Germanium: Properties, Production and Applications: Properties, Production and Applications [1 ed.] 9781624175282, 9781612092058

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Germanium: Properties, Production and Applications: Properties, Production and Applications [1 ed.]
 9781624175282, 9781612092058

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Copyright © 2011. Nova Science Publishers, Incorporated. All rights reserved. Germanium: Properties, Production and Applications : Properties, Production and Applications, Nova Science Publishers, Incorporated, 2011. ProQuest

Copyright © 2011. Nova Science Publishers, Incorporated. All rights reserved. Germanium: Properties, Production and Applications : Properties, Production and Applications, Nova Science Publishers, Incorporated, 2011.

CHEMICAL ENGINEERING METHODS AND TECHNOLOGY

GERMANIUM

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PROPERTIES, PRODUCTION AND APPLICATIONS

No part of this digital document may be reproduced, stored in a retrieval system or transmitted in any form or by any means. The publisher has taken reasonable care in the preparation of this digital document, but makes no expressed or implied warranty of any kind and assumes no responsibility for any errors or omissions. No liability is assumed for incidental or consequential damages in connection with or arising out of information contained herein. This digital document is sold with the clear understanding that the publisher is not engaged in rendering legal, medical or any other professional services. Germanium: Properties, Production and Applications : Properties, Production and Applications, Nova Science Publishers, Incorporated, 2011.

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Germanium: Properties, Production and Applications : Properties, Production and Applications, Nova Science Publishers, Incorporated, 2011.

CHEMICAL ENGINEERING METHODS AND TECHNOLOGY

GERMANIUM PROPERTIES, PRODUCTION AND APPLICATIONS

REGINA V. GERMANNO

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EDITOR

Nova Science Publishers, Inc. New York Germanium: Properties, Production and Applications : Properties, Production and Applications, Nova Science Publishers, Incorporated, 2011.

Copyright © 2012 by Nova Science Publishers, Inc. All rights reserved. No part of this book may be reproduced, stored in a retrieval system or transmitted in any form or by any means: electronic, electrostatic, magnetic, tape, mechanical photocopying, recording or otherwise without the written permission of the Publisher. For permission to use material from this book please contact us: Telephone 631-231-7269; Fax 631-231-8175 Web Site: http://www.novapublishers.com NOTICE TO THE READER The Publisher has taken reasonable care in the preparation of this book, but makes no expressed or implied warranty of any kind and assumes no responsibility for any errors or omissions. No liability is assumed for incidental or consequential damages in connection with or arising out of information contained in this book. The Publisher shall not be liable for any special, consequential, or exemplary damages resulting, in whole or in part, from the readers‘ use of, or reliance upon, this material. Any parts of this book based on government reports are so indicated and copyright is claimed for those parts to the extent applicable to compilations of such works.

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Independent verification should be sought for any data, advice or recommendations contained in this book. In addition, no responsibility is assumed by the publisher for any injury and/or damage to persons or property arising from any methods, products, instructions, ideas or otherwise contained in this publication. This publication is designed to provide accurate and authoritative information with regard to the subject matter covered herein. It is sold with the clear understanding that the Publisher is not engaged in rendering legal or any other professional services. If legal or any other expert assistance is required, the services of a competent person should be sought. FROM A DECLARATION OF PARTICIPANTS JOINTLY ADOPTED BY A COMMITTEE OF THE AMERICAN BAR ASSOCIATION AND A COMMITTEE OF PUBLISHERS. Additional color graphics may be available in the e-book version of this book.

LIBRARY OF CONGRESS CATALOGING-IN-PUBLICATION DATA Germanium : properties, production, and applications / editor, Regina V. Germanno. p. cm. Includes index.

ISBN:  (eBook)

1. Germanium. I. Germanno, Regina V. QD181.G5G475 2010 546'.684--dc22 2010047026

Published by Nova Science Publishers, Inc. † New York Germanium: Properties, Production and Applications : Properties, Production and Applications, Nova Science Publishers, Incorporated, 2011.

CONTENTS Preface Chapter 1

Defects in Germanium: Theoretical Aspects A. Carvalho, J. Coutinho and R. Jones

Chapter 2

Properties and Generation by Irradiation of Germanium Point Defects in Ge-Doped Silica A. Alessi, S. Agnell and F. M. Gelardi

Chapter 3

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vii

Chapter 5

Chapter 6

Chapter 7

Germanium Encaged Fullerene-Synthesis, Extraction, Theoretical Calculation and their Possible Application Debmalya Roy, B. Shastri, C. N. Ramachandran, B. K. Mishra, K. Mukhopadhyay, N. Sathyamurthy and K. U. Bhasker Rao Change the Properties of Silicon and Germanium Structures with Films of Oxide and Fluoride Rare Earth Elements During External Impacts M. B. Shalimova and E. N. Khavdey

1

75

151

187

Applications of RF Sputtered GexSi1-x and GexSi1-xOy Thin Films for Uncooled Infrared Detectors Mukti M. Rana and Donald P. Butler

233

New Generation Germanium Detectors for Double Beta Decay Searches S. Cebrián, H. Gómez and J. A. Villar

269

Growth of Ge Crystals with Extremely Low Dislocation Density Toshinori Taishi and Ichiro Yonenaga

Index

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299 317

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PREFACE Germanium is an important semiconductor material used in transistors and various other electronic devices. Its major end uses are fiber-optic systems and infrared optics, but it is also used for polymerization catalysts, as well as in electronics and solar cell applications. This book presents current research in the study of germanium, including properties and generation by irradiation of germanium point defects in Ge-doped silica; Germanium encaged fullerenesynthesis; research of silicon and germanium structures with films of oxides and fluoride rare earth elements and new generation germanium detectors for double beta decay searches. Chapter 1 – Identification of point and extended defects plays a key role in the development of semiconductor materials for microelectronics and detector applications. The electronic and optic properties of semiconductors are very sensitive to the presence of defects, even if they are as small as one atom. The concentration of free charge carriers is primarily determined by the concentration of active doping impurities, but the lifetime of these carriers can be changed by the presence of deep centers with a concentration lower by orders of magnitude. Defects also change drastically the optical absorption yield, luminescence and vibrational spectra of the material. Germanium is one of the purest materials that can be grown. Germanium crystals for gamma-ray detection must have an electrically active impurity concentration as low as 109– 2 × 1010 cm−3, which is approximately equivalent to one electrically active impurity for each 1012 Ge atoms [1, 2]. Inactive impurities, such as carbon, can be present in concentrations of up to 1014 cm−1, but they play an important role in the neutralization or segregation of other defects or impurities. For example, germanium crystals can be grown dislocation-free, but then the concentration of a hydrogen-related deep center is then raised up to 1011 cm−1 [1]. Hence, ideal conditions for growth of crystals targeted to different applications are a delicate equilibrium between a number of factors, and therefore identifying and understanding the defects behind the measurable properties is of utmost importance. Over the last decade, germanium has attracted much attention due to its high mobility and the possibility of being used as channel material for post-CMOS devices, and research in the identification and characterization of defects in germanium has been bursting with activity. In a few years, we have seen many exciting new findings related to the observation, identification and control of intrinsic defects, oxygen- and hydrogen-related defects and metals. The mechanisms of diffusion of many impurities and the origin of the doping limitations has also become clearer. From decades of identification and characterization of defects in silicon, we have learned to combine experimental and theoretical means, bridging their independent results in an effort to

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viii

Regina V. Germanno

reach the fundamentals of the problem. In this review, we will focus on the theoretical aspects of the physics of defects in germanium. Nevertheless, we always endeavor to give the practical context of the problems considered, explaining how theory contributed to the identification of a defect or to clarify its properties. Chapter 2 – Ge doped amorphous silicon dioxide (Ge doped silica) has attracted the attention of researchers for more than 50 years. This material is used in many different technological fields from electronics, to telecommunication, to optics. In particular, it is widely used for the production of optical fibers and linear and nonlinear optical devices. The optical fibers, which allow to transmit optical signals with high speed avoiding interferences, are constituted by two regions with different refractive index values: core (inner part) and cladding (external part). To increase the refractive index of the core with respect to that of cladding, Ge doping of silica is commonly used. Moreover, in the Ge doped fiber two main radiation effects are observed: the photosensitivity and the second harmonic generation (SHG). The photosensitivity permits the induction of a spatial modulation of the core refractive index (Fiber Bragg Grating (FBG)) and together with the SHG, is useful to produce a great number of devices. The Ge related point defects are considered relevant for the photosensitivity and the SHG, but at the same time they are also causes of the degradation of the fiber transmission properties. For these reasons and for new application fields as the silica-based systems for nuclear environments, the defect structures, their properties, their associated optical activities, their generation and conversion processes have been widely studied and represent crucial arguments for ongoing research. These arguments have double valence, as they can be considered from a physical point of view and from the technological one. In this chapter, we will consider many aspects of the generation processes of the defects by irradiation, with particular attention to paramagnetic defects Ge(1), Ge(2) and E‘Ge, and to oxygen deficient optically active defects as the Germanium Lone Pair Center (GLPC). Some connections between material properties and defects generation will be investigated too. We will start providing a background on the literature dealing with the Ge doped glasses, their applications, the effects of the irradiation and the principal types of defects. After that, the principal properties of the investigated materials will be briefly described. The main part of the chapter will be dedicated to the presentation and the discussion of experimental data. These data concern the γ and the β radiation effects on various samples and the studies on some properties of the induced defects. Finally, we will present the main conclusions that can be derived by the data. Chapter 3 – Fullerenes have unique cage-like structures, which create a typical inner space. A range of metal atoms can be trapped inside this space to form endohedral metallofullerenes. These new materials exhibit potential applications as new type of superconductors, organic ferromagnets, nonlinear optical materials, functional molecular devices, magnetic resonance imaging agents, energy conversion devices and biological tracing agents, etc. A great deal of experimental and theoretical studies have been focused on endohedral metallofullerenes of group III metals, most of the lanthanide series elements, group II metals, alkali metals and some tetravalent metals. However, no experimental and very few theoretical studies have so far been carried out on Ge which has a comparable atomic size and weight to that of metal ions inserted earlier in the fullerene cage. The atomic radius of Ge is slightly smaller than other reported endohedral metal atoms. However, it is big enough to get trapped inside the fullerene cage. In this chapter we describe

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Preface

ix

the process for encapsulating Ge in a fullerene cage by arcing method. Solvent extraction and then exploiting the differential solubility of the metallofullerene and empty fullerenes in nitrogenous solvent were used to isolate the metallofullerene from the starting carbon soot. The insertion of Ge inside the fullerene was proven by different experimental techniques. Confined metals inside the fullerene cage strongly interact with the bonding and antibonding orbitals of fullerene and drastically alter the electrical and conduction properties of pristine fullerene. Our theoretical studies suggest that the electronic properties of fullerene could be extensively modified by encapsulation of Ge. Density functional theoretical calculations using B3LYP parametrization and 6-31G* basis set suggest that Ge as well as Ge2 can be trapped inside C60. Rotational barrier calculations for Ge2 inside C60 indicate a cross over between singlet and triplet states of the complex with a variation in the orientation angle. The energy gap between the HOMO and LUMO of C60 is reduced significantly by the encapsulation of the guest species. Recently, the development of light weight, flexible organic solar cells utilizing nanostructured materials has attracted a lot of attention. In the spectrum of solar radiation, 5% of the total spectral wavelengths is from UV whereas 46% is from visible and 49% is from near IR region. Ge has a fairly good amount of absorption in the near IR region. Therefore a range of absorption from UV, visible and NIR region could be achieved which leads to harvest more photons from sunlight and makes this metallofullerene potentially more efficient for photovoltaic application. Chapter 4 – Research of silicon and germanium structures for film oxides and fluoride rare earth elements (REE) are described. Surface morphology of the film's fluoride and oxides of rare earth elements were investigated using an atomic force microscope. Film oxides and fluoride rare earth elements manufactured by a thermal spray vacuum, feature a powdery fluoride REE and the oxidation of a metal mirror. Manufacturing these oxides REE has the possibility in multiple electroforming processes. Electroforming is the phenomenon of using conductance memory switching for films of fluoride and oxides REE, under the action of electric fields. During this process, the isolator film creates a local inhomogeneous area with high conductivity. Transition structures change to a state of high resistance as a result of some threshold value current. Impact from the electric field on the sample in the electroforming process allows for subsequent monitoring of parameter structures after each electroforming cycle. It was discovered when applying electrical fields in the order of 108 V/m, the density of surface states grow with the growth of the electroforming cycle number. This indicated additional defects at the isolator/semiconductor interface. Analysis of this experimental results show that the generated electroforming process traps have small response times, giving contribution to the capacity of the structure in mode inversions, measuring at the frequency of 1 MHz. The germanium/fluoride REE interface manifest mainly for donor type traps, which contribute an increase in a positively charged structure. These donor traps located on 0.160.18 eV below the edge of germanium conductance band, and in inversion mode is located above the Fermi level at 0.10-0.14 eV, as represented by ≈ (4-5.6) kT. Trap capacity measured in inversion mode was considerable. The effects of substrates processing to generate traps were studied. In processing the germanium surface with solution HF leads reduced the primary interface state density, and the impact of electroforming on the 𝐷𝑖𝑡 increased. Surface treatment leads also reduced the shift

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Regina V. Germanno

flatband voltage. The lower energy level occurred with donor type traps for only processed surfaces. The electroforming process for oxide REE structure swith silicon substrates experience captured positive and negative charges. To explain this experimental results one must take into account the donor and acceptor type traps. Silicon p-type structure revealed little characteristic change during multiple electroforming cycles. The main characteristic of the electroforming phenomenon indicates a similarity in these processes when a negative bias thermal instability occurred. Chapter 5 – Uncooled infrared detectors or microbolometers are the thermal detectors whose resistance changes when infrared radiation falls onto it. Radio Frequency (RF) sputtered thin films of GexSi1-x and GexSi1-xOyhave the property of changing their resistance by the heating produced when the infrared radiation falls on top of them. The thin films of GexSi1-x and GexSi1-xOy deposited by RF magnetron sputtering at room temperature from a single target of GexSi1-x in Ar or Ar : O2 environment result in a temperature coefficient of resistance (TCR) of ~5%/K at room temperature with moderate resistivity. The variations of silicon and oxygen concentrations in GexSi1-xOy thin films provide the opportunity for a parametric investigation of the dependence of the electrical and optical characteristics of the thin films on composition. As the Si concentration increases in GexSi1-x films, the TCR decreases. For GexSi1-xOy films, the addition of oxygen to GexSi1-x increases the activation energy, and TCR. The optical bandgap increases with the increasing concentration of oxygenin GexSi1-xOy. The volume normalized Hooge coefficientincreases with the increasing concentration of O2 indicating higher 1/f-noise associated with it. With the addition of O2 toGexSi1-x, the transmittance of the films increases while the reflectance remains almost constant. The optical bandgap increases with the increasing concentration of O2. Ge0.15Si0.85O0.0236 provides the optimum atomic compositions for uncooled infrared detector applications with a TCR of 5.10 %/K. Fabricated microbolometers of doped SixGe1-x exhibit TCR of -1.25%/K with a device resistance of 41.4 kΩ. Thermal conductivity is 1 × 10-5 WK-1 for these doped SixGe1xmicrobolometers.The presence of high 1/f-noise degrades the bolometers performance. Fabricated uncooled Ge0.15Si0.85O0.0236:Hmicrobolometers exhibit the highest TCR,responsivity, detectivity and lowest thermal conductivity of -4.80 (%/K), 1.05 × 104 (V/W), 8.27 × 106 (cm-Hz1/2/W) and 4 × 10-8 (WK-1) respectively at room temperature. Forming gas passivation done at 250 oC for different intervals of time reduces the value of normalized Hooge coefficient for 1/f-noise (Kf) from 7.54 × 10-7 to 2.21×10-10 after 8 hours of annealing. Being a member of Silicon-Germanium family, the processing of GexSi1-xOy thin films and microbolmeters are fully compatible with current complementary metal oxide semiconductor (CMOS) processing technology. The improved performance showed by the uncooled Ge0.15Si0.85O0.0236:Hmicrobolometers provided the opportunity to replace the material currently in use for commercial microbolometers (VOx). Chapter 6 – Double beta decay (DBD, ββ) is a rare nuclear process where a nucleus changes into an isobar with the emission of two electrons and two antineutrinos; although rare, this process has been observed for ten nuclei. A non-standard version of this decay without the emission of antineutrinos (0νββ) has been proposed and great efforts are being devoted to its observation due to the outstanding implications of its occurrence: violation of

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xi

leptonic number, confirmation of the Majorana nature of neutrinos and even an estimate of the neutrino mass scale. The direct observation of DBD by measuring the two emitted electrons, just using a germanium detector, was first proposed in the sixties. Germanium detectors offer many advantages for studying DBD of 76Ge like a very good energy resolution, a very high efficiency to signal in the approach detector=source (that is, containing the detector itself the DBD emitters) and a high radiopurity for reducing backgrounds entangling the expected signal. Experiments developed in the nineties in underground laboratories using several conventional 2-kg HPGe detectors enriched in 76Ge isotope gave, in absence of a positive signal for the neutrinoless DBD, bounds to the neutrino mass which have been for years the most stringent ones. The development of segmented and broad-energy germanium detectors has opened new possibilities for a further improvement of this kind of experiments. Since the neutrinoless DBD signal is expected to be mono-site, a significant reduction of the background measured by the detector is possible thanks to the rejection of events with energy deposition in more than one segment and also by the analysis of pulse shapes of net and transient signals allowing a 3D location of energy deposits. The first part of this chapter will be devoted to present the DBD and its physics relevance (section 1.) and to summarize the different detection strategies followed for its identification (section 2.), highlighting the important role of experiments using Ge detectors. In the second part of the chapter, the high potential of new generation germanium detectors for identifying the neutrinoless DBD will be presented (section 3.) and the achievable sensitivities thanks to the use of different background reduction strategies will be discussed and assessed (section 4.). Chapter 7 – Germanium (Ge) single crystals with an extremely low density of or almost free from grown-in dislocations were grown by the Czochralski technique using boron oxide (B2O3) and a silica crucible, where generation of GeO2 particles, harmful for dislocation-free crystal growth, was effectively suppressed by the partially- or fully-coverage of the melt surface with B2O3 liquid. In a further evolution of the above growth technique, Ge crystals with various concentrations of interstitially dissolved oxygen atoms up to 5.5  1017 cm-3, two orders higher than that in a conventionally grown Ge crystals, were grown by full coverage of the Ge melt surface with B2O3 liquid and addition of GeO2 powder. The effective segregation coefficient of oxygen atoms was estimated to be 1.0–1.4. These Ge crystals are expected for application as high quality and thermo-mechanically stable materials, free from grow-in dislocations, for high-speed ULSI devices and GaAs solar cell substrates.

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In: Germanium: Properties, Production and Applications ISBN 978-1-61209-205-8 c 2012 Nova Science Publishers, Inc. Editor: Regina V. Germanno

Chapter 1

D EFECTS IN G ERMANIUM : T HEORETICAL A SPECTS 1

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1.

A. Carvalho1 , J. Coutinho1 and R. Jones2 Department of Physics, I3N, University of Aveiro, Aveiro, Portugal 2 School of Physics, University of Exeter, Exeter, UK

Introduction

Identification of point and extended defects plays a key role in the development of semiconductor materials for microelectronics and detector applications. The electronic and optical properties of semiconductors are very sensitive to the presence of defects, even if they are as small as one atom. The concentration of free charge carriers is primarily determined by the concentration of active doping impurities, but the lifetime of these carriers can be changed by the presence of deep centers with a concentration lower by orders of magnitude. Defects also change drastically the optical absorption yield, luminescence and vibrational spectra of the material. Germanium is one of the purest materials that can be grown. Germanium crystals for gamma-ray detection must have an electrically active impurity concentration as low as 109 – 2 × 1010 cm−3 , which is approximately equivalent to one electrically active impurity for each 1012 Ge atoms [1, 2]. Inactive impurities, such as carbon, can be present in concentrations of up to 1014 cm−1 , and they play an important role in the neutralization or segregation of other defects or impurities. For example, germanium crystals can be grown dislocation-free, but then the concentration of a hydrogen-related deep center is then raised up to 1011 cm−1 [1]. Hence, ideal conditions for growth of crystals targeted to different applications are a delicate equilibrium between a number of factors, and therefore identifying and understanding the defects behind the measurable properties is of utmost importance. Over the last decade, germanium has attracted much attention due to its high mobility and the possibility of being used as channel material for post-CMOS devices, and research in the identification and characterization of defects in germanium has been bursting with activity. In a few years, we have seen many exciting new findings related to the observation, identification and control of intrinsic defects, oxygen- and hydrogen-related defects and metals. The mechanisms of diffusion of many impurities and the origin of the doping limitations has also become clearer. From decades of identification and characterization of

Germanium: Properties, Production and Applications : Properties, Production and Applications, Nova Science Publishers, Incorporated, 2011.

2

A. Carvalho, J. Coutinho and R. Jones

defects in silicon, we have learned to combine experimental and theoretical means, bridging their independent results in an effort to reach the fundamentals of the problem. In this review, we will focus on the theoretical aspects of the physics of defects in germanium. Nevertheless, we always endeavor to give the practical context of the problems considered, explaining how theory contributed to the identification of a defect or to clarify its properties.

2.

Techniques for identification of defects in germanium

Various experimental methods can be used to reveal defect properties. A measurable property that can be related to an unique defect and used to detect its presence is often referred to as the defect signature. Identifying the defect means identifying the chemical species of the atoms involved in the defect and their atomic arrangement, thus connecting the defect signature to a defect model. Once a defect model is validated it is possible, using theoretical methods, to determine other defect properties, and this is useful for example in linking defect signatures detected by different experimental methods to the same defect. Defect models are also useful to understand the defect reactions and the conditions of formation and annealing. Theoretical models can be very detailed and provide quantitative information that can be directly compared with experiment. In the next two sections, we will briefly outline how some observables can be calculated, and what experimental methods can be used to measure them. 1

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2.1.

Theoretical methods

Quantum mechanical methods can be used to calculate the energy of a system of atoms or molecules from first-principles, or ab-initio i.e., without experimental input. Approximate empirical methods are faster and applicable to systems with a larger number of atoms, but the quality of the result always depends on the accuracy of the input data and the quality of the fitting parameters to the system under study. In contrast, first-principles calculations are by definition parameter-free, and the accuracy of the result depends only on the validity of the theoretical approximations and the accuracy of the numerical methods employed. A quantum-mechanical calculation of the total energy of the system requires the solution of the Schr¨odinger equation, ˆ TOT |ψTOT i = ETOT |ψTOT i, H

(1)

where ETOT is the total energy and ψTOT is the wavefunction of the whole system composed by electrons and nuclei, ψTOT ≡ ψTOT (r1 , s1 , ..., rN , sN , R1 , ..., RNn ),

(2)

which is a function of the coordinates of electrons and nuclei including spin coordinates si . 1

A more detailed introduction to the techniques used for the identification of defects in semiconductors can be found in Ref. [3] Germanium: Properties, Production and Applications : Properties, Production and Applications, Nova Science Publishers, Incorporated, 2011.

Defects in Germanium: Theoretical Aspects

3

The Hamiltonian has the form ˆ TOT = Tˆe + Tˆi + Vˆi−e + Vˆe−e + Vˆi−i = H X 1 X 1X 2 Za = − ∇r j − ∇2Ra − + 2 2Ma |Ra − rj | a j

+

j,a

1 X 1 1 X Za Zb + , 2 |rj − rk | 2 |Ra − Rb | j,k:j6=k

(3)

a,b:a6=b

where Ma , Ra and Za are the mass, position and charge of the a-th nucleus, respectively, and ri is the coordinate of the i-th electron (in atomic units). The solution of this equation for complex systems always involves a certain degree of simplification2. A first approximation is the separation of nuclear and electronic degrees of freedom (Born-Oppenheimer approximation). Another problem is expressing the electronelectron interaction (Vˆe−e). Two principal schemes are Hartree-Fock (HF) and DensityFunctional Theory (DFT). While the former has been used for some defect studies, the latter has become increasingly popular in solid state physics due to its success in treating a variety of systems, from metals to insulators, and will be considered in the next section. Further, it is necessary to account for the distinct behavior of the wavefunctions in the core region, close to the nuclei, and in the interstitial region; a popular scheme consists in separating valence electrons from core electrons, building a potential weaker than the true potential, but that gives rise to the same charge density in the valence region (pseudopotential) 3 .

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2.1.1.

Density functional theory

The density functional theory is an exact variational principle, where the variable is the electron density n(r) of the ground state |Ψi. The key result behind DFT is that the relation between the charge density and the external potential is a bijective: the probability density is a functional of v, but it can be proved that v is also an unique functional of n [7]. Consequently, the charge density is sufficient to describe the fundamental state of the system, with all its properties, including its energy: Z Z n(r)n(r0) ETOT [n] = T [n] + n(r)v(r)dr + drdr0 + Exc[n], (4) |r − r0 |

where T is the kinetic energy and Exc[n] is the exchange correlation energy. The density can be expressed in terms of auxiliary functions ψl (r) (the Kohn-Sham states): occ X l

|ψl (r)|2 = n(r)

(5)

and occ X 1 hψl | − ∇2 |ψl i, T [n] = 2

(6)

l=1

2

For an introduction to many-body theory, the reader is referred to Ref. [4]. A review concerning its implementation to computer modeling of solids can be found in Ref. [5]. 3 A discussion of the influence of core-valence interactions in the bandstructure of Ge can be found in Ref. [6]. Germanium: Properties, Production and Applications : Properties, Production and Applications, Nova Science Publishers, Incorporated, 2011.

4

A. Carvalho, J. Coutinho and R. Jones

where index l runs over all occupied levels. Note that the electrostatic potential acting on electron i by the other electrons, has been replaced by an average over the positions of the other electrons. Equations 4–6 can be solved numerically through a self-consistency iterative procedure. The difficulty resides in determining an expression for Exc[n], which is only known for the homogeneous electron gas. This can be used as a good approximation in solids and is named local density approximation (LDA). The underestimation of the energy of excited states is one of the drawbacks of the attractive LDA. When applied to semiconductor physics, it invariably leads to very small bandgaps. The value of the bandgap can be expressed in terms of the difference between highest occupied and lowest unoccupied Kohn-Sham states (ELUKS and EHOKS ) [8] Eg = ELUKS − EHOKS − ∆xc.

(7)

The additional term in the right-hand side of Eq. 7 is the discontinuity, as a function of the occupation number, of the exchange correlation potential at the Fermi level. The bandgap underestimation in semiconductors arises both from i) the self-interaction error inherent to the LDA potential ii) the vanishing of the discontinuity ∆xc of the LDA exchange potential as a function of the level occupancy at the Fermi level. Germanium is a drastic case, where the LDA fails to predict the existence of a non-vanishing bandgap between occupied and unoccupied bands [9].

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2.1.2.

Boundary conditions: clusters and supercells

The next step is to build a model for the defective lattice that the quantum mechanical methods can be applied to. Two different approaches are usually employed, based on supercell or cluster approximations. A supercell is a volume of solid that repeats itself periodically in space. This is an exact representation of a perfect crystal. On the other hand, the cluster consists of a finite portion of solid whose surface is passivated, generally with hydrogen, to eliminate free radicals. Although cluster calculations have been extensively used in the past, the supercell method is now usually preferred because of its simplicity, and specially for providing an exact representation of the bulk of the semiconductor. Nevertheless, in germanium the cluster method has some advantages. As an artifact of the quantum confinement, the bandgaps in the clusters turn out to be much larger than those found using supercells, and decrease with increasing size of the cluster[5]. The cancellation of the LDA bandgap error by the finite size effect error in clusters eliminates some serious problems of LDA calculations in supercells, where the unphysical crossing of the energy levels that can occur for some k-points limits the amount of reliable information that can be extracted from supercell calculations[10, 11]. A surprising success of LDA cluster calculations is the accuracy of ionization levels of deep centers in germanium. The reason behind seems to be the fact that calculations with local exchange-energy functionals yield the correct distance between localized defect levels, but position them wrongly relative to the band edges (Fig. 1) [12], and similarly, in nanocrystals the position of many impurity levels remains approximately constant with the

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Defects in Germanium: Theoretical Aspects

5

crystal size [13]. Still, despite the important results obtained with this simple approximation, the bandgap problem should be solved from its roots, by improving the description of the exchange and correlation energy. 2.1.3.

Tackling the bandgap problem

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Semi-local approximations for the exchange energy functional including gradients of the density (generalized gradient approximations, GGAs) produce some improvements over the energies [14], but do not eliminate the bandgap problem [8]. Semi-empirical pseudopotentials fitted to give a bandgap close to the experimental value do not require extra computational effort, but lose the transferability conferred by a fully ab-initio approach. Other methods have been proposed to correct for several deficiencies of the semi-local implementations of density-functional theory, and consequently the calculated bandgap 4 , including the self-interaction correction (SIC), which corrects for the spurious selfinteraction intrinsic to the Kohn-Sham approach[16], quasiparticle calculations in the GW approximation (GWA)[17], exact exchange and hybrid methods, which used improved expressions for the exchange energy[18, 19, 20], and the LDA+Hubbard U (LDA+U) method, which eliminates the orbital-independence of the one-electron potential by adding a localized term to the potential of strongly correlated electron orbitals [21]. We describe below four approximations that have already been applied to germanium in an effort to tackle the bandgap problem. Screened exchange. The modified LDA scheme known as screened exchange was introduced by Bylander and Kleinman [18]. Within this approach, the exchange operator is ˆ SX and a remaindivided into two parts, a Thomas-Fermi screened exchange operator H der. The remainder and correlation are treated in the local-density approximation, while the screened exchange matrix elements are exactly evaluated: LDA δESX δEcLDA ˆ xc = H ˆ SX + δEx H − + . δn δn δn

(8)

Here ExLDA is the LDA functional for the exchange energy, EcLDA is a LDA correlation energy functional, and ESX is the LDA screened energy functional, given by the expression 3 ESX [n] = − 2

 1 3 3 4 n 3 F (z), π

(9)

with    2      z2 z 4 2 8 F (z) = 1 − 1− + 3 log 1 + 2 + arctan , 6 4 z z z

(10)

where z = Ks /kF . The non-local screened exchange operator HˆSX is calculated with the screened Coulomb interaction e−Ks r r1 . One difficulty is choosing the screening parameter 4

Although we have no formal mathematical grounds to compare the difference between the highest occupied and lowest unoccupied Kohn-Sham eigenvalues with the experimentally measured bandgap, this is often done for non-local formalisms including a part of the discontinuity ∆xc into the eigenvalue gap [15]. Germanium: Properties, Production and Applications : Properties, Production and Applications, Nova Science Publishers, Incorporated, 2011.

6

A. Carvalho, J. Coutinho and R. Jones

Figure 1. Valence and conduction band edges (VB and CB) of Ge and dangling bond defect levels calculated using hybrid functionals of the form given in Eq. 11, as a function of α. (+/0) and (0/-) ionization levels are represented respectively as squares (red online) c by the American and circles (blue online). (Reprinted with permission from Ref. [12]. Physical Society 2008.)

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2 = Ks , which can be taken for example to be the Thomas-Fermi wave-vector Ks2 = KTF 1 2 2 4kF/3. Calculations for Si with Ks = 2 KTF result in much improved band structures and binding energies [18], and this method has the advantage of being easily coupled with conventional LDA calculations. Applied to germanium, screened exchange improves the bandgap width (0.28 eV at Γ) but used with LDA pseudopotentials give a wrong conduction band dispersion [15, 22]. This problem seems to arise from the deficient treatment of valence-core interactions [6], as it has been reported that calculations with pseudopotentials built with screened exchange correctly yield the conduction band minimum at L [22].

Hybrid functionals It is possible to derive hybrid functionals simply by replacing a fraction of LDA or GGA exchange by an exact non-local expression. A class of these functionals based on the PBE formulation for the GGA functional[14] has been proposed by Perdew, Ernzerhof and Burke [20] ExPBEhybrid(α) = αExexact + (1 − α)ExPBE .

(11)

Using a variational principle, α = 1/4 was found for a benchmark set of molecules [20]. The functional given by Eq. 11 for α = 1/4 is known as PBE0 functional. Another approach corresponds to use α as a fitting parameter to yield the experimental bandgap. For Ge, this is obtained for α = 0.15 (Fig. 1) [12]. The calculations with this class of hybrid functionals have a high computational cost. Screened Coulomb potential hybrid functionals The idea of eliminating the 1/r dependence of the Coulomb functional by using a screened potential was applied by Heyd, Scuseria and Ernzerhof to formulate a hybrid density functional known as HSE [19]. Heyd et al. proposed another hybrid functional based on a screened Coulomb potential where, unlike in the scheme by Bylander and Kleinman [18], the screening is applied only to the

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7

exchange interaction. The separation between long range and short range is achieved by splitting the Coulomb operator in two parts: 1 erfc(wr) erf(wr) = + , r r r

(12)

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with erfc(wr) + erf(wr) = 1 and where w is an adjustable parameter. The first term is short-ranged, and the screening is applied to the second, long-ranged component only. The screened exchange contribution decays exponentially even for metallic systems, thus eliminating the divergence of the derivative of the orbital energies with respect to k which causes problems in regular HF calculations in metals. The HSE functional is equivalent to PBE0 for ω → ∞ [23], but is computationally more efficient. HSE corrects the bandgap of germanium to 0.56 eV [9]. Strong correlation effects: LDA+U For strongly correlated systems, specially with semi-filled d and/or f electrons, the Coulomb interaction between these localized orbitals can be strong enough to change the nature of the ground state [21]. For such systems, an LDA exchange-correlation functional, obtained for the homogenous electron gas, is not appropriate. The LDA+U approach tackles this problem by adding a Hubbard-like, localized term, to the LDA density functional. This is usually done by separating the localized d or f electrons, on which the Hubbard term will act, from the delocalized ones (usually s and p electrons), which are correctly described by the usual LDA calculation. The double counting of the correlation part for localized electrons is then avoided by subtracting another term (the double-counting correction) [24]. The parameter U can be obtained from photoemission experiments, by fitting the bandstructure or from calculations for the isolated atoms. The LDA+U method (or a variation built upon a GGA) has been applied not only to systems with valence d and f electrons, but also to nitrides, oxides and Ge [25, 26], which have semi-core d shells. Even if the shell is filled, the d states interact and hybridize with the states at the valence-band maximum, shifting its position [25]. Nevertheless, for Ge the improvement of the bandgap (between Kohn-Sham eigenvalues) is very modest, namely 0.2 eV for a U calculated from first principles for the Ge atom [26]. It is apparent that most, if not all, of these methods require the choice, more or less arbitrary, of parameters, and the exactness of the respective results is difficult to evaluate when there is no experimental data available for comparison. Moreover, all these methods are computationally very expensive and their application to defects in semiconductors is still in its infancy. Nevertheless, we believe that germanium is one of the materials where the price to pay for an improved bandstructure description is more justified; and as the developments of the theory are accompanied by the improvement of the computational power and algorithm efficiency, improved methods based on density functional theory will make their way to standard defect calculations. 2.1.4.

Calculation of observables

Computer models would be of little use if measurable properties could not be calculated. Fortunately, this is not the case, as density functional theory can be used to obtain many properties that can also be obtained experimentally, for example: Germanium: Properties, Production and Applications : Properties, Production and Applications, Nova Science Publishers, Incorporated, 2011.

8

A. Carvalho, J. Coutinho and R. Jones • Defect structures, calculated by minimizing the total energy with respect to the atomic coordinates; • Local and pseudo-local vibrational mode frequencies, obtained by direct diagonalization of the dynamical matrix of second derivatives of the total energy with respect to the atomic coordinates; • Ionization levels, obtained from the defect formation energy, or semi-empirically by comparing the ionization energy with known defects (marker method); • Diffusion barriers, obtained by determining the position of the saddle point in the minimum energy path between minima of the adiabatic energy surface; • Electric field gradient, obtained from the second derivative of the Coulomb potential.

In general, properties of the ground state are more accurately determined within the DFT formalism than those involving energies and/or wavefunctions of excited states.

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2.2.

Experimental methods

Experimental characterization of defects in germanium also has its challenges. Many of the techniques which have contributed to a deep understanding of solid-state and defect reactions in Si and other semiconductors have limited application in germanium: due to the short spin-orbit relaxation time and variety of stable isotopes, electron paramagnetic resonance (EPR) signals are weak, and have complex hyperfine splitting patterns which result in broad lines [27]; observation of vibrational absorption, with very few exceptions [28], is limited to neutral impurities, since the free-carrier absorption makes the vibrational bands from electrically active impurities very difficult to observe; and deep level transient spectroscopy (DLTS) has been until very recently confined to n-type Ge due to the difficulties in making good rectifying junctions in p-type material [29]. In contrast, other techniques such as Perturbed Angular γ-γ Correlation spectroscopy (PACs) have provided important information on the properties of defects in germanium. Some of the experimental techniques providing measures directly comparable to the calculations and often mentioned through out this review are listed below. Electron Paramagnetic Resonance (EPR) Electron paramagnetic resonance consists of the resonant absorption of electromagnetic radiation by systems with an electron magnetic dipole [30, 31]. In most cases, the magnetic dipole of the electron arises from the spin angular momentum, with a small contribution from the orbital momentum. A magnetic field is used to lift the spin degeneracy. Absorption is detected when the energy separation between levels equals the energy of the electromagnetic resonance. EPR spectroscopy can provide detailed information on the defect spin, chemical species, symmetry, number of atoms in each atom shell of the defect and details of the electronic structure of the defect but, as discussed above, this technique has limited application in Ge. Examples of defects in germanium characterized with the aid of EPR are the vacancy-oxygen complex (VO) [32, 33] and the thermal donors [34, 35].

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9

Hall effect Hall effect techniques measure the quantity RH = (en)−1 , where n is the free carrier concentration and e the electron charge [30]. Together with conductivity measurements, it also provides the also the carrier mobility. The position of donor and acceptor levels can be obtained from the temperature dependence of n. These techniques have been used extensively, specially in the early decades of research on defects in germanium (19601980’s), providing information on radiation damage, metals and other defects.

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Deep Level Transient Spectroscopy (DLTS) The basic principle behind the deep level transient spectroscopy technique is that the rate of thermal emission or capture of charge carriers from defects in the depletion region of a p-n junction under a reverse-bias pulse can be obtained from the transient of the junction capacitance[36]. DLTS is a major source of information about the capture cross sections, concentrations and activation energies of deep carrier traps that, unlike optical methods, can be used to detect non-radiative centers. Together with Laplace DLTS [37], it has been used to detect many dopant-related complexes, metals and other deep centers, and it is used for quality control of commercial germanium materials. Infra-Red (IR) absorption spectroscopy and Raman scattering spectroscopy Fouriertransform IR absorption (FTIR) spectrometers are widely used to measure the frequencies of the local vibrational modes of defects in semiconductors [3, 28]. For harmonic oscillations, a mode is IR-active if the associated movement of the defect atom or atoms give ˆ of the center. Thus, IR absorption experiments rise to a change in the dipole moment p with polarized light can also give information on the symmetry of the vibrational mode. Raman spectroscopy can also be used to measure vibrational mode frequencies, but the Raman scattering power cross section is a measure of the change of the optical susceptibility tensor components. Vibrational modes not active in IR absorption can therefore be observed in Raman spectroscopy and vice-versa, making IR absorption and Raman scattering spectroscopy complementary techniques. Vibrational mode spectroscopy can be used to detect electrically inactive centers such as interstitial oxygen and oxygen dimers, carbon and hydrogen molecules. Perturbed angular γ-γ correlation spectroscopy (PACs) The PACs technique is designed to measure the electric field gradient in a non-cubic site or in the proximity of a defect by using a suitably chosen radioactive probe nucleus [3]. It can be used to provide information on the defect symmetry, ionization levels and mobility. PACs and other experiments with nuclear probes have been used in germanium to characterize the self-interstitial and the vacancy[38].

3.

Intrinsic defects

Self-interstitials and vacancies, the primary intrinsic defects, are invariably present in semiconductor crystals. They can be formed thermally, by interchange of atoms with the surface, or introduced in higher concentrations by irradiation with fast electrons, γ-rays, neutrons and heavier particles, quenching, deformation (dislocation climbing) or other damaging

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A. Carvalho, J. Coutinho and R. Jones

treatments. Highly mobile and reactive, the self-interstitial and the vacancy take part in many defect reactions in a wide temperature range, compensating dopants and mediating the diffusion of impurities at high temperatures. Thus, knowing their properties is essential to control and understand the evolution of point and extended defects. However, their high mobility and reactivity, even at low temperatures, makes them very difficult to detect and identify in the isolated state. Hence, although radiation damage in germanium has been object of attention since the early stages of research on nuclear physics in the mid-60s [39, 40], for a long time very little was known about the basic intrinsic point defects. Recently, first-principles calculations, as well as recent advances in PAC and DLTS spectroscopy[41, 42] have contributed to the identification and characterization of the selfinterstitial and vacancy, but fundamental unanswered questions persist.

3.1.

The self-interstitial

The self-interstitial in Ge has been modeled within the density-functional theory framework, using different approximations: LDA and GGA calculations with supercells [43, 44, 45, 46] or clusters [47, 46], as well as LDA+U/GGA+U calculations with Coulomb U repulsion applied to the d orbitals of Ge [26].

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3.1.1.

Structure and energetics

A variety of geometries can be conceived for the self-interstitial. The possible configurations studied here can be divided into split-interstitial (or “dumbbell”) configurations and caged configurations. The split-interstitial configurations are obtained by replacing a germanium atom at the lattice site by a pair of interstitial atoms aligned along a particular direction, while caged self-interstitials are placed in the cavities of the diamond lattice, at or close to one of the high-symmetry sites. Those are√the tetrahedral (T ) interstitial site, characterized by four nearest neighbors at a distance 3/4a0 from the center and six second-nearest neighbors (2NN) at a distance of a0 /2, and the puckered hexagonal (H) site, the mid-point between two nearest-neighbor T sites. At the T site, the distance of the interstitial to the nearest lattice atoms is maximized. The potential energy surface for the self-interstitial depends on the charge state, limiting the use of LDA supercell models. Cluster LDA calculations and LDA+U supercell calculations agree qualitatively on the minimum energy geometries. The variations on the calculated relative energies are justified by the fact that the LDA+U calculations still yield a very small bandgap of 0.19 eV[26], whereas cluster calculations have a very large bandgap (typically around 2 eV for clusters of 300-500 atoms) due to confinement effects. According to the cluster calculations and LDA+U supercell calculations, the h110i-split interstitial is the lowest energy configuration of the neutral interstitial [43, 44, 47, 26] (Table 1). Both Ref. [44] and Ref. [46] have highlighted the importance of the convergence with the supercell size and Brillouin zone sampling in supercell calculations. This hides a more serious problem. Essentially, as germanium is metallic in the LDA or GGA, depending on the k-points used for reciprocal space sampling, the defect-related levels or the bulk may be occupied, often leading to unphysical charge localizations [48, 49]. Thus, in small supercells the neutral dumbbell interstitial is found to be more stable, whereas in large

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Defects in Germanium: Theoretical Aspects

a)

11

b) I++ F

E

I+ I0

A+ B+

B

A C

[001] [110]

Figure 2. Charge dependent structures of the self-interstitial: a) split-interstitial and b) caged interstitial, with the positions of the interstitial atom(s) in the neutral, positive and double positive charge states represented in light gray, white and dark gray, respectively. Atoms are labeled with letters.

Table 1. Calculated relative energies Er (eV) of germanium self-interstitials in the h110i-split interstitial (D), hexagonal (H) and tetrahedral (T ) configurations. Letters indicate an unstable initial configuration, and the structure it relaxes to (if available).

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Method

Configuration

Er (−)

Er (0)

Er (+)

Er (2+)

LDA 128 at. supercell

D H T

0.00 0.65 0.90

LDA 128 at. supercell

D H T T

0.66

Hd

0.00 0.44 0.29 0.00

0.00

LDA Ge329 H172 cluster

D/Dd H/Hd T

0.00 0.73 1.10

0.00 0.50 H

0.08 0.00 Hd

T T 0.00

LDA+U 64 at. supercell

D/Dd H/Hd

0.00

0.00 0.42

0.32

0.94

GGA 512 at. supercell

D/Dd H/Hd T

Ref. [43]

[44]

0.30 T 0.00

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[47]

[26] [46]

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A. Carvalho, J. Coutinho and R. Jones

Figure 3. Self-interstitial in germanium close to a [110] surface, as observed by aberrationcorrected transmission-electron microscopy. (a) model of a neutral S interstitial obtained in a Ge slab; (b-c) Aberration-corrected images of IT interstitials, (d) IH or bond-centered interstitial and (e) self-interstitial at an off-center site. (Reprinted with permission from c by the American Physical Society 2008.) Ref. [46]. supercells, the IT is lower in energy [46]. Even for a converged supercell model, there is no guaranty that the correct states are being populated. In contrast, the defect geometry is already converged in cluster models with only about 300 atoms [50]. The disadvantage of the cluster models resides in the difficulty in evaluating the effects resulting from the confinement, specially for charged defects inducing a long-range polarization of the lattice.

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3.1.2.

Ionization levels

The self-interstitial is a double donor. The electrical levels were calculated in Ref. [47] (Table 9) using the marker method and later confirmed by DLTS measurements[42]. At low temperatures, the caged self-interstitial and the dumbbell self-interstitial will co-exist independently. According to Carvalho et al., the two have very different electrical properties. The h110i split-interstitial was found to be electrically inactive. The (0/+) donor level is 0.10 eV below the the valence band, and the acceptor level is above the ´ conduction band bottom. The LDA+U calculations of Spiewak et al., using the formation energy method, found a donor level at Ev + 0.45 eV, but as this level is already above the calculated conduction band minimum (at Ev + 0.19 eV), there is a difficulty in interpreting the meaning of this calculated level. In contrast, the caged interstitial, is a double donor, with E(+/2+) ' Ec − 0.1 eV and E(0/+) ' Ec − 0.2 eV [47]. This is agreement with the subsequent DLTS measurements of Mesli et al. (placing these levels respectively at Ec − 0.24 and Ec − 0.08 eV) and also close to the level suggested by the PAC spectroscopy experiments (Ec − 0.04 eV) [42, 52]. It is important to note that the difference between the calculated E(+/2+) and E(0/+) levels associated with the caged interstitial is within the calculational error, and therefore it cannot be concluded whether those two levels are in negative-U order. In fact, experimental observations suggest that the levels of the self-interstitial are in regular order [53], and formation energy calculations using LDA+U place the (0/+) level above the (+/ + +) level (respectively at Ev + 0.46 eV and Ev + 0.11 eV).

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Defects in Germanium: Theoretical Aspects 2+ +

13

T 2+ +2 e

H d+ +e

D d+ +e H d+ +e

0.29 0.10

0.08

0.08

0

H0 0.76 0.53

0.50

D0

D

H

T

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Figure 4. Proposed configuration-coordinate diagram for the germanium self-interstitial for c by the American Physical Society electrons. (Reprinted with permission from Ref. [47]. 2008.) However, we note that the lowest energy structures for the neutral and positive charge states are different. Thus, neutral IH may be a frozen metastable state at low temperatures, but at higher temperatures the relative populations of IH and ID will be given by a Boltzmann distribution. This requires that the average thermal energy of the defect is higher than the potential energy barrier separating the split-interstitial and caged interstitial forms (kB T & WD→H ) (Fig. 4). The (0/+) level associated with the ID 0 →IH + + e− transformation, is found in (0/+) Ref. [47] to be close below the valence band maximum, at Ev − 0.03 eV. The ID→H level is (+/2+) well below the IH→T level at Ec −0.2 eV, and the defect will be thermodynamically stable only in the neutral and double positive charge states, with (0/2+) at about mid-gap. the defect exists in two different forms, an inactive dumbbell and a double donor caged interstitial, and the rate of transformation between the two is very slow, at high temperatures the defect takes the D configuration when neutral and the T configuration when double positive, and has negative U with the (0/2+) level around mid-gap. This theoretical model has been used to explain several features of electron-irradiated Ge[47] as well as other defect reactions at higher temperatures, which will be consider in the next sections. 3.1.3.

Diffusion

Long-range migration paths can be decomposed into single barrier jumps between the energy minimum points. These elementary steps comprise transformations between different interstitial structures [Fig. 5-a)], defect reorientations [Fig. 5-b)] and jumps between equivalent configurations [Fig. 5-c) and d)]. The migration steps and their respective energies have been described in Ref.[54]. • In the neutral charge state, the activation energy required to transform ID into IH , as depicted in Fig. 5-a), was found to be only 0.53 eV. This makes the succession of

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A. Carvalho, J. Coutinho and R. Jones

Figure 5. Structural transformations involved in the migration of the self-interstitial. (a) Reconfiguration of the neutral defect (step 1) from a split-interstitial structure to the nearest H site; (b) reorientation of I+ Hd , through the undistorted H site (step 2), and reorientation inside the cage (step 3); (c) h111i migration of IH (step 4) through the T site and (d) migration of I2+ T along the h111i chain (step 5) or by knock-on (step 6). (Reprinted with permission c Institute of Physics and IOP Publishing Limited 2008.) from Ref. [54]. step 1

step 1

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reconfigurations D −−−→ H −−−→ D 0 a preferred path for long range diffusion. • In the positive charge state, the potential energy surface for the self-interstitial has a minimum at an intermediate position between the T and H sites (IHd ). Long range migration has to produce a net displacement to the vicinity of a distinct T cage. This can be accomplished via a succession of the reorientations 2 and 3 shown in Fig. 5-b). step 3 Hd −−−→ H d 0 is a reorientation inside the interstitial cage, in the neighborhood of the T site, and requires very little energy. The dominant energy for the long range diffusion is given by step 2, a jump over the 0.29 eV energy barrier centered at the undistorted H site. • The double positive self-interstitial was only found to be stable in the T interstitial site, and unlike for I+ , its potential energy surface is very steep. The preferred migration energy is a zig-zag motion along the h111i (step 5), as represented in Fig. 5-d). The energy at the saddle point, the H site, is 1.23 eV higher than at T . In addition to the ordinary thermally-activated diffusion, under light excitation or irradiation there is strong indication that the self-interstitial can migrate via a BourgoinCorbett mechanism. It was shown that the potential energy transverse for the caged selfinterstitial (IH /IT ) between T and H sites varies with charge state, so that the saddle point for I0 is an equilibrium position for I2+ and vice-versa (Fig. 4). Hence, in addition to the thermal migration processes described, it is possible that under ionizing conditions the migration of self-interstitials through the cages of the diamond lattice is enhanced by the Bourgoin-Corbett mechanism and/or energy release mechanism [55, 56]. A possible

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Defects in Germanium: Theoretical Aspects

15

Table 2. Lowest calculated migration energies (eV) and respective diffusion paths of the self-interstitial, without charge state change, from Ref. [54]. When there was more than one saddle point along the minimum energy path, Wmig was taken to be the dominant energy barrier. Primes (0 ) indicate the same defect in different positions (Fig. 5). charge suggested mechanism Wmig 0 + 2+

step 1

step 1

D −−−→ H −−−→ D 0 step 2

Hd −−−→ H d step 5

T −−−→T 0

step 3 0− −−→

Hd

0.53 00

0.29 1.23

Bourgoin-Corbett migration mechanism for the self-interstitial can be conceived as follows: the equilibrium position for I2+ is the T site, but if it traps two electrons, the I0T structure is no longer stable. The double electron capture is then followed by a spontaneous relaxation to one of the two neighboring H sites. Then, a subsequent trapping of two holes would leave the self-interstitial in the I2+ H state forcing a relaxation to one of the neighboring T sites. This provides a possible process for athermal migration in the presence of excess free carriers, as during irradiation or under other source of excitation, similar to what has been suggested to happen in p-Si [56], which may be in the origin of the radiation annealing and light-induced annealing at cryogenic temperatures reported in n-type and p-type Ge [57, 58, 59, 60].

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3.2.

The vacancy

It is generally accepted that vacancies have a lower formation energy than self-interstitials and therefore they are believed to dominate self-diffusion[61]. Moreover, a careful control of the formation of vacancies during Czocharlskii growth is crucial to prevent the formation of pits and voids in Ge crystals[62]. Thus, there has been an intense theoretical research effort aimed at clarifying the properties of the isolated vacancy and vacancy clusters at different levels of theory. At first-principles level, the structure, electronic properties and migration energies of the vacancies in germanium have been investigates using supercell and cluster methods [63, 64], LDA+U calculations [65] and hybrid functional calculations [66]. Additionally, vacancy diffusion and self-diffusion and vacancy clustering has been explored by molecular dynamics [62] and kinetic Monte-Carlo simulations [67]. The vacancy is known to be an acceptor with an ionization level at about Ev + 0.2 eV [42, 52], but the stable charge states are not yet established. The migration barriers have also been measured [68, 52], but often it is difficult to assign them to a charge state. At higher temperatures, quenching experiments suggest that the formation energy of the uncharged vacancy should be 0.37 eV higher than that of the negatively charged vacancy, whereas that of the double negatively charged vacancy should be 0.13 eV lower [69]. LDA cluster calculations account very well for the properties of germanium vacancies, reproducing closely the measured electrical levels and migration energies[70, 63]. The

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16

A. Carvalho, J. Coutinho and R. Jones

relative success of this model is justified by the possibility of charging the defect and for the absence of the spurious defect-defect interactions present in periodic systems.

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3.2.1.

Geometry and electronic structure

The removal of a Ge atom from the lattice produces four sp3 radicals located at the vertices of a perfect tetrahedron (Fig. 6). Each radical may form reconstructed bonds with its three neighbors, and within Td symmetry they hybridize as a1 and t2 states. The singlet is resonant within the valence band, whereas the triplet is located within the gap. Analogously to the Si vacancy[71], a doubly positive vacancy (V ++ ) has an empty t2 gap state, and is perfectly tetrahedral. When this state is partially occupied, electron-phonon coupling drives JahnTeller distortion of the structure, and multiple energy-degenerate structures are present. The occupancy of the single-electron states follows Hund’s rule. Jahn-Teller distortions were investigated for charge states between 2+ and 3−[63]. In the neutral charge state, the Td vacancy has a degenerate ground state with a double occupancy of the t2 state, and Jahn-Teller distortion leads to a structure with D2d symmetry, splitting the triplet into a fully occupied b2 state and a doublet higher in energy. The respective Jahn-Teller energy is 0.10 eV, lower than in Si [72]. There is a volume change of −29% relative to the unrelaxed vacancy. In the single negative charge state, the vacancy adopts a tetragonal symmetry (D2 [63] or C2h [70] ) and the volume is decreased 34% with respect to the ideal vacancy. The double negative vacancy also suffers a tetragonal distortion, to D2d symmetry. However, its geometry and electronic structure are different from those of V0 and V+ , as in V−2 the four t2 electrons are in a e4 b02 configuration(Fig. 6), and the volume is about 60% of that of the original vacancy. The vacancy was found to be an acceptor with levels E(−/0) = Ev + 0.20 eV and E(−2/−) = Ec − 0.55 ∼ Ev + 0.19 eV, using the marker method (with Aus as marker) [63]. The calculated levels are very close to the values measured by PAC spectroscopy (at Ev + 0.20 eV) and DLTS (Ev + 0.14 eV) at low temperature. A triple acceptor level was also calculated at about 0.2 eV from the conduction band edge, but this is unlikely to be meaningful given the underestimation of the electron self-interaction in the overcharged cluster. The calculated migration energies also agree well with those found in Ref. [64] using a cluster calculation (Table 3), but the energies found in the same study using the supercell are severely underestimated, because of problems arising from the bandgap underestimation [73]. Also, they are very close to the range of values suggested by the interpretation of low-temperature radiation experiments (Table 3). Density functional calculations including an on-site Coulomb interaction for the d orbitals of germanium (LDA+U) has also been applied to neutral and charged vacancy supercell models [76]. The calculated levels are close to those given above, determined using cluster models [63], but with a larger positive U (Table 9). This possibly results from the improved treatment of correlation effects and not directly from the change in bandgap (note that the same effect was not observed in the LDA calculation of Ref. [77], which had a bandgap of 0.4 eV resulting from other effects).

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Defects in Germanium: Theoretical Aspects

V ++ (T d) b

V − (D2)

V 0 (D2d) a

a

b

17

V = (D2d) a

b

b

[001]

c

c

[100] d

c

d

b2

b2 e

+a − b− c + d

t2

b1 +a + b− c − d

c

d

√ (+ a + b− c − d)/ √ 2 (+ a − b− c + d)/ 2

e

b3

b2

Figure 6. LCAO scheme of the structural distortions in a Ge vacancy for several charge states of interest. (top) Defect geometry; Unoccupied, highest occupied and lower (fully occupied) levels are represented in white, light gray and dark gray bonds, respectively. (bottom) schematic representation of the occupation and splitting of the triplet (t2 ) level. c (Reprinted with permission from Ref. [63]. Institute of Physics and IOP Publishing Limited 2005.)

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Table 3. Calculated and experimental migration energies of the vacancy in germanium (eV), compared with experimental values. Method Cluster LDA Ref. [64] V0 V− V−2

3.2.2.

0.7 0.5 0.3

&

Exp. [68, 74, 75] 0.52 0.42 0.1–0.2

Formation energies

An accurate determination of the vacancy formation energy is of high interest, for it determines its density and diffusivity at high temperatures, and is used to calculate the diffusivity of many impurities. Although theoretically the calculation of the absolute defect formation energy in semiconductors suffers from serious limitations associated with the evaluation of the exchange-correlation functional, in Ge good agreement has been achieved between calculated and experimental formation energies (Table 4). Even the simplest approximations yield reasonable formation energies provided that convergence with the supercell size is achieved.

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18

A. Carvalho, J. Coutinho and R. Jones Table 4. Calculated and experimental vacancy and self-interstitial formation energies. Ef (V0 )

Method LDA LDA LDA with PAW LDA+U with PAW Exp.

2.34 2.33 2.35

a)

b)

ag

Ref.

1.9 3.55

[77] [44] [65] [65, 26] [45]

3.17

c)

b

a

Ef (I0 )

b

a

bg eg

bu

au

c

c

ag

bg eu

au SR B

D 3d

W RB

WP

V

V

bu

V

V

SP

a

c

b

a

c

b

b

c

a

b

c

a

c

c

[001]

[1¯10]

b

a

[001]

[1¯10]

b

a

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Figure 7. Ordering of the one-electron energy levels of the divacancy for the strong and weak resonant bonding (SRB and WRB) and strong and weak pairing (SP and WP) C2h distortions. (a) single-electron level diagram, (b) Kohn-Sham orbitals for the ungerade split c 2005, component au and (b) bu states. (Reprinted with permission from Ref. [48]. American Institute of Physics.)

3.3.

The divacancy

In germanium, divancancies are unlikely to be formed by association of two diffusing monovacancies since, as discussed in the previous section, the vacancy is negatively charged over a broad range of Fermi energies. However, it is expected to be a dominant defect in Ge samples exposed to alpha-particle irradiation [78, 79]. Theoretically, the divacancy (V2 ) is simply created by removing two adjacent Ge atoms. The resulting undistorted structure has D3d symmetry. The six dangling bonds hybridize in two levels under the valence band top with a1u and a1g symmetry and two doubledegenerated gap levels eu and eg . Each e level can accommodate up to four electrons and in result of the occupancy the degeneracy is lifted and the symmetry of the structure is lowered by the Jahn-Teller distortion. In silicon, the neutral divacancy is C2h [80]. There are two possible C2h configurations for the first shell of atoms around the divacancy: pairing (P) and resonant bonding (RB) [Fig. 7-a]. In silicon, stress-induced alignment studies determined that the C2h distortion occurs in a pairing sense [80]. Analogous to the case of the monovacancy, both the magnitudes and spatial extents of the Jahn-Teller relaxations were found to be smaller than in Si [70, 48]. The pairing distortions do not induce a crossing of the a levels as it happens in Si. This happens for all charge states, and the comparison suggests that in Ge both pairing and RB type Jahn-Teller

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Defects in Germanium: Theoretical Aspects

19

distortions are plausible candidates for the ground state structure, with the RB structures being slightly favorable. Similar calculations of Coutinho et al. using spin-polarized DFT-LDA found that this − result is strongly dependent on the lattice parameter used for both V+ 2 and V2 [48]. The theoretical lattice parameter was found to favor a weak pairing reconstruction, with the bu state being lower in energy than the au state, but if the experimental lattice parameter is used this ordering is inverted and a weak resonant bonding distortion is found favorable. On the other hand, the electric levels were shown to be fairly independent from the lattice parameter used [48]. Using the SbV pair as a marker, two acceptor levels and a donor level were found (Table 9). The calculated ionization levels are extraordinary close to the divacancy levels assigned by Bourgoin, Mooney and Poulin in the 1980’s[81], but at variance with the properties of a center assigned by later work by Fage-Pedersen et al. [82]. The latter, however, was recently suggested to be a di-interstitial and not a divacancy[79, 83]. Using cluster calculations, Janke et al. modeled the dissociation and migration of the divacancy [11]. The respective activation energy barriers are 1.5-1.7 eV (where the migration energy of the single vacancy is included) and 1.1 eV, corresponding approximately to a thermal stability of 400 K. However, the divacancy is likely to be annihilated at much lower temperatures (∼ 200 K) by mobile self-interstitials.

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3.4.

Further vacancy clustering

Small multi-vacancy clusters form at high temperatures during growth [62] or after annealing of germanium irradiated or implanted in very high doses [84]. Acceptor levels in the lower region of the bandgap have been related to multi-vacancy defects, but beyond di-vacancy no definite assignment has been achieved yet [85, 79]. Compact clusters with up to 14 vacancies (Vn ) were investigated by Janke et al. using first-principles models [49]. At low temperature, neutral vacancies, if existent, interact only up to fourth-nearest neighbor distance. Up to n = 14, the formation energy per vacancy is monotonic, decreasing with increasing n, and n=6, 10 and 14 are magic numbers, minimizing the number of dangling bonds per vacancy. For n stands for the two bonds formed with two O atoms and ●● is the electron lone pair) respectively, the 5.15 eV band being also correlated to two emission bands.

1.4.1. The Oxygen Mono Vacancy The 5.06 eV band was attributed to the NOMV in [49] basing on the observation that the exposition to an UV lamp induces the bleaching of an optical absorption component at 5.06 eV with a FWHM of 0.38 eV, without modifications in photoluminescence activity, and simultaneously, the generation of the E‘Ge defects ( Ge●, where ● stands for a an unpaired electron). The attribution is based on the idea that the NOMV is ionized by a single photon process to form an E‘Ge. It is important to remind that, as we will show in the following, a silica intrinsic defect is suggested to be responsible for an optical band at ~5.02 eV with a FWHM of ~0.36 eV [19]. In general it is worth to remark that the formation of the oxygen deficient Ge related defects has been studied in [50] using the density functional technique. The authors show that a NOMV requires a formation energy of ~ 3.3 eV, if formed near a Ge

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atom, whereas it requires additional 0.4 eV if formed near a Si atom. In addition, the mono vacancy and the Ge impurity tend approach each other to decrease the energy of the system, as confirmed also by other ab initio simulations [51]. Moreover, the authors of [52], using ab initio calculations, have estimated the formation energy of the twofold coordinated Si, Ge and Sn (>T●● where T=Si/Ge/Sn) finding that such an energy for defects on Ge atoms is 2.3 eV less than that required for the generation on Si atoms. These data evidence that the oxygen deficient status is favoured when Ge is present as doping element in SiO2.

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1.4.2. Germanium Lone Pair Center (GLPC) The first studies dedicated to the absorption and the emission activities in SiO2 were presented in the fifties [53-55] and three emission bands peaked at ~2.7, ~3.2 and ~4.3 eV were observed under ~5 eV excitation: these bands were named γ, β and α, respectively. In 1956, the previously observed optical absorption band at ~5 eV was named B2 band [56]. This optical activity was associated to oxygen deficient defects because it was observed in neutron irradiated samples [55]. In 1978, Skuja et al associated the 4.3 eV emission to a singlet-singlet transition [57], being its lifetime equal or lower than 10 ns. Successively, it was proposed a composite nature of the B2 [58] and the overlap of two components named B2α and B2β was suggested. The B2β band is peaked at ~5.15 eV with a full width at half maximum (FWHM) of 0.46 eV and two photoluminescence (PL) bands have been related to it [19,29,59]: one is peaked at ~ 4.3 eV (αE band) with a FWHM of 0.43 eV, the other is peaked at ~ 3.2 eV (β band) with a FWHM of 0.48 eV.

Figure 1.2. a) Electronic energy levels scheme for GLPC point defects. S0 is the singlet ground state, S1 is the first singlet excited state and T1 is the first triplet excited state. The radiative processes are indicated by the continuous arrows;

K RF

and

K RP

are the emission rates from the S1 and the T1 states; F

P

KISC is the rate of the intersystem crossing process while K NR and K NR are the rates of the no radiative channels, indicated by the broken arrows, from S1 and T1 to S0 [19,29], the thin lines represent vibrational levels of the various electronic states; b) structural model of the Germanium Lone Pair Centers.

The energy levels scheme proposed to explain this activity is reported in figure 1.2a; it consists of three energy states, the electronic ground singlet state indicated by S0, the first excited singlet electronic state named S1 and the first triplet excited state indicated by T1. According to this energy levels scheme, the B2β band is attributed to the transition S0→S1, whereas the two emission bands are attributed to the S1→S0 (αE band) and to the T1→S0 (β

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A. Alessi, S. Agnello and F. M. Gelardi

band) transitions, with the T1 state fed by an intersystem crossing process (ISC) due to the interaction of the luminescent defect with the surrounding glass network. This energy levels scheme and the commonly accepted microscopic structure (figure 1.2b) of these defects are the results of various investigations. In [60], basing on photoluminescence polarization studies, a C2ν symmetry and a consequent two fold coordinated model was proposed to explain an optical band peaked at 5.02 eV, with two associated luminescence bands peaked at 2.7 and 4.4 eV. This activity is associated to an intrinsic defect as confirmed by its presence in as manufactured and irradiated high purity silica samples [61-63]. This defect is the twofold coordinated Si, which is constituted by an electron lone pair localized on a Si atom bonded with two O ones. In [29], Skuja has reported an investigation regarding Ge doped, Sn doped and pure SiO2 samples. In all three types of samples, he observed the presence of an emission at ~4 eV and of an emission component at ~ 3 eV, with the peak positions depending on the sample. Through the measurements of the emission intensity decay of the low energy components, it was found that the lifetimes of these bands (~ 10 ms for pure SiO2 sample, ~ 113 μs for Ge doped samples, and ~ 10 μs for Sn doped samples) were related to the spin-orbit coupling energy (of the free Si, Ge and Sn atoms) and to the emission energy (experimentally observed) by a dependence compatible with that expected for triplet-singlet transitions of the >T●● structural model. To enforce the energy levels scheme of figure 1.2a and the attribution of the emission bands peaked at ~ 4 eV to a singlet-singlet transition of twofold coordinated defects, it is important to note that these bands have lifetimes of ~4ns (>Si●●), of ~7 ns (>Ge●●) and of ~10 ns (>Sn●●) [64-66]. In conclusion, the model of the twofold coordinated has been strongly supported by these investigations, and applies in particular to B2β and the related emissions. The GLPC has been frequently chosen to investigate the effects of the glass network on the optical features of the defect, in general, GLPC [52,67,68] and the isoelectronic sequence (Si, Ge, Sn) [19,29,60,69-71] have been widely investigated to this aim. For the data reported in the following of this chapter, it is important to remind the studies regarding the intersystem crossing process (ISC). It is known that the effects of no radiative channels, which connect F p and K NR in figure 1.2a), the excited states to the ground one (dashed arrows marked by K NR can be neglected for the GLPC [19,72] generated during the production of the materials and named native in the future. As a consequence, the ISC is the only process in competition with the emission from S1. According to this finding, the ratio between the integrated intensities of the two emission bands is equal to the ratio between the rate of the singlet-singlet transition F

and that of the ISC process, indicated as K R and as K ISC [19] (see figure 1.2a). Moreover, because of the absence of other deexcitation channels from the excited states, the lifetime of F

F

the 4.3 eV band is equal to ( K R + K ISC )-1 at room temperature and to ( K R )-1 at low temperature, being the ISC a phonon assisted process that is frozen at low temperature. The KISC dependence on temperature in the range 140-300 K can be described by an Arrhenius law [19]:

K ISC  A  e



U K BT

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(1.1)

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in which ΔU is the activation energy of the process, KB is the Boltzmann constant, and A is a pre-exponential factor determined by an entropic contribution [70,72], the spin-orbit coupling and structural features [70]. At variance, for temperatures lower than 140 K, KISC deviates from the Arrhenius law and tends to a constant value [19,72]. The presence of this plateau has been interpreted as the consequence of the inhomogeneity due to the fact that in an amorphous solid different defects experience different environments [19,65,70]. Similar behaviors are also observed for the >Si●● or the >Sn●● point defects [70] or if the surface defects are studied instead of the bulk ones [73]. In the following of this chapter, we will use another experimental datum, evidenced in previous investigation for GLPC, that is the correlation of the amplitude of the B2β with that of an absorption band peaked at ~ 3.7 eV. The ratio between the absorption coefficients at 5.15 and 3.7 eV is ~ 1032 [59], and this latter band has been attributed to the S0→T1 transition [29] of the GLPC. For completeness, we have to recall two studies that have proposed alternative structural models. In the first one [74], it was proposed that the B2β and the related photoluminescence bands are the result of the modification introduced by the presence of an impurity (not only the Ge atoms) near the two fold coordinated Si. The second model suggests that the above reported optical activity is related to a double monovacancy located on a Ge atom, which is bonded with two Si/Ge and with two O [75].

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1.5. Radiation Effects The exposure to beams of electrons, gamma photons, neutrons or other irradiation types, creates damage to the structure of the irradiated material. In particular, it can induce the generation of point defects that can modify the macroscopic properties of the material. The two mechanisms that dominate the point defect generation in solid materials are named knock-on and radiolysis processes. In the first, the impact between the bullet and an atom of the glass network supplies to this latter the necessary kinetic energy to move from the original position. In the case of silica, in order to create a defect through a knock-on it is necessary an energy of 10eV for an oxygen atom and 20eV for a silicon atom, being the Si-O bond energy about 5 eV. It is worth to remind that the energy of the Ge-O bond is lower (~ 3.6 eV [76]), so that the breaking of these bonds is more probable with respect to that of the Si-O one (this is true not only for the knock-on process) [77]. In the radiolysis process, the photons generate ionization and electronic excitations, which later may lead to the formation of point defects. Most of the electron-hole pairs generated by the radiolysis process gives rise to luminescence, through their recombination, the remaining, interacting with phonons, may cause the displacement of some atoms from their original position, or can break some bonds. Furthermore, some of the electrons or holes can be trapped in some impurities present in the material. From the experimental point of view, it is known that the interaction of the Ge doped SiO2 with ionizing radiation (UV, X , γ or β ray) could give rise to the generation of various optical absorption bands, and of different electron paramagnetic resonance (EPR) signals and to the decrease of the B2β [59,78,79]. So that in addition to the above reported investigation regarding the photosensitivity and the SHG, the studies devoted to the irradiation effects on the Ge doped SiO2 have been carried out to several topics: determine the structural models of

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the radiation induced Ge related point defects (Ge(1), Ge(2) and E‘Ge); obtain the relation between these point defects and the observed growth of the optical absorption coefficient in the spectral range from ~ 3 to 6 eV; investigate the processes that determine the generation of the defects.

1.6. Structural Models of the Paramagnetic Point Defects In the first proposed model, the irradiation induced Ge related defects have been named Ge(n) with n=0,1,2,3. The defects have been distinguished basing on their thermal stability and by the dose dependence of their generation efficiency. Table 1.1. gi values of the Ge(n) paramagnetic point defects in Ge doped SiO2 [82]

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Paramagnetic defects Ge(0) Ge(1) Ge(2) Ge(3)(E'Ge)

g1 2.0009±0.0002 2.0007±0.0001 2.0010±0.0001 2.0011±0.0001

g2 1.9943 1.9994 1.9978 1.9945

g3 1.9943 1.9930 1.9868 1.9945

To all these defects an E‘γ-like structure was associated ( Si● an electron localized on a Si atom bonded with three oxygen ones [80,81]) and the differences were attributed to the number n, of Ge atoms present in the first neighbors tetrahedrons [82]. Using the different thermal stability and EPR line shapes simulations, the authors of ref [82] determined the g values of each defect from the EPR spectra, recorded on irradiated Ge doped SiO2 fiber. These values are reported in table 1.1. After this study, the hyperfine structure generated by the presence of 73Ge (natural abundance 7.76% and nuclear spin IN=9/2 ) atoms has been investigated [83,84]. These studies have shown that the structure of the Ge(1) point defect is that of an electron trapped by a tetra-coordinated Ge atom (see figure 1.3a), as confirmed also by the experiments performed on Ce doped samples [85]. In these experiments, the different photo-ionization energies of the GLPC and of the Ce were used. In fact, an optical absorption band at 3.9 eV is associated to the Ce3+, and the authors irradiated the samples with light inside this band causing the consequent conversion Ce3+→ Ce4+ and the trapping of an electron on a tetracoordinated Ge atom. It is important to remark that for low exposures the authors observed the presence of the Ge(1), but they didn‘t observe signals associated to other Ge related defects. An important experimental data regarding the Ge(1) is that its EPR signal is not observed in pure GeO2 [80], in agreement with the fact that the electron should localize on a Ge atom and that this condition occurs when a Ge atom is surrounded by Si and O atoms. Some quanto-mechanic computations have shown that the tetra-coordinated Ge atoms are electron traps and that the trapping of an electron is followed by a structural relaxation [86]. This distortion makes the structure stable and is the reason of the orthorhombic features of the EPR signal [50,87]. In another calculation, it was proposed that the Ge(1) is constituted by a tetra-coordinated Ge atom and by an alkaline one ([GeO4-/Na+]0, [GeO4-/Li+]0 ) or by [GeO4/STH]0 (STH standing for self trapped hole) [88]. To conclude this part devoted to the Ge(1)

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structural model, we remind that Chiodini et al [89], studying the spectral features of the EPR signal, the generation and thermal properties, have suggested that the Ge(1) has the same structure of an intrinsic point defect on Si. The name of this latter defect is E‘α that, as confirmed by recent experimental studies, is related to a hole trapped in an oxygen vacancy of Si, its structure being that of back-projected E‘γ [90].

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Figure 1.3. structural model of the Ge(1) (panel a) and of E‘Ge (panel b).

The Ge(0) and Ge(3) defects have been considered as two variants of the same center, since the similarity of the g values and the difference in thermal stability of the two defects. This point defect was called E'Ge because of the similarity of its EPR resonance line with that of E'Si and the presence of a similar resonance in pure GeO2 [91]. Differing from the Ge(1) and the Ge(2) point defects, the E‘Ge can be observed in EPR spectra before irradiation [82,92]. Figure 1.3b shows the structural model of the E‘Ge defects. In this model, the Ge atom is three-coordinated, forming three covalent bonds with three different O atoms, and it has an unpaired electron in a sp3 orbital [84,87]. This structural model has been supported by the EPR investigation on the hyperfine structures recorded on samples containing 73Ge [83]. In ref [91] it has been shown that g 3 ( E ' Ge)   (Ge) (Δg3=ge-g3, ge=2.0023 free-electron g  ( Si) g 3 ( E ' Si) value, λ(Ge) and λ(Si) are the spin-orbit coupling constants of the Ge and Si atom, respectively); this finding agrees with the similarity between the E‘Ge and E‘Si structure. As above mentioned, in the first model the Ge(2) was considered as an E‘γ-like defect having two Ge atoms as second neighbors. Successively, the same authors, basing on the studies of the hyperfine EPR signal due to the 73Ge, in analogy to the Ge(1) defect, proposed the model of an electron trapped on a Ge atom placed at the center of a tetrahedron with a second Ge atom in the adjacent tetrahedron [59,84] (see figure 1.4). This model is not in agreement with the experimental observation of a Ge(2)-like signal in irradiated pure GeO2 [93], suggesting that the EPR signal does not depend on the number of the next neighbor Ge atoms. The supposed electron trapping process that should generate the Ge(2) is not confirmed by the experimental data obtained using Ge-Ce co-doped silica samples [85], and the author of [85] suggests that the Ge(2) is an hole center.

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Figure 1.4. a) structure of Ge(2) defects considered as an electron trap center [84]; b) structure of Ge(2) considered as the results of the GLPC ionization [78].

In 1998, Fujimaki et al [78], using three different sources to irradiate Ge doped SiO2 samples with different doping levels, proposed that the Ge(2) is a positively ionized GLPC: GLPC+. This conclusion was based on the following considerations: 1) the authors observed a proportionality between the Ge(1) and Ge(2) generation and the decrease of the intensity of the B2β optical absorption band, suggesting that by laser irradiation the electrons are released from the GLPC and electron trapped centers are generated; 2) the EPR spectra, in addition to the two signals of the Ge(1) and Ge(2), didn‘t show a third signal attributable to the GLPC+; 3) the number of induced Ge(1) was similar to that of the Ge(2); 4) this latter signal was not detected in H2 loaded samples, (the high hydrogen content promotes the generation of another defect related to the GLPC, this type of defect is called H(II) and is described in the following). Finally, Fujimaki et al., performing thermally stimulated luminescence measurements, observed a band peaked at ~ 3.1 eV, the recovery of the B2β band and the decreasing of other two absorption bands at 4.5 and 5.8 eV that, according to some models, can be attributed to Ge(1). They suggested that a reverse reaction acts, in which the electrons are detrapped from Ge(1) and are captured by the GLPC+ (Ge(2)). In this process, the recovered GLPC moves back to its ground state via the triplet-singlet transition causing the observed thermally stimulated luminescence.

1.7. H(II) Paramagnetic Point Defects Another defect generated by the radiation in the Ge doped SiO2 samples is the H(II) paramagnetic point defect. Its signal consists of two components, separated by ~119 Gauss, generated by the hyperfine interaction of the electron spin with the nuclear spin of the H atom [94]. The H(II) point defect consists of an unpaired electron located on a Ge atom bonded with two oxygen atoms and with an H atom (>Ge●-H) and it can be considered a GLPC bonded with an H atom [29,52]. In fact as regards the H(II) generation, it was proposed that this type of defect is generated by the reaction of the GLPC with diffusing H atoms, which are released by photoinduced reactions [95,96].

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1.8. Radiation Induced Absorption Bands As above remembered, one of the basic topics regarding the radiation effects on Ge doped SiO2 is to understand the relation between the induced paramagnetic point defects and the induced optical activity. In the model that considered the Ge(1) and Ge(2) as electron trapping centers, the induced optical band peaked at ~ 4.5 eV was attributed to the Ge(1), that one peaked at ~ 5.8 eV was attributed to the Ge(2), whereas that one peaked at ~ 6.2 eV was related to the E‘Ge defects [59,84]. The most discussed attribution is that of 5.8 eV optical band. In fact we note that this band is observed in samples in which the Ge(2) EPR signal is absent, so it was related to the Ge(1) [79, 89], also because a linear relation between the 5.8 eV band and the 4.5 eV band was observed [78]. In another investigation [97] using optically detected magnetic resonance, it was shown the relation of an optical absorption band at 4.4 eV with the Ge(1), whereas only a weak evidence of a paramagnetic nature of 5.7 eV band was found. The existence of a diamagnetic defect responsible for the 5.8 eV band has been proposed in [98]. This defect was considered as the result of a compression or of a photoinization followed by a recombination of a GLPC and the existence of this defect was used to justify the data reported in [32,92]. Table 1.2. Principal attributions of the optical absorption bands Peak position 6.3 eV 5.8 eV

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4.5 eV

Associated defect E‘Ge [59,84] Ge(2) [59,84] Ge(1) [79,89] Diamagnetic defects [98] Ge(1) [59,79,84]

In addition to these problems regarding the assignment of the 5.8 eV band, we have to remember that Poumellec et al. have questioned the nature of the 4.5 eV band [99]. In these studies, the authors have proposed that the 4.5 and the 5.8 eV bands are generated by Ge related defects different from both the Ge(1) and the Ge(2). To conclude this section, it is important to remember that no luminescence have been associated to the bands attributed to the Ge paramagnetic defects. Table 1.2 summarizes the main attributions of the induced optical absorption bands with the different point defects.

1.9. Generation Mechanisms The debates regarding the structures of the different types of Ge related defects have been accompanied by that concerning the mechanisms of their generation. As regards the generation of the E‘Ge defect, it was proposed that it can be the result of the ionization of a neutral oxygen mono vacancy [49, 100,101]. We note that the released electron could be trapped on a substitutional Ge atom forming a Ge(1). Another process proposed to explain the E‘Ge generation is reported in figure 1.5 GEC stands for germanium

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electron center and it can be the Ge(1), or the Ge(2) if this latter is considered a variant of the Ge(1), whereas NBO indicates non bridging oxygen, which is a negative charged and diamagnetic defect. GEC → E‘Ge + NBO Figure 1.5. Conversion of a GEC point defect into a E‘Ge defect [101].

GeO4  GLPC  GEC  GLPC Ge (1)



Ge ( 2 )

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Figure 1.6. Formation of Ge(1) and Ge(2) defects starting from tetracoordinated Ge atom and GLPC.

Figure 1.7. Photo-induced defect generation mechanisms of the Ge doped SiO2 [103].

In figure 1.6, it is reported a generation mechanism that consists in the ionization of a GLPC (considered to be the precursor of the Ge(2)) and the trapping of the released electron on a tetra-coordinated Ge atom to form a Ge(1) [78,102]. We note that, if this is the only involved mechanism, the two types of defects should be generated in equal concentration. The above reported photo-processes have been inserted in a more general scheme (see figure 1.7) [103], in which the back conversion mechanisms are considered too. From this point of view, it is important to note that the trapping of an electron, released during the E‘Ge generation, by the GLPC+ (Ge(2)) is proposed; so, the consequence of the irradiation can be the production of all three kinds of defects, but also the induction of only E‘Ge and Ge(1). The trapping of an electron by the GLPC+ (Ge(2)) introduces a destruction process of this latter type of defects, which could be the cause of the growth of the E‘Ge observed for high dose simultaneously to a decreasing of the Ge(2) concentration. Moreover, the electron released by the NOMV or by the GLPC ionization could be trapped in other structures, different from the tetracoordinated Ge. For example, the electron could be trapped in structures not paramagnetic, or the two electrons could be involved in the generation of two Ge(1) defects.

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A more complex process that relates the GLPC, the Ge(1) and the E‘Ge defects was proposed in [27] in this investigation, the authors show a correlation between the 5.15 eV optical absorption band decrease and the growth of the 4.5 and of the 5.8 eV, considering the 5.15 eV component related to the Ge(2) precursor and the other two bands related to the Ge(1) and to the Ge(2), respectively. They suggest that a GLPC can be converted into a NOMV by a two photon process and that this defect is then converted into an E‘Ge, with the released electron trapped by a substitutional Ge atom to form a Ge(1) point defect. It is important to note that the model was proposed using absorption results and that it is based on a specific attribution of the optical bands, which is a discussed argument. The connection between the GLPC and the E‘Ge defects was proposed also in [104] and in [105]. In this latter case, it was proposed that two E‘Ge defects are generated from the GLPC. An interesting generation mechanism of the Ge(1) has been proposed in [106]. In this case, the experiment has been performed at low temperature, 77 K, using a pulsed KrF laser. Basing on the data, the authors proposed that a Ge(1) and a self trapped hole (STH) are generated simultaneously, this latter kind of center having as precursor a normal site of the matrix and not an oxygen vacancy. In the same experiment, the authors observed that at room temperature the STH disappears. The destruction of the STH requires the presence of a hole trapping structure that is supposed to be a GLPC. This latter point of the process was confirmed in [102] where, to explain the experimental data, the interaction of a STH with a GLPC and the consequent generation of a Ge(2) simultaneously with that of an bridging oxygen have been proposed. We note that this scheme is compatible with that of figure 1.7, and that the STH appears as an intermediate step. Concerning the discussion on the generation mechanisms of the Ge related defects, it is important to recall that using Transmission Electron Microscopy (TEM) the presence of nanoclusters of GeO2 (size ~ 6-10 nm) has been proposed in a VAD (Vapor Axial Deposition) produced fiber preform [107] and that Tamura el al. estimated, through quantomechanic calculations, that the interface region of nanocluster can constitute electron trapping structures [108]. Finally, it is important to remark that in [109] using first principle calculations, it was shown that if an E‘Si is generated close to a Ge atom a migration can take place, with the consequent formation of an E‘Ge defect. This fact can be considered in agreement to the high generation efficiency of the E‘Ge defects often observed [59].

2. MATERIALS 2.1. Sol-Gel Preparation Technique The sol-gel technique is a preparation procedure used to obtain silica samples. It is considered a low temperature preparation method, because during the synthesis phase the employed temperatures are about 1000 °C instead of about 2000 °C as in other techniques.

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The sol-gel synthesis is constituted by several steps that are described in the following [110], and it is particularly useful for the preparation of the doped glasses due to the advantage of the use of solutions. A) The starting step is the preparation of an aqueous solution named sol that is a suspension of colloidal particles. As regards the materials used for the experiments reported in the following, the starting sol was constituted by a mixture of tetra-etilorthosilicate (TEOS) and tetra-etil-orthogermanate (TEOG). B) The second step is the gelation. In this phase the sol condenses in the gel, and a unique network occupying the entire volume of the container is created. At this stage the substance contains a great number of pores with solvent, sol and chemical reaction products inside. C) In the following step the gel is consolidated by chemical reaction inside the pores. D) Gel drying phase: the drying part of the sol-gel method is a critical stage in which the solvent is extracted by the pores. There are two procedures to remove the solvent and they are named evaporation and supercritical evaporation extraction. Using the former the samples are dried slowly maintaining them at room temperature for some weeks. The resulting material is called xerogel, it has significantly smaller dimensions with respect to the initial material, and it is characterized by a density similar to that of the silica glass. The supercritical evaporation extraction consists in the heating of the gel in conditions that permit to extract the solvent without boiling. The specimens so treated are called aerogels, they are low density and high porosity systems with dimensions similar to the starting gel. It is important to remind that in this case the pores contain air instead of the solvent and chemical products. E) Finally the obtained material is densificated (densification or sintering process) using thermal treatments and controlled atmosphere to eliminate the residual porosity. Using these treatments the specimens reach the same density (2.2 103 Kg/m3) of silica samples obtained by traditional and quenching processes [111].

2.2. Plasma-Activated Chemical Vapour Deposition Plasma-activated Chemical Vapour Deposition (PCVD) is an inside-tube Chemical Vapour Deposition process, in which glass layers are deposited on the inside wall of a cleaned silica tube, used as substrate. A resonator, enclosing a segment of the tube, couples several kilowatts of microwave energy, which arrive from a waveguide, into the gas mixture contained inside the silica tube. The microwave energy generates a plasma and the gases react each other, while the electrons move at a speed equivalent to a temperature much higher than that maintained by the furnace. In the specific case of the Ge doped silica (core of the fiber), mixtures of SiCl4, GeCl4, O2 are injected inside the tube to let them react; reaction between SiCl4 and O2 creates SiO2, whereas reaction between GeCl4 and O2 creates GeO2. Freon gas (C2F6) can be inserted too, to obtain F doped layers with a lower refractive index (cladding of the fiber) [112]. The possibility to control the type and the quantity of the gases introduced inside the silica tube allows to deposit many thousands of micron-thin glass layers with specific proprieties, as the dopant element and quantity, which influence the refractive index of the layers. In a second step of the PCVD procedure, the tube is consolidated. In particular,

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the tube is rotated and heated to about 2200°C using a transverse oxygen hydrogen burner. During this phase, the fluid tube consolidates into a solid rod. In the specific case of the Ge doped silica sample, the collapsing process generates the sublimation of GeO2 in the inner layers. As regards this negative aspect, to produce the employed samples a patented process is usually applied, this minimizes the axial difference in the Ge doping level.

2.3. Samples In this paragraph we will briefly summarize the proprieties of the employed samples, specifying their doping and the principal distinguishable features. Apart from the sample named HD, which has been produced by the Prof. M. Suszynska (Institute of low temperature and structure research Polish Academy of Sciences Wroclow, Poland), the sol-gel samples used for this chapter are aerogel samples and have been produced at the Department of Physical Chemistry of the University of Pavia.

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Table 2.1. Name of the investigated samples; for sol-gel produced materials the letters indicate the Ge atoms content, from A to E the Ge content decreases, whereas the numbers indicate the type of thermal treatment used to obtain the sample Sample

Ge content (Atoms/cm3)

GLPC (Defects/cm3)

A1 B0 B1 B2 B3 B4 B5/A B5/B C1 C3 C4 C5 D1 D3 D4 D5 E1 E5 PCVD20/A PCVD20/B PCVD4 HD

2.2 x 1021 2.2 x 1020 2.2 x 1020 2.2 x 1020 1.4 x 1020* 1.4 x 1020* 1.3 x 1020** 2.2 x 1020 2.2 x 1019 2.7 x 1019* 2.7 x 1019* 1.8 x 1019** 2.2 x 1018 5.5 x 1018* 5.5 x 1018* 1.7 x 1018** 2.2 x 1017 2.6 x 1017** 3.7 x 1021*** 3.7 x 1021*** 8.3 x 1020*** 2.2 x 1019

(1.7 ± 0.5) x 1017 Not detected (2.2 ± 0.8) x 1016 (1.5 ± 0.5) x 1017 (4.9 ± 1.2 ) x 1017 (2.5 ± 0.5) x 1018 (6.0 ± 1.5) x 1018 (5.0 ± 1.5) x 1018 (1.0 ± 0.5 ) x 1015 (1.2 ± 0.6) x 1016 (5.6 ± 1.2) x 1017 (4.5 ± 1.2) x 1017 Not detected Not detected (3.0 ± 1.5) x 1015 (7 ± 2) x 1016 Not detected Not detected Not detected (7 ± 2) x 1018 (3 ± 1) x 1018 Not detected

* Determined by Inductively Coupled Plasma Mass spectrometry, error ~10%. ** Determined by Instrumental Neutron Activation Analysis [113], the error is ±2% for all the samples, apart from the sample E5 for which it is ±8.5 %. *** Determined by the producer. In all the other cases the content is the nominal one.

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Their Ge content changes from ~2.2 x 1017 to ~2.2 x 1021 atoms/cm3, which are equivalent to 10 and to 105 part per million molar (0.0012 and 12 weight % or 0.001 and 10 mol %). The PCVD samples are doped with ~20 and ~4.5 weight % and are of industrial origin. In table 2.1, the Ge content and the GLPC concentrations of the samples are reported. These latter are usually estimated by the Smakula equation, and from the B2β band amplitude at ~ 5.13 eV assuming an oscillator strength of ~0.l that is the average of the values reported in literature [1,49,59,63,79]. For the samples B5 and PCVD20/B, the GLPC contents have been estimated by the absorption coefficient at ~3.8 eV, since the B2β amplitude was higher than the detection limit value of the used instrument (~ 4 optical density). This absorption component, attributed to the ground singlet state-first excited triplet state transition, is ~ 1032 less intense than the B2β band [59], and, as consequence, it never saturates. For the samples C1, C3 and D4, the GLPC content has been determined by the comparison of their PL activity with that of samples with a measurable B2β band, because in these cases the optical absorption band was not detectable due to the low concentration and to the low sample thickness.

A

in 0.6

600 500

0.2

in

1300 1200 1100

C/ m

~10 atm (~10-7atm) -5

O2

24h

D

900

He 1/2 h

800 700 600 500 400 300 200

mi n

Vacuum

in

500

Type 4

C/

600

1000

Temperature (˚C)

C

700

0.3

Temperature (˚C)

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Time (h)

800

200

O2 + N2 (O2 + N2) 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90

1100

Type 5 (Type 3)

N2 (amb)

0

24h

1200

300

400

Time (h)

1300

400

500

100

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90

900

600

200

O2 + N2

0

1000

He (amb)

700

300

m

C/

900 800

0.3

100

N2

4h

400 300 200

He

C/m

700

1000

in

900 800

B

Type 2 (Type 0)

1100

m

1000

0.75h

1200

C/

1.2 C/m

in

1100

Temperature (˚C)

1300

0.5h

0.3

Type 1

1200

Temperature (˚C)

1300

Vacuum ~5x10-8atm

O2

100

100

0

0 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90

Time (h)

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90

Time (h)

Figure 2.1. a) Thermal treatment used for the densification of type 1 samples; b) thermal treatment used for the densification type 2 and type 0 samples; c) thermal treatment used for the densification of type 5 and type 3 samples; d) thermal treatment used for the densification of type 4 samples.

In table 2.1, the name of each sol-gel sample, except the sample HD, is assigned by a letter and by a number; the first is chosen according to the Ge doping level; in particular, the letter A is used for the sample with ~2.2 x 1021 (highest content among the sol-gel samples) Germanium: Properties, Production and Applications : Properties, Production and Applications, Nova Science Publishers, Incorporated, 2011.

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and the letter E is used for the samples with ~2.2 x 1017 Ge atoms/cm3, all the other letters indicate intermediate doping level. The numbers are used to identify the thermal treatment used in the densification phase. As reported in figure 2.1b, the sample B0 was heated up to 1200 °C with a rate of 0.3 °C/min, then it was kept at this temperature for ~ 45 min before to be cooled down to room temperature. Up to 800 °C, the sample was under a constant flux of O2 and N2, while during the other parts of the treatment it was in ambient atmosphere. The sample B2 was obtained using a procedure similar as for the B0 sample, with the only difference that, starting from 800 °C, it was kept in He atmosphere, and then it was cooled in N2 atmosphere (see figure 2.1b). As shown in figure 2.1a, the samples B1, C1 and D1 were heated with a rate of 0.2 °C/min from room temperature up to 400 °C, and they were kept at this temperature for 4 hours before to reach 800 °C with a rate of 0.6 °C/min. During this treatment, the samples were kept in a O2 and N2 atmosphere. After these routes, they were heated up to 1200 °C in a He atmosphere with a rate of 1.2 °C/min, and maintained for half an hour in these conditions before to return to room temperature in N2 atmosphere. The samples named B3, C3, D3 and that named B4, C4 and D4 have been obtained by the same gel. They were heated with a rate of 0.3 °C/min from 25 °C to 1150 °C, then they were kept at this temperature for 24 hours before returning to room temperature. Until 700 °C, the samples were under a O2 flux, while during the other part of the process a low pressure atmosphere was used. The difference in the preparation of the two sample sets is the fact that the B4, C4 and D4 materials were kept under a He flux for 30 minutes at 700°C, before to go to the low pressure (see figure 2.1c and 2.1d). The value of this latter, ~5x10 -8 atm, is one order of magnitude lower than that used for the B3, C3 and D3 samples. Finally, the samples B5, C5, D5 were obtained using the same route of samples A3, B3 and C3 but with different vacuum value (see figure 2.1c). As regards the PCVD samples, they are obtained cutting the industrial preforms to take only the Ge doped region.

3. GENERATION OF GE PARAMAGNETIC POINT DEFECTS 3.1. Induced EPR Activity: General Features In figure 3.1, the spectra acquired at the dose of ~ 3kGy for the samples PCVD4 and PCVD20/B are shown together with the EPR spectrum (range 3450-3500 Gauss) of the sample B4. All the spectra are normalized to the EPR amplitude of the negative peak at ~3485 Gauss. In this way it is possible to evidence not only the main spectral features ascribable to the different paramagnetic point defects, but also that in the sample B4 the EPR spectrum goes from ~3456 to ~3492 Gauss, whereas in the sample PCVD20/B the EPR spectrum goes from ~3457 to ~3492 Gauss. In details, we note that the positive peak in sample B4 is measured at a lower magnetic field value than in sample PCVD20/B. It is worth to note that these types of differences are not observed for all the samples having doping level lower than 1 % by weight. The reported spectra are constituted by more than one signal. In fact, in the spectra it is possible to observe a number of negative peaks that is inconsistent with that of a single EPR resonance. In particular, these spectra are constituted by the overlap

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of three signals that can be recognized by some spectral features. The presence of Ge(1) defects can be suggested by a sharp positive peak at 3460 Gauss, whereas that of the Ge(2) is testified by the presence of a negative peak at 3485 Gauss. As regards the E‘Ge defects, their contribution is evidenced in sample B4 by the signal at 3472 Gauss, whereas a more quantitative analysis is required to determine their presence and contribution in samples PCVD4 and PCVD20/B.

Ge(1)

EPR signal (arb.units)

EPR Signal (arb.units)

0.0 -0.2 -0.4 -0.6 -0.8 -1.0 -1.2 3480

3485

3490

3495

Magnetic Field (Gauss)

Ge(2) PCVD20/B PCVD4 B4

E'Ge

3460 3480 3500 Magnetic Field (Gauss) Figure 3.1. EPR spectra recorded at the dose of ~ 3kGy for samples PCVD20/A (▬), PCVD4 (▬) and B4 (▬).

a

C4 20Gy 800Gy 8 kGy 102kGy

6

3

0

-3 3450

3460 3470 3480 3490 Magnetic Field (Gauss)

(A)

Normalized EPR Signal (a.u.)

Normalized EPR Signal (a.u.)

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9

9

b 6

PCVD20/B 200Gy 1kGy 100kGy 1MGy

3

0

-3 3450

3460 3470 3480 3490 Magnetic Field (Gauss)

(B)

Figure 3.2. a) EPR spectra recorded in the sample C4 at the doses of 20Gy (▬), 800 Gy (▬), 8 kGy (▬) and 102 kGy (▬); b) EPR spectra recorded in the sample PCVD20/B at the doses of 200 Gy (▬), 1 kGy (▬), 100 kGy (▬) and 1MGy (▬).

In figure 3.2, we report the EPR spectra (normalized to their double integral) recorded in samples C4 and PCVD20/B for different irradiation doses. The spectra show the variations induced by the increase of dose. From a general point of view, in sol-gel samples the line Germanium: Properties, Production and Applications : Properties, Production and Applications, Nova Science Publishers, Incorporated, 2011.

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shape of the EPR signal up to 200 Gy does not show significant variations. As regards the PCVD samples, the lowest investigated dose is ~200 Gy so we cannot know the line shape behavior for lower doses. However, we observe that the EPR spectra recorded at 200 Gy and 1 kGy are equal; moreover they slightly differ from that recorded at 100 kGy. In general, by increasing the dose, we observe a systematic modification of the EPR spectrum. The modifications consist in: the increase of the relative amplitude of the negative peak at ~3472 Gauss (due to the E‘Ge defect), the decrease of the relative amplitude of the positive peak located at ~ 3460 Gauss, and, in many cases, the decrease of the relative amplitude of the negative peak at 3485 Gauss (if present). These modifications go on with the increase of the irradiation; so, more the dose is high more the EPR spectrum is similar to that of the E‘Ge defects. Using the above reported spectral modifications, we can qualitatively suggest that, typically, the E‘Ge defects are generated with lower efficiency with respect to other Ge related paramagnetic defects at low doses; on the contrary, at high doses they continue to be induced when the other defects are generated with slower rate or have reached a maximum concentration value. At high doses, it is possible also to observe the presence of the E‘Si EPR signal. The dose at which it becomes evident depends on the sample and, for example, in sample E5, which has lowest concentration of Ge related paramagnetic point defects, the E‘Si signal is clearly evidenced starting from the dose of ~100 kGy.

EPR Signal (arb.units)

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3.2. EPR Line Shape of the Ge Related Defects

E'Ge

3450

3460

3470

3480

3490

Magnetic Field (Gauss)

Figure 3.3. EPR line shape of the signal of the E‘Ge defect, as recorded in a 2% Ge doped silica sol-gel sample UV irradiated.

The overlapping of the signals of different Ge related paramagnetic point defects requires to know the line shape of the different components to decompose the overall EPR spectra and to obtain the concentration of the induced defects. The EPR line shape associated to the E‘Ge has been obtained performing measurements on a sample2 in which only its signal was detected. This signal is shown in figure 3.3; we observe that the EPR line shape of this paramagnetic point defect is independent from the Ge content of the investigated samples. In addition, it is important to note that the gi (g1=2.0012 g2=1.9951 g3=1.9941) and Δgij values (Δg12=0.0061, Δg13=0.0071) reported in Table 3.1 are in sufficiently good agreement with those reported in [114], which have been obtained in a not irradiated sample containing ~ 10 2

The sample was a 2% Ge doped silica sol-gel sample UV irradiated.

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mol % of GeO2. For these reasons, we will use the EPR line shape derived from the spectrum of figure 3.3 to evaluate the concentrations of E‘Ge induced in all the investigated samples at different doses. The EPR line shapes of the Ge(1) and the Ge(2) defects have been determined considering their different thermal stabilities that were already evidenced in [59,82]. In particular, it was observed that the Ge(1) is thermally less stable with respect to Ge(2) and E‘Ge, this latter being the more stable among the Ge related paramagnetic point defects. So, using isochronal thermal treatments it was possible to investigate the EPR signals associated to the Ge(1) and Ge(2) centers, in samples doped with different amounts of Ge. To obtain these EPR line shapes we have used four samples: a sample B0 (Ge content ~ 1% by weight) at the dose of 1 kGy, a PCVD4 (Ge content ~ 4.5 % by weight), an A1 (Ge content ~ 12 % by weight) and a PCVD20/A (Ge content ~ 20 % by weight) irradiated at the dose of 2 kGy. After the irradiation, we have isochronally thermally treated (15 minutes at each temperature) the samples in a temperature range from 60 °C to 140 °C (the temperature was increased by 20°C at each step). From the difference of the spectra after each step of the thermal treatment (in the range 25-140° C) of the sample B0, it was possible to isolate the Ge(1) signal reported in figure 3.4 (black curve). The reference line shape of the Ge(2) defect (black curve in figure 3.5) was determined then from the residuals of the decompositions of the spectra of a sample B5/B, using the Ge(1) and E‘Ge reference line shapes. It is important to remark that it was possible to decompose the EPR spectra of all samples with Ge content inferior to 1 % by weight using the reference signals of the Ge(1) and Ge(2) defects obtained in samples with ~ 1 % by weight of Ge (~ 2.2 1020 atoms/cm3). For the samples doped with ~ 20 % by weight of Ge, the procedure was the same as above reported; the Ge(1) signal was isolated by the variations of the EPR signals on the thermal treatment of the sample PCVD20/A (figure 3.4). The Ge(2) reference signal (figure 3.5) was obtained from the residual of the decomposition of the spectra of the sample PCVD20/B using the Ge(1) and E‘Ge reference signals.

EPR Signal (arb.units)

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96

Ge(1)

3450

3460

Ge content wt% ~ 1% ~ 4.5% ~ 12% ~ 20%

3470

3480

3490

Magnetic Field (Gauss) Figure 3.4. EPR signal associated to the Ge(1) defects in samples with different Ge content, (▬) Ge content ≤ 1 % wt, (▬) Ge content ~ 4.5 % wt, (▬) Ge content ~12 % wt, (▬) Ge content ~20 % wt.

For the doping levels of ~ 4.5 % and ~12 % by weight, the Ge(1) signals have been isolated not only by the variations of the EPR spectra but also using computer simulations of Germanium: Properties, Production and Applications : Properties, Production and Applications, Nova Science Publishers, Incorporated, 2011.

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EPR Signal (arb.units)

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the signal. The computer simulation was employed because for these doping levels we had only samples in which Ge(1) and Ge(2) are induced together and because the small difference in the thermal stability of the two type of defects makes difficult to pick out their signals. To determine the concentration of Ge(1) induced in samples PCVD4 (4.5 %) and A1 (12 %) a average line shape between the experimental and the simulated one was used (figure 3.4). As regards the Ge(2) reference signal (see figure 3.5) we have used that one obtained after the last temperature of the thermal treatment of the sample PCVD4 because it represents about the 60 % of the total signal. At variance, in the case of the sample A1 we have used a simulated signal (reported in figure 3.5) describing the residual of the higher investigated temperature, because the experimental curves were affected by a too low signal to noise ratio. As reported in figure 3.4, the most important variations of the Ge(1) signal as a function of the Ge content are the width of the positive peak and the position of the zero crossing corresponding to the g2 value of Table 3.1. We note that the g1 and g3 values are compatible with those reported in [82] and that the Δg13 values are sufficiently compatible too. At variance, the Δg13 determined for the sample with ~20 % wt of Ge is significantly lower. Larger differences are observed for the g2 and the Δg12 values. In figure 3.5 the Ge(2) signals determined in samples with different doping levels are reported. Also in this case, the signal is independent from Ge content when this is lower than ~1% by weight, whereas the signal changes by further increasing the Ge content. We note that by increasing the Ge content, the Δg13 decreases, essentially because g3 increases (see also Table 3.1), being the g1 almost independent from the doping level. Furthermore, the width of the negative peak at ~3485 Gauss increases with the increase of the doping level. It is important to remind that, in this spectral range the Ge(2) are the only defects that contribute to the EPR signal; so that, the use of a simulated curve for the sample doped with ~12 % wt does not affect the conclusion regarding the modification of the Ge(2) negative peak at ~3485 Gauss. Ge(2)

3450

Ge content wt% ~ 1% ~ 4.5% ~ 12% ~ 20%

3460 3470 3480 3490 Magnetic Field (Gauss)

Figure 3.5. EPR signal associated to the Ge(2) defects in samples with different Ge content, (▬) Ge content ≤ 1 % wt, (▬) Ge content ~ 4.5 % wt, (▬) Ge content ~12 % wt, (▬) Ge content ~20 % wt.

As regards g2 and Δg12, the decrease of the former and increase of the latter are evidenced by the data of the samples doped with ~1, 4.5 and 20%. The incoherence of the data regarding the sample~12% doped could be due to the fact that, in this case, the Ge(2) signal was obtained by a computer simulation because of a low signal to noise ratio. For this reason, the

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line shape can be used to determine the Ge(2) concentration, but it could fail in the determination of specific features of the real Ge(2) EPR signal. In fact, unlike for the g3, which is estimated in a magnetic field region where only the signal of Ge(2) is observed, the g2 is estimated by the EPR signal detected in the range of the zero crossing of the experimental EPR signals, where the signals of the different paramagnetic point defects overlap. The invariance of the E‘Ge signal in samples doped with different amounts of Ge seems less surprising if we consider that in pure GeO2 its g values (~ 2.0013, ~ 1.9953 and ~1.9937) [91] are close to those here reported. However, the comprehension of this invariance with respect to the variability observed for the Ge(1) and Ge(2) related EPR signals remains interesting. Although further studies are necessary to deeply understand the nature of the variations observed in the line shapes of the Ge(1) and of the Ge(2) EPR signals, these appear independent from the production procedure. We note also that previous studies regarding the Raman spectra of GeO2-SiO2 glasses have evidenced changes of the matrix network starting from ~ 1% Ge doping [16]. On the basis of these observations we can tentatively ascribe the modification in the EPR signals to the modification of the defects surrounding. From this point of view, the alteration of the Ge(1) signal detected in samples doped with ~ 20 % of Ge seems to be very interesting for future investigations, because for this doping level the probability to found a second Ge atom in the second coordination sphere is high enough.

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Table 3.1. gi and Δgij values of the Ge related paramagnetic point defects in samples with different Ge content; the error of the g value is ±0.0003, whereas the error of the Δgij is ±0.0001 1% E‘Ge Ge(1) Ge(2)

g1 2.0012 2.0006 2.0010

g2 1.9951 2.0000 1.9989

g3 1.9941 1.9930 1.9867

g1-g2 0.0061 0.0006 0.0021

g1-g3 0.0071 0.0076 0.0143

4.5% E‘Ge Ge(1) Ge(2)

g1 2.0012 2.0007 2.0011

g2 1.9951 2.0000 1.9984

g3 1.9941 1.9932 1.9868

g1-g2 0.0061 0.0007 0.0027

g1-g3 0.0071 0.0075 0.0143

12% E‘Ge Ge(1) Ge(2)

g1 2.0012 2.0005 2.0010

g2 1.9951 1.9997 1.9986

g3 1.9941 1.9931 1.9870

g1-g2 0.0061 0.0008 0.0024

g1-g3 0.0071 0.0074 0.0140

20% E‘Ge Ge(1) Ge(2)

g1 2.0012 2.0008 2.0010

g2 1.9951 1.9990 1.9980

g3 1.9941 1.9935 1.9873

g1-g2 0.0061 0.0018 0.0030

g1-g3 0.0071 0.0073 0.0137

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3.3. Decomposition of the Experimental EPR Spectra

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Using the above reported EPR line shapes associated to the different paramagnetic point defects and fixing their relative positions, it is possible to perform a decomposition of the experimental spectra to obtain the contribution of each defect and, as a consequence, its concentration. As examples of this procedure, in figure 3.6, we report the comparison between the EPR experimental spectra recorded in the sample C4 irradiated at the dose of 20Gy, in the sample PCVD20/B irradiated at the dose 100kGy and that obtained by the sum of the line shapes associated to the different defects. In details, the weight of each component in every spectrum has been determined minimizing the difference between the experimental spectrum and the spectrum obtained by the sum of the different signals above reported. In this way, for sample C4 at the dose 20Gy (figure 3.6a) the weight of Ge(1) is ~39%, that of Ge(2) is ~49% and that of E‘Ge is ~ 8%; for the sample PCVD20/B at the dose 100kGy (figure 3.6b) the weight of Ge(1) is 28% that of Ge(2) is ~ 60% and that of the E‘Ge is ~ 9%. In general, the differences between the experimental spectra and that obtained summing the different components are ≤10 %. Due to the procedures used to determine the reference line shapes and to the decomposition of the experimental EPR spectra, we estimate a maximum error in the concentrations of about 20%.

Figure 3.6. a) Experimental EPR spectrum (▬) recorded in sample C4 irradiated at the dose of 20Gy and line shape (▬) obtained summing the Ge(1), Ge(2) and E‘Ge signals; b) Experimental EPR spectrum (▬) recorded in sample PCVD20/B irradiated at the dose of 100kGy and line shape (▬) obtained summing the Ge(1), Ge(2) and E‘Ge signals.

3.4. Paramagnetic Point Defect Concentrations Induced by Irradiation In this section, we will present the dose dependence of the concentrations of Ge(1), Ge(2) and E‘Ge defects in the different samples. We will report the data dividing the samples according to their preparation procedure. In particular, we will start from type 1 sample (A1,

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B1, C1 and D1), whereas the data regarding the B0 sample will be present in the following together with the dose dependence of the induced GLPC. The interpretation of the data in terms of generation mechanisms is reported in the successive paragraphs 3.5 and 3.6. Apart from PCVD samples all the other samples were γ irradiated.

3.4.1. Type 1 Samples In figure 3.7a the Ge(1) concentrations induced in samples A1, B1, C1 and D1 are reported as a function of the dose. In all samples, the Ge(1) dependence on dose can be described by the law A( 1-e-B x ), where x is the dose, A represents the saturation value of the induced concentration and 1/B is a characteristic saturation dose. We note that even if the Ge content changes from ~2 1018 to ~2 1021 the maximum value of the induced Ge(1) concentration changes from ~0.5 to ~1.5 1017 defects/cm3 and that similar concentration of defects are induced in all the samples for low irradiation dose. In figure 3.7b, we report the induced concentrations of E‘Ge defects as a function of the dose. For this type of defects, a saturation of the induced concentration is not observed, but for the D1 sample, even if they show a sublinear dependence for doses higher than 104 Gy. Furthermore, no particular differences are observed at low doses changing the doping level of the sample. As regards the Ge(2), they are induced only in the sample A1, and their dependence on dose is reported in figure 3.7c. The concentrations of the induced Ge(1), Ge(2) and E‘Ge in this set of samples don‘t evidence specific correlations. In addition, we note that in samples B1, C1 and D1 the Ge(2) are not induced, suggesting the presence of another electron donor for the Ge(1).

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Table 3.2. Values of the A and B parameters obtained by the fitting of the Ge(1) and Ge(2) concentrations of the different samples with the law A( 1-e-B x ), where x is the dose Ge(1) Sample

A Defects/cm3

B A error Defects/cm3 Gy-1

B error Gy-1

A1

1.5 x1017

0.5 x 1017

0.00040

0.00020

B1

1.2 x10

17

0.00037

0.00015

C1

16

0.00070

0.00020

8 x 10

0.3 x10 2 x 10

16

17

16 16

D1

4.3 x 10

1.8 x 10

0.00080

0.00040

Sample

A Defects/cm3

Ge(2) A error Defects/cm3

B Gy-1

B error Gy-1

A1

2.0 x 1016

0.5 x 1016

0.00050

0.00020

B1

ND

ND

ND

ND

C1

ND

ND

ND

ND

D1

ND

ND

ND

ND

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Properties and Generation by Irradiation of Germanium Point Defects …

18

18

10

10

a

b

17

10

3

E'Ge Conc.(Defects/cm )

3

Ge(1) Conc.(Defects/cm )

101

16

10

15

10

A1 B1 C1 D1

14

10

13

17

10

16

10

15

10

A1 B1 C1 D1

14

10

13

10

0

1

2

3

4

5

6

7

10

8

0

1

2

3

4

5

6

7

8

10 10 10 10 10 10 10 10 10

10 10 10 10 10 10 10 10 10

Dose(Gray)

Dose (Gray) 18

c

3

Ge(2) Conc.(defects/cm )

10

17

10

16

10

15

10

14

10

A1 13

10

0

1

2

3

4

5

6

7

8

Copyright © 2011. Nova Science Publishers, Incorporated. All rights reserved.

10 10 10 10 10 10 10 10 10 Dose (Gray)

Figure 3.7. a) induced Ge(1) concentrations in samples A1 (○), B1 (■), C1 (●) and D1 (□), and their fits ), C1 (--) and D1(--); b) E‘Ge induced concentration in different samples A1 (○), B1 (■), law of the fits is A(1-e-B x ).

3.4.2. Type 3 Samples In figure 3.8a we report the concentrations of Ge(1) induced in the samples B3, C3 and D3 together with the curves obtained fitting the data with the law A (1-e-B x ). The A and B parameters obtained for the different samples are reported in Table 3.3. Also in this case, we note that the induced concentrations of Ge(1) are almost independent of the Ge content for low doses, whereas increasing the dose the induced amounts of defects in the three samples become more and more different. Moreover, for these samples we note a monotonic dependence of the B parameter on the Ge content, in particular it increases from 4 x 10 -4 Gy-1 to 17 x 10-4 Gy-1 with the decrease of the Ge doping level. The induced amounts of the E‘Ge defects, reported in figure 3.8b, don‘t show a clear saturation trend. Furthermore, the E‘Ge defects are induced in different amounts, and in particular, in sample B3 the radiation induces

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a larger quantity of these defects with respect to those observed in samples C3 and D3. It is important to note that the concentrations in samples C3 and D3 are similar to those induced in samples A1, B1, C1 and D1. As regards the Ge(2), they are induced in detectable amount only in the sample B3. Their dependence on dose is reported in figure 3.8c together with the fitting curve. In sample B3, due to the similarities in the growth kinetics, the Ge(1) and Ge(2) dose dependences could be interpreted as the result of the following photoreaction GLPC + Ge→ Ge(2) (GLPC+) + Ge(1). However, the absence of the Ge(2) in the samples C3 and D3 speaks for the lack of a direct relation between these two defects in this set of samples; the presence of different electron donors can be suggested to justify the Ge(1) generation in the samples C3 and B3. 18

10

18

10

b

17

10

3

E'Ge Conc.(defects/cm )

3

Ge(1) Conc.(Defects/cm )

a

16

10

15

10

B3 C3 D3

14

10

13

10

0

1

2

3

4

5

6

7

17

10

16

10

15

10

B3 C3 D3

14

10

13

10

8

10 10 10 10 10 10 10 10 10

0

1

2

3

4

5

6

7

8

10 10 10 10 10 10 10 10 10

Dose (Gray)

Dose (Gray)

18

c

3

Ge(2) Conc.(Defects/cm )

Copyright © 2011. Nova Science Publishers, Incorporated. All rights reserved.

10

17

10

16

10

15

10

14

10

B3 13

10

0

1

2

3

4

5

6

7

8

10 10 10 10 10 10 10 10 10 Dose (Gray)

Figure 3.8. a) Induced Ge(1) concentrations in samples B3 (■), C3 (●), D3 (□) and their fits B3 (- -), s B3 (■), C3 (●) and in D3 (□); c) C3 ( induced Ge(2) concentrations in sample B3 (■) and fit (- -). The fit law is A( 1-e-B x ).

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Table 3.3. Values of the A and B parameters obtained by the fitting of the Ge(1) and Ge(2) concentrations of the different samples with the law A( 1-e-B x ) where x is the dose Ge(1) Sample

A Defects/cm3

B A error Defects/cm3 Gy-1

B error Gy-1

B3

1.1 x 1017

0.3 x 1017

0.00040

0.00015

C3

16

16

0.00070

0.00030

16

4.3 x 10

16

1.5 x 10

D3

2.2 x 10

0.5 x 10

0.00170

0.00070

Sample

A Defects/cm3

Ge(2) A error Defects/cm3

B Gy-1

B error Gy-1

B3

1.0 x 1017

0.3 x 1017

0.00045

0.00015

C3

ND

ND

ND

ND

D3

ND

ND

ND

ND

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3.4.3. Type 4 Samples The Ge(1) concentrations induced in samples B4, C4 and D4 as a function of the dose are reported in figure 3.9a. In the same figure, we show the fitting curves obtained using the law A( 1-e-B x ). The A and B parameters so obtained for the different samples are reported in Table 3.4. For these samples, a larger variability of the maximum value of the induced concentrations is observed with respect to those of the other sets of samples. More variability is observed also for the concentrations induced at low doses. Table 3.4. Values of the A and B parameters obtained by the fitting of the Ge(1) and Ge(2) concentrations of the different samples with the law A( 1-e-B x ) where x is the dose Ge(1) Sample B4 C4 D4

A Defects/cm3 17

2.3 x 10

16

9.2 x 10

16

2.6 x 10

A error Defects/cm

B Gy-1

B error Gy-1

0.5 x1017

3

0.00040

0.00015

16

0.00085

0.00035

16

0.00200

0.00100

2.5 x 10 0.8 x 10

Ge(2) Sample

A Defects/cm3

B A error Defects/cm3 Gy-1

B error Gy-1

B4

4.3 x 1017

0.5 x 1017

0.00040

0.00010

0.00120

0.00030

ND

ND

C4

8.6 x10

D4

ND

16

1.5 x 10 ND

16

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Nevertheless, the Ge(1) concentrations differ of about a factor of 2 even if the Ge content changes within two orders of magnitude; so that, we can suggest that the Ge(1) concentration induced at low doses is weakly dependent on the Ge content for this set of samples. 18

10

18

10

b 3

E'Ge conc. (Defects/cm )

3

Ge(1) Conc.(Defects/cm )

a 17

10

16

10

15

10

B4 C4 D4

14

10

17

10

16

10

15

10

B4 C4 D4

14

10

13

10

13

10

0

0

1

2

3

4

5

6

7

10

8

10 10 10 10 10 10 10 10 10

1

2

10

10

3

10

4

10

5

10

6

10

Dose (Gray)

Dose(Gray)

18

c

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3

Ge(2) Conc. (Defects/cm )

10

17

10

16

10

15

10

14

10

B4 C4

13

10

0

1

2

3

4

5

6

7

8

10 10 10 10 10 10 10 10 10 Dose (Gray)

Figure 3.9: a) induced Ge(1) concentrations in samples B4 (■), C4 (●) and D4 (□), and their fits B4 ) and D4 (--); b) E‘Ge induced concentration in different samples B4 (■), C4 (●) and in D4 C4 ( ). The fit law is A( 1-e-B x ).

The data on the induced amount of E‘Ge defects are reported in figure 3.9b. These data show that in the samples B4 and C4 the E‘Ge concentrations have a different dependence on dose with respect to that observed in the most part of the previous samples, showing a tendency to levelling. At variance, in sample D4 the E‘Ge features a behaviour compatible with those of the previous samples. We remind that in samples B4 and C4 the concentration of the GLPC are ~2.5 x 1018 and ~ 6 x 1017 defects/cm3 respectively and that their behaviours are similar to that of sample B3, which has a GLPC content of ~ 5 x 1017 defects/cm3.

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Figure 3.9c illustrates the induced concentration of the Ge(2) defects as a function of the dose in the samples B4 and C4. In both samples, the dependence on dose is described by a linear growth followed by a deviation from linearity and by a levelling of the induced amount of defects. The lines are the best fit curves obtained using the law A(1- e-B x ), whereas the values of the A and B parameters are reported in Table 3.4. We note that in the sample B4, which contains a larger number of GLPC, a larger concentration of Ge(2) is measured. Furthermore, we note that in this sample the Ge(2) concentration is higher than that of the Ge(1); so that, it is possible to suggest the presence of other electron traps and the absence of a one to one correlation between the two centers. At variance, the data of the sample C4 don‘t disagree with the exchange of an electron from a GLPC to a Ge tetracoordinated atom to form a Ge(2) and a Ge(1). Finally, the data of sample D4 confirm the presence of other electron donors that permit to generate the Ge(1) defects even when the Ge(2) are not detected.

3.4.4. Type 5 Samples In figure 3.10 and in Table 3.5 we report the experimental data recorded after irradiation of samples B5, C5 and D5 and the result obtained by the fits of the Ge(1) and Ge(2) induced concentrations. As observed for the samples of type 4, the Ge(1) concentration shows a higher dependence on the Ge content even if the maximum induced concentration changes within an order of magnitude (see figure 3.10a) while the Ge content changes from ~ 1020 to ~1018 atoms/cm3. Furthermore, also in this case the differences in the Ge(1) concentrations are less than an order of magnitude for low doses, even if these differences are larger than those observed in the other sets of samples.

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Table 3.5. Values of the A and B parameters obtained by the fitting of the Ge(1) and Ge(2) concentrations of the different samples with the law A( 1-e-B x ) where x is the dose Ge(1) Sample

A Defects/cm3

B A error Defects/cm3 Gy-1

B error Gy-1

B5/A

1.9 x 1017

0.3 x 1017

0.00060

0.00012

16

16

C5

8.9 x 10

1.5 x 10

0.00080

0.00020

D5

1.8 x 1016

0.5 x 1016

0.00220

0.00090

Ge(2) Sample

A Defects/cm3

B A error Defects/cm3 Gy-1

B error Gy-1

B5/A

6 x 1017

1 x 1017

0.00040

0.00012

16

16

C5

8.0 x 10

1.6 x 10

0.00110

0.00040

D5

ND

ND

ND

ND

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18

18

10

10

b E'Ge Conc.(defects/cm )

10

3

3

Ge(1) Conc.(Defects/cm )

a 17

16

10

15

10

B5/A C5 D5

14

10

13

17

10

16

10

15

10

B5/A C5 D5

14

10

13

10

10 0

1

2

3

4

5

6

7

8

0

1

2

3

4

5

6

7

8

10 10 10 10 10 10 10 10 10

10 10 10 10 10 10 10 10 10

Dose (Gray)

Dose (Gray) 18

10 3

Ge(2) Conc.(Defects/cm )

c 17

10

16

10

15

10

B5/A C5

14

10

13

10

0

1

2

3

4

5

6

7

8

Copyright © 2011. Nova Science Publishers, Incorporated. All rights reserved.

10 10 10 10 10 10 10 10 10 Dose (Gray)

Figure 3.10. a) induced Ge(1) concentrations in samples B5/A (■), C5 (●) and D5 (□), and their fits --) and D5 ( ); b) E‘Ge induced concentration in different samples B5/A (■), C5 (●) and in D5 (□); c) induced Ge(2) concentrations in sample B5/A (■) and in sample C5 (●) and their fit ). The fit law is A( 1-e-B x ).

From the E‘Ge concentration (figure 3.10b) we observe that in the sample D5 the concentration seems to reach a limit value, whereas in the sample B5/A it grows linearly up to 104 Gy and then shows a slight sub linear dose dependence. As regards the sample C5 the data do not clarify if the dose dependence is similar to that of sample B5/A or to that of D5, showing however that a very slow growth rate is reached at high dose. In this set of samples, the E‘Ge generation appears to be dependent on the GLPC content that increases from ~ 7 x 1016 defects/cm3 (sample D5) to ~6 x 1018 defects/cm3 (sample B5/A). From this point of view, these data could suggest that a generation process involving oxygen deficient precursors takes place, as for example the generation from the ionization of neutral monovacancy involving a Ge atom [103] or the generation from GLPC, as proposed in [27]. The Ge(2) defects are observed in samples B5/A and C5. The Ge(2) concentration increases linearly with the dose and then it reaches a limit value. The range of the linear

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growth and the saturation value depend on the sample. The data have been fitted with the same law used for the other samples and the fitting results are reported in Table 3.5. We note that in sample C5 the Ge(1) and the Ge(2) dose dependencies are compatible with the photoreaction: GLPC + Ge→ Ge(2) (GLPC+) + Ge(1), whereas the data of the sample B5/A (in which [Ge(2)]>[Ge(1)]) suggest the presence of electron trap different from the Ge tetracoordinated atoms; the data of the sample D5 suggest the presence of other electron donors. Finally, the defects induced in sample B5/B, in general, show similar dose dependence3. The main difference between these two samples is that in sample B5/A the Ge content was measured using Instrumental Neutron Activation Analysis.

3.4.5. PCVD Samples 18

18

10

a E'Ge Conc. (defects/cm )

17

3

3

Ge(1) Conc. (defects/cm )

10 10

16

10

15

10

14

 Irrad.  Irrad.

10

13

b

17

10

16

10

15

10

14

10

 Irrad.  Irrad.

13

10

10 0

1

2

3

4

5

6

7

8

0

1

2

3

4

5

6

7

8

10 10 10 10 10 10 10 10 10

10 10 10 10 10 10 10 10 10

Dose (Gray)

Dose (Gray)

18

Copyright © 2011. Nova Science Publishers, Incorporated. All rights reserved.

3

Ge(2) Conc. (defects/cm )

10

c

17

10

16

10

15

10

14

10

 Irrad.  Irrad.

13

10

0

1

2

3

4

5

6

7

8

10 10 10 10 10 10 10 10 10 Dose (Gray)

Figure 3.11. A) Ge(1) concentration induced in the B2 sample γ (●) and β (○) irradiated; B) E‘Ge concentration induced in the B2 sample γ (●) and β (○) irradiated; C) Ge(2) concentration induced in the B2 sample γ (●) and β (○) irradiated.

The samples PCVD20/A, PCVD20/B and PCVD4 have been β irradiated 4; so, before to present the concentrations of the induced Ge(1), Ge(2) and E‘Ge as a function of the dose, we 3

The saturation value of the Ge(1) concentration in sample B5/B is higher of ~ 30% whereas the B parameter is (5 ±1 ) 10-4 Gy-1; as regards the E‘Ge and the Ge(2) the two samples show similar dose dependencies. 4 The irradiation have been performed at the ENEA C.R. (Frascati Italy) using the LINAC electron accelerator. Germanium: Properties, Production and Applications : Properties, Production and Applications, Nova Science Publishers, Incorporated, 2011.

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report (see figure 3.11) the comparison between the concentration of Ge(1), Ge(2) and the E‘Ge defects induced in a sample B2 by γ and β irradiation. The data of figure 3.11 show that for all type of defects no significant differences are observed between the two types of irradiation with the consequence that we can compare the data obtained from the β irradiation with those obtained from the γ exposition. In particular, the Ge(1) induced concentration grows linearly up to a dose of ~ 103 Gy and then it tends to a limit value of ~ 1.5 x 1017 defects/cm3 for both the γ and β irradiated specimens. Also the Ge(2) concentration shows a linear growth and then tends to a limit value of ~1.8 x 1016 defects/cm3 in the two irradiated samples. Finally, the E‘Ge concentration increases with the increase of the accumulated dose without showing a limit value. In particular, the dose dependence is linear up to ~ 103 Gy and sub linear for higher doses, for both irradiation types. In figure 3.12a the Ge(1) concentrations induced in samples PCVD20/A, PCVD20/B and PCVD4 are reported as a function of the accumulated dose. In the same figure, the best fit curves are reported (the parameters obtained by the fit are reported in Table 3.6). We note that in samples PCVD20/B and PCVD4 the Ge(1) defect concentrations grow linearly and then reach a limit value, which is ~ 1 x 1017 defects/cm3 in the sample PCVD20/B, and ~ 2 x 1017 defects/cm3 in sample PCVD4. At variance, in sample PCVD20/A the Ge(1) concentration does not show a saturation value, and the dose dependence shows a linear growth (for low doses) followed by a sublinear one. This finding could be explained by the presence of two generation processes, the first dominant for low doses and the second at high doses. Table 3.6. Values of the A and B parameters obtained by the fitting of the Ge(1) and Ge(2) concentrations of the different samples with the law A( 1-e-B x ) where x is the dose

Copyright © 2011. Nova Science Publishers, Incorporated. All rights reserved.

Ge(1) Sample

A Defects/cm3

B A error Defects/cm3 Gy-1

B error Gy-1

PCVD20/B

1.10 x 1017

0.14 x 1017

0.00090

0.00020

0.00055

0.00015

PCVD4

17

1.9 x 10

17

0.3 x 10

PCVD20/A Ge(2) Sample

A Defects/cm3

B A error Defects/cm3 Gy-1

B error Gy-1

PCVD20/B

2.4 x 1017

0.6 x 1017

0.00050

0.00020

17

17

PCVD4

2.5 x 10

0.4 x 10

0.00054

0.00015

PCVD20/A

ND

ND

ND

ND

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18

10

18

b 3

E'Ge Conc. (Defects/cm )

a

3

Ge(1) Conc. (defects/cm )

10

17

10

16

10

15

10

PCVD20/A PCVD20/B PCVD4

17

10

16

10

15

10

PCVD20/A PCVD20/B PCVD4

14

10

14

0

10

0

1

2

3

4

5

6

7

1

2

3

4

5

6

7

8

10 10 10 10 10 10 10 10 10

8

10 10 10 10 10 10 10 10 10

Dose (Gray)

Dose (Gray) 18

c

3

Ge(2) Conc. (Defects/cm )

10

17

10

16

10

15

10

PCVD20/B PCVD4

14

10

0

1

2

3

4

5

6

7

8

Copyright © 2011. Nova Science Publishers, Incorporated. All rights reserved.

10 10 10 10 10 10 10 10 10 Dose (Gray)

Figure 3.12: a) Ge(1) concentration induced in sample PCVD20/A (■), PCVD20/B (○) and PCVD4 (●) ); b) E‘Ge concentration induced in sample PCVD20/A (■), PCVD20/B (○) and PCVD4 (●); c) Ge(2) defects induced in sample PCVD20/B (○) and PCVD4 (●) ). The fit law is A( 1-e-B x ).

Figure 3.12b illustrates the induced concentrations of E‘Ge in all the three samples. In details, we observe that in sample PCVD20A the E‘Ge amount grows with a sublinear dependence on dose without reaching a limit value. In sample PCVD20/B at variance, the concentration increases linearly up to ~ 103 Gy and then seems to reach a saturation value followed by a second sublinear growth. The second process could be the same that determines the E‘Ge generation in sample PCVD20/A, in fact we note that at the last two investigated doses the E‘Ge defects induced in these two samples feature similar concentrations. Finally, it is worth to note that up to 10 4 Gy in sample PCVD4 the E‘Ge EPR signal is only ~ 1% of the total EPR spectrum, and that the E‘Ge defects were present in the spectrum recorded before any irradiation (~ 4.6 x 1014 defects/cm3). For these reasons in figure 3.12b we have reported only the E‘Ge concentrations

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estimated for doses higher than 104 Gy. However, even if we would consider the induced concentrations for lower doses, their values will be similar to that reported for the sample PCVD20/A. In figure 3.12c we show the Ge(2) concentration induced in samples PCVD20/B and PCVD4 together with the respective fitting curves (the fit parameters are reported in Table 3.6). We note that in the two samples the Ge(2) features almost the same behavior even if they contain different Ge and GLPC amounts. Furthermore, in sample PCVD4 the Ge(1) and Ge(2) concentrations appear correlated and of the same amount. At variance, Ge(2) are present in greater number than the Ge(1) in sample PCVD20/B suggesting the presence of other electron traps. At variance, in sample PCVD20/A the absence of Ge(2) can suggest the presence of other electron donors. Before to conclude the presentation of the data recorded after the irradiation of the different samples, we report in figure 3.13 the Ge(1) (panel a) and the E‘Ge (panel b) concentrations measured in the sample HD, which has a Ge content of ~ 2 x 1019 atoms/cm3 and in which the GLPC optical activity was not detected. For comparison, in the same figure we show the concentrations induced in the sample C1 that has similar Ge content and a low GLPC content (~ 1015 defects/cm3). The concentration of the Ge(1) defects induced in sample HD features the same dependence on dose observed in sample C1. Similar concentrations are induced also for the E‘Ge defects up to the dose of ~ 104 Gy, whereas for higher doses a slightly larger difference is observed. Anyway, for the generation mechanisms of the E‘Ge and Ge(1) defects we can suggest that the effects of the irradiation on the two samples are similar. 18

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Figure 3.13. a) Ge(1) concentration induced in sample HD (○) and in sample C1 (●); b) E‘Ge concentration induced in sample HD (○) and in sample C1 (●).

3.5. Ge(1) Point Defects The above reported data illustrate a complex scenario as regards the Ge(1) generation processes. In fact, we have observed cases in which the Ge(1) are induced when Ge(2) are absent, or induced in lower concentration, and cases in which the induced Ge(2) concentration overcomes that of the Ge(1). These considerations suggest the presence of other

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electron donors and electron traps, with concentrations that, in general, can depend on the sample production procedure. Furthermore, from the comparison of the dose dependence of the E‘Ge and of Ge(1) a clear relation between these two types of defects does not emerge. In general, for low irradiation doses, the Ge(1) concentrations induced in different samples appear almost independent from the Ge content. In addition, we note that a saturation value of the concentration is always observed, apart from the sample PCVD20/A. The possibility to describe the Ge(1) growth with the law: A(1- e-B x) suggests to consider the Ge(1) generation as the result of the competition between generation and destruction processes. So, even if these channels cannot be clearly identified, in a general scheme we can write the following equation to justify the Ge(1) generation:

d [Ge(1)]  K ([Ge]  [Gedefects ])  b[Ge(1)] dx

(3.1)

where x is the dose, K is the probability to generate a Ge(1), [Gedefects] is the total amount of defective Ge atom, b is the probability to destroy a Ge(1) and [Ge] and [Ge(1)] are the Ge and the Ge(1) contents respectively. It is important to remark that, in general, in the explored dose range the total concentration of the induced defects (Ge(1), E‘Ge, Ge(2) and H(II)) plus the concentration of the starting GLPC is lower than the Ge content of about one order of magnitude; so that, we can approximate the equation 3.1 as:

d [Ge(1)]  K [Ge]  b[Ge(1)] dx

(3.2)

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the solution of this equation, assuming that at x=0 [Ge(1)]=0 is:

[Ge(1)] 

K[Ge] (1  e bx ) b

(3.3)

and for low doses:

[Ge(1)]  K [Ge]x

(3.4)

According to equation (3.3), the A parameter, estimated by the fits, is equal to K[Ge]/b, whereas the parameter B is equal to b. The fact that for low doses the induced concentrations of Ge(1) are almost independent of the Ge content, on the basis of equation 3.4, suggests that K should depend on Ge with a law similar to [Ge]-α with α ~1. To enforce this suggestion, in figure 3.14 we plot as a function of the Ge doping level the values of K derived from the fit of the data reported in previous paragraphs: AB/[Ge]. The data show the decrease of K with the increase of the Ge content of the investigated samples, and in particular, this decrease appears compatible with the power law [Ge]-1 illustrated by the gray line of the figure 3.14. It is important to note that this behavior is observed in samples produced in different ways, sol-gel (densificated with different thermal treatments) and PCVD, with different GLPC contents and in samples with various dose dependencies of the Ge(2) and E‘Ge concentrations. On these

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bases we can suggest that the observed dependence on Ge of K is related to a specific feature of the electron trapping process of the tetracoordinated Ge atom. It is worth to note that K depends on the concentrations and the species of the electron donors. In particular, it is expected that K increases with the increase of the GLPC. Unfortunately, the presence of other electron donor and electron trap defects or structures prevents to evidence this aspect. -4

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Figure 3.14. K values (●) calculated by the fit parameters A and B reported previously in this chapter; the gray line represents the law [Ge]-1. -5

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In figure 3.15, we report the K values for the sample of types C and B as a function of the GLPC/Ge ratio (considered as a measure of the oxygen deficiency). The data for the sample of D type are not shown because the Ge content changes from 1.7 to 5.5 1018 atoms/cm3 making more difficult the comprehension of the dependence from the GLPC. For the type B samples, we note a slight increase of K as a function of the GLPC/Ge ratio ascribable to the increase of the GLPC content. At variance, for the type C samples K decreases from C1 to C3 and then increases in C4 and C5 probably because of the high GLPC content of these two latter samples. On these bases, we can suggest that the oxygen deficiency does not ensure a

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clear increase of the probability of the Ge(1) generation. However, we note that high GLPC contents could affect the Ge(1) concentration induced at low doses; so that, the larger variability in the Ge(1) concentrations induced at low doses observed in the samples of type 4 and 5 can be justified by the larger variations of the GLPC content of these samples. In other words, for high oxygen deficiency the relevance of this parameter becomes more evident, whereas at low oxygen deficiency the dependence of K from Ge ([Ge]-α with α~1) content overcomes its relevance. The other parameter that determines the dose dependence of the [Ge(1)] is B. This parameter represents the probability to destroy the Ge(1). In figure 3.16a, we report the B factor estimated by the fit of the experimental data of each sample as a function of the Ge content. The data show that, apart from the sample D1 (Ge content ~ 2.2 1018 atoms/cm3), when the Ge content is within the range 1018-1020 atoms/cm3 the B factor tends to decrease with the Ge content, then B appears to be independent of Ge and, finally, seems to increase (last point PCVD20). In the range 1018-1020 atoms/cm3, we can consider the described tendency as the result of the fact that increasing the Ge content the probability that an electron released by the destruction of a Ge(1) is trapped by another Ge atom increases, lowering the destruction efficiency. In other words, higher is the Ge content less relevant is the presence of other traps contained as impurity. 18

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Figure 3.16. a) B factor of the samples of type 1 (●), type 3 (○), type 4 (●), type 5 (■) and PCVD (■); a) Ge(1) concentration induced in sample E1 (●), and in sample E5 (■).

To explain the behaviour of B found for higher Ge content (see in particular the data referring to samples PCVD4, A1 and PCVD20/B), it is important to consider that in pure GeO2 the Ge(1) has not been observed [59]. A possible explanation of this aspect could be that the electron cannot be trapped by a Ge atom having other 4 Ge atoms as neighbours. On these bases, enhancing the Ge content one could expect, in addition to the decrease of K, also an increase of the probability of Ge(1) destruction. This increase, on the basis of the data reported in figure 3.16a, could start from doping levels higher than 10%. Nevertheless, the investigation of other samples doped with the same amount of Ge, or better with higher content, is necessary for a deeper comprehension of this aspect. As regards the samples of type D, it can be suggested that the main reason of the difference between the Ge(1) concentrations in D1 and D5 is the difference observed in the B

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parameter. The data indicate that for low doping levels in the non oxygen deficient samples the probability to destroy the Ge(1) decreases (see the point at ~ 2.2 1018 Ge atom/cm3 of figure 3.16a). This suggestion is confirmed and enforced by the data recorded on the samples E1 and E5, with doping levels of ~ 2 x 1017Ge atoms/cm3, and produced as D1 and D5 respectively. The Ge(1) concentrations induced in these two samples are reported in figure 3.16b. In both samples, the concentration grows linearly and then tends to a limit value. In particular, in sample E1 the linear growth is observed up to ~ 800Gy and the limit value is ~ 5 x1016 defects/cm3, whereas in sample E5 the concentration increases linearly up to ~100 Gy and the limit value is ~ 7 x 1015 defects/cm3. Nevertheless, at low doses, the induced concentrations are similar. Basing on about the same creation rate, we can conclude that K values of E1 and E5 are similar5, and that the main reason of the different saturation values is the difference in the destruction probability of the Ge(1), which is lower in the E1 samples, produced as the D1 sample. Considering that the E5 sample has higher oxygen deficiency6, the comparison between the data recorded on samples E1 and E5 evidences that for low Ge doping level the oxygen deficiency has negative effects on the Ge(1) generation. The concentration of Ge(1) induced in sample PCVD20/A at low doses seems to disagree with the proposed dependence of K on Ge content (see figure 3.12a). This discrepancy could be due to the fact that the electron donors involved in the Ge(1) generation at low doses in this sample are in a too low concentration, so lowering the value of K. This picture is confirmed by the fact that at higher doses the Ge(1) shows a new growth, proving that up to 104 Gy the generation was limited by the electron donor and not by the Ge(1) properties.

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3.6. Ge(2) and E’Ge Point Defects The Ge(2) signal was observed only in samples in which the GLPC were present in concentration higher than 1 x 1017defects/cm3. For example, we have not observed the presence of the Ge(2) EPR signal in a sample as the PCVD20/A containing ~ 3.7 x 1021 Ge atoms/cm3 and no GLPC, whereas the Ge(2) presence is observed in samples as C5 that has a lower Ge content but in which the GLPC are present ( ~4.5 x 1017 defects/cm3). These considerations disagree with the assignment of the Ge(2) EPR signal to a Ge(1)-like structure modified by the presence of a second Ge atom. In fact, in the sample PCVD20/A the probability to obtain this structure is high, but the Ge(2) are not induced. We note that, apart from the sample PCVD20/B, the ratio Cmax/GLPC assumes values inside the range 0.1-0.2. According to these findings, we can suggest that the Ge(2) EPR signal is related to an ionized GLPC. Basing on these considerations, in samples B1 and D5 we should expect Ge(2) induced concentrations of ~3 x 1015 and of ~ 1 x 1016 defects/cm3, respectively. The absence of the Ge(2) signal in both materials could be due to the fact that the quantity of the released electrons by other donors is so high to prevent the Ge(2) formation in these samples. As regards the sample PCVD20/B, the lower ratio between the induced Ge(2) defects and the starting GLPC concentration could be attributed to the fact that the equilibrium between 5

The K value estimated in sample E5 is (1.4 ± 0.8) x 10-4 Gy-1 and is sufficiently in agreement with the dependence of K on Ge content obtained from the data of the other samples with higher Ge content. 6 The oxygen deficiencies of the E1 and E5 sample are extrapolated by that observed in the other samples of type 1 and type 5 produced with the same procedure but with higher Ge content.

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generation and destruction mechanisms in the electron trapping processes is reached before than in other samples. The data of figure 3.7b suggest the existence of a generation channel almost independent of the Ge content for the E‘Ge. In fact, in the samples of type 1 the Ge content changes from ~1018 to 1021 Ge atoms/cm3, whereas the E‘Ge concentrations differ by a factor lower than 10 for doses lower than 106 Gy and only for higher doses a greater variability is observed. The existence of such a generation channel can be suggested also basing on the data recorded for the sample PCVD20/A. In particular, as shown in figure 3.17, in this sample the E‘Ge are generated in similar way to that of the type 1 material (we report the concentration of sample C1 for comparison). Changing the GLPC/Ge ratio a higher variability is found, and in the samples of the type 4 and 5 the induced E‘Ge concentration increases with the increase of the GLPC and Ge content. However, even if in the B samples (samples with ~ 2 x 1020 Ge atoms/cm3) the E‘Ge concentrations induced by the irradiation increase with the increase of the starting GLPC concentrations, the relation between the GLPC and the E‘Ge generation is not immediate. In fact, two other experimental data have to be considered. The first is the behaviour of the sample PCVD4. In this sample, the E‘Ge generation doesn‘t appear enhanced by the high values of GLPC and Ge content. The second regards the comparison between the E‘Ge defects induced in samples E1 and E5 (with a nominal Ge content of ~2 x 1017 Ge atoms/cm3). 18

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Figure 3.17. Induced concentration of the E‘Ge defects in the sample (●) PCVD20/A and in the sample (○) C1 as a function of the irradiation dose.

As reported in figure 3.18, in sample E1 the E‘Ge are generated with a higher efficiency with respect to that of sample E5; in fact in sample E1 we measure a maximum concentration of ~ 2 x 1017 E‘Ge defects/cm3, whereas in sample E5 the maximum induced concentration is ~ 1 x 1016 defects/cm3. This finding suggests that for low Ge doping level the oxygen deficiency does not ensure an increase of the E‘Ge production. Furthermore, it is important to note that the E‘Ge concentration induced in sample E1 is similar to those observed in samples A1,B1 and C1, supporting the idea of an E‘Ge generation channel independent of the doping level for doses lower than 106 Gy. Finally, it is interesting to note that in many of the investigated samples the growths of the E‘Ge concentrations are not described by a law of the type Vmax (1 – e-Rx). At variance, their growths are often described by the sum of the law

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Vmax (1 – e-Rx) (for low doses) and of a subliner dose dependence (for high doses), suggesting the occurrence of two generation channels: one from precursors, inducing a growth with saturation, and one from a more complex mechanism giving the sublinear growth. 18

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Figure 3.18. E‘Ge concentration induced in sample E1 (●), and in sample E5 (■).

4. REFRACTIVE INDEX VARIATIONS

In figure 4.1 the differences between the OA spectra acquired for the samples B0, B2 and B4 at the dose of ~10kGy and the spectra recorded for the as-grown samples are reported. From the comparison of these spectra, we observe that the amplitude of the induced optical absorption (Δα) at 4.5 and 5.8 eV is similar for the B0 and B2 samples whereas the amplitude, at these energies, is higher in the B4 sample. In particular, the induced absorption coefficient at 4.5 and 5.8 eV is 8 and 12 cm-1 in B0, 7.8 and 12 cm-1 in B2, whereas it is 14 and 26 cm-1 in B4. 30 B0 B2 B4

25 20

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4.1. Absorption Induced Activity

15 10 5 0 2

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Energy (eV) Figure 4.1. Induced optical absorption coefficient (Δα) in samples B0 (▬), B2 (▬) and B4 ( irradiation dose of ~ 10 kGy.

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) at the

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In the spectra of figure 4.1, the dip at ~5.2 eV in the sample B4, can be considered as the consequence of the partial bleaching of the B2β activity, in agreement with the data reported in [79]. Instead, the different profiles at energies higher than 6 eV could be influenced by the different concentrations of the induced E‘Ge. Similar results are observed at different doses, as shown in figure 4.2 for the doses of 1 kGy (panel a) and 40 kGy (panel b). The presence of the 5.8 eV band in every employed material leads to some considerations regarding the attribution of this band to the Ge(2) defect. In fact, at 10 kGy the samples B0 and B2 have similar Ge(1) concentrations (~1017 defects/cm3) and show similar values of the induced absorption coefficient (~ 12 cm-1) at 5.8 eV; furthermore, the B4 sample, with a double Ge(1) concentration (2.3 x 1017 defects/cm3), has double induced absorption at 5.8 eV (~26 cm-1). These latter findings, together with the absence of Ge(2) in B0, the low concentration (~ 0.2 x 1017 defects/cm3) observed in sample B2 and the high Ge(2) content of B4 (~ 4.3 x 1017 defects/cm3), suggest that this latter defect does not significantly affect the optical absorption at 5.8 eV, which at variance should be related to the Ge(1), as proposed in [79,89]. 10

40 B0 B2 B4

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2 0 Copyright © 2011. Nova Science Publishers, Incorporated. All rights reserved.

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Figure 4.2. Induced optical absorption coefficient (Δα) in samples B0 (▬), B2 (▬) and B4 ( irradiation dose of ~ 1 kGy a) panel and of ~ 40 kGy b) panel.

) at the

This suggestion is confirmed also by the data recorded for different doses: at 1 and 40 kGy the samples B0 and B2 have similar Ge(1) concentrations, ~ 0.3 and 1.4 x 1017 defects/cm3, and show similar induced absorption coefficient at 5.8 eV. On the contrary, the B4 sample, with about double Ge(1) concentration ( ~0.7 and ~2.5 x 1017 defects/cm3), has an induced absorption coefficient at 5.8 eV of ~ 7.2 and ~34 cm-1, comparable with that expected assigning a relation between the 5.8 eV band and the Ge(1). In general, the shapes of the OA spectra of the other samples show main contributions at 4.5 and 5.8 eV, as observed for sample B0, B2 and B4. Moreover, we note that, depending on the sample, by increasing the dose the presence of a band peak at ~ 6.3 eV becomes more evident, according with the assignment of a 6.3 eV band to the E‘Ge defects [59,84].

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4.2. Dependence of the Refractive Index Changes on Ge(1) Defects The relations between the induced optical absorption bands and the paramagnetic point defects are an interesting point not only from the physical point of view, but also for application aims. In this latter field, the relevance of the induced absorption activity is related with the variations of the refractive index (Δn) of the materials. These changes are estimable through the Kramers-Kronig relations. In this section, we will present the data regarding the Δn obtained from OA spectra and we will elucidate the relation between these data and the induced concentration of point defects. The Δn values have been calculated using a decomposition of the induced OA by fitting with sets of Gaussian bands, and employing the equation [26]:

n( w) 

 i Bi 2 2 i w

c

w  i

(4.1)

in which c is the speed of light in vacuum, Δαi is the variation of the absorption coefficient at the maximum of the i-th component peaked at the frequency wi, Bi is √2σ (σ is the standard deviation) of the i-th Gaussian component and w is the frequency corresponding to 1500 nm. We used the above procedure to estimate the induced Δn in the samples of type B, C and D irradiated at the doses of ~ 2 and ~10 kGy. In figure 4.3a we report the Δn induced in these samples for these two doses as a function of the induced concentration of Ge(1). The data go from Δn ~ 10-5 to 10-4 whereas the Ge(1) concentration changes from ~ 2 x 1016 to 3 x 1017. -3

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Figure 4.3. a) Δn (●) as function of the induced Ge(1) concentration, and linear fit (▬); b) Δn (■) as function of the induced E‘Ge concentration. Data refer to the sample of type B,C and D irradiated at the doses of ~ 2 and 10 kGy.

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From figure 4.3, we observe that the refractive index variation grows linearly with the increase of the Ge(1) concentration, and, in particular, that to describe the relation between these two quantities the following law can be used: Δn = κ Ge(1)conc, where Ge(1)conc is the Ge(1) concentration and κ = (4.5 ± 1.5) 10-22 cm3. At the same time, the refractive index changes do not show a relation with the E‘Ge, as illustrated in figure 4.3b. In fact, we note that when the Δn is ~ 3 x 10-5 the induced concentration of E‘Ge can change by an order of magnitude and, on the other side, when the E‘Ge concentration is ~ 1.5 x 1016 the induced Δn can differ by a factor 4. It is important to remark that the correlation between Δn and the Ge(1) concentration has been obtained using different samples, despite the fact that in each sample the Ge(1) generation process may be different. To further investigate the relation between Δn and the Ge(1), and the dose dependence of Δn, we have extended the previous study using a larger set of samples and a larger number of irradiation doses. In figure 4.4, we report the results obtained analyzing the induced OA activities in various samples. In particular, in the main panels, Δn is shown as a function of the dose in the range from ~ 103 to ~105 Gy, and in the inset of each panel the relation between Δn and the Ge(1) concentrations is shown. The first experimental observation is that Δn initially increases linearly with the dose and then it tends to a limit value. The range of the linear growth and the limit value depend on the sample. In general we note that the induced maximum variations are of the order of ~10-4. The data reported in the inset of each panel of figure 4.4, illustrate the linear correlation between the Ge(1) induced concentration and Δn value. Firstly, it is important to note that in sample PCVD4 (doped with ~ 1021 Ge atoms/cm3) the slope of the line is (4.7 ± 1.3) 10-22 cm3, in agreement with the value previously obtained using sol-gel produced samples. This finding is interesting because this sample is a typical material used for the production of optical fiber. Secondly, we note that for the sample A1, doped with ~ 2 x 1021 Ge atoms/cm3, the slope is in agreement with the previous estimation, being (5.3 ± 1.6) 10 -22 cm3. As regards the other samples B and C, the slope of the lines changes between 3 and 6 10-22 cm3. From the data of these samples, we obtain a proportionality factor of (5 ± 2) 10-22 cm3 for the dose range 103-105 Gy, compatible with the factor found using the data recorded for the irradiation doses at 2 and 10 KGy. A more complicated scenario emerges from the analysis of the samples with lower doping level. In fact, in samples as D4 (see figure 4.4f), D3 and D1 we observe linear correlations between Ge(1) and Δn, compatible with the previous ones, whereas in other ones, in particular for samples D5, we do not observe a clear relation between the two quantities in the dose range 103-105 Gy. For this sample it is important to note that the maximum Ge(1) concentration is ~2 1016 defect/cm3 and that this is near to the minimum value reported in figure 4.3. Moreover, the Ge(1) concentration stops to increase at ~1 kGy; so, the effects of the generation of other defects seems to affect the relation between the Ge(1) concentration and Δn. Similar problems are found for some samples E. These findings suggest that high Ge contents can be useful to produce materials in which the induced refractive index changes can be predicted, better than in the low doped samples.

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-4

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10

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0 0.0

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17

2.0x10

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Figure 4.4. a) Δn (▼) of sample A1; b) Δn (▲) of sample PCVD4; c) Δn (○) of sample B0; d) Δn (□) of sample B3 e) Δn (■) of sample C3; f) Δn (●) of sample D4; in the main panel the data are reported as a function of the dose, whereas in the insets they are reported as a function of the Ge(1) concentration, lines (▬) represent the linear fits of the data.

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5. INDUCED GLPC 5.1. PL Spectra of the Induced GLPC In different Ge-doped materials we have observed, after irradiation, the generation of GLPC in addition to other Ge related defects. In particular, it is important to note that the GLPC creation was observed even in materials, as the B0, in which the optical activity related to this defect was absent in the spectra recorded for the as-grown sample. Figure 5.1 illustrates a normalized PL spectrum of the induced GLPC, obtained on the sample B0, γ-ray irradiated at the dose of 5 MGy; it is representative of the spectra recorded also in other samples at different doses. We note that the presence of other Ge related defects induces optical absorption bands in the energy range 3.5-4.8 eV, and, for this reason, it is necessary to correct the PL spectra of GLPC for the overall absorption coefficient to obtain the real PL line shape.

1.4 Induced GLPC

Normalized PL

1.2 1.0 0.8 0.6 0.4

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0.2 0.0 2.60

3.15

3.70

4.25

4.80

Energy Figure 5.1. PL spectrum of the induced GLPC recorded in sample B0 γ irradiated at the dose of 5 MGy.

The spectrum of figure 5.1 shows two emission bands peaked at ~3.2 and ~ 4.3 eV in strong analogy with the PL activity of the GLPC generated during the synthesis of many Ge doped materials (native GLPC). The first characterization of the irradiation induced PL activity has been carried out on the band peaked at 3.2 eV. In particular, in figure 5.2a, we report the PL spectra, in the range 2.5 - 3.7 eV, of the sample B0 irradiated at 1 MGy recorded using different excitation energies. These spectra evidence spectral changes of the ~3.2 eV band. A more detailed comparison is reported in figure 5.2b, where the variations of the ~3.2 eV maximum position and of its FWHM (inset) as a function of the excitation energy (Eexc) are shown for the irradiated sample and for a Ge doped sample containing native GLPC.

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Figure 5.2. a) Normalized PL spectra of 3.2 eV band, recorded on B0 sample  irradiated at 1 MGy exciting at different energies; b) variation of the peak position as function of excitation energy: (●) 1 MGy irradiated sample B0, (○) sample with native GLPC; in the inset, the dependence of FWHM on excitation energy is reported.

In particular, the peak position of the ~3.2 eV band of the irradiated sample changes with the Eexc in the same way as the non irradiated sample, increasing almost monotonically on increasing Eexc. At variance, the FWHM in the investigated materials depend on Eexc in different ways. In details, in the sample with native activity it increases monotonically with Eexc, whereas in the irradiated B0 sample the FWHM has lower dependence changing only from 0.44 to 0.48 eV (with an error of ~ 0.02 eV). A similar comparison could not be made for the ~4.3 eV emission, as the correction procedure for the high absorption in the irradiated sample gives a large error of the E band peak position, avoiding the accurate investigation of its dependence on excitation energy.

5.1.2. PLE Spectra of the Induced GLPC Figure 5.3 shows the PLE spectra acquired on the sample B0 irradiated at the dose of 5 MGy and on a sample with native GLPC. In particular, the spectra have been recorded fixing the emission energies at ~4.3 eV (panel a) and at ~3.2 (panel b). The spectra have been recorded at HASYLAB (Hamburg) using the reflection geometry, and the reported curves are not corrected for the absorption coefficient because of the lack of the measurement of this latter for energies higher than ~ 6.2 eV and of a precise measurement of the angle between incident light and sample. The comparison between the two signals, normalized at the intensity at ~ 5 eV, supplies different information. The first one regards the similarity of the PLE spectra for energies ≤ 5 eV, which confirms previous results. The second one regards the presence, in the spectra of the induced GLPC, of PLE at E exc > 7 eV, in analogy with the spectra of the native GLPC and according to the PL excitation through to the S0-S2 transition (S2 being the second excited singlet state) [72]. Finally, in both the spectra recorded for the GLPC induced at the dose of 5 MGy it is observed a peak at ~ 5.6 eV, which is absent in the spectra of the native GLPC suggesting a further excitation channel.

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Properties and Generation by Irradiation of Germanium Point Defects …

2.0

2.0

a

b

EEm~ 4.3 eV

1.5

PLE Intensity (a.u.)

PLE Intensity (a.u.)

123

Native GLPC Induced GLPC

1.0

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0.0

EEm~ 3.2 eV Native GLPC Induced GLPC

1.5

1.0

0.5

0.0

4

5

6

7

8

9

4

Energy (eV)

5

6 7 8 Energy (eV)

9

5.1.3. Time Decay Measurements of the Induced β Band To further compare the PL activity of induced GLPC with that of native defects, we investigated the PL time decay of the 3.2 eV band, under pulsed excitation at 4.9 eV at 300 K. In figure 5.4, the ln(I(t)/I0) (I(t) indicating the PL intensity as a function of time and I0 the intensity at the end of excitation pulse), is reported. In particular, we report the data regarding the B0 sample irradiated at 1 MGy and the data obtained by the same measurement in sample C4 (we recall that it is a Ge doped sample with native GLPC). For both activities, the decay is a single exponential and the estimated lifetimes are τ = (97 ± 2) μs in the irradiated sample B0, and τ = (109 ± 2) μs in the sample C4, this latter being in good agreement with the value reported by Skuja [29]. 0

ln(I(t)/I0)

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Figure 5.3. PLE spectra of the GLPC induced at 5 MGy in the sample B0 (▬) and of native GLPC (▬), the measurements have been acquired fixing the emission at ~4.3 eV (panel a) and at ~3.2 eV (panel b).

B0 (1 MGy) Fit B0 C4 Fit C4

-1

-2

-3 0

200 Time (s)

400

Figure 5.4. PL emission at 3.2 eV as a function of time under pulsed excitation at 4.9 eV: (□) experimental data of 1 MGy irradiated sample B0, (○) experimental data of sample C4, the reported data are normalized to the maximum emission; the full lines represent best fits with single exponential laws.

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It is worth to note that performing time decay measurements of the induced β band for different accumulated doses and in different samples (with no native GLPC) the values of τ is always ~ 100 μs. The GLPC have been induced by γ-ray also in samples with native GLPC as B1 (native content ~ 2 1016 defects/cm3). In this latter case, after the irradiation at the dose of 10 MGy the GLPC concentration is ~ 6.2 1016 defects/cm3 and the observed τ is ~ 104 μs; so that, the small lifetime difference could be due to the presence of both native and induced GLPC that contribute to the emission.

5.1.4. Temperature Dependence of the PL Spectra The study of the PL activity as a function of the temperature T is a useful tool to obtain more information regarding the processes that determine the PL emission. For this reason, the temperature dependence of the emission bands related to the induced GLPC has been investigated to determine the compatibility with the feature of the native GLPC. In particular, the measurements have been performed in the temperature range 40-300 K at the SUPERLUMI station on the I-beamline of HASYLAB at DESY, using the pulsed excitation at 5.17 eV of the synchrotron. For the experiment, we have used the sample B0, irradiated at 5 MGy, containing γ induced GLPC, and a sample containing native GLPC7. The PL bands of the induced GLPC show opposite dependencies on temperature: in particular, while the β band decreases, the αE increases with the decrease of T. This dependence has been already reported in [19], for the emission bands of the native defects.

3.0

M0 of PL (arb. units)

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Induced M0 of induced  band M0 of induced E band Total M0 of the Induced PL

2.5 2.0 1.5 1.0 0.5 0.0 0

100

200

300

400

Temperature (K) Figure 5.5. M0 of the induced β band (●), αE band (○) and total M0 (●) determined in sample B0 at the dose of 5 MGy. All the measurements have been recorded at I-beamline of HASYLAB.

7

PL spectra of B0 sample have been corrected for the re-absorption effects by comparison of the measurements carried out at the same temperature (300K) and excitation energy at HASYLAB and in the Palermo laboratory, were we are able to determine the correction.

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A quantitative study of the temperature dependence of the two bands has been performed calculating the zero moment of the two emission bands: 

M0 

 s( E )dE



(5.1)

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where s(E) is the spectral distribution of the emission and E indicates the energy. Every value of M0 has been calculated after the subtraction of a baseline tangent to each band minima. The study of the zero moments of the induced GLPC present in the sample B0 is reported in figure 5.5 together with their sum (total M0): the data regarding the M0 of the two bands confirm the different dependences on temperature. In fact, at room temperature the β band M0 is about 80% of the total emission and the αE band M0 is a minor contribution, whereas the opposite happens at ~ 40 K, the αE being about 90% of the total emission. As regards the total M0 of the induced emission in sample B0, we observe that it is independent of the temperature. Similar independence is observed for the PL activity related to native GLPC, in agreement with previous studies [19]. The independence of the total M0 from temperature is an important information that was known for the native defects [19], and now it is observed for the induced GLPC activities too. This finding enables to conclude that an energy level scheme as that shown in figure 1.2 can be applied and no non-radiative channels, apart from ISC, are relevant for induced GLPC as well as native ones.

5.1.5. Time Dependence of the Emission Complementary information on the processes that determine the emission features of the GLPC arises from the study of the emission intensity as a function of time, recorded at different temperatures. This investigation was performed by the measurements at the Ibeamline of HASYLAB using the pulsed excitation at 5.17 eV of the synchrotron. As for the study of the PL dependence on temperature, we have performed the measurements on both the sample containing γ induced GLPC (sample B0 irradiated at 5MGy) and the sample containing native GLPC. The measurements of the intensity I at ~ 4.27 eV, performed as a function of the time for temperatures from ~ 10 K to ~ 300 K, are reported in figure 5.6. Two important experimental findings are pointed out by the data: the first is that the PL decay rate increases with increasing T; the second regards the law that describes the decay. In particular, the decay up to 140 K, is single exponential I(t)  exp(-t/τ), where τ is the characteristic lifetime of the emission amplitude. At variance, for higher T, the data are described by a stretched exponential decay law I(t)  exp(-(t/τ)), in which  is a stretching factor, which indicates the deviation from the single exponential decay. We observed this behaviour also for the sample with native GLPC (data not reported), in agreement with previous findings [72].

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2 1

ln(I(t)/Imax)

300K 260K 230K 200K 170K 140K 106K 74K 41K 10K

Induced GLPC

0 -1 -2 -3 -4 0

5

10 15 Time (ns)

20

Figure 5.6. Natural logarithm of normalized emission intensity I(t) at ~ 4.27 eV of the induced GLPC recorded at 300K (▬) , at 10 K (▬) and at intermediate temperatures (─). All the measurements have been recorded at I-beamline of HASYLAB.

In figure 5.7, we report the lifetimes and the stretching factors (inset of the figure) of the native and the induced activity evaluated as a function of the temperature by fitting every set of experimental data by a stretched exponential time decay law. In particular, we observe that at low temperature, up to 140 K, the lifetime is (7.7  0.5) ns and (8.2  0.5) ns for the F

induced and the native activities, respectively, suggesting that K R is very similar for both

Stretching factor 

15

Lifetime (ns)

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defects.

10

1.0

0.8

0.6

0.4 0

100 200 300 Temperature (K)

400

Native Induced

5

0 0

100 200 300 Temperature (K)

400

Figure 5.7. Lifetimes of the induced (●) and of native (●) emission at ~ 4.27 eV as a function of the temperature. In the inset we report the stretching factor γ of the induced (●) and of the native (●) emission as a function of the temperature.

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For higher temperatures the lifetime decreases and it reaches the value of ~ 1.4 ns at room temperature for both activities. Also the stretching factor (inset of figure 5.7) is ~ 1 independent on T below 140 K, then it starts to decrease and finally at room temperature it assumes the value of ~0.6 for both the induced and the native emission, with very similar temperature dependence.

5.1.6. Intersystem Crossing Process in the Induced GLPC The investigation of the total M0 of the PL bands of the induced GLPC, as a function of the temperature, suggests that we can neglect the effects of the no radiative channels that connect the excited states to the ground one. In fact, the independence of the total M0 of the induced activity indicates that all the processes, connecting the excited states S1 and T1 with the ground one S0, are radiative also at room temperature. As a consequence of this finding, we can write the following equations that relate the rates of the emission and of the intersystem crossing processes with the lifetime of the αE band and with the ratio η between the M0 of the two emission bands8:

M 0 E KF    R M0 K ISC

 

1 at room temperature K  K ISC

5.3)

 

1 at low temperature K RF

(5.4)

E

E

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(5.2)

F R

Starting from these bases, using the data regarding the intensity decay at low temperature, F

we can evaluate that the efficiency K R of the S1 → S0 transition of the induced GLPC is ~ F

1.3 108 s-1, a value very similar to that of the native GLPC ( K R ~ 1.2 108 s-1). As already noted for the native defects, the temperature dependence of τ can be related to the KISC temperature dependence [19,72]. In addition, the fact that increasing the temperature the intensity time decay departs more and more from a single exponential law (see inset of figure 5.7) can be justified by the existence of a KISC distribution [19,70]. From this point of view the data regarding  (figure 5.7) suggest the presence of a similar distribution in both the induced and the native GLPC. To deeply compare the intersystem crossing process of the induced GLPC with respect to that of native defects, it is interesting to study the ratio of their η parameters.

8

The three equations can be obtained by the energy level scheme of figure 1.2 as reported in [19], when non radiative channels can be neglected.

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A. Alessi, S. Agnello and F. M. Gelardi This ratio is indicated as θ in the following and is given by:

K ISC  Native A   Native  Native e  A K ISC

U Native U K BT

(5.5)

where the Arrhenius law dependence (equation 1.1) has been used for KISC, and the F

similarity of K R at low temperature for all the investigated defects has been considered. In general, the ratio θ can be useful to determine the value of the activation energy and of the pre-exponential factor. In fact, we can estimate the pre-exponential factor ratio of the induced and native GLPC from the value that θ assumes at high temperature ((ΔUnative-ΔU) 140 K is reported.

In figure 5.8a we report the θ values evaluated from the PL spectra of the induced GLPC as a function of the temperature. The data suggest that the pre-exponential factor of the induced GLPC is ~ 0.85 with respect to that of the native GLPC. As regards the activation energy barrier of the induced GLPC, we can obtain information on it considering the dependence on T of the η parameters down to 140 K. In particular, in figure 5.8b we report Max as a function of 1000/T, the natural logarithm of the quantity ((1/η)/(1/η)MAX)= K ISC / K ISC whereas in the inset it is shown a zoom of the data regarding the temperature range 300-170 K. The data indicate that the ISC of native and induced GLPC have similar dependencies on temperature. Furthermore, from this representation of the data we can estimate ΔU by the

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slope of the line fitting the data recorded up to 140 K. The result of this procedure indicates that the induced activity has an activation energy barrier of (100 20) meV similar to that of the native GLPC. The overall obtained results evidence that very similar pre-exponential factor and activation energy apply to the native and to the induced GLPC. It is worth to recall that the pre-exponential factor is representative of the local disorder and of the spin-orbit coupling and that the activation energy is related to the local vibrational mode energy. Furthermore, we recall that the lifetime of the induced β band (transition T1 → S0 ) is determined by the spinorbit coupling, which can be considered unchanged since the lifetime of the induced defects is ~100 μs that is only 10 % lower than that of the native band (~110 μs). On these bases, we guess that all the features of the induced and native defects are similar.

5.1.7. Paramagnetic Defects Related to the Induced GLPC As a further proof of the GLPC generation, we have looked for the presence of H(II) defects. It is important to remember that this type of paramagnetic defect is a product of GLPC and results from its reaction with an H atom. In figure 5.9a, we report the EPR spectra recorded in a range of ~200 G centred at ~ 3465 G for the samples B0 and B2 irradiated at 1MGy. The central part of the spectrum is omitted for convenience. Note that for both samples a doublet of lines is present, denoting the presence of the H(II) centers. The reported spectra evidence also the similar splitting of the lines related to the H(II) defects. In particular, by comparing the spectra we note that the separation (~ 120 Gauss) between the two resonance lines of the H(II) defects, generated by the reaction of a induced GLPC with an H atom, is close to that measured in the case of the H(II) generated by the reaction of a native GLPC with an H atom.

B0 dose 1MGy B2 dose 1MGy

1

0

3380

3400

3420 3520 3540 3560

Magnetic Field (Gauss)

EPR Signal (arb. units)

1.2

a EPR Signal (arb. units)

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2

0.8

b

1 MGy 5 MGy 10 MGy

0.4 0.0 -0.4

Sample B0 -0.8 3505 3515 3525 3535 3545 3555

Magnetic Field (Gauss)

Figure 5.9. a) EPR spectra of sample B0(▬) and B2 (▬) irradiated at the dose of 1 MGy; the central part of the spectra is omitted for clarity, the spectra are shifted to overlap the line at ~ 3520 Gauss and normalized to its amplitude; b) Normalized EPR spectra of the H(II) resonance line peaked at ~3520 Gauss, (▬) spectrum recorded at 1 MGy, (▬) spectrum recorded at 5 MGy and (▬) spectrum recorded at 10 MGy.

The separation between the two resonance lines of the H(II) defects induced in the sample B0 is of ~ 120 Gauss also for the other investigated doses. Furthermore, the line shape Germanium: Properties, Production and Applications : Properties, Production and Applications, Nova Science Publishers, Incorporated, 2011.

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of the H(II) signal does not change as evidenced by the resonance line reported in figure 5.9b, in which the spectra recorded at 1 MGy, at 5 MGy and at 10 MGy are shown (all the spectra are normalized to the intensity measured at 3520 Gauss). The H(II) centers are induced also in other samples showing native GLPC before irradiation. The observed EPR spectra show essentially the same features in all of them with a doublet split by ~120 Gauss. Figure 5.10 shows the high magnetic field EPR resonance of H(II) defects recorded in different samples (B2, B4 and C4) at different doses (1 MGy, 40kGy and 3 kGy)9, together with the signal recorded in the sample B0 at the dose of 1 MGy. By the comparison of these spectra, we note that the signal of B0 sample has small differences with respect to those observed in the other samples.

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Figure 5.10. Spectra of the 3520 Gauss line of the H(II) defects recorded in samples B0 (▬), B2 (▬), B4 (▬) and C4 (○) irradiated at different doses.

5.1.8. GLPC Generation in PCVD Material In this section we will report the data that show the possibility to induce the GLPC also in samples not produced by the sol-gel preparation technique. In particular, in figure 5.11a it is shown the PL spectrum recorded on the sample PCVD/A β-ray irradiated at the dose of ~1MGy (see paragraph 5.3 for the analogy of β and γ irradiation) under excitation at 5 eV. The spectrum shows the presence of two emission bands peaked at ~3.11 and at ~4.24 eV, respectively. It is important to note that this spectrum is obtained after the correction of the recorded one for the effects related to the absorption coefficient (shown in figure 5.11b). The FWHM of the band peaked at 3.11 eV is ~0.47 eV, whereas that of the band peaked at 4.24 eV is ~0.43 eV. We note that the peak of β band is shifted of ~ 0.05 eV with respect to that observed in other samples whereas its FWHM is similar to that measured in samples containing native GLPC. Similarly, the peak position of the αE band appears shifted by analogous quantity, whereas its FWHM is close to that observed for the native GLPC. Even if the nature of the differences has to be considered an open question, the spectrum of figure 5.11a can be attributed to the GLPC and, by considering the value of the absorption 9

The native GLPC content is ~1.5 x 1017, ~ 2.5 x 1018 and ~ 5.6 x 1017 defects/cm3 in B2, B4 and C4 respectively, whereas the H(II) induced concentration is ~6.8 x 1015, ~2.1 x 1016 and ~1.7 defects/cm3 x 1016 in B2, B4 and C4 respectively.

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coefficient at the excitation energy (~5 eV), the induced concentration of the GLPC is ~5 x 1015 centers/cm3. 1.2

a

20

PCVD20/A

b

PCVD20/A

-1

Absorption coef.  (cm )

PL (arb. units)

1.0 0.8 0.6 0.4 0.2 0.0 2.60

3.15

3.70

4.25

Energy (eV)

4.80

10

0 2

3 4 5 Energy (eV)

6

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Figure 5.11. a) Photoluminescence spectrum acquired on the sample PCVD20/A at the dose of ~ 1 MGy; b) absorption spectrum recorded on the sample PCVD20/A at the dose of ~1 MGy.

The generation of the GLPC in the PCVD materials suggests that the possibility of their formation under ionizing radiation is a general feature of the Ge doped silica. The study of the dependence of the efficiency of their generation as a function of the preparation technique and of the different proprieties of the materials will be useful to understand better the generation mechanisms. As regards this aspect, we note that the PCVD material here investigated does not contain OH groups, whereas the as-grown sol-gel samples contain this type of defects in different amounts. In this context, the contribution of OH species or their irradiation products seems to be not necessary in the formation of GLPC. This aspect is very relevant for application, as it suggests that the GLPC can be induced essentially in any type of Ge doped silica.

5.1.9. Discussion on the Emission of the Induced GLPC From the comparison of the above reported data, we can conclude that the γ irradiation is able to induce GLPC point defects. In fact, we observe in irradiated samples two characteristic PL bands, centered at ~3.2 eV and ~4.3 eV, related to the GLPC centers and usually generated during sample synthesis (native defects) and observed in as grown natural silica [19]. The fact that the induced PL band at 3.2 eV shows a lifetime similar (10 % lower) to that of the 3.2 eV band (β band), related to the native GLPC, is a further support to identify this defect in irradiated samples. We note that the peak position of the 3.2 eV induced PL component depends on excitation energy similarly to the native one, whereas its FWHM shows weaker dependence. Moreover, the PLE spectra of the two types of GLPC are comparable for energies lower than 5.3 eV and in the energy range in which the S0-S2 transition is involved (above ~7 eV). At variance, more studies are required to understand the nature of the peak at ~5.6 eV that could be originated from a further excitation channel, probably through an excitation transfer. Further supports to the GLPC generation by irradiation arise from the temperature investigations of the emission of the induced GLPC. In fact, they have revealed: that the presence of non-radiative channels, connecting the S1 and T1

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states with the ground one, can be neglected as in the native GLPC; that the singlet-singlet transition rate and the activation energy barrier of the ISC are very similar to those of the native GLPC; that the pre-exponential factor of the Arrhenius law, describing the ISC, is similar to that of the native GLPC. In addition, the generation of GLPC is also proved by the experimental detection of the H(II) paramagnetic defects, which are generated by the reaction of GLPC with an H atom. We note that the separation between the two EPR lines of the H(II) defects induced in sample B0 is equal to that of the H(II) generated by the reaction of an H atom with native GLPC, whereas the shape of the resonance line at higher magnetic field shows a small difference. Finally, it is important to note that the GLPC have been induced also in the HD sample (not produced at the Department of Physical Chemistry of the University of Pavia) and in PCVD material. As regard the HD sample, the induced concentration is (1.5 ± 0.6) x 1015 defects/cm3 at the dose of ~ 300 kGy. This low concentration and the absorption activity at ~4.3 eV allow to detect only the β band, but the GLPC generation is confirmed by the presence, in the EPR spectra, from the dose of ~100 kGy, of the H(II) signal, whose intensity at ~ 300 kGy reveals a concentration of ~ 8 x 1014 defects/cm3.

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5.2. Dose Dependence of the Induced Point Defects in Sample B0 The GLPC growth as a function of the irradiation dose has been firstly explored in the sol-gel samples. As shown in figure 5.12a, the GLPC concentration, in the range explored 105-107 Gy, features a linear growth up to ~5 MGy and then, in spite of a doubled dose, it seems to reach a limit value. The linear growth kinetic reported in figure 5.12a evidences that, in the range 105-107 Gy, the generation mechanism overcomes the possible destruction ones. In analogy with creation of the twofold coordinated Si by γ irradiation [61,64], it can be suggested that the GLPC are generated by displacing oxygen atoms from the normal bonding configuration. Actually, a difference in the generation mechanisms emerges, since the GLPC show a growth typical of creation from precursors, with a linear dose dependence at low doses and a limit concentration value at higher doses, whereas the twofold coordinated Si has a power law dependence on dose compatible with the generation from regular sites of the matrix [115]. Figure 5.12b illustrates the H(II) concentration as a function of the dose: we note that the H(II) amount increases linearly up to 5 MGy and then it shows a decrease at the last irradiation dose. The first part of the growth is compatible with the growth found for the GLPC on the basis of the connection between these two types of defects. On the other hand, the reason of the H(II) decrease at high dose is not clear and can suggest a more complex relation between the generation by irradiation of the GLPC and the H(II), which will be confirmed by other data reported in the following.

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Figure 5.12. a) Concentration of the induced GLPC (●); b) concentration of the induced H (II) (●); c) concentration of the induced Ge(1) (○) and fitting curve (▬); concentration of the induced E‘Ge (■).

In figure 5.12c, we report the Ge(1) concentration as a function of the dose, together with the best-fit curve obtained using the law A(1- e-B x); the best-fit parameters are A=(1.3  0.4) x 1017 defects/cm3 and B=(3.1  1.2) x 10-4 Gy-1. On the other hand, as shown in figure 5.12d, in the B0 sample also the E‘Ge creation is observed. This defect growth continues up to the maximum dose of 10 MGy without a limit value, as in other samples. In this respect, we guess that no simple connection between E‘Ge and induced GLPC exists.

5.3. Comparison of the γ and the β Irradiations In this section a comparison between the γ and β ray irradiation effects is presented, with particular attention to the induced GLPC and to the H(II) defects. In details, we have irradiated the samples E1 and E5. The γ irradiation were performed at the IGS3 irradiator of the Nuclear Engineering Department of the University of Palermo and at the SCK-CEN (Mol, Belgium) facility, whereas the β ray irradiation were carried out at the National Institute for Laser, Plasma and Radiation Physics (Magurele, Romania). The concentrations of the induced Ge(1) as a function of the irradiation dose are reported in figure 5.13a. From the data acquired for the γ irradiated samples we observe that the Ge(1)

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concentration grows linearly and then it reaches a limit value. The data regarding the β irradiated samples show that there are not significant differences in the concentrations of induced Ge(1) with respect to those measured for the γ irradiated samples. 18

18

10

a E'Ge Conc.(Defects/cm )

17

3

3

Ge(1) Conc. (Defects/cm )

10 10

16

10

15

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E1- Irrad. E1- Irrad. E5- Irrad. E5- Irrad.

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Dose (Gray)

In figure 5.13b, we report the concentrations of the E‘Ge defects induced by irradiation in the samples E1 and E5. The comparison between the γ and the β ray induced concentrations of E‘Ge defects shows that also in this case there are not significant differences between the two types of irradiation. Moreover, we remark that in both materials no significant differences of E‘Si concentrations (not shown) induced by similar doses of γ or β irradiation have been evidenced.

17

10

E1- Irrad. E1- Irrad. E5- Irrad. E5- Irrad.

3

H(II)-Conc. (Defects/cm )

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Figure 5.13. a) Concentrations of the Ge(1) point defects induced by γ (●) and β (○) irradiation in sample E1, and those induced by γ (■) and β (□) irradiation in sample E5; b) concentrations of the E‘Ge point defects induced by γ (●) and β (○) irradiation in sample E1, and those induced by γ (■) and β (□) irradiation in sample E5.

16

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4

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5

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6

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7

10

8

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Dose (Gray)

Figure 5.14. Concentrations of the H(II) point defects induced by β (○) and γ (●) radiation in sample E1, and those induced by β (□) and γ (■) radiation in sample E5.

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In addition to these types of paramagnetic defects, starting from the dose of ~ 105 Gy we observed the generation of the H(II) point defects. We remark that no particular line shape differences have been observed in the spectra acquired for the β and γ irradiated samples. In particular, the separation between the doublet of the H(II) resonance is ~120 Gauss and the spectral features of the EPR lines in β and γ irradiated samples are similar. The concentrations of the H(II) defects generated in the materials E1 and E5 by γ and β irradiations are reported in figure 5.14. In sample E1, the induced H(II) defect concentration increases with increasing the accumulated dose and, apart from the first one, the γ ray induced concentration is higher than that produced by β ray irradiation. A similar difference is observed in sample E5, where we note that the induced amount of H(II) appears almost independent on the dose, but γ rays induce more defects than β rays. Before to present the data regarding the induced concentration of GLPC we briefly illustrate the variation in the OA spectra of the employed samples. In figure 5.15a we report the experimental OA spectra acquired for the material E1 before any type of irradiation and those recorded after γ and β ray expositions. In the post irradiation spectra, we note the presence of various induced features and, by comparison of the spectra recorded at the dose of ~1 MGy, we can guess that the two irradiation types induce the same OA activities. Figure 5.15b shows the OA spectra acquired for sample E5 before and after irradiations at the dose of 1.4 MGy (γ irradiated sample) and of 1.1 MGy (β irradiated sample). Again, we observe similarities in the spectra. It is worth to note that the absorption features observed are in agreement with the formation of Ge(1), E‘Ge and E‘Si defects.

30

8 a

b E1 (0 Gy) E1 (1 MGy) Irrad E1 (1.1 MGy) Irrad

E5 (0 Gy) E5 (1.4 MGy)  Irrad E5 (1.1 MGy)  Irrad

6 -1

 (cm )

20

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 (cm )

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25

15

4

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2 5 0

0 2

3 4 Energy (eV)

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4 5 Energy (eV)

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Figure 5.15. a) Absorption spectra of sample E1 before irradiation (▬▬), and after a γ ray dose of 1 MGy (▬ ▬) and a β ray dose of 1.1 MGy (▬▬); b) Absorption spectra of sample E5 before irradiation (▬▬), and after a γ ray dose of 1.4 MGy (▬ ▬) and a β ray dose of 1.1 MGy (▬▬).

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E1- Irrad. 1.1MGy E1- Irrad. 1 MGy

Normalized PL

1.0 0.8 0.6 0.4 0.2 0.0 2.8

3.2

3.6 4.0

4.4

4.8

Energy (eV)

Figure 5.16. Photoluminescence spectra of γ irradiated (▬) and β irradiated (○) sample E1 at the dose of 1 and 1.1 MGy, respectively.

Figure 5.16 illustrates the PL spectra under excitation energy at 5.0 eV of the sample E1, β or γ irradiated at the dose of ~1 MGy. The 3.2 eV and the 4.3 eV bands appear with the same features for both irradiations. It is important to remark that the signal acquired for the irradiated samples should be corrected for the re-absorption effects due to not zero absorption coefficient in the region around 4.3 eV. 17

E1- Irrad. E1- Irrad. E5- Irrad. E5- Irrad.

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3

GLPC-Conc. (Defects/cm )

10

16

10

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4

10

5

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7

10

8

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Dose (Gray)

Figure 5.17. Concentrations of the GLPC induced by β (○) and γ (●) radiation in sample E1, and those induced by β (□) and γ (■) radiation in sample E5.

For this reason, we have chosen to obtain the GLPC concentrations from the PL amplitude at 3.2 eV; indeed, at this energy the induced absorption coefficient is always below ~1 cm-1 and the re-absorption effect can be neglected. In figure 5.17, the concentrations of GLPC induced in the materials E1 and E510 by β or by γ irradiation as a function of dose are 10

The GLPC PL signal was not detected in the two samples before the irradiation. The detection threshold for the E1 sample is ~3 x 1014 defects/cm3, its thickness being ~ 1mm, whereas the detection threshold for the E5 sample is ~6 x 1014 defects/cm3, its thickness being ~ 0.5 mm

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reported. We observe that the GLPC concentration increases on increasing the dose in sample E1, with the same sub linear dependence for both types of irradiations. Similarly, the data acquired for the sample E5 show that the GLPC have the same concentration for all the investigated doses and both irradiation types. The data regarding the induced concentrations of Ge(1) and E‘Ge centers as a function of dose (see figure 5.13) suggest that the two employed types of irradiation are able to induce similar amount of defects, confirming the data on B2 sample (reported in figure 3.11). As regards the OA spectra acquired after the irradiation with γ or β ray, we have observed that they are similar in the range up to 6 eV for both investigated samples. The irradiation by β ray is able to induce the GLPC in a sample having none of these defects before irradiation. This effect is compatible with that observed by γ rays and the data indicate that the GLPC are generated with similar concentration values by both γ and β rays. Together with the formation of GLPC, we have observed the growth of H(II) centers by both irradiation types even if the γ induced H(II) are always more than the β ray induced. By considering that the H(II) defects are produced by the reaction of a GLPC with an H atom [1]: O=Ge+H  O=Ge─H, and that no GLPC were detected before irradiation, the total amount of induced GLPC should be the sum of those H-compensated (the H(II), determined by EPR) and the normal GLPC ones (determined by OA and PL). This overall GLPC concentrations (GLPC+H(II)) is reported in figure 5.18. The data evidence that, by increasing the dose, the overall GLPC concentration is larger for γ rays. However, looking at the concentrations of H(II) and GLPC separately (figure 5.14 and figure 5.17) we find that, whereas the concentration of the first ones changes and is always larger by γ rays, the concentration of the latter ones has the same dose dependence for both irradiation types.

Figure 5.18. Sum of the induced concentrations of GLPC optically detected and of the GLPC that have formed H(II) point defects in sample E1 (○) β and γ (●) irradiated and in sample E5 (□) β and γ (■).

We can exclude that the difference in the H(II) content is due to defects annealing during irradiation of the samples because the Ge(1) concentrations observed in the γ and β irradiated samples (Figure 5.13a) are very similar, and because the H(II) and Ge(1) defects start to be annealed at similar temperatures (~ 80 °C), as reported in [1] for H(II) and in [59] for Ge(1).This result can then be interpreted considering that the irradiation induces the H(II)

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through a complex mechanism, in which an H atom released by irradiation diffuses and reacts with a given GLPC site. However, the absence of a simple direct connection between the H(II) and the irradiation induced GLPC is evidenced by the data reported in figures 5.14 and 5.17. In fact, we note that for sample E1, the H(II) content produced by β irradiation is less than the GLPC content, whereas in sample E5 they reach the same amount. The opposite result is found by γ rays; indeed, the GLPC concentration is similar to that of the H(II) in sample E1, whereas in sample E5 the GLPC concentration is less than the H(II) one. These considerations highlight that the formation of H(II) is always present and should involve some features of the materials, also including the H diffusion and its origin, and probably other defects than the GLPC. In particular, since we used γ and β irradiation with comparable dose rates, 80 kGy/h and 120 kGy/h, respectively, it seems that the process is specific of the type of irradiation. Even if further investigation is necessary to evaluate the specific mechanism of H(II) generation and to determine the properties of the H diffusion that could affect the H(II) formation, we can state that the two irradiations induce similar modification of the optical properties and this aspect is relevant for application as waveguide writing by ebeam.

5.4. Thermal Stability of the Induced GLPC and PL Profile Modification

17

10 3

Defects conc. (Defects/cm )

Induced GLPC 0.20

16

Optical Density

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In order to complete the characterization of the irradiation induced GLPC, after the maximum irradiation step (10 MGy) we have investigated their thermal stability. In particular, we investigated the sample B0 subjecting it to thermal treatments in air, and no significant difference was observed in the concentration value during the two initial isothermal treatments at 100 °C and 190 °C up to ~14 hours, respectively. Successively, we have studied the concentration as a function of temperature, performing isochronal treatments (15 minutes at every fixed temperature).

10

Native B 2 B 2 after 10 hours at 415°C

0.15 0.10 0.05 0.00 3

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6

Energy (eV)

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0

100 200 300 400 500 Temperature (°C)

Figure 5.19. Concentration of the induced GLPC (●) as a function of thermal treatment temperature. In the inset we report the optical absorption spectra of a sample containing native GLPC, the spectra have been recorded before (▬) and after (▬) a thermal treatment of 10 hours at 415 °C. Germanium: Properties, Production and Applications : Properties, Production and Applications, Nova Science Publishers, Incorporated, 2011.

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The experimental data are reported in figure 5.19 and they show that the induced GLPC are stable up to ~300 °C and then their concentration decreases. At variance, we have verified that in a sample with native GPLC after 10 hours at 415 °C the defect concentration estimated by OA and PL measurements is unchanged, evidencing a higher thermal stability (data reported in the inset of figure 5.19). 1.6 3.2eV

Native GLPC TT at 415°C

4.3eV

0.8 0.6

=M0

Normalized PL

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b

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/ M0

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3.70

4.25

4.80

5.0 5.2 5.4 Energy (eV)

5.6

Energy (eV)

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Figure 5.20. a) Normalized PL spectrum of native GLPC (▬) and normalized PL spectrum recorded in sample B0 irradiated at 10 MGy after the thermal treatment up to 415 °C (▬), (both spectra are recorded exciting at 5.0 eV); b) Ratio  of 4.3 eV and 3.2 eV PL bands areas for residual (●), and native (○) GLPC as a function of the excitation energy. The errors attributed to these data are ~0.02 and are comparable to the symbols size.

The PL spectrum, due to the defects present after the thermal annealing of the irradiated sample, hereafter defined as residual GLPC, shows some significant modifications in the line shape with respect to that of the native GLPC. In particular, as reported in figure 5.20a, the ratio between the 4.3 eV and the 3.2 eV band is increased, becoming about twice that of the native GLPC. Furthermore, these changes start during the isothermal treatment at 190°C when, as reported in figure 5.19, the estimated concentration is constant; so, even if at 10 MGy the ratio between the PL intensity of the peak of the αE and β bands is ~30% higher than that observed in the native, the thermal treatment seems able to modify the GLPC emission activity. However, it is important to underline the possibility to investigate GLPC defects with emission properties different from those of the native defects. For this reason and to investigate the possibility of a selective annealing of the induced defects, the spectroscopic characteristics of the residual GLPC at 415 °C were studied. In figure 5.20, the ratio  between the zero-th moments (M0) of the bands peaked at ~4.3 eV and at ~3.2 eV is reported for the native GLPC PL activity and for the residual one as a function of the excitation energy. We note that the similar trends observed for  suggest that the residual defects are distributed in energy similarly to the native ones.

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A. Alessi, S. Agnello and F. M. Gelardi 4.6

3.2 E Band Peak (eV)

Residual Native

3.1

 Band FWHM (eV)

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Energy (eV)

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4.8

5.0 5.2 5.4 Energy (eV)

5.6

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Figure 5.21. Peak positions and FWHMs (insets) of αE (a) and β (b) bands for native GLPC (○) and residual (●) ones.

In figure 5.21, the peak positions and the FWHM of emission bands of native and residual GLPC are reported as a function of the excitation energy (Eexc). In both cases, we found that the αE peak position decreases with increasing Eexc, while that of the β band increases. We note that the αE component of residual GLPC has a systematic red shift of ~ 0.04 eV respect to the values observed for the native activity, while for the β band this shift is ~0.01 eV. The data reported in the insets of figure 5.21 show that the FWHM of native and residual bands increases with increasing the excitation energy, even if the residual bands are systematically broader of ~0.04 eV. It can be guessed that, by changing the Eexc, we explore in both systems centers with smaller distance between S1 and S0, and greater distance between T1 and S0, but the defects appear distributed in energy in similar way [19]. By the way, we note that the data on the αE exclude the possibility that a contribution to its intensity comes from the αR band (related to the two fold coordinated Si) [19], since this band is peaked at ~ 4.4 eV, whereas the αE band observed for the residual GLPC is shifted forward energies lower than those of the native ones (see figure 5.21). The found thermal stability for the γ induced GLPC is inferior to that of the native one, and it can be considered a feature of the irradiation products. Even if we have not completely removed the GLPC created by irradiation, the data shown in figure 5.19 evidence that these defects start to be annihilated at about 300°C. Previous studies on thermal annealing of point defects in silica have shown that this temperature of annealing is typical of diffusion limited reactions involving O2 or H2O [62]. The spectral differences are observed from 190°C, suggesting that they probably originate from changes of the defect environment, since the defect concentration is still the same than at room temperature. The detailed study of the PL spectral features of the residual defects carried out after the treatment at 415°C, has shown that the parameter , the peak positions and the FWHMs of the PL bands differ from those of the native defects. Similar dependences on the excitation energy of these parameters are found for the native and the residual defects, suggesting that they have similar distribution in energy. These features contradict the possibility of a selective thermal annealing of induced GLPC. In fact, in that case we should expect more evident changes in the curves reported in

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figure 5.20b and 5.21, localized at given excitation energies corresponding to annihilated or transformed defects. As reported in [19,29], the ratio  is equivalent to the ratio between the fluorescence rate Ks and the ISC rate, KISC. In this frame, it is expected that the modification of  should be due to changes in Ks or KISC or to the presence of non radiative channels from T1 to S0. We have observed that the triplet lifetime changes about 10% from native to residual GLPC, so that modifications in non radiative channels from T1 are negligible and the observed changes of  should have a different origin. To deeply understand the nature of observed differences in the PL profile, the study of the temperature dependence of the overall emission was performed and we will report the data in the following sections.

5.5. Temperature Dependence of the PL Spectra of the Residual GLPC

3.2

PL Intensity (arb.unit.)

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In this section, the study of the dependence on T of the emission, recorded for the residual GLPC present in the sample B0, after the irradiation and the thermal treatment, is presented. For this experiment, we performed the measurements at the laboratory of the Physical and Astronomical Sciences Department of Palermo using the excitation at 5.17 eV of a laser (Vibrant OPOTEK). It is important to remark that also in this experiment we have recorded the PL spectra of a sample containing native GLPC in the same experimental condition. In figure 5.22, we illustrate the spectra recorded at different temperatures (250, 160, 20 K) on the sample B0 containing the residual GLPC. We note that the two bands related to the residual GLPC show two opposite behaviours; in particular, while the αE band amplitude increases, the β band decreases on decreasing the temperature. These two dependencies are similar to those observed, at the same temperatures and experimental conditions, for the native activity and for the bands induced at 5 MGy by γ irradiation.

2.4

1.6

250 K 160 K 20 K Residual

0.8

0.0 2.60

3.15

3.70

4.25

4.80

Energy(eV) Figure 5.22. PL spectra of sample B0 (having residual GLPC) at 250 K (▬), at 160 K (∙∙∙) and at 20 K (▬).

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M0 of PL (arb.units)

3.0

Residual

2.5

M0 of residual  band M0 of residual E band Total M0 of the residual PL

2.0 1.5 1.0 0.5 0.0 0

100 200 300 Temperature (K)

400

Figure 5.23. M0 of the residual β band (●), M0 of the residual αE band (○) and total M0 of the induced emission activity (●). All the spectra have been recorded in Palermo laboratory.

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Also in this case, we have calculated the zero moment of the two emission bands and the total one, indicated by the grey full circles in figure 5.23. These data point out that this quantity is quite independent from T also for the residual GLPC. This independence of the total M0 of the temperature is an important information that permits to apply equations 5.2, 5.3 and 5.4 to the PL activity of the residual GLPC. Before to deeper consider the consequences of these findings, in the next section we will present the data regarding the lifetime of the residual αE band to complete the presentation of the data regarding the temperature dependence of the proprieties of the residual GLPC emission.

5.6. Time Dependence of the Emission of the Residual GLPC In figure 5.24, we illustrate the time decay of the emission intensity at ~4.27 eV, of the GLPC induced at 5MGy and of the residual GLPC at the temperatures of 300 K and of 10 K, the measurements performed at this latter temperature being reported in the inset. The measurements have been performed at the laboratories of the Physical and Astronomical Sciences Department of Palermo and the zero of the time axis has been chosen in correspondence of the end of the laser pulse. At low temperature, the intensity of the emitted light decreases in time in similar way in both samples. In particular, we observe that the lifetime is ~7.5 ns and the decay is almost a single exponential. At variance, at room temperature we find that the intensities of the two investigated systems decrease with different dependencies on time. In particular, the τ obtained by fitting the data with stretching exponential laws, for the induced and for the residual GLPC, are ~5.7 ns and 6.3 ns respectively, with an error of ~ 0.2 ns in their comparison and an absolute error of 0.5 ns, and

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for both case the stretching factor γ is ~0.8511. The data show that at room temperature the lifetime of the residual GLPC is larger than that of the induced GLPC, suggesting a slightly lower value of the intersystem crossing of the residual defects. At the same time, the comparison of the data recorded at low temperature suggests that the radiative rates of the two systems are very similar.

1.0 0.5

ln(I(t)/Imax)

0.5

ln(I(t)/Imax)

0.0 -0.5

T=10K

0.0 -0.5 -1.0 -1.5 -2.0

0

5

10

15

Time (ns)

-1.0 -1.5

Residual 300K Induced 300K

-2.0 -2.5 0

5

10 Time (ns)

15

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Figure 5.24. Natural logarithm of the normalized intensity I(t)at 4.27 eV as function of time recorded for the induced (▬) and for the residual (○) emission at room temperature. In the inset it is reported the logarithm of the normalized I(t) recorded for the induced (▬) and for the residual (○) emission at ~10 K. All measurements have been performed in Palermo laboratory.

5.7. Intersystem Crossing Process of the Residual GLPC The investigation of the total M0 of the emission attributed to the residual GLPC, as a function of the temperature, suggests that we can neglect, as made for the native and the induced GLPC, the effects of the no radiative channels connecting the excited states to the ground one. As a consequence of this finding, as anticipated, we can apply the equations 5.2, 5.3 and 5.4 also to the residual activity. From these equations, using the data on the emission F

decay at low temperature, we can evaluate that the efficiency K R of the S1 → S0 transition of the residual GLPC is ~ 1.3 108 s-1. To investigate the intersystem crossing process of the residual GLPC with respect to that of native defects, we can use the θ (see equation 5.5) values as a function of T and the natural Max logarithm of the normalized values of 1/η ((1/η)/(1/η)MAX)= K ISC / K ISC as a function of 1000/T. The data reported in figure 5.25a, regarding the θ values evaluated for the residual GLPC, indicate that the pre-exponential factor of the residual GLPC is ~0.6 of the native, as 11

The differences in the values of τ recorded at 300 K at HASYLAB (figure 5.7) and in Palermo (figure 5.24) have to be ascribed to the different excitation pulse width and to the different dead-time of the two experimental setups.

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evidenced by the experimental points in the range 150-300K. At variance, the data of figure 5.25b and the zoom at the temperatures higher than 140 K (inset of figure 5.25b) indicate that the KISC of the residual GLPC has similar dependence on temperature with respect to the native defects, and also in this case the activation barrier is ~ 100 meV. Finally, we note that θ changes within the range 0.4-0.6 if we calculate it as a function of the excitation energy, using the data of the η parameter of native and of residual GLPC (data reported in figure 5.20b). This finding suggests that the observed changes are almost independent from Eexc and that the observed changes involve the overall ensemble of defects.

a

2 Res

2

b

Nat

Native Residual

]) Max

ln([KISC/K

])

1

0

ISC

Max

ln([KISC/K

Res

2 KISC/KISC

Native

KISC/KISC

ISC

3

-2

0

-2

-4 3.0 3.5 4.0 4.5 5.0 5.5 6.0 -1 1000/T (1K )

-4

0 0

100 200 300 Temperature (K)

400

0

10 20 30 -1 1000/T (1K )

40

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Figure 5.25. a) θ values evaluated from the PL spectra for the residual GLPC (●); b) Natural logarithm of the normalized values of KISC as a function of 1000/T evaluated for the native (●) and for the induced (●) GLPC, in the inset a zoom relative to T>140 K is reported.

As above mentioned, the pre-exponential factor depends on spin-orbit coupling and on defect structure. As regards the spin-orbit coupling, in the residual GLPC it can be considered unchanged because the lifetime of the radiative decay from T1 to S0 (β emission band), determined by the spin-orbit coupling, is ~ 100 μs. As a consequence, the change of the A factor in the residual defects can be considered the result of changes in the entropic contribution or in some structural parameter. In contrast, the similarity of the activation barrier ΔU of residual defects, with respect to that of the native GLPC, suggests that they are equally sensible to their environments.

CONCLUSION One of the main results consists in highlighting the possibility to induce the GLPC using ionizing radiation. This is a new finding, since until now this type of defect was induced during the synthesis phase or in H2 loaded sample by UV irradiation. The generation of the GLPC in the present work has been observed both in sol-gel and in PCVD samples. The generation of the GLPC in a PCVD sample, with no detectable OH content, indicates that the

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presence of the hydrogen is not ―condicio sine qua non‖ for the generation of the GLPC, but that this latter is related to some intrinsic process. The reported data show that the induced GLPC have properties similar to the native ones (defects generated during the preparation of the samples). In fact, for the induced GLPC we F

P

have found that the K R (S1→S0 emission rate), K R (T1→S0 emission rate) and K ISC (rate of the intersystem crossing from S1 to T1) are similar to those of the native defects, and that the effects of other non-radiative processes can be neglected. Furthermore, we have observed that the induced GLPC can react with hydrogen to generate the H(II) defects with spectroscopic features close to those of the H(II) defects generated by the H reaction with native GLPC. The finding of a range of doses in which GLPC concentration increases has been found. This observation suggests that the GLPC generation processes overcome the destruction or the conversion ones, induced by the same irradiation. As regards the generation mechanisms we can suggest, in analogy with the generation of the twofold coordinated Si, that the GLPC are generated by tetracoordinated Ge, even if other generation channels or multi-step processes can not be excluded and could represent the object of future experiments. We have found that, unlike the native GLPC, the induced GLPC start to be thermally annealed at ~300 °C. Basing on the studies regarding the O2 and H2O diffusion in silica, we can suggest that the different thermal stability of the induced GLPC is related to the diffusion, thermally activated, and the reaction with these molecules produced during the irradiation. Together with the generation of the GLPC, we have observed the possibility to obtain GLPC with modified optical properties. These defects have been called residual, and the main difference with respect to the native GLPC is constituted by the decrease of the preexponential factor of the Arrhenius law, which describes the temperature dependence of F

intersystem crossing process. On the contrary, the activation barrier of the ISC, the K R and P

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the K R are close to the analogous parameters of native defects. The comparison between the γ and β irradiation effects has pointed out that the two types of irradiations induce similar GLPC concentrations. At variance, the H(II) concentrations are higher in the γ irradiated samples, and their dependence on both the radiation dose and the sample type shows a complex relation between the GLPC generation and the H(II) creation. Even if some causes of this difference have been excluded, a deeper understanding of this effect requires further experiments and, at present, can be related to the hydrogen release and diffusion. Moving to the other irradiation effects, the investigation of the paramagnetic point defects induced by the irradiation, in samples doped with different levels of Ge, has evidenced a dependence on the Ge content of the EPR signals of the Ge(1) and of the Ge(2) defects, unknown up until now. This dependence on the Ge content is interpreted on the basis of the glass network modifications induced by the doping. These modifications have been already reported in literature using different experimental techniques and in particular by the Raman spectroscopy. The relation between the EPR variations and the network changes appears corroborated by the fact that both becomes relevant, starting from the doping level of ~ 1% wt. However we remark that a deeper comprehension of this topic requires further studies. This aspect, together with the detailed studies of the optical properties of the Ge related point defects as a function of the doping level, is one of the most important fields to be considered in the future.

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As regards the generation mechanism of the Ge(1), Ge(2) and E‘Ge defects, our data do not evidence clear correlations between the different types of defects, but have allowed us to find general features of their generation. In fact, for the Ge(1) we have observed the possibility to describe the dose dependence through the competition between a generation and a destruction term. In particular, we have evidenced that the generation probability is inversely proportional to the Ge content, whereas a destruction probability is related to the Ge content by a more complicated law. In addition, the data indicated that, for low doping levels (0.01% by weight), the oxygen deficiency has a negative effect on the Ge(1) generation, the destruction probability being higher than those of other non oxygen deficient samples, whereas high GLPC content can increase the generation probability. As regards the Ge(2), our data support the structural model of the ionized GLPC, since they are observed in high concentration in samples with high GLPC contents even if their Ge doping level is low. In addition, the Ge(2) are not observed in samples with high Ge content but with undetectable GLPC concentration. For the E‘Ge, together with the lack of a clear relation with the initial GLPC content, we have observed the presence of a generation channel almost independent of the doping level. Our study has evidenced also that all these irradiation effects are very similar for both γ and β rays. On the front of the optical features, our data agree with the assignment of the induced 5.8 eV optical absorption band to the Ge(1), and evidence that the Ge(2) does not affect significantly the absorption in this spectral region. In the context of the relation between the optical induced changes and the generation of the paramagnetic point defects, our data have shown a linear correlation between the induced changes of the refractive index and the concentration of the Ge(1). This latter finding is relevant for the explanation of part of the photosensitivity of Ge doped silica and its possible connection to specific point defects. Basing on the correlation between the refractive index changes Δn and the Ge(1) concentrations, and on the upper limit expected for such a concentration, we expect that the maximum Δn due to Ge(1) is of the order of 10-4 and unlikely it could reach 10-3. As the laser irradiation is widely used in technological applications of the Ge doped silica (Fiber Bragg Grating and Second Harmonic Generation), the studies regarding the possibility to induce GLPC using laser irradiation, and the investigation of the radiation effects on samples with higher Ge doping, appear as interesting future extensions of this work. Another argument of research could be the possible generation of Ge(2), from the induced or from the residual GLPC, by using laser sources.

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In: Germanium: Properties, Production and Applications ISBN 978-1-61209-205-8 Editor: Regina V. Germanno © 2012 Nova Science Publishers, Inc.

Chapter 3

GERMANIUM ENCAGED FULLERENE-SYNTHESIS, EXTRACTION, THEORETICAL CALCULATION AND THEIR POSSIBLE APPLICATION Debmalya Roya, B. Shastria, C. N. Ramachandranb, B. K. Mishrab, K. Mukhopadhyaya, N. Sathyamurthyb,c and K. U. Bhasker Raoa a

Defence Materials and Stores Research & Development Establishment (DMSRDE), Kanpur, India b Department of Chemistry, Indian Institute of Technology Kanpur, Kanpur, India c Indian Institute of Science Education and Research (IISER) Mohali, Chandigarh, India

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1. ABSTRACT Fullerenes have unique cage-like structures, which create a typical inner space. A range of metal atoms can be trapped inside this space to form endohedral metallofullerenes. These new materials exhibit potential applications as new type of superconductors, organic ferromagnets, nonlinear optical materials, functional molecular devices, magnetic resonance imaging agents, energy conversion devices and biological tracing agents, etc. A great deal of experimental and theoretical studies have been focused on endohedral metallofullerenes of group III metals, most of the lanthanide series elements, group II metals, alkali metals and some tetravalent metals. However, no experimental and very few theoretical studies have so far been carried out on Ge which has a comparable atomic size and weight to that of metal ions inserted earlier in the fullerene cage. The atomic radius of Ge is slightly smaller than other reported endohedral metal atoms. However, it is big enough to get trapped inside the fullerene cage. In this chapter we describe the process for encapsulating Ge in a fullerene cage by arcing method. Solvent extraction and then exploiting the differential solubility of the metallofullerene and empty fullerenes in nitrogenous solvent were used to isolate the metallofullerene 

Corresponding author. Tel.: +91 512 2451759-78; fax: +91 512 2404774/+91 512 2450404 E-mail address: [email protected] (Dr. Debmalya Roy). Germanium: Properties, Production and Applications : Properties, Production and Applications, Nova Science Publishers, Incorporated, 2011.

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Debmalya Roy, B. Shastri, C. N. Ramachandran et al. from the starting carbon soot. The insertion of Ge inside the fullerene was proven by different experimental techniques. Confined metals inside the fullerene cage strongly interact with the bonding and antibonding orbitals of fullerene and drastically alter the electrical and conduction properties of pristine fullerene. Our theoretical studies suggest that the electronic properties of fullerene could be extensively modified by encapsulation of Ge. Density functional theoretical calculations using B3LYP parametrization and 6-31G* basis set suggest that Ge as well as Ge2 can be trapped inside C60. Rotational barrier calculations for Ge2 inside C60 indicate a cross over between singlet and triplet states of the complex with a variation in the orientation angle. The energy gap between the HOMO and LUMO of C60 is reduced significantly by the encapsulation of the guest species. Recently, the development of light weight, flexible organic solar cells utilizing nanostructured materials has attracted a lot of attention. In the spectrum of solar radiation, 5% of the total spectral wavelengths is from UV whereas 46% is from visible and 49% is from near IR region. Ge has a fairly good amount of absorption in the near IR region. Therefore a range of absorption from UV, visible and NIR region could be achieved which leads to harvest more photons from sunlight and makes this metallofullerene potentially more efficient for photovoltaic application.

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2. INTRODUCTION Dmitri Mendeleev predicted the existence of an element in the IVa column of his much celebrated periodic table between the known elements of silicon and tin, which he designated as unknown element ―eka-silicon‖ [1]. In 1886 Clemens Winkler, a renowned inorganic chemist at the Bergakademie, Freiberg, Germany discovered the ―missing‖ element in the silver-rich mineral argyrodite and named it as Germanium [2-3]. The birth of ―Semiconductor Age,‖ the successor to the Stone-, Bronze- and Iron Ages was soon initiated by the demonstration of the germanium point contact transistor in 1947 by J.Bardeen and W. Brattain followed shortly by the invention of the germanium junction transistor by W. Shockley [4, 5]. Detailed account of all the fascinating developments associated with this unusual element is beyond the scope of this chapter. However, many good references [6-10] and other chapters of this book could guide the reader to an exciting story of the transition of germanium from the ―Physics of Dirt‖ to the beginning of modern semiconductor physics and solid state electronics.

Figure 1. Pencil sketch of C.A. Winkler and D.I. Mendeleev. Germanium: Properties, Production and Applications : Properties, Production and Applications, Nova Science Publishers, Incorporated, 2011.

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Fullerene C60 was discovered in 1985 in the laboratory of Prof. Smalley of Rice University, Houston, USA and the authors published their findings in Nature [11]. They named C60 as Buckminsterfullerene due to the similarity with the geodesic structure which has been widely credited to R. Buckminster Fuller [12]. Robert F Curl, Richard E Smalley and Harold W Kroto were awarded Nobel Prize in chemistry for their discovery in the year 1996 [13]. Soon after the discovery of C60, the physicists, chemists and materials scientists from all over the world jumped into this field and discovered an entire family of "buckybabies" with 32 carbon atoms (C32) to giant fullerenes with 960 carbon atoms (C960) [14-17]. C60 has a unique shape. It has 12 pentagons that are required to transform a network into a spheroid, as demonstrated by the 18th century Swiss mathematician Leonhard Euler and the remaining carbon atoms are in 20 hexagons to form highly symmetrical truncated icosahedron geometry. In this structure, none of the pentagons make contact with each other and they obey the so-called isolated pentagon rule (IPR). C70 has 25 hexagons and its shape is more like a rugby ball. Giant fullerenes generally take on a pentagonal shape where as the smaller fullerenes look like asteroids. The unique structure-property relationship and the enormous potential applications of this most amazing new class of molecules were eventually revealed by many experimentations and theoretical investigations and in 1991, Science magazine named the fullerene "molecule of the year‖ [12, 18-22].

Figure 2. The corrannulene structure: Building blocks for C60.

Ability to synthesize C60 in pure and macroscopic quantities opened up a plethora of opportunities to develop an exciting new arena of ―three-dimensional‖ chemistry of spherical and polyfunctional molecules. To tailor the position and the nature of functional group on the fullerene moiety for technological applications, a clear understanding of the structureproperty relationship of fullerene is utmost important. C60 behaves as an electron deficient strained polyalkene and it has soon become an essential building block in organic chemistry [12, 19]. One of the properties which make the C60 fullerene unique is the 0.07 Å difference in the bondlength at the junctions of two hexagons (6-6 bonds) when compared to that of a hexagon and a pentagon (5-6 bonds). The lowest energy Kekulé structure of C60 can be considered a sphere built up of fused [5]radialene and cyclohexatriene units with a complete delocalization of the conjugated π electrons and therefore it does not usually follow the chemistry of an aromatic compound [23, 24]. The highly pyramidalized carbon atoms in spherical C60 cause a large amount of strain within the molecule. C60 has a low-lying, triplydegenerate lowest unoccupied molecular orbitals (LUMOs) and fivefold-degenerate highest occupied molecular orbitals (HOMOs) which makes it electronegative and thus it is difficult to oxidize C60 but easy to reduce. Due to the orbital rehybridization of the sp² with the π

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orbitals in C60, a new set of sp2.27 orbital is generated and the lobes with predominately p characters extended further outside the C60 topography and make it more electronegative [2527]. All these special properties of C60 result in the intriguing and characteristic features of the fullerene chemistry and some of the trademark reactions of fullerene are enlisted in Figure 3.

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Figure 3. Schematic representation of the characteristic chemical reactivity of C60.

There has been a debate among the scientific community after the discovery of C60 about its cage structure as no experimental evidence was put forward to convincingly prove the spherical shape and empty space inside the carbon cage. The Smalley research group from Rice University synthesized the first lanthanum C60 complex by laser vaporization of a LaCl2impregnated graphite rod [28]. They found a series of Cn+ and LaCn+ ionic species with LaC60+ as a ―magic number‖ ion in the mass spectrum and concluded that one La atom was encaged within the hollow space of C60. It was also been reported [29] that LaC60+ ions do not react with H2, O2, NO and NH3, which further confirmed the fact that reactive La metal atom is protected from the surrounding gases and is indeed trapped inside the C60 cage. This was the first experimental evidence of the empty space inside the fullerene carbon cage and gave birth to the concept of endohedral metallofullerene. The symbol ―@‖ is used to represents the fact that atom(s) placed to the left of the @ symbol is encaged inside the fullerene [30]. For example, if a metal M is encaged inside C60, then it is written as M@C60. However, the IUPAC nomenclature of endohedral metallofullerene is different from the conventional and popular representation of M@C60. The standard IUPAC nomenclature of the La@C60, for example is, ―[60] fullerene-incar-lanthanum‖ and is to be written iLaC60 [31]. The confined metal atom inside the nanometre size fullerene interacts with the frontier molecular orbitals of the fullerene and gives rise to the novel physical and chemical properties. Endohedral metallofullerenes are very important for their potential applications as

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the new types of superconductors, organic ferromagnets, nonlinear optical materials, functional molecular devices, magnetic resonance imaging agents, as electron acceptor materials and biological tracing agents, etc., which will have great influence over electronics, optics, electromagnetism, and medicine [32-35]. Despite the huge potentials, the applications of metallofullerenes are still in laboratory scale. This is mainly due to the difficulty in preparing substantial amount of pure endohedral metallofullerenes. Endohedral metallofullerenes can be prepared by several techniques which are in principle identical to the production of empty fullerenes involving the generation of a carbon-rich vapour or plasma in inert gas atmosphere [32, 33]. Two methods have been extensively used for preparing macroscopic amounts of metallofullerenes. One is the laser furnace method, which incorporates laser vaporization of composite rods under high temperature and the second is DC electric arc discharge of metal/graphite composite rods used as positive electrodes. Both methods produce simultaneously a mixture of empty or hollow fullerenes (C60, C70, C76, C78, C84, etc.) in addition to a small amount of metallofullerenes and other carbonaceous impurities [36].

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Figure 4. Schematic illustration of fullerene/endohedral metallofullerene production.

Isolation of endohedral metallofullerenes from the soot is generally inefficient. The yield is normally below 1.5 % of the original soot [32, 33]. It must be emphasized that the isolation of metallofullerenes from the soot is a very time-consuming procedure and the development of advanced methods for the synthesis and isolation of metallofullerene is essential. Difficulties associated with the isolation of substantial amount of pure metallofullerene hinder a thorough investigation of the properties of metallofullerenes. In this context, theoretical studies of endohedral metallofullerenes have made an important contribution and the symmetry of the cage, the position of metal atom(s) inside the cage, dynamics of metal atom(s), the number of electron transfer between the metal atom(s) and the fullerene cage etc. have been studied using computer simulation and algorithms [37, 38]. Theoretical studies on the effect of encapsulation of iso-electronic species like F-, He, Ne, Na+, Mg2+ and Al3+ in C60 showed that the guest species were located at the centre of the cage. However, for alkali metals and ions, the stabilization of these guest species are reported at an off-centre position inside the fullerene cage [39, 40]. The encapsulation of molecular species inside the fullerene cage has also been investigated. The encapsulation of small diatomic molecules e.g. H2, N2, CO, HF, LiH and LiF showed that the C60 cage acts as a polarizable sphere and that it stabilizes polar molecules and destabilizes nonpolar molecules [41]. A small degree of van der Waals interaction between the host and the guest molecules introduces an attractive or stabilizing inphase, while a larger overlap produces a repulsive or destabilizing interaction [42]. The structure and stability of small water clusters inside a nonpolar environment was

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examined taking C60 as a means of confinement and it has shown that water clusters assume unusual geometries inside C60, breaking the hydrogen bonds between them [43]. Confinement effects on iso-electronic molecules like HF, H2O, NH3 and CH4 inside C60 have been investigated and it was found that these molecules are stable inside the cage [44]. The growth mechanism of metallofullerenes was studied using molecular dynamic simulation methods. To simulate the basic reaction process occurred in the arc-discharge or the laser vaporization method, the clustering process of randomly located isolated carbon atoms and metals were considered as basic building blocks for formation of metallofullerene at a specific temperature and density conditions [45]. The classical molecular dynamics simulations with the Brenner potential for carbon-carbon interaction and the metal-carbon potentials due to the nearly covalent bonding term and the Columbic potential term for the charge transfer from the metal atom to the carbon clusters can reproduce the important precursors of the growth process [36, 46].

Figure 5. The geometry of water clusters in the gas phase and inside the confines of the fullerene cage.

Macroscopic quantities of endohedral metallofullerenes were first produced by the Rice university group in 1991 [30]. They used high-temperature laser vaporization of La2O3/graphite composite rods and the corresponding contact arc technique to produce various sizes of lanthanofullerenes. Much to the surprise, only the La@C82 fullerene was extracted in solvent even though La@C60 and La@C70 were also seen in the mass spectra of the sublimed film from soot. Most endohedral metallofullerenes isolated to date have cages of 80 carbons or greater with one or two metal atoms inside and the most common being C82 monometallofullerenes [47, 48]. The periodic table of the trapped species inside the fullerene cage is shown in Table 1 [49].

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Table 1. Shaded areas of the periodic table represent the elements which are successfully encapsulated in fullerene cages IA

IIA

IIIB

IVB

VB

VIB

VIIB

VIII

VIII

VIII

IB

IIB

IIIA

IVA

VA

VIA

VIIA

H

0 He

Be

B

C

N

O

F

Ne

Na

Mg

Al

Si

P

S

Cl

Ar

K

Ca

Sc

Ti

V

Cr

Mn

Fe

Co

Ni

Cu

Zn

Ga

Ge

As

Se

Br

Kr

Rb

Sr

Y

Zr

Nb

Mo

Tc

Ru

Rh

Pd

Aq

Cd

In

Sn

Sb

Te

I

Xe

Cs

Ba

La*

Hf

Ta

W

Re

Os

Ir

Pt

Au

Hg

Tl

Pb

Bi

Po

At

Rn

Fr

Ra

Ac**

Lanthanides *

Ce

Pr

Nd

Pm

Sm

Eu

Gd

Tb

Dy

Ho

Er

Tm

Yb

Lu

Actinides **

Th

Pa

U

Np

Pu

Am

Cm

Bk

Cf

Es

Fm

Md

No

Lr

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Li

n?docID=3021747.

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Smaller endometallofullerenes (C60, C70) are almost insoluble in common organic solvents mainly due to their unusual reactivity towards air and moisture and therefore very difficult to extract by solvent [50]. Metal encapsulated C60 are sparingly soluble in amine bases such as aniline and pyridine by forming weak complexes with their non bonding electrons. C82 endohedral metallofullerenes are comparatively more soluble in common organic solvents and thus more abundant in the isolated endometallofullerene. Empty cage C72, C74, C76 etc, which have only a limited number of isolated pentagon rule (IPR) satisfying cage isomers, could not been isolated successfully by solvent extraction methods due to their unusually low stability. However, contrary to expectation, La@C72 or La2@C72, La@C74 or La2@C74 and La@C76 or La2@C76 could be extractable by the organic solvents and therefore in agreement with the hypothesis of metal mediated stabilization of the smaller cages (e.g., C70-C76) [51-53]. A number of metal atoms have been trapped inside the fullerene cage and their physical and chemical properties have been investigated [19, 32, 33, 45, 50]. The metallofullerenes are readily produced out of group II and III metal atoms, lanthanide group and some tetravalent and alkali metal atoms. Germanium, an intrinsic semiconductor has not been tried experimentally for endohedral encapsulation, although it has comparable physical and chemical properties to that of the other reported endohedral metal atoms (Table 2) [54, 55]. Table 2. Comparison of physical properties of other endohedral metal atoms with germanium Calcium (Ca) 40.08

Scandium (Sc) 44.95

Zirconium (Zr) 91.22

Potassium (K) 39.09

Lanthanum (La) 138.90

Germaniu m (Ge) 72.61

Electronic configuration Atomic radius (Å) Melting point (0C) Electronegativity

[Ar]4s2

[Ar]4s23d1

[Kr]5s24d2

[Ar]4s1

[Xe]6s25d1

1.80

1.60

1.55

2.20

1.95

[Ar]4s23d104 p2 1.25

842.00

1541.00

1855.00

63.38

920.00

938.25

1.00

1.36

1.33

0.82

1.10

2.01

1st Ionization potential (eV) 2nd Ionization potential (eV) 3rd Ionization potential (eV) Density at 298 K (g/cm3) Specific heat (STP) (J/gK)

6.11

6.56

6.63

4.34

5.57

7.90

11.87

12.80

13.13

31.63

11.06

15.93

50.91

24.75

22.99

45.80

19.17

34.22

1.54

2.99

6.52

0.89

6.15

5.32

0.65

0.57

0.28

0.76

0.195

0.32

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Atomic weight

Group II-IV semiconductor quantum dots exhibit tremendous enhanced properties in electronic devices. Ge in the bulk shows indirect transition. However, it shows promising

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properties in nanocrystals due to the direct optical band gap transition for the breakage of translational symmetry [56, 57]. Recombination process in the direct band gap transition does not involve phonons and hence the lifetime of excitons is reduced drastically. Synthesis of Ge nanocrystals with the desired size and shape is still an open challenge as the lack of surface dipoles weakens the binding of surfactant to the nanoparticles during synthesis, making the reaction extremely difficult to control [58]. Ge encapsulated fullerenes could be an alternative to Ge nanocrystals as they are also expected to show a direct band gap transition. The bohr radius of Ge is large as compared to that of Si. Therefore, prominent quantum confinement effect is expected for the encaged Ge inside the nanometre size cage of fullerene [59].

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3. OVERVIEW In this chapter we first discuss the methodology adopted for the synthesis of Ge endohedral metallofullerene and then discuss the modifications done in the standard synthetic method to encapsulate Ge, which has an electronic configuration that is altogether different from that of the group II and III metal atoms, lanthanide group, tetravalent and alkali metal atoms. Extraction and purification of trace amounts of Ge metallofullerene from a large quantity of different types of carbonaceous species is a challenging task. We have thoroughly discussed in this chapter all the procedures followed for the extraction and purification of Ge metallofullerene. To conclusively prove that Ge metal is trapped inside the fullerene cage, the following spectroscopic techniques were used: ultra violet-visible (UV-VIS) absorption spectroscopy, fast-atom bombardment (FAB) and matrix assisted laser desorption ionizationtime of flight (MALDI-TOF) mass spectrometry, Fourier transform infrared (FT-IR) spectrometry, nuclear magnetic resonance (NMR) spectrometry, energy-dispersive X-Ray (EDX) spectrometry and X-ray photoelectron spectrometry (XPS). The mass spectrometric analysis was performed by FAB mass and MALDI-TOF techniques. The FAB mass spectra were recorded on a JEOL SX 102/DA-6000 Mass Spectrometer/Data System with argon /xenon as the FAB gas. The acceleration voltage was 10 kV and the spectra were recorded at room temperature. M-nitrobenzyl alcohol was used as the matrix. MALDI-TOF spectra were recorded in a Bruker FLEX-PC2 ultraflex TOF mass spectrometer. Measurements were carried out with 3, 5-dimethoxy-4-hydroxycinnamic acid as the matrix using laser pulses of different wavelengths. XPS was recorded on a Perkin Elmer PHI 1257 X-ray Photo Electron Spectrometer. Ge and carbon core level experiments were carried out using Al Kα (1486.6 eV photon source) at different sputtering times (1x10-6 vacuum, 4 kV, 15 mA). NMR spectra were recorded on a Bruker 400MHz FT-NMR spectrometer. FT-IR spectrum was recorded below 400 cm-1 using CsBr/ CsI crystal discs using the Bruker make (Model no.: Vector 22) spectrophotometer. The spectra were obtained by co-addition of 100 scans with a resolution of 1 cm−1 in the range. The EDX spectrum was recorded on a Carl Zeiss SUPRA 40VP NTS scanning electron microscope. The UV-VIS spectra were recorded on a Varian CARY 500 UV-VIS-NIR spectrometer in spectroscopic grade DMF solvent using DMF as the standard reference. Geometry optimization for Ge2, C60, Ge@C60 and Ge2@C60 was carried out by the density functional theoretical method using B3LYP parametrization and the 6-31G* basis set using Gaussian03 suite of programs [60]. The optimizations were carried out by setting the

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root mean square of the force at the default value of 0.0003 au except for the triplet state of Ge2@C60, for which the value of 0.0017 au was used for convergence. Vibrational frequencies were computed for the optimized structures to distinguish between the saddle points and the minima. Time-dependent density functional theoretic calculations were carried out of those species using the same functional and the basis set to study the optical absorption of these complexes. Natural bond orbital (NBO) analysis [61] was also carried out to study the interaction between the guest species and the host cage. The stabilization energy (ΔEstab) of the endohedral complex was calculated by the supermolecule approach as ΔEstab = Ecomplex – Ecage- Eguest The ground state of Ge is a triplet (3P0) with the electronic configuration 1s 2s22p63s23p63d104s24p2. However, ESR experiments indicated that Ge metallofullerene is diamagnetic. For a photovoltaic application of Ge metallofullerene, a photoactive layer was form using the metallofullerene and regio regular poly 3-hexyl thiophene (rr-P3HT). rr-P3HT was purchased from Sigma–Aldrich Chemical and was used as received. For properties and characterization of rr-P3HT, we followed the standard procedure. Nanocomposite of rr-P3HT and Ge endometallofullerene was assembled from chlorobenzene with a desired weight percentage of 1 to 10. The mixture was kept overnight at 750C and a stream of N2 gas was flown over the sample to evaporate the organic solvent. The nanocomposite was finally mixed thoroughly using a ball-milling machine at 200 rpm for 30 min. Comparative resistivity was studied on the pellets made out of rr-P3HT and rr-P3HT with one weight percentage of Ge endometallofullerene. The electrical resistance of the samples was measured using four-probe low-temperature-resistance measurements in the temperature range of 500–10 K. Keithley‘s current source model-220 and a nano-voltmeter model 2182 were used to record the resistance at different temperatures. The samples were cooled down by a closed-cycle refrigerator (CTI Cryogenics make). The ohmic contacts were made by silver paste. Comparative photoluminescence (PL) of the thin films of rr-P3HT and different weight percentages of Ge endometallofullerene was recorded at λex= 480 nm. Thin films for PL measurement were prepared by drop casting of the samples homogeneously dispersed in acetone on quartz plates. Atomic force microscopy (AFM) images were recorded on an AFM Nanoscope II (Digital Instruments, USA). rr-P3HT and Ge endohedral metallofullerene were dissolved in chlorobenzene at 100:1 weight ratios and thin films were spin casted on silicon wafer using a high-speed spin coater. Thin film on Silicon wafer was annealed in vacuum for 30 min at required temperatures and then the images of the surface were taken by AFM.

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2

4. SYNTHESIS OF Ge ENDOHEDRAL METALLOFULLERENE Synthesis of endohedral Ge doped fullerene was carried out by the method of Krätschmer-Huffman [62] using arc-vaporization of composite graphite rod in helium atmosphere. Ge impregnated 6 mm diameter graphite rod was used as anode whereas pure graphite electrode of same diameter was used as cathode. Composite graphite rod was prepared by mixing graphite powder and GeO2 in a ball milling machine for 15 minutes at

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400 rpm and then this mixture was filled through a 3mm hole at the centre of the graphite rod. The total Ge and carbon ratio was maintained at 2.5:100. The percentage and distribution of metal in the composite electrode are extremely crucial to get a higher yield of metallofullerene in the soot. The optimum percentage to get a soluble Ge doped monometallo C82 fullerene was found to be around 2.5% by weight [63]. At a lower metal content, the percentage of monometallo C60 fullerene would increase. This is in keeping with the experimental finding of the dependence of the percentage of metal:carbon ratio for gadolinium metallofullerene [64].

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Figure 6. Horizontal fully automatic arc ablation instrument.

The uniform mixing of GeO2 with the graphite soot and tight packing of the mixture into the cavity play a positive role in obtaining a higher percentage of Ge endometallofullerene in the soot. Preheat treatment of the composite graphite rod before arc burning showed an enhancement of metallofullerene percentage in the starting soot. This thermal activation process in the vacuum converts GeO2 to GeC, which requires a lower energy for bond cleavage as the bond enthalpy of Ge-C and Ge-O is 460 and 659.4 kJ/mol respectively. The uniform mixing of GeO2 with the graphite soot and tight packing of the mixture into the cavity actually help to convert GeO2 into GeC efficiently. The Ge metallofullerene percentage generally decreases drastically if we directly fill the GeO2 into the cavity of graphite rod without properly mixing with graphite powder. The composite graphite rod was annealed by resistive heating by touching the cathode and the anode inside the arc ablator at a 0.028 mbar vacuum with the continuous pumping for 45 minutes to convert GeO2 to GeC. The conversion reaction of GeO2 to GeC outside the arc ablation unit and then transfer of the composite rod into arcing unit for arcing is not found suitable for a higher yield of metallofullerene. The exposure of GeC composite graphite rod to ambient atmosphere during transfer to arc ablation unit may again deactivate the Ge graphite electrode. The helium gas and the distance between the cathode and the anode during arcing play a critical role on the yield of Ge metallofullerene [65]. The lower helium gas pressure, e.g.

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~100 mbar increases the amount of empty fullerene in the soot. The higher partial pressure of helium gas in arc plasma seems to dilute the carbon vapour concentration and thereby increases the chance of formation of clusters of the isolated carbon atoms and metals. It is worth to mention here that the very high helium pressure (~500 mbar) produces carbon nanotube as the low concentration of ionized carbon atoms produce an ideal add atom conditions inside the arc ablation unit [66, 67]. The distance between the cathode and the anode during arcing seems to have a similar effect. A distance of 3-4 mm between the cathode and the anode is ideal for fullerene formation whereas a distance of 5-6 mm produces metallofullerene. The dumping of a huge electrical power at a small distance between the cathode and the anode produces a higher temperature which in turn increases the concentration of carbon plasma by fast burning of the anode. The optimized conditions for annealing and arcing conditions for the higher yield of soluble Ge monometallofullerene are enlisted in Table 3 for comparison [63]. Table 3. Conditions of annealing and arcing of GeO2-graphite composite rod as anode and pure graphite as cathode Condition of annealing Vacuum Voltage (mbar) (V)

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0.028 10 Condition of arcing 0.023 38-40

Current (A)

Amount of He (mbar)

Time (min.)

0

Distance between cathode and anode (mm) 0

65 95-100

135

5-6

5-6

45

5. ISOLATION AND PURIFICATION OF Ge ENDOHEDRAL METALLOFULLERENE The extraction and purification of metallofullerene is always a difficult task due to the very similar redox properties of metallofullerene and the larger empty fullerenes like C80 to C100 [32, 33]. A majority of the purification processes for metallofullerene, therefore, depend upon chromatographic separation, particularly high performance liquid chromatographic (HPLC) separation of metallofullerenes and empty fullerenes [68, 69]. However, the amount in HPLC separation of metallofullerene is extremely low and insufficient. Therefore, it is still a challenge to obtain bulk amounts of highly pure metallofullerene. By exploiting the chemical and redox properties of the minority metallofullerene from the majority empty fullerene, metallofullerene species is selectively oxidized or reduced to its cation or anion and then separated from empty fullerene [70-71]. The chemical and redox properties of C60 and C70 are distinctly different from that of soluble metallofullerene. However, the difference between the larger empty fullerenes and metallofullerene is generally very less, so some amount of empty larger fullerenes always comes with the metallofullerene by this method [73]. Various solvent extraction procedures have been tried by which the content of metallofullerene was enriched relative to empty fullerenes. Typically these procedures use polar solvents to extract higher ratio of metallofullerene relative to the empty fullerene in the

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arc produced soot. The most frequently used solvents are N, N-dimethylformamide (DMF), aniline and pyridine. Non bonding electrons of these nitrogenous solvents form the weak complex with the metal atom of the metallofullerene and dissolve in the nitrogenous solvent [74-76].

Figure 7. Schematic representation of the extraction procedure adopted for isolation of Ge endometallofullerenes.

The extraction of Ge endohedral metallofullerene was carried out by a three step solvent extraction method using the soxhlet apparatus under inert atmosphere at solvent boiling point. Prior to the soxhlet extraction, the starting soot was kept inside acetone and then in diethyl ether for three hours to remove amorphous carbon and other carbonaceous nanoparticles [63, 77]. o-xylene was used first followed by DMF. Freshly distilled aniline was then used to isolate Ge metallofullerene. Details of the extraction process are schematically represented in Figure 7. In o-xylene, empty fullerenes, mainly C60 and C70 were extracted whereas larger

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fullerenes and a small amount of Ge metallofullerenes were soluble in DMF [63, 77]. The aniline extract was filtered and the solvent was evaporated on a rotary evaporator. The sticky material was washed thoroughly with acetone followed by annealing in air to remove trapped aniline, oxidized aniline and some amount of oligomers of aniline. The mass spectrum shows a characteristic peak for metallofullerene along with the some amount of impurities [78]. To increase the purity and the yield of metallofullerene, we have adopted a one pot extraction methodology. Solubility of Ge metallofullerene in aniline is more compared to empty fullerenes due to the interaction of the metal atom inside the fullerene with the lone pair of electrons in the solvent. Exploiting this property, Ge metallofullerene is separated from empty fullerenes by one step extraction method. The yield of metallofullerene reduces in each step of isolation procedure. Therefore, lesser the number of steps involved in the extraction process, the higher will be the yield. As the metallofullerenes are very sensitive to oxygen and moisture, the one step process reduces the chance of oxidation and contamination by impurities compared to the multi steps extraction process. The one step extraction process as shown in Figure 8 is thus more suited to bulk production of metallofullerene. However, it is worth mentioning here that some amount of larger fullerenes and C60 and C70 also extracted along with the Ge@C82 by this one pot isolation process in aniline. We found that dissolving this not so pure Ge@C82 in aniline again and then concentrating the mixture to 15mg/100ml by reduced pressure distillation followed by a standing time of 12 hours in inert atmosphere, selectively precipitate empty fullerenes and leaves the metallofullerene in solvent. By repeating this method, very pure Ge@C82 could be isolated. However, in each step, the yield of metallofullerene would be reduced. The solubility of empty fullerenes in a polar solvent is limited, especially for the symmetric C60 and C70. When the aniline extract is concentrated by solvent evaporation, the empty fullerenes become supersaturated and most of them crystallize and precipitated out from the solvent [79]. Therefore, by simply concentrating the extract, C60, C70 and as well as some giant fullerenes like C84, C86, C88 etc could be separated from the metallofullerene. However, the removal efficiencies of C60 and C70 are much higher than those of the giant fullerenes. This is because of the highly symmetrical structure of C60 and C70 result in lower polarizabilities and hence lower solubility in a polar solvent. Most of the endohedral metallofullerenes are left in the concentrated solution due to the much higher solubility in polar solvents like aniline. Exploiting the differential solubility of empty fullerenes and endohedral fullerenes in a polar solvent with lone pair of electrons, better isolation of endohedral metallofullerene could be achieved.

6. CHARACTERIZATION OF Ge ENDOHEDRAL METALLOFULLERENE A lot of modern sophisticated characterization techniques have been employed for obtaining the evidence of formation, mechanism of formation and structure-property correlations of endohedral metallofullerenes. Mass spectroscopic technique is an elementary and most essential characterization tool for the evidence of the formation of fullerenes as well as metallofullerenes [80-82]. Fast Atomic Bombardment (FAB) mass technique was not preferred due to its low resolution and the difficulty in identification of molecular ion peak and fragmented peaks of the metallofullerene and empty fullerenes mixture.

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Figure 8. Schematic illustration of the one step extraction procedure adopted for the separation of Ge endometallofullerenes from empty fullerenes.

Recent advances in soft ionization techniques for high resolution mass spectrometry make it possible to determine the mass of intact molecular ions [83, 84]. The entire molecular mass distribution of the sample can be accurately measured even if present in a small amount. The commonly used soft ionization methods are electrospray ionization (ESI) and matrixassisted laser desorption ionization (MALDI). Although ESI has been very popular for biological samples, it was not successful for characterization of fullerenes and metallofullerenes due to their low solubility in the commonly used solvents like water, alcohol, acetonitrile etc. Positive and negative high resolution MALDI-TOF spectroscopic techniques have been extensively used to characterize fullerenes and metallofullerenes. The nanometre sized clusters of fullerene and metallofullerene could easily be ionized without the help of the matrix. In these cases, therefore, no matrix is required and the mass spectral technique is popularly called laser desorption ionization-time of flight (LDI-TOF) technique

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[79]. Fourier transform ion cyclotron resonance (FT-ICR) mass spectrometer has also been used to study clusters, especially the metal-carbon binary clusters. The high mass resolution of FTICR is convenient route for the assignment of complicated mass signals of metallofullerenes in gas phase [36]. The endohedral nature of the fullerene cannot be ascertained from the mass spectrometric technique. Extended X-ray absorption fine structure (EXAFS) experiments have been performed to prove that the metal atom is indeed caught inside the fullerene cage [85]. However, the impure metallofullerene sample and most importantly, some amounts of trapped metal atoms in the sample make the EXAFS experimental results very misleading [86]. Preparative HPLC purified metallofullerene sample had to be used for EXAFS study to get the correct experimental inference. The first microscopic evidence of the endohedral nature was first demonstrated by the IBM Almaden group using a high-resolution transmission electron microscopy (HRTEM) experiment on a purified Sc2@C84 material which suggests that the two scandium atoms are encapsulated inside the C84 cage [87]. The spherical shape of Sc2@C84 and Y@C82 adsorbed on clean silicon and copper surfaces seen by the sophisticated ultra-high vacuum scanning tunnelling microscopy (UHV-STM) strongly indicates that the metal atoms are encapsulated inside the fullerene cages [88, 89]. The first conclusive experimental evidence for the endohedral nature of a metallofullerene, Y@C82, was shown by Shinohara‘s research group using a synchrotron X-ray diffraction study. Electron density distribution map using maximum entropy method (MEM) proved (Figure 9) that the yttrium atom is encapsulated within the C82 fullerene and is strongly bound to the carbon cage [90, 91].

Figure 9. The MEM electron density distribution of Y@C82 for the (001) section. The contour lines are drawn from 0.0 (e Å−3) with a 0.5 (e Å−3) step width. The high-density position corresponds to the Y atom [32]. Germanium: Properties, Production and Applications : Properties, Production and Applications, Nova Science Publishers, Incorporated, 2011.

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The dynamics of metal atoms inside the cage was studied theoretically by molecular dynamics simulation method [90] and experimentally by the spin relaxation method using nuclear magnetic resonance (NMR) spectroscopy [93]. On the basis of 13C NMR and 139La NMR studies of La2C80, a circular motion of encaged La atoms in the C80 cage was reported. The degrees of freedom of the metal atom inside the fullerene cage are extremely useful for the design of molecular devices. By determining the metal-carbon bond distance in metallofullerene crystal structure, the structure of metallofullerene has been ascertained [94]. The microcrystals of La@C82 grown from solution showed different crystal structures due to the presence of solvent molecules compared to the microcrystals of La@C82 grown by solvent-free (sublimation) conditions [95, 96]. Electron spin resonance (ESR) and UV-Vis-NIR absorption spectroscopic methods have been extensively used to study the electronic properties of metallofullerenes. The mechanism and the amount of electron transfer from the metal to the fullerene cage has been investigated by examining the hyperfine splitting of ESR lines due to the isotropic electron-nuclear hyperfine coupling [97, 98]. The different structural isomers of metallofullerenes have also been identified and predicted by the hyperfine splitting patterns. They were experimentally isolated later by the preparative HPLC technique [99, 100]. The absorption spectrum of a metallofullerene is characteristically different from that of empty fullerene in the UV, visible and near IR regions. The absorption spectrum of a metallofullerene generally exhibits a monotonically decreasing intensity as a function of wavelength extending down upto 2300 nm [101]. Incorporation of a single atom inside a C82 fullerene cage results in a broad absorption band with a maximum at 1400 nm and a sharp absorption peak around 1000 nm [102]. These absorption peaks could be due to an intrafullerene electron transfer from the encaged metal atom to the carbon cage. The open-shell electronic configuration of the encaged single trivalent ion like La, Y and Gd inside the C82 fullerene cage results in an absorption peak in NIR region whereas the closed shell electronic structure of C806- in M2@C80 is likely to account for the absence of NIR absorption peaks in the spectrum. The extent of electron sharing and the coupling of frontier molecular orbitals of the encaged metal and the fullerene can be correlated to its characteristic absorption features [103, 104]. To understand the oxidation state of the metal inside the fullerene cage, which to a large extent determines the chemical behaviour of the metallofullerene, X-ray photoelectron spectroscopy (XPS) and UV photoelectron spectroscopy (UPS) characterization techniques have been employed [105, 106]. The XPS of deep core level provides a direct measure of the valency of each atom in the compound and has been shown to be a suitable probe of the chemical state of metal in metallofullerene. We found that the small amount of trapped metal atoms in the metallofullerene sample makes the interpretation of XPS data very challenging. The vibrational features of metallofullerenes have been studied by IR and Raman spectroscopy [107]. It was found that the some of the vibrational peaks of metallofullerene have been strongly enhanced compared to the empty fullerene, indicating that the strong interactions between the metal atom and the carbon cage. The metal to cage vibration modes which is directly related to the charge state of the metal could be studied by Raman and FT-IR spectroscopy below the 400 cm-1. However, here also the small amount of trapped metal could mislead the experimental findings. The formation and the endohedral nature of the Ge metallofullerene was investigated by the characterization techniques like FAB & MALDI-TOF mass spectrometry, FT-IR, FTNMR, EDX, UV-VIS-NIR absorption spectroscopy and XPS [63, 77-78]. Mass spectrum

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(Figure 10) of the purified aniline extract of Ge metallofullerene showed an intense peak around 1058 m/z indicating the abundance of Ge@C82 in the soluble fraction of metallofullerene. Figure 10A reproduces the FAB mass whereas 10B reproduces the MALDITOF mass spectrum. A comparison of the two mass spectra clearly indicates the low resolution of FAB mass spectrum as the highest count was only 25 compared to 3000 that of the MALDI-TOF. Therefore, the signal to noise ratio of MALDI-TOF spectrum is much better than FAB mass spectrum.

Figure 10. Comparative mass spectra of aniline extract of the Ge metallofullerene: Figure 10A reproduces the FAB mass spectrum whereas Figure 10B reproduces MALDI-TOF spectrum.

However, in FAB mass spectrum also we could assign the molecular ion peaks of the different mass species in conformity with the MALDI-TOF mass spectrum. It can be noticed from the FAB mass spectrum that the mass range for larger fullerenes is not well resolved when compared to the lower mass region. This suggests that it is easier to fragment the larger empty fullerene than the stable C60 and C70 which were also extracted along with Ge@C82

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[108, 109]. A weak peak at 794 m/z indicates the formation of Ge@C60. However, due to aerobic condition of the extraction procedure, the concentration of Ge@C60 is low in the final isolated product. Aniline extract of the Ge metallofullerene was washed thoroughly with acetone to remove the trapped aniline and oligomers of aniline. The black powder was then heated in air to remove the unreacted aniline and its oligomers and empty larger fullerenes. However, the mass spectra clearly show that some amount of aniline adducts with the metallofullerene is still present in the soluble fraction of Ge@C82. The presence of aniline in the extract could be attributed to the formation of aniline adduct with fullerene and metallofullerene during reflux with aniline. The FT-NMR (Figure 11A) and FT-IR (Figure 11B) spectra also confirmed the presence of aniline in the soluble fraction of Ge@C82. The signals around 8 ppm and 3.5 ppm in the FT-NMR spectrum indicate the presence of aniline units in the annealed aniline extract of Ge encapsulated fullerene. The C-N type resonance stretching frequency has been noticed at 1259 cm-1 whereas the N-H bending is seen at 1629 cm-1 and the N-H bond stretching was found at 3448cm-1 in the FT-IR spectrum [63, 77].

Figure 11. Figure 11A represents the FT-NMR spectrum of purified aniline extract of the Ge metallofullerene whereas Figure 11B illustrates the FT-IR spectrum of purified aniline extract of the Ge metallofullerene.

To prove that the purified aniline extract actually contains germanium, the black coloured purified sample was taken on the quartz plate and heated at 5000C in air and it was found that a white powder of GeO2 was left out on the quartz plate after 30 minutes of heating. This clearly shows that at 5000C, fullerene and metallofullerene get oxidized and then Ge was oxidized to GeO2. To further confirm this observation EDX (Figure 12) study was carried out on the purified aniline extract. Characteristic peaks of Ge at 1.18 KeV and 1.21 KeV for Lα and Lβ whereas peaks at 9.88 KeV and 10.98KeV for Kα and Kβ. The peak between 1.3 and 1.4 keV is due to the substrate silicon wafer on which the purified aniline extract of Ge metallofullerene was drop casted. For clarity, carbon and oxygen signals were removed from the EDX spectrum of Ge metallofullerene [63, 77-78].

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Figure 12. Energy dispersive X-ray spectrum of the purified aniline extract of Ge encapsulated fullerene film on Si substrate grown by drop casting of aniline extract.

Figure 13. UV–Vis–NIR spectrum of the purified aniline extract of Ge endometallofullerene in spectroscopic grade DMF solvent. In the inset, the UV and visible ranges are presented to show the monotonic decreasing intensity as a function of wavelength, which is typical of metallofullerene.

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As has been discussed earlier, the absorption spectra of metallofullerenes have long tails to the red region, the same is seen in Ge doped fullerene also. The absence of any sharp peak in the UV region suggests the insertion of Ge into the fullerene cage. The absorption spectra of monometallofullerenes M@C82 (M = Sc, Y, La) showed a sharp peak around 1000 nm [101, 102]. This absorption peak was assigned to an intrafullerene electron transfer from the encaged metal atom to the carbon cage. UV-Vis-NIR spectrum (Figure 13) of Ge doped fullerene shows a similar pattern like the other endohedral metallofullerenes. However, the absence of a sharp peak around 1000 nm in the UV spectrum suggests a different distribution of electron density in Ge encaged fullerene compared to other endohedral metallofullerenes [63, 77]. The fitting of Ge core level XPS spectrum (Figure 14) reveals that three peaks at 29.2, 30.5 and 33 eV respectively. The peak at 29.2 eV indicates that Ge is in zerovalent state. A small shoulder at 27.9 eV confirms the interaction of fullerene core with the Ge orbital [110]. The peaks at 30.5 and 33 eV are for germanium in +1 and +2 oxidation states. This could either be due to an electron transfer from Ge to the carbon cage resulting in the formation of a stable ion pair or it could well be the GeO and GeO2, respectively [63, 77]. The presence of GeO and GeO2 could be attributed to the unreacted starting germanium oxide which is also extracted along with the metallofullerene. Preparative HPLC pure Ge metallofullerene would be used for obtaining the conclusive evidence of electron transfer from encaged Ge metal to fullerene cage.

Figure 14. Core level XPS spectrum of Ge after 6 minutes of sputtering at 1x 10-6 mbar vacuum, 4 KV, 15 mA. The black thick line represents the 20 points FFT smoothing of data, the scattered box symbol represents the fitted spectrum and dotted lines represent three fitted peaks at 29.2, 30.5 and 33 eV for Ge at the 0, +1 and +2 oxidation state, respectively.

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To confirm further that there is no Ge-fullerene exohedral complex formation we have recorded the carbon 1s XPS spectrum (Figure 15). The presence of a peak at 284.4 eV corresponding to the C-C bond and the absence of a characteristic peak at 283.8 eV for Ge-C bond indicate that Ge is caught inside the fullerene cage [111]. FT-IR spectrum below 400 cm-1 obtained using CsI crystal does not show any significant metal-carbon signal. This also reiterates the view that Ge metal is inside the cage. However, it should be mentioned here that due to very low signal to noise ratio of FT-IR spectrum below 400 cm-1, encaged metal and carbon cage vibrational signals could not be detected. Surface enhanced and resonance raman spectroscopic techniques would be employed for detection of very low intensity encapsulated metal and carbon cage vibrational frequencies.

Figure 15. Carbon 1s XPS spectrum after 6 minutes of sputtering at 1x 10-6 mbar vacuum, 4 KV, 15 mA. The black thick line represents the 20 points FFT smoothing of data, the scattered box symbol represents fitted spectrum and dotted lines represent two fitted peaks at 284.4 and 286 ev for C-C and C-H bond respectively.

7. THEORETICAL CALCULATIONS OF Ge ENDOHEDRAL METALLOFULLERENE The DFT calculations showed that the singlet state of Ge@C60 is stabilized by 4.7 kcal/mol compared to the ground state of the isolated C60 and Ge. In the optimized geometry, Ge was found to be slightly off-center by a distance of 0.09Å. Molecular orbital analysis revealed that the considerable mixing of the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) of Ge with the LUMO of C60 resulting in a new set of frontier orbitals for Ge@C60 as illustrated in Figure 16A. The energy levels of the

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frontier orbitals of C60, Ge (3P0) and Ge@C60 plotted in Figure 16B show that the energy gap between the HOMO and the LUMO of the endohedral fullerene is only 20.4 kcal/mol, compared to 63.7 kcal/mol for C60.

Figure 16. The frontier orbitals of Ge@C60 (S0) are represented in 16A and the energy levels of the frontier orbitals of C60, Ge@C60 and 3Ge are plotted in 16B.

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The ground electronic state of C60 (1A1g) and the nearest lying excited states of C60 are of gerade symmetry. Thus the transitions between these levels are symmetry forbidden and the allowed transition is expected to occur in the ultraviolet region. The observed weak absorption observed in the visible region for C60 arises from vibronic coupling.

7.1. Encapsulation of Ge2 Inside C60 It was shown in the previous section that an atom of Ge can form a stable complex with C60. Considering the size of C60, it may be possible to encapsulate Ge2 inside the cage. However, there is no experimental evidence for such an encapsulation so far. Therefore, a theoretical investigation has been carried out to check the possibility of encapsulation of Ge 2 inside C60. For this purpose, keeping the center-of-mass of Ge2 at the center of the C60 cage, the GeGe bond was oriented along the centers of the two opposite pentagons (C5 axis). Geometry optimization was carried out for this orientation for both the singlet and the triplet state using the methodology described above. Frequency calculations for the optimized geometries indicate that Ge2@C60 in its singlet state corresponds to a minimum whereas the presence of three imaginary frequencies for the triplet state showed that it corresponds to a third order saddle point in the potential energy surface. The ground state of Ge2 is a triplet (3Σg ) [112-114]. Stabilization energies of the optimized geometries were calculated relative to the isolated C60 and Ge2 (3Σg ). The results in Table 4 show clearly that the singlet Ge2@C60 is less stable than the well separated Ge2 (3Σg )

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and C60 (1A1g). However, it does not mean that Ge2@C60 cannot be formed. The destabilization energy of the endohedral complex is much less than the C-C bond energy of the cage. It is important to add that the singlet Ge2@C60 is more stable than the separated Ge2 (1Σg+) and C60. The bond length and the stretching frequency of the Ge-Ge bond in its free state and in the encapsulated state for the singlet and triplet states are also listed in Table 4. Although the properties of the Ge-Ge bond are different for the singlet and the triplet states, the corresponding values are comparable to each other for the singlet and triplet states of Ge2@C60. Ge2 in its ground state (3Σg ) undergoes a shortening of its bond length and a blue shift in its stretching frequency as was the case for XHn species reported earlier [44]. Table 4. Stabilization energy and molecular parameters of Ge2@C60 computed at DFT(B3LYP)/6-31G* level of calculation Ge-Ge Bond Length/(Å)

Ge-Ge Stretching Frequency/(cm-1)a

Free

Inside C60

Free

Inside C60

Singlet

Stabilization Energy/(kcal/mol) With respect With respect to C60 + to C60 + Ge2(3Σg-) Ge2(1Σg+) 2.7 -24.0

2.1490

2.1701

343

298

Triplet

6.9

2.3841

2.1885

275

300

Multiplicity of the system

a

-19.8

scaled by a factor of 0.98

-75

Energy/(kcal/mol)

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-50

-100

-125

-150

α β C60 (1A1g) [Ge2@C60] (S0) [Ge2@C60] (T1)

α

β

Ge2 (3Σg-)

Ge2 (1Σg+)

Figure 17. Energy level diagram for the frontier molecular orbitals of Ge2@C60 along with those of the separated species.

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The energies of the molecular orbitals of Ge2@C60 in its singlet and triplet states and the corresponding isolated species are plotted in Figure 17, along with the electron filling pattern for all the species. It is clear that the energy gap between the HOMO and the LUMO of C60 is reduced by the encapsulation of Ge2. The HOMOs and the LUMOs of the complex in its singlet and triplet states are formed by the mixing of the frontier orbitals of C60 and Ge2. However, the HOMOs are formed largely from the orbitals of Ge2 and the LUMOs from the orbitals of C60. These molecular orbitals are shown schematically in the Figure 18. A careful analysis of the diagram indicates that the energy gap between the HOMO and the LUMO of Ge2@C60 in its singlet state is larger than the corresponding energy gap for Ge2 (1Σg+). In contrast, the corresponding energy gap for the triplet state of Ge2@C60 is less than that of Ge2(3Σg ). Thus Ge2 in its singlet (excited) state is stabilized more than the triplet (ground) state inside C60. NBO analysis for the optimized geometry of the complexes reveals a strong interaction between the 4pz orbitals of Ge and the C-C bonds of the pentagons of C60 for the singlet state. However, for the triplet state no such interaction is observed. Therefore, the energy of the singlet state is lower than that of the triplet state as is evident from the Table 4. For the triplet state, the electron occupancy in the 4pz orbitals of both the Ge atoms showed an increase inside C60 when compared to its free state.

-50

Energy/(kcal/mol)

-50

Energy/(kcal/mol)

-90

z 3

-110

3

x

4 5 4

-70

y

5

7 8

-90

7

8

z

z -110

3

y

x

6

1 2

-130

x

y

1

2

6

3

-130

1 2 -150

1

2

-150

Ge2 (1Σg+)

(d)

(c)

β

α

Ge2 (3Σg-)

-50

-70

3 4 5

3

5

4

-90 1 2 -110

1

2

Energy/(kcal/mol)

-50

Energy/(kcal/mol)

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-70

y

x

(b)

(a)

-70 4,5

4

9 8 7

-90

5

8

3

7

2

6

9

3 -110

2

6

1

-130

-130

-150

-150 [Ge2@C60] (S0)

β α [Ge2@C60] (T1)

1

Figure 18. Frontier orbitals of (a) Ge2 in its singlet state (b) Ge2 in its triplet state (c) Ge2@C60 in its singlet state and (d) Ge2@C60 in its triplet state.

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There seems to be a flow of electrons from 4px and 4py orbitals of Ge to the 4pz orbital. As a result the Ge-Ge bond length is decreased inside the cage. It was also found that the d electrons of Ge do not have much role in the interaction between Ge and C60. The cage of fullerene was found to be polarized in the presence of Ge2. The carbon atoms of the cage close to the Ge atoms become slightly negatively charged. As was mentioned above, C60 absorbs weakly in the visible region. The encapsulation of Ge2 inside C60 shifts the allowed absorption band from the ultraviolet region to the visible region. TDDFT calculations using the B3LYP parametrization and 6-31G* basis set were carried out for the optimized geometries of the complex in its singlet and triplet states. The absorption maximum for the complex in its singlet state is predicted to occur at 716 nm with an oscillator strength of 0.014. The calculations showed no absorption in the visible region for the complex in its triplet state. Keeping C60 and Ge2 bond parameters fixed as in the above mentioned optimized geometries, single point energy calculations were carried out by varying the orientation angle (θ) of the Ge-Ge bond axis with respect to the C5 axis of C60 at regular intervals of 10°. The results are plotted in Figure 19. The energy of the complex in its singlet state with the Ge2 bond aligned with the C5 axis is taken as the zero of energy.

Relative energy/(kcal/mol)

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18 Singlet Triplet

15

12

9

6

3

0 0

30

60

90

120

150

180

Angle of rotation/degree

Figure 19. Relative energies of Ge2@C60 for different orientations of Ge2 inside C60 for the singlet and the triplet state. The figure in the lower panel shows the part of the C60 cage towards which the Ge-Ge bond is oriented. The arrows show the points on the surface of the cage to which the Ge-Ge bond is oriented.

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The plot shows that the barrier for rotation is less for the triplet state than for the singlet state. For θ = 0 and 180° the singlet state is the lowest in energy. For 20° < θ 1.8 m was not able to switch to lowresistance state even when the applied voltage increased to 1000 V. On the other hand, structure thickness layer of fluoride and oxides REE d < 0.18 m irreversibly switched in low-resistance state when the applied voltage exceeded the threshold. Kinetic characteristics in switching researched the mode of structure filming on a single rectangular voltage pulse. Figure 15 illustrates the dynamics to switch silicon MIS-structure with isolator layers of fluoride erbium from high resistance to low-resistance state under the action of a single rectangular pulse voltage of duration  = 10 s. The upper curve characterizes a pulse voltage and the amplitude at the bottom is proportional to the current through the structure, and matches the fall of voltage on series resistance Rl = 50 . The sample‘s character parameters for the kinetic characteristics is a delay time switching del, after a fast switch from one state to another by an intrinsic switching time, s. Mean delay time switching decrease, when Ush increase. Initial current surges on the kinetic characteristics switch corresponds to the recharge capacity of the research structure. In the future, current, that takes place through the structure at a low-resistance state, relaxes in the stationary value. As evident from the kinetic characteristics, the value of the capacitor current and the relaxation time reduces with the amplitude pulse voltage. Intrinsic switching time, s at 0.4 and 0.8 s were used for the switching samples of fluoride rare earth element films in low-resistance state and back, respectively. For film structures of oxides REE intrinsic time the switching had almost no dependence on the amplitude of the applied voltage pulse; 0.2 and 0.4 s was used to switch samples from high conductivity state and back, respectively.

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Figure 15. Kinetic characteristics switch from high resistance in the low-resistance state of MIS structure of Al-ErF3-nSi. 1-impulse voltage pulse  = 10 s; 2-signal, a subject with series resistance Rl = 50 : (a) Ush = 28 V, del = 6.3 s; (b) Ush = 80 V, del = 2 s.

The time delay depends on the applied voltage pulse value of Ush under an experimental formula: 𝜏𝑑𝑒𝑙 = Aexp(−B𝑈𝑠𝑕 ),

(2)

Where, A and B are constants. Dependence of time delay del when switching from high resistance to a low-resistance state is presented in Figure 16 for the Al-Gd2O3-Si structure. It is clear that the electric field operates on the entire isolator under the metal contact during the time delay. Setting the normal electroforming voltage of ~ 30 V this time is ~ del = 3 s.

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Figure 16. The dependence of the time delay switching from high resistance in the low-resistance state of the applied voltage for the structure of Al-Gd2O3-Si.

Experiments on structures with different metal electrode area (from 0.03 to 3 mm2) showed a lack of any substantial dependence for electroforming characteristics in the electrode area. The condition of conductance switching from high resistance to low-resistance state and back; were equally well observed on structures with different deposited electrodes of aluminum, nickel, molybdenum, with point contacts from brass or tungsten. The process that reverses switch conductivity structure from low-resistance to high resistance state is also characterized by latency and its own switch time, and then the structure becomes stable in a high resistance state. This voltage reverse switch were for various samples within U = 3-20 V. Probably low-resistance state first develops in the form of a power cord while memory switching takes place during the phase transition in the cord area and in the matrix of dielectric layers form in the channel of high conductivity. The metal –isolator – metal (MIM) structure with fluoride and oxides REE in low-resistance state have a positive temperature coefficient resistance (TCR) in a broad area of temperatures 77 – 400 K, and different samples values were between TCR = (0 - 4.6)×10-3 grad-1. Volt – current characteristics of MIM-structures in the low-resistance state are linear and symmetrical, and their resistance is R = (3×10-2-10) . This suggests that conductivity channel mainly consists in a metal phase.

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IV. THE IMPACT OF ELECTRIC FIELD A. Structure with Fluoride Rare Earth Elements Films

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1. Assessment High-Frequency Interface Traps Capacity A MIS-structure can be represented as a serial connection capacity isolator layers 𝐶𝐷 with parallel chain capacity for spatial charge 𝐶𝑠 and interface state 𝐶𝑖𝑡 . Figure 17 shows the simplest equivalent scheme MIS -structure.

Figure 17. MIS-structure simplest equivalent scheme.

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Figure 18 shows an example of how changes C-V characteristics in a germanium structure with film of yttrium fluoride, measured at 1 MHz, during several consecutive electroforming cycles. The figure next to the marker indicates the number of electroforming cycles, original state corresponds to the "0". The status of the primary charge structure is characterized by the total positive charge 𝑄𝑓 captured in volume by the isolator layer and at the isolator/semiconductor interface. Skewing characteristics when the number of electroforming cycles is increased, shows an increase in the interface states density, at the same time increasing the capacity value in inversion.

Figure 18. Modified C-V characteristics of Al–YF3–Ge structure with several consecutive cycles electroforming (0-original state).

Calculations show change for example structures with the minimum capacity value (capacity in mode inversions Cinv) in successive cycles of electroforming with 𝐷𝑖𝑡 evolution, the interface states density. Therefore, some of the traps at the isolator/semiconductor interface are sufficiently fast traps, giving contribution to the high frequency capacity. The capacity of these traps can be shown as an expression, representing the full capacity of MIS-structures, in accordance with the equivalent schema shown in Figure 17: 1 𝐶

=

1 𝐶𝐷

+

1 𝐶𝑠 +𝐶𝑖𝑡

,

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(3)

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M. B. Shalimova and E. N. Khavdey

0 where C is the capacity of MIS-structure. Let 𝐶inv - structure capacity be the mode 𝑘 inversion in its original state, i.e. without the impact electric fields; 𝐶inv - structure capacity be 0 the mode inversion after k-cycle electroforming; 𝐶it - traps capacity at the isolator/ semiconductor interface structure in its original condition; 𝐶it𝑘 - interface states capacity after k -cycle electroforming. Then 1 0 𝐶inv

=

1 𝐶𝐷

+

1 𝐶𝑠 +𝐶it0

1

,

=

𝑘 𝐶inv

1 𝐶𝐷

+

1 𝐶𝑠 +𝐶it𝑘

,

(4)

where should: 𝐶𝑠 + 𝐶it0 =

0 𝐶𝐷 𝐶inv

0 𝐶𝐷 −𝐶inv

𝐶𝑠 + 𝐶it𝑘 =

,

𝑘 𝐶𝐷 𝐶inv

𝑘 𝐶𝐷 −𝐶inv

.

(5)

Given that the capacity of the depleted layer is not dependent on the number of cycle electroforming, i.e., considering 𝐶𝑠 = const in inversions mode. Therefore, in this case the capacity of the spatial charge semiconductor is defined only by its own concentration value for the semiconductor. By the level of doping and temperature, we get ∆𝐶𝑖𝑡𝑘 = 𝐶it𝑘 − 𝐶it0 =

𝑘 0 𝐶𝐷2 𝐶inv −𝐶inv

𝑘 𝐶𝐷 −𝐶inv

0 𝐶𝐷 −𝐶inv

.

(6)

Therefore, capacity of interface states is defined as follows:

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𝐶it𝑘 = 𝐶it0 +

0 𝑘 −𝐶inv 𝐶𝐷2 𝐶inv

𝑘 𝐶𝐷 −𝐶inv

0 𝐶𝐷 −𝐶inv

.

(7)

Assuming that traps on the interface isolator/semiconductor structure are in its original state, in the first approximation can be neglected, i.e., considering 𝐶it0 = 0 we obtain: 𝐶it𝑘 =

𝑘 0 𝐶𝐷2 𝐶inv −𝐶inv

𝑘 𝐶𝐷 −𝐶inv

0 𝐶𝐷 −𝐶inv

.

(8)

Calculated capacity for the interface states according to Eq. (8) give value changing within 𝐶it𝑘 = (0.000 046-0.017) F/m2. Figure 19 shows a data chart from interface states capacity calculated by Eq. (8) for various experimental samples with fluoride rare earth element films on germanium substrates. 𝑘 Thus, the upper limit changes 𝐶it𝑘 two orders exceed 𝐶inv value. Also, the capacity of interface states is comparable to the capacity 𝐶𝑠 of the depletion layer, and considerably affects the experimental results. In this situation, it is clear that it cannot be overlooked.

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Figure 19. Chart spacing of change capacity surface rapid traps, calculated for different samples by Eq. (8).

Figures 20 and 21 each show the dependence of the interface states capacity on the electroforming cycles for structures with films of ErF3 and YF3, respectively. The data clearly reveals non-monotonic dependences, and this is pattern for all researched structures.

2. Assessment of Traps Energy Situation in Germanium Band Gap Steady-state differential capacity for interface states (when MIS-structure is in the thermal equilibrium conditions) can be defined by the expression [19] 𝐶𝑖𝑡 =

𝑑𝑄𝑖𝑡 𝑑 𝑆

,

(9)

where 𝑄𝑖𝑡 is the density of interface states charge, and 𝑆 - the surface electric potential. Local energy levels in the band gap that correspond to the interface states can be acceptor or donor types. Usually it is assumed that acceptor levels are mostly in the upper half band gap and donor is at the bottom.

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Figure 20. The interface states capacity for different structures of Al - ErF3 – nGe.

Figure 21. The interface states capacity of structures Al - YF3 – nGe.

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An empty acceptor level is neutral, and claims an electron-negatively charged. An empty donor level that is positively charged (captures a positively charged hole), and claims an electron-neutral. If these considered levels are a one-fold charged acceptor, as 𝑁𝑡𝑎 density, the charge density that captured them can be written as 𝑄𝑡𝑎 𝑆 = −𝑒𝑁𝑡𝑎 𝑓𝑡0 𝑆 .

(10)

where 𝑓𝑡0 is the equilibrium distribution function of electrons on local levels in the band gap. This is determined by the expression 𝑓𝑡0 =

1 𝛽 𝑡−1 exp 𝐸𝑡 −𝐸𝐹

𝑆

𝑘𝑇 +1

.

(11)

Here 𝛽𝑡 - factor quantitative-mechanical degradation of interface states, 𝐸𝑡 − 𝐸𝐹 𝑆 energy gap between local trap level and the Fermi level on the surface semiconductor. Factor quantitative -mechanical degradation of interface states may be taken into account by the replacement of the 𝐸𝑡 level for some effective 𝐸𝑡∗ = 𝐸𝑡 − 𝑘𝑇ln𝛽𝑡 value, so this coefficient later is ignored. The energy band profiles in Figure 22 show 𝐸𝑡 − 𝐸𝐹

𝑆

= 𝐸𝑡 − 𝐸𝐹

𝐹𝐵

− 𝑒𝑆 ,

(12)

where 𝐸𝑡 − 𝐸𝐹 𝐹𝐵 -energy gap between 𝐸𝑡 and 𝐸𝐹 levels in the case of flat bands. Band bending downward corresponds to the positive 𝑆 value, up - to negative. Then the probability for local levels with energy 𝐸𝑡 with an occupied electron will be given by

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𝑓𝑡0 =

1 exp

𝐸𝑡 −𝐸𝐹

𝐹𝐵 −𝑒 𝑆

𝑘𝑇 +1

.

(13)

Accordingly, the probability levels are absence in the electrons 1 − 𝑓𝑡0 =

1 exp

𝐸𝐹 −𝐸𝑡

𝐹𝐵 +𝑒 𝑆

𝑘𝑇 +1

.

(14)

The expression for the equilibrium charge as captured in the one-fold donor states with 𝑁𝑡𝑑 density can be written as follows: 𝑄𝑡𝑑 𝑆 = 𝑒𝑁𝑡𝑑 1 − 𝑓𝑡0 𝑆 .

(15)

The charge of 𝑄𝑡𝑑 𝑆 is positive and at maximum when donor levels are above the

Fermi level, and is otherwise zero. The charge of 𝑄𝑡𝑎 𝑆 is negative and at minimum by absolute value when the Fermi level on the surface semiconductor is above the level of 𝐸𝑡 on the (2-3) kT. In that case, 𝑓𝑡0 ≅ 1 and 𝑄𝑡𝑎 𝑆 = −𝑒𝑁𝑡𝑎 . If the Fermi level on the surface semiconductor is below 𝐸𝑡 on the (2-3) kT, 𝑓𝑡0 ≤ 0.1 and 𝑄𝑡𝑎 𝑆

≤ 0.1𝑒𝑁𝑡𝑎 . Finally, then

match Fermi level on the surface semiconductor by 𝐸𝑡 , there is 𝑄𝑡𝑎 𝑆 = −0.5𝑒𝑁𝑡𝑎 .

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Figure 22. The energy band profiles n-type semiconductor with mono-energy interface states.

In the case of mono-energy interface states as acceptor and donor type, we can get interface states capacity, according to Eq. (9), by taking the derivative of 𝑆 from 𝑄𝑡𝑎 or 𝑄𝑡𝑑 . In both cases, we have 𝐶𝑖𝑡 =

𝑒2 𝑘𝑇

𝑁𝑡0 𝑓𝑡0 1 − 𝑓𝑡0 ,

(16)

where 𝑁𝑡0 = 𝑁𝑡𝑎 or 𝑁𝑡0 = 𝑁𝑡𝑑 . Figure 23 shows the dependence of the capacity traps at the isolator/semiconductor interface for the electrostatic value potential on the surface and energy situation of the active traps. Figure 24 gives the outline schedule at marked levels. Maximum capacity of mono-energy interface states is achieved when the Fermi level crosses the traps‘ level, i.e., provided 𝐸𝑡 − 𝐸𝐹 𝐹𝐵 ≅ 𝑒𝑆

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Figure 23. Dependency interface states capacity of surface electrostatic potential and energy situation traps (T = 300 K, 𝑁𝑡0 = 1.1 × 1016 m-2).

Figure 24. Bulleted line levels are the relevant interface states capacity (F/m2) for surface as shown in Figure 23.

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For n-type germanium structures addressed in this chapter, the inversion mode according to the experimental data has a negative value for the electrostatic potential, 𝑆 ≅ −0.1 V value. Thus, to get the values of the interface capacity for these observed experiment conditions it was necessary that the traps at the isolator/semiconductor interface were below or near Fermi level energy during the flat bands. During the flat band voltage, the difference between Fermi level and bottom of conductance band is: 𝐸𝐶 − 𝐸𝐹 𝐹𝐵 = 0.245 eV. In accordance with the capacity values as observed in the experiment, this corresponds to the energy situation of traps in the band gap of germanium between energy 𝐸𝐶 − 𝐸𝑡 = 0.2450.445 eV. Maximum capacity for the maximum change charge of mono-energy traps would be at 𝐸𝐶 − 𝐸𝑡 = 0.345 eV. Given that the width of germanium band gap is 𝐸𝑔 = 0.66 eV (at 300 K), maximum change in the structure‘s charge for mode inversions will be for traps in the bottom half of the band gap, or near its middle. If these are donor type traps, the Fermi level crossing shall be charged positively, and contribute to the interface states capacity. This is likely because when we increase the number of electroforming cycles it has the predominating C-V shift characteristics in the area for negative voltages, which then corresponds to the acquisition of a positive charge (Figure 18).

Figure 25. Dependency interface states capacity of energy situation traps and their density.

Assuming that the process of electroforming generated new traps, with energy below the Fermi level, this will change the 𝐶𝑖𝑡 value. Figure 25 shows the dependence for the interface states capacity in energy situation traps and their 𝑁𝑡0 density as calculated as, 𝑆 =

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−0.11 eV; i.e., structures in mode inversions. Figure 26 shows an outline that corresponds to the schedule as marked by the surface levels shown in Figure 25. The conclusion from the Figures 25 and 26 should be the following: any pair values 𝐶𝑖𝑡 , 𝑁𝑡0 always correspond to two values, 𝐸𝑡 − 𝐸𝐹 𝐹𝐵 , i.e., two energy level traps (the exception in this case is when 𝐸𝑡𝑎 = 𝐸𝑡𝑑 = 𝑒𝑆 ). The axis of symmetry position between these two levels is determined by the value of the surface electrostatic potential in mode inversions, i.e., 𝑆 = −0.11 eV. To determine which level is the donor and acceptor type, we must calculate the dependence of the interface states charge on the energy situation of traps.

Figure 26. Bulleted line levels are the relevant capacity interface states (F/m2) for surface as shown in Figure 25.

Calculation for the dependence of donor type interface states charge in energy situation traps and their density are given in Eq. (15) and shown in Figure 27. Bulleted line levels corresponding to this surface are shown in Figure 28. Figures 29 and 30 illustrate the estimated dependence of interface states charge for acceptor type and their appropriate bulleted line levels. If an 𝑁𝑡0 = 4 × 1015 m-2, 𝑄𝑡 = ± 0.000 6 C/m2, the donor levels get the value 𝐸𝑡𝑑 − 𝐸𝐹 𝐹𝐵 ≅ -0.04 eV, and acceptor - 𝐸𝑡𝑎 − 𝐸𝐹 𝐹𝐵 ≅ -0.18 eV. Thus, in this case the energy level traps for acceptor and donor type are below the level of Fermi during flat bands, but donor type are above the acceptor type traps with the energy value equal to 𝑒𝑆 ≅ −0.11 eV.

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Figure 27. Dependency density charge donor type interface states of energy situation traps and their density.

Figure 28. Bulleted line levels are the relevant charges in the donor type interface states (C/m2) for surface as shown in Figure 27. Germanium: Properties, Production and Applications : Properties, Production and Applications, Nova Science Publishers, Incorporated, 2011.

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Figure 29. Dependency density for charge acceptor type interface states in energy situation traps and their density.

Figure 30. Bulleted line levels are the relevant charges in the acceptor type interface states (C/m2) for surface depicted in Figure 29. Germanium: Properties, Production and Applications : Properties, Production and Applications, Nova Science Publishers, Incorporated, 2011.

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We can calculate the energy situation of traps in band gap semiconductor by Eqs. (16), (15) and (10). Then, to define relations as: 𝑄𝑡𝑎 𝐶𝑖𝑡

=−

𝑘𝑇

1

𝑒 1−𝑓𝑡0

𝑄𝑡𝑑

,

𝐶𝑖𝑡

=

𝑘𝑇 1 𝑒 𝑓𝑡0

,

(17)

where should: 𝑒

𝑄𝑡𝑎

𝐸𝑡𝑎 − 𝐸𝐹

𝐹𝐵

= 𝑒𝑆 − 𝑘𝑇ln

𝑘𝑇 𝐶𝑖𝑡

𝐸𝑡𝑑 − 𝐸𝐹

𝐹𝐵

= 𝑒𝑆 + 𝑘𝑇ln

𝑘𝑇 𝐶𝑖𝑡

𝑒 𝑄𝑡𝑑

−1 ,

(18)

−1 .

(19)

Assessment of the 𝑄𝑡𝑎 , 𝑄𝑡𝑑 charge can be based on C-V characteristics, and on the value of the shifted flat band voltage UFB, defined expression: 𝑈𝐹𝐵 = 𝑚𝑠 −

𝑄𝑓∗ 𝐶𝐷



𝑄𝑡0 𝐶𝐷

,

(20)

where 𝑚𝑠 is the difference in work functions for the metal/semiconductor, 𝑄𝑓∗ is the density for the oxide charge. Parameters that may lead to a shift in flat band voltage that are the oxide bulk charge density 𝑄𝑓∗ and the trap charge density 𝑄𝑡0 at the interface. Often there is no clear relative balance charge for the interface states and/or bulk traps; so, it would be convenient to discuss the "effective" captured charge density

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𝑄𝑓 = 𝑄𝑓∗ + 𝑄𝑡0 .

(21)

Assuming the charge density in oxide 𝑄𝑓∗ = 0, the 𝑄𝑓 = 𝑄𝑡0 , i.e., the flat band voltage would be determined by the value of the interface states charge only. Consider our work in this experiment; after each electroforming procedure (the return to high resistance state) with C-V measured characteristics, the data can then be defined in spatial charge capacity values, 𝐶𝑠 at different voltages. The posted interface states capacity is calculated by Eq. (7). This will in turn enable us to determine the surface electrostatic potential 𝑆 values using this dependence [19]: 𝐶𝑠 = where

−1 𝑁 𝛽𝑁 =

1 2 𝑒 𝑘𝑇

𝜀 𝑟 𝜀 0 𝑁 1−exp −𝛽 𝑁 𝑆 −−1 𝑁 1−exp 𝛽 𝑁 𝑆 2𝐿𝐷 𝐹𝑁 𝛽 𝑁 ,𝑆 ,𝑁

,

(22)

𝐹𝑁 𝛽𝑁 , 𝑆 , 𝑁 = −1 𝑁 exp 𝛽𝑁 𝑆 − 1 + 𝑁 exp −𝛽𝑁 𝑆 − 1 + 𝛽𝑁 𝑆 𝑁 − , 𝑁 =

𝑝0 𝑛𝑖

– for p-type semiconductor, and 𝑁 =

𝑛𝑖 𝑛0

– for n-type semiconductor,

, 𝜀𝑟 is dielectric constant semiconductor, e - elementary charge, k is Boltzmann

constant, T is the absolute temperature, 𝐿𝐷 =

𝜀 𝑟 𝜀 0 𝑘𝑇 2𝑒 2 𝑛 𝑖

– the length of the screening, 𝑛0 𝑝0

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the concentration of electrons (holes) in the semiconductor, 𝑛𝑖 is intrinsic carrier concentration. The data is then modified by the dependence of the surface electric potential voltage. This relationship determined the value of the flat band voltage 𝑈𝐹𝐵 when the surface electric potential is equal to zero. Interface states charge density were determined by this formula 𝑄𝑡0 = 𝑈𝐹𝐵 𝐶𝐷 .

(23)

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The calculated energy situation traps indicate the acceptor and donor type by Eqs. (18) and (19). As an example, Figure 31 shows the calculation results for Al-ErF3-nGe structure.

Figure 31. Dependency energy situation donor and acceptor traps at the interface ErF3-nGe of electroforming cycle number (flat bands).

The average value for the energy level in the germanium band gap with a trap donor type for ErF3-nGe and YF3-nGe interfaces were: 𝐸𝑡𝑑 − 𝐸𝐹 𝐹𝐵 = 0.05 eV. Traps for the acceptor type did not exist in electrical measurements data, since the shift in the experiment for C-V characteristics were positive voltages, i.e., this was observed by the capture of a negative charge. For traps that have the acceptor type, and if they were present in our structures, the appropriate value would be 𝐸𝑡𝑎 − 𝐸𝐹 𝐹𝐵 = -0.18 eV. Figure 32 shows the energy band diagram of the Al - ErF3 – nGe structure when the surface potential is in the absence of voltage, 0𝑆 = 0.09 V. The band diagram for this same structure with mode inversions is represented in Figure 33. In Figures 32 and 33, we compared the level trap situation for both the acceptor and donor types. Flat band donor type trap levels are above the Fermi level at 0.05 eV. Acceptor type traps are below the Fermi

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level at 0.18 eV. In the absence of voltage trap levels, donor and acceptor type lie below the Fermi level, because on the surface the bands bend downward in mode enrichment. For the mode inversion donor type traps, energy levels are based on the Fermi level above 0.1 eV, and trap levels of acceptor type based on a Fermi level that is below 0.1 eV. As previously mentioned, our measurements have manifested themselves only for donor type traps. For mode inversions in donor type traps, their levels are near the Fermi level on the surface; their difference in energy was ≈ 4kT. When the amplitude AC signal is ~ 0.25 V, data traps can make a tangible contribution to the measured capacity only if their recharging times remain low, i.e., less than a measuring signal period. For the frequency of a measuring signal 1 MHz the recharging traps time must be less than 10-6 s.

Figure 32. The band diagram for Al-ErF3-nGe structure in the absence of voltage.

Figure 33. The band diagram of Al-ErF3-nGe structure in mode inversions.

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There is a reduction in energy levels for donor traps (an increase for acceptor) when the number of electroforming cycles increased for all researched structures. The speed was 0.012 eV/cycle value. For this case, the trap level moved to the Fermi level in mode inversions, this enhancement on the trap capacity at the isolator/semiconductor interface seems appropriate.

3. Change the Distribution of the Interface States Energy Density in Germanium Band Gap during the Electroforming Process The dependence in surface potential for voltage U can calculate the distribution of interface states density 𝐷𝑖𝑡 in germanium band gap by the formula: 𝐷𝑖𝑡 =

𝐶𝐷

𝑑𝑈

𝑒2

𝑑 𝑆

−1 +

𝐶𝑠 𝑒2

.

(24)

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This method gives a U-shape view of the distribution for interface states energy density over the energy gap for germanium and the researched structures. When calculating 𝐷𝑖𝑡 change in two parameters, namely electroforming cycle number and Fermi level position relative to the edge of conduction band on the semiconductor surface 𝐸𝐶 − 𝐸𝐹 𝑆 . Better understanding of the process can provide this surface that is built by these coordinates. For example, Figure 34 shows a similar surface for Al-ErF3-nGe structure. It increased the 𝐷𝑖𝑡 values when enhanced by electroforming cycle number m.

Figure 34. The 𝐷𝑖𝑡 distribution of the germanium band gap on the given electroforming cycle number of Al-ErF3-nGe structure.

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In general, increase the electroforming cycle number leads to non-monotone densification interface states. Example based on the trap energy density of the electroforming cycle‘s number is shown in Figure 35, which levels lay below the edge of the conduction band at 0.18 eV. Such non-monotone dependency also characterized changes in the interface states capacity and charge calculated by Eqs. (8) and (23), respectively (see, for example, Figure 20). Stress voltage in all electroforming cycles was maintained and stayed permanent at about 30 V. Thus, multiple cycles in electroforming under the same conditions of stress caused an unequivalent shift in the flat bands voltage, as well as a unequivalent change in value for interface states. Surface semiconductor treatment solution of HF reduces the primary interface states density, and also reduces the electroforming impact on 𝐷𝑖𝑡 growth. Surface treatment reduces shift flat band voltage. There is a reduction observed for processed donor trap energy levels than for those that do not have a processed surface. Thus, in flat band mode processed the surface received average values 𝐸𝑡𝑑 − 𝐸𝐹

𝐹𝐵

= 0.03 eV, 𝐸𝑡𝑎 − 𝐸𝐹

𝐹𝐵 =

– 0.2 eV

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In this case, a decline was also observed for donor trap energy level when the electroforming cycle number increased.The speed was less one than for those structures that were not processed (Figure 36), where the average value indicated was 0.003 eV/cycles. This may be defined as less dependence on structures characteristics when using multiple electroforming cycles in this case.

Figure 35. Dependencies interface states energy density in the germanium band gap of the electroforming cycle number for structures Al – ErF3 – nGe and Al – YF3 – nGe (when 𝐸𝐶 − 𝐸𝐹 0.18 eV). Germanium: Properties, Production and Applications : Properties, Production and Applications, Nova Science Publishers, Incorporated, 2011.

𝑆

=

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219

Figure 36. Energy situation traps for acceptor and donor type during electroforming for the processed Al-YF3-nGe structure.

Our main parameters studied germanium structures with yttrium and erbium fluoride films for the first electroforming cycle and are presented in Table 3. Analysis shows the different effects at various settings on the properties of structures. Here, two selected points are given:

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The capacity value in mode inversions is defined 𝐸𝑡𝑑 − 𝐸𝐹

inv

or 𝐸𝑡𝑎 − 𝐸𝐹

inv .

The

smaller its value, then the stronger the traps influence is on the capacity in mode inversions. The structure‘s effective charge and flat band voltage values are defined whether it‘s a charged or neutral trap. For example, suppose that the acceptor trap energy situation is significantly below the Fermi level for the n-type structure, and not discharged, when the moving structure from a regime indicates enrichment to inversion. The trap cannot contribute to the value by registering interface states energy density, but contributes to the effective charge of the structure. Table 3. Options for germanium structures with films of fluoride REE received in the first electroforming cycle

Structure

𝑬𝑪 − 𝑬𝒅𝒕 (eV)

𝑬𝒂𝒕 − 𝑬𝒗 (eV)

Al–ErF3–nGe Al–YF3–nGe Al–YF3–nGe Processing

0.18 0.16 0.21

0.25 0.23 0.21

𝑬𝒅𝒕 − 𝑬𝑭 (eV) 0.10 0.14 0.11

𝐢𝐧𝐯

𝑬𝒂𝒕 − 𝑬𝑭 (eV) –0.10 –0.14 –0.11

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𝐢𝐧𝐯

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Analysis of experimental results show the process of electroforming is not created by a high inner electric field that is often sufficient to create bulk traps in isolator layer; where the volume density of all traps for isolator layers remains constant. However, in this case, creates new traps at the isolator/semiconductor interface. Probably electroforming stress conditions at the isolator/semiconductor interface that is similar to negative bias temperature instability (NBTI) when almost excluded hot carriers create only interface states (𝐷𝑖𝑡 ) [5]. Or negative gate voltage, or elevated temperature may cause NBTI with more strong and rapid effects which create their joint action. This effect occurs predominantly in MOSFETs with inversion channel p-type and a negative gate voltage. When it is a positive gate voltage for a inversion channel MOSFETs with n-type (positive and negative gate voltage) the apparent effect is small. It was found that the degradation that was caused by NBTI may be partly removed during annealing at high temperatures, by deleted NBTI stress voltage. The electric field exerted during annealing can play a role in recovery after NBTI degradation [20]. A positive shift during annealing can allow the most recovery characteristics by the device. Similarity in the occurring processes for electroforming and NBTI may give proof to the electro thermal nature of the electroforming phenomenon. In this case, the temperature distribution and current density by a defined electric field value creates a conductive path for a sharply limited cord in fluoride REE isolator film. As a result the positive feedback dramatically increases the power granted in unit volume, considerably increasing the temperature in the area of power cord. This is reflected in our study structures when switching to low resistance status for a station negative differential resistance S-shaped type. The joint action by the electric field and temperature, apparently break the ion connection of fluoride REE and form rare earth metal ionst o create a metal channel in the layer of fluoride REE. The resulting low resistance condition is stable and is saved with the absence of voltage. In the case where there is opposite polarity current, whose value is greater than the threshold one, the channel material is warmed to create mutual diffusion atoms with REE and fluorine. This causes a chemical interaction between the materials and makes the formation of REE fluoride. Our studies have shown substrate conduction channel region in film fluoride REE is separated by a tunneling-thin insulator layer, i.e., the insulator/semiconductor interface themselves can not transform the insulator/metal interface [21]. Therefore, traps generated by the electric field and high temperature on the interface remain there, and after the return to the original structure is in a high resistance state. However, when the structure status is checked during the switching from low- to high resistance state, this can restore partial properties in the isolator/semiconductor interface, if there is a positive gate voltage and high temperature as with NBTI. It is believed that when inner electric field becomes sufficiently high to induce some additional hot carriers such as hot electrons or holes, there is Fowler-Nordheim stress, or stress in the hot carriers. The Fowler-Nordheim stress effects not only 𝐷𝑖𝑡 but also the traps in the layer of gate oxide [5]. Thus, the electroforming phenomenon starts earlier than it appears for the hot electrons or holes with sufficient energy to interact with the insulator material in its entirety and where bulk traps form.

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B. Structure with Rare Earth Element Oxide Films

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1. REE Oxides on n-Type Silicon Substrates Structures with rare earth element oxide films are also exposed to electrical fields in the electroforming process. Film structures with fluoride REE on a germanium substrate exhibit a positive charge increases when the number of electroforming cycles increase. The REE oxide film structures on silicon substrate exhibit an increase that has both a positive and negative charge. For example, Figure 37 shows C-V characteristic for the Al-Ho2O3-nSi structure, where the electroforming cycles number show an observed increase and a shift characteristic of a positive voltage that corresponds to the capture of negative charge. Also, to further compare Figure 37,this represented an ideal low frequency C-V characteristic calculated for this structure. Figure 38 shows the interface states density change calculated by Eq. (24) for the trap levels, as 0.32 eV from the edge of conduction band on the silicon surface, an effective charge calculated by Eq. (23). In its original state the effective charge structure is positive; impact electric field in the electroforming process raises the negative charge. At the same time increases the 𝐷𝑖𝑡 value.

Figure 37. The C-V characteristics for the structure Al – Ho2O3 – nSi (insert is the specified electroforming cycle number).

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Figure 38. The density change for interface states and effective charge during multiple electroforming cycles in the structure Al – Ho2O3 – nSi.

Calculation of the traps energy situation for the silicon band gap in our structure leads to an energy band diagram as shown in Figures 39 and 40. Here, it should be reasoned that in Figure 39 the surface band bending structure the original state, then after the second electroforming cycle on the surface it generates a layer depletion. Regime inversion corresponds to the 𝑆 = −0.35 eV value of the surface electrostatic potential. A negative charge acquisition for a structure in the electroforming process indicates the formation of an acceptor type trap on the oxide/silicon interface. Here, represented for comparison are acceptor and donor type traps. Under this band diagram, these traps are below the Fermi level, and hence, capture electrons and acquire the negative charge. When a structure moves from a regime of enrichment to an inversion, the traps do not discharge. The estimated energy difference between the level in the acceptor (donor) type traps and the surface Fermi level in mode inversions for these structures is ≈ 8kT, which is two times more than for germanium structures. Therefore, it should be expected to have a weak contribution to the interface states capacity. The structure importance is for full capacity, as observed experimentally. The yttrium oxide structure using n-silicon initially had a positive effective charge (Figure 41). During the first electroforming cycle, it acquired a negative charge, in all other subsequent electroforming cycles the structure‘s charge again reverted to positive. Figure 42 presented dependences for the interface states density (at 𝐸𝐶 − 𝐸𝐹 𝑆 = 0.31 eV) and effective charge of the Al-Y2O3-nSi structure.

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Change the Properties of Silicon and Germanium Structures …

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Figure 39. The band diagram for Al-Ho2O3-nSi structure in the absence of voltage.

Figure 40. The band diagram for the Al-Ho2O3-nSi structure during mode inversion.

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Figure 42 clearly shows the changes in the effective charge when the interface states density can change fully: these two dependencies almost mirror each other. To explain these dependencies, this cannot be shown when using only one type of trap: donor or acceptor. Therefore, effective charge must be law: 𝑄𝑓 = 𝑄𝑓0 + 𝑄𝑡𝑎 𝑆 + 𝑄𝑡𝑑 𝑆 ,

(25)

where 𝑄𝑓0 is initial structure charge (for our structures, positive). Analysis in literature references show that similar charge change scenarios were observed by other authors [6].

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Figure 41. The C-V characteristics in the Al-Y2O3-nSi structure.

Figure 42. The density changes for interface states and effective charge during multiple electroforming cycles for Al-Y2O3-nSi structure. Germanium: Properties, Production and Applications : Properties, Production and Applications, Nova Science Publishers, Incorporated, 2011.

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225

Calculation in the traps energy situation for our structures with yttrium oxide gives these values 𝐸𝑡𝑑 − 𝐸𝐹

𝐹𝐵

= – 0.06 eV, 𝐸𝑡𝑎 − 𝐸𝐹

𝐹𝐵 =

– 0.13 eV.

In mode inversions, donor traps are above the Fermi level with an energy reading of 0.14 eV; and for the acceptor trap that is below the Fermi level, it can have the same amount of energy. During the transition, from the regime of enrichment to the inversion; acceptor traps cannot recharge because they all are below the Fermi level. Since the traps are charged negative, they cannot be registered as new interface states. However, they can contribute to the effective charge of the structure. Newly created and before existing donor traps,they cross Fermi level positively charged, to be registered as interface states and contribute to the effective charge of the structure. Research for silicon structures with films of oxide erbium showed that the initial structure has a negative charge, i.e., there exists on the silicon surface a layer of depletion. The first electroforming cycle led to a shift in the C-V characteristics in the area of negative voltages and for subsequent cycles the charge structures remain positive, but as observed with each decrease and increase charge. The difference in energy between the acceptor (donor) type traps and the structure‘s surface Fermi level in mode inversions was ≈ 8kT; so there were no significant changes in its capacity when electroforming the structures of Al-Er2O3-nSi. A positive charge in the structures reveals that donor type traps predominantly form in the electroforming process. Table 4 outlines the options in the structures studied for oxides REE films received after the first electroforming cycle. Table 4 show the silicon surface with REE oxide films and the variety of options when compared with REE fluoride films.

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Table 4. Options silicon structures n-type and p-type with films of oxides REE received for the first electroforming cycle Structure

𝑬𝑪 − 𝑬𝒅𝒕 (eV)

𝑬𝒂𝒕 − 𝑬𝒗 (eV)

Al–Er2O3–nSi Al–Y2O3–nSi Al–Ho2O3–nSi Al–Ho2O3–pSi Al–Y2O3–pSi

0.29 0.32 0.40 0.21 0.40

0.39 0.48 0.25 0.36 0.31

𝑬𝒅𝒕 − 𝑬𝑭 (eV) 0.20 0.14 0.20 0.25 0.19

𝐢𝐧𝐯

𝑬𝒂𝒕 − 𝑬𝑭 (eV)

𝐢𝐧𝐯

–0.20 –0.14 –0.20 –0.25 –0.19

In mode inversions the change capacity in silicon structures with REE oxide films were found to have orders less than germanium structures with REE fluoride films at 𝐶𝑖𝑡 = (0.000 005-0.006 873) F/m2 for silicon n-type structures. Thus, these calculations show that, in this case, donor traps located at the upper half of the band gap and acceptor traps were at the bottom. However, with consideration for the energy band diagram as in Figure 39, Figure 40 shows that although these traps can affect the effective charge structure, by charging it negative, the traps cannot affect the value of interface states energy density. Only by recharging from the regime of enrichment in the

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inversion donor traps while charging positive can affect density. This is contrary to Figure 38, where simultaneously the value of interface states densities increases the negative charge. A similar situation is presented in Figure 42 for the structure of yttrium oxide film, where growth interface states densities have a decreasing positive charge. And while generally a positive charge structure grows, it is clear that recharging from regime enrichment to the regime inverse only for donor traps contribute to the negatively charged structure. Traps that give contribution to the positive charge structure where there is no recharging show their number increases (or increases the bulk positive charge of isolator layer). Analysis of literary references indicate that on silicon wafers n-type there are dangling bonds of silicon (Pb -centers), which induce two discrete energy levels within the band gap Si [22]. These centers are amphoteric and can introduce interface state levels, (0/-) in the upper and (+/0) in the lower half of the silicon band gap. Zhang et al., [23] received double peaks distribution density for interface states at the Si/SiO2 interface, about 0.2 eV above and below the mid band gap, in the absence of hydrogen supply. Single peak distribution is created by hydrogen induced interface states, which claimed responsibility for the hydrogen presence for single or double peaks in the distribution. Cherkaoui et al., [22] discusses the Pb-centers (0/-) on the interface Si/HfO2, localized at 0.29 eV above mid band gap. Thus, acceptor trap levels, in these cases, are located at the oxide/silicon interface above donor traps levels. In Eqs. (18) and (19), analysis shows that acceptor levels for traps at the silicon/oxide REE interface are located above donor in band gap Si when logarithmic function accepts negative values. This means the run ratio: 0
1.0 × 1023 y and hmν i < .7 − 4.9 eV for 82 Se with Q=2295 keV. The project SuperNEMO is based on the same approach, increasing the mass of the sources (82 Se, 150 Nd) to the scale of hundreds of kg, which requires a change in the detector geometry. Improving some experimental parameters, the sensitivity to the effective neutrino mass could reach ∼50 meV. One module of the SuperNEMO project could be in operation in some years. The NEXT project is developing a novel detection concept for investigating the neutrinoless DBD of 136 Xe [24]. This concept is based on a Time Projection Chamber (TPC) filled with high-pressure gaseous xenon, and with separated-function capabilities for calorimetry and tracking. Thanks to its excellent energy resolution, together with its powerful background rejection provided by the distinct DBD topological signature, it could be competitive with other next-generation neutrinoless DBD experiments. They plan to construct a detector with 100 kg fiducial mass in isotope 136 Xe, to be installed in the Canfranc Underground Laboratory, in Spain. Also the EXO experiment in USA is focused on the study of 136 Xe. Other DBD experiments are at different stages of development, like MOON (100 Mo) and CANDLES (48 Ca) in Japan, COBRA (116 Cd and 130 Te) in Italy, CARVEL (48 Ca) in Ucraine, and SNO++ (150 Nd) in Canada. Germanium: Properties, Production and Applications : Properties, Production and Applications, Nova Science Publishers, Incorporated, 2011.

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3.

277

New Generation Germanium Experiments

In new Ge DBD experiments a background level of 10−3 c/(keV kg y) in the region where the signal is expected to appear must be achieved, in order to explore effective neutrino masses around 40 meV; this means a reduction of two orders of magnitude in the background levels registered in previous experiments. Underground operation, passive and active shieldings and extreme control of primordial and cosmogenic radioactivity in materials are mandatory, but also the implementation of new background rejection techniques based on the use of segmented Ge detectors and the analysis of pulse shapes in signals taken from the detector. Important advances in high-purity germanium detector technologies have been achieved [25, 26, 27], allowing the construction of large efficiency HPGe crystals and developing the monolithic segmentation technique which provides both interaction position and energy information. Pulse shape discrimination of the DBD signal from background in coaxial Ge detectors is possible thanks to the fact that the former leave generally only one energy deposit inside the crystal (”monosite” events), whereas the latter leave in many cases more than one (”multisite” events). Number and features of the lobes in the current signals from the detector depend on the number and position of energy deposits produced by particle interaction. Conventional, non-segmented DBD detectors have shown good discrimination capabilities, having spatial resolution only in the radial direction [11, 28, 29, 30, 31], but further background reduction can be expected thanks to segmentation. First results of the operation of segmented Ge crystals within DBD projects have been obtained in the last years [32, 33, 34, 35, 36]. The immediate approach to background rejection is to keep only events with energy deposits in one segment and to apply discrimination techniques to the signal from that segment; the power of this technique has been already evaluated considering different methods [32, 37, 38, 39, 40, 41]. But the Pulse Shape Analysis (PSA) in segmented Ge detectors taking into account not only net signals in a segment but also induced transient signals in the neighboring segments has revealed as a promising technique for three-dimensional position determination [42] and important achievements have been obtained in other contexts for the spatial resolution of events (see for instance Refs. [43, 44, 45, 46, 47, 48]); therefore, PSA in segmented detectors could offer a better background rejection in DBD experiments. It must be noted that apart from segmented detectors, the potential of PSA with broad-energy Ge detectors has been recently explored too [49, 50].

4.

Background Reduction and Sensitivity

It is therefore important to evaluate the background reduction attainable at present for new generation germanium detectors in the region between 2 and 2.1 MeV where the neutrinoless DBD signal of 76 Ge is expected to appear, in order to asses the sensitivity of this kind of experiments. Reduction of background can be based on the granularity of the detector system, on the segmentation of each individual germanium detector and on the application of Pulse Shape Analysis (PSA) techniques to discriminate signal from background events. First results of this study, completely developed in [51], were presented in [37], based on the analysis of simulated expected signal and backgrounds. In this section, main features of the

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simulations performed will be presented. Then, the analysis of the effects of each one of the three reduction strategies considered (granularity, segmentation and PSA) for the different background sources will be presented. Detection efficiency to the neutrinoless DBD signal and corresponding sensitivity will be studied assuming the different background rejection scenarios and finally results and conclusions will be discussed.

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4.1.

Simulation

A set of simulated events for both neutrinoless DBD signal and the most relevant components of background have been taken into consideration in order to quantify background rejection factors and the detection efficiency to the signal for the different rejection methods. In underground experiments searching for rare events like the nuclear DBD, the background entangling the expected signal comes mainly from environmental gamma radiations (including radon emissions) and neutrons at the laboratory, radioactive impurities (either primordial or cosmogenically induced) in the materials of the experimental set-up and cosmic muons arriving even deep underground [52, 53]. The two main sources of the background registered in the region of interest for the neutrinoless DBD of 76 Ge have been identified in previous experiments like IGEX to be cosmogenic activation of germanium detectors (mainly 68 Ge and 60 Co) [13] and external gamma background above 2 MeV coming from 232 Th and 238 U chains. In fact, in present projects of new experiments these two sources continue to be a dominant background [20, 21]. Therefore, in this work the particular background components thought to be the most significant ones were first taken into account: cosmogenic 68 Ge and 60 Co produced in the germanium crystal [54] and the 2614.5 keV emission from 208 Tl in the 232 Th chain. Precise conditions necessary to achieve a background level ∼10−3 c keV−1 kg−1 y−1 in the region of interest from these sources will be discussed. A Monte Carlo study of the background achievable in the GERDA experiment by anti-coincidence cuts between crystals and segments has been published considering the main radioactive impurities in the set-up [55]; it has also been shown in the context of this experiment that muon-induced contribution to background can be of ∼10−4 c keV−1 kg−1 y−1 provided a muon veto system is used [56]. A set of Monte Carlo simulations using GEANT4 [57] package has been developed. As the first goal was focused on the crystal geometry, a natural germanium crystal without shielding has been defined as detector. Internal contaminations of the crystal are emitted homogeneously inside it, whereas for external sources, the corresponding gammas were emitted homogeneously and isotropically from the surface of an external sphere. Standard GEANT4 models, including those specific for low energy, have been used for all the processes, isotopes decays, and particles simulated. Double beta decays (either as signal in the neutrinoless case or as background in the two neutrino channel) have been generated using the DECAY0 code [58]. For every simulation made, position and energy of each interaction produced in an event have been registered. This information has allowed us to make different analysis of the obtained data in the Region of Interest (RoI) between 2 and 2.1 MeV. It has been simulated a number of events big enough to obtain a negligible statistical error (below 2% for all the studies made). In this way, an attempt has been made to estimate the raw contributions to the detector

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279

counting rates coming from the main sources of background taken into account, before applying any technique for background reduction. • Cosmogenic production rates in germanium of 5 kg−1 d−1 (with an exposure time of 30 days) for 60 Co and 1/10 kg−1 d−1 (with an exposure time of 180 days and a cooling time of 180/730 days) for 68 Ge have been considered (more details can be found in [37]). • The evaluation of the expected background coming from the 2614.5 keV line from 208 Tl has been made considering both the environmental gamma background in the laboratory and the 232 Th intrinsic radioimpurities in the lead shielding expected to be surrounding detectors. The response to 2614.5 keV photons for the counting rates in the 2-2.1 MeV region of interest in 2-kg and 4-kg germanium detectors has been estimated by Monte Carlo simulation. A flux of ∼0.1 cm−2 s−1 for environmental 2614.5 keV photons has been assumed, according to measurements in the Canfranc Underground Laboratory [59], and an activity of 1 µBq/kg of 232 Th in lead has been considered just as a reference value. In these estimates, a spherical cavity with radius R=30 cm for placing detectors inside has been supposed, and two different shielding configurations with 30 and 40 cm of lead surrounding the cavity have been taken into account.

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• Other background sources considered include external 214 Bi emission, with a measured gamma flux in the Canfranc Underground Laboratory of ∼0.38 cm−2 s−1 , 60 Co impurities in the copper cryostats containing the Ge crystals (assuming an activity of 1 mBq/kg) and the DBD with emission of neutrinos of 76 Ge. Rates presented in Table 1 for all these background components correspond to conventional germanium detectors, that is, without taking into account neither segmentation nor PSA techniques. Last row in this and other tables shows the total detection rate, obtained summing all the contributions assuming the best conditions. Uncertainties in the estimates of raw backgrounds presented in Table 1 come in principle from the simulations of the response of detectors to the different background sources as well as from the inputs considered for production rates of cosmogenic isotopes or gamma fluxes. Counting rates are directly proportional to these inputs, which are thought to be the main source of error since GEANT4 can reproduce electromagnetic processes with a few per cent error and statistical errors in simulations have always been kept below 2% as stated before. Production rate of 60 Co has an uncertainty of ∼50% (when considering different available estimates) and for 68 Ge it could be up to one order of magnitude. Environmental gamma fluxes depend on the particular underground location. For 232 Th impurities in very pure lead just upper bounds have been derived (see Refs. [60, 61]) and therefore the assumed value must be taken just as a reference.

4.2.

Rejection of Background

Three strategies, as pointed out before, can be followed to reduce the background level in the region of interest: granularity of the experiment detectors, segmentation of the crystals and analysis of the obtained pulses. Germanium: Properties, Production and Applications : Properties, Production and Applications, Nova Science Publishers, Incorporated, 2011.

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Table 1. Estimate of the detection rate (10−3 c keV−1 kg−1 y−1 ) at the RoI due to the different background components for germanium crystals of 2 and 4 kg. Mass (kg) Internal 60 Co Internal 68 Gea Internal 68 Geb 60 Co in cryostat 232 Th in lead External 232 Th 30 cm lead External 232 Th 40 cm lead External 214 Bi 30 cm lead External 214 Bi 40 cm lead 2νββ Best total a b

4.00 3.73 15.81 38.66

28.47 2.82

33.67 2.25

39.76

31.72

0.38

0.30

20.73

17.16

0.17 0.09 47.0

0.14 0.09 55.7

For a production rate of 1 kg−1 d −1 and a cooling time of 180 d. For a production rate of 10 kg−1 d −1 and a cooling time of 730 d.

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2.00 2.90 12.50 30.56

Granularity

A first step to determine the best set-up of an experiment consists in analyzing what could be the optimal mass of the detectors that build the whole experiment to have a background level as low as possible, if a fixed total mass of germanium is assumed. With this purpose, cylindrical crystals with the same value for diameter and height and masses between 0.1 and 4 kg have been simulated. If only the events with an energy deposit between 2 and 2.1 MeV are taken into account, we can see how for internal contaminations and a given specific activity, the higher mass detectors register a higher background level (see Figs.3 a,b). 4-kg detectors register 28% (26%) more events for 60 Co (68 Ge) than 2-kg ones. This is not the case for external contaminations, because for a given activity, the heavier detectors have a lower background (see Fig.3 c). 4-kg detectors register 54% less events coming from 2614.5 keV photons than 2kg detectors. These values confirm that the optimal configuration of an experiment depends on what kind of background we want to reduce more, that coming from internal contaminations or from external ones, taking also into account that the dependency between the mass of the detectors and the background events registered is stronger for the external contamination. These data together with conclusions obtained from the study of the segmentation of the crystal and pulse analysis, as explained later, will determine the best configuration.

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2.5

2

1.5

1

0.5

0 0

0.5

1

1.5

2

2.5

3

3.5 4 4.5 Detector Mass (kg)

2.5

3

3.5 4 4.5 Detector Mass (kg)

2.5

3

3.5 4 4.5 Detector Mass (kg)

c/keV every 10^4 decays per kg

a) 3

2.5

2

1.5

1

0.5

0 0

0.5

1

1.5

2

c/keV/kg every 10^4 interacting photons

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b)

50

40

30

20

10

0 0

0.5

1

1.5

2

c) Figure 3. Background level in the 2-2.1 keV region of interest depending on the component detector mass. For internal contaminations, 60 Co (a) and 68 Ge (b), it is represented in counts per keV every 104 decays per kg. For external photons of 2614.5 keV (c), it is represented in counts per keV per kg every 104 interacting photons.

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Figure 4. Segmentation scheme for a germanium crystal with 9 transversal slices and 6 longitudinal sectors to obtain 54 segments.

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4.2.2.

Segmentation

Regardless of the mass of the used detectors, other way to reduce the background level is by segmentation of the crystals and further application of anticoincidence techniques between segments. The aim was to quantify the maximum background reduction that could be obtained from segmentation of the crystals, beyond the reduction by just anticoincidence between different detectors. For the cylindrical detectors studied, two different ways to divide it were considered: segmentation in planes and segmentation in sectors (longitudinal and transversal segmentation respectively) (see Fig. 4). For a 4 kg detector with the highest number of segments studied (66 segments distributed in 11 transversal slices and 6 angular sectors), approximately only 2 out of 100 events will not be rejected by anticoincidence techniques for 60 Co contamination. For 68 Ge the ratio is around 5 out of 100 events and for 2614.5 keV external gammas, less than a half of total events. This reduction can be observed qualitatively in the spectra obtained from simulations for the different background sources studied (see Fig. 5). It is clear that for higher number of segments in the crystal, we are able to reject more background events. But the segmentation of a crystal is limited for some reasons. First of them is the difficulty associated to the reduction of the width of the transversal segments. It is also necessary to make a segmentation to reject a high number of background events without losing too much efficiency in the double beta decay events detection. The different segmentation configurations studied have transversal segments with a width of 1 cm approximately. This size is reachable using actual segmentation techniques and provides a good efficiency for the detection of double beta decay events. Considering the biggest segmentation of all studied and applying the reduction factors obtained to the raw rates for different background sources estimated, the resulting rates can be derived and are presented in Tables 2,3 for 2 and 4-kg crystals.

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b) 105 104 103 102 10

1 0

500

1000

1500

c) Figure 5. Comparison between the spectra obtained for the different contaminations studied: 60 Co (a), 68 Ge (b) and 2614.5 keV photons (c), for a 4-kg detector without segmentation (black line), with 11 transversal segments (blue line) and with 66 segments, 11 transversal by 6 longitudinal (red line).

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Table 2. Estimate of the detection rate (10−3 c keV−1 kg−1 y−1 ) in the RoI by applying anticoincidence techniques for segmented 2-kg crystals, for different segmentation schemes. Segmentation Internal 60 Co Internal 68 Gea Internal 68 Geb 60 Co in cryostat 232 Th in lead External 232 Th 30 cm lead External 232 Th 40 cm lead External 214 Bi 30 cm lead External 214 Bi 40 cm lead 2νββ Best total a

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b

7 planes 0.22 1.74 4.26

9 planes 0.12 1.16 2.83

6×7 0.10 0.93 2.30

6×9 0.05 0.61 1.51

2.32 1.68

1.68 1.57

1.02 1.47

0.79 1.38

23.63

22.11

20.70

19.46

0.22

0.21

0.20

0.18

13.99

12.93

12.71

11.85

0.11 0.08 6.4

0.10 0.08 4.9

0.10 0.08 3.9

0.09 0.08 3.2

For a production rate of 1 kg−1 d −1 and a cooling time of 180 d. For a production rate of 10 kg−1 d −1 and a cooling time of 730 d.

4.2.3.

PSA

Besides the improvements made in the detector, like the segmentation of the crystal, a reduction of the background level from the analysis of the pulses registered can also be obtained. For this purpose, as pointed out before, it is necessary to distinguish between background and real double beta decay events in order to reject the first ones. Application of PSA in segmented crystals allows to increase the spatial resolution of conventional germanium detectors to obtain the position of energy deposits with a very good accuracy in all the dimensions [46] or at least a correct identification of the number of interaction points [62]. The data obtained in the simulations can be reanalyzed for a given spatial resolution, grouping all the partial energy deposits with a separation lower than the resolution and considering these groups like indivisible energy deposits. Then, it is possible to determine how many of these indivisible deposits each background event has. In figure 6, distributions of the number of energy deposits per event for different background sources and 4-kg detectors are showed, assuming 2 different values for the spatial resolution, 3 and 5 mm, which seem to be at reach today according to the work developed in Ref. [46]1 ; it is worth noting 1

A genetic algorithm for the decomposition of multiple hit events is presented in Ref. [46], considering the features of a cylindrical closed-end germanium detector with a mass of almost 2 kg and 6 angular sectors and Germanium: Properties, Production and Applications : Properties, Production and Applications, Nova Science Publishers, Incorporated, 2011.

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Table 3. Estimate of the detection rate (10−3 c keV−1 kg−1 y−1 ) in the RoI by applying anticoincidence techniques for segmented 4-kg crystals, for different segmentation schemes. Segmentation Internal 60 Co Internal 68 Gea Internal 68 Geb 60 Co in cryostat 232 Th in lead External 232 Th 30 cm lead External 232 Th 40 cm lead External 214 Bi 30 cm lead External 214 Bi 40 cm lead 2νββ Best total a

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b

9 planes 0.19 1.61 3.95

11 planes 0.12 1.15 2.81

6×9 0.09 0.78 1.91

6×11 0.06 0.67 1.63

5.62 1.23

3.22 1.13

1.98 1.07

1.31 1.01

17.31

16.05

15.01

14.23

0.16

0.15

0.14

0.13

10.85

10.41

10.01

9.71

0.09 0.08 9.0

0.08 0.08 6.0

0.08 0.08 4.2

0.08 0.08 3.3

For a production rate of 1 kg−1 d −1 and a cooling time of 180 d. For a production rate of 10 kg−1 d −1 and a cooling time of 730 d.

that these distributions have been obtained without making any particular definition of the segmentation scheme. The worst value of the spatial resolution can give an idea of the loss of rejection efficiency depending on the spatial resolution finally achieved. For the heaviest crystal and assuming a 3 mm spatial resolution, it is possible to reject 99.9% of background events coming from 60 Co, 99.2% from 68 Ge and 60.3% from 2614.5 keV photons; the values are 99.5%, 97.8% and 56.5% respectively if a resolution of 5 mm is considered. Spatial resolution of the detectors allows to reject more or less background events depending on how the energy of these events is distributed in the crystal. One way to predict what could be the maximum reduction factor consists in determining the maximum distance between all the energy deposits of the same event (that we call maximum interdistance Dmax , see Eq. 6) and studying how it is distributed. q

Dmax = max[ (xi − xj )2 + (yi − yj )2 + (zi − zj )2 ]

(6)

This maximum interdistance depends on different factors like the mass of the detector, the scheme of the decay of the isotope that produces the background event or the origin of the event, because it is different if the contamination is located inside the crystal or if comes 4 transversal slices. However, it is reported that the approach has no limitation concerning the geometry of the crystal, the number and layout of the segments or the number of interactions.

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b)

103

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c) Figure 6. Distribution of the number of energy deposits per event in the 2-2.1 MeV region of interest for all the background contributions studied: 60 Co (a), 68 Ge (b) and 2614.5 keV photons (c), for 4-kg detector and considering a spatial resolution of 3 (solid line) and 5 mm (dashed line). Monosite events are singled out in red (blue) for 3 (5) mm resolution.

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from outside of the experimental setup. In Fig. 7, the distribution of these maximum interdistances for 2 and 4-kg detectors and all the background sources studied are presented, showing how all the factors mentioned previously have influence on these distributions. From these plots in Fig. 7, rejection factors for any considered experimental spatial resolution can be deduced knowing that all events with a maximum interdistance lower than the spatial resolution will be labelled as monosite like double beta events. Table 4 show the expected counting rates in the 2-2.1 MeV region of interest for background contributions in 2-kg and 4-kg germanium detectors, applying the reduction factors obtained when considering a 3D spatial resolution of 3 mm from PSA on the raw background estimated. Total background levels have been calculated (see last row in Table 4) using the most favorable conditions.

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Table 4. Estimate of the detection rate (10−3 c keV−1 kg−1 y−1 ) in the RoI for 2 and 4-kg crystals, by applying PSA techniques and assuming different spatial resolutions. Spatial resolution Internal 60 Co Internal68 Gea Internal 68 Geb 60 Co in cryostat 232 Th in lead External 232 Th 30 cm lead External 232 Th 40 cm lead External 214 Bi 30 cm lead External 214 Bi 40 cm lead 2νββ Best total a b

2 kg 3 mm 5 mm 0.01 0.03 0.13 0.38 0.32 0.92

4 kg 3 mm 5 mm 2 =

m2e FD FN

(7)

with me the electron mass and FN the nuclear factor-of-merit, defined as FN =G0ν |M0ν |2 , being G0ν a kinematical factor and M0ν the nuclear matrix element qualifying the likeliness of the transition. These matrix elements can be evaluated in the framework of different nuclear models [66, 67]; differences between different estimates are unfortunately not negligible, although some convergence is being achieved [68, 69, 70]. The background level b achievable in germanium experiments has been analyzed in previous sections under different background reduction schemes; but the application of anticoincidence rejection or PSA techniques unfortunately affects also the efficiency for the detection of the neutrinoless DBD signal. Therefore, a study of this efficiency has been carried out and is presented here. 4.3.1.

Efficiency to Signal

In order to evaluate the dependency between background reduction techniques and loss of efficiency, it is necessary to simulate neutrinoless DBD events inside the detector to apply them the same treatment that a background event. This procedure allows to estimate the percentage of 0νββ events rejected losing detection efficiency. Signal events can be missed either because of the escape of the Bremsstrahlung radiation produced by electrons or because 0νββ events are mistaken as background due to the spatial distribution of their energy deposits. To define 0νββ events in the simulations, two electrons with sum energy of 2040 keV (Q value for 76 Ge DBD) have been considered, neglecting in first approach the angular correlation between electrons. In order to check if this angular correlation could have substantial influence to detect a 0νββ event, a first study was made simulating two electrons

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100

95

90

85

80

75

70 1000

1200

1400

1600 1800 2000 Energy of the most energetic electron (keV)

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Figure 9. Detection efficiency versus the energy of the most energetic electron of a 0νββ event in a 4-kg detector considering a full crystal detector (black points), anticoincidences in 11 x 6 segmented crystals (blue squares), and PSA with 3 mm (red triangles) and 5 mm (white circles) spatial resolution. of 1020 keV each emitted randomly, with the same and with opposite directions. Decays are distributed homogenously in the crystals, for 2 and 4 kg detectors. The differences between the detection efficiency factors in the cases described before are less than 1% for the different angular correlations considered, validating the approximation taken. Another point in the simulation of 0νββ events is the energy distribution of the two electrons. Four different configurations were studied: two electrons of 1020 keV each (half of the total energy), two electrons of 1500 and 540 keV, two electrons of 1734 and 306 keV (75% and 25% of the full energy respectively) and one electron of 2040 keV. It is important to point that the last case is not a real case but could be useful to obtain limit values in the detection efficiency because Bremsstrahlung probability is higher for more energetic electrons. For all these energy configurations, the electrons were emitted in random directions using the same simulation package that for the background events. Figure 9 shows the detection efficiencies obtained in a 4-kg detector for the different energy configurations in 0νββ events. As it can be seen, PSA techniques offer better detection efficiency than background rejection based just on crystal segmentation. The explanation is that the anticoincidence between segments rejects all the 0νββ events with energy deposits in two or more segments of the crystal, while PSA rejects events with two separated energy deposits, typically due to Bremsstrahlung but, in principle, could allow events close to the borders. A useful information to understand this is the maximum distance between all the energy deposits obtained in the simulation for 0νββ events (the maximum interdistance defined before and calculated using Eq. 6). Figure 10 shows the distribution of the interdistances for signal events and for all the energy configurations studied in a 4-kg detector. In all the cases, most of the events have a maximum interdistance below 3 mm, ensuring that they will be considered as monosite events by PSA and can be separated safely from background ones.

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N

292 105

104

103

102

0

1

2

3

4

5

6

7

8

9 10 Distance (mm)

Figure 10. Distribution of the maximum interdistance between energy deposits of the same 0νββ event at the peak in a 4-kg detector for 2 electrons of 1020 keV each (green), 1500 + 540 keV electrons (red), 1734 + 306 keV electrons (blue) and one 2040 keV electron (black).

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Other important point is the dependency between the efficiency and the energy of the most energetic electron of the 0νββ event. The more equal the electron energies, the higher the detection efficiency. This relationship is logical due to the Bremsstrahlung probability, that grows proportional to the energy of the electron. For this reason, the non real case of a 2040 keV electron can be useful to estimate the lower limit of the detection efficiency. 4.3.2.

Sensitivity

The overall detection efficiency to signal estimated above has been used together with Eq. 7 to compare the sensitivity of germanium DBD experiments using different background rejection schemes. Three different situations have been taken into consideration: no rejection technique, the application of anticoincidence rejection for crystals with 6×11 segments, and the use of PSA techniques assuming a 3 mm spatial resolution. Detectors enriched in 76 Ge at 86% and total exposures of MT=100 and 1000 kg·y have been assumed. An energy window of 3.5 keV has been considered, as in Ref. [9]. Values of background level and corresponding detection efficiency deduced in this work for 4-kg crystals have been used for each situation. Table 5 summarizes the evaluated sensitivities, presenting the FD values and the corresponding effective neutrino masses considering the average nuclear factor-of-merit FN =7.3×10−14 y−1 used in Ref. [9]. Neutrino masses below 50 meV can be explored with very segmented crystals or applying PSA techniques and for high enough exposures. To achieve a certain sensitivity to the effective neutrino mass, the required exposure of an experiment depends on the background level in the region of interest and the detection efficiency to the signal; both background level and efficiency are different when different background rejection schemes are considered. Figure 11 shows this dependency between the exposure and the efficiency in the three background rejection schemes considered be-

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Table 5. Comparison of the sensitivity of germanium DBD experiments under different background rejection schemes (see text).

MT (kg y)

no rejection 6×11 segmentation PSA (3 mm resolution) no rejection 6×11 segmentation PSA (3 mm resolution)

MT (kg·y) 100 100 100 1000 1000 1000

b (c keV−1 kg−1 y−1 ) 0.022 0.0019 0.0011 0.022 0.0019 0.0011

 (%) 93.8 80.3 85.4 93.8 80.3 85.4

FD (1026 y) 1.6 4.7 6.5 5.1 15 21

(meV) 149 88 74 84 49 42

105

104

103

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102 0.7

0.75

0.8

0.85

0.9

0.95

1 Efficiency

Figure 11. Exposure MT (in kg·y) necessary to reach the sensitivity to explore neutrino effective masses < mν > of 40 meV, versus the detection efficiency to 0νββ events considering full crystals (line), anticoincidences in 11 x 6 segmented crystals (dashed line), and PSA with a spatial resolution for PSA of 3 mm (dots and dashed line). fore. Using the overall signal efficiency values previously estimated, it can be deduced from this plot that despite the loss of efficiency, segmented crystals working in anticoincidence require an exposure one order of magnitude lower than that of non segmented detectors to explore the same range of neutrino masses. If PSA techniques are used with 3 mm of energy resolution, an additional factor of ∼two of reduction is achieved in the necessary exposure.

5.

Conclusion

The DBD with the emission of neutrinos is a rare nuclear process observed for several nuclei, but the neutrinoless channel, implying the violation of leptonic number conservation, has not be evidenced. Its identification would be outstanding in Neutrino Physics, since this would confirm the Majorana nature of neutrinos, inform on the neutrino mass scale and shed light on CP violation. DBD experiments with various emitters use different techniques for semiconductors,

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scintillators, chambers and cryogenic detectors. The extremely low expected rates impose underground operation and the development of background rejection. Although each approach has pros and cons, what make different experiments necessary (also due to the nuclear uncertainties) germanium detectors have played a prominent role in the field. IGEX and HM produced the leading results for years and now, once finished CUORICINO and NEMO3 and before the starting of CUORE and SuperNEMO, GERDA can become the front-runner experiment. Some conclusions can be drawn from the analysis of the different strategies for background reduction in germanium double beta decay experiments. The study of the granularity of the detector system shows that heavier crystals are better to reduce the contribution of external radioimpurities, but worse to reduce background coming from internal contaminations. By applying the most powerful segmentation techniques taken here into consideration in a 4-kg detector, 2(5) out of 100 events due to internal impurities from 60 Co (68 Ge) would remain in the RoI, while for external contaminations, about half of the events would be rejected. A 3-dimensional spatial resolution of 3 mm, obtained by means of PSA in segmented detectors, would allow to reject more than 99% of background events due to cosmogenic isotopes induced in the crystal, and around 60% of those coming from external 2614.5 keV photons. According to numbers presented in Table 4, a background level of 1.3 (1.8) 10−3 c keV−1 kg−1 y−1 due to the studied background sources could be achieved using 4 (2)-kg crystals when considering very precise conditions. For the production of 60 Co (68 Ge), the exposure time is of 30 (180) days and the production rate is 5 (1) kg−1 d−1 . In the case of 68 Ge, a cooling time of 180 days has been also taken into account. For the external 2614.5 keV, an environmental flux of 0.1 cm−2 s−1 has been assumed and the use of a 40-cm-thick lead shield considered. For intrinsic 232 Th impurities in the lead shielding, the activity supposed is 1 µBq/kg. In these optimal conditions, the raw background is reduced by more than one order of magnitude thanks to a 3 mm spatial resolution achieved by PSA in segmented detectors. The overall detection efficiency to neutrinoless DBD signals has been evaluated by Monte Carlo simulation for the different background rejection scenarios, finding for 4kg crystals a reduction from ∼94% to ∼80% when considering anticoincidences in 11×6 segments and to ∼85% if PSA techniques are applied with a 3 mm spatial resolution. The sensitivity of DBD experiments depends on both achieved background level in the RoI and detection efficiency; it has been shown that the improvement in the former thanks to rejection techniques largely compensate the loss in the latter since experiments with these techniques require much lower exposure for a fixed sensitivity. In summary, it seems that contribution from dominant background sources in previous germanium double beta decay experiments could be reduced down to 10−3 c keV−1 kg−1 y−1 in the RoI, which would allow to explore effective neutrino masses even below 50 meV, using new generation Ge detector technologies.

Acknowledgments This work is dedicated to the memory of our colleague Professor Julio Morales, passed away in 2009. Many of the results presented here were produced in close collaboration

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with him. We deeply acknowledge his dedicated work and always kind friendliness.

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In: Germanium: Properties, Production and Applications ISBN 978-1-61209-205-8 Editor: Regina V. Germanno © 2012 Nova Science Publishers, Inc.

Chapter 7

GROWTH OF Ge CRYSTALS WITH EXTREMELY LOW DISLOCATION DENSITY Toshinori Taishia and Ichiro Yonenaga*b a

Institute of Carbon Science and Technology, Shinshu University, Nagano, Japan b Institute for Materials Research, Tohoku University, Sendai, Japan

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ABSTRACT Germanium (Ge) single crystals with an extremely low density of or almost free from grown-in dislocations were grown by the Czochralski technique using boron oxide (B2O3) and a silica crucible, where generation of GeO2 particles, harmful for dislocationfree crystal growth, was effectively suppressed by the partially- or fully-coverage of the melt surface with B2O3 liquid. In a further evolution of the above growth technique, Ge crystals with various concentrations of interstitially dissolved oxygen atoms up to 5.5  1017 cm-3, two orders higher than that in a conventionally grown Ge crystals, were grown by full coverage of the Ge melt surface with B2O3 liquid and addition of GeO2 powder. The effective segregation coefficient of oxygen atoms was estimated to be 1.0–1.4. These Ge crystals are expected for application as high quality and thermo-mechanically stable materials, free from grow-in dislocations, for high-speed ULSI devices and GaAs solar cell substrates.

I. INTRODUCTION Recently, there is a renaissance of interest in germanium (Ge) for possible use in the next generation of high-speed ULSI devices due to its superior low-field carrier mobilities as well as lower temperature device fabrication processes in semiconductor industries [1, 2]. Ge is a favorable material for channel, source and drain in MOSFET, since electron and hole in Ge move faster than in silicon (Si) by 2.5 and 4 times, respectively. Though Ge can be used as lens and window materials for infrared optical systems, its use as substrates for gallium *

Corresponding author Tel.: +81-22-215-2040, Fax.: +81-22-215-2041, E-mail address: [email protected]

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arsenide (GaAs) solar cells is promising as it enables higher energy-conversion efficiency than Si in the future [1]. The historical fact that scientific and practical interests in semiconductor fields shifted to Si from Ge is partially based on that Ge is thermomechanically unstable and easily dislocated during growth and device fabrication processes in comparison with Si. For exploring the above-noted renewed applications in semiconductor industries, it is necessary to grow high quality Ge with high thermo-mechanical stability free from dislocations. In Si industry during crystal growth and manufacturing, interstitially dissolved oxygen (O) impurity has done a critical role against suppression of dislocation generation in bulk crystals through dislocation-impurity interaction, resulting in strengthening Si crystals [3]. It is reasonable to expect that oxygen can play the similar role in Ge crystals. However, fundamental information of the role of oxygen in Ge crystal growth is seriously limited. For example, though in the 1950s and 1960s a huge amount of data on solubility and segregation of various kinds of impurities in Ge were investigated by various research groups [4], solubility and segregation of oxygen atoms in Ge are not well established even now. Thus, roles of oxygen in Ge for dislocation-free crystal growth together with its segregation behavior should be clarified from a current point of view. Here we review our recent results on growth of Ge with extremely low dislocations density [5-7]. First, we present a new Czochralski (CZ) method for growing Ge crystals with an extremely low dislocation density using boron oxide B2O3. By the method, Ge single crystals 1 inch in diameter and 50 mm in length were successfully grown with a dislocation density being 0–1  103 cm-2, which was remarkably lower than that in Ge crystals grown by the conventional CZ technique. Then, we show enrichment of oxygen concentration in Ge single crystals by intentional doping of germanium oxide GeO2 during the crystal growth. Oxygen concentrations in Ge crystals grown with such method increased up to 5.5  1017 cm-3 two orders of magnitude higher than that in conventionally grown Ge crystals. Finally, segregation behavior of oxygen during Ge growth evaluated by measuring optical vibrations of oxygen atoms in the grown crystals is shown.

II. DISLOCATION-FREE Ge CRYSTAL GROWTH BY THE NEW CZOCHRALSKI METHOD A. Difficulty in Growth of Dislocation-Free Ge Crystals Dislocation-free crystals are essential in order to avoid their negative influence as severe carrier killers in various kinds of electronic devices and also in substrates for epitaxial growth for applications. Currently, dislocation-free Ge single crystals up to 300 mm in diameter are grown by the Czochralski (CZ) technique [1]. However, in commercial base Ge is very hard to grow dislocation-free crystals technologically. Usually, Ge crystals are grown using a carbon crucible in a vacuum. During such growth, some particles appear and float on a Ge melt surface as shown in Fig. 1(a) and attach to the growing Ge crystal in Fig. 1(b), which results in generation of dislocations and their penetration into the crystal. The particles are thought to be germanium dioxide (GeO2), the melting point of which is 1115˚C [8] higher than that of Ge (938˚C). They are formed in the melt originating in the oxide layer on the

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surface of charged Ge raw material, air leakage of the chamber or residual moisture in the growth furnace.

Figure 1. Photographs of (a) Ge melt with GeO2 floating particles on the surface and (b) grown Ge boule with GeO2.

We developed a new CZ method for growing Ge crystals with an extremely low dislocation density using boron oxide (B2O3) in order to control or prevent such particle formation on the melt surface. The Ge melt was covered with liquid B2O3 glass. As a result, indeed, generation of such articles was well suppressed observed on the B2O3-covered melt. From such Ge melt covered with liquid B2O3 we succeeded in growing Ge single crystals [5].

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B. Procedure of New CZ Growth Ge poly-crystal ingots with a purity of better than 4N (50Ωcm, n-type) weighing ~ 150 g were charged into a fused-silica crucible of 50 mm in diameter with a graphite susceptor. B2O3 blocks of 7.5 g in total mass, with residual moisture content of 100–200 ppm, were set on the Ge ingots. After evacuation up to a pressure of ~0.1 Pa in ambient, Ar gas with a purity of 99.99995% was made to flow under an atmospheric pressure of 1 atm. Ge melt, the surface of which was partially covered by liquid B2O3, was made by heating the Ge with a carbon heater. A Ge single crystal in the [111] orientation with a size of 4.5  4.5  50 mm3 was used as a seed. Ge crystals of 1 inch in diameter were grown by the CZ method at a pulling rate of 10 mm/h at 1 atm under a flowing Ar gas atmosphere at 1 liter/min. The crystal and crucible were rotated at 6 and 1.8 rpm in opposite directions, respectively. Thin necking and tailing treatments were carried out to eliminate generated dislocations during the seeding stage and to suppress dislocation generation in the growth termination stage, respectively. For comparison, one Ge crystal was grown from a Ge melt under the same growth conditions without liquid B2O3. Figures 2(a), (b), and (c) show illustrations of the arrangement of Ge, B2O3, and the silica crucible in material charging, after B2O3 melting, and after Ge melting, respectively. At charging, B2O3 blocks are put on Ge ingots in a silica crucible as shown in Fig. 2(a). During heating, the B2O3 blocks start to melt at 480˚C as shown in Fig. 2(b), and then Ge melts at

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938˚C. Since the density of B2O3 liquid is smaller than that of Ge melt and B2O3 liquid wets well to silica glass, the Ge melt and B2O3 liquid maintains the arrangement shown in Fig. 2(c). Indeed, only the outside region of the Ge melt was covered with the liquid B2O3, as shown in Figs. 3(a) and (b). Because of the low wetting ability of Ge melt against silica glass, the B2O3 liquid in the central region on the surface of the Ge melt moves to the outside close to the wall of the silica crucible, then rises up along the wall, and finally reaches the arrangement as shown in Fig. 3(c). Particles floating on the melt surface are caught by the B2O3 liquid and are moved outside of the Ge melt surface with the B2O3 liquid. Finally, a clean Ge melt surface ―window‖ free from any particles is realized in the central region of the crucible, making it possible to grow a Ge crystal from such a ―clean‖ Ge melt shown in Fig. 4(a). Figure 4(b) shows one scene during the crystal growth from such a melt. If the amount of the charged B2O3 chunk is suitably selected as 20 g in the present case, the Ge melt will be fully covered with B2O3 liquid as illustrated in Fig. 2(d). The Ge melt can be observed below the transparent B2O3 liquid layer during the growth. First, the seed was descended through the B2O3 liquid until it dipped into the Ge melt. Then, the crystal was pulled up through the B2O3 liquid layer during the crystal growth. No evaporation of B2O3 liquid was detected during heating and crystal growth in the adopted Ar gas atmosphere at 1 atm.

Figure 2. Illustrations of arrangement of Ge, B2O3, and silica crucible: (a) after charging, (b) after melting of B2O3, and (c) and (d) after Ge melting. (c) and (d): Ge melt partially and fully covered by B2O3, respectively.

Figure 3. (a) A photograph of particle-free Ge melt surface partially covered with B2O3 liquid. (b) An illustration corresponding to (a). (c) A cross-sectional image for Ge melt and B2O3 liquid in the silica crucible.

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Figure 4. (a) An illustration of Ge growth from B2O3-partially-covered melt. (b) A photograph during the crystal growth, corresponding to (a).

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C. Grown Ge Boules Figures 5 (a) and (b) show Ge boules grown from Ge melt partially and fully covered with B2O3, respectively. Their diameter was about 1 inch and the length was 90–100 mm. In both crystals no grain boundaries were observed in the whole part of the crystal until the tail, and their surfaces were smooth with no particles. Three habit lines could be clearly observed, implying that the crystals were single crystalline. The dislocation density at the top of the crystal shown in Fig. 5 (a) was evaluated by the preferential etching method in comparison with that of a Ge crystal grown by the conventional CZ method. Wafers cut from the grown crystals were mechanically lapped and chemically polished using a mixture of HF : HNO3 = 1 : 5 at 85˚C for 3–5 min, and then they were preferentially etched by the Billig etchant [9] at 85˚C for 3 min. Figures 6 (a) and (b) show optical micrographs of the Ge crystal grown by the present new method and by the conventional CZ method, respectively. No etch pits were observed as shown in Fig. 6 (a). It should be noted that the crystal was not dislocation-free perfectly. There existed some dislocations in the tail part of the crystal with a density in the range of 0.1–1  103 cm-2. Such dislocations were not in the periphery of the crystal but in the central region, implying at least that they were not generated due to the attachment of the particles to the crystal during the growth. On the other hand, in the conventionally grown Ge crystal, many etch pits about 2  104 cm-2 were observed as seen in Fig 6 (b), where dislocation density was higher at the periphery than in the central region. Indeed, a number of particles floating on the melt were observed and attached to the crystal during the growth, resulting in that the crystal dislocated. In a Ge crystal grown from a B2O3 fully covered melt, the dislocation density was 1.0  103 cm-2, also lower than that in crystals grown conventionally. Figure 7 shows a transmission Xray topographic image of a Ge crystal grown from B2O3-partially-covered melt, taken by using MoK1 radiation (RIGAKU RU-500). Some number of grown-in dislocations can be

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detected, but the density is low. Thus, it is well understood that generation of dislocations can be considerably suppressed in the new CZ-Ge growth method with covering Ge melt by B2O3 liquid.

Figure 5. Photographs of Ge single crystals (a) grown from B2O3-partially-covered melt and (b) grown from B2O3-fully-covered melt.

Figure 6. Optical micrographs of etch pits in Ge crystals (a) grown from B2O3-partially-covered Ge melt and (b) grown by the conventional CZ method.

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Figure 7. An X-ray topographic image of a wafer prepared from the top region of Ge crystal grown from B2O3-partially-covered melt. The diffraction vector g is 220.

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D. Electrical and Chemical Valuation of Grown Ge Crystals

Electrical and chemical properties of the grown Ge crystals by the new CZ method are shown in Table 1. Carrier concentrations and mobilities in specimens with dimensions of 5  5  1.5 mm3 prepared from the grown crystals were determined by Hall-effect measurement with the Van der Pauw method at room temperature (RT) [5-7]. Ge crystals grown from the B2O3 partially covered melt were n-type and the carrier concentration and electron mobility determined by Hall-effect measurement were 2–7  1014 cm-3 and 3.2  103 cm2/Vs,

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respectively. Also, a Ge crystal from the fully covered melt was n-type in a carrier concentration of 3.3  1015 cm-3. The fact of low carrier concentrations in the crystals was also supported by SIMS analysis. B concentrations in the crystals were evaluated to be less than the detection limit (2  1015 cm-3) by secondary ion mass spectroscopy (SIMS) using CAMECA IMS-4f. Since all the grown crystals kept n-type conduction, we can suppose that the contamination level of B from covered B2O3 liquid is very low chemically and also electrically [5].

E. Evaluation of Grown Ge Crystals by Infrared Absorption

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Interstitially dissolved oxygen concentrations in the grown crystals were determined by measuring optical absorption peak intensity at 855 cm-1 [6-17], originating in the antisymmetric stretching mode 3 of Ge-Oi-Ge quasi-molecules, as discussed later. Ge blocks of 3–9 mm thickness prepared from the grown crystals were lapped and chemically polished, and then the infrared absorption of each block was measured at RT using a Fourier-transform spectrometer (JASCO FT-IR 610). A high-purity polycrystalline Ge ingot with the same thickness was used as a reference. The spectral resolution was 1 cm-1. The interstitially dissolved oxygen concentration was determined from the absorption peak height using the calibration coefficient of 1.05  1017 cm-2 [15].

Figure 8. Infrared absorption spectra of Ge crystals measured at RT. Thick and thin Arrows indicate oxygen-related peak positions in Ge and Si, respectively. Inset shows enlarged spectra in the range 800–900 cm-1. Ilustration in the inset shows vibration of oxygen in Ge. (See the text.)

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Figure 8 shows infrared absorption spectra of grown crystals in the range 700–1300 cm-1. Spectrum a is for Ge grown by the conventional method and spectra b and c for Ge grown from Ge melt partially and fully covered with B2O3, respectively. Ge blocks were prepared from the top part of each crystal (solidified fraction, g < 0.2). In the spectra a-c very faint absorption peaks can be observed at 855 cm-1. As shown in Table 1, the oxygen concentrations in Ge crystals grown from melts partially and fully covered B2O3 liquid were 1.6  1016 and 1.7  1016 cm-3, respectively, comparable to that in the conventionally grown crystal 8.5  1015 cm-3. It should note that absorption peaks were not observed at 1106 cm-1, related to the 3 stretching mode of Si-Oi-Si quasi-molecules, or at 1225 cm-1, related to SiO2 precipitates, in any infrared spectra, implying that the concentration of Si-O-related defects should be lower than the detection limits in all the Ge crystals.

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F. Role of B2O3 Liquid in Growth of Ge Crystals The above results mean that B2O3 liquid does not contribute to any enhancement of the oxygen concentration. That is, we can assume that there was no dissolution of oxygen atoms either from B2O3 liquid or from the silica-glass crucible into Ge melt. These conclusions are supported by two results: First, the B concentration in crystals was below the detection limit of SIMS. Second, no absorption peaks except the optical vibration of Ge-Oi-Ge quasimolecules were observed in the infrared spectra. Here, it may note that the oxygen atoms in Ge crystal grown by the conventional CZ method came mainly from thin oxide films covering the Ge raw materials and residual moisture in the furnace. They slightly dissolved into the Ge melt and oxygen atoms segregated into the crystal during the growth. Such an oxygen concentration level is very low. Since the wetting ability between the Ge melt and silica glass is poor, no reaction between the Ge melt and silica glass would have occurred. Indeed, the weight of the crucible did not change from before to after the growth. Therefore, the dissolution of oxygen atoms from the silica crucible seems to be very small and can be neglected. Why is B2O3 liquid so stable or does not dissociate to B and O in Ge melt ? Figure 9 shows the Ellingham diagram of relevant oxides in the growth [18]. The Gibbs standard free energy of B2O3 formation (-3.04 kJ/mol) is lower than those of Ge-related oxides such as GeO (3.04 kJ/mol) and GeO2 (-3.41 kJ/mol) at a temperature around the melting point of Ge. In addition, B2O3 is thermodynamically stable, almost comparable to SiO2 (-6.80 kJ/mol). Thus, it can be understood that formation of GeO2 particles is strongly suppressed or dissociated by B2O3 in the present CZ crystal growth from B2O3 covered melt. In the present new CZ method, B2O3 works as a dissolver and remover of GeO2 floating on the Ge melt, which is very effective for reduction of grown-in dislocation density. This effect may be realized in a suitable condition on wetting ability and thermo-dynamical reactivity among Ge melt, silica-glass crucible, and B2O3 liquid.

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Figure 9. Ellingham diagram of relevant oxides in the Ge crystal growth.

III. OXYGEN-ENRICHED Ge CRYSTAL GROWTH BY THE NEW CZOCHRALSKI METHOD Copyright © 2011. Nova Science Publishers, Incorporated. All rights reserved.

A. Oxygen in Ge The thermo-mechanical stability of crystals is curious for avoiding dislocation generation during the device fabrication process. Czochralski-grown (CZ-)Si crystals, containing oxygen atoms in a concentration of approximately 1018 cm-3, are being used widely in industry for their high mechanical stability and also usage for gettering of harmful impurities in comparison with float-zone-grown (FZ-)Si crystals. Basically, oxygen impurities interstitially dissolved in Si crystals are clarified to preferentially segregate on and to immobilize dislocations, leading to high mechanical strength of the crystal [19, 20]. Oxygen in Ge can be expected to offer a similar advantage for the wide application of Ge crystals [15, 16]. However, Ge crystals are generally grown by the CZ method using a graphite crucible in a vacuum for avoiding incorporation of oxygen atoms, since oxygen atoms form stable oxide particles (GeO2) on the melt surface as described in the preceding section. Thus, the knowledge of the effects of oxygen in Ge growth is very limited. Up to now, the maximum solid solubility of oxygen atoms in Ge has been supposed to be 2  1018 cm-3 in several growth trials under Ar and O ambient [11], where the highest concentration of oxygen atoms was reported to be 6  1017 cm-3. In the preceding section, we showed a new CZ growth method for achieving dislocationfree Ge crystal growth from a Ge melt using B2O3 liquid. In the growth method, furthermore, we can expect an ability of B2O3 as a suitable encapuslant for suppressing evaporation of

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volatile elements in crystal growth as known for GaAs, GaP, and InP [21, 22]. In the above concept, we developed a growth method in order to enrich oxygen atoms in a growing Ge single crystal. That is, Ge single crystals were grown by the new CZ technique with covering by B2O3 liquid, where GeO2 powder was intentionally added into the Ge melt. Such Ge crystals can be expected to show high mechanical stability similar to CZ-Si crystals. The interstitially-dissolved oxygen concentration in CZ-Ge crystals grown from GeO2 added Ge melt, both with and without a covering by B2O3 liquid, was investigated by the absorption band at 855cm-1 of the infrared absorption spectrum originating in the anti-symmetric (3) stretching mode of Ge-Oi-Ge quasi-molecules at RT [6, 7].

B. Procedure of O-Enriched Ge Crystal Growth

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Ge melt added with suitable amount of GeO2 powder was fully covered by B2O3 liquid glass as illustrated in Fig. 10(a). Figure 10(b) shows a photograph of initial set up of Ge, B2O3 chunk, GeO2 powder (purity of 5N), and silica-glass crucible in a material charging stage. The conditions for crystal growth were kept to be same as those described in the preceding section.

Figure 10. (a) An illustration of Ge growth from B2O3-fully-covered melt. (b) A photograph of initial set up of Ge, B2O3 chunk, GeO2 powder, and silica-glass crucible.

C. O-Enriched Ge Boules Figures 11(a) and (b) show Ge boules grown from B2O3 fully covered melt with addition of GeO2 powder at 0.04 and 0.42 at%, respectively. Both crystals were single. The crystal in Fig. 11(b) was conducted with thin Dash necking for elimination of dislocations generated at

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the seeding stage. When the Ge starting materials were fully melted, the Ge melt was cloudy. Then, the melt gradually became fully transparent during the crystal growth. The grown-in dislocation density in crystals of Figs. 11(a) and (b) was 1.3  103 and 3  103 cm-2, respectively. Both crystals were n-type with a carrier concentration of 3.3  1015 cm-3. Table 1 summarizes the growth conditions and some characteristics of the grown crystals.

Figure 11. Photographs of Ge crystals grown from B2O3-fully-covered Ge melt with addition of (a) 0.04 and (b) 0.42 at% GeO2 powder, respectively.

D. Evaluation of Oxygen Concentration in O-Enriched Ge Crystals by Infrared Absorption Figure 8 shows infrared absorption spectra of grown crystals in the range 700–1300 cm-1. Spectra e and f are for Ge grown from a melt fully covered by B2O3 liquid with addition of GeO2 powder at 0.04 and 0.42 at%, respectively. Observed Ge blocks were prepared from the top part of each crystal (solidified fraction, g < 0.2). For comparison sake, an absorption spectrum of a Ge crystal (noted d) grown from a melt partially covered by B2O3 liquid with addition of 0.04 at % GeO2 is also shown in the figure. Remarkable absorption peaks were observed at 855 cm-1 in each crystal, but the height of the peaks was quite different, depending on the doped amount of GeO2. Concentrations of interstitially dissolved oxygen atoms in crystals grown from a fully B2O3 covered melt with addition of GeO2 at 0.04 and

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0.42 at% were determined to be from 2.2  1017 to 5.5  1017 cm-3, respectively, using the calibration coefficient of 1.05  1017 cm-2 [15]. In addition, very small absorption peaks at 1264 cm-1, related to the combination of anti-symmetric and symmetric stretching modes (3 + 1) of the Ge-Oi-Ge quasi-molecules [12, 13, 15, 16], were observed in crystals doped with GeO2. Figure 12 shows enlarged spectra in the range 1200–1300 cm-1 of Ge crystals (a, e, f). In oxygen-enriched Ge crystals the peak height of the absorption at 1264 cm-1 shows a relationship proportional to that of absorption at 855 cm-1 of the ratio 91. Thus, we can determine an oxygen concentration in Ge crystals from the absorption peak height at 1264 cm-1 with the calibration coefficient of 1.15  1019 cm-2 [7].

Figure 12. Enlarged infrared spectra of Ge crystals (a, e, f) in the range 1200–1300 cm-1. Crystal (a) was grown by the conventional CZ method. Crystals (e and f) grown from B2O3 fully covered melt with 0.04 and 0.42 at% GeO2, respectively.

Here, it can be noted in the inset of Fig. 8: No peaks were observed in the range of 855– 900 cm-1, indicating that there were no Ge-O related precipitates [16] or that the concentration should be lower than the detection limits in all the Ge crystals. In addition, even in Ge crystals intentionally added with GeO2, absorption peaks were not observed at 1106 cm-1, related to the 3 stretching mode of Si-Oi-Si quasi-molecules, or at 1225 cm-1, related to SiO2 precipitates. This means that the concentration of Si-O-related defects should be lower than the detection limits in all the Ge crystals. In crystals shown in Figs. 11(a) and (b), total oxygen concentrations evaluated chemically by SIMS analysis were 1.8  1017 and 6.5  1017 cm-3, respectively, which are almost comparable to the results of the infrared absorption in a consideration of the accuracy of the respective measurement systems. Thus, it is found that almost all the oxygen atoms are interstitially dissolved in the crystals, not in a form of precipitates.

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These results indicate the following two mechanisms: (i) Observed increase in oxygen concentration was caused by the decomposition of GeO2 into Ge and 2O under the existence of B2O3 liquid. This may be supported by the fact, as mentioned previously, that B2O3 is more stable than GeO2 at the melting point of Ge according to the Gibbs standard free energy [18]. (ii) Oxygen atoms resulting from decomposition of GeO2 in the Ge melt are suppressed to evaporate from B2O3 fully covered Ge melt. Therefore, we can conclude that full coverage of Ge melt by B2O3 liquid and addition of GeO2 are both keys for the enhancement of the oxygen concentration in Ge crystals.

IV. SOLUBILITY AND SEGREGATION OF OXYGEN INTO Ge

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The interstitially dissolved oxygen concentrations in crystals grown from a melt fully or partially covered by B2O3 were measured at positions with various solidified fractions g. Figure 13 shows the relationship of the oxygen concentration in various crystals against the solidified fraction. The oxygen concentration decreases from the top part to the bottom in crystals (e and d) grown from B2O3 fully and partially covered melt with 0.04 at% GeO2 powder, respectively, while the oxygen concentration measured for the crystal (f) grown from B2O3 fully covered melt with 0.42 at% GeO2 is around 5.5  1017 cm-3, almost constant independent of the crystal position.

Figure 13. Variation of interstitial oxygen concentrations in Ge crystals (d - f): Crystals (d and e) grown from B2O3 partially and fully covered melt with 0.04 at% GeO2 powder, respectively. Crystal (f) grown from B2O3 fully covered melt with 0.42 at% GeO2.

In an assumption that all the oxygen atoms in Ge crystals are interstitially dissolved, the effective segregation coefficients of oxygen in the Ge crystals can be estimated according to the normal freezing mechanism [23] in the complete mixing of a melt: CS(g) = kC0(1 - g)k-1 = CS(0)(1 - g)k-1

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where CS(g) is the oxygen concentration in the crystal with a solidified fraction of g, k is the effective segregation coefficient, and C0 is the initial concentration of oxygen in the Ge melt before starting the crystal growth. Here, C0 is difficult to determine exactly. However, the experimental results can be fitted by suitably setting magnitudes of k and CS(0). Indeed, the experimental results were well expressed by the dotted lines shown in Fig. 13, and the effective segregation coefficients were estimated to be k = 1.2 and 1.4 for crystals (e and d) grown from B2O3 fully and partially covered melt with 0.04 at% GeO2, respectively. Here, in the procedure the relative error of the estimated segregation coefficient by fitting is approximately 3 %. Estimated values of the effective segregation coefficient of oxygen in Ge may include effects of segregation and also those of other oxygen transportations such as evaporation from the Ge melt, reaction of oxygen atoms during the crystal growth, and so on. An assumption that the evaporation of oxygen from the Ge melt would be suppressed or strongly reduced by fully covered B2O3 liquid on the melt will be reasonable in comparison with the case of B2O3 partial coverage. In fact, the obtained segregation coefficient for the latter case is 1.4, higher than that for the former case 1.2. Larger segregation coefficient generally means larger consumption of oxygen from the melt, including transportations besides segregation. Thus, it can be considered that the segregation coefficient of 1.2 obtained for the grown crystal is close to the real value with no or a quite small effect of the evaporation. The oxygen concentration in the crystal grown from B2O3 fully covered melt with 0.42 at% GeO2 powder was approximately 5.5  1017 cm-3, independent of the solidified fraction. The corresponding total oxygen concentration was evaluated chemically by SIMS analysis to 6.5  1017 cm-3. This means that the segregation coefficient is obtained to be 1.0. This result has two possible interpretations: First, the magnitude may be the solid solubility of oxygen in Ge solid. Kaiser and Thurmond supposed a maximum solid solubility of oxygen into Ge to be 2  1018 cm-3 from several experimental results at lower temperatures [11]. In their experiments the highest oxygen concentration was 6  1017 cm-3 determined by vacuum fusion gas analysis. The magnitude is close to the value found in the present research. It has also been reported that the oxygen concentration saturated at 5.9  1017 cm-3 in a Ge crystal grown under a mixed nitrogen and oxygen ambient [10]. The value was newly calculated from the infrared absorption coefficient with the recent calibration coefficient of 1.05  1017 cm-2 [15]. The value is very close to the oxygen concentration in the present research. It should be noted that in the former case many particles or precipitates could be observed in the crystals due to the saturation of oxygen atoms in the Ge crystal. However, in our grown crystals no visible defects were observed by optical microscopy after the preferential etching. Second, it may be affected by the solid solubility of oxygen in Ge melt at temperatures close to the melting point. We may consider that the oxygen concentration in crystal grown from B2O3 fully covered melt with 0.42 at% GeO2 powder was constant. The following may be assumed: The Ge melt was saturated with oxygen atoms. Some GeO2 powder may remain undecomposed in the Ge melt. During the crystal growth, oxygen atoms generating from decomposition in the Ge melt segregated into the crystal and are newly and continuously supplied by decomposition of the remaining GeO2 powder, resulting in apparently a constant oxygen concentration in the crystal irrespective of the solidified fraction. This assumption can be supported by the experimental observation that Ge melt was cloudy in the beginning of the growth and then became fully transparent during the crystal growth. In the case, the apparent

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314

Toshinori Taishi and Ichiro Yonenaga

segregation coefficient becomes close to 1. However, the real effective segregation coefficient k of oxygen in Ge is thought to be higher than 1. This is consistent with the estimation of k = 1.2 and 1.4 for crystals grown from B2O3 fully and partially covered melt with 0.04 at% GeO2 powder, respectively.

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CONCLUSION Ge has keen interest as a material for next-generation ULSI devices and solar cells. For such applications, at present, Ge has some difficulties: dislocation introduction during crystal growth and low thermo-mechanical stability due to easy motion of dislocations. In the viewpoints, we explored a new CZ technique of Ge crystal growth and then conducted an intentional addition of O impurity for suppressing dislocation motion in Ge crystals. (1) In a conventional Ge crystal growth, GeO2 particles, appearing on the melt surface, lead to generation of dislocations in the growing Ge crystal by attaching to the crystal surface. By the new CZ technique using boron oxide B2O3 and a silica crucible, we succeeded in growing Ge crystals 1 inch in diameter and about 100 mm in length with low density of or almost free from grown-in dislocations being 0–1  103 cm-2. In the method, Ge melt surface was covered partially or fully by B2O3 liquid that removed such GeO2 particles perfectly from the Ge melt surface. (2) In Si, interstitially dissolved impurity oxygen has an important role in suppressing dislocation activities. We expect a similar role of oxygen in Ge. Since oxygen concentration is less than 1016 cm-3 in a conventionally grown Ge crystal, we enriched concentration of oxygen in Ge single crystals by an intentional addition of GeO2 powder during the new CZ growth technique. Oxygen concentrations in Ge crystals grown by the method increased up to 5.5  1017 cm-3 two orders of magnitude higher than that in a conventionally grown Ge crystal. It was observed in infrared absorption analysis that oxygen atoms were interstitially dissolved as a form of Ge-Oi-Ge quasi-molecule, leading to vibration peaks at 855 and 1264 cm-1 in the crystals. (3) As a fundamental phenomenon in solidification, segregation behavior of oxygen during crystal growth was evaluated by measuring the optical vibration intensities of oxygen in Ge. The effective segregation coefficient of oxygen in the grown Ge crystals was roughly estimated to be between 1.0 and 1.4. In the O-enriched Ge melt, the concentration of oxygen was supposed to be saturated dynamically in a balance of the consumption for segregation into the crystal and supply through the decomposition of the remaining GeO2 powder. We are now investigating oxygen effects on dislocation activities and mechanical strength of the grown Ge crystals, which can be reported elsewhere.

ACKNOWLEDGMENTS This work was performed under the Inter-University Cooperative Research Program of the Institute for Materials Research, Tohoku University. TT would like to thank the Ministry of Education, Science, Sports and Culture (grants 20760003 and 22686002) for support for this work.

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Depuydt, B; Theuwis, A.; Romandic, I. Mater. Sci. Semicond. Process. 2006, 9, 437443. Vanhellemonta, J.; Simoen, E. J. Electrochem. Soc. 2007, 154, H572-H583. Sumino, K.; Yonenaga, I. In Semiconductor and Semimetals, Vol. 42; Academic Press, Inc, San Diego, CA, 1994, pp. 449-511. As a comprehensive review: Trumbore, F. A. Bell Syst. Tech. J. 1960, 39, 203-233. Taishi, T.; Ohno, Y.; Yonenaga, I. J. Cryst. Growth 2009, 311, 4615-4618. Taishi, T.; Ise, H.; Murao, Y.; Ohsawa, T.; Suezawa, M.; Tokumoto, Y.; Ohno, Y.; Hoshikawa, K.; Y.; Yonenaga, I. J. Cryst. Growth 2010, 312, 2783-2787. Taishi, T.; Ise, H.; Murao, Y.; Ohsawa, T.; Tokumoto, Y.; Ohno, Y.; Yonenaga, I. Microelectron. Eng. 2011, in press. Okamoto, H, In Binary Alloy Phase Diagram II; Massalski, T. B.; Ed.; American Society for Metals, OH, 1996; p. 358. Billig, E. Proc. Roy. Soc. A 1956, 235, 37-55. Bloem, J.; Haas, C.; Penning, P. J. Phys. Chem. Solids 1959, 12, 22-27. Kaiser, W.; Thurmond, C.D. J. Appl. Phys. 1961, 32, 115-118. Kaiser, W. J. Phys. Chem. Solids 1962, 23, 255-260. Clauws, P. Mat. Sci. Eng. B 1996, 36, 213-220. Vanmeerbeek, P.; Clauws, P. Phys. Rev. B 2001, 64, 245201. Litvinov, V. V.; Svensson, B. G.; Murin, L. I.; Lindström, J. L.; Markevich, V. P.; Peaker, A. R. J. Appl. Phys. 2006, 100, 033525. De Gryse, O.; Vanmeerbeek, P.; Vanhellemont, J.; Clauws, P. Physica B 2006, 376377, 113-116. De Gryse, O.; Vanhellemont, J.; Clauws, P. Mater. Sci. Semicond. Process. 2006, 9 246-251. Barin, I. In Thermochemical Data of Pure Substances, Parts I and Part II; VCH, Weinheim, 1989. Sumino, K.; Harada, H.; Yonenaga, I. Jpn. J. Appl. Phys. 1980, 19, L49-L52. Yonenaga, I.; Sumino, K. J. Appl. Phys. 1996, 80, 734-738. Mullin, J. B.; Straughan, B. W.; Bricknell, J. J. Phys. Chem. Solids 1965, 26, 782-784. Kohda, H.; Yamada, K.; Nakanishi, H.; Kobayashi, T.; Hoshikawa, K. J. Cryst. Growth 1985, 71, 813-816. Pfann, W. G. J. Metals 1952, 4, 747-753.

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INDEX A

B

absorption spectra, 138, 171, 178, 306, 307, 310 absorption spectroscopy, 77, 159, 167 accelerator, 107 acetone, 160, 163, 169, 189, 194 acetonitrile, 165 acid, 159, 177, 194 activation energy, x, 83, 128, 129, 132, 233, 239, 243, 244, 245, 246, 247, 249, 252, 263, 264, 265 aerogels, 90 amine, 158 ammonia, 194 amplitude, 78, 83, 92, 93, 95, 116, 125, 129, 136, 141, 199, 216 aniline, 158, 163, 164, 168, 169, 170 annealing, x, 79, 137, 139, 140, 162, 164, 220, 234, 240, 255, 258, 260, 262, 263, 265 antineutrinos, x argon, 159 Arrhenius law, 83, 128, 132, 145 asymmetry, 177 atmosphere, 90, 93, 155, 160, 161, 163, 164, 242, 301, 302 atmospheric pressure, 301 atomic force, ix, 187, 189, 192, 195, 229 atomic force microscope, ix, 187, 189, 192, 195, 229 atoms, vii, viii, xi, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 91, 92, 93, 96, 105, 107, 110, 112, 113, 114, 115, 119, 132, 151, 153, 156, 158, 159, 162, 166, 167, 175, 177, 182, 220, 263, 299, 300, 307, 308, 309, 310, 311, 312, 313, 314 attachment, 303 attribution, 80, 82, 87, 89, 117 authority, 231

background noise, 257 band gap, 76, 159, 177, 205, 207, 210, 214, 215, 217, 218, 222, 225, 226, 229, 230, 236, 246 bandgap, x, 233, 234, 243, 246, 247, 248, 249 bandwidth, 239 base, 241, 300 beams, 79, 83 behaviors, 83, 264 Belgium, 133 bending, 169, 207, 222 bias, x, 188, 220, 229, 230, 237, 240, 246, 253, 255, 258, 260, 265 biological samples, 165 bleaching, 80, 117 Boltzmann constant, 83, 214, 237, 257 bonding, ix, 132, 152, 158, 163, 241, 263 bonds, 77, 78, 80, 83, 153, 175, 226, 262, 263, 264, 265 bounds, xi, 246 brass, 201 breakdown, 188 building blocks, 156

C calibration, 306, 311, 313 candidates, 188 carbon, vii, ix, 152, 153, 154, 155, 156, 159, 161, 162, 163, 166, 167, 169, 171, 172, 176, 240, 300, 301 carbon atoms, 153, 156, 162, 176 casting, 160, 170 cation, 162 ceramic, 252 cerium, 189, 192 charge coupled device, 188

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318 charge density, 207, 214, 215 chemical, 77, 78, 90, 154, 158, 162, 167, 194, 220, 240, 263, 305 chemical interaction, 220 chemical properties, 154, 158, 305 chemical reactivity, 154 chemical vapor deposition, 194, 240 chlorobenzene, 160 cladding, viii, 75, 77, 78, 90 clarity, 129, 169, 226, 230 cleaning, 189 cleavage, 161 clustering, 156 clusters, 156, 162, 165, 263 combined effect, 253 commercial, x, 234, 256, 300 community, 154 compaction, 79 compatibility, 124 competition, 82, 111, 146 composition, x, 77, 194, 233, 241, 242, 246, 250, 252, 260, 263, 264 compounds, 240 comprehension, 76, 98, 112, 113, 145 compression, 87 computer, 96, 97, 155, 236 computer simulations, 96 computing, 246 conductance, ix, 178, 187, 198, 201, 210, 237, 238, 252, 253, 263, 265 conduction, ix, 152, 189, 217, 218, 220, 221, 229, 236, 237, 249, 262, 306 conductivity, ix, x, 177, 179, 187, 199, 201, 229, 234, 241, 253 conductor, 181 configuration, 132, 158, 159, 160, 167 confinement, 156 conformity, 168 construction, 236 consumption, 313, 314 contamination, 164, 241, 306 contour, 166 convergence, 160 conversion reaction, 161 cooling, 236 coordination, 98 copper, 166 correlation, 80, 83, 89, 105, 119, 146 correlations, 100, 119, 146, 164 costs of production, 80 coupling constants, 85 covalent bond, 76, 85, 156 covalent bonding, 156

Index covering, 304, 307, 309 cracks, 236 crystal growth, xi, 299, 300, 302, 303, 307, 308, 309, 310, 313, 314 crystal structure, 167, 242 crystalline, 76, 78, 177, 194, 260, 266, 303 crystallinity, 179, 240, 260 crystals, vii, xi, 189, 190, 191, 192, 193, 195, 198, 229, 260, 299, 300, 301, 303, 304, 305, 306, 307, 308, 309, 310, 311, 312, 313, 314 CVD, 194, 240, 241, 255 cycles, x, 188, 199, 203, 205, 210, 217, 218, 221, 222, 224, 225, 227, 229, 230, 236

D decay, vii, x, 82, 123, 124, 125, 126, 127, 142, 143, 144 decomposition, 96, 99, 118, 312, 313, 314 defects, vii, viii, ix, 75, 76, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 94, 95, 96, 97, 98, 99, 100, 101, 104, 105, 106, 108, 109, 110, 111, 112, 114, 115, 117, 118, 119, 121, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 139, 140, 143, 144, 145, 146, 187, 189, 262, 263, 265, 307, 311, 313 deficiencies, 114 deficiency, 79, 80, 112, 114, 115, 146 degenerate, 153 degradation, viii, 75, 179, 188, 189, 207, 220 deposition, xi, 189, 194, 240, 241, 242, 255 deposits, xi, 189 desorption, 159, 165 destruction, 88, 89, 111, 113, 114, 115, 132, 145, 146 destruction processes, 111 detectable, 92, 102, 144 detection, vii, xi, 92, 132, 136, 172, 237, 306, 307, 311 deviation, 105, 125 DFT, 172, 174 dielectric constant, 188, 189, 214 diffraction, 76, 305 diffusion, vii, 138, 140, 145, 220 dimethylformamide, 163 direct measure, 167 direct observation, xi discs, 159 dislocation, vii, xi, 299, 300, 301, 303, 307, 308, 310, 314 disorder, 77, 129, 249 displacement, 83

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Index dissolved oxygen, xi, 299, 300, 306, 309, 310, 312 distillation, 164 distilled water, 189, 194 distribution, 77, 125, 127, 140, 161, 165, 166, 171, 207, 217, 220, 226, 229, 230, 262, 263 distribution function, 207 DMF, 159, 163, 170 donors, 102, 105, 107, 110, 111, 112, 114 doping, vii, viii, 75, 77, 78, 81, 86, 91, 92, 93, 96, 97, 98, 100, 101, 111, 113, 114, 115, 119, 145, 146, 204, 300 drying, 90 dumping, 162

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E electric field, ix, 80, 187, 188, 200, 204, 220, 221, 226, 229 electrical fields, ix, 187, 189, 198, 199, 221 electrical properties, 243, 252 electrical resistance, 160 electrodes, 155, 195, 201 electromagnetism, 155 electron, 79, 80, 82, 83, 84, 85, 86, 87, 88, 89, 100, 102, 105, 107, 110, 111, 112, 113, 114, 115, 153, 155, 159, 166, 167, 171, 175, 177, 178, 188, 207, 236, 258, 263, 264, 299, 305 electron density distribution, 166 electron paramagnetic resonance (EPR), 83, 84, 85, 86, 87, 93, 94, 95, 96, 97, 98, 99, 109, 114, 129, 130, 132, 135, 137, 145 electronic structure, 167 electrons, x, 78, 83, 86, 88, 90, 114, 153, 158, 163, 164, 176, 207, 215, 220, 222, 236, 262 emission, x, 80, 81, 82, 121, 122, 123, 124, 125, 126, 127, 130, 131, 139, 140, 141, 142, 143, 144, 145 emitters, xi employment, 79 encapsulation, ix, 152, 155, 158, 173, 175, 176 energy, viii, ix, x, xi, 77, 79, 80, 81, 83, 90, 121, 122, 124, 125, 127, 128, 129, 131, 136, 139, 140, 144, 151, 152, 153, 159, 160, 161, 172, 173, 174, 175, 176, 188, 189, 205, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 222, 225, 226, 227, 228, 229, 230, 234, 235, 236, 237, 242, 243, 246, 248, 249, 252, 253, 256, 263, 264, 300 energy density, 217, 218, 219, 225 energy transfer, 79 engineering, 147, 177 entropy, 166

319 environment, x, 140, 155, 233, 235, 242, 264 epitaxial growth, 300 equilibrium, vii, 114, 205, 207, 263 erbium, 189, 191, 195, 199, 219, 225 ESI, 165 ESR, 160, 167 ester, 177 etching, 303, 313 evacuation, 301 evaporation, 90, 164, 189, 194, 302, 308, 313 evidence, 81, 87, 93, 100, 112, 121, 129, 137, 140, 146, 154, 164, 166, 171, 173 evolution, xi, 203, 229, 299 EXAFS, 166 excitation, 80, 81, 121, 122, 123, 124, 125, 130, 131, 136, 139, 140, 141, 143, 144, 249 experimental condition, 141 exposure, 83, 161 extraction, ix, 90, 151, 158, 159, 162, 163, 164, 165, 169

F fabrication, 177, 240, 250, 299, 308 Fermi level, ix, 187, 189, 207, 208, 210, 215, 216, 217, 219, 222, 225, 227, 229, 230 ferromagnets, viii, 151, 155 FFT, 171, 172 fiber, vii, viii, 75, 77, 78, 80, 84, 89, 90 film thickness, 194, 248 films, vii, ix, x, 160, 187, 189, 190, 194, 195, 198, 199, 204, 205, 219, 221, 225, 226, 229, 230, 233, 234, 241, 242, 243, 246, 249, 263, 264, 307 flight, 159, 165 fluctuations, 77, 263 fluid, 91 fluorescence, 141 fluorine, 220 force, 160, 237 formation, 77, 79, 80, 83, 89, 114, 131, 135, 137, 138, 156, 162, 164, 167, 169, 171, 172, 220, 222, 301, 307 formula, 200, 215, 217, 246, 260 free energy, 307, 312 freedom, 167 freezing, 312 FTICR, 166 full capacity, 203, 222 fullerene, vii, viii, ix, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 162, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 176, 177, 182

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320

Index

G

I

gadolinium, 161 gallium, 299 gel, 77, 90, 92, 93 gelation, 90 geometry, 122, 153, 156, 172, 175, 237, 263 germanium, vii, ix, xi, 77, 87, 152, 158, 169, 171, 187, 188, 189, 190, 203, 204, 210, 215, 217, 218, 219, 221, 222, 225, 226, 229, 230, 234, 240, 299, 300 Germany, 152 glasses, viii, 76, 77, 79, 90, 98 glow discharge, 263 grain boundaries, 263, 264, 303 grants, 314 graphite, 154, 155, 156, 160, 161, 162, 301, 308 growth, vii, ix, xi, 84, 88, 89, 102, 105, 106, 107, 108, 109, 111, 114, 116, 119, 132, 133, 137, 156, 187, 188, 189, 194, 218, 226, 230, 299, 300, 301, 302, 303, 307, 308, 309, 310, 313, 314 growth mechanism, 156 growth rate, 106 growth temperature, 189

ideal, vii, 77, 162, 221, 260 identification, vii, xi, 164 image, 179, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 235, 302, 303, 305 imaging systems, 240 immersion, 189, 194 impurities, vii, 78, 83, 155, 164, 250, 300, 308 independence, 125, 127, 142 India, 151 induction, viii, 75, 78, 88 industrial processing, 236 industries, 299 industry, 235, 300, 308 inhomogeneity, 83 insertion, ix, 152, 171 interface, ix, 89, 178, 179, 187, 188, 189, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 217, 218, 219, 220, 221, 222, 224, 225, 226, 229, 230, 263, 264 interfacial layer, 189 interference, 79 inversion, ix, 187, 203, 204, 210, 216, 219, 220, 222, 223, 225, 226, 227, 228, 229, 230 ionization, 83, 84, 86, 87, 88, 106, 159, 165 ionizing radiation, 78, 83, 131, 144 ions, 154, 155, 165 IPR, 153, 158 IR spectra, 180 IR spectroscopy, 167 irradiation, vii, viii, 75, 76, 79, 80, 83, 84, 85, 86, 88, 94, 95, 96, 100, 105, 107, 108, 109, 110, 111, 115, 116, 117, 119, 121, 124, 130, 131, 132, 133, 134, 135, 136, 137, 138, 140, 141, 145, 146, 188 ISC, 82, 125, 128, 132, 141, 145 isolation, 155, 163, 164, 178, 253, 265 isomers, 158, 167 isotope, xi Italy, 75, 107

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H harvesting, 178 heat capacity, 237 heat loss, 237 heat transfer, 237 height, 189, 306, 310 helium, 160, 161 history, 181 holmium, 195 host, 155, 160 hot spots, 236 House, 182 HRTEM, 166 human, 235 human body, 235 hydrogen, vii, 86, 91, 145, 156, 226, 255, 262, 263, 265 hydrogen atoms, 263 hydrogen bonds, 156 hydrogenation, 264 hyperfine interaction, 86 hypothesis, 158, 265

J Japan, 299

K kinetics, 102

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Index

L lanthanide, viii, 151, 158, 159 lanthanum, 154, 189, 193 laser radiation, 79, 80 latency, 201 law enforcement, 235 laws, 123, 142, 230 lead, 83, 178, 214, 255, 263, 265, 314 leakage, 301 lens, 299 lifetime, vii, 81, 82, 124, 125, 126, 127, 129, 131, 141, 142, 144, 159, 188 light, ix, 77, 78, 80, 84, 122, 142, 152, 234, 236, 237, 252 linear dependence, 137 low temperatures, 128, 179, 194 luminescence, vii, 82, 83, 86, 87 lying, 153, 173

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M magnetic field, 93, 98, 130, 132 magnetic resonance, viii, 87, 151, 155, 177 magnetic resonance imaging (MRI), viii, 151, 155, 177 magnitude, vii, 93, 104, 105, 111, 119, 246, 256, 263, 300, 313, 314 majority, 162, 227 MALDI, 180 manufacturing, 300 mass, xi, 154, 156, 159, 164, 166, 167, 168, 169, 173, 180, 237, 301, 306 mass spectrometry, 159, 165, 167 materials, vii, viii, xi, 76, 78, 79, 82, 83, 90, 91, 93, 114, 118, 119, 121, 122, 131, 134, 135, 136, 138, 147, 151, 153, 155, 177, 178, 179, 195, 220, 236, 240, 262, 299, 310 matrix, 79, 89, 98, 132, 159, 165, 178, 179, 180, 201 matter, iv, 226, 230 measurements, 76, 77, 82, 86, 95, 123, 124, 125, 126, 139, 141, 142, 143, 160, 178, 180, 215, 216, 252 meat, 235 mechanical degradation, 207 mechanical stress, 188 media, 230 medical, 177, 235 medicine, 155 melt, xi, 299, 300, 301, 302, 303, 304, 305, 307, 308, 309, 310, 311, 312, 313, 314

321 melting, 300, 301, 302, 307, 312, 313 melts, 301, 307 memory, ix, 187, 198, 201 Mendeleev, 152 metal ion, viii, 151, 220 metal ions, viii, 151, 220 metals, vii, viii, ix, 151, 152, 155, 162, 194, 195, 241 methodology, 159, 164, 173 Mg2+, 155 microelectronics, vii micrometer, 177, 194 microscope, 159, 189, 252 microscopy, 160 migration, 89 Ministry of Education, 314 mixing, 77, 160, 161, 172, 175, 312 models, 79, 83, 86 modifications, 80, 95, 139, 141, 145, 159 moisture, 158, 164, 301, 307 moisture content, 301 molecular dynamics, 156, 167 molecular mass, 165 molecules, 80, 145, 153, 155, 306, 307, 309, 311 molybdenum, 201 momentum, 177 Moon, 266 morphology, ix, 187, 189, 191, 192, 193, 195, 229

N Na+, 84, 155 nanocrystals, 159 nanoparticles, 159, 163 nanostructured materials, ix, 152, 177 Nanostructures, 182 nanotube, 162 negative effects, 114 neglect, 127, 143 neutral, 80, 87, 106, 207, 219 neutrinos, xi neutrons, 83 next generation, 299 nickel, 201, 250 NIR, ix, 152, 159, 167, 170, 171, 178, 234 nitrogen, 313 NMR, 77, 159, 167, 169, 180 Nobel Prize, 153 NPL, 180 nuclear magnetic resonance, 159, 167 Nuclear Magnetic Resonance, 77

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322

Index

O oligomers, 164, 169 opportunities, 153 optical activity, 81, 83, 87, 110, 121 optical density, 92, 178 optical fiber, viii, 75, 77, 119 optical micrographs, 303 optical microscopy, 313 optical properties, 138, 145, 177, 243, 264 optical systems, 299 optimization, 159, 173 orbit, 82, 83, 85, 129, 144 organic solvents, 158 overlap, 81, 93, 98, 129, 155 ownership, 230 oxidation, ix, 164, 167, 171, 187, 256 oxygen, vii, viii, x, xi, 75, 76, 77, 79, 80, 81, 83, 84, 85, 86, 87, 89, 91, 106, 112, 114, 115, 132, 146, 164, 169, 195, 233, 241, 242, 243, 246, 247, 248, 249, 256, 263, 264, 299, 300, 306, 307, 308, 309, 311, 312, 313, 314 oxygen plasma, 256

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P parallel, 202 passivation, x, 234, 246, 252, 255, 258, 260, 261, 262, 263, 264, 265 permit, 90, 105 peroxide, 194 phonons, 83, 159 photoelectron spectroscopy, 167 photoluminescence, 80, 81, 82, 83, 160, 177, 178, 180 photons, ix, 80, 83, 152, 178, 236 photosensitivity, viii, 75, 78, 79, 83, 146 physical characteristics, 229 physical properties, 77, 158 physics, viii, xi, 147, 150, 152, 181 PL spectrum, 121, 130, 139 point defects, vii, viii, 75, 78, 79, 80, 81, 83, 84, 85, 87, 93, 95, 96, 98, 99, 118, 131, 134, 135, 137, 140, 145, 146 Poland, 91 polar, 155, 162, 164 polarity, 199, 220 polarization, 82 polyimide, 251, 258, 265 polymer, 177, 178, 179 polymer chain, 179 polymer chains, 179

polymer matrix, 177, 178, 179 polymerization, vii polymers, 178 porosity, 90 positive feedback, 220, 229 preparation, iv, 89, 90, 93, 99, 130, 131, 145 probability, 98, 111, 113, 114, 146, 207 probe, 160, 167, 243, 258 probe station, 243, 258 propagation, 234 proportionality, 86, 119 protons, 177 purification, 159, 162, 189 purity, 82, 164, 195, 301, 306, 309

Q quantum confinement, 159 quantum dot, 158 quantum dots, 158 quartz, 76, 160, 169

R radiation, viii, ix, x, 75, 76, 78, 79, 84, 86, 87, 101, 134, 136, 145, 146, 152, 233, 234, 235, 236, 237, 238, 250, 255, 256, 257, 303 radio, 226, 230, 241 radius, viii, 151, 158, 159 Raman spectra, 98 Raman spectroscopy, 77, 145, 167 rare earth elements, vii, ix, 187, 189, 194, 198 raw materials, 307 reactions, 86, 140, 154 reactivity, 158, 189, 307 reading, 225 recall, 83, 89, 123, 129 recombination, 83, 87, 178, 260, 263 recommendations, iv recovery, 86, 220 red shift, 140 refractive index, viii, 75, 77, 78, 79, 80, 90, 118, 119, 146, 243 refractive index variation, 79, 119 rejection, xi relaxation, 167, 177, 199 relaxation rate, 177 relevance, xi, 113, 118 renaissance, 299 repair, 236, 265 reproduction, 230 researchers, viii, 75

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Index residuals, 96 resistance, ix, x, 160, 178, 179, 180, 187, 199, 200, 201, 214, 220, 233, 234, 236, 237, 238, 241, 243, 246, 249, 252, 253, 256, 258, 263 resolution, xi, 159, 164, 166, 168, 306 resonator, 90 response, ix, 187, 226, 230, 237, 238, 256, 257 response time, ix, 187 rings, 77 rods, 155, 156 Romania, 133 room temperature, x, 82, 89, 90, 93, 125, 127, 140, 142, 143, 159, 233, 234, 235, 237, 240, 258, 264, 305 root, 160 roughness, 190, 198 routes, 93 rugby, 153

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S saturation, 100, 101, 107, 108, 109, 111, 114, 116, 313 scandium, 166 scanning tunnelling microscopy, 166 scattering, 77, 262, 265 schema, 203 science, 147, 150 scope, 152 seed, 301, 302 seeding, 301, 310 segregation, vii, xi, 299, 300, 312, 313, 314 semiconductor, vii, ix, x, 152, 158, 181, 187, 188, 189, 194, 198, 203, 204, 207, 208, 210, 214, 217, 218, 220, 227, 229, 234, 238, 240, 241, 248, 260, 263, 299 semiconductors, vii, 177, 242, 249, 260, 263 sensing, 237, 240, 241, 242, 249, 250, 255, 258, 260, 262, 263, 265 sensitivity, 246 sensors, 79, 234 shape, 95, 96, 97, 98, 99, 121, 129, 132, 135, 139, 153, 154, 159, 166, 217 showing, 104, 106, 108, 130 Si3N4, 241, 251 signals, viii, xi, 75, 83, 84, 86, 94, 95, 96, 97, 98, 99, 122, 145, 166, 169, 172, 234 silica, vii, viii, xi, 75, 76, 77, 78, 79, 80, 82, 83, 85, 89, 90, 95, 131, 140, 145, 146, 189, 299, 301, 302, 307, 309, 314 silicon, vii, viii, ix, x, 75, 76, 77, 83, 152, 160, 166, 169, 187, 188, 189, 194, 195, 198, 199,

323 221, 222, 225, 226, 229, 230, 233, 234, 240, 246, 248, 251, 252, 263, 264, 299 silver, 152, 160 simulation, 97, 155, 167, 180 simulations, 81, 84, 156 single crystals, xi, 299, 300, 301, 304, 309, 314 sintering, 90 SiO2, 76, 77, 78, 79, 81, 82, 83, 84, 86, 87, 88, 90, 98, 146, 188, 189, 194, 226, 260, 263, 264, 307, 311 smoothing, 171, 172 solar cells, ix, 152, 177, 249, 300, 314 sol-gel, 89, 90, 91, 92, 94, 95, 111, 119, 130, 131, 132, 144 solid state, 152 solidification, 314 solubility, ix, 151, 164, 165, 300, 308, 313 solution, ix, 90, 111, 164, 167, 188, 189, 194, 218, 230 solvent molecules, 167 solvents, 158, 162, 164, 165 species, ix, 78, 112, 131, 152, 154, 155, 156, 159, 160, 162, 168, 174, 175 spectroscopic techniques, 159, 165, 172 spectroscopy, 167, 306 speed of light, 118, 234 spin, 82, 83, 84, 85, 86, 129, 144, 160, 167 stability, 139, 155, 158, 300, 308, 309, 314 stabilization, 155, 158, 160, 188, 227 staff members, 180 standard deviation, 118 STM, 166 stress, 79, 188, 218, 220, 263 stretching, 125, 126, 142, 169, 174, 306, 307, 309, 311 strong interaction, 167, 175, 177, 178 structural relaxation, 84 structure, ix, x, 76, 77, 78, 82, 83, 84, 85, 86, 89, 91, 114, 144, 153, 154, 155, 164, 166, 167, 187, 188, 195, 198, 199, 200, 201, 202, 203, 204, 205, 210, 215, 216, 217, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 241, 249, 263, 264 substrate, 90, 169, 170, 188, 189, 220, 221, 230, 237, 242, 246, 250, 253, 258, 260 subtraction, 125 Sun, 181, 182, 183 suppression, 300 surfactant, 159 surveillance, 236 symmetry, 80, 82, 155, 159, 173, 211 synthesis, vii, 77, 89, 121, 131, 144, 155, 159

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324

Index

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T target, x, 233, 240, 241, 242, 243, 264 TCR, x, 201, 233, 234, 238, 239, 240, 241, 243, 244, 245, 246, 247, 250, 252, 253, 254, 264, 265 techniques, ix, 89, 145, 152, 155, 159, 164, 167, 177, 258 technology, x, 188, 234, 240, 241, 264 temperature, x, 82, 89, 90, 91, 93, 96, 97, 124, 125, 126, 127, 128, 131, 138, 140, 141, 142, 143, 144, 145, 155, 156, 160, 162, 177, 178, 179, 180, 188, 201, 204, 214, 220, 229, 230, 233, 234, 235, 237, 238, 239, 240, 241, 242, 243, 252, 254, 257, 258, 260, 263, 265, 299, 307 temperature dependence, 124, 125, 127, 141, 142, 145 tension, 229 TEOS, 90 theoretical assumptions, 226 thermal activation, 161 thermal energy, 179 thermal evaporation, 195 thermal oxidation, 194 thermal properties, 85 thermal stability, 84, 85, 97, 138, 140, 145, 188 thermal treatment, 90, 91, 92, 93, 96, 97, 111, 138, 139, 141 thin films, x, 160, 194, 233, 234, 242, 243, 244, 245, 246, 248, 249, 252, 258, 263, 264 tin, 152 Toyota, 182 transistor, 152, 188 transition rate, 132 transmission, viii, 75, 166, 236, 246, 303 Transmission Electron Microscopy (TEM), 89 transport, 239, 252 treatment, ix, 92, 93, 138, 139, 140, 161, 188, 194, 195, 218, 230, 240 triggers, 179 tungsten, 201, 240 tunneling, 220

U uniform, 161, 195 United, 185, 230 United States (USA), 153, 160, 181, 182, 185, 230, 233 UV irradiation, 144 UV spectrum, 171

V vacancies, 189 vacuum, ix, 93, 118, 159, 160, 161, 166, 171, 172, 187, 189, 194, 195, 300, 308, 313 valence, viii, 75 vanadium, 240 vapor, 194, 263 variations, x, 78, 79, 94, 96, 97, 98, 113, 118, 119, 121, 145, 233 vector, 305 vibration, 167, 179, 306, 307, 314 vision, 235

W water, 155, 156, 165, 177, 236 water clusters, 155, 156 wavelengths, ix, 79, 152, 159, 234, 240, 246, 252, 256, 264, 265 weight ratio, 160 wetting, 302, 307

X xenon, 159 XPS, 159, 167, 171, 172, 180 X-ray diffraction, 76, 166, 242 X-ray diffraction (XRD), 242 X-ray photoelectron spectroscopy (XPS), 167 XRD, 260, 263

Y yield, vii, 155, 161, 164 yttrium, 166, 189, 195, 203, 219, 222, 225, 226

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