 133, pp. 163–169. 72. Urbain, F., et al. (2016). Light-induced degradation of adapted quadruple junction thin film silicon solar cells for photoelectrochemical water splitting, Solar Energy Materials and Solar Cells, 145, pp. 142–147. 73. Carlson, D. E. (2003). Monolithic amorphous silicon alloy solar modules, Solar Energy Materials and Solar Cells, 78, pp. 627–645.

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74. Multone, X., et al. (2015). Triple-junction amorphous/microcrystalline silicon solar cells: Towards industrially viable thin film solar technology, Solar Energy Materials and Solar Cells, 140, pp. 388–395. 75. Adachi, D., Hernandez, J. L., and Yamamoto, K. (2015). Impact of carrier recombination on fill factor for large area heterojunction crystalline Si solar cell with 25.1% efficiency, Applied Physics Letters, 107, pp. 233506-1-3. 76. Masuko, K., et al. (2014). Achievement of more than 25% conversion efficiency with crystalline silicon heterojunction solar cell, IEEE Journal of Photovoltaics, 4, pp. 1433–1435. 77. Haschke, J., Dupr´e, O., Boccard, M., and Ballif, C. (2018). Silicon heterojunction solar cells: Recent technological development and practical aspects — From lab to industry, Solar Energy Materials and Solar Cells, 187, pp. 140–153. 78. Chen, R., et al. (2017). Optimized n-type amorphous silicon window layers via hydrogen dilution for silicon heterojunction solar cells by catalytic chemical vapor deposition, Journal of Applied Physics, 122, pp. 125110-1-7. 79. Koida, T., Fujiwara, H., and Kondo, M. (2008). Reduction of optical loss in hydrogenated amorphous silicon/crystalline silicon heterojunction solar cells by high-mobility hydrogen-doped In2 O3 transparent conductive oxide, Applied Physics Express, 1, pp. 041501-1–041501-3. 80. Kobayashi, E., et al. (2016). Light-induced performance increase of silicon heterojunction solar cells, Applied Physics Letters, 109, pp. 153503-1-5. 81. Feldmann, F., et al. (2014). Tunnel oxide passivated contacts as an alternative to partial rear contacts, Solar Energy Materials and Solar Cells, 131, pp. 46–50. 82. Peibst, R., et al. (2017). Working principle of carrier selective poly-Si/ c-Si junctions: Is tunneling the whole story? Solar Energy Materials and Solar Cells, 158, pp. 60–67. 83. Zhang, Z., et al. (2018). Carrier transport through the ultrathin siliconoxide layer in tunnel oxide passivated contact (TOPCon) c-Si solar cells, Solar Energy Materials and Solar Cells, 187, pp. 113–122. 84. Tong, H., et al. (2018). A strong-oxidizing mixed acid derived highquality silicon oxide tunneling layer for polysilicon passivated contact silicon solar cell, Solar Energy Materials and Solar Cells, 188, pp. 149–155. 85. Yan, D., et al. (2018). 23% efficient p-type crystalline silicon solar cells with hole-selective passivating contacts based on physical vapor deposition of doped silicon films, Applied Physics Letters, 113, pp. 061603-1-4.

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86. Tao, K., et al. (2017). Application of a-Si/μc-Si hybrid layer in tunnel oxide passivated contact n-type silicon solar cells, Solar Energy, 144, pp. 735–739. 87. Morisset, A., et al. (2019). Highly passivating and blister-free hole selective poly-silicon based contact for large area crystalline silicon solar cells, Solar Energy Materials and Solar Cells, 200, pp. 109912-1-8. 88. Ingenito, A., et al. (2018), A passivating contact for silicon solar cells formed during a single firing thermal annealing, Nature Energy, 3, pp. 800–808. 89. Nandakumar, N., et al. (2018). Approaching 23% with large-area monoPoly cells using screen-printed and fired rear passivating contacts fabricated by inline PECVD, Progress in Photovoltaics: Research and Applications, 27, pp. 1–6. 90. Duttagupta, S., et al. (2018). MonoPolyTMcells: Large-area crystalline silicon solar cells with fire-through screen printed contact to doped polysilicon surfaces, Solar Energy Materials and Solar Cells, 187, pp. 76–81. 91. Feldmann, F., et al. (2019). Large area TOPCon cells realized by a PECVD tube process, 36th European PV Solar Energy Conference and Exhibition, Paper 2EO.1.4. 92. Schmidt, J., Peibst, R., and Brendel, R. (2018). Surface passivation of crystalline silicon solar cells: Present and future, Solar Energy Materials and Solar Cells, 187, pp. 39–54.

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CHAPTER 10

Amorphous Silicon Microbolometers for IR Imaging Athanasios J. Syllaios, Vincent C. Lopes, Chris L. Littler, and Kiran Shrestha University of North Texas, USA

Oh Langley devised the bolometer: It’s really a kind of thermometer Which measures the heat From a polar bear’s feet At a distance of half a kilometre.∗ ∗ “A

random walk in science”, R. L. Weber and R. Mendoza, IOP, 1973, p. 84

10.1. Introduction Bolometers belong to a group of thermal sensors used for radiation detection in the Near InfraRed (NIR) to TeraHertz (THz) spectral range. Applications of IR radiation detection include defense, security, astronomy, and medical and scientific research. Detection of this radiation can be accomplished by photon sensors utilizing narrow bandgap materials such as HgCdTe, InSb, and III–V superlattices, or by thermal sensors. Thermal sensors include opto-acoustic sensors such as Golay cells, thermopiles, pyroelectric detectors, and 409

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bolometers. Thermopiles are thermocouples typically connected in series, which convert heat into an electrical signal. In the case of pyroelectric materials, heat causes a slight rearrangement of the atoms in the crystal, resulting in a change in electrical polarization of the material and therefore a change in voltage across the crystal. Bolometers measure resistance changes induced by heating, utilizing materials whose resistance is temperature dependent. Samuel Pierpont Langley invented the bolometer in 1878 while working on measurements of the solar radiation intensity at various wavelengths. He used a thin metal strip approximately 1 micron thick as one arm of a Wheatstone bridge and, with the aid of galvanometer, was able to measure temperature differences of one hundred thousandth of a degree Celsius (0.00001◦ C). He named the metal strip a “bolometer” (βoλη μετ ρoν ) or “ray measurer” to signify that it quantitatively measures radiation and is not just an indicator [1, 2]. Microbolometers are composed of low thermal mass, thermally isolated thin films. Typical lateral dimensions are in the range of 10–50 μm and thicknesses are in the range of 50–200 nm. To increase thermal isolation and absorption of incident IR radiation flux, the films are suspended by long thermal isolation legs utilizing a resonantly absorbing quarter-wave Fabry-Perot cavity design. The material properties that control the performance of microbolometers are the temperature coefficient of resistance (TCR) and the electrical noise. Reported microbolometer materials include amorphous SiGe, poly-SiGe, amorphous SiGeO, YBaCuO, and carbon nanotubes. For current IR imaging technologies, vanadium oxide (VOx ) and hydrogenated amorphous silicon (a-Si:H) are the materials of choice. Single element microbolometer detectors [3–5] and imaging focal plane arrays [6, 7] utilizing a-Si:H have been developed due to the high TCR and low noise of this amorphous semiconductor as well as the advantages of a-Si:H thin films in microbolometer device fabrication and processing. These include the following: — a-Si:H is compatible with silicon IC and MEMS manufacturing; — a-Si:H is fabricated with a well-established low temperature deposition technology, for example, plasma enhanced chemical vapor deposition (PECVD);

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— a-Si:H is an amorphous material, implying that hetero-interfaces can be easily formed while maintaining good interface properties, for example, Type I interfaces with crystalline silicon (c-Si), nanocrystalline silicon (nc-Si), amorphous silicon–germanium (a-SiGe) alloys, amorphous silicon–carbide (a-SiC) alloys, and a-SiNx ; — a-Si:H is a hard material (Vickers Hardness HV = 1500– 2000 kg/mm2 ) and can be finely patterned with photolithographic technology, well below submicron level; and, finally, — a-Si:H is a nontoxic material. In this chapter, we will focus on amorphous silicon material and its properties relevant to microbolometer performance for IR imaging applications. We will first present an introduction to uncooled microbolometer IR imaging technology, illustrating the important design parameters for optimal sensing of IR radiation. We will then summarize the key elements of microbolometer detection, with an emphasis on the required material properties and design considerations that optimize detector performance based on the resistance requirements for the readout electronics. The balance of the chapter provides a tutorial introduction to the mechanisms controlling bolometric detection in a-Si:H, that is, electrical conductivity and noise, with examples that illustrate the importance of each to the final design and operation of microbolometer focal plane arrays. 10.2. Uncooled Microbolometer IR Imaging Technology A major application of microbolometers is in IR imaging technology [8–11]. Microbolometer cameras operate at ambient temperature and thus are uncooled, that is, they do not require cooling to cryogenic temperatures. Microbolometer imaging arrays consist of a focal plane of pixels that are suspended above a read out integrated circuit (ROIC) and thermally isolated with narrow supporting legs, as shown in Fig. 10.1 The electrically active a-Si:H film is encapsulated by insulator films such as amorphous silicon nitride that electrically passivate the a-Si:H surface. A thin metal over the

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Al Reflector

Absorber Metal SiNx

Electrical Contact Metal

α -SiNx:H/α-Si:H/α-SiNx:H/Absorber membrane ~2000 Å thick

d

α-Si SiNx

Current Flow

d

Metal Reflector

ROIC

(a)

(b)

Fig. 10.1. Infrared (IR) resonant cavity pixel structure for a microbolometer based on hydrogenated amorphous silicon (a-Si:H).

100

5λ λ/4

90

3λ/4-resonance λ MWIR

λ/4-resonance λ LWIR

80

% Absorptance

70 60 50 40 30 20 10 0 2

3

4

5

6

7

8

9

10

11

12

13

14

15

Wavelength (um)

Fig. 10.2. Absorptance of a resonant cavity pixel utilizing a hydrogenated amorphous silicon (a-Si:H) quarter-wave design that exhibits λ/4, 3λ/4, and 5λ/4 resonances. Midwave infrared (MWIR) and long wave infrared (LWIR) resonances are indicated.

top insulator is used to increase the pixel absorption. Also, the multilayer pixel membrane is designed to adjust total stress for pixel planarity. The pixel membrane is part of a Fabry–Perot resonant cavity architecture [12] that enhances the IR absorptance, as depicted in Fig. 10.2. The resonant cavity involves an absorbing membrane

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(a)

(b)

413

(c)

Fig. 10.3. (a) Visible picture of a house, (b) 8 μm–14 μm infrared image of the same house, and (c) infrared image of a cat taken at night. These images were obtained looking through a microbolometer array camera.

suspended a distance d above the cavity reflector metal. The resonant absorptance peaks correspond to the condition for minimum reflectance. The figure shows the first three resonance absorptance peaks including the fundamental λ/4-resonance spanning the long wavelength infrared (LWIR) spectral band, the 3λ/4-resonance at nominally one-third the fundamental wavelength, and the 5λ/4resonance at nominally one-fifth the fundamental wavelength. Thermal imaging by a microbolometer array is generated as follows. Incident IR flux, ΔΦ, from a scene is focused onto the array, causing the pixels to heat up by an amount ΔT proportional to the IR flux and the thermal resistance Rth of each pixel. The integrated circuit below the pixels measures the change in resistance ΔR, as a change in voltage ΔV at constant current, and generates a composite thermal image of the entire scene captured by the array. IR images are thus temperature maps of the imaged scene in gray scale or false color. Shades of gray are assigned to temperatures, that is, the hotter the object the whiter it will appear (when set to white hot polarity). Example of thermal images are shown in Fig. 10.3. 10.3. Detection of IR Radiation Multiple authors have mathematically analyzed microbolometer detection [9, 13]. Here we summarize the key results, illustrating the interplay of material properties and design considerations. IR radiation incident upon the membrane will cause the pixel temperature to increase. The assumptions used are that the only

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heat loss is through the legs and that power dissipated in a pixel due to the applied bias current is negligible. Equation (10.1) describes the heat flow in the pixel: ηP = ηP0 e−jωt = C

d (ΔTpixel ) + G(ΔTpixel ), dt

(10.1)

where C is the heat capacity, G is the thermal conductance of the supporting structure (legs), η is the fraction of incident radiation absorbed, P0 is the incident radiant power, and ω is the angular frequency of modulation of the radiation. The increase in pixel temperature is ΔT pixel =

ηP0 , G(1 + ω 2 τ 2 )1/2

(10.2)

where τ ≡ C G is the thermal response time constant of the pixel. The increase in pixel temperature ΔTpixel depends on the absorption efficiency, heat capacity, thermal conductance, and frequency of the incident radiation. The heat capacity and thermal conductance are given by C≡

mcΔTpixel ΔQ = = mc, ΔTpixel ΔTpixel

G=k

1 A = . lleg Rth

and

(10.3) (10.4)

The heat capacity C depends on the specific heat and mass of the sensing element, and therefore on the pixel dimensions. The thermal conductance G depends on the thermal conductivity of the legs and their geometry, where k is the thermal conductivity, A is the crosssectional area, lleg is the length, and τ is a measure of how fast the pixel will heat and cool. The thermal conductance is inversely proportional to the thermal resistance Rth . Pixels should be designed 1 , where f is the camera frame rate. A larger frame such that τ ∼ 3f rate results in a better video image; (gaming is 60 frames/s, which would result in τ = 5.6 ms). As a result, there are design trade-offs

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related to pixel material and dimensions and support leg material and dimensions. 10.3.1. Signal Voltage and Responsivity The resistance change due to heating of the pixel is ΔR = αTCR R0 ΔT pixel ,

(10.5)

where αTCR is the TCR and R0 is the pixel resistance. A bias current applied to the pixel results in a signal voltage, given by Vsig = ibias ΔR,

or

Vsig = ibias αTCR R0

ηP0 . G(1 + ω 2 τ 2 )1/2

(10.6) (10.7)

The signal voltage depends on the absorption efficiency, the pixel’s heat capacity, the legs’ thermal conductance, and the pixel’s resistance and TCR. The responsivity of the pixel is normalized to the incident radiation power, where R≡

ibias αTCR R0 η Vsig = . P0 G(1 + ω 2 τ 2 )1/2

(10.8)

10.3.2. Noise Equivalent Temperature Difference Perhaps the key figure of merit (FOM) of a microbolometer is its noise equivalent temperature difference (NETD). It is a measure of a scene temperature difference that an array can differentiate. Quantitatively, NETD = Fsystem

optics

Vnoise , Apixel R(ΔP /ΔTBlackbody )

(10.9)

where Vnoise is the detector electrical noise, R is the responsivity, Apixel is the pixel area, ΔP /ΔTBlackbody is the change in power radiated by a blackbody (object) per change in blackbody (object) temperature, and Fsystem optics is the pre-factor taking into account the optical configuration. Alternatively, the NETD can be

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expressed by NETD ∼

GV noise Vnoise ∝ . Vsig αTCR

(10.10)

Thus, the noise equivalent temperature is proportional to the thermal conductance and the noise voltage whereas it is inversely proportional to the TCR. Electrical noise contributions include 1/f noise, Johnson noise, thermal noise, and ROIC noise. Since our focus is on the material and structural properties of amorphous silicon that will affect NETD, noise and the TCR are the leading parameters of concern. 10.3.3. Thermal Time Constant Another FOM for microbolometers is the pixel thermal time constant, τ , given by τ≡

C = Rth mpixel c ∝ Rth × Apixel tpixel . G

(10.11)

The thermal resistance Rth is determined by the legs. For fixed Rth , the thermal response time is determined by the pixel mass. Reduction in pixel mass by a reduction in pixel area or thickness will result in lower thermal response time (Table 10.1). Figure 10.4 illustrates the effect of pixel design on thermal time constant. This figure shows the calculated thermal time constant as a function of a-Si:H thickness for a fixed thermal resistance of 2 × 108 K/W and pixel areas of 10 μm × 10 μm, 17 μm × 17 μm, and 25 μm × 25 μm. In this calculation, only a-Si:H was considered. For a fixed pixel size of 17 μm × 17 μm, the thermal time constant is approximately 5 ms at a thickness of 500 ˚ A and increases with Table 10.1. Reported thermal response time and the corresponding thermal conductance and pixel size. τ (ms)

Rth (K/W)

Pixel size (μm)

Reference

5 11 5, 8.7 7

4 × 107 4 × 107

48 48 30, 50 17

[14] [11] [15] [16]

2 × 108

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Fig. 10.4. Thickness dependence of thermal time constant for three different pixel sizes.

increasing pixel thickness. For fixed pixel thickness, the thermal time constant increases with increasing pixel area. Generally, low mass thin films are required to obtain a low thermal time constant, setting an upper thickness limit. The low thickness or volume limit is determined by the noise requirements since low noise is associated with low resistivity and large pixel volume, that is, a large number of carriers, according to Hooge’s noise model [17]. To a certain extent, the transport properties of a-Si:H are interdependent: higher resistivity a-Si:H exhibits higher TCR and noise. 10.3.4. Figure of Merit As shown in Eq. (10.10), increasing the thermal conductance G degrades the NETD. Decreasing G to improve NETD degrades the thermal time constant τ . The FOM of microbolometer imaging devices at the pixel level is defined as the product of the NETD and the thermal time constant τ as follows [18] FOM = NETD ∗ τ.

(10.12)

The introduction of a FOM addresses the trade-offs between the NETD and the thermal time constant. Low FOM signifies a higher

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120

FOM = 200 mKms

NETD (mK)

100 80 60 40 20 0 0

5

10

15

20

Thermal Time Constant (ms)

Fig. 10.5. Calculated noise equivalent temperature difference (NETD) versus thermal time constant for two figures of merit.

performance microbolometer pixel. The units of FOM are (mK ms). The relationship of NETD to thermal time constant for two FOM values is shown in Fig. 10.5. 10.3.5. Microbolometer Pixel Design Considerations The specific properties required for application of a-Si:H films in microbolometer array technology are determined by the design requirements of the detector arrays and readout electronics. In general, a high TCR with low 1/f noise is desired at a conductivity dictated by the IC design. This minimizes the NETD as shown in Eq. (10.10), maximizes detector responsivity, while providing the ability to build large format arrays. Typically, however, there are competing effects that lead to trade-offs between these key film properties. Such optimization of the transport properties of a-Si:H films starts by first determining the pixel resistance range for a particular array class and ROIC design. Selecting a resistance range determines the required a-Si:H resistivity for a specific thickness. Generally, thin films are required to obtain a low thermal time constant, setting an upper thickness limit. The low limit is determined by the emergence of surface and interface controlling effects on a-Si:H film growth and transport properties. To a certain extent, resistivity determines the

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419

Thermal Time Constant

Resisvity

Pixel Geometry: Size, Layer Thickness

Temperature coefficient of resistance (TCR)

Noise

Stress

SixNy insulator SixNy/a-Si:H interface

a-Si:H p-or n-type Deposion parameters: Tsub, Power, Pressure, Dep. rate, Precursors, Doping level, H-diluon Post-deposion annealing Input requirements Control parameters and processes

Fig. 10.6. Balancing material requirements in microbolometer design.

associated values of TCR and noise. Higher resistivity a-Si:H exhibits higher TCR and noise. The interdependence of transport properties is illustrated in Fig. 10.6. Control of resistivity and independent control of TCR and noise can be accomplished by a-Si:H material selection and processing. 10.4. Conductivity and TCR of Microbolometer Materials The conductivity of materials used in microbolometer technology is generally described as following a thermal activation process of the form − k ET

σ(T ) = σ0 e

B

T0

= σ0 e− T ,

(10.13)

where σ0 is the conductivity pre-factor, E is an activation energy, T0 = E/kB is a material characteristic temperature, and kB is the Boltzmann constant. Thermal activation has been reported for VOx [19], and a-Si:H [20, 21] and amorphous silicon–germanium alloys

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(a-Six Ge1−x :H) [22]. These measurements are usually in the temperature range near room temperature and higher. When conductivity measurements are extended to low temperatures, it is found that the conductivity of such materials is controlled by carrier hopping. 10.4.1. Hopping Conduction Hopping conduction involves the electrical transport of localized charge carriers. In materials with a high density of trapping center defects, hopping is the main type of conductivity over a wide temperature range. Depending on the details of the charge carrier interaction, different types of hopping conduction are observed including nearest neighbor hopping (NNH) and variable range hopping (VRH) either without a Coulomb gap at the Fermi level (Mott conduction (M)), or with a Coulomb gap (Efros–Shklovskii (ES)) conduction. The general expression for the temperature dependent conductivity, σ(T ), in the regime of hopping transport is given by −

σ (T ) = σ0 e

“

T0 T

”p

,

(10.14)

where T0 is the characteristic temperature, T is the material temperature, and σ0 is the conductivity pre-factor. In the case of VRH transport, where the long range Coulomb interaction between carriers is neglected, Mott [23] found that the conductivity could be described by Eq. (10.14) with p = 1/4, where T0 is the characteristic temperature, obtained assuming the density of states (DOS) is a constant in the vicinity of the Fermi level. When the long-range Coulomb interaction is not neglected, Efros and Shklovskii [24] found that the VRH conductivity could be described by Eq. (10.14) with p = 1/2. In this case, when the Fermi energy lies within a range of energies where the states are localized, the Coulomb interaction leads to a gap in the DOS at the Fermi level [25, 26]. The appearance of this “Coulomb gap” by electron correlations can be considered as arising from a minimum energy required for a hopping conduction process to occur between the localized states with finite energy and spatial distribution [24, 27]. Finally, when transport is carried out

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Cross Over Temperature

by hopping between nearest neighbor atomic sites, the form of the conductivity is given by Eq. (10.14) with p = 1 [24, 27]. In the NNH case, Eq. (10.14) for p = 1 resembles Eq. (10.13), which describes thermally activated conduction but due to an entirely different mechanism. In most materials the Coulomb gap is small, and ES type conductivity is observed only at low temperature. For intermediate temperatures, there is a crossover from ES to M conduction, and, at high temperatures, both the M type and ES type mechanisms transition to NNH conduction. The temperature where the crossover occurs depends on the DOS at the Fermi level, N (EF ), the dielectric constant of the material, and the trap nearest neighbor distance [25]. Figure 10.7 shows a qualitative plot of the crossover temperature versus the DOS at the Fermi level N (EF ). Shown are the crossover temperatures for the three transitions: ES to M and M to NNH for p-type a-Si:H, and ES to NNH for n-type a-Si:H. An example of the crossover from ES to M is seen in Fig. 10.8. At low temperatures, the observed conductivity for higher conductivity p-type samples is seen to deviate from Mott conduction. These samples are grown by PECVD with boron dopant to silane ratio r = [B]/[SiH4 ] = 0.32, and hydrogen dilution of silane RH = [H2 ]/[SiH4 ] = 4. The conductivity

NNH ~ T-1 p-type a-Si:H MOTT ~ T-1/4

n-type a-Si:H E-S ~ T-1/2

Increasing DOS, N(E F)

Fig. 10.7. Hopping conduction diagram.

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1.E+00 1.E-01 1.E-02 1.E-03 1.E-04 1.E-05 1.E-06 1.E-07 1

3

5

7

9

11

13

15

1000/T (1/K)

Fig. 10.8. Temperature dependent conductivity for RH = 4 and r = 0.32, showing the contributions of Mott (M) and Efros–Shklovskii (ES) conductivity and the fit to the experimental results. The diamonds represent the measured conductivities, the blue line is the M fit to the high temperature data, the black line is the ES fit to the lower temperature data, and the red line is the addition of the M and ES conductivities.

of these samples can be described in terms of a combination of M and ES mechanisms, where the total conductivity is given by σ = σM + σES . The result of this analysis for a typical sample is shown in Fig. 10.8. The crossover point from ES to M in Fig. 10.8, is ∼100 K. Assuming this value in models [24, 25] relating the crossover temperature to the DOS yields ∼5× 1020 cm−3 , close to the expected value for the boron doping ratio used. 10.4.2. Conductivity and TCR of p-type a-Si:H In this section, we discuss methods for determining the underlying conduction mechanisms in amorphous materials, using the results from p-type a-Si:H for illustration. The use of differential analysis is seen to be necessary to differentiate among the different conduction mechanisms. 10.4.2.1. Electrical Conductivity The temperature dependence of conductivity and TCR were measured on hydrogenated p-type a-Si:H films grown by PECVD at differing boron dopant source concentrations, r = [B]/[SiH4 ],

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Temperature range: 200 K- 450 K

Conducvity (Ω-cm)-1

1.E-01 1.E-02 1.E-03 1.E-04 1.E-05 1.E-06 0.21

0.23

0.25

0.27

1/T1/4 (1/K1/4) Fig. 10.9. Conductivity as a function of 1/T 1/4 for p-type hydrogenated amorphous silicon (a-Si:H).

and hydrogen dilutions, RH = [H2 ]/[SiH4 ], relative to the silane precursor. It was found that the temperature dependent electrical conductivity σ(T ) can be described by Mott variable range hopping (MVRH) conduction, Eq. (10.14) with p = 1/4. Figure 10.9 shows the conductivity as a function of temperature for a p-type a-Si:H film. The solid line in the figure is the exponential fit to the data using p = 1/4. An almost identical fit is obtained, however, from an exponential using p = 1/2, and when fit over a smaller range of temperatures around 300 K, even p = 1 yields an acceptable fit. This has led to a long standing conclusion that impurity conduction dominates near room temperature, and the conductivity has been described using an extrinsic conduction model with an activation energy. Clarification of the conduction mechanism in p-type a-Si:H has come from applying differential analysis techniques, such as resistance curve derivative analysis (RCDA) [28]. In the RCDA method, the logarithmic conductivity data are numerically differentiated versus temperature, and the quantity w, given by d(log σ) =p w(T ) = d(log T )



T0 T

p ,

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log [W]

424

13:9

1.12 1.10 1.08 1.06 1.04 1.02 1.00 0.98 2.30

y = -0.27x + 1.73

2.40

2.50

2.60

2.70

log [T(K)] Fig. 10.10. Resistance curve derivative analysis (RCDA) of hydrogenated amorphous silicon (a-Si:H) conductivity data shown in Fig. 10.9.

is determined. The exponent p is obtained from the slope and the characteristic temperature T0 from the y-intercept by plotting: log w = −p log T + log p(T0 )p .

(10.15)

Figure 10.10 shows the results of the RCDA analysis for the a-Si:H data plotted in Fig. 10.9. The derived value of the exponent is 0.27, close to p = 1/4, confirming that the conductivity is due to MVRH as expected for this material system and temperature range [29, 30]. 10.4.2.2. Temperature Coefficient of Resistance The TCR depends on the conductivity regime specified by the exponent p and the characteristic temperature T0 in that regime. The dependence is given by    1 dσ  T0p   = p p+1 , (10.16) |TCR| =  σ dT  T which is derived from the expression for conductivity in Eq. (10.14). For each hopping regime, the TCR has a T −(p+1) power law temperature dependence and is controlled by the characteristic temperature T0 . Rewriting Eq. (10.16) using p = 1/4 yields: 1

|TCR|Mott

4 1 T0M = , 4 T 54

(10.17)

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Fig. 10.11. Temperature coefficient of resistance (TCR) relationship to the Mott characteristic temperature T0M .

showing that the TCR in the Mott regime is proportional to the 1/4 characteristic temperature T0M . For a specific temperature, the TCR is determined from the value of T0M , which in turn is controlled by the growth parameters, including the hydrogen dilution of the silane precursor RH and the dopant to silane ratio r. 1/4 Figure 10.11 shows TCR results plotted versus T0M for a series of amorphous silicon films. Superimposed on the data is a plot of 1/4 TCR versus T0M from Eq. (10.17), which is in agreement with the experimental data. The TCR was determined using numerical differentiation of the measured conductivity data versus temperature. The characteristic temperature T0M was determined either from the conductivity versus T −1/4 fits or from RCDA analysis. It is clear that MVRH dominates for a-Si:H near room temperature, regardless of doping or hydrogen dilution. As shown in Fig. 10.12, the Mott characteristic temperature, T0M , depends on the PECVD growth parameters. The Mott characteristic temperature T0M is observed to increase with increasing hydrogen dilution and to decrease with increasing boron doping. As shown in Fig. 10.13, the M conductivity pre-factor σ0M depends on the Mott characteristic temperature T0M according to

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RH= const

1.2E+09 1.1E+09

1.3E+09

T0M (K)

T0M (K)

1.0E+09 9.0E+08

9.0E+08 8.0E+08

5.0E+08 7.0E+08 6.0E+08

1.0E+08 0

50 100 Hydrogen Diluon RH (AU)

0.1

150

0.2

0.3

0.4

Boron doping rao r (AU)

Fig. 10.12. Dependence of Mott characteristic temperature T0M on the growth parameters of hydrogen dilution and B doping.

1.E+17

y = 1.64e0.1961x R² = 0.9959

1.E+16

σ0M (Ω-cm)-1

1.E+15 1.E+14 1.E+13 1.E+12 1.E+11 1.E+10 1.E+09 100

120

140

T0M1/4

160

180

200

(K1/4)

Fig. 10.13. Mott variable range hopping and Meyer–Neldel effect.

the Meyer–Neldel (MN) effect [31], where  1 T0M 4 . σ0M = σ00 TMN

(10.18)

For the results shown in Fig. 10.13, the MN pre-factor is σ00 ≈ 1.64 (Ω-cm)−1 and the MN temperature is TMN ≈ 676 K. Since the conductivity pre-factor depends on T0M , the MVRH conductivity in p-type a-Si:H is determined by the characteristic temperature T0M .

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10.5. Electrical Noise Electrical noise is due to conductivity fluctuations. The total noise measured is comprised of 1/f noise, Johnson noise, thermal noise, and potentially generation-recombination (G-R) noise. 1/f or low frequency noise is due to conductivity fluctuations that exhibit an inverse frequency dependence; Johnson noise is due to the random motion of charge carriers; thermal noise is a result of thermal fluctuations of the membrane; and G-R noise is due to charge trapping. 10.5.1. Theory Table 10.2 summarizes the equations for the noise per unit bandwidth and noise within the bandwidth. The electrical bandwidth is determined from the frequencies of the device operating time (typically f2 ∼ 8000 Hz) and the frame rate (f1 = frame rate/2) [32]. The thermal bandwidth is 1/(4τthermal ) [19]. Hooge’s model [17] can be used to describe 1/f noise. Quantitatively, this model yields 2 V1/f

Δf

=

2 2 αH VBias αH VBias B = = γ. γ γ P f pV f f

(10.19)

Table 10.2. Equations for the various electrical noise constituents. Noise per unit bandwidth 1/f Noise

2 αH VBias pV f

Noise in bandwidth “ ” αH V 2 ln ff21 pV bias

Johnson Noise

4kB T Rdet

4kB T Rdet Δfelectrical

Thermal Noise

(αTCR Vbias )2 kBGT

G-R Noise

2 At τ VBias 1+(2πτ f )2

Total Noise

2 V1/f

Δf

+

+

2 VJohnson Δf

2 VG−R Δf

2

2

(αTCR Vbias )2 kBGT Δfthermal At V 2 [tan−1 (2πτ f2 ) 2π bias − tan−1 (2πτ f 1 )]

+

2 VThermal Δf

2 2 2 V1/f + VJohnson + Vthermal 2 + VG−R

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2 , P is the total number of carriers, In Eq. (10.19), B = [αH /(pV )]VBias p is the carrier density, V is the device volume, VBias is the device bias, and γ is the frequency exponent. Noise is considered 1/f in nature if γ is in the range from 0.9 to 1.1. The normalized Hooge parameter is αH /p, where αH is the Hooge coefficient. For the Hooge model,  √ αH VBias , B= (10.20) pAt

or

 B=

αH 2 V pt Bias



1 , A

(10.21)

where A is the device area and t is the film thickness. As a result, √ B ∝ VBias , and B ∝ 1/A. The G-R noise for a single trap is described by [33–35] 2 2 At τtrap VBias VG-R = , Δf 1 + (2πτtrap f )2

(10.22)

where τtrap is the trap time constant and At = nt /Vp 2 . Here, nt is the trap density, V is the device volume, and p is the carrier density. The noise waveform can be analyzed for trapping by f

2 2 /Δf ) − (Vwhite /Δf ) (Vnoise f At τtrap αH + = . 2 P 1 + (2πτtrap f )2 VBias

(10.23)

Eq. (10.23) can be normalized to the device volume [36] with  2  2 Vnoise /Δf ) − (Vwhite /Δf f (nt /p2 )τtrap αH + V = . Wn ≡ f 2 p 1 + (2πτtrap f )2 VBias (10.24) Here it is assumed that the exponent γ of the 1/f noise frequency is equal to 1. For the case of a single trap, a plot of Wn (determined from the measured noise data) as a function of frequency yields a horizontal line (of value αH /p) with a superimposed Lorentzian (the trap contribution).

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1/f Noise

G-R (10Hz)

Wn (total)

Wn (1/f)

G-R(10Hz)

G-R(40Hz)

429

G-R (40Hz) 1.7E-22

1.0E-09

Wn (arb. units)

1.6E-22

V2/Δf (V2/Hz)

1.0E-10

y = 1.30E-10× -0.968 R² = 9.99E-01 1.0E-11

1.5E-22 1.4E-22 1.3E-22 1.2E-22 1.1E-22

1.0E-12

1.0E-22 9.0E-23

1.0E-13

8.0E-23 1

10

100

Frequency (Hz)

1

10

100

Frequency (Hz)

Fig. 10.14. Representative, idealized noise power graph (left) with contributions from 1/f noise and two G-R traps at 10 and 40 Hz for comparison with the Wn function (right).

Figure 10.14 shows a representative, idealized noise power graph (left) with contributions from 1/f noise and two G-R traps at 10 and 40 Hz compared to the Wn function (right). Note that the exponent for the power fit (dashed line) yields γ between 0.9 and 1.1, within the acceptable range for 1/f noise. Relying strictly on the noise power waveform, the contributions of G-R noise may be easily overlooked compared to the Wn function for the same waveform. 10.5.2. Noise and Pixel Size Figure 10.15 shows the calculated noise per unit bandwidth as a function of frequency for the various noise mechanisms assuming pixel areas of (left) 25 μm × 25 μm and (right) 10 μm × 10 μm. The parameters used are listed in the figure caption. In these examples, the G-R noise is assumed to be negligible. In both cases, the Johnson noise and thermal noise per unit bandwidth are equal. However, the 1/f noise depends on pixel volume. The 1/f noise for the 25 μm × 25 μm pixel is less than the 1/f noise for the 10 μm × 10 μm pixel. The 1/f noise dominates the total noise at frequencies less than

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Fig. 10.15. Noise per unit bandwidth as a function of frequency and the noise in the bandwidth. Parameters used in calculating the noise are pixel thickness of 500 ˚ A; resistivity of 200 Ω · cm; αH /p = 1 × 10−21 cm3 , bias voltage of 1 V, αTCR = 0.0251/◦ C, G = 5 × 10−9 W/◦ C. Table 10.3. Comparison of bandwidth noise for 25 μm × 25 μm and 10 μm × 10 μm pixels.

1/f Noise Johnson Noise Thermal Noise Total Noise

25 μm × 25 μm

10 μm × 10μm

1.3 × 10−5 V 7.2 × 10−5 V 1.9 × 10−6 V 7.3 × 10−5 V

3.3 × 10−5 V 7.2 × 10−5 V 4.9 × 10−6 V 8.0 × 10−5 V

10 Hz for the 25 μm × 25 μm pixel size and less than 100 Hz for the 10 μm × 10 μm size. Table 10.3 compares the calculated bandwidth noise for the 25 μm × 25 μm and 10 μm × 10 μm pixel sizes. The 1/f noise and thermal noise increase with decreasing pixel volume. In the case of the 1/f noise, the total number of carriers decreases. In the case of the thermal noise, the thermal noise bandwidth increases; (the thermal time constant decreases because the heat capacity decreases). The calculated thermal noise bandwidths correspond to 25 and 150 ms for 25 μm × 25 μm and 10 μm × 10 μm pixel sizes, respectively. In both cases, the total noise in the bandwidth is primarily due to the Johnson noise, which is related to the material resistivity and pixel dimensions. Figure 10.15 and Table 10.3 show that as the pixel size is reduced, the electrical noise increases. This in turn results in an increased NETD, since Vnoise increases and Vsignal decreases.

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10.5.3. Summary of Past Noise Results in a-Si:H Several investigators have reported electrical noise measurements made on a-Si, a-Si:H, and p-type a-Si:H films. D’Amico [37] found that in non-hydrogenated a-Si, conductivity is due to NNH at room temperature and VRH at temperatures less than 165 K. Electrical noise was attributed to phonon assisted hopping. Verleg [38, 39] measured noise from approximately 290 K to 30 K in intrinsic a-Si:H films. The relative noise power (at selected frequencies) as a function of temperature exhibited characteristics of G-R noise. Johanson [40] reviewed noise measurements made on a-Si:H materials. For p-type films, they report that the frequency exponent is approximately 1 at room temperature and increases to near 1.4 at 400 K. At temperatures greater than 430 K, the noise spectrum deviates from 1/f in nature at frequencies less than 20 Hz. Baciocchi [41] made measurements of intrinsic and boron doped a-Si:H films. From the conductivity and noise data, they determined that the Hooge coefficient, αH , decreased with increasing hydrogen dilution for both the intrinsic and boron doped films. Saint John [42] found that 1/f noise increased with increasing hydrogen dilution for boron doped p-type a-Si:H films. 10.5.4. Example of Room Temperature Noise Data and Analysis Room temperature noise waveforms for an a-Si:H film with RH = 40 and r = 0.32 were also analyzed using Eq. (10.24). Figure 10.16(a) shows the left side of Eq. (10.24) plotted as a function of frequency for the various bias voltage noise scans. As measurements were made on device sizes of 30 μm × 300 μm and 50 μm × 1000 μm, the data were normalized by the volumes. The waveforms are independent of frequency without a Lorentzian contribution; thus, the magnitude of Wn is αH /p. Figure 10.16(b) shows the average and corresponding standard deviation for the waveforms shown in Fig. 10.16(a). The analysis effectively yields a horizontal line of magnitude near 1 × 10−21 cm3 . The standard deviation of the waveforms is approximately 15%. Given the error in this analysis,

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432 2.0

2.0

T = 296 K

RH = 40, r = 0.32

T = 296 K

1.5

WN (x 10-21 cm3)

WN (x 10-21 cm3)

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1.5

1.0

Avg Stdev

0.5

RH = 40, r = 0.32 0.0

1

10

100

0.0 1

10

Frequency (Hz)

Frequency (Hz)

(a)

(b)

100

Fig. 10.16. (a) Wn as a function of frequency for various bias voltages and device dimensions and (b) the average and standard deviation of the scans shown in (a).

the average value of the waveforms of 0.97 × 10−21 cm3 is in reasonably good agreement with αH /p determined by the Hooge model (0.8 × 10−21 cm3 ). 10.5.5. 1/f Noise Correlation with Boron Dopant, Hydrogen Dilution, and Mott Temperature Room temperature noise measurements were made on various films prepared with different hydrogen dilutions and different boron dopant levels. In addition, conductivity measurements were made previously on these films to determine the Mott temperature. The set of graphs in Fig. 10.17 shows the correlation of the noise and conductivity measurements. In this set of graphs, the reported data are from films that were prepared with a fixed boron dopant level and varying hydrogen dilution levels. Figure 10.17(a) shows that as the dilution increases, the Mott temperature increases. This result implies that the DOS at the Fermi level decreases with hydrogen dilution. This description is consistent with Savvides [30] who also found that the DOS in a-Si:H decreases with increasing hydrogen dilution. The reduction in the DOS may be due to the improvements in both short-range order (SRO — nearest neighbors) and mid-range order (MRO — third or fourth nearest neighbors) with increased hydrogen dilution as well as to a reduction in the extent of the valence band tail of defect states. In Fig. 10.17(b), the normalized Hooge parameter increases with increasing hydrogen dilution. The Hooge parameter, αH , has been related to crystal quality as well as

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1.40

1.0E+09

1.20

α H/p (x 10-21 cm3 )

T0M (K)

Amorphous Silicon Microbolometers for IR Imaging

8.0E+08 6.0E+08 4.0E+08

r = 0.32

2.0E+08 0.0E+00

0

20

40

60

80

100

120

433

r = 0.32

1.00 0.80 0.60 0.40 0.20 0.00

0

20

40

60

Hydrogen Diluon R H

Hydrogen Diluon R H

(a)

(b)

80

100

α H/p ( x 10-21 cm3 )

1.6 1.4

r = 0.32

1.2 1 0.8 0.6 0.4 0.2 0 0.0E+00

2.0E+08

4.0E+08

6.0E+08

8.0E+08

1.0E+09

1.2E+09

T0M (K)

(c)

Fig. 10.17. (a) Mott temperature as a function of hydrogen dilution, (b) room temperature Hooge parameter αH /p as a function of hydrogen dilution, and (c) room temperature Hooge parameter αH /p as a function of Mott temperature. These films were grown with varying hydrogen dilution levels and fixed boron doping level.

to scattering mechanisms that limit mobility (Hooge [17]), whereby αH decreases with improved structure. The carrier concentration involved in the hopping process can be estimated as p = kB TN (EF ). As a result, the carrier concentration is expected to decrease with increasing hydrogen dilution (as the DOS decreases). While it is difficult to make an unambiguous conclusion, the increase in αH /p may be simply due to the carrier concentration decreasing at a faster rate than αH with increasing dilution. This description is consistent with that reported by Saint John [42], who found that the noise voltage increases with increasing hydrogen dilution, and Baciocchi [41], who found that the Hooge parameter decreases with increasing hydrogen dilution. Figure 10.17(c) shows the normalized Hooge parameter as a function of the Mott temperature for these same films. The normalized Hooge parameter, which is proportional to the 1/f spectral noise density, is observed to correlate with the Mott characteristic temperature.

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1.4E+09

2.5

α H/p (10-21 cm3 )

1.2E+09

ToM (K)

1.0E+09 8.0E+08 6.0E+08 4.0E+08

RH = 60

2.0E+08 0.0E+00

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0.1

0.2

0.3

0.4

2.0 1.5

RH = 60

1.0 0.5 0.0

0

0.1

Boron Dopant Rao r

0.2

0.3

0.4

Boron Dopant Rao r

(a)

(b)

α H/p (x 10-21 cm3 )

2.5 2.0

RH = 60

1.5 1.0 0.5 0.0 5.0E+08

7.0E+08

9.0E+08

1.1E+09

1.3E+09

ToM (K)

(c)

Fig. 10.18. (a) Mott temperature as a function of boron doping level, (b) room temperature normalized Hooge parameter αH /p as a function of boron dopant level, and (c) room temperature Hooge parameter αH /p as a function of Mott temperature. The films were grown with varying boron doping levels and a fixed hydrogen dilution level.

The graphs in Fig. 10.18 show an additional correlation of the noise and the conductivity measurements. In this set of graphs, the reported data are from films prepared with a fixed hydrogen dilution level and varying boron dopant levels. In Fig. 10.18(a), as the boron dopant level is increased, the Mott temperature decreases, which in turn implies that the DOS increases. Street [43] reported that the addition of boron in a-Si:H films increases the number of valence band tail defect states. Since increasing boron incorporation into the films will result in an increase in B–H bonds and a decrease Si–H bonds [44], we speculate that the B–H bond may be associated with the valence band tail defect states. As a result, as the boron doping level increases, there is an increase in the carrier density due to an increase in the DOS at the Fermi energy. In Fig. 10.18(b), the normalized Hooge parameter decreases with increasing boron incorporation into the film, consistent with Fig. 10.18(a). Figure 10.18(c) shows αH /p as a function of the Mott temperature. Here, αH /p is observed to increase with increasing Mott temperature. If only p

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changed with boron dopant levels and αH remained constant, αH /p should decrease. As a result, αH presumably increases due to the degradation of the SRO with the increased boron levels. 10.5.6. Low Frequency Noise versus Temperature Figure 10.19(a) shows the low frequency noise as a function of temperature. The low frequency noise SLFN is defined as the device noise at 1 Hz, at a bias voltage of 1 V, and is normalized with respect to device volume. SLFN appears to have a slight temperature dependence for temperatures between 210 and 380 K. However, for temperatures greater than 400 K, the low frequency noise increases significantly with increasing temperature. These data suggest that there are different noise contributions for these two temperature ranges. Figure 10.19(b) shows the low frequency exponent γ as a function of temperature. The exponents were determined by power law fits to the device noise data. The frequency exponent is typically between 0.9 and 1.1 for temperatures less than 400 K and so is indicative of 1/f noise. For temperatures greater than 400 K, the exponent is greater than 1.1 and is indicative that the device low frequency noise is comprised of more than 1/f noise. For temperatures above 400 K, the low frequency noise increases more rapidly with increasing temperature and the frequency exponent γ is significantly larger than 1. As a result, the noise waveforms were analyzed for trapping using Eq. (10.21). Figure 10.20 shows Wn as a function of frequency for temperatures of 360 K, 380 K, 400 K, 420 K, and 440 K. For temperatures of 360 K and 380 K, the curves 1.6

7.0

1.4

RH = 40, r = 0.32

6.0 5.0 4.0

1.0

3.0 2.0

0.8

1.0 0.0

RH = 40, r = 0.32

1.2

γ

SLFN (x10-21 V 2⋅cm3 /Hz)

8.0

200

250

300

350

400

450

500

0.6

200

250

300

350

T (K)

T (K)

(a)

(b)

400

450

500

Fig. 10.19. (a) The low frequency noise as a function of temperature and (b) the frequency exponent as a function of temperature.

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WN (x 10-21 cm3)

3.5

RH = 40, r = 0.32

3.0 2.5

440 K

2.0

420 K

1.5

400 K

1.0

380 K

0.5

360 K

0.0

1

10

100

Frequency (Hz)

Fig. 10.20. Wn as a function of frequency according to Eq. (10.21) at temperatures of 360 K, 380 K, 400 K, 420 K, and 440 K.

have no slope, indicating that the measured low frequency noise is 1/f noise only. The values of these curves are equal to αH /p (on the order of 10−21 cm3 ). For temperatures of 400 K and above, the curves at low frequency (less than 10 Hz) increase with increasing temperature. This phenomenon is characteristic of a trap contributing to the total noise voltage. It is believed that this behavior is due to a deep trap in a-Si:H. Crandall [45] used the deep-level transient spectroscopy (DLTS) technique to characterize trapping in Schottky barrier and p-i-n a-Si:H structures. The DLTS measurements revealed an electron trap with a characteristic temperature near 450 K for both structures. As a result, such a trap could provide conductivity fluctuations, which would result in G-R noise, as observed in Fig. 10.20. Electrical noise in a-Si:H is clearly related to pixel geometry and material properties. The magnitude of the noise is determined by the pixel area and thickness and by the film’s deposition conditions (hydrogen dilution, boron dopant level, etc.). Application trade-offs in pixel size and deposition conditions specific to focal plane arrays are required for optimal microbolometer performance. 10.6. Summary Bolometers belong to a group of thermal sensors used for radiation detection in the NIR to THz spectral range. Microbolometers

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are composed of low thermal mass, thermally isolated thin films. The performance of thin-film microbolometer IR imaging arrays operating at ambient temperature is controlled by the conduction mechanism and associated material properties including the TCR and noise. The p-type a-Si:H system is one of the leading thin-film microbolometer materials used in the production of microbolometer focal plane arrays for ambient temperature operation. The dominant conduction mechanism in p-type a-Si:H is MVRH. The Mott characteristic temperature depends on the deposition parameters of hydrogen dilution and doping level. For temperatures between 220 K and 380 K, the low frequency noise is 1/f in nature and is believed to be related to hopping conduction. For temperatures greater than 400 K, there is a strong G-R noise component, presumably resulting from a deep trapping level. Acknowledgments This research was supported in part by the Army Research Office Grant W911NF-10-1-0410, William W. Clark, Program Manager. References 1. Langley, S. P. (May 1880–June 1881). Proceedings of the American Academy of Arts and Sciences, 16, pp. 342–358. doi.org/10.2307/ 25138616. 2. Loettgers, A. (2003). Physics in Perspective, 5, pp. 262–280; 1422– 6944/03/030262–19. doi.org/10.1007/s00016-003-0143-5. 3. Liddiard, K. C. (1986). Infrared Physics, 26, pp. 43–49. doi.org/ 10.1016/0020-0891(86)90046-1. 4. Hornbeck, L. J. (1991). U.S. Patent No. 5,021,663. 5. Keenan, W. F. (1994). U.S. Patent No. 5,367,167. 6. Tissot, J. L., et al. (1998). Proceedings of SPIE, 3436, pp. 605–610. doi.org/10.1117/12.328060. 7. Brady, J., et al. (1999). Proceedings of SPIE, 3698, pp. 161–167. 8. Kruse, P. W. (1997). In: Uncooled Infrared Imaging Arrays and Systems, Semiconductors and Semimetals, Vol. 47, edited by Kruse, P. W., and Skatrud, D. D. (New York, Academic Press), Chapter 2, pp. 17–42. 9. Wood, R. A. (1997). In: Uncooled Infrared Imaging Arrays and Systems, Semiconductors and Semimetals, Vol. 47, edited by Kruse, P. W.,

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and Skatrud, D. D. (New York, Academic Press), Chapter 3, pp. 43– 121. Niklaus, F., Vieider, C., and Jakobsen, H. (2008). In: MEMS/MOEMS Technologies and Applications III, 68360D, 4 January 2008, Proceedings of SPIE, 6836 (Bellingham, WA, SPIE), pp. 68360D: 1–15. doi 10.1117/12.755128. Syllaios, A. J., et al. (2000). Amorphous silicon microbolometer technology, Materials Research Society Symposium Proceedings, 609, art. no. A14.4. doi.org/ 10.1557/PROC-609-A14.4. Schimert, T., et al. (April 17, 2008). In: Infrared Technology and Applications XXXIV, Proceedings of SPIE, 6940 (Bellingham, WA, SPIE), p. 694023. doi.org/10.1117/12.784661. Kruse, P. W. (2001). SPIE Tutorial Texts in Optical Engineering, Vol. TT51 (Bellingham, WA, SPIE). ISBN-13: 978-0819441225. Schimert, T., et al. (1999). Proceedings of SPIE, 3713, pp. 101–111. doi.org/ 10.1117/12.357125. Syllaios, A. J., Ha, M. J., McCardel, W. L., and Schimert, T. R. (2005). In: Infrared Technology and Applications XXXI, Proceedings of SPIE, 5783 (Bellingham, WA, SPIE). doi.org/10.1117/12.603153. Schimert, T., et al. (2009). Infrared Technology and Applications XXXV, Proceedings of SPIE, 7298 (Bellingham, WA, SPIE). https://doi.org/10.1117/12.818576. Hooge, F. (1994). IEEE Transactions on Electron Devices, 41, pp. 1926–1935. doi.org/ 10.1109/16.333808. Kohin, M., and Butler, N. (2004). In: Infrared Technology and Applications XXX, edited by Andresen, B. F., and Fulop, G. F. Proceedings of SPIE, 5406 (Bellingham, WA, SPIE), pp. 447–453. doi.org/10.1117/12.542482. Wood, R. A. (1997). Semiconductors and Semimetals, Vol. 47. (New York, Academic Press), pp. 43–121. Street, R. A. (1991). Hydrogenated Amorphous Silicon (Cambridge, UK, Cambridge University Press), p. 227. ISBN 10: 0521019346. Ajmera, S. K., et al. (2010). Proceedings of SPIE, 7660, pp. 766012-1– 766012-8. doi.org/ 10.1007/s11664-017-5571-0. Torres, A. M., Moreno, M., Kosarev, A., and Heredia, A. (2008). Journal of Non-Crystalline Solids, 354, pp. 2556–2560. doi.org/10.1016/ j.jnoncrysol.2007.09.112. Mott, N. F., and Davis, E. A. (1979). Electronic Processes in Non-crystalline Materials (Oxford, UK, Clarendon Press). ISBN 10: 0198512880. Efros, A. L., and Shklovskii, B. I. (1984). Electronic Properties of Doped Semiconductors (Berlin, Springer-Verlag). ISBN 0387129952.

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25. Rosenbaum, R. (1991). Phys. Rev. B, 44, pp. 3599–3603. doi.org/10. 1103/PhysRevB.44.3599. 26. Abraham, T., Bansal, C., Kumeran, J. T. T., and Chatterjee, A. J. (2012). Journal of Applied Physics, 111, pp. 104318: 1–4. doi.org/10. 1063/1.4716006. 27. Kang, M. S., Sahu, A., Norris, D. J., and Frisbie, C. D. (2011). Nano Letters, 11, pp. 3887–3892. doi.org/10.1021/nl2020153. 28. Zabrodskii, A. G. (2001). Philosophical Magazine B, 81, pp. 1131–1151. doi.org/10.1080/13642810108205796. 29. Lewis, A. (1972). Physical Review Letters, 29, pp. 1555–1558. doi.org/ 10.1103/PhysRevLett.30.1238. 30. Savvides, N. J. (1984). Journal of Applied Physics, 56, pp. 2788–2792. doi.org/10.1063/1.333810. 31. Dalvi, A., Reddy, P. N., and Agarwal, S. C. (2012). Solid State Communications, 152, pp. 612–615. doi.org/10.1016/j.ssc.2012.01.018. 32. Hanson, C. M., et al. (2010). In: Infrared Technology and Applications XXXVI, Proceedings of SPIE, 7660 (SPIE, Bellingham, WA). doi.org/ 10.1117/12.852511. 33. Mouetsi, S., El Hdiy, A., and Bouchemat, M. (2010). Moroccan Journal of Condensed Matter, 12, pp. 204–207. 34. Rice, A. K., and Malloy, K. J. (2000). Journal of Applied Physics, 87, pp. 7892–7995. doi.org/10.1016/j.jnoncrysol.2017.01.014. 35. Vandamme, L. K. J. (1994). IEEE Transactions on Electron Devices, 41, pp. 2176–2187. doi.org/10.1109/16.333839. 36. Lopes, V. C., Syllaios, A. J., and Littler, C. L. (2017). Journal of Non-Crystalline Solids, 459, pp. 176–183. doi.org/10.1016/ j.jnoncrysol.2017.01.014. 37. D’Amico, A., Fortunato, G., and Van Vliet, C. M. (1985). Solid-State Electronics, 28, pp. 837–8444. doi.org/10.1016/0038-1101(85)90072-3. 38. Verleg, P. A. W. E., and Dijkhuis, J. I. (1998). Journal of NonCrystalline Solids, 227–230, pp. 172–175. doi.org/10.1016/S00223093(98)00221-X. 39. Verleg, P. A. W. E., and Dijkhuis, J. I. (1998). Physical Review B, 58, pp. 3904–3916. doi.org/10.1103/PhysRevB.58.3904. 40. Johanson, R. E., Gunes, M., and Kasap, S. O. (2002). IEE Proceedings — Circuits Devices and Systems, 149, pp. 68–74. doi.org/10.1049/ ip-cds:20020333. 41. Baciocchi, M., D’Amico, A., and Van Vliet, C. M. (1991). SolidState Electronics, 34, pp. 1439–1447. doi.org/10.1016/0038-1101(91) 90042-W. 42. Saint John, D. B., et al. (2011). Journal of Applied Physics, 110, pp. 033714: 1–7. doi.org/10.1063/1.3610422.

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43. Street, R. A. (1985). Journal of Non-Crystalline Solids, 77 and 78, pp. 1–16. doi.org/10.1016/0022-3093(85)90599-X. 44. Ross, N., et al. (2013). Materials Research Society Proceedings, 1536, pp. 127–132. 45. Crandall, R. (1981). Physical Review B, 24, pp. 7457–7459. doi.org/10.1103/PhysRevB.24.7457.

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Index

1/f noise, 270, 271 (a + nc) → a, 20 (a + nc) → nc, 11, 12, 13, 15, 16–18, 250 a → (a + nc), 11, 12, 13, 14–18, 16, 24, 25, 255, 250, 251 a → a, 11, 12, 13, 17, 21–23, 26, 252, 255, 257

absorption coefficient, 88, 91, 100, 130, 133, 141, 143, 146, 158, 211, 214, 222 a-Si:H, 216 generation rate dependence, 216 optical, 215 sub-bandgap, 221, 223, 224, 234 thin-film Si:H, xvii absorption efficiency microbolometer pixel, 414, 415 absorption kinetics sub-bandgap, 230 absorption loss doped thin-film silicon, 399 absorption onset, xvii, 129, 133, 139, 142, 143, 145–147 amorphous semiconductor, xxi band-to-band, 157, 158 absorption onset function, 145, 146, 153, 155, 156, 157 absorption onset parameter, 170 absorption spectrum a-Si:H, 67 a-Si:H sub-bandgap, xviii crystalline silicon, 66, 67 generation rate dependence, 216 nc-Si:H, 66, 67 sub-bandgap, 216, 224, 237 acceptor-like state, 236 acceptor a-Si:H, 37

a-Si1−x Cx :H, 160, 247, 286, 294, 305, 309, 312, 318 a-Si1−x Gex :H, 160, 247, 286, 293, 318 a-Si:H based solar cells, 87 absorbance, 130 absorber, 87 narrow bandgap, 398 absorber layer, 102, 106, 109, 111–114, 119 absorptance infrared resonant, 412, 413 long wavelength infrared resonant, 413 multilayer device, xx absorption, 131 a-Si:H sub-bandgap, 230 Lorentz oscillator, xvii optical, 63, 129, 207, 215, 221 sub-bandgap, 133, 170, 208, 225, 228, 234–236, 239 Urbach, 146 441

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alloy, 247, 280 a-Si:H based, xix amorphous semiconductor, 160 group IV amorphous semiconductor, 155 hydrogenated amorphous silicon-germanium, 153, 154, 196 alpha regime PECVD, 345 aluminum oxide passivation layer, 391, 395 AM1.5 illumination, 228, 230, 233 amorphous materials tetrahedrally-bonded, 35 amorphous network, 85–87 amorphous phase, 180 amorphous semiconductor, 155, 169 group IV alloy, 155 transition lifetime, 132 amorphous semiconductor, chalcogenide, 155 amorphous silicon conductivity unhydrogenated, 431 dielectric function, 171, 172 hydrogenated, 168 low pressure CVD, 392 sputtered, 172 unhydrogenated, 38 volume fraction, 171 amorphous silicon nitride passivation, 411 amorphous silicon-germanium hydrogenated, 153, 154 amorphous to amorphous roughening transition a → a, 7, 249 amorphous to mixed-phase amorphous + nanocrystalline transition a → (a + nc), 3, 6, 249 amorphous to nanocrystalline transition, 286 thin-film Si:H, xxii

amorphous + nanocrystalline Si:H three-phase model, 54 two-phase model, 53 amorphous + nanocrystalline mixed-phase silicon, 387 amphoteric defect state, 236 amplitude Lorentz oscillator resonance, 134, 157, 160, 170, 171, 173, 178, 189, 200 analysis multi-time, 182, 190, 195 virtual interface, 183–185, 192, 193, 195, 200, 201 annealed state, 228–230 a-Si:H, xviii gap state parameters, 238 annealing, 88, 115–118 nc-Si:H, 61, 62 reversible defect, 60, 208 annealing amorphous precursor layer thermal, 392 annealing kinetics, 230 anti-bonding sp3 state, 171 anti-reflection coating, xxii, 282, 342, 359, 360, 399 heterojunction with intrinsic thin layer (HIT) solar cell, 389 application a-Si:H, 71 nc-Si:H, 71 optoelectronic, 129 thin-film Si:H, xi approximation pseudo-substrate, 194 array a-Si:H-based microbolometer focal plane, xxiii infrared imaging, 437 microbolometer, 413 microbolometer focal plane, 410, 411, 413, 436, 437 atomic scale self-shadowing, 7, 12

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Index attenuated total reflectance (ATR) spectroscopy, 92 Auger recombination, 396 B2 H6 , 10 B(CH3 )3 , 10 back contact metal diffusion, 341 back field contact, 386 back field contact layer doped a-Si:H, xiv back field junction, 384 back reflector, 18 solar cell, 341, 342, 361–370, 372, 381, 398 thin-film Si:H solar cell, xxii band conduction, 170, 209, 218, 221 valence, 170, 209, 218, 221 band diagram, 335 a-S:H solar cell, 336 c-Si solar cell, 334 band gap profile, 268 band structure electronic, 130 band tail, 63 absorption, xvii exponential, 221 valence, 209 band tail state, 37, 38 conduction, 223 localized, 65, 68, 70 localized conduction, 67 localized valence, 67 valence, 222, 223 band-to-band absorption amorphous semiconductor, xxi bandgap, 88, 104, 106–108, 110, 113, 119, 129–131, 134, 137, 142, 143, 155–157, 159, 189, 196, 198, 200, 255, 259, 260, 262, 265, 266, 268, 270, 280, 281, 285, 289, 290, 292–294, 297, 312, 313, 318 a-Si:H, 167, 176

443

a-Si:H-based materials, 199 amorphous semiconductor, xxi, 132–134 crystalline semiconductor, 131 crystalline silicon lowest direct, 202 direct, 131, 198 indirect, 131, 198 narrowing, 269, 409 p-type thin-film silicon, 348 silicon, 64 silicon carbon alloy, 264 thin-film Si:H, xvii widening, 269 bandgap determination amorphous material, 133 amorphous semiconductor, xvii effect of thickness, 142 single crystal semiconductor, 133 thin-film Si:H, xvi bandgap engineering, 292, 320 a-Si:H based alloy, xx, xxi bandgap grading a-SiC:H, 349 bandgap plots, 131 bandgap profiling a-Si1−x Gex :H solar cell absorber, xxii battery, 119 bending mode, 93, 95, 99 BF3 , 10, 340 bias light, 215 dual-beam photoconductivity, 223 bifacial rate, 332 Bohr magneton, 56 bolometer, 409, 410 bolometric detection a-Si:H, xxiii bolometric detector a-Si:H, xiv Boltzmann distribution, 219 bond silicon dangling, 226 weak Si-Si, 226

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bond angle distortion, xix bond length variation, xix bonding local order, 44 Si-H, 46 Si-H2 , 46 silicon-hydrogen, 36, 167 bonding configurations, 86, 87 bonding modes, 93 bonding sp3 state, 171 bonding structure of hydrogen, 5 boron doping gas to silane ratio PECVD, 421, 422, 425, 426, 431, 432, 434–437 boron doping a-Si:H PECVD, 421, 422, 425, 426, 431, 432, 434–437 boron trifluoride p-type doping, 10, 340 boron-silicon bonds, 98 bridge Wheatstone, 410 broadening, 262, 265, 266 dielectric function, 252, 257, 258 Lorentz oscillator, 134, 137, 157, 189, 197, 198, 201, 202 broadening parameter, 139, 141 Lorentz oscillator, 137 Bruggeman effective medium approximation, 171, 178, 185, 200, 299, 300, 309 buffer layer a-SiC:H, 349 building integrated photovoltaics system, 332 built-in electric field, 316 bulk layer thickness, 182, 183, 188–190, 193, 196, 197 bulk/roughness model two-layer, 182 bus bars, 382

camera microbolometer array, 413 capacity heat, 414, 415, 430 capillary driven diffusion, 12 carbon-hydrogen bonds, 96, 97 carrier photogenerated, 209 carrier collection profile, 315 carrier concentration, 269, 271, 428 free, 218 TCO, 389 carrier diffusion, 71 carrier dynamics, 69 a-Si:H, 63 carrier excitation, 68 carrier recombination, 210, 231 a-Si:H, 207 carrier relaxation, 68 carrier thermalization, 71 carrier transport, 210 a-Si:H, 207 cavity a-Si:H resonant, 412 Fabry-Perot resonant, 410, 412 infrared resonant, 412 optomechanical, 73 cell Golay, 409 photovoltaic, 130 charge carrier density, 428 charge carrier recombination, 89 charge neutrality, 219, 220, 225 charged defect, 226, 239 a-Si:H, xix charged defect state, 236, 239 light-induced, 231 negative, 236, 237 positive, 236, 237 chemical etching transparent conducting oxide, 360 chemical shift interaction, 45, 46 chemical shift tensor, 46

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Index chemical vapor deposition, 1, 85, 86, 171, 180, 396 catalytic, 387 hot wire, 387 low pressure, 361, 392, 393, 400 plasma-enhanced, xi, 40, 72, 154, 173–175, 177, 180, 181, 188, 190–192, 200, 212, 410, 421, 425 clustered hydrogen phase, 54 coalescence nanocrystallite, 180 coating a-Si:H mirror, 73 high index of refraction, 73 thermal noise, 73 Cody–Lorentz oscillator, 262, 265 coefficient absorption, 211, 214 columnar structure, 169 commutation relations, 140 complex dielectric function, 171, 185 complex optical response, 4, 252 conductance thermal, 414–417 conducting oxide transparent, 193, 201 conduction Efros–Shklovskii, 420–422 hopping, 420, 421, 437 Mott, 420–422 conduction band, 63, 64, 131, 136, 140, 170, 209, 218, 221, 236 tail state, 348 conductivity, 431 a-Si, 431 activation energy, 398, 419 characteristic temperature, 419, 420, 424 characteristic temperature Mott, 425, 426, 432–434, 437 dark, 226, 398 doped a-Si:H, 386 electrical, 411 microbolometer materials, 419

445

nc-Si:H, 353 p-type a-Si:H, 422, 423, 426 prefactor, 419 prefactor Mott, 425 temperature dependent, 420, 422 conductivity fluctuations, 427, 436 conductivity ratio of photo/dark, 398 cone growth model, 186, 251 conical structures nanocrystalline, 180 constant dipole (CD) matrix element, 285, 287–289, 291–293, 299, 302–304, 308, 318, 320 constant momentum (CM) matrix element, 295, 296, 318, 320 constant photocurrent method, 214, 215, 221, 224 a-Si:H, 235 continuous random network, 93, 94 continuum model, 7 conversion weak-bond → dangling-bond, 226 Coulomb gap, 420, 421 critical point, 139, 198 band structure, 131, 132, 180 broadening parameter, 132 c-Si, 180, 202 exponent, 132 phase, 132 critical point analysis, 132 critical point energy, 198 cross sectional transmission electron microscopy nc-Si:H, 357, 358 cross-section capture, 225 electron capture, 218, 219, 236 hole capture, 218, 219, 237 crystalline fraction, 69 nc-Si:H, 65 crystalline semiconductor transition lifetime, 132 Urbach tail, 132

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crystalline silicon, 350 bifacial tunnel oxide passivation contact (TOPCon) solar cell, 390, 391 dielectric function, 138 direct absorption onset, 187 heterojunction with intrinsic thin layer (HIT) solar cell, 332, 384–389, 399, 400 indirect bandgap, 340 interface, 387, 389 ion bombardment, 36 mono-facial tunnel oxide passivation contact (TOPCon) solar cell, 390, 391 n-type emitter, 333 n-type wafer, 385, 389, 390 p-type wafer, 333, 335, 389, 391, 395 Passivated Emitter and Rear Localized contact (PERL) solar cell, 400 Passivated Emitter Rear Cell (PERC), 333 Passivated Emitter Rear Contact (PERC) solar cell, 399, 400 Passivated Emitter Rear Totally diffused (PERT) solar cell, 400 passivation, 391 photovoltaics technology, xiv, xxii, 384 solar cell, 331–336, 384, 397, 399 solar cell production, 378 solar module, 332, 378, 384 solar module manufacturing, 332 surface, 388 tunnel oxide passivation contact (TOPCon) solar cell, 332, 384, 390, 391, 393, 395, 396, 400 crystalline volume fraction nc-Si:H, 65, 356, 357 crystallinity nc-Si:H, 40

crystallite, 54 ellipsoidal, 55 silicon, 39 crystallite evolution nc-Si:H, 357 crystallite growth, 356 crystallite interface, 51, 55, 58, 66 dehydrogenated, 63 partially hydrogenated, 56 crystallite nucleation, 16, 20 crystallite radius in-plane, 188 crystallite size, 41, 52, 188 nc-Si:H, 42 crystallization a-Si:H, 332 current microbolometer bias, 414 microbolometer pixel bias, 415 short circuit, 334 current density short circuit, 334 current matching multi-junction solar cell, 374 current-voltage characteristic a-SiGe:H solar cell, 353 nc-Si:H solar cell, 355, 366, 367, 369 nc-Si:H/a-SiGe:H/a-Si:H triple-junction solar cell, 376 triple-junction solar cell, 375 CVD, 26 dangling bond, 86–88, 94, 115 a-Si:H, xix, 329 metastable neutral, 226 negatively charged, 235 neutral, 208, 227, 228, 231, 235, 237 passivation by H, 173 silicon, 37–39, 56, 60, 226 dangling bond defect, 169 a-SiGe:H, 350

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Index a-Si:H, xiii neutral, 234 dangling-bond state neutral, 233 dark conductivity a-Si:H, 226 Staebler–Wronski effect, 227 decomposition partial fraction, 150, 151 deep-level transient spectroscopy a-Si:H, 436 defect, 119 dangling bond, 38, 60, 169 metastable, 226 defect creation reversible, 208 defect density a-Si:H, 59, 60, 194, 201, 329, 344 absorber layer, 398 dangling-bond, 234 nc-Si:H, 63 defect evolution, 60 defect generation reversible, 60 defect state, 89, 220, 233 a-Si:H, 208 amphoteric, 236 band tail, 38 charged, 224, 236, 238, 239 dangling-bond, 224 grain boundary, 67 light-induced, 227 light-induced charged, 231 localized, 68 mid-bandgap, 223 defects, 86, 105, 110, 115 a-Si:H, 35 charged, 226, 239, 312 light-induced, 233 nc-Si:H, 35 paramagnetic, 56 degradation a-Si:H, 217

447

light-induced, 60, 71, 208 nc-Si:H, 71 degradation kinetics t−1/3 , 231–233 degraded state gap state parameters, 238 degraded steady-state, 228, 233 demarcation level electron trap, 220 hole trap, 220 density, 86, 88, 102 a-Si:H, 54 bond packing, 192 defect, 194 photocurrent, 209, 210 density deficit Si-Si bond packing, 171 density of states, 63, 133, 140, 141, 144, 170 a-Si:H, xvii, 64, 221, 222, 433 conduction band, 139, 156 defect, 225 Fermi level, 432 Gaussian distribution defect, 225 joint, 134, 139 light-induced, 216 linear, 156, 157 mid-bandgap, 224 p-type a-Si:H, 422, 434 PECVD a-Si:H with H2 dilution, 432 square root, 140, 143, 156–158 valence band, 139, 156 deposition chemical vapor, 171 deposition conditions, 86, 96, 105–107, 109–114, 119 deposition rate a-Si:H PECVD, 344, 346 PECVD, 345 deposition sequence a-Si:H solar cell, 338 deposition uniformity, 73 depth profile step-wise, 171

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depth profiling, 169 depth-resolved composition, 269 desorption temperature programmed, 55, 60, 61 detection, 409 microbolometer, 413 near-infrared, 409 terahertz, 409 detector gravitational wave, 73 light, 130 near-infrared radiation, 436 pyroelectric, 409 single element microbolometer, 410 terahertz radiation, 436 deuterium, 99, 100 deviation root mean square, 154, 182, 188, 189 device quality, 86, 87 device structure optical analysis, xx di-hydrides a-Si:H PECVD, 346 diborane p-type doping, 10, 340 dielectric high-k, 155 dielectric function, 8, 88, 90, 168, 261–263, 265, 266, 279, 283, 284, 286, 302, 303, 309 a-Si, 171, 172 a-Si1−x Gex :H, 196, 198, 260 a-Si:H, 167, 174, 175 a-Si:H based alloy, xix, xx amorphous semiconductor, 134 broadening, 8, 17, 260 complex, 130, 135, 145, 153, 158, 169, 171, 185 constant contribution to real part, 134, 154 crystalline silicon, 138

hydrogenated amorphous silicon, 137, 138 hydrogenated nanocrystalline silicon, 137, 138 imaginary part, 136, 221 parametric, 176 single crystal semiconductor, 134 temperature dependence, 195, 196, 199 thickness-independent, 189 thin-film Si:H, xiii diffusion, 303, 304, 318 carrier, 71 H, 313 diffusion length, 7, 8, 12, 13, 21, 252, 258 dipolar interaction nuclear, 45 dipole matrix element, 222 constant, 170, 172, 179, 181–184, 187, 193, 195, 196, 198–201 dipole-dipole interaction H–H, 46 nuclear, 51 direct bandgap, 198 discharge radio-frequency, 35 disilane Si2 H6 , 9, 24 disorder, 141, 222, 302, 303, 312, 320 a-Si:H, 63 dopant-induced disorder, 305 static, 132, 133, 137, 319 static site, 132 substrate-induced, 194, 201 thermal site, 132 disordered network, 93, 94 display active-matrix liquid crystal, 73 distortion bond angle, xix divacancy, 5, 87, 103 donor-like state, 236 donors a-Si:H, 37

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Index dopant atoms, 2, 98 doped amorphous alloy, 269 doped layer heterojunction with intrinsic thin layer (HIT) solar cell, 388 doping, 312 a-Si:H, 36 doping efficiency, 348 nanocrystalline silicon based thin film, 388 nc-Si:H, 352 thin-film silicon, 399 double-junction solar cell, 370, 371, 374 drift, 209 drift length hole, 337 drift mobility electron, 210, 339 hole, 210, 338, 339 drift velocity electron, 209 hole, 209 dual beam photoconductivity DBPC, 287, 288, 319 echo experiment nuclear magnetic resonance, 48 edge material a-Si:H, 347 effective medium approximation, 142, 188 Bruggeman, 171, 178, 185, 200 effective medium theory, 168, 170, 172, 173 efficiency, 111–113, 306 generation, 211, 214 microbolometer pixel absorption, 414, 415 solar cell, 334, 335 effusion hydrogen, 61 electric field, 210 optical, 130 electrical conductivity

449

temperature dependence, xxiii thin-film Si:H, xxiii electrical noise, 430, 431 a-Si:H, 436 detector, 415 microbolometer, 416 thin-film Si:H, xxiii electrical noise constituents, 427 electrical resistance microbolometer pixel, 415, 418 electrical transport properties, 269 electrochemical passivation, 381 electrode gap a-Si:H PECVD, 346 PECVD, 345 electron conduction band tail, 64 free, 209 trapped, 219 electron capture, 221 electron charge, 135 electron concentration free, 218, 220 electron emission, 221 electron lifetime, 213, 230 electron mass, 135 electron spin resonance, 38, 234 a-Si:H, 37, 56, 224, 225, 235 nc-Si:H, 56, 63 optically-induced, 38, 64, 68 1 t 3 behavior, 59 thin-film Si:H, xv electron spin resonance lineshape a-Si:H, 58 kinetics, 59 nc-Si:H, 58 electron transition, 225 electron–electron double resonance, 39 electron–hole pair, 63 photogenerated, 333, 337, 339, 397 electron–lattice interaction, 36

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electron–phonon interaction, 132, 139, 144 electron-nuclear double resonance, 39 electronic defect a-Si:H, 37 electronic properties a-Si:H based alloy, xix electronic spin operator, 56 electronic state a-Si:H, 64 electronic transition, 209, 221, 222, 224 ellipsometry in situ spectroscopic, 178, 196 real time spectroscopic, 168, 169, 178–184, 188–190, 192, 195, 200, 201 spectroscopic, 132, 159, 191 ellipsometry angles, 154 emission gap state electron, 221 gap state hole, 221 emission probability electron thermal, 218 hole thermal, 218 emitter B-difused, 391 rear TOPCon, 392 emitter layer doped a-Si:H, xiv encapsulation a-Si:H, 411 photovoltaic module, 380, 383 energy bandgap, 130 conduction band, 131 critical point, 137, 198 Lorentz oscillator resonance, 134, 157, 159, 160, 189 photon, 129 transition, 189, 197, 200 valence band, 131 epitaxial breakdown, 4

epitaxial growth c-Si, 399 interfacial c-Si, 387, 388 epitaxy, 6, 16, 17, 20 error root mean square, 187, 190, 193 etching, 254, 255, 258 ethylene-vinyl acetate encapsulation, 380, 383 evanescent wave, 92 evaporation a-Si electron beam, 392 excitation optical, 71 excited state lifetime band-to-band, 201 excitonic interaction, 144 expanding thermal plasma, 1 extended state, 223 conduction band, 63 valence band, 63 external quantum efficiency EQE, 282, 305, 306, 313–315, 317, 321 nc-Si:H solar cell, 354, 355, 362, 365, 367 nc-Si:H/a-SiGe:H/a-Si:H triple-junction solar cell, 376 thin-film Si:H solar cell, xxi triple-junction solar cell, 375 extinction coefficient, 88, 89, 115, 129 a-Si:H, 191, 192 Fabry–Perot cavity, 410, 412 detector element, xxii feature size nc-Si:H, 62 Fermi level a-Si:H, 348 Coulomb gap, 420 dark, 215, 223 density of states, 421, 432 ferroelectric, 155 figure of merit microbolometer, 415–418

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Index fill factor solar cell, 111–114, 234, 272, 306, 316, 335 film stress, 2 film-side spectroscopic ellipsometry, 307, 311 fine structure interaction, 56, 57 fine structure tensor, 57 flexible photovoltaic module, 380 thin-film silicon, 383 Fourier transform fast, 216 Fourier transform infrared spectroscopy, 4, 5, 90, 114, 118 fraction crystalline, 65 frame rate thermal imaging camera, 414, 427 free induction decay, 46, 47 Fourier transform, 48 free-induction decay lineshape a-Si:H, 50 nc-Si:H, 50 fringe interference, 216 FTIR spectroscopy, 4, 5, 90, 114, 118 g-value a-Si:H, 57 free electron, 57 nc-Si:H, 58 galvanometer, 410 gamma regime PECVD, 345 gap Coulomb, 420, 421 gap state, 213, 215, 219, 221, 223, 230 a-Si:H, 218 capture cross-section, 238 density, 238 energy distribution, 217, 218, 235, 238 energy location, 238 Gaussian distribution, 235–237

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gap state distribution a-Si:H, xviii, 237 operational parameters, 240 gap state parameters, 239, 240 annealed state, 238 degraded state, 238 numerical modeling, 235 gas flow ratio hydrogen, 195 germane, 198 gas purifier nc-Si:H PECVD, 354, 355 Ge–H chemical bond, 96, 97, 350 generation efficiency, 211, 214 generation rate, 210–215, 220, 223–225, 230, 239 carrier, 209 photocarrier, 338 generation-recombination, 218 geometrical cone growth model, 251 germane GeH4 , 10, 249 germanium-hydrogen bond, 96, 97, 350 glass chalcogenide, 36 glass substrate, 193 glass-based photovoltaics technology thin-film silicon, 379 glass-side spectroscopic ellipsometry, 307, 308, 311 glow discharge a-Si:H, 329 graded composition alloy silicon carbon alloy, 267 silicon germanium alloy, 268 grain boundary, 105, 106 crystalline, 66–70 defect states, 67 nc-Si:H, xii, 50, 51, 65 grain boundary passivation, 86 grain size nc-Si:H, 44

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grating a-Si:H and ZnO, 369 flattened, 368, 369 gravitational wave detector, 73 gray scale infrared image, 413 grids metal, 342, 382, 386 growth evolution, 6, 21, 28, 248 substrate dependent behavior, 17 growth evolution diagram, 11, 13, 16, 255 a-Si:H based alloy, xix electrode configuration, 259, 261 gas composition dependence, 26 plasma frequency dependence, 25 plasma power dependence, 22 pressure dependence, 23 silicon germanium alloy, 250, 253, 254, 256 sputtered Si:H, 28 substrate dependence, 19 temperature dependence, 24, 257, 258 thin-film Si:H, xiii–xv, xviii gyromagnetic ratio nuclear, 45 gyromagnetic tensor, 56 Hamiltonian electron spin resonance, 56 nuclear magnetic resonance, 45, 46 hardness Vickers, 411 hardware open source, 211 haze spectrum light trapping, 361 heat capacity microbolometer pixel, 414, 415, 430 heterogeneity, 180 a-Si, 170

a-Si:H, 169, 179 structural, 170 heterojunction solar cells, 88, 92, 103, 106, 119 heterojunction with intrinsic thin layer HIT, 9, 10, 20 high resolution transmission electron microscopy, 347 HIT photovoltaics production line, 390 hole free, 209, 218, 220 trapped, 219 valence band tail, 64 hole capture, 221 hole collection length a-SiGe:H, 352 hole concentration free, 218, 220 hole diffusion length, 316 hole emission, 221 hole mobility-lifetime product, 397 Hooge noise parameter, 270–272, 432–436 hopping conduction, 421, 431 Mott variable range, 423–426, 437 nearest neighbor, 420, 421, 431 p-type a-Si:H, 437 variable range, 420, 423–426, 431, 437 hot-wire CVD, 1 hydrogen, 86, 87, 93–95, 100–102, 105, 110, 115, 118, 120 a-Si:H, 35 cluster size, 39 clustered, 37, 39, 45, 54, 55 isolated, 45, 54, 55 molecular, 45 motion in a-Si:H, 330 nc-Si:H, 35 randomly distributed, 37

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Index hydrogen atom cluster crystallite grain boundary, xv thin-film Si:H, xv hydrogen atomic percent a-Si:H, 174, 176 hydrogen bonding, 37, 99 a-Si:H, 192 clustered, 47, 50, 51 random, 47, 50 silicon, 39 thin-film Si:H, xii hydrogen bonding configurations, 2 hydrogen content, 86, 87 effect on a-Si:H bandgap, 349 nc-Si:H, 55 hydrogen dilution of source gas, 282, 318 a-Si:H material, 213, 216, 229, 230, 232, 233, 235, 238, 239 a-Si:H PECVD, xxii, 331, 340, 344, 346, 421, 423, 425, 426, 431–434, 436, 437 plasma-enhanced chemical vapor deposition, 212 thin-film Si:H PECVD, xviii hydrogen dilution profiling a-Si:H PECVD, 388 nc-Si:H PECVD, xxii, 357–359 hydrogen effusion, 51, 61, 256, 258 hydrogen evolution, 60 hydrogen incorporation a-Si:H, 46, 208, 227, 343 hydrogen plasma treatment, 349 hydrogen to reactive gas flow ratio, 10, 249 hydrogen to silane flow ratio, 10, 13 PECVD, 421–423, 425, 426, 431–434, 436, 437 R = [H2 ]/[SiH4 ], 10, 13 hydrogen-induced crystallinity, 256 hydrogenated amorphous silicon, 85, 87, 91, 93, 96, 98, 100–120, 135, 168 applications, 330 bandgap, 176, 349, 350

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boron doped, 340, 347, 348, 385, 431 boron doping, 10, 421, 422, 425, 426, 431, 432, 434–437 buffer layer, 351 carrier mobility, 331, 336 components of c-Si solar cells, 332 crystallization, 400 defects, 35 density of states, 433 density of states p-type, 422, 434 dielectric function, 138, 174, 175 doped back field contact layer, 399 doped emitter layer, 399 doped layer, 372, 389, 392, 394 doping, 331, 336 double-junction solar cell, 370, 372, 373 edge material, 347 extinction coefficient, 191 grating with ZnO, 368 hydrogen content, 174, 176 hydrogen dilution, 347, 421, 423, 425, 426, 431–434, 436, 437 hydrogen incorporation, 35 incubation layer, 356, 357 index of refraction, 191 interface, 350, 387, 389 intrinsic layer, 341, 343, 385, 388, 389, 398, 431 lifetime, 336 microbolometer, 412 microvoids, 355 mobility-lifetime product, 359 n-type, 331, 336, 369, 384 n-type layer, 368, 386 phosphorus doped, 347, 348, 385 p-type, 331, 336, 340, 384, 431, 437 p-type conductivity, 422, 423, 426 p-type layer, 386

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passivation layer, xxii, 332, 386, 387, 389, 392, 394, 399 photoconductivity, 330 photoelectronic quality, 188 plasma-enhanced chemical vapor deposition, 393, 395 precursor layer, 393–396, 400 resistivity, 418, 419 resonant cavity, 412 Schottky barrier, 436 solar cell, 330, 335–340, 343, 344, 348, 350, 352, 354 solar cell applications, 332 solar panel, 360 structure, 35 surface passivation layer, 384 thin-film deposition, xii top cell of multi-junction solar cell, 370, 374, 375 transition to nc-Si:H, 347 volume fraction, 186 hydrogenated amorphous silicon, single-phase, 181 hydrogenated amorphous silicon-carbon alloy, 160, 200, 331 B-doped, 340, 348, 394 precursor layer, 394 top cell of quadruple-junction solar cell, 377 hydrogenated amorphous silicon-germanium alloy, 98, 153, 154, 160, 195, 197, 199, 201, 331 alloy grading, 351 alloying, 350 bandgap, 350, 373 bandgap profile, 351 bottom and middle cells of triple-junction solar cell, 350, 352, 353, 370, 374–376 bottom cell of double-junction solar cell, 350, 370, 373, 374, 379 bottom cell of multi-junction solar cell, 373, 375 intrinsic layer, 351, 373

low Ge content, 350 middle cell of triple-junction solar cell, 350, 376, 377 mobility-lifetime product, 352 multi-junction solar cell, 398 optimization, 350 quadruple-junction solar cell, 377, 378 solar cell, 349, 352, 363, 373, 374 hydrogenated amorphous + nanocrystalline silicon, 65 hydrogenated nanocrystalline silicon, xi, 103, 105–108, 113, 118, 135, 168, 331 B-doped, 348 bandgap, 340 bottom and middle cells of multi-junction solar cell, 377, 379–381 bottom cell of multi-junction solar cell, 363, 370, 371, 375–377, 379–381, 399 carrier mobility, 362 conductivity, 389 crystalline volume fraction, 356 defect, 35 dielectric function, 138 doped layer, 372, 388, 389 hydrogen dilution profiling, 388 hydrogen incorporation, 35 indirect bandgap, 348, 361 intrinsic layer, 362, 365, 366 light trapping, 361 microcracking, 363, 367 microvoid, 355, 368 microvoid density, 355 middle cell of multi-junction solar cell, 376, 377, 379–381 O and N shallow donors, 353 P-doped, 348 p-type, 340, 349 plasma-enhanced chemical vapor deposition, 393 seed layer, 357, 394

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Index single phase, 180, 181 solar cell, 341, 346, 352–355, 357, 358, 362, 363, 365, 367–370, 374 stable phase, 181 structure, 35, 356, 358 thin-film deposition, xii transition from a-Si:H, 347 volume fraction, 185, 186, 188 hydrogenated silicon, xi hydrogenation a-Si:H, 329 hyperfine interaction, 56, 57 hyperfine tensor, 57 illumination intensity, 233 prolonged, 231, 233, 238 imaging infrared, 409–411, 413 impurity contamination nc-Si:H solar cell, 354 impurity penetration from ambient nc-Si:H, 355–357 in-situ cleaning PECVD system, 394 inclusions crystalline, 167 incubation layer a-Si:H, 349, 356, 357 index of refraction, 88 a-Si:H, 191, 192 complex, 129 real, 129 thin-film Si:H, xvii indirect bandgap, 198 indium oxide hydrogen-doped, 389, 399 tungsten-doped, 389, 399 indium tin oxide deoxidation reaction, 340 transparent conducting oxide, 340, 342, 369, 381, 382, 389, 399

455

infrared absorption band a-Si:H, xvi infrared absorption spectra a-Si:H, xiii infrared detection, 409, 413 long-wave, xxiii near, 409 optimal, 411 infrared flux, 410 infrared image, 413 gray scale, 413 infrared imaging, xxii, 413, 437 infrared sensors, 247, 248 infrared spectroscopy thin-film Si:H, xvi inhomogeneity a-Si:H, 192, 226, 236 insulator film encapsulation, 411 integral exponential, 153 principal value, 147 integrated absorption strength, 100 integrated circuit microbolometer array read out, 411, 418 read out, 416 integration Kramers–Kronig, 134, 135, 143, 145, 147, 157, 158 partial fraction method, 135 inter-reflection layer multi-junction solar cell, 374 interconnection monolithic, 379, 380 interface c-Si/a-Si:H, 387, 389 crystalline, 71 crystallite, 55, 58, 66 heterojunction with intrinsic thin layer (HIT), 387 interface defect density a-SiGe:H, 351, 352 interface defect state, 348 interface design, 398

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interference fringe, 216 interferometry precision, xii, 73 ion bombardment, 256, 257 a-Si:H PECVD, 346, 349, 387, 399 ion coupled plasma, 1 ion flux a-Si:H PECVD, 344 IR absorptance, 93, 96, 104 IR spectroscopy, 89 isolated hydrogen phase, 54 Jeener–Broekaert three-pulse sequence, 49 kinetics annealing, 230 degradation, 231–233 recombination, 214, 225, 228, 230 Kramer–Kronig consistency, 88, 90, 115, 288 complex dielectric function, xvii Kramers–Kronig analysis, 141 Kramers–Kronig integral Urbach tail, 152 Kramers–Kronig integration, 134, 135, 145–147, 157, 158 lamp halogen, 215 laser scribing, 379, 380 layer LP-CVD wraparound, 393 surface roughness, 171, 182–184, 190, 192 least squares regression analysis, 297 lifetime, 291 band-to-band transition, xix, 135 carrier, 336 constant photoconductive, 215 electron, 210, 213, 230 excited state, 132, 136, 201 minority carrier, 389

photogenerated carrier, 215 recombination, 209, 212, 338 light soaking, 88, 111–113, 115–118 a-Si:H, 60 nc-Si:H solar cell, 355 light trapping, 341, 398 a-Si:H solar cell, 359–362 nc-Si:H solar cell, 361–363 ZnO layer, 364 light-induced defect a-Si:H, 330 light-induced degradation, 87, 88, 96, 103, 110, 112, 113, 118, 119, 208, 398 a-Si:H, xviii nc-Si:H, xvi heterojunction with intrinsic thin layer (HIT) solar cell, 389 light-soaked state a-Si:H, xviii lineshape, 136, 137 critical point, 137 electron spin resonance, 57 Fourier transform of free induction decay, 48 Lorentzian, 136 nuclear magnetic resonance, 44 lineshape function, 144, 146 liquid crystal display active-matrix, 73 lock-in amplifier, 216 long range order, 2, 8, 41 Lorentz oscillator, 133–135, 137, 144–147, 155, 157, 160, 172, 173, 181, 184, 187, 189, 193, 198, 201, 285, 288, 290, 291, 294–296, 312, 319, 320 broadening, 290, 291, 293, 294, 303, 319 resonance amplitude, 171, 173, 178 resonance energy, 170 resonance width, 170 Lorentz oscillator parameter, 170

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Index loss electrical, 343 magnesium fluoride anti-reflection coating, 360 magnetic field, 45, 56 magnetic moment nuclear, 45 magnetic resonance, xii, 40 electrically detected, 39 nuclear, 36 optically detected, 38, 39 magnetic rollers, 381 manufacturing a-Si:H scalable, 73 material microbolometer, 410 narrow bandgap, 409 pyroelectric, 410 material requirements microbolometer design, 419 matrix element, 133 average dipole, 140, 141 average momentum, 139, 141, 144 constant dipole, 134, 147, 153, 154, 157–159, 169, 170, 172, 179, 181–184, 187, 193, 195, 196, 198–201 constant momentum, 133, 145, 153, 154, 157–160, 169, 170, 174, 176, 177, 181, 184, 187, 200 dipole, 132, 140, 222 momentum, 131, 136, 139, 140 optical transition, xvii, 225 mean free path, 139 electron, 137 mean square error MSE, 299–301 mechanical properties nc-Si:H, 73 thin-film Si:H, xi, xii medium-range order, 2

metal contact back-reflector, 342 metal grids, 342, 382, 386 metastability, 2 metastable defect, 226 methane CH4 , 10, 249 Meyer–Neldel rule, 426 micro-electro-mechanical systems, xxiii microbolometer, 271, 410, 436 a-Si:H, 409, 412 figure of merit, 415–418 p-type a-Si:H, 437 single element, 410 uncooled, 411 microbolometer array, 410, 411 uncooled a-Si:H, xxii, xxiii microbolometer camera, 411 microbolometer design material requirements, 419 microbolometer detection, 413 microbolometer material, 410, 419 thin-film, 437 microbolometer pixel structure, 412 microcracking nc-Si:H, 355 microdoping nc-Si:H, 353 microstructure a-Si:H, 208, 226, 233 silicon–hydrogen, 36 microstructure parameter a-Si:H, xvi microvoid a-Si:H, 51 nc-Si:H, 367 minority carrier lifetime, 389 minority carrier mobility, 385 mixed-phase silicon, 41, 42 mixed-phase hydrogenated amorphous + nanocrystalline silicon, 65

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mixed-phase to single-phase nanocrystalline transition (a + nc) → nc, 3, 6, 249 mixture effective medium, 184, 187 mobility, 269, 271 a-Si:H based alloy carrier, xix carrier, 336 drift, 210, 339 electron drift, 339 hole drift, 339 minority carrier, 385 mobility edge, 38, 63 mobility gap, 146 mobility-lifetime product, 213 a-Si:H, xviii, 213, 214, 234, 239 a-SiGe:H, 352 degraded steady-state, 239 electron, 237 generation rate dependence, 213, 214, 228, 229, 231, 232, 236, 238, 239 hole, 397 kinetics, 230–234 rapid light-induced change, 228, 229 thin-film silicon, 397 model cone growth, 186 parametric, 185 virtual interface, 182, 185 molecular hydrogen a-Si:H, 37, 48 nc-Si:H, 51 momentum matrix element constant, 169, 170, 174, 176, 177, 181, 184, 187, 200 momentum transfer vector, 42, 52 monochromator, 215 monolithic interconnection, 379, 380 monovacancy, 87 multi-hydrides a-Si:H PECVD, 346 multi-junction photovoltaics, xxi

multi-junction solar cell, 259, 272, 370, 372, 373, 398 multilayer optical analysis, xx, xxi muon spin resonance, 39 n-i-p, 260 n-layer, 20 n-type, 18, 20, 260, 269, 306, 312 a-Si:H, 210, 305 nanocrystal nucleation, 200 silicon, 179, 180, 187 nanocrystalline silicon hydrogenated, xi, 168 nanocrystalline silicon oxide bandgap, 340 doped layers, 388 inter-reflection layer, 374 p-type, 340, 386 nanocrystalline silicon-carbon bandgap, 340 doped layer, 388 p-type, 340 nanocrystallite inverted conical, 186 silicon, 180, 185 nanoparticle silicon, 72 nanosized voids, 87, 88, 93, 94, 100–105, 110, 116, 119 nanostructure, 88, 93, 100, 103, 114, 119, 120 correlation with Si-H bonding, xvi nc-Si:H, 60 nanostructure parameter, 103, 104, 109, 110, 113, 114, 116, 119 nc → (a + nc), 17 nc-Si:H, 362 near-infrared detection, 409 near-infrared detector, 436 negative-U hydrogen pair, 63

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Index network tetrahedrally-bonded, 169 neutral dangling bond, 227 neutrality charge, 219, 220, 225 neutron scattering small angle, 355 nitrogen impurities nc-Si:H, 353, 354 nitrogen tolerance a-Si:H solar cell, 355 nc-Si:H solar cell, 355 noise 1/f, 427–433, 435, 436 1/f spectral, 433 detector electrical, 415 electrical, 410, 411, 427, 430, 431, 436 frequency dependent, 428 generation-recombination, 427–429, 431, 436 Hooge’s model, 432 Johnson, 427, 429, 430 Lorentzian trap contribution to frequency dependent, 431 low frequency, 435 microbolometer 1/f, 416, 418 microbolometer electrical, 416 microbolometer Johnson, 416 microbolometer read out integrated circuit, 416 microbolometer thermal, 416 thermal, 416, 427, 429, 430 thin-film Si:H electrical, xxiii trap contribution to frequency dependent, 428, 431 noise equivalent temperature difference, 416 microbolometer, 415–418 microbolometer pixel, 430 noise exponent low frequency, 435 noise model Hooge’s, 417, 427, 428

459

noise parameter Hooge, 428, 432–436 noise per unit bandwidth, 427, 429, 430 non-uniformity spatial, 169 Nordheim rule, 197 nuclear magnetic resonance, 44 1 H, 45 a-Si:H, 36, 37, 51 double resonance, 38 free induction decay, 47, 55 free induction decay (Gaussian), 47 free induction decay (Lorentzian), 47 Jeener–Broekaert sequence, 49, 60 magic angle spinning, 38 multiple quantum, xv, 38, 39 nc-Si:H, 50, 51, 54, 61 nuclei other than 1 H, 37 Pake doublet, 50 solid echo experiment, 48 thin-film Si:H, xv nuclear spin, 45 nucleation nc-Si:H, 200 nucleation density of crystallites, 15 occupation function, 223, 225, 237 electron, 218, 219 hole, 218, 219 one-step absorber, 306, 312–314, 316 open circuit voltage, 104, 110–113, 272, 306, 312, 334 optical absorption onset, 139 optical absorption, 139, 207, 215, 221 optical absorption spectra a-Si:H, 67 crystalline silicon, 67 nc-Si:H, 67

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optical analysis device structure, xx thin-film Si:H multilayer device, xiii optical constants, 130 optical excitation, 64, 71 optical functions, 130 optical losses thin-film Si:H solar cell, xxi optical properties, 88, 142 a-Si:H based alloy, xix amorphous semiconductors, 133, 142 crystalline semiconductors, 133, 142 semiconductor, 135 thin-film Si:H, xii optical response, 86, 88, 90, 91, 96, 102, 119 amorphous semiconductor, 135 hydrogenated amorphous silicon, 158 linear, 129, 157 near-infrared to ultraviolet, 129 parametric representation, 129 optical transition, 131, 136 band-to-band, 134, 135 broadening, 141, 142, 144 forbidden direct, 131 forbidden indirect, 131 optical transition matrix element a-Si:H, xvii optically-graded thin film, 168 optically-induced electron spin resonance a-Si:H lineshape, 65, 66 nc-Si:H, 68 nc-Si:H lineshape, 64–66 optoelectronic applications thin-film Si:H, xxii optoelectronic device, 158 thin-film a-Si:H, xii optoelectronic properties a-Si:H, 207 nc-Si:H, 73 thin-film Si:H, xi

optomechanical cavity, xii, 73 order a-Si:H medium range, 347 a-Si:H short range, 347 medium range, 432 short range, 432, 435 Si:H network, xviii ortho-hydrogen, 49 lineshape, 50 oscillator Lorentz, 144 oxidation surface, 159 oxidation of crystalline silicon acidic, 392 ozone, 392 plasma-enhanced, 392 thermal, 392 oxide transparent conducting, 193, 201 oxide thin film, 155 oxygen impurities nc-Si:H, 353, 354 oxygen tolerance a-Si:H solar cell, 355 nc-Si:H solar cell, 355 p-i-n, 260, 308 p-n junction semiconductor, 333, 337 p-type semiconductor, 18, 20, 260, 269, 305, 309, 312 p-type a-Si:H, 305 Pake doublet, 50 para-hydrogen, 49 paramagnetic defects, xv, 51, 56 parameter Lorentz oscillator, 155, 170 structural, 200 parametric expression complex dielectric function, xx partial fractions method, 148 Paschen’s law, 344

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Index passivating layer a-Si:H, 194 passivation amorphous silicon nitride, 411 nc-Si:H grain boundary, xxii Si:H, xv SiOx /poly-Si, 390 passivation layer a-Si:H, xiv, 386, 387 a-SiNx :H, 386 PECVD, 13, 15, 17, 19, 21, 28, 248, 250, 251, 255 PECVD system in-situ cleaning, 394 penetration depth optical, 178 PERC photovoltaics production line, 390 PERL photovoltaics production line, 390 permittivity absolute, 130 complex relative, 130 free space, 136 PH3 , 10 phase amorphous, 180, 200 hydrogenated amorphous silicon, 180, 186 hydrogenated nanocrystalline silicon, 180, 186 nanocrystalline, 200 phonon interaction electron, 132, 139, 144 photoconductive measurements, 280 photoconductive spectroscopy, 215 photoconductivity, 63, 207, 210, 211 a-Si:H, xiii, xviii, 36, 59, 208, 210, 212, 213, 221, 226 a-Si:H steady-state, 212 a-Si:H sub-bandgap, 214 dual beam, 141, 159, 191, 192, 201, 214, 215, 221, 223, 224, 236

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dual-beam measurement system, 215 generation rate dependence, 212–214 kinetics, 231, 233, 236 nc-Si:H, 353 rapid light-induced change, 228, 229 Staebler–Wronski effect, 227 steady-state, 210, 211, 223 sub-bandgap, 214, 216 photocurrent a-Si:H solar cell, 338 photocurrent density, 209, 210, 337 photocurrent method constant, 214, 215, 221, 224 photocurrent spectroscopy, 214 photodiode, 333 photoelectronic quality a-Si:H, 188 photogenerated carrier, 209 photolithography, 411 photoluminescence, 63 a-Si:H, 67, 68 nc-Si:H, 67, 68 photon energy, 129 photon flux, 211 photonic integrated circuits, 115, 117–119 photonics, 88, 116, 117 photothermal deflection spectroscopy, 66, 236 photovoltaic device a-Si:H, 71, 207 crystalline silicon, 71 photovoltaic device applications thin-film Si:H, xxi photovoltaic module flexible, 380 photovoltaic module fabrication, 379, 381 photovoltaic module production, 378, 380 photovoltaic thermal system, 240

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photovoltaics, 20 building-integrated, 383 thin-film silicon, 396 photovoltaics applications third generation, xii photovoltaics laminate thin-film silicon, 399 photovoltaics manufacturing, 384 HIT cell, 385 TOPCon, 394 photovoltaics production system thin-film silicon, 380 photovoltaics production technology heterojunction with intrinsic thin layer (HIT), 400 tunnel oxide passivation contact (TOPCon), 390, 400 photovoltaics technology thin-film silicon, 378, 399 physical vapor deposition, 1, 396, 399, 400 roll-to-roll, 399 sputtering, 1 pinhole TOPCon solar cell, 391 pixel area, 429 microbolometer, 416 pixel design microbolometer, 416 pixel electrical resistance, 415 pixel planarity microbolometer, 412 pixel size microbolometer, 430 pixel structure microbolometer, 412 plasma excitation frequency, 23 plasma excitation power a-Si:H PECVD, 343, 344, 346, 387 dynamic control in PECVD, 387 plasma power control system PECVD, 387 plasma sheath PECVD, 345, 346

plasma-enhanced chemical vapor deposition, xi, 1, 9, 10, 22–26, 40, 72, 106, 154, 173–175, 177, 180, 181, 188, 190–192, 200, 212, 279, 283, 284, 286, 298, 410, 421 a-Si:H, 331, 392, 393, 395, 399, 400, 425 a-Si:H based alloy, xix a-SiGe:H, 350 anodic, 196 cathodic, 195–198 direct current, 379 gas gate, 381 high-rate VHF, 394 low pressure, 399 microwave, 331, 344 p-type a-Si:H, 422 powder formation, 394 radio frequency, 344 rate, 345 roll-to-roll, 380–382, 399 system design, 345 technology, 393 thin-film Si:H, xiv TOPCon solar cells, 394 tube system, 394, 395 very high frequency, 331, 344 plasma-enhanced chemical vapor deposition system triple-electrode, 376 plasmonic absorption, 342, 361, 363 plasmonic resonance frequency, 363 polarizability, 171 silicon-hydogen bond, 176 polarization, 130 electrical, 410 polarization direction, 136 polycrystalline silicon-carbon n-type, 392 polysilicon doped contact layer, 390–392 doped layer in TOPCon solar cell, 332, 400 doped rear field contact layer, 391

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Index fabrication, 395 layer in TOPCon solar cell, 394–396 passivation/contact layer, 384 solar cell, 384 solar module, 389 porosity nc-Si:H, 355, 357 porous films, 2 potential built-in, 338, 347, 348, 388, 397, 398 potential fluctuations, 226, 236 powder formation a-Si:H PECVD, 349 powder pattern nc-Si:H, 42 precursor layer a-Si:H, 384 preferential orientation (220) in nc-Si:H, 42, 44 pressure PECVD, 345 probe beam dual-beam photoconductivity, 223 process-property-performance relationships thin-film Si:H devices, xiv profile graded nanocrystalline, 180 thin film depth, 169 properties structural, 180 protocrystalline silicon, 15–17, 249, 305, 306, 316, 347 protocrystallinity, 200 pseudo-substrate, 169 semi-infinite, 183 pyroelectric detector, 409 pyroelectric material, 410 quadruple-junction solar cell, 377, 378 quadrupole interaction nuclear, 45

463

quadrupole moment nuclear, 46 quantum dot silicon, 72 quantum efficiency spectra nc-Si:H solar cell, 355, 362, 365, 367 nc-Si:H/a-SiGe:H/a-Si:H triple-junction solar cell, 376 thin-film Si:H solar cell, xxi triple-junction solar cell, 375, 376 quasi-Fermi level, xviii, 210, 212, 215, 219, 221 electron, 223, 237 hole, 223, 237 R, 11 radiation, 409 infrared, 409, 410 radiation detection electromagnetic, 409 infrared, 413 near-infrared, 436 terahertz, 436 Raman spectroscopy, 4, 40, 66, 347 a-Si:H, 41 nc-Si:H, 41, 356, 357 rate generation, 210, 230 read out integrated circuit microbolometer, 418 real time spectroscopic ellipsometry RTSE, 11, 193, 262, 263, 265–268, 283, 284 rear emitter, 386 recombination, 209, 282, 316 a-Si:H, 217 carrier, 71, 207, 210, 231 geminate, 39 non-geminate, 39 photocarrier, 337 radiative, 67

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recombination center, 212, 213, 223, 237 bandgap, 210 distribution, 217 light-induced, 232 recombination kinetics, 214, 220, 225, 228, 230 recombination statistics, 217 recombination tunnel junction, 372, 373 reflectance, 130, 211 multilayer device, xx reflectance and transmittance spectroscopy thin-film Si:H, xvii reflectance spectroscopy, 191, 192, 201, 211 reflectance spectrum back-reflector, 364, 365 reflection coefficients, 297 refractive index, 88, 115–117, 222 relative permittivity complex, 135 relaxation pathway nc-Si:H, 69 relaxation time spin-lattice, 48, 49, 52 remote plasma, 1 residual alloying gas, 268 resistance a-Si:H temperature coefficient, 417 microbolometer pixel electrical, 415 microbolometer pixel thermal, 413 series, 335 shunt, 335 temperature coefficient, 410, 415, 416, 418, 419, 424, 425, 437 thermal, 414, 416 thin-film Si:H temperature coefficient, xxiii

resistance curve derivative analysis, 423 a-Si:H, 424, 425 resistivity, 269–272 a-Si:H, 418, 419 contact, 343 microbolometer pixel, 417, 430 resonance electron-electron double, 39 electron-nuclear double, 39 resonance energy Lorentz oscillator, 170, 189 resonance frequency, 89 resonant infrared absorption, xxiii response time photoconductive, 223 responsivity microbolometer pixel, 415 reversibility Staebler-Wronski effect, 226 rocking mode, 93, 95 roll-to-roll deposition, 299 roll-to-roll process thin-film silicon, 378 root mean square deviation, 188, 190, 193 rotating compensator multichannel ellipsometer, 299 roughening transition amorphous growth, xix roughness surface, 171, 190 Rutherford backscattering spectroscopy, 266 scanning electron microscopy ZnO:Al, 361 scattering a-Si:H and ZnO grating, 368 back-reflector, 360, 361, 363, 365 light, 359 scattering feature size nc-Si:H, 62 Scherrer equation, 41

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Index Schottky barrier a-Si:H p-i-n, 436 Schottky barrier solar cell a-Si:H, xviii secondary ion mass spectrometry, 266–268 seed layer nc-Si:H, 357 semiconductor, 129 absorption onset, 139 amorphous, 137, 157, 169 crystalline, 137, 157 optical properties, 135 sensor thermal, 409 thermocouple, 410 thermopile, 409, 410 series resistance, 306, 335, 399 shallow trap, 221 Shockley–Read–Hall statistics, 217, 218 short circuit current, 334 short circuit current density, 111–113, 271, 272, 306, 312, 334 short-range order, 2 shunt resistance, 306, 335 Si–H chemical bond, 350 silane SiH4 , 9, 24 silica fused, 190, 192 silicon crystalline, 35 hydrogenated, xi hydrogenated microcrystalline, 40 hydrogenated nanoocrystalline, 40 protocrystalline, 347 single crystal, 198 silicon crystallite hydrogenated, 58 silicon crystallite inclusions thin-film Si:H, xv silicon dangling bond, xv

465

silicon di-hydride radical, 346 silicon nanocrystal nucleation a-Si:H based alloys, xix silicon nanoparticle, 72 silicon nitride anti-reflection coating, 386 layer in TOPCon solar cell, 391 passivation layer, 395 silicon oxide passivation layer, 332 passivation layer in TOPCon solar cell, 384, 390–392, 395, 396, 400 silicon quantum dot, 72 silicon tri-hydride radical, 346 silicon-carbon alloy hydrogenated amorphous, xiii, xix, xx, 200 silicon-fluorine bonds, 98 silicon-germanium alloy hydrogenated amorphous, xiii, xix, xx, 195–197, 199, 201 silicon-hydrogen bonding, 86, 88, 89, 95, 96, 101, 105, 110, 114 a-Si:H, xiii thin-film Si:H, xv, xvi silicon-oxygen bonding, 99 Simmons and Taylor statistics, 217, 218, 225 single-junction solar cell, 370 size distribution scattering, 53 slope Urbach tail, 170 small angle neutron scattering nc-Si:H, 355 small angle X-ray scattering, 42, 43 effect of annealing nc-Si:H, 62 feature size, 52 nc-Si:H, 43, 44, 51–54, 58, 61, 62 nc-Si:H feature size, 63 preferential orientation, 53 SnO2 , 307 SnO2 :F, 307, 309

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soda lime glass, 307 solar cell, 5, 8, 10, 18, 20, 25, 87, 110, 113–116, 118, 247, 248, 252, 259, 266, 269, 271, 282, 295, 306, 309, 314, 321, 349 a-Si:H, 193, 194, 208, 209, 228, 329–332, 336, 338, 343, 346, 348, 359, 396, 398 a-Si:H based double-junction, 350, 398 a-Si:H based multi-junction, 371, 399 a-Si:H based p-i-n, 399 a-Si:H based quadruple-junction, 398 a-Si:H based triple-junction, 350, 352, 353, 374, 398 a-Si:H double-junction, 373 a-Si:H i-layer thickness, 341 a-Si:H n-i-p, 240, 331, 338, 339, 342, 398 a-Si:H p-i-n, 60, 240, 331, 338–340, 342, 398 a-Si:H Schottky barrier, 228, 234 a-Si:H/a-SiGe:H p-i-n double-junction, 379 a-Si:H/a-SiGe:H/nc-Si:H/ncSi:H quadruple junction, 377 a-Si:H/nc-Si:H double-junction, 374 a-Si:H/nc-Si:H/nc-Si:H p-i-n triple-junction, 380, 381 a-Si:H/nc-Si:H/nc-Si:H triple-junction, 376, 380, 381 a-SiGe:H, 349, 350, 352, 363, 373, 375, 398 a-SiGe:H bandgap profile, 351 a-SiGe:H bottom cell of multi-junction, 350, 373 a-SiGe:H middle cell of multi-junction, 350 a-SiGe:H n-i-p, 353 a-SiGe:H/a-Si:H double-junction, 370, 373, 374

a-SiGe:H/a-SiGe:H/a-Si:H triple-junction, 374–376 band diagram, 336 bifacial HIT, 385, 386 bifacial thin-film, 341 bifacial tunnel oxide passivation contact (TOPCon), 391 c-Si/a-Si:H heterojunction, 384 crystalline silicon, 72, 211, 332, 333, 335, 336, 359, 384, 390, 399, 400 degradation, 233 degradation nc-Si:H, 355 degraded steady-state, 240 doped layer in a-Si:H, 348 double-sided tunnel oxide passivation contact (TOPCon), 392 efficiency, 334, 335 fill factor, 335 flexible thin-film, 342, 380 flexible thin-film silicon-based, 383 graded layers in a-Si:H, 349 heterojunction with intrinsic thin layer (HIT), xxii, 332, 384–390, 392–394, 399, 400 heterojunction, 291 high deposition rate a-Si:H, 344 high efficiency, 331, 384 high H2 -dilution a-Si:H, 347, 388 high efficiency c-Si, 384 HIT with interdigitated back contact, 385, 386 homojunction c-Si, 389 hydrogen treatment of a-Si:H, 349 III-V semiconductor, 377 impurity content a-Si:H, 354, 355 impurity content nc-Si:H, 354, 355 instability of a-Si:H, 330 light management, 359, 361 light trapping in a-Si:H, 360 light trapping in nc-Si:H, 363

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Index manufacturing, 396 mono-facial tunnel oxide passivation contact (TOPCon), 391 mono-facial HIT, 385, 386 multi-junction, 299, 331, 372 multi-junction a-Si:H-based, 370 multi-junction design, 372 multi-junction thin-film silicon, 370 n-i-p, 18, 20, 284, 295 nc-Si:H, 329, 346, 352–354, 357–360, 362, 363, 365–367, 369, 374, 375, 398 nc-Si:H bottom cell in multi-junction, 353, 369–371 nc-Si:H in double-junction, 362 nc-Si:H in triple-junction, 362 nc-Si:H n-i-p, 368 nc-Si:H/a-SiGe:H/a-Si:H triple-junction, 376, 378 optimization, 343, 347, 349 optimization nc-Si:H, 357 optimization HIT, 388 p-i-n, 18, 20, 305, 307, 314, 316, 317 p-layer in a-Si:H, 348 p-type c-Si wafer, 334, 389 p-type layer in a-Si:H, 349 Passivated Emitter and Rear Localized contact (PERL), 390, 391, 400 Passivated Emitter Rear Contact (PERC), 390, 395, 399, 400 Passivated Emitter Rear Totally diffused (PERT), 400 performance parameters, 334 plasma-enhanced chemical vapor deposition a-Si:H, 344 polycrystalline Si, 384 porosity nc-Si:H, 355 principle, 333 production line, 333 rear junction bifacial HIT, 385 Schottky barrier, 209, 238

467

Si:H based n-i-p, xxi Si:H based p-i-n, xxi six-junction, 377 tandem, 72 thin-film photovoltaic, 330 thin-film Si in crystalline silicon, 384 thin-film silicon, xiii, 333, 337, 343, 359, 393, 396, 397, 399 thin-film silicon based n-i-p, 380 thin-film silicon double-junction, 372 thin-film silicon multi-junction, 377 thin-film silicon n-i-p, 361, 362 thin-film silicon p-i-n, 360 thin-film silicon quadruple-junction, 377, 378 thin-film silicon triple-junction, 378, 379 third-generation, 71 tunnel oxide passivation contact (TOPCon), xxii, 332, 333, 384, 390–396, 400 solar cell characteristic double-junction, 373 solar cell structure, 194 solar module flexible thin-film, 381 thin-film silicon, 399 solar spectrum AM1.5, 335 solar thermal energy, 240 solution process, 1 sp3 wavefunction silicon, 57 spectra transmittance and reflectance, 130 spectral range, 169, 171 spectroscopic ellipsometry, 4, 5, 91, 92, 132, 141, 159, 191, 262, 266, 298, 314, 317 in situ, 178, 196

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real time, xix, xx, 154, 159, 168, 169, 178–184, 188–190, 192, 193, 195, 200, 201, 280, 319 spectroscopy absorption, 223 deep-level transient, 436 photoconductive, 215 photocurrent, 214 photothermal deflection, 236 reflectance, 211 transmittance, 141, 142, 211, 214 transmittance and reflectance, 133, 141, 158, 159, 191, 192, 201, 215, 236 speed of light, 222 spin-lattice relaxation, 37 spin density nc-Si:H, 58 spin operator electronic, 56 spin-lattice relaxation time, 48 a-Si:H, 49, 52 nc-Si:H, 52 sputtered amorphous silicon, 172 dielectric function, 171 sputtered Si:H, 26 sputtering, 26, 28 a-Si, 392, 395 B-doped a-Si, 395 roll-to-roll, 380, 381 zinc oxide, 360 stability, 110, 117, 306 a-Si:H, xvi, 70, 207 nc-Si:H, 60, 70 stable surface, 7 Staebler–Wronski effect, xv, xviii, 37, 38, 59, 60, 71, 88, 103, 114–116, 119, 207, 226, 272, 330 mechanism, 233 mixed-phase materials, 40 reversibility, 226 standard test condition solar cell, 335 state acceptor-like, 209, 236

amphoteric, 217 annealed, 209, 228–230 bandgap, 210, 213, 215, 218, 219, 221, 223, 230 dangling-bond, 208 defect, 208, 220, 233 density, 170, 420, 421 donor-like, 208, 236 energy distribution, 240 extended, 223 extended conduction band, 69 extended valence band, 69 initial annealed, 226 light-degraded, 209 light-soaked, 226 localized, 207, 420 localized band tail, 68 localized bandgap, 222 localized grain boundary, 66 trivalent dangling-bond, 217 single-electron, 217 static disorder, 291 statistics recombination, 217 Shockley–Read–Hall, 217, 218 Simmons and Taylor, 217, 218, 225 steady-state degraded, 228, 233 stress, 107, 119 stress-induced birefringence, 307 stretching mode, 90, 93, 94–96, 98, 101, 103–105, 110, 113, 117, 118 Si-H bond, xvi structural defect formation nc-Si:H, 367 structural evolution, 248 structural parameter, 102 a-Si:H, 200 nc-Si:H, 185 structural properties, 180 structural transitions, 248 structure a-Si:H, 35, 40, 167 columnar, 169

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Index hydrogen bonding, 173 nc-Si:H, 35, 40 solar cell, 193, 194 thin-film Si:H, xii sub-gap absorption, 89, 96, 115, 235, 236 degraded steady-state, 239 dependence on bias illumination, 236 dependence on generation rate, 238, 239 kinetics, 231, 236 sub-gap absorption spectra a-Si:H, xviii sub-surface modification, 268 substrate actual, 169 c-Si/SiO2 , 192 fused silica, 190, 192 glass, 193, 340 polymer, 340 pseudo-, 169 smooth, 192, 201 stainless steel foil, 341, 380 substrate dependence a-Si:H PECVD, 387 substrate surface roughness, 367 substrate temperature, 174, 176, 179, 180, 182 a-Si:H, 175, 343, 344 sum rule, 144 superstrate transparent, 339 surface diffusion coefficient Si radical, 346 surface driven capillary diffusion, 7 surface roughness, 159, 182, 192 substrate, 367 surface roughness evolution, 14, 22 surface roughness layer, 171, 182–184 thickness, 190 tail state exponential, 236 Tauc plot, 133

469

Tauc–Lorentz oscillator, 262, 264 TCR temperature coefficient of resistance, 270–272 technology photolithographic, 411 temperature deposition, 191, 195, 196, 198, 201 substrate, 173–177, 179, 180, 182, 197, 200 temperature coefficient bandgap, 198, 202 c-Si solar cell, 400 critical point energy, 198 dielectric function parameter, 167, 168, 201 heterojunction with intrinsic thin layer (HIT) solar cell, 389 temperature coefficient of resistance TCR, 270–272, 410, 415, 416 a-Si:H, 417–419, 424, 425, 437 microbolometer materials, 419 temperature coefficient of resistivity p-type a-Si:H, 422 temperature programmed desorption nc-Si:H, 61 template, 169, 179, 188, 195, 199, 209 terahertz radiation detection, 409, 436 terahertz spectroscopy a-Si:H, 70 nc-Si:H, 70 time resolved, 69–70 tetrahedral coordination silicon, 57 texture back-reflector, 363, 368–370 dielectric layer, 363 metal, 363 porous surface layer, 360 random, 369 Si wafer, 385, 386

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silver layer, 364, 365, 367 ZnO:Al, 360, 361 thermal activation energy, 270, 271 thermal conductance microbolometer supporting structure, 414–417 thermal emission probability, 218 thermal mass bolometer, 410 thermal noise, 73 thermal relaxation, 370 thermal resistance microbolometer pixel, 413 microbolometer supporting structure, 414, 416 thermal time constant microbolometer, 416–418 thermal velocity, 218 electron, 137 thermalization carrier, 69, 71 thermocouple sensor, 410 thermopile sensor, 409, 410 thickness bulk layer, 154, 182–185, 188–190, 193, 196, 197 film, 159, 211 nucleation, 183 surface roughness layer, 154, 184, 190, 192 thin film bulk layer, 169 optically graded, 168 oxide, 155 thin-film silicon photovoltaics technology, 384 thin-film solar cells, 102 thin-film transistor a-Si:H, 73, 330 PECVD a-Si:H, 393 three-phase model amorphous + nanocrystalline Si:H, 54

time constant microbolometer thermal, 416–418 thermal, 430 tin oxide fluorine-doped transparent conducting oxide, 193, 340, 360 TOPCon photovoltaics production line, 390 transition amorphous-to-nanocrystalline Si:H, 201, 349 electronic, 209, 221, 222, 224, 225 transition energy absorption onset to Lorentz oscillator, 173, 189, 197, 200 transmission electron microscopy, 66 silicon nanoparticle, 72 transmittance, 130, 142 multilayer device, xx ZnO:Al, 361 transmittance and reflectance spectroscopy T & R, 5, 262, 280, 319 thin-film Si:H, xvii transmittance spectroscopy, 191, 192, 201, 211, 214, 297 transparency, SnO2 :F, 194 transparent conducting oxide, 18, 340–343, 360, 361, 379, 380, 386, 389, 392, 398, 399 transport carrier, 207, 210 trap shallow, 221 trapping charge carrier, 427 free carrier, 237 level, 217 tri-methyl boron p-type doping, 340

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Index triple-junction solar cell, 255, 370, 371, 374, 379, 381 nc-Si:H/a-Si1−x Gex :H/a-Si:H, xxi tritium, 99, 100 tube-PECVD 40 kHz pulse, 395 tunneling TOPCon solar cell, 391 two-phase mixture a-Si:H + nc-Si:H, 181, 184, 185, 187 two-phase model a-Si:H + nc-Si:H, 53 two-step absorber, 306, 313, 316, 317 ultralight photovoltaic module, 383 ultralight photovoltaics applications, 383 unpolarized transmittance and reflectance spectroscopy, 4 Urbach absorption tail, 132, 134, 146, 152, 153, 157, 159, 172, 193, 195, 288, 318 amorphous semiconductor, xxi Kramers–Kronig integral, 152 Urbach energy, 291 Urbach tail slope, 170 V-shaped bandgap profile a-Si1−x Gex :H solar cell absorber, xxii, 351, 352 vacancy, 88, 93, 94, 100–102, 104, 105, 119 silicon, 63 valence band, 63, 64, 131, 136, 140, 170, 209, 218, 221, 236 tail state, 338, 348 van Hove singularity, 137 velocity drift, 209 thermal, 218 vibrational modes, 89, 90, 92, 98

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virtual interface, 182, 192, 193 virtual interface analysis, 183, 185, 192, 193, 200, 201, 266, 292–295 pseudo-substrate, 293 virtual interface approximation, 168, 320 void, 107, 108 a-Si:H, 43, 46 nano-sized, 43 nc-Si:H, 55 spherical, 43 volume fraction, 171, 192 void region a-Si:H, 47 voltage microbolometer pixel bias, 430 open-circuit, 334 volume fraction crystalline, 64, 68 nc-Si:H, 186, 188, 201 wagging mode, 93, 95, 98, 99 Wheatstone bridge, 410 width Lorentz oscillator resonance, 160, 170, 189, 190, 193, 201 window layer, 305, 318 wide bandgap, 348 X-ray diffraction, 4, 40, 41 crystallite size, 52 nc-Si:H, 42, 44, 54, 58 powder pattern, 41 X-ray photoelectron spectroscopy, 266, 295, 296 X-ray scattering nc-Si:H, 355 small-angle, 42, 43 Zeeman interaction electronic, 56 nuclear, 45, 46

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zinc oxide aluminum-doped transparent conducting oxide, 340, 342, 360, 361, 389 back-reflector layer, 342, 361–368, 370, 373, 381

boron-doped transparent conducting oxide, 340, 342, 360, 389 grating with a-Si:H, 368 textured, 363

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Materials and Energy (Continuation of series card page) Vol. 13

Theory and Methods of Photovoltaic Material Characterization: Optical and Electrical Measurement Techniques by Richard K. Ahrenkiel (Colorado School of Mines, USA and National Renewable Energy Laboratory, USA) and S. Phil Ahrenkiel (South Dakota School of Mines & Technology, USA)

Vol. 12

World Scientific Handbook of Organic Optoelectronic Devices (Volumes 1 & 2) edited by Franky So (North Carolina State University, USA)

Vol. 11

Industrial Applications of Ultrafast Lasers by Richard Haight (IBM TJ Watson Research Center, USA) and Adra V. Carr (IBM TJ Watson Research Center, USA)

Vol. 10

World Scientific Reference on Spin in Organics (In 4 Volumes) edited by Zeev Valy Vardeny (University of Utah, USA) and Markus Wohlgenannt (University of Iowa, USA)

Vol. 9

Conjugated Polymers and Oligomers: Structural and Soft Matter Aspects edited by Matti Knaapila (Technical University of Denmark, Denmark)

Vol. 8

Thin Films on Silicon: Electronic and Photonic Applications edited by Vijay Narayanan (IBM Thomas J Watson Research Center, USA), Martin M. Frank (IBM Thomas J Watson Research Center, USA) and Alexander A. Demkov (The University of Texas at Austin, USA)

Vol. 7

The WSPC Reference on Organic Electronics: Organic Semiconductors (In 2 Volumes) edited by Jean-Luc Brédas (King Abdullah University of Science & Technology, Saudi Arabia & Georgia Institute of Technology, USA) and Seth R. Marder (Georgia Institute of Technology, USA)

Vol. 6

Handbook of Solid State Batteries (Second Edition) edited by Nancy J. Dudney (Oak Ridge National Laboratory, USA), William C. West (Nagoya University, Japan) and Jagjit Nanda (Oak Ridge National Laboratory, USA)

Vol. 5

Handbook of Green Materials: Processing Technologies, Properties and Applications (In 4 Volumes) edited by Kristiina Oksman (Luleå University of Technology, Sweden), Aji P. Mathew (Luleå University of Technology, Sweden), Alexander Bismarck (Vienna University of Technology, Austria), Orlando Rojas (North Carolina State University, USA), and Mohini Sain (University of Toronto, Canada)

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