New Research on Semiconductors

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NEW RESEARCH ON SEMICONDUCTORS

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.

NEW RESEARCH ON SEMICONDUCTORS

THOMAS B. ELLIOT EDITOR

Nova Science Publishers, Inc. New York

Copyright © 2006 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. 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. LIBRARY OF CONGRESS CATALOGING-IN-PUBLICATION DATA New research on semiconductors / Thomas B. Elliot (editor). p. cm. Includes bibliographical references and index. ISBN 978-1-60876-510-2 (E-Book) 1. Semiconductors--Research. 2. Semiconductor nanocrystals--Research. 3. Semiconductor films--Research. I. Elliot, Thomas B. QC611.26.N497 2006 537.6'22072--dc22 2005034761

Published by Nova Science Publishers, Inc.

New York

CONTENTS Preface

vii

Chapter 1

Crystal Growth of Ternary and Quaternary Alloy Semiconductors by Rotational Bridgman Method Yasuhiro Hayakawa, M.Haris, Masashi Kumagawa and Tetsuo Ozawa

Chapter 2

Formation of Grown-in Microdefects in Dislocation-free Silicon Monocrystals V.I. Talanin and I.E. Talanin

31

Chapter 3

Laser-induced Phase Transformation in Nanocrystalline Silicon Thin Films R.H. Buitrago and S.B. Conari

69

Chapter 4

Monte Carlo Simulation of Hot-Phonon Effects in Biased Nitride Channels M. Ramonas and A. Matulionis

95

Chapter 5

Researches of Growth and Device Based on ZnO by Plasma Assisted Molecular Beam Epitaxy Y. M. Lu, D. Z. Shen, J. Y. Zhang, Y. C. Liu and X. W. Fan

123

Chapter 6

Structural Disorder in Cds-x-se-1-x Thin Film Probed by Microdiffraction and Optical Spectroscopes V. Capozzi, G. Perna, S. Pagliara and L. Sangaletti

143

Chapter 7

Electrodeposition of CuInSe2 Photovoltaic Cell Application Shigeyuki Nakamura

159

Index

1

209

PREFACE This book includes within its scope studies of the structural, electrical, optical and acoustical properties of bulk, low-dimensional and amorphous semiconductors; computational semiconductor physics; interface properties, including the physics and chemistry of heterojunctions, metal-semiconductor and insulator-semiconductor junctions; all multi-layered structures involving semiconductor components. Dopant incorporation. Growth and preparation of materials, including both epitaxial (e.g. molecular beam and chemical vapour methods) and bulk techniques; in situ monitoring of epitaxial growth processes, also included are appropriate aspects of surface science such as the influence of growth kinetics and chemical processing on layer and device properties. The physics of semiconductor electronic and optoelectronic devices are examined , including theoretical modelling and experimental demonstration; all aspects of the technology of semiconductor device and circuit fabrication. Relevant areas of 'molecular electronics' and semiconductor structures incorporating Langmuir- Blodgett films; resists, lithography and metallization where they are concerned with the definition of small geometry structure. The structural, electrical and optical characterization of materials and device structures are also included. The scope encompasses materials and device reliability: reliability evaluation of technologies; failure analysis and advanced analysis techniques such as SEM, E-beam, optical emission microscopy, acoustic microscopy techniques; liquid crystal techniques; noise measurement, reliability prediction and simulation; reliability indicators; failure mechanisms, including charge migration, trapping, oxide breakdown, hot carrier effects, electro-migration, stress migration; package- related failure mechanisms; effects of operational and environmental stresses on reliability. As outlined in Chapter 1, ternary and quaternary alloy crystals of semiconductors are important materials for optoelectronic devices because fundamental properties such as lattice constant and band gap can be controlled by adjusting composition ratio. In order to grow high quality ternary bulk crystals, various techniques have been carried out. Nakajima et al. succeeded in growing compositionaly graded InxGa1-xAs (x=0.5-3.30) single crystals by the Brigman method. Hayakawa et. al. introduced ultrasonic vibration into the melt from the bottom of the crucible in the Czochralski method to prevent the occurrence of constitutional supercooling. This method was applied for the growth of InxGa1-xSb single crystals, and it was found that the growth thickness in the single crystalline state was increased with an increase of the output power of ultrasonic vibrations. We have modified the Czochralski method in order to improve the homogeneous distribution of impurities by making a seed

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crystal rotate alternately clockwise and counterclockwise within a narrow range of angle. We have also modified the Brigman method to stir the melt. In Section 2, the growth of InSb1xBix ternary bulk crystals and the results analysed are presented. Chapter 2 presents a general scheme that depicts the formation and transformation mechanisms of the grown-in microdefects in dislocation-free silicon single crystals grown by the floating-zone (FZ-Si) and Czochralski (CZ-Si) methods as a function of a crystal growth rate. The distribution patterns and physical nature (the sign of the lattice strain) of grown-in microdefects FZ-Si and CZ-Si crystals were studied by selective etching and transmission electron microscopy. A heterogeneous mechanism of formation and transformation of grownin microdefects are proposed. It is experimentally established and confirmed by thermodynamic analysis that in single FZ-Si and CZ-Si crystals close to the crystallization front the recombination process of intrinsic point defects is hampered by a recombinational barrier. Сooling-induced decomposition of the oversaturated solid solution of point defects in silicon follows two mechanisms: vacancy-type and interstitial-type. Therefore vacancies and self-interstitials find drains in the form of atoms of background impurities like oxygen and carbon. Depending on growth conditions (e.g. parameter V/G, where V is a crystal growth rate; G is an axial temperature gradient) the silicon crystals grow in vacancy-interstitial and (or) interstitial regimes. The parameter V/G is determined experimentally with allowance for crystal diameter, cooling rate and radial temperature gradient. In vacancy-interstitial growth regime of FZ-Si and CZ-Si crystals during disintegration of the supersaturated vacancies solid solution the oxygen-vacancy aggregate occurs causing SiO2 presipitates to be formed. During disintegration of the supersaturated self-interstitials solid solution the interstitials-carbon aggregate occurs causing the aggregates, which consist of self-interstitials, atoms of carbon and oxygen, to be formed. During the formation of such aggregates the carbon atoms act as catalysts. The point defects aggregation in vacancy-interstitial and interstitial growth regimes under certain thermal growth conditions during the crystal cooling may result in the formation of secondary defects near the primary oxygen-vacancy and carbon-interstitial aggregates, namely octahedral vacancy microvoids and interstitial dislocation loops accordingly. It is experimentally established that A-microdefects may occur in the course of two different formation mechanisms: condensations of self-interstitials and generation of interstitial dislocation loops, which is called by a field of elastic deformation all around the presipitates. As is established, the nature and behaviour of processes of the grown-in microdefects formation in FZ-Si and CZ-Si crystals are identical. The uniform classification of grown-in microdefects is offered and the heterogeneous mechanism of formation and transformation of grown-in microdefects in dislocation-free silicon single crystals is confirmed experimentally. On the ground of experimental results the physical classification of grown-in microdefects is offered. Such a classification follows from the heterogeneous mechanism of formation and transformation of grown-in microdefects. A comprehensive knowledge of the so-called micro or nanocrystalline silicon has not been reached till now. Nanocrystalline silicon structure network is quite complex. It consists of crystallites of around 10 to 30 nm grain size. Because of the little crystallites’ size, a large grain boundary tissue as well as amorphous phase is present, providing particular optical and electrical properties. Being that the nanocrystalline silicon is thermodynamically more stable

Preface

ix

and with less light-induced degradation than the amorphous one, this material presents a great interest to scientists and technologists in thin films solar cells. The technology used to prepare silicon solar cells is at present well known. The deposition techniques take place at high temperature and because of the low thickness of the films, they present very high residual tensions. In the other side, the deposition rate determines the crystallite grain size. As light differences in crystalline volume fraction and grain size result in quite different optical and electrical properties, it appears of considerable interest to study phase transformation processes in nanocrystalline silicon, to know more about the transition from amorphous to microcrystalline silicon under compression tension and temperature, which is still not really understood. In Chapter 3 an up-to-date art’s state of pressure-induced phase transformation processes in silicon are made. Also results of laser-induced phase transformation processes in intrinsic and boron-doped silicon thin films prepared by Plasma Enhanced Chemical Vapor Deposition technique (PECVD) are presented and analyzed. Through Raman spectroscopy, it is possible to determine that the induced phase transformation is interrelated with the silane flow rate, and boron concentration in the silane diluted with hydrogen used as a reactive gasses in the preparation of the films, on the grain size, and the crystalline volume fraction of them. Measurements of dark conductivity, Transmission Electron Microscopy (TEM), X-ray and Atomic-Force Microscopy (AFM) help to corroborate the Raman measurements. The results show that the laser-induced phase transformation processes in nanocrystalline silicon thin films present different characteristics from the well known ones produced in single-crystal silicon by hydrostatic experiments. A model for hot-spot phase transformation is discussed to explain the laser-induced phase transformation processes in the silicon thin films. The little volume exposed to the laser beam reaches high temperature and is under high compress tensions due to the cooler surrounding material. In these conditions, phase Si-XII emerges and becomes more stable than Si-I. These two phases are present in equilibrium with the amorphous phase in the silicon thin films with no presence of other crystalline phases. Recent progress in Monte Carlo simulation of hot electron transport and fluctuations in nominally undoped AlGaN/GaN and AlGaN/AlN/GaN heterostructures with degenerate twodimensional electron gas channels is reviewed in Chapter 4. Input scattering probabilities of the electrons are calculated in a semiclassical approach from the confined-electron envelope wavefunctions obtained through a self-consistent Poisson– Schrödinger method. Additional scattering due to accumulation of nonequilibrium longitudinal optical phonons, termed hot phonons, is treated together with ”lattice” heating and other scattering mechanisms of importance for electron transport at high electric fields applied in the plane of electron confinement. Possible ways to treat electron gas degeneracy and hot-phonon effects through Monte Carlo procedures are described. Hot-electron and hot-phonon distribution functions are presented for indepth discussion of the results. Complementary information on hot phonons is extracted from electron energy dissipation and fluctuations. In nitride channels, the hot phonons are found to slow down electron energy dissipation and establish the hot-electron distribution controlled by the electron temperature. The hot electron temperatures are evaluated from the electron distribution functions calculated at different electric field strengths. The obtained dependence of hot-electron temperature on supplied power is in a good agreement with the available experimental data on microwave noise.

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In Chapter 5, the ZnO based materials, such as ZnO thin film and its heterostructure, were prepared on c-plans sapphire (Al2O3) substrates by plasma-assisted molecular beam epitaxy (P-MBE). The influence of growth temperature on ZnO film quality was investigated. The result reveals a change of the growth mode from three-dimensional (3D) nucleation to two-dimensional (2D) nucleation. The photoluminescence (PL) spectra exhibit a strong ultraviolet (UV) emission and a weaker visible emission for all samples. By the measurements of PL spectra at different temperature, the origin of UV emission peak at RT is considered to be from free exciton emission and the shift of UV emission peak position is attributed to quantum confinement effect due to different crystal grain sizes. In addition, the carrier concentration of ZnO thin films decreases with increasing growth temperature. In the optimum growth condition, the carrier concentration is N=7.66 ×1016 / cm3 which is closed to that of bulk ZnO. On the other hands, N-doped p-type ZnO thin films were grown by P-MBE on c-plane Al2O3 using radical NO as oxygen source and nitrogen dopant. The reproducing ZnO thin films have maximum hole concentration of 1.2×1019cm-3and lower resistivity of 9.95Ω·cm. In absorption spectra, the subbandgap related to N in the ZnO band gap was observed. Comparing with optical emission spectra (OES) of radical nitrogen, a difference between radical NO and N2 was found. The OES of radical nitrogen show strong ultraviolet emission related to radical nitrogen (N2*), which is a shallow double donor in the ZnO films. While the radical atoms (N*) are dominant in the OES of radical NO. The experiment result indicates that p-type ZnO is realized by employing radical NO as N dopant. A n-ZnO/p-GaN heterostructure and its light emitting diode were fabricated by P-MBE. And the optoelectrical properties of the heterojunction are investigated. The device exhibited rectifying I-V characteristics to the diode. Under forward bias voltage, electroluminescence spectrum shows that a blue emission from GaN layer at the room temperature. To improve the luminescence properties of the device and make emission from ZnO layer, we designed the device structure and fabricated a p-GaN/i-ZnO/n-ZnO p-i-n heterojunction. Comparing with p-n heterojunction, the emission peaks shifts to high-energy side in the EL spectrum of p-i-n heterojunction. The origin is attributed to the emissions from i-ZnO layer of p-i-n heterojunction. As presented in Chapter 6, X-ray diffraction with a large area detector from CdSxSe1-x alloy thin films, deposited on Si (111)-oriented substrates by laser ablation technique, allowed us to point out the effects of structural disorder which can not be observed by conventional θ2θ diffractometers. The X-ray spectra measured by using conventional θ-2θ diffractometer have shown that the CdSxSe1-x films grow oriented along the (002)-direction in the hexagonal phase with the c-axis perpendicular to the film layers. The width of the 002 reflection is probably related to substitutional disorder arisng from alloying. However, further disorder effects are detected when one resorts to microdiffraction. Indeed, the broadening along the Debye rings reveals that the films are not perfectly epitaxially grown. Moreover, only two families of planes are present in the microdiffraction spectra of all samples. This finding is discussed by considering a structural disorder not related to alloying. An attempt to simulate this structural disorder has been carried out on the basis of symmetry considerations and discussed. A correlation is found with the results of luminescence and Raman spectroscopies that give evidence of disorder effects in terms of excitation localization in photoluminescence and a broad, disorder activated, band in the Raman spectra.

Preface

xi

Chapter 7 describes preparation of a ternary chalcopyrite semiconductor, copper indium diselenide (CuInSe2:CIS), thin films as a light absorption layer for thin film solar cells by electrodeposition. This semiconductor is very attractive for an absorber material in the thin film solar cell because of its suitable bandgap and a large absorption coefficient. CuInSe2 has the bandgap of about 1.0 eV and the absorption coefficient of ~ 105 cm−1. The large absorption coefficient enables us to realize the thin film solar cell. Although the highest theoretical efficiency is obtained with the semiconductor whose bandgap is ranging from 1.4 to 1.5 eV, the bandgap of CIS can be enlarged up to 1.68 eV by adding Ga to form solid solution of Cu(InxGa1−x)Se2 (CIGS). Electrodeposition as a method for thin film semiconductor preparation is a good approach with respect to economic consideration. An important advantage of electrodeposition as a method for thin film preparation is that films with a large area can be prepared without a vacuum, using simple and low-cost equipments. However, conversion efficiencies ever reported for the cells fabricated by this method are considerably lower than those reported for the cells fabricated by other methods. One of the important problems for development of this technique is to control sample compositions. Understanding of deposition mechanisms of each species is essential in order to achieve higher controllability and reproducibility of film composition and then to improve performance of the photovoltaic cell prepared by electrodeposition. Moreover, an excellent morphology is also essential to achieve higher conversion efficiency. A poor morphology causes short-circuiting between the front and back electrodes. Voids and cracks in thin films degrade the conversion efficiency. On the basis of above mentioned, following subjects were studied. Electrodeposition of Cu-In-Se films has been studied with an aqueous solution containing CuCl2, InCl3 and SeO2, in terms of composition control of deposited films for the preparation of CuInSe2. When a Si wafer is employed as a substrate, both the electrode potential dependence of In/Cu ratio in the film and a stirring effect on film composition are found to become small, compared with Mo substrate. This is explained by taking account of the existence of a space charge layer at the semiconductor surface. From the relationship between In/Cu or Se/Cu ratio in the bath and that in the deposited films, ratios of mass-transfer coefficients for In and Cu, k(In)/k(Cu) or for Se and Cu, k(Se)/k(Cu), have been obtained and their dependencies on deposition current density or stirring of the solution have been studied. The rate-determining step in the deposition process for each ion, “reaction-limited” or “diffusion-limited”, has been also discussed. By employing the stirring, a remarkable improvement, by a factor of 3, is attained for run-to-run and position-to-position fluctuation of the In/Cu ratio in the films. X-ray diffraction patterns show that CuInSe2 is contained in as-deposited films. In order to improve surface morphology, a revers bias is applied after electrodeposition in the same electrolyte. Pluse-plated electrodeposition was demonstrated for the same purpose. In order to improve crystallinity, as-deposited films were annealed in an inert atomosphere. Annealing effects on film properties, such as crystallinity, morphology and chemical composition, were investigated. Effects of Se concentration were also investigated. Excess Se is found to degrade controllability of composition and crystallinity. The conversion efficiency of 0.866 % (Voc=0.47 V, Isc=1.9 mA/cm2, FF=0.533) is obtained with a chemical bath deposited CdS buffer layer on the electrodeposited CIS layer without any transparent conductive oxide layers. Preparation of CuInSe2 thin films with a

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bilayer structure by electrodeposition were studied. Change in a Cu/In ratio with depth is essential to obtain higher conversion efficiency. Thus, a new electrodeposition technique for preparing CuInSe2 thin films with controlled depth profile were developed. The CuInSe2 thin films with both Cu-rich and In-rich layers are deposited by changing substrate potential during electrodeposition.

In: New Research on Semiconductors Editor: Thomas B. Elliot, pp. 1-30

ISBN: 1-59454-920-6 © 2006 Nova Science Publishers, Inc.

Chapter 1

CRYSTAL GROWTH OF TERNARY AND QUATERNARY ALLOY SEMICONDUCTORS BY ROTATIONAL BRIDGMAN METHOD Yasuhiro Hayakawa*, M.Haris, Masashi Kumagawa Research Institute of Electronics, Shizuoka University, 3-5-1 Johoku, Hamamatsu, Shizuoka 432-8011, Japan

Tetsuo Ozawa Department of Electrical Engineering, Shizuoka Institute of Science and Technology, 2200-2 Toyosawa, Fukuroi, Shizuoka 437-8555, Japan

Abstract Ternary and quaternary alloy crystals of semiconductors are important materials for optoelectronic devices because fundamental properties such as lattice constant and band gap can be controlled by adjusting composition ratio. In order to grow high quality ternary bulk crystals, various techniques have been carried out. Nakajima et al. succeeded in growing compositionaly graded InxGa1-xAs (x=0.5-3.30) single crystals by the Brigman method. Hayakawa et. al. introduced ultrasonic vibration into the melt from the bottom of the crucible in the Czochralski method to prevent the occurrence of constitutional supercooling. This method was applied for the growth of InxGa1-xSb single crystals, and it was found that the growth thickness in the single crystalline state was increased with an increase of the output power of ultrasonic vibrations. We have modified the Czochralski method in order to improve the homogeneous distribution of impurities by making a seed crystal rotate alternately clockwise and counterclockwise within a narrow range of angle. We have also modified the Brigman method to stir the melt. In Section 2, the growth of InSb1-xBix ternary bulk crystals and the results analysed are presented.

*

E-mail address: [email protected], Tel: 81-53-478-1310

2

1

Yasuhiro Hayakawa, Tetsuo Ozawa, M. Haris et al.

Introduction

Ternary and quaternary alloy crystals of semiconductors are important materials for optoelectronic devices because fundamental properties such as lattice constant and band gap can be controlled by adjusting composition ratio. The alloy crystals offer the possibility to reduce the problem of lattice mismatch at the interface between a substrate and an epilayer. Ternary alloy crystals such as InGaAs [1], GaAsP [2], InGaSb [3], InAsP [4] and quaternary alloy crystals such as GaInAsSb [5], InAsSb [6] have been grown until now. However, it is very difficult to grow large single ternary alloy crystals of high quality, because there are three major problems which must be overcome. The first is the constitutional supercooling which appears in the source solution ahead of the growth interface. Since the separation between liquidus and solidus lines is wide, the degree of constitutional supercooling becomes large which brings about the growth of polycrystals [7,8]. The second is the occurrence of composition changes both in the grown crystal and in the solution during growth. This means that the composition ratio in the alloy crystal continues to change because the segregation coefficient of each component is not unity. The third relates to the flows caused by heat and mass transfer. The quality of alloy crystals is strongly affected by these flow patterns. InSb1-xBix is a very interesting material because InBi has a semi-metallic character and the band gap energy is controlled and can be reduced by replacing Bi into Sb sites. This crystal is useful for detectors in the middle infrared region (7.4-16ȝm) [9]. InxGa1-xSb is the ternary alloy between InSb and GaSb binary alloys which can modulate the wavelength region uniquely from 1.7 to 6.8ȝm by adjusting the indium to gallium composition ratio; it can be used as a device material in infrared region and further well suitable for thermophotovoltaic cells. InxGa1-xAs is an important material to fabricate thermo-photovoltaic cells in the near infrared region, because the energy gap and the lattice constant can be tuned in the range of 0.87-3.5µm and 5.6533-6.0584 Å by adjusting the indium composition. InGaSbBi quaternary bulk single crystals, which have not been grown up to the present is very attractive, because it is composed of semimetal (InBi) and semiconductors (InSb and GaSb). The band-gap and lattice constant can be separately varied in the wide range. In order to grow high quality ternary bulk crystals, various techniques have been carried out. Nakajima et al. succeeded in growing compositionally graded InxGa1-xAs (x=0.05-0.30) single crystals by the Bridgman method. These graded crystals were used as an InGaAs seed on which In0.25Ga0.75As bulk crystal was grown under lattice-matched condition [10]. Kodama et al. grew a 28 mm long single-crystalline InxGa1-xAs (x=0.3) ternary bulk crystal on GaAs seed crystal using the two-step multi component zone melting method. The furnace temperature decreased to increase InAs content in growing crystal and kept constant to grow homogeneous crystal [11]. Sheibani et al. improved liquid phase electro epitaxy system by the application of an external static magnetic field to grow, flat, thick and uniform In0.04Ga0.96As single crystals [12]. Hayakawa et.al introduced ultrasonic vibration into the melt from the bottom of the crucible in the Czochralski method to prevent the occurrence of constitutional supercooling [13-18]. The facet region located in the centre of the InSb single crystal shifted toward the periphery of the crystal and decreased in size by introducing ultrasonic vibrations. Furthermore, the difference in impurity concentration between the facet and the off-facet regions became smaller. This method was applied for the growth of InxGa1íxSb single

Crystal Growth of Ternary and Quaternary Alloy Semiconductors by Rotational…

3

crystals, and it was found that the growth thickness in the single crystalline state was increased with an increase of the output power of ultrasonic vibrations [19-22]. We have modified the Czochralski method in order to improve the homogeneous distribution of impurities by making a seed crystal rotate alternately clockwise and counterclockwise within a narrow range of angle [23,24]. We have also modified the Bridgman method to stir the melt. The method (which we called "rotational Bridgman method") is similar to the tipping method developed by Nelson [25]. However, to increase the stirring effect, a relative motion between the growing surface and the solution can be given by rotating the growth ampoule at high speed, where the growing surface covered about 60–90% with the solution. We adopted this method to grow InSb1íxBix, InxGa1íxSb, In1íxGaxSb1-yBiy and Ga1íxInxAsySb1íy alloy crystals [26-31]. The growth of crystals was controlled by decreasing the temperature or by moving the ampoule to the lower temperature region along with the ampoule rotation. The effect of ampoule-moving rate and rotation rate on the growth rate and the indium composition profile in the InxGa1-xAs (x=0.02-0.03) crystals was investigated using the impurity striations intentionally introduced into the growing crystal by thermal pulse technique [32]. To investigate the solution convection in the rotational Bridgman method, both flow patterns and temperature distribution were calculated by solving Navier-Stokes, continuity and energy equations in 3-dimensional model. By increasing the ampoule rotation rate from 0 rpm to 100 rpm, the flow velocity in the solution increased and the temperature distribution tended to be uniform [33,34]. In Section 2, the growth of InSb1-xBix ternary bulk crystals and the results analysed are presented. The growth of InxGa1-xAs ternary bulk crystals and the determination of growth rate with respect to the ampoule moving rates and rotation rates are investigated, and are described in Section 3. The mechanism of the diffusion of both Ga and Bi into InSb seeds during the growth of InGaSbBi and the formation of domains in the InSb seed crystal is analysed. The results have been compared with the InSb1-yBiy and InxGa1-xSb crystals and are described in Section 4. The numerical simulation results of the effect of ampoule rotation are explained in Section 5. The important results and the conclusions are summarized in Section 6.

2

Growth of InSb1-XBiX Bulk Crystals

InSb1-xBix ternary crystals were grown by the following two kinds of improved Bridgman method (1) with high speed ampoule rotation and (2) with both high speed rotation and continuous source feeding (continuous feeding rotationary Bridgman method (CFRBM)). The growth procedure of each method and the results are as follows.

2.1

Rotationary Bridgman Method (RBM)

Fig. 1 shows schematic diagram of growth arrangement used for the growth of InSb1-xBix. The gold furnace, which is semi-transparent, was fixed on one side of a seesaw plate. The plate could be inclined by driving a motor (C). Prior to crystal growth, a silk hat shaped InSb seed crystal and In-Sb-Bi source materials were charged in the quartz ampoule. After

4


alternative evacuation and filling with nitrogen gas several times, the ampoule was sealed to about 5×10-4 Pa and set to a connecting rod of motor (A). By inclining the seesaw plate to the opposite direction, the seeding procedure was carried out by connecting the seed with the solution. Crystal growth was initiated by lowering the furnace temperature at the rate of 0.6 to 1.8ºC/h. The gold coated furnace was very useful to make the seeding procedure easy, because inside of a growth ampoule can be seen during growth. Gold furnace In-Sb-Bi solution In-Sb-Bi grown crystal InSb seed Carbon block Mov eme nt o

f amMotor (A) poul e

Motor (B) Motor (C) Seesaw plate

Fig. 1 Schematic diagram of rotationary growth arrangement used for the growth of InSb1-x Bix.

Fig. 2(a) A roughly polished surface of InSb1-xBix. This crystal was grown from the solution of 1 part InSb and 1 part InBi. (b) The profile of bismuth composition ratio (x) along the growth direction.


5

Fig. 2(a) shows a roughly polished surface of InSb1-xBix. This crystal was grown from the solution of 1 part InSb and 1 part InBi. The crystal was grown at a cooling rate of 1.2ºC/h from 480ºC to 250ºC with the ampoule rotation rate of 100rpm. InSb1-xBix grew in the single crystalline state on the InSb seed crystal of 13 mm in diameter. The length of the single crystal was about 17mm. High speed ampoule rotation enhances the relative motion between the crystal and the solution, and further it supports the solution move back and forth in parallel to the ampoule axis just like the tide. This motion suppresses the occurrence of contitutional supercooling. As a result, the single crystal was grown. The profile of bismuth component ratio (x) along the growth direction is shown in Fig. 2(b). The value of x was 0.015 at first, and increased to about 0.03 at 17mm. Since the segregation coefficient of bismuth was smaller than unity, the Bismuth composition in the crystal was smaller than that in the solution. When the crystal was growing, the Bismuth component was rejected and starts accumulating in the solution. As a result, the Bismuth concentration increased as the growth was progressed. The result agrees well with the solidus curve in the InSb-InBi phase diagram [35] which is shown in Fig. 3.

Fig. 3 InSb-InBi phase diagram.

2.2

Continuous Rotationary Feeding Bridgman Method (CFRBM)

Figs. 4(a) and (b) show a schematic representation of growth ampoule and the corresponding temperature profile in the furnace, respectively. InSb was used as a seed crystal and a feeding source. The inclination of the ampoule is adjusted so that the solution can contact both seed and feed crystals. The seed crystal was set in a slightly lower temperature but higher temperature gradient region than the feeding source. Grown crystals were cut along the growth direction. They were polished roughly at first and then mirror polished with alumina abrasive. They were etched with a KMnO4:HF:CH3COOH etchant solution. Fig. 5(a) shows a polished surface of an InSb1-xBix crystal grown using CFRBM. A starting temperature of 490ºC, a cooling rate of 1.8ºC/h and an ampoule rotation rate of 100 rpm was applied in this case. The upper part of the crystal was polycrystalline. However, the length of the single crystal region in a part of the grown crystal was about 15 mm. This result suggests that longsized single crystals can be grown if a large amount of the source is fed in the solution. Profiles of bismuth component ratio along the growth direction and the diameter far 2mm from the seed-grown crystal interface are given in Figs. 5(b) and 5(c), respectively. The

6


bismuth comcentration was nearly constant through the grown crystal. It indicated that the InSb component was supplied from the InSb feeding source into the solution during growth. So CFRBM is an adequate technique to grow homogeneous InSb1-xBix ternary crystals.

Fig. 4(a) A schematic representation of growth ampoule, (b) the corresponding temperature profile in the furnace.

Fig. 5 Profiles of bismuth composition ratio along (a) the growth direction and (b) the diameter far 2mm from the seed-grown crystal interface.


3

7

Growth of InXGa1íXAs Ternary Bulk Crystals

Fig. 6 shows schematic diagram of growth arrangement used for the growth of InxGa1-xAs. The gold furnace, which is semi-transparent, was fixed on one side of a seesaw plate. Prior to crystal growth, a silk hat shaped GaAs seed crystal, a polycrystalline GaAs feed and In-Ga-As source materials were charged in the quartz ampoule. GaAs (100) single and poly crystals were used to prepare the seed and feed crystals, respectively. The ampoule was sealed under about 5×10-4 Pa and set to a connecting rod of motor (A). Feeding from polycrystalline source to the solution was done by inclining the seesaw plate (using motor(C)) until the solution was saturated. By inclining the seesaw plate to the opposite direction, the seeding procedure was carried out by connecting both seed and feed crystals with the solution. Crystal growth was initiated by moving the ampoule toward the low temperature region of the furnace using a motor (B). For maintaining the temperature profile in the furnace, the seed was set at higher temperature gradient region than the feeding source as shown in Fig. 7.

Fig. 6 Schematic diagram of growth arrangement used for the growth of InxGa1-xAs.

Fig. 7 Temperature profile in the furnace where the seed was set at higher temperature gradient region than the feeding source.

8

3.1


Direct Growth Method

Fig. 8 shows a roughly polished surface of an InxGa1íxAs crystal directly grown on GaAs seed, where the nominal indium composition is 0.10. The growth was carried out with an ampoule-moving rate was 0.5mm/h with the seed-rotation rate of 75 rpm. The length of InxGa1íxAs single crystal was 6.5mm. The shape of the growth interface was convex towards the seed. Fig. 9 shows the indium composition profiles along the growth direction of the crystals. When the indium composition ratio (x) was less than 0.12, the indium profile was nearly uniform. This indicates that the GaAs component was fed continuously into the In-GaAs solution during growth. When the x value is 0.20, the indium composition increased slightly along the growth direction. This means the supply of GaAs is not enough in this case.

Fig. 8 Roughly polished surfaces of InxGa1íxAs crystal directly grown on GaAs seed, where the nominal indium composition is 0.10.

Fig. 9 Indium composition profiles along the growth direction of the InxGa1-xAs crystals.

The relationship between indium composition ratio x and normalized FWHM of XRD in the InxGa1íxAs crystals is shown in Fig. 10. FWHM of the grown crystals was normalized by that of GaAs seed crystal. The normalized FWHM increased with an increase of indium composition ratio. This indicated that the quality of the crystals became poor by increasing indium composition because the lattice mismatch between the grown crystal and the seed was increased.


9

Fig. 10 Relationship between indium composition ratio x and normalized FWHM of XRD in the InxGa1íxAs crystals.

3.2

Multi-step Growth Method

Fig. 11 shows the temperature-time profile of multi-step growth. InxGa1-xAs ternary crystal was grown by adopting three growth steps. InxGa1-xAs (x=0.03) was grown on a GaAs seed, and then InxGa1-xAs (x=0.05) was grown on InxGa1-xAs (x=0.03). Finally InxGa1-xAs (x=0.07) was grown on InxGa1-xAs (x=0.05). To increase the indium composition step by step, the temperature of the solution at each step were adjusted at 700˚C, 800˚C and 900˚C, respectively. Figs. 12(a) and (b) show feeding process and growth processes, respectively. In (a) GaAs component was fed from GaAs feed source to the In-Ga-As solution until the solution was saturated. In (b) crystal growth was started by moving the ampoule toward the low temperature region of the furnace with a moving rate of 0.75mm/day. The main feature of the multi-step growth was that feeding and growth processes were repeated and the indium composition in the InxGa1íxAs crystal increased step by step.

Fig. 11 Temperature-time profile of multi-step growth.

10


Fig. 12 (a) Feeding process and (b) growth processes.

Fig. 13 shows indium composition profile in an InxGa1íxAs crystal grown by the multistep growth method. The lengths of the single crystalline portion were 1mm, 1.5mm and 6.5mm at each step region. The indium composition in the first and second step regions was nearly constant throughout the grown crystals. In the third step region, the indium composition was homogeneous in the wide region. It proved that the GaAs component was fed continuously into the In-Ga-As solution at each step.

Fig. 13 Indium composition profiles in the InxGa1íxAs crystals grown by the multi-step growth method.

Fig. 14 XRD FWHM profiles along the growth direction in the InxGa1íxAs (x=0.10) grown by (a) the direct growth method and (b) the multi-step growth method.


11

Fig. 14 shows the XRD FWHM profiles along the growth direction in the InxGa1íxAs (x=0.10) grown by the direct and the multi-step growth methods. In the InxGa1íxAs crystal grown directly on GaAs, XRD-FWHM was in the range of 140 arcsec, whereas the FWHM of the seed crystal was 35 arcsec. In the InxGa1íxAs grown by the multi-step growth method, FWHM at the interface of the seed and the first step region was 120 arcsec. This was similar to the value of the crystal directly grown on the seed. However, FWHM in the second step region decreased to 70 arcsec. Furthermore, FWHM in the third step region was nearly equal to that of the seed crystal. FWHM decreased to one fourth the value of the direct growth. This indicates that the influence of lattice mismatch decreased by using the multi-step growth method.

Fig. 15(a) Interface between GaAs seed and InxGa1-xAs(x=0.07) crystal of the direct growth, (b) interface between InxGa1-xAs(x=0.05) and InxGa1-xAs(x=0.07) of the multi-step growth.

Figs. 15(a) and (b) show the interface between GaAs seed and InxGa1-xAs(x=0.07) crystal grown using direct growth process, and the interface between InxGa1-xAs(x=0.05) and InxGa1xAs(x=0.07) crystal regions grown using multi-step growth process, respectively. The interface was irregular and many inclusions were incorporated in the crystal grown using direct growth. On the contrary, the interface became smooth and the number of inclusions decreased in the crystal grown using multi-step growth process. When InxGa1-xAs (x=0.07) was grown directly on a GaAs seed crystal, the lattice mismatch between them was 0.5%. On the other hand, when InxGa1-xAs (x=0.03) was grown on GaAs seed and then InxGa1-xAs (x=0.05) and InxGa1-xAs (x=0.07) were grown, the lattice mismatch at each interface could be decreased to 0.21%, 0.14% and 0.14%, respectively. Therefore, the quality of the crystals was improved by the multi-step growth process.

3.3

Effect of Ampoule- moving Rate

To investigate the effect of ampoule-moving rate on the growth rate and the indium composition profile, the moving rates were changed step by step as 20, 30, and 40 µm/h under the constant rotation rate of 40 rpm. The thermal pulse technique was used to investigate the real growth rate [36,37]. A small amount of tellurium having a concentration of about 1.0 x 1019cm-3 was added to the In-Ga-As solution as an impurity. While crystal growing, the temperature was raised to 5˚C above the real temperature (i.e.from 800˚C to 805˚C) in oneminute duration, hold it for 1 min and again lowered to 800˚C in one-minute duration. This procedure was repeated for every 10 hours. Impurity striations were revealed by etching the polished surface using chemical etchant (HF: H2O2: H2O = 10:1:1 (vol%)) under light

12


irradiation for 90 seconds. The real growth rates were calculated from the thermal pulse striations observed using optical microscope.

Fig. 16(a) (010) cut surface of the InGaAs grown crystal. Ampoule-moving rates were changed step by step as 20, 30, and 40 µm/h under the constant rotation rate of 40 rpm. (b) An enlarged photograph of the region near the GaAs seed and the InGaAs grown crystal. Impurity striations caused by thermal pulses were clearly seen in the grown region

Fig. 17(a) Growth rate and (b) indium composition profile measured along the line ST shown in Fig. 16(a).


13

Fig. 16(a) shows a (010) cut surface of the crystal. About 8 mm thick InGaAs crystal with diameter of 12 mm was grown. Several cracks were seen but InGaAs crystal directly grown on GaAs seed was single crystalline. The shape of the growth interface was convex towards the seed. Fig.16 (b) shows an enlarged photograph of the region near the GaAs seed and the InGaAs grown crystal as indicated by N in Fig.16 (a). There was no striation in the seed, while the impurity striations caused by thermal pulses were clearly seen in the grown crystal. Since the thermal pulse modulated Te impurity concentration, these striations were formed. The distance between the striations was short near the seed, and it gradually increased as the crystal was grown. It indicated that the growth rate was not constant during growth. Fig.17 (a) indicates the growth rate calculated by measuring the distance of the striations. The growth did not follow the ampoule-moving rate. The growth rate gradually increased from 5µm/h to 20µm/h. As inferred from the phase diagram of In-Ga-As at the temperature 800ºC, the atomic concentrations of indium, gallium and arsenic are 41.5, 53.2, 5.3 (at%), respectively. Compared with the indium and gallium concentrations, the arsenic concentration was very small. When the InxGa1-xAs crystal was grown, 50 at% arsenic was incorporated into the crystal. Therefore, the arsenic in the solution was deficient. It suggested that the growth rate was mainly determined by the amount of arsenic. The growth rate was small at the initial growth stage, but it increased gradually because the arsenic was supplied by dissolving the GaAs feed in the solution during growth. When the ampoule-moving rate increased to 30 µm/h, the growth rate decreased from 20 µm/h to 10 µm/h, and then increased. The change of the moving rate brought instability of mass transfer. The growth rate followed the same trend for all the ampoule moving rates. Fig.17(b) shows the indium composition profile measured along the line ST shown in Fig.16(a). The average indium value was 0.022 with a fluctuation of 0.001. The indium composition was nearly uniform even if the growth rate was not constant. Since the growth rate was less than the ampoule-moving rate, the growth temperature should decrease during growth and the indium composition should increase gradually. Two reasons were considered. One was that the change of the solidus composition at about 0.02 was not sensitive to the temperature at nearly 800ºC as shown from the In-Ga-As ternary phase diagram [38]. The second was that the gallium was supplied by dissolving the GaAs feed in the solution and was transported towards the growth interface mainly by convection. Therefore, the sufficient gallium was supplied during growth to compensate the increase of indium.

3.4

Effect of Ampoule Rotation Rate

In order to investigate the ampoule rotation rate on the growth rate and the indium composition, the rotation rates was changed as 8, 40, 80 rpm during growth under the constant ampoule-moving rate of 20µm/h. Fig. 18 shows a (010) cut surface of the crystal. About 8.5 mm thick InGaAs crystal with a diameter of 12 mm was grown. Twin structures of {111} plane were formed at the middle region of the crystal. They started to grow from the ampoule wall. However, InGaAs crystal directly grown on GaAs seed was monocrystalline. Also the shape of the interface becomes convex towards the grown crystal thereby indicating the influence of rotation rate on the shape of the interface.

14


Fig. 18. (010) cut surface of the InGaAs grown crystal. Ampoule rotation rate was changed as 8, 40, 80 rpm during growth under the constant ampoule moving rate of 20µm/h.

Fig. 19 (a) Growth rate and (b) indium composition profile measured along the line PQ shown in Fig. 18.

Fig. 19(a) indicates the growth rate along the line shown by PQ in Fig. 18. The growth rate vastly increased from 8 to 47 ȝm/hr by increasing the rotation rate from 8 rpm to 40 rpm. The length of the liquid zone is approximately about 16mm. It should be noted that the liquidus zone would cover only half cylindrical part of the ampoule. The inner diameter of the ampoule is 12 mm. Hence the volume of the In-Ga-As solution is approximately 0.9 cm3. After that the growth rate was decreasing and approaching to the value of the ampoulemoving rate. It was because the solute transport from the feed to the growth interface was enhanced due to convection. Furthermore, the temperature decreased by 4q since dissipation of heat increased by increasing the rotation rate as the quartz ampoule was surrounded by air. It indicated that the change of ampoule rotation from 8 to 40 rpm brought about the instability


15

of mass and heat transfers. On the other hand, the change of growth rate was small when the rotation rate increased from 40 to 80 rpm. It suggested that the effect of ampoule rotation on mass and heat transfers was not significant compared with the rotation change from 8 to 40 rpm. Fig. 19(b) shows the indium composition profile of the crystal along the PQ line. The indium composition ranged between 0.02 and 0.03 and it did not follow the change of growth rate.

4 4.1

Growth and Analysis of In1-xGaxSb1-yBiy Quaternary Crystals Growth Morphology

Fig. 20 shows a roughly polished surface of an In1-xGaxSb1-yBiy crystal. The initial composition ratio of a source solution was In : Ga : Sb : Bi = 48 : 2 : 25 : 25 (at%). Crystal growth was performed by lowering the solution temperature from 480qC at a speed of 0.6qC/h with the ampoule rotation rate of 100 rpm by using motor (A)(refer Fig.1). A seed crystal of silk-hat shape at the left-hand side was InSb, and an InGaSbBi crystal grew to the right-handside direction. From the observations by X-ray Laue patterns and growth morphology, the orientation of crystal was different from at the end of the grown crystal, but about 13 mm thickness of crystal was single. As seen clearly in Fig. 20, white and small areas were present in the InSb seed crystal. To confirm the growth morphology more clearly, an X-ray topograph of the seed region was taken using the KD1 line from an Ag target as given in Fig.21. After the crystal was polished to 400Pm thick, an X-ray of (220) diffraction was detected. A broken line indicates the boundary between InSb and InGaSbBi. Many black areas were clearly seen and corresponded to the white and small areas in Fig. 20. These specular areas are domains. They were about 2 mm long and 100 - 200Pm wide near the interface, but they reduced gradually in size towards the left-hand side from the growth interface. At a distance of about 6.5 mm from the interface, the domains disappeared suddenly. Although many vertical lines were seen on the X-ray photograph, they were wrinkles of emulsion on the film.

Fig. 20 Roughly polished surface of an InGaSbBi crystal. The initial composition ratio of a source solution was In : Ga : Sb : Bi = 48 : 2 : 25 : 25 (at%).

16


Fig. 21 X-ray topograph of the seed region taken using the KD1 line from an Ag target.

Fig. 22 InGaSbBi quaternary crystal grown from the solution of different ratio of In : Ga : Sb : Bi = 46 : 4 : 25 : 25 (at. %).

Fig. 22 shows an InGaSbBi quaternary crystal grown from the solution of different ratio of In : Ga : Sb : Bi = 46 : 4 : 25 : 25 (at. %). Compared with the grown crystal shown in Fig. 20, the gallium composition ratio in the solution was larger by 2 at%, the starting growth temperature (495qC) was higher by 15qC, and the period of growth (133h) was longer by 32 h. The length of single crystal reached about 12.5 mm. The rotational Bridgman method served as a good way of growing InGaSbBi quaternary crystals with higher Ga ratio. In this crystal, many domains were seen not only in the InSb seed but also in a part of the grown crystals near the interface.

4.2

Composition Profiles

Fig. 23 indicates composition ratios of Ga(x) and Bi(y) in the InGaSbBi crystal shown in Fig. 20. Solid and opened circles denote x and y values, respectively. The measurement was carried out so as not to cross the domains along the line AB. In the grown InGaSbBi crystal,


17

the gallium composition ratio had the maximum value of 0.13 at the interface and gradually decreased to 0.037 at a distance of 11mm. This was because the segregation coefficient of gallium was larger than unity. On the contrary, the ratio of bismuth was very low, and there was a slight increase owing to the segregation coefficient less than unity. Therefore, it was found that the bismuth composition in the solution played a role as a solvent and further made the melting point of solution reduce below 525qC of that of InSb. Both gallium and bismuth compositions were incorporated in the InSb seed,. The gallium composition ratio decreased gradually from the interface toward the end of the seed, and finally became zero at the distance of -6.5 mm. This distance corresponds to the position where the domains disappeared suddenly.

Fig. 23 Composition ratios of Ga(x) and Bi(y) in the InGaSbBi crystal shown in Fig.20.

Fig. 24 Composition ratios of Ga(x) and Bi(y) in the InGaSbBi crystal shown in Fig.22.

Fig. 24 shows composition profile of the sample grown from the source solution contained 4 at.% gallium, as seen in Fig. 22. The measurement was carried out so as not to cross the domains along the line CD. The gallium value at the interface was 0.21, which was higher than that of the crystals grown from the 2 at.% gallium solution as indicated in Fig. 23 The difference in gallium ratio at the interface resulted from the gallium composition ratio in the solution. In the inside of grown InGaSbBi, the gallium ratio decreased steadily to 0.033

18


with growing. On the contrary, the gallium composition profile in the InSb seed crystal was very different from the corresponding one in Fig. 23 The gallium value reduced abruptly to about 0.15 in composition ratio near the interface, and it was almost constant until the seed end. It was found that the incorporation of gallium was promoted by both higher growth temperature and longer growth period.

4.3

Lattice Constant

The XRD FWHM was measured by four-crystal X-ray diffractometry (model SLX-1, Rigaku Co., Ltd.). The X-ray intensity profile with respect to 2T of the crystal grown from 2 at.% gallium solutions is illustrated in Figs. 25(a) and (b). The Cu target was used as an X-ray source. At a place of -7.0 mm, there was only one peak corresponding to the (220) diffraction of InSb; however, two peaks appeared at -5 mm. The higher angle peak indicated with B reduced in intensity and broadened in width than the peak of lower angle of A. The peak B corresponded to InGaSbBi, because the diffraction peak shifted towards the higher angle with an increase of the gallium composition ratio and vice versa. The peak from InSb was sharper than that from the InGaSbBi grown crystal. It indicated that the quality of the InGaSbBigrown crystals was inferior to that of InSb. Fig. 26 represents lattice constant calculated from Figs. 25(a) and (b). The lattice constant increased from the interface (distance = 0mm) towards both the InGaSbBi-grown crystals and the seed. Since the lattice constant of InSb is larger than that of GaSb, this suggested that the gallium atoms were substituted for indium atoms in the InSb seed.

Fig. 25 The X-ray intensity profile with respect to 2T of the crystal grown from 2 at.% gallium solutions. (a) seed, (b) grown crystal.


19

Fig. 26. Lattice constant calculated from Figs. 25(a) and (b).

4.4

Formation of Domains in the InSb Seed Crystal

On the formation of domains formed in the InSb seed crystal, their compositions were measured. Respective area profiles of In, Ga, Sb and Bi measured by Energy Dispersive Spectroscopy (EDS) (model: JED-2000, Nippon-denshi Co., Ltd.) are illustrated in Figs. 27(a)-28(d), respectively. White points denote the existence of each composition and the intensity is proportional to the weight ratio of the composition. The intensity of bismuth was strong inside a domain. The indium composition had roughly the same tendency as antimony, although it was not completely zero inside of a domain. In the inside and the outside of the domain, respective depth profiles measured by secondary-ion-mass spectroscopy (SIMS) (model: ims4f, Cameca Co., Ltd.) are illustrated in Figs. 28(a) and (b). Although quantitative values can not be decided due to the lack of standard samples, SIMS measurement has higher sensitivity than EDS. Cs+ ions were implanted for 6000s, but the dipped depth was quite different inside and outside of the domain. The domain was about 20 times easier to be dipped than the outside of the domain. The atomic bond energy of Bi-Bi is 25.0 kcal/mol and that of Sb-Sb is 30.2 kcal/mol [39]. Although the values of other atomic bonds such as In-In, Ga-Ga, In-Ga, Ga-Sb were not known, the above results suggest that the bismuth-rich domain had a weaker atomic bond than that that of InGaSbBi crystal. The counting rate of bismuth in the domain reached to nearly 5x103, though it was extremely low in the outside of the domain. On the other hand, the value of indium was not zero in the domain and it decreased to about 1/10 compared with that of the outside. This corresponded to the result of Fig. 27(a) which showed that a small amount of indium was incorporated in the domain. The compositions of antimony and gallium were below the detection limit of the SIMS analysis. This indicated that the domain was mainly composed of bismuth and indium. EPMA measurement was performed in order to determine the atomic ratio of the compositions in the domains. Fig. 29 shows composition ratios of Ga(x) and Bi(y) along the distance in the domains in the crystal shown in Fig. 20. The gallium and antimony atomic ratios were almost zero, and the composition ratios of indium and bismuth were nearly unity. This indicated that the InBi compound was formed in every domain.

20


Fig. 27 Respective area profiles of (a) indium, (b) gallium, (c) antimony and (d) bismuth measured by EDS.

Fig. 28 Composition profiles in the crystal shown in Fig. 22 analyzed by SIMS: (a) inside, (b) outside of the domain.


21

Fig. 29 Composition ratios of gallium(x) and bismuth(y) along the distance in the domains in the crystal shown in Fig. 20.

4.5

Growth of InSb1-yBiy and In1-xGaxSb Ternary Crystals

In order to investigate the incorporation of gallium and bismuth into the InSb seed more clearly, InSb1-yBiy and In1-xGaxSb ternary crystals were grown and compared with the composition profiles of InGaSbBi. The value of bismuth composition ratio y in the InSb1-yBiy ternary crystal is measured along the growth direction by EPMA and is shown in Fig. 30. The initial composition ratio in the solution was In : Ga : Sb : Bi = 50 : 0 : 25 : 25(at%). The starting growth temperature and the growth period were 474qC and 182 h, respectively. Since the equilibrium segregation coefficient of bismuth in InSb was less than unity, the value of y increased gradually from 0.002 to about 0.005 in mole fraction with crystal growth. On the contrary, the bismuth composition was not present in the InSb seed. These results indicated that the bismuth atoms could not diffuse into the InSb seed if there was no gallium.

Fig. 30 Bismuth composition ratio y along the growth direction of the InSb1-yBiy ternary crystal measured by EPMA. The initial composition ratio in the solution was In : Ga : Sb : Bi = 50 : 0 : 25 : 25.

22


Fig. 31 Gallium composition ratio x along the growth direction of the InxGa1-xSb ternary crystal measured by EPMA. The initial composition ratio in the solution was In : Ga : Sb : Bi = 62.81 : 3.75 : 33.44 : 0(at.%).

The profile of gallium in the In1-xGaxSb crystal measured by EPMA is given in Fig. 31. The initial composition ratio in the solution was In : Ga : Sb : Bi = 62.81 : 3.75 : 33.44 : 0 (at.%). The starting growth temperature and the growth period were 506qC and 86 h, respectively. Since the seed contacted with the solution for 118 h before the start of growth, the total period was 204h. The gallium ratio at the interface was 0.16, and it gradually decreased toward the end of the InGaSb-grown crystal. The gallium was incorporated in the InSb seed, and the value of gallium became zero at the distance of -7.8mm. From the wellknown Einstein`s equation L = (Dt)1/2 and the Boltzmann-Matano analysis [40], the value of D was estimated to be on the order of 10-8 - 10-7 cm2/s, where L is diffusion length, D diffusion coefficient of gallium, and t the time. This value was extremely high in contrast to self-diffusion coefficients of indium and antimony in InSb [41] which ranged from the order of 10-16 to 10-14 cm2/s in the temperature range from 475qC to 517qC. This result suggested that gallium atoms were easily diffusing in the InSb seed crystal. As seen in Fig. 30, bismuth atoms were not able to diffuse into the InSb seed during the growth of InSbBi, and there were no domains in the InSb seed. In the growth of InGaSb, gallium atoms were easy to diffuse in the seed, and domains of indium were formed. In the case of InGaSbBi crystals, both bismuth and gallium were incorporated in the InSb seed, and domains of InBi compound were precipitated in the seed. From these results, the contribution of gallium was necessary for the diffusion of bismuth into the InSb seed. one of the explanations for the mechanism of these processes is as follows. The incorportation of gallium atoms in the InSb produces the excess indium atoms. This brings about the precipitation of indium and the formation of dislocations. Therefore, the diffusion process takes place quickly and the diffusion of bismuth becomes possible. Finally, InBi compound are formed in the InSb seed crystal.


5 5.1

23

Numerical Simulation of Effect of Ampoule Rotation for the Growth of Ingasb by Rotational Bridgman Method Numerical Analysis

Fig. 32(a) shows a schematic RBM growth system and temperature profile in the furnace. The temperature profile in the furnace is symmetric for the central axis. The temperature is the highest at the center of the solution (TH) and the lowest at the seed and feed (TL). In-Ga-Sb solution was put between GaSb seed and feed crystals, where the seed and the feed crystals were cylindrical in shape and the In-Ga-Sb solution were semi-cylindrical. The ampoule rotational rates were changed in the range 0-100 rpm. Crystal growth was initiated by moving the ampoule toward the low-temperature region of the furnace. Fig. 32(b) shows a threedimensional model, which simulates In-Ga-Sb solution region in the RBM experimental system. The GaSb seed and feed crystals formed in the semi-circle shape are put at both ends of the semi-cylinder. The flat top plate of the semi-cylinder means the free surface of In-GaSb solution. The sidewall of the semi-cylinder is made of quartz glass. The In-Ga-Sb solution region consists of 18×15×20 segments. R and Z are lengths of radial and axial directions of the growth solution reservoir. The symbol T is the angle of rotational direction. The governing equations are given as follows: Navier–Stokes equations

wu wu w wu wu v u wt wr r wT wz wv wv w wv wv w2 v u wt wr r wT wz r

§ w 2u 1 wu 1 w 2u w 2u · 1 wP v¨ 2 ¸ U wz r wr r 2 wT 2 wz 2 ¹ © wr

§ w 2 v 1 wv 1 w 2 v w 2 v v 2 ww · 1 wP v¨ 2 ¸ g E 'T , r wr r 2 wT 2 wz 2 r r 2 wT ¹ U wr © wr

ww ww w ww ww vw v u r wt wr r wT wz

(1)

(2)

§ w 2 w 1 ww 1 w 2 w 2 w 2v w · 1 wP v¨ 2 ¸ (3) U r wT r wr r 2 wT 2 r 2 wT 2 r 2 ¹ © wr

Continuity equation:

1 w (vr ) 1 ww wu r wr r wT wz

0

(4)

Energy equation:

wT wT w wT wT v u wt wr r wT wz

§ w 2 1 wT 1 w 2T w 2T · N¨ 2 ¸ r wr r 2 wT 2 wz 2 ¹ © wr

(5)

24


Fig. 32 (a) Schematic of rotational Bridgman method growth system and temperature profile in the furnace. (b) three-dimensional model, which simulated the experimental system.

Here r, z and T are the respective coordinate axes in the radial, axial and angular directions respectively. Symbols of u, v, w are axial, radial, and angular flow components of the fluid velocity, respectively. P is the pressure, g the gravitational acceleration, ȕ the volume expansion coefficient, T the temperature, Q the kinematic viscosity and ț is the thermal conductivity. The following boundary conditions for velocity and temperature were employed. The non-slip condition was applied at the quartz glass wall and the solid–liquid interface. At the interface between the seed and the solution: u = 0, v = 0, w = Ȧ(rpm), T = 660(qC)

(6)

At the quartz glass wall: u = 0, v = 0, w =Ȧ(rpm), T(z) = - az2 + 660 + (TH-TL)

(7)

where a is a constant. At the interface between the feed and the solution: u = 0, v = 0, w = Ȧ(rpm), T = 660(qC)

(8)


25

In the numerical analysis, the rotational rates of the growth ampoule, the temperature differences between the highest temperature TH and the lowest temperature TL in the furnace, and the aspect ratios (axial length/radius length) were changed in the ranges 0-100(rpm), 10140°C, and 1-4, respectively. The flow vector and temperature were calculated under a steady-state condition. The numerical analysis was performed by the finite differential method.

5.2

Analysis Results

Fig. 33 shows flow patterns of z–r cross section in the In-Ga-Sb solution for the aspect ratios of 1, 2 and 4 when the ampoule rotation rates are 0 and 50 (rpm). The temperature difference (TH-TL) in the furnace was 30°C. At 0rpm, natural convection generated at the bottom of the In-Ga-Sb solution, because the flux heated at the middle of the ampoule wall moved upward the free surface.The flow patterns separated into two large flows. One of them, in the left region, moved up the center and down along the GaSb seed wall. The right one flowed symmetrically in the opposite direction. With the increase of the aspect ratio, the flow velocity increased slightly. But, flow pattern was the same as that of the other aspect ratios. On the contrary, the ampoule rotation brought about the large effect on flow patterns. At 50rpm, centrifugal force due to the amoule rotation led to a change in the fluid flow. The flow velocity became stronger near the interface of seed and feed crystals. The fluid was concentrated at the center of the solution by centrifugal force, and moved up to the free surface. The flow velocity increased with the increase of the ampoule rotation rate. In comparison with the result of 0rpm, average flow velocity of 50rpm increased by about 100 times. As a result, the forced convection brought by the ampoule rotation was dominant in the solution. At an aspect ratio of 4, flow pattern was different from that of 1 and 2, because the flow generated by the centrifugal force near the solid-liquid interface was spiral flow and became weak at the center of the solution. The flow direction was opposite to that of the aspect ratio of 1 and 2.

Fig. 33 Flow patterns of z–r cross section in the In-Ga-Sb solution for the aspect ratios of 1, 2 and 4, where each aspect ratio was calculated under ampoule rotation rates of 0 and 50 (rpm), respectively.

26


Fig. 34 Isothermal curves of z–r cross section in the In–Ga–Sb solution, where the temperature interval was 2°C.

Fig. 34 illustrates the isothermal curves of z–r cross section in the In-Ga-Sb solution, where the temperature interval was 2°C. The temperature profiles changed dramatically by increasing ampoule rotation rates. At 0rpm, the temperature was low at the GaSb seed and feed sides, and high at the center of the ampoule wall. The spacings between isothermal curves became narrow near the interface of the seed and feed crystals. On the contrary, the temperature distribution became homogeneous in spite of the size of growth reservoir by increasing the ampoule rotation rate.

Fig. 35 Temperature difference (ǻT) at the solid–liquid interface divided by (TH - TL) as a function of aspect ratio when (TH - TL) was 30°C.

Fig. 35 shows the temperature difference (ǻT) at the solid-liquid interface divided by (TH - TL) as a function of aspect ratio when (TH - TL) was 30°C. At 0rpm, the temperature difference increased with an increase of the aspect ratio. At 10rpm, however, the temperature difference decreased at the aspect ratio of 2 and increase at 4. It may be because the flow


27

pattern was changed as shown in Fig. 33. At 50rpm, the temperature distribution in the solution became homogeneous. It was due to the centrifugal force generated near solid-liquid interface.

Fig. 36 ǻTȦ normalized by ǻT0rpm as a function of rotation rate. Here, ǻTȦ and ǻT0rpm indicate the temperature differences when the ampoule rotation rates are Ȧ and 0rpm, respectively.

Fig. 36 shows ǻTȦ normalized by ǻT0rpm as a function of rotation rate. Here, ǻTȦ and ǻT0rpm indicate the temperature differences when the ampoule rotation rates are Ȧ and 0rpm, respectively. The normalized value at 100rpm was one-fifth smaller than that at 0rpm irrespective of the value of (TH - TL). It indicated that the temperature distribution became uniform with increasing the ampoule rotation rate. The stirring effect of ampoule rotation enhanced with an increase of the rotation rates as the forced convection became dominant in the solution.

6

Conclusion

Rotational Bridgman method was carried out to grow InSb1íxBix, InxGa1íxSb and InxGa1íxSb1yBiy alloy crystals. Both flow patterns and temperature distributions were calculated to investigate the solution convection in the rotational Bridgman method . (1) InSb1-xBix crystals were grown on InSb seeds in the single crystalline state by the rotational Bridgman method. The bismuth composition ratio changes from 0.015 at the initial stage to 0.03 at the final stage due to segregation. By supplying the InSb component into the solution during growth, homogeneous crystals were grown. (2) InxGa1íxAs single crystals with x values up to 0.12 were grown by the direct growth on GaAs seed. The maximum thickness of the InxGa1íxAs single crystals was 6.5 mm. The indium composition ratios in the crystals were homogeneous due to the feeding GaAs sources continuously into the In-Ga-As solution. However, the XRD FWHM increased with increasing of indium composition. InxGa1íxAs crystals were grown by the multi-step method.

28


As a result, the XRD FWHM decreased to the value of seed crystal. These results suggest that the multi-step growth is useful to improve the quality of ternary crystals. (3) InxGa1-xAs ternary alloy bulk crystals were grown on a GaAs (100) seed by the rotational Bridgman method. Experiments have been conducted on various ampoule-moving rate and rotation rate in order to find out the growth rates of InGaAs crystals. The thermal pulse technique was employed for introducing the impurity striations, which was helpful in measuring the growth rates for different moving and rotation rates. It has been found that different moving rate and rotation rates did not affect the composition but had affected largely on the growth rate. Since the growth rate is weakly connected with the pulling rate, it can be concluded that heat transfer did not control the process, but it was controlled by mass transfer and was similar to growth from solution. (4) In1-xGaxSb1-yBiy (0<xd0.21,0 Vr, D-microdefects usually converge in a channel, which afterwards at V t Vcrit begins to diverge towards the periphery of the crystal (Cmicrodefects in accordance with classification [10]). If the crystal growth rate continues to rise, the ring size diminishes (in plane (111)), and at V ~ 8 mm/min the ring of D(ɋ)microdefects disappears. Fig.1c and Fig.1e shows the difference between the images of FZ-Si crystals selective etching at V = 6 mm/min (D-microdefects) and at V = 8 mm/min ((I+V)microdefects). Thus, as the crystal growth rate decreases, the grown-in microdefects are continuously transformed. As for SZ-Si crystals growing, the growth rates are moved to smaller values. The appearance of uniform defect distribution is typical for the values: 1.5 mm/min < V < 2 mm/min. Though, according to Voronkov’s model, interstitial-type A- and B-swirls should appear only at V < Vcrit 1, where Vcrit 1 is defined as a theoretical value characterised by the vacancy-type microdefects appearance and the interstitial-type microdefects disappearance [14, 27]. Data in Fig.2b makes it clear that D-microdefects are not detected in CZ-Si in

Formation of Grown-in Microdefects in Dislocation-Free Silicon Monocrystals

39

channel distribution. This may be concerned with the following. The change in thermal growth conditions causes the suppression of remelting phenomenon (this phenomenon is responsible for striated distribution of A- and B-microdefects) that appears in FZ-Si at interstitial-type growth (i.e. at Vr < Vcrit) and in CZ-Si at vacancy-interstitial-type growth (i.e. at Vr > Vcrit). Furthermore, oxygen and carbon are present in CZ-Si crystal in much greater concentrations than in FZ-Si. Therefore, oxygen precipitation is in close interrelation with the CZ-Si defect structure and leads to interstitial-type dislocation loops (A-microdefects) appearance outside the D(C)-microdefects distribution (i.e. outside the D(C)-microdefects ring in plane (111)). Consequently, as the crystal growth rate increases, the crystallisation front curvature decreases, thus conducing to that the plane (111) emerges to the crystallisation front and the channel and ring distribution of D-microdefects are formed. This process proves the heterogeneous nature of microdefect generation. Decreasing the crystallisation front curvature results in the temperature gradient reducing. However, in its turn, the axial temperature gradient is not constant through the entire crystal diameter. Thus, ɋcrit = V/G(r) (where G(r) generally increases from the crystal center to its edge) [37], that leads to generating V-shaped distribution of D(ɋ)-microdefects in plane (112). Growth rate values, at which the ring-shaped distribution in plane (111) of D(C)microdefects is observed, range within 1 to 2 mm/min for CZ-Si crystals of 80 mm in diameter and within a 0.5 to 0.8 mm/min for CZ-Si crystals of 300 mm in diameter [20]. The ring-shaped distribution of D(C)-microdefects can be defined as ring OSF-defects after thermal processing. Ravi suggested [38], that microprecipitates SiO2 as well as microprecipitates SiC are responsible for generation of stacking faults. We regard the defects within the area of ring-shaped distribution as ones similar to D(C)microdefects in FZ-Si crystals. Therefore, varying the thermal growth conditions results in that D(C)-microdefects in CZ-Si crystals are observed only in the ring-shaped distribution. The ring-shaped uniform distribution of D(C)-microdefects serves as the boundary between the interstitial microdefects area in the striated distribution (A-microdefects) and (I+V)microdefects. Ring-shaped distribution of D(C)-microdefects is formed as a result of Si crystal thermal growth conditions and after the plane (111) is transposed to the crystallization front (edge effect). V-type distribution of D(C)-microdefects in plane (112) is the experimental representation of V/G ratio. Obtained experimental results allow suggesting that the defect formation mechanism (and classification of the grown-in microdefects) in FZ-Si is identical to that in CZ-Si.

2.2

Quenched Crystals Study

It is essential to study initial stages of defect formation in order to determine the mechanism of grown-in microdefects formation and transformation. With this purpose the FZ-Si single crystals grown at various growth rates (2.0, 3.0, 6.0, 9.0 mm/min) were subjected to quenching. One of most effective crystal quenching methods was applied, namely melting zone decantation, when at a certain moment a zone is blown with the directed argon flow. The temperature of grown-in microdefects was determined experimentally and by theoretical calculation. Neimark et al [39] measured thermal fields, which take place during growth of

40

V.I. Talanin and I.E. Talanin

silicon single crystals, by the thermocouple. They suggested the following empirical formula to describe the dependence of an axial temperature gradient on the growth rate of crystal: dT/dL = 10 + (L - 16)2exp(-61.2V – 0.28),

(1)

where L is a distance from crystallization front, cm; V is a crystal growth rate, cm/s. The experimental values well coincide with values calculated from (1). The error between the calculations from (1) and experimental values does not exceed r2%. Our experiments allowed defining the temperatures of grown-in microdefects formation. When studying a detachment surface, we established that microdefects have been not detected directly at the crystallization front because of introducing dislocations due to a thermal impact [4]. Therefore it is hard to define the exact starting moment of the formation process of B- and (I+V)-microdefects. Although we can assume that at the given growth conditions the ȼ- and (I+V)-microdefects are formed as soon as cooling starts due to complexation of silicon interstitial atoms, vacancies and impurity atoms. Distance from the front of crystallization, where the dislocations are observed, is not more 1 to 3 mm and theoretically tends to zero (Fig.3). Table 1. The temperature of grown-in microdefects formation Growth rate, mm/min 2.0 3.0 6.0 6.0, 9.0

Conditions of treatment Quenching Quenching Quenching Quenching

Type of grownin microdefects Ⱥ ȼ D I+V

Distance from the front of crystallization, mm 23 26 -

Temperature of formation, r 20 Ʉ ɌȺ = 1373 Ɍȼ = 1653 ɌD = 1423 TI+V=1653

Fig.3. Schematic distribution grown-in microdefects in FZ-Si crystals after quenching: a) V = 2 mm/min; b) V = 3 mm/min; c) V = 6 mm/min; d) V = 9 mm/min.


41

Experiments in crystal quenching demonstrate that the (I+V)-microdefects are first to appear near the crystallization front and then during the cooling the D(ɋ)-microdefects, Bmicrodefects and A-microdefects are formed. It is worth to note that ɋZ-Si and FZ-Si crystals thermal processing also gives rise to transformation of interstitial-type microdefects in direction as follows: D(ɋ)-microdefects o B-microdefects o A-microdefects [16, 40]. When quenching the FZ-Si crystals grown at V = 6 mm/min, the so-called defect-free area between the crystallyzation front and D-microdefects area is generated. The TEM study imaged this defect-free area as black-white spots (similar to Fig.4d). Such a contrast is known to be caused by dynamic conditions of electron reflection from crystallographic planes near the defect. In the thin parts of samples these defects are imaged as black spots for kinematic conditions of electron reflection. It should be noted that kinematic images of defects are more useful for the evaluation of the size of these defects. For the majority of the observed defects it is 3 to 7 nm. The concentration of defects found by electron microscopy is a 4.51013 ɫm-3. The view of defect images did not yet allow defining the geometric shape of these defects. To state the physical nature of the observed microdefects (the sign of the imperfection around it), their black-white contrast with all the peculiarities of their behaviour has been investigated in dependence on the depth of the microdefect position in thin crystals [41]. For an unambiguous identification of observed defects the method 2.5D has been applied (observation of stereocouples of underfocused and overfocused images) [42]. These methods reveal that the defect-free area contains interstitial-type and vacancy-type defects. Defects have similar image contrast, but vacancy defects on the whole are somewhat greater in size than defects of interstitial type. It should be noted that area with D-microdefects contains only interstitial-type defects a half as large again that size of (I+V)-microdefects, while the concentration of D-microdefects is three times less than the concentration of (I+V)microdefects. In addition, with use of ɌȿɆ study made for FZ-Si crystals grown at V = 9 mm/min and then quenched, the interstitial-type and vacancy-type microdefects have been revealed near the crystallization front in concentrations comparable with each other. Thus, defect-free areas near the crystallization front indeed contain defects of both deformation types, which should be interpreted as quite new and rather substantial fact. Furthermore, it makes clear from these experiments why we introduce the term “(I+V)-microdefects” into the classification of grown-in microdefects. Experimental results obtained in the quenched crystals study demonstrate that the recombination process of intrinsic point defects near the crystallization front is hindered due to the recombination barrier. Microscopic model of such a barrier was developed in detail in papers by Gosele [43-45]. The root of model lies in that the configuration of intrinsic point defects at high temperatures defines the barrier's dependence on temperature. As is assumed within the model’s framework, at high temperatures the self-interstitials and vacancies are extended through several atomic volumes (11 atoms occupies 10 cells), i.e. there is a disordered area around the point defect, which is isotropic-extended up to the atoms of the second coordination sphere. Recombination only occurs if both defects are simultaneously contracted all-around the same atomic volume. As the extended defect configurations have more microstates than the point defect, such a contraction reduces entropy and, consequently, an entropy barrier 'S 0 exists. As temperature is lowering, the barrier decreases and disappears at low temperatures at all and defects recombine easily. This is connected with

42


changing in configuration of intrinsic point defects, which are extended at high temperatures and have a point-like dumbbell shaped configuration at low temperatures, as shown in [45, 46]. It should be emphasized that a theory of extended defect configurations as well as the theory of recombination barrier has been acknowledged in a number of up-to date papers [47-50]. Taking into consideration the available dynamic equilibrium between the vacancies and intrinsic points of silicon atoms as a result of competition between the recombination and continuous thermal generation of Frenkel pairs and considering the local equilibrium

CI CV

CIeqvCVeqv ,

(2)

which is established regardless the generating technique of the concentration ratio of eqv

vacancies (CV) to intrinsic interstitial atoms (CI), where C I

is an equilibrium concentration

eqv

of intrinsic interstitial atoms, CV is an equilibrium concentration of vacancies, accordingly, then the time required to reach equilibrium provided the there is no recombination barrier may be determined by:

Wd

: 4SD S r0 ,

(3)

where : is a volume cell; DS is a self-diffusion coefficient; r0 is an effective recombination cross-section [14]. Assuming that the recombination is defined not only by diffusion but also by height of the recombination barrier, which exceeds free diffusion energy on the value of

'G

'H T'S ,

(4)

as well as that the recombination barrier is defined by the entropy component of the expression (4) and applying the concept of extended defect configurations for entropy barrier microscopic model [45], we obtained the barrier value at Ɍ = 1685 Ʉ (the crystallization temperature), which is 'G = 1.674 eV [4]. Then, we can estimate W value from (3) allowing for existing recombination barrier:

W

: 4SD S r0 exp( 'G

kT

)

(5)

With regard to 'G value, we obtain W | 5.3 min. Therefore the recombination does not get through when standard silicon ingots and standard time of its growth are taken. Such discrepancies may be explained as follows. The Voronkov’s model, firstly, assumes the theory of enthalpy barrier and, secondly, denies the fact that intrinsic point defects of both types co-exist simultaneously. Besides, according to Voronkov’s model W is determined individually for interstitial-type and vacancy-type growth modes proposed by him, without


43

taking into consideration the coefficient of vacancy and intrinsic interstitials joint selfdiffusion. Experimentally obtained results, proving the co-existence of vacancy-type and interstitial-type microdefects and, consequently, occurrence of both types of intrinsic point defects near the crystallization front, may be only explained within the framework of theory, which allows for such a fact and theory of entropy barrier. Since at temperatures close to the melting temperature the equilibrium concentrations of vacancies and self-interstitial atoms co-exist simultaneously in dislocation-free silicon singlecrystals, the oversaturated solid-state solution of intrinsic point defects has been decomposing concurrently at two mechanisms: vacancy-type and interstitial-type. Depending on growth conditions (in particular, on the V/G ratio) the silicon crystals grow under the vacancyinterstitial and interstitial growth modes. This definition of crystal growth modes is concerned with the nature of grown-in microdefects.

2.3

Physical Nature of the Grown-in Microdefects

TEM study of FZ-Si and ɋZ-Si crystals grown at accelerated growth rates gave us a possibility to define the physical nature of (I+V)-microdefects, D-microdefects and Cmicrodefects (see Fig.2). We were first who observed these defects in FZ-Si [15]. Fig.4 shows the typical TEM images of (I+V)-microdefects, C-microdefects and D-microdefects.

Fig.4. TEM images grown-in microdefects in FZ-Si: a) D-microdefects, g b) D-microdefects, g

( 220) , light field, s ! 0 ; c) C-microdefects, g

(I+V)-microdefects (1 – V-defects, 2 – I-defects), TEM, g

( 220) , dark field, s

(202) , dark field, s

( 220) , dark field,

s

0.

0; 0 ; d)

44


TEM study was performed similar to above mentioned in section 2.2. We investigated more than 1000 specimens to establish the statistical relevance of our results. We carried out the TEM study on electronic microscope with accelerating voltage 100 kV, thus excluding the introduction of radiation defects. As the strain field around the defect exceeds the defect size, the shape of the defect is not visible. Main results for FZ-Si [4, 15]: í í

í

D-microdefects constitute clusters of interstitial-type point defects with size of 4 to 10 nm; they may be considered as uniform B-microdefect distribution; C-microdefects are entirely identical to D-microdefects as contrast of TEM images and the sign of lattice imperfection is concerned; they only differ by the distribution geometry. Therefore, there is no need to separate them into a distinct type; At high growth rates (exceeding 6 mm/min), the interstitial-type microdefects occur simultaneously with the vacancy-type microdefects and localize themselves in the same areas – (I+V)-microdefects.

Evaluation of quantitative ratio for vacancy to interstitial-type defects gave us a value a1:4 (at V = 7.5 mm/min). When accelerating the crystal growth, the share of vacancy-type microdefects increases in total number of defects. It is established in crystals with Dmicrodefects that the growth rate accelerating gives diminishing in defect sizes. When CZ-Si 50-mm crystals are grown at a changing growth rate, an area of uniform defect distribution are formed at V > 2 mm/min with its increase in diameter as the growth rate is raising (Fig.5a).

Fig.5. D(ɋ)-microdefects and (I+V)-microdefects in ɋZ-Si (V = 1.8…2.8 mm/min): a) selective etching, plane (112): 1 – “defect-free” area with (I+V)-microdefects, 2 – ring D(C)-microdefects, 3 – (A+B)-microdefects; b) D(C)-microdefects, TEM, g ( 220) , dark field, s 0 ; c) (I+V)-microdefects (1 – V-defects, 2 – I-defects), TEM, g

( 220) , dark field, s

0.


45

Quite often preferential etching does not reveal the defects in the center of the crystal. However, in this case, the central region is surrounded by high-density uniform defect distribution. According to classification [10] and researches presented in [11, 12], we identified these defects as D(ɋ)-microdefects that correspond to D-microdefects in FZ-Si. In plane (111) one can observe a ring of D(ɋ)-microdefects containing so-called "defect-free" area inside. It will be observed that this ring of defects is often called OSF-ring in publications. But "oxidation-induced stacking faults" do not pertain to grown-in microdefects, because they occur after different thermal treatment procedures [17]. As the growth rate increases, the ring of D-microdefects moves to the crystal periphery while the "defect-free" area inside the ring increases in diameter. At V = 3 mm/min the ring of D-microdefects disappears completely. We conducted TEM directly within the ring of D(C)-microdefects and inside this ring (in the "defect-free" area). Within the ring of D(C)-microdefects we observed black-white contrast defects. Their concentration was 1013 to 1014 cm-3, and their size was 4 to 12 nm. A. Bourret [8] was first who observed these defects in CZ-Si, however the sign of lattice imperfection has not been determined yet. By black-white and 2.5D methods we determined that these defects only induce interstitial-type CZ-Si lattice strain. In defect-free area inside the ring of D(C)-microdefects we observed defects of the same size and concentration. The contrast analysis of TEM-images showed both vacancy-type and interstitial-type defects. To establish the defect nature by the black-white contrast method we determined the sign of the product g l on images obtained in dynamic conditions and also determined the defect depth to avoid ambiguities in the interpretation of the black-white contrast. We applied the stereomicrophotography of crystals to determine the defect depth. We investigated 500 specimens to establish the statistical relevance of our results. TEM-observation of CZ-Si grown at V = 3 mm/min also prove the coexistence of both vacancy-type and interstitial-type microdefects. Obtained experimental results are consistent with experimental results for FZ-Si [4]. We analyzed the white-black contrast of D(C)-microdefects image at dynamic imaging conditions. Such analysis helps to define the crystallographic properties of these defects [51]. Inclusions, dislocations dipoles, dislocation loops may be characterized as small-size lattice imperfections with localized strain fields [41, 52]. The contrast analysis proved that D(C)microdefects may be theoretically considered as dislocation loops with Burgers vector b = 1/2[100] and b = 1/2[110]. Planes {100}, {110}, {111} can be possible planes of dislocation loops occurrence [4]. These experimental results were obtained with use of TEM for the case of amplitude contrast by means of analyzing the diffraction image with black-white imaging contrast and 2.5D techniques. However, these techniques have certain weaknesses and restrictions, related both to uncertain depth of defect occurrence and to especially small size of defects being investigated. That is why D-microdefects study using the independent TEM technique by the lattice direct resolution [15] is of great value. Being armed with this method based on phase contrast and giving the lattice image of a 0.2 nm resolution, we obtained detailed information of D-microdefects fine structure. We have been studying n-type undoped FZ-Si singlecrystals with U = 2000 cm, which were vacuum-grown at V = 6 mm/min. Oxygen and carbon concentration was determined by infrared absorption spectrum and amounted to:
80 %) in the doped films. Low diborane concentrations lead to crystalline fraction superior to 40 %. However, when increasing diborane concentration above 5000 ppm, crystalline fraction decreases. The peak position of TO Raman signal is 520 cm -1 for crystalline phase I, but it shifts to lower frequencies (510 - 514 cm -1) as microcrystallites grain size decreases (Tsu et al., 2003).

5.5

Optical Measurements

Hydrogen induces changes in Si–Si bondings so differences in optical and electrical properties as well as in the structure of thin silicon films with different hydrogen content are expected. In this section the results of refraction index, absorption coefficient, optical gap and activation energy are presented. Table III shows the values obtained for refraction index (n) derived by Swanepoel´s method (extrapolated to wavelength O o f) from transmittance spectra (Swanepoel, 1983). These values agree within the 3 % with the values obtained from the method of HernándezRojas et al. (1992). Deposition rate was ~ 1 Å/s. Table III. Refraction index of intrinsic nc-Si:H films. Sample

I2

I3

I4

I5

I6

n

2.8

3.5

2.8

3.1

3.0

Table IV. Refraction index of doped nc-Si:H films. Sample

P0

P7

P15

P30

P60

P100

P750

P3000

P4500

P6000

n

3.3

3.1

3.0

3.0

3.1

3.0

3.0

3.1

3.2

3.0

Table V shows values of absorption coefficient (D) obtained for all samples in the energy range of 2.0 - 2.6 eV. It can be seen that D decreases with hydrogen dilution in this range. VƟprek et al. (1981) have attributed this fact to the improvement of optical path due to internal dispersion by grain boundary or tensioned regions, or due to superficial roughness. But mean roughness of samples measured by AFM (Figures 3 and 4) of around 6 - 8 nm is very much smaller than the incident photon wavelength in that range. So the absorption 2

Dey’s relation for silicon is: 0.5 ī (cm-2) =7.5 + 3 'ș ( ˚ ). A value'ș > 6˚ indicates presence of great amorphous complex density in the material. 'ș § 3.5˚ indicates transition amorphous-crystalline and 'ș < 3˚ corresponds to a crystalline material.

Laser-Induced Phase Transformation in Nanocrystalline Silicon Thin Films

85

increment of these films would not be explained in terms of the light scattering on the rough surface. The optic transition in intrinsic films prepared at dilution higher than 5 % are dominantly indirect with an approximate gap of 1.4 eV, we interpret, as Kalkan and Fonash (1997) have proposed, that the small grain size of nc-Si:H films produces phonon confinement, which induce a change in the phonon distribution density, increasing the relative amount of acoustical phonon. This effect favors indirect optic transitions and so the increment of light absorption. This correlation of D increasing with small grain size has already been reported by Scholten and Akimov (1993). This increasing of absorption has also been correlated with broadening and asymmetry of Raman peak at ~520 cm-1 (see Figure 8). Both effects are attributed in this model to spatial confinement of phonons in microcrystalline grains as well as others authors have done (Richter et al., 1981; Campbell and Fauchet, 1986 and Dey et al., 2000). This confinement has been also observed in amorphous silicon (Diehl et al., 1998). Table V. Absorption coefficient at 2 eV and optical gap for doped nc-Si:H films Sample

P0

P7

D (cm-1) 9.5x103 9.2x103 Eg (eV)

6

0.99

1.04

P15

P30

P60

P100

P750

P3000

P4500

P6000

7.9x103

7.6x103

8.9x103

9.0x103

9.4x103

9.0x103

7.5x103

7.6x103

1.44

1.30

1.35

1.00

1.03

1.43

1.50

0.90

Laser-Induced Phase Transformation

In this section the results of several Raman scattering experiments are presented. Silicon thin films were exposed to a power laser beam of 40 mW. In-situ spectra were registered as are shown in Figure 9. In the spectra of samples I5 and I6 it can be observed three peaks. A slightly asymmetric one at 520 cm-1 (phase Si-I), another quite wide at ~ 480 cm-1 (amorphous phase) and a wide and no symmetric one at ~ 353 cm-1. This last peak does not appear in the micro-Raman spectra of Figure 8. Presence of peak at ~ 353 cm-1 has not been informed in the bibliography of Silicon thin films. Spectra of Raman dispersion generally are taken in the frequency range of 400 - 650 cm-1, and usually low power laser is used to neglect temperature effects. For that reasons it is possible that signal at ~ 353 cm-1 has not been detected until now in Silicon thin films. Effects of the Raman equipment were discharged by obtaining spectra of the samples at other frequency ranges as well as spectra of other materials in the range of interest. No spectra showed any extra peak as the one at ~ 353 cm-1. As was described in section 3, phase Si-XII (r8) has a principal TO Raman scattering signal at 350-353 cm-1 (Piltz et al., 1995; Kailer et al., 1997; Gogotsi et al., 1999) and it is present in phase transformation processes in bulk single-crystal Silicon. We have identified the peak at ~ 353 cm-1 detected in the Raman spectra of the intrinsic samples as the principal TO signal of crystalline phase Si-XII (r8) (Piltz et al., 1995; Kailer et al., 1997; Gogotsi et al., 1999). As it follows, experiments that corroborate this statement are analyzed.

86

R. H. Buitrago and S. B. Concari

a

Intensity (a.u.)

I6

I5 I4 I3 I2 325

350

375

400

425

450

475

500

525

-1

Raman shift (cm ) b P15

Intensity (a.u.)

P60

P3000 P4500

P6000 325 350 375 400 425 450 475 500 525 550 575 -1

Raman shift (cm )

Figure 9. Raman scattering spectra obtained at ~100 kW/cm2 and one scan of 40 s from (a) intrinsic (from Concari et al., 2003) and (b) p-doped nc-Si:H films (from Concari et al., 2004). Spectra are normalized to the peak of 520 cm-1

In the spectra of samples I4, I3 and I2 in Figure 9 the peak from the amorphous tissue disappears while it is present in the spectra of samples I6 and with low height in spectrum of sample I5. Also the peak at 520 cm-1 becomes wider and more asymmetric and the one at 353 cm-1 diminishes its height in the spectra of samples I4, I3 and I2 with respect to those of samples I5 and I6. Comparing these spectra with the micro-Raman spectra of Figure 8, we interpret that both amorphous Silicon fraction and nanocrystalline in phase I present in the films have been transformed and phase XII in now present too. Being the films very thin the substrate effect could be important. The substrate effects in the laser-induced phase transformation as well as the laser power and exposition time were investigated. If local temperature has an important effect, ultra-thin films deposited on substrate with different thermal conductivity should present differences in the laser-induced phase transformation processes. Films of variable thickness from 10 to 60 nm were simultaneously deposited on 7059 Corning glass, Tin Oxide coating layer (TCO) and stainless steel (SS) using 6% of diluted silane and 5000 ppm. The registered Raman spectra of these films are shown in Figure 10. In


87

the spectra of the film deposited on glass, two peaks are observed at ~520 cmí1 and ~353 cmí1. They appear even on the films with the minimum thickness after exposing for 40 s to the laser power of 40 mW. On the other hand, a thickness greater than 40 nm was necessary to observe the formation of crystalline phases on a dominant amorphous base in films deposited on stainless steel. The crystals growth is evidenced by the existence of the scattering Raman peak at 520 cm-1, witch is present in the first 100 Å on glass while the first layers on TCO and SS are amorphous. Thickness of amorphous material is greater than 230 Å on SS and 150 Å on TCO. These minimum incubation thickness of nc-Si would be associated to the selective interaction between growing layer and the substrate as has been explained by Roca i Cabarrocas et al. (1995). Also the peak at 353 cm-1 is present in layers of 15 nm on glass while it takes a double thickness of films deposited on TCO and SS showing a laser-induced phase transformation substrate dependent (Concari, 2004).

a

Intensity (a.u.)

60 nm

35 nm

17 nm 12 nm*

6 nm*

350

400

450

500

550

-1

Raman shift (cm )

Intensity (a.u.)

b 35 nm

17 nm

12 nm 6 nm* 350

400

450

500

550 -1

Raman shift (cm )

Figure 10. Raman scattering spectra from p-doped nc-Si films registered at 40 mW and 100 s deposited on (a) TCO and (b) 7059 Corning glass. Spectra are normalized to the peak at 520 cm-1. The film thickness is indicated for each spectrum. The substrate spectrum has been subtracted for sample indicated with (*)

88


It has been reported that in phase transformation processes in single-crystal Silicon the presence of phase III (bc8) (Crain et al., 1994; Piltz et al., 1995; Lucazeau and Abello, 1997; Kailer et al., 1997; Tanikella, 1996), but phase III (bc8) is not detected in the films as there is no differentiated peak at ~ 430 cm -1 in the Raman scattering spectra of Figure 9. The absence of a 430 cm -1 peak and other peaks indicates that nc-Si:H and nc-Si:H:B phase transformations present different characteristics from those which are produced in the singlecrystal Silicon. These differences could lie in the fact that the temperature of the sample in this study is much higher than room temperature. For the power and diameter of the laser used, the mean temperature could be approximately 260 ºC (Lucazeau and Abello, 1997), but it could even reach ~ 700 ºC at the center spot (Viera and Boufendi, 2001). In order to study heating of the illuminated sample area effect a third experiment was carried on. In-situ Raman spectra of intrinsic samples I6 (amorphous) and I2 (most crystalline) were registered at different temperatures (TR) in an inert atmosphere of Nitrogen. TR was varied from 20 ƕC to 220 ƕC. In all the spectra (see Figure 11 for sample I2) only the two peaks at 520 cm-1 and 353 cm-1 were observed. As was expected, the peaks height diminishes with the increasing temperature due to the growing phonon dispersion in the nanocrystallites. The peak at 520 cmí1 being more sensitive disappeared at 160 ƕC in the spectrum of sample I2. This experiment proves that the peak at 353 cmí1 corresponds to a quite stable crystalline phase at high temperature. Phase assigned to signal at 353 cm-1 decreases when the difference between the temperature of the exposed volume and the surrounding material decreases.

o

T ( C) 20 60 100 140 160 300

350

400

450

500

550

600

Figure 11. Raman scattering spectra from sample I2 registered at increasing temperature which is indicated for each spectrum (from Concari et al., 2003)

From Figure 9a we can observe that the relative height of the peak at ~ 353 cm -1 decreases with Hydrogen dilution. As Hydrogen bonded in any way to Si atoms is believed to


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contribute to the relief of stress in the samples (Street, 1991), sample I6 is expected to be the most stressed one. Figure 9b also shows that the relative amount of phase Si-XII decreases with boron concentration. The amount of the Si-XII phase in the sample P3000 is the smallest one. This film has the greater crystalline fraction and the larger grain size. As the presence of the Si-XII phase is assigned to compression tensions in the films, we can conclude that residual tensions in the nc-Si:H:B decrease with increasing crystalline fraction. As we have analyzed above, volume crystal fraction of the films depends on the diborane doping. The presence of phase Si-XII occurs in stressed material, so we think that the films with high crystalline fraction have higher thermal conductivity and lower residual stress than those films with low crystal fraction, that contain amorphous phase, such as P6000 and I6. The presence of crystalline phase Si-XII in both nc-Si:H and nc-Si:H:B films could be explained as a structure transformation originated in a small volume corresponding to the zone exposed to the laser beam. As the spot is at a higher temperature than the rest of the film due to its low thermal conductivity, the sampling volume is compressed by the cooler surrounding material, thus inducing a higher compression state. As exposition time increases, local temperature also rises. So we can assume higher compression given an increase of the intensity of the phase Si-XII peak related to the phase I peak. It has been proved that in intrinsic nc-Si:H films the phase XII is a crystalline phase more stable at higher temperature than phase I (Concari and Buitrago, 2003). On the other hand, the sampling volume at a high temperature could present a different pattern of structure phase transformation than at room temperature. The Si-XII phase, more stable and may be requiring less compression, would prevail over the Si-III phase. An interesting fact to note in Figure 11 it is that the peak of phase I and XII remain in the same position, within the experimental error. However, increasing temperature should make the TO Raman peak shift toward lower frequencies (Viera et al., 2001; Cerqueira and Ferreira, 1999). This can be explained as follows: as it has been well established for both crystalline and amorphous silicon that the increase of the compressive stress makes the TO peak shift to higher frequencies (Hishikawa, 1987; Danesh et al., 1996), the effects of temperature could then be compensate with the effects of the compressive stress over the sample volume in our films. Another experiment to study the laser power effect on the induced-phase transformation processes was developed. Raman spectra of a thin piece of a single-crystal registered for increasing laser power and exposures are plotted in Figure 12. It can be observed that the peak at 353 cm-1 appears and grows progressively more than the 520 cm-1signal while other peak is detected. The Raman spectra obtained at low power (40 mW) and low exposures (15 and 20 s) do not present the peak at ~ 350 cm-1. This peak appears for exposure greater than 50 s. A simple calculus leads to a minimum power of 2 W for the laser used to induce the phase XII in crystalline Silicon. For a height of peak at 353 cm-1 be comparable to that of the peak at 520 cm-1 minimum power of 400 mW and a exposure of 1,100 seconds are required. Peak at 353 cm-1 decreases when locate heating is suspended. Si-XII is a meta-stable phase which can co-exist with phase I at normal pressure and room temperature but is reversible with a simple heating at 100 C during two hours. The same results was obtained by Piltz et al. (1995) in bulk single-crystal Si.

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Figure 12. Raman scattering spectra from single c-Si registered for 200 s and normalized to the peak at 520 cm-1. Laser power and exposition time are indicated.

Peak at ~ 353 cm-1 is asymmetric and can be fitted with two Lorenzian curves centered at 353 cm-1 and 349 cm-1 respectively with a area rate of A(353) / A(349) = 0.45 (see Figure 13). The asymmetry could be due to the superposition of two effects, one the locate compression that originates the transformation to phase XII and second, a phonon confinement in the small volume of Si-XII. By increasing the laser exposure the area rate becomes equal to the unit. This is a evidence of a greater material volume of phase XII witch is surrounding by Si-I. The confinement effects that produces the asymmetry of the peak decreases with the laser exposure.

Figure 13. Fitting of the Si-XII peak (...) with Lorentzians curves at 348 cm-1 (-.-) and 352 cm-1 (- -)

The spectra of Figure 9 were registered with a laser power of 40 mW and a exposure compatible with base noise of 40 s. By increasing the exposure time up to 100 s (Figure 14) it


91

is observed as happens in the single-crystal Si, the growing of phase XII. In the case of ncSi:H this induced-phase transformation is more important as can be seen for sample I6, where height of Si-XII peak is close to the Si-I one.

Figure 14. Raman scattering spectra from intrinsic samples registered at 40 mW and 100 s. Spectra are normalized to the signal at 520 cm-1

Measurements accomplished on totally amorphous material show that both Si-I and SiXII phases grow simultaneously. So, the crystallization induced by the laser beam in nanocrystalline silicon films is summarized in the transformation of the amorphous phase into phase I and then by compression tensions, to phase Si-XII. Reinterpretation of the asymmetry of the peak at 520 cm -1, may be done in terms of a non-homogenous distribution of grain size, instead of the presence of phase Si-IV. Also Kobliska and Solin (1972) have found no evidence of a transformation from Si-III to this wurzite phase caused by sample heating in the focused laser. They did observe however, a weak line at 355 cm -1. At that time they were not able to identify it with any known Si phase. As Tsu et. al. (2003) state, rather than offering evidence for of intermediate order, like phase Si-IV, the 510 – 514 cm-1 Raman scattering can be considered due to the nanocrystallites, where small particle effects lead to observing more of the phonon spectrum, thus causing the apparent shift to lower frequencies as shown by Richter et al. (1981). The differences in phase Si-XII growth in the films deposited on glass and stainless steel can also be explained in terms of a thermal effect. Thermal conductivity and dissipation of stainless steel are greater than those of glass. Therefore, the temperature of the sampling volume and compression tensions of films deposited on stainless steel would be smaller than those deposited on glass. On the other hand, the sampling volume at a high temperature could present a different pattern of structure phase transformation than at room temperature. The Si-XII phase, more stable and may be requiring less compression, would prevail over the Si-III phase. However, at present, there are factors that are not known about these transformations. Gupta and Ruoff (1980) have shown that for single-crystals in the (111) direction, semiconducting–metallic transition is activated at a lower compressive stress than along the (100) direction on single crystals. As X-ray diffraction spectra showed a preferential growth on the (111) direction of our microcrystalline films, no presence of phase III could be explained by this fact.

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The latter reveals that the relative amount of the Si-XII phase is smallest for the sample I2, corresponding to the greater crystalline fraction and presumably the larger grain size. As the presence of the Si-XII phase is assigned to compression tensions in the films, we can conclude that residual tensions in the nc-Si decrease with crystalline fraction.

7

Synthesis and Conclusions

The characterization methods used point out that the sample series under study are nanocrystalline with different degrees of volume crystal fraction. Results of AFM and conductivity measurements are consistent with the Raman spectra. Increasing the Raman spot laser power produces a change in the film structure. Both Si-I and a-Si transform to an intermediate phase Si-XII. The presence of crystalline phase Si-XII in nc-Si:H films could be explained as a structure transformation originated in a small volume corresponding to the zone exposed to the laser beam. As the spot is at a higher temperature than the rest of the film due to its low thermal conductivity, the sampling volume is compressed by the cooler surrounding material, thus inducing a higher compression state. As exposition time increases, local temperature also rises. So we can assume higher compression given an increase of the intensity of the phase SiXII peak related to the phase I peak. From what has been reported here, we can conclude that crystalline phase Si-III, present in single crystals under compression tensions at room temperature and in equilibrium with phase Si-XII and Si-I, is not detected in the intrinsic and p-doped nc-Si:H thin films. In the same way, other effects overlap peak shift from 520 cm -1 toward 510 cm -1, but we do not think it is due to the presence of phase Si-IV. TO Raman peak can be found at lower frequencies than 520 cm -1 (even as low as 508 cm-1) due to small particle effects (Tsu et al., 2003). Therefore, we propose a model of phase-transformation process for the silicon in the form of amorphous or nanocrystalline thin films as the following: the amorphous phase crystallizes directly in Si-I phase by the effect of the temperature. This one arrives at phase Si-XII without going through phase Si-III due to the effect of high temperature and compression stress in the films. The Si-XII phase is presented with other phases in single-crystal silicon submitted to pressures in the range 1.6 – 2.6 GPa (Piltz et al., 1995). The residual tensions in the amorphous silicon, always present surrounding the nanocrystals and measured by different methods (de Lima et al., 1999; Spanakis et al., 2001; Danesh et al., 2001) are in the range 0.7 – 1.0 GPa. The occurrence of a Raman peak at ~ 350 cm-1, attributed to the Si-XII phase, is suggesting that the focalized high power laser beam should increase the residual tensions of the thin films to values higher than 1.6 GPa.

Acknowledgements Authors would like to thank the American Institute of Physics (AIP), the Institute of Physics Publishing (IOP) and Elsevier for the permissions to reproduce material from the papers published in the Journal of Applied Physics (Concari et al., 2003), Semiconductor Science


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and Technology (Concari and Buitrago, 2003) and the Journal of Non Crystalline Solids (Concari and Buitrago, 2004), respectively.

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ISBN 1-59454-920-6 c 2006 Nova Science Publishers, Inc.

Chapter 4

M ONTE C ARLO S IMULATION OF H OT-P HONON E FFECTS IN B IASED N ITRIDE C HANNELS M. Ramonas∗ and A. Matulionis Semiconductor Physics Institute, A. Goˇstauto 11, Vilnius 01108, Lithuania

Abstract Recent progress in Monte Carlo simulation of hot electron transport and fluctuations in nominally undoped AlGaN/GaN and AlGaN/AlN/GaN heterostructures with degenerate two-dimensional electron gas channels is reviewed. Input scattering probabilities of the electrons are calculated in a semiclassical approach from the confined-electron envelope wavefunctions obtained through a self-consistent Poisson– Schrödinger method. Additional scattering due to accumulation of nonequilibrium longitudinal optical phonons, termed hot phonons, is treated together with ”lattice” heating and other scattering mechanisms of importance for electron transport at high electric fields applied in the plane of electron confinement. Possible ways to treat electron gas degeneracy and hot-phonon effects through Monte Carlo procedures are described. Hot-electron and hot-phonon distribution functions are presented for indepth discussion of the results. Complementary information on hot phonons is extracted from electron energy dissipation and fluctuations. In nitride channels, the hot phonons are found to slow down electron energy dissipation and establish the hot-electron distribution controlled by the electron temperature. The hot electron temperatures are evaluated from the electron distribution functions calculated at different electric field strengths. The obtained dependence of hot-electron temperature on supplied power is in a good agreement with the available experimental data on microwave noise.

Keywords: Monte Carlo simulation, electron transport, nitride heterostructures, hotphonons, degeneracy, energy dissipation. ∗

E-mail address: [email protected]

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1

M. Ramonas and A. Matulionis

Introduction

Semiconductor heterostructure channels with two-dimensional electron gas (2DEG) are under intense investigation due to excellent frequency and noise performance of field-effect transistors. The 2DEG channels for microwave applications contain a high electron density, they operate at high electric fields and, consequently, must withstand dissipated powers of a high density. An adequate understanding of energy dissipation and electron transport under these specific conditions is vital for device engineering [1, 2]. Theoretic investigation of electron transport at a microscopic level requires analysis of the Boltzmann kinetic equation. Since analytical solutions are possible only for a limited number of simple models, device engineering prefers approaches based on coupled energy and momentum balance equations. Yet, the validity of these equations under conditions of small volumes subjected to high electric fields is questionable. Monte Carlo technique seems to be the most appropriate way for studying electronic processes in biased two- and three-dimensional channels and devices [3, 4, 5]. Emission of longitudinal optical phonons (LO phonons) is the main energy dissipation mechanism for high-energy electrons [6, 7]. Because of low group velocity, the emitted LO phonons stay in the channel until they either decay into other phonon modes or are reabsorbed by the electrons. The accumulated nonequilibrium LO phonons are termed hot phonons. Possible effects of hot phonons on electron energy dissipation and transport have been treated theoretically through Monte Carlo simulation [8]. The simulation is equivalent to solution of coupled kinetic equations for hot electrons and hot phonons. The latter are found to bottleneck the energy relaxation of hot electrons. Recent interest in hot-phonon problem is stimulated by GaN-based high-power devices. Extremely strong electron coupling with LO phonons and a high electric power supplied to the electrons necessitates reconsidering the hot-phonon effects on electron transport and energy dissipation with a special emphasize on nitride 2DEG channels. Gallium nitride and related heterostructures are of increasing interest for use in advanced semiconductor devices [1]. In nitride heterostructures, a high-density 2DEG forms without an intentional doping [9]. A wide band gap of GaN, together with a high thermal conductivity bodes well for transistor high-power operation. The measured electron drift velocity reaches high values at high electric fields [10, 11]. These features predict, for nitride field-effect transistors, an excellent performance at microwave frequencies. Indeed, an AlGaN/GaN high electron mobility transistor (HEMT) is the best device for generation of microwave power at 10 GHz microwave frequency [12, 13, 14, 15]. The cutoff frequency of AlGaN/GaN HEMTs is determined by electron drift velocity [16] unless parasitic capacitances and resistances decide the frequency range. The drift velocity, extracted from the cutoff frequency of HEMTs is ∼ 1.2 × 107 cm/s [16, 17]. There is some room for improvement of the frequency performance, since, in a GaN p-i-n diode, the measured drift velocity peaks at 7 × 107 cm/s [10]. However, the electron transport conditions differ in p-i-n diodes and HEMTs, and an in-depth investigation of electronic processes is needed for a better understanding of electron transport limitations in 2DEG channels at high electric fields. Several sources of such discrepancy can be pointed out. Since a nitride 2DEG channel usually contains a high-density electron gas, a highenergy electron does not emit an LO phonon if the final low-energy state is occupied. Thus, the electron gas degeneracy plays its role [18].

Monte Carlo Simulation of Hot-Phonon Effects in Biased Nitride Channels

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Under a high bias and a small volume, the supplied electric power density is extremely high, and channel self-heating takes place. The Joule heat is known to reduce electron drift velocity. Short voltage pulses have been used to avoid the self-heating effect during experimental investigation of electron drift velocity [19, 20, 21]. In nitride 2DEG channels, the LO-phonon decay time, termed hot-phonon lifetime, exceeds considerably the time of LO-phonon emission by a hot electron. Moreover, the maximum dissipated power per electron 10-100 times exceeds that in arsenide 2DEG channels [14]. As a result, the mentioned accumulation of hot phonons is the most essential feature of biased nitride channels [18, 22, 23, 24, 25]. In particular, an almost immediate absorption of a hot LO phonon after emission of another LO phonon changes direction of the electron motion with the resultant negative contribution to the drift velocity. The present chapter starts with the section on self-consistent Shrödinger–Poisson calculations of the electron wavefunctions for nitride heterostructures. The electron scattering mechanisms included into Monte Carlo model are outlined in the sect. 3. The Monte Carlo model is shortly introduced in sec. 4. Section 5 deals with the hot-phonon effect. The electron drift velocity in nitride channels in presence of channel self-heating, hot-phonons, and electron gas degeneracy is discussed in sec. 6. The Monte Carlo results for the electron temperature and the noise temperature are presented in sec. 7. The electron power dissipation is discussed in sec. 8. The chapter ends with the conclusions.

2 Conduction Band Profile and Electron Wavefunctions Electron wavefunctions enter expressions for matrix elements of electron scattering rates. In a simple approach, the electron wavefunctions are calculated in the low electron density approximation, without the charge of free electrons taken into account. Analytical expressions for the electron wavefunctions are available for rectangular potential profiles (double heterojunction structures) and triangular potential barriers (single heterojunction quantum wells). As mentioned, nitride channels for high power applications usually contain a high density 2DEG, and one cannot ignore the charge of conduction electrons. The charge distribution is needed in order to solve Poisson equation. However, the charge density is not available before the energy bands are obtained from Shrödinger equation where the solution of the Poisson equation is a prerequisite. Thus, for the 2DEG confined in a quantum well, the electron envelope wavefunctions follow through a self-consistent solution of the Schrödinger and Poisson equations, for example within the numerical finite-difference method [26]. Let the electrons be confined by the potential V (z) defined by: V (z) = −eφe (z) + ∆Ec (z),

(1)

where z denotes the direction normal to the 2DEG plane, e is the electronic charge, φe (z) is the electrostatic potential and ∆Ec (z) is the step function of the interface barrier. The electrostatic potential is related to the charge distribution by the Poisson equation: d −e (Nf (z) − n(z)) d εs (z) φe (z) = , (2) dz dz ε0

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where εs (z) is the static dielectric constant, ε0 is the permittivity of free space, Nf (z) is the space-dependent fixed charge that includes the charges induced by piezoelectric and spontaneous polarization, the surface charge, and that of ionized donors and acceptors. The charge distribution of the quantum-confined electrons is: m∗ (z)kB T0 Ef − εi n(z) = ln 1 + exp (3) |ψi (z)|2 , π2 kB T0 i

where kB is the Boltzmann constant, T0 is the absolute temperature, Ef is the Fermi energy, εi is the eigenenergy for the ith subband and ψi (z) is the normalized to unity envelope wavefunction of an electron in the ith subband. It is important to use Fermi statistics instead of Boltzmann statistics, as the electronic gas in the subbands can be degenerate. In this approach, the charge of two-dimensionally confined electrons is determined through solution of the one-dimensional Schrödinger equation within the effective mass approximation for the subband envelope functions and eigenenergies: d 1 2 d (4) ψi (z) + V (z)ψi (z) = εi ψi (z). − 2 dz m∗ (z) dz A conventional approach to the solution of the Shrödinger equation is the finitedifference method. Real space is divided into discrete mesh points and the wavefunction is solved within those discrete spacings. The Runge–Kutta method is used to solve the discretized Shrödinger equation. The electron wavefunctions should vanish far away from the well inside the confining barriers, and a two-point boundary value problem have to be solved. The electron wavefunction is chosen to be zero inside one barrier far away from the quantum well. The electron energy eigenvalue εi in the Shrödinger equation is adjusted to receive a vanishing electron wavefunction in the other barrier. The Poisson equation is discretized the same way as the Shrödinger equation. The derivative of the electrostatic potential is taken to be zero in the barrier layers far away from the quantum well. An iteration procedure is used to obtain solutions for equations (2) and (4). Starting with a trial potential V (z), the wavefunctions and their eigenenergies are obtained from equation (4). They are used to calculate the electron density distribution n(z) from equation (3) and further φe (z) from equation (2). Now, equation (1) provides with the new potential V (z). The subsequent iterations yield the final self-consistent solutions for φe (z) and ψi (z) with the required accuracy. The wurtzite group III nitrides, GaN and AlN, are tetrahedrally coordinated semiconductors; a hexagonal Bravais lattice contains four atoms per unit cell. For binary compounds with wurtzite structure, the sequence of atomic layers of the two constituents is reversed along the c-axis. In the case of GaN, a basal surface is either Ga- or N- faced. In the following, we shall deal with AlGaN/AlN/GaN heterostructure that consists of a 12 nm Al0.33 Ga0.67 N layer, 1.5 nm AlN layer and a thick GaN layer. The investigated AlGaN/GaN heterostructure consists of a 25 nm Al0.15 Ga0.85 N layer and a thick GaN layer. The structures are chosen to be Ga-face with c-axis taken to be perpendicular to the heterointerfaces.


99

The heterostructures are intentionally undoped. In nitride structures, a high density 2DEG forms without doping due to polarization difference in the layers [9]. Spontaneous polarization of AlN, GaN and AlGaN exists at zero strain. It is a convention that the positive direction of a polarization goes from a gallium atom (cation) to the nearest nitrogen (anion) atom. The spontaneous polarization PSP is negative, and its value differs in AlN, GaN and AlGaN [9]: PSP (Alx Ga1−x N) = (−0.052x − 0.029)C/m2 . (5) Under strain, a piezoelectric polarization is induced in addition to the spontaneous polarization. The values of the piezoelectric constants in GaN, InN and AlN exceed those in GaAs-based crystals up to ten times. The piezoelectric polarization is negative for tensile and positive for compressive strained layers, respectively. In the heterostructures under consideration, thin AlGaN and AlN layers grown onto a thick GaN buffer layer are under tensile strain. The piezoelectric polarization in the AlGaN alloy layer grown on the GaN, in the direction of the c axis, can be determined by: PPE (Alx Ga1−x N) = a(0) − a(x) 2 a(x)

C13 (x) e31 (x) − e33 (x) C33 (x)

,

(6)

where a(0) and a(x) are the lattice constants in GaN and AlGaN, respectively, PPE is the piezoelectric polarization, eij are the piezoelectric coefficients, Cij are the elastic constants. The piezoelectric and spontaneous polarizations point in the same direction; this increases the difference in the values of the overall polarization of the heterostructure layers. The spatial gradient of the polarization at an abrupt interface between the top and the bottom layers induces the fixed charge density given by: σ=

[PPE (bottom) + PSP (bottom)] − [PPE (top) + PSP (top)] .

(7)

For the AlGaN/AlN/GaN heterostructure, the charge density σ/e is negative at the AlGaN/AlN interface (−4.5 × 1013 cm−2 ), and the charge density is positive between AlN and GaN layers (6.4 × 1013 cm−2 ). The resultant fixed polarization-induced charge is positive, and free electrons tend to compensate it. For the AlGaN/GaN heterostructure, the positive piezoelectric charge 8.15 × 1012 cm−2 is generated at the AlGaN/GaN interface. The polarization-induced charge causes formation of the 2DEG in the GaN layer near the interface. The 2DEG density is assumed to be 1.4 ×1013 cm−2 for the AlGaN/AlN/GaN heterostructure and 6 × 1012 cm−2 for the AlGaN/GaN heterostructure. An additional negative charge on the AlGaN surface takes into account surface states occupied by electrons. The negative residual acceptor charge is introduced in the GaN buffer for a better 2DEG confinement. The self-consistent results for the potential profile and the first three envelope functions at zero electric field and 300 K temperature are shown in Fig. 1. For the AlGaN/GaN heterostructure, due to the low interface barrier between AlGaN and GaN, the envelope functions penetrate into AlGaN considerably: the higher-subband electrons are shared by

100

M. Ramonas and A. Matulionis 1.0

3.5

(a) AlGaN/GaN 300K

(b)

3.0

AlGaN/AlN/GaN 300K

2.5

Energy (eV)

Energy (eV)

0.8 0.6 0.4

2.0 1.5 1.0

0.2

0.5 0.0

0

10

20

30

Distance (nm)

40

50

0.0

0

10

20

30

Distance (nm)

Figure 1: The potential profile (solid line) and the first three confined-electron wavefunctions, for AlGaN/GaN (a) and AlGaN/AlN/GaN (b) heterostructures. The dashed, doted and short-doted lines indicate the envelope functions of the first, second and third subbands respectively. The envelope functions are plotted in arbitrary units, and the zero of each wavefunction is the corresponding eigenenergy. Dash-doted line is the Fermi energy. Reprinted with permission from [25]. Copyright (2005) by the American Physical Society.

AlGaN and GaN layers (Fig. 1 (a)). The effective mass of a two-dimensional electron moving in parallel to the quantum well plane will be composed of the electron effective mass in the AlGaN barrier and the electron effective mass in the GaN proportionally to the probabilities of finding an electron in the well and in the barrier. So, the electron penetration into the barrier material will change the effective mass and the scattering rates. The electron penetration into the barrier material is avoided when a thin AlN layer is inserted between AlGaN barrier and GaN channel. The high AlN/GaN interface barrier confines the electrons in the GaN layer (Fig. 1 (b)) and induces a high-density 2DEG. Because of the lattice mismatch, only a thin strained (pseudomorphic) layer of AlN can be grown on a thick GaN layer without strain relaxation and cracking. Under bias, the electron distribution in the subbands changes. Consequently, the electron wavefunctions and the electron scattering rates should be reevaluated during the simulation of the electron transport. Thus the Shrödinger–Poisson equations should be solved and the electron scattering rates should be calculated periodically during the Monte Carlo simulation until the self-consistency is achieved for the steady state. This iterative scheme requires enormous computational time. As a rule, the equilibrium Fermi–Dirac distribution function is used in the Poisson–Shrödinger solver (3), and the electron wavefunctions are calculated once at the beginning of the simulation. At high electron densities, the electron temperature approximation is known to work, and Fermi distribution function can be used in Poisson-Shrödinger solver (3) with the electron temperature Te as a parameter. Figure 2 shows the first and second subband eigenenergy and the Fermi level for the AlGaN/AlN/GaN heterostructure. The electron population redistribution alters the potential given by the electrons and changes the electron wavefunctions and eigenenergies. The effect of electron heating on the eigenenergy of the first subband is almost negligible in the investigated range of electron temperatures. The eigenenergy of the second subband rises as the electron temperature increases, but the change is

Monte Carlo Simulation of Hot-Phonon Effects in Biased Nitride Channels 0.65

101

AlGaN/AlN/GaN 300K

Energy (eV)

0.60 0.55 0.50 0.45 0.40 0.35

0

500

1000

1500

2000

Electron temperature (K)

Figure 2: The first (dotted line) and the second (dashed line) subband eigenenergies and the Fermi level (dash-dotted line) as functions of the electron temperature.

below 20 %. Therefore, the subband energies and the wavefunctions can be assumed to remain constant and equal to the equilibrium values in order to save computation time.

3

Electron Scattering Rates

Scattering rates are essential input data for Monte Carlo transport simulation [3]. The scattering rates are calculated starting from the Fermi Golden Rule. The electron scattering probability from the state i to the state f is: Wi→f =

2π |Hi,f |2 δ(εf − εi ),

(8)

where Hi,f is the interaction matrix element calculated for self-consistent electron wavefunctions, εi and εf are energies of the initial and the final states. In this approach, the dynamics of electron interactions is assumed to be independent of the applied field, and the collisions are assumed to occur instantaneously in the framework of the first-order approximation, thus only two-body interactions are included. The scattering mechanisms included in our Monte Carlo simulator for 2DEG nitride channel are acoustic phonon scattering and LO-phonon scattering. As a first step, the model neglects ionized impurity scattering, interelectron collisions and electron scattering by the interface roughness, dislocations and other structural defects. The electron scattering by acoustic phonons at room temperature is often treated as an elastic process because the energies of the involved acoustic phonons are small. However, this approximation would mean that electrons could not dissipate energy unless they were accelerated to the energies greater than the LO-phonon energy. For GaN, the LO-phonon energy is quite large, and the low-field results in the elastic approximation may lead to an inaccurate evaluation of the electron energy dissipation. In our simulation, the electron scattering by acoustic phonons is treated as an inelastic process. In the two-dimensional case, the integration over the final electron states is complicated by the fuzziness of the conservation of transverse momentum. To simplify integration the approximation qz q

102


can be adopted, where q is the in-plane component of the acoustic phonon wave vector q, and qz is the transverse one [27]. The electrons interact with acoustic phonons through deformation potential and electrostatic polarization associated with atom vibrations. The nitrides exhibit strong piezoelectric effects, and the piezoelectric scattering is comparable to the deformation potential scattering at 300 K. In wurtzite structures, the deformation potential in the central valley is a diagonal second rank tensor. The value of Dzz is generally expected to be different from Dxx = Dyy . To our knowledge, no experimental value is available for GaN to date. Usually equal diagonal elements are assumed, and the deformation potential tensor is treated as a scalar quantity [28]. The electron transition probability per unit time from the state (k, i) in ith subband to the state (k , f ) in f th subband for acoustic deformation potential scattering is: Wi→f (k, k‘) =

πD2 q 1 1 Mi→f (qz ){Nac (q ) + ± } V vl 2 2 ×δ(εf (k ) − εi (k) ± vl q ),

(9)

where the upper and the lower symbols refer to emission and absorption, respectively, i and f are the indexes of the initial and final subbands, is the crystal mass density, V is the crystal volume, vl is the longitudinal sound velocity, D is the deformation potential, εi (k) is the electron energy, and 2π is the Planck constant. The overlap integrals Mi→f (qz ) are calculated using the self-consistent electron wavefunctions ψi (z): 2 Mi→f (qz ) = | ψi (z)ejqz z ψf (z)dz| . (10) Nac (q ) stands for the average acoustic phonon number, in equilibrium: Nac (q ) =

1 v q exp( kBlT0 )

−1

.

(11)

The strength of electron scattering with acoustic phonons via piezoelectric interaction is determined by the dimensionless electromechanical coupling coefficient. This quantity contains contributions both for longitudinal (LA) and transverse (TA) acoustical phonons. After angular averaging the electromechanical coupling coefficient acquires the following form[29]: e∗2 e∗2 LA TA K2 = + , (12) ε0 εs cLA ε0 εs cTA where cLA , cTA , e∗LA and e∗TA are the angular averages of the elastic and piezoelectric constants, ε0 is the permittivity of free space and εs is the static dielectric constant. The electron transition rate for acoustic piezoelectric interaction is: Wi→f (k, k‘) =

q2 πe2 K 2 vl Mi→f (qz ) ε0 εs V q (q + q0 )2 1 1 ×{Nac (q ) + ± } 2 2 ×δ(εf (k ) − εi (k) ± vl q ),

(13)


103

where q0 is the inverse screening length. The electron–LO-phonon coupling in wurtzite crystals is different from the well-known cubic case. The electrons interact both with LO-like and TO-like modes, rather than with a single LO mode as in the cubic case. But recently it has been shown [30] that the TOlike scattering rate is more than two orders of magnitude lower than the LO-like scattering rate. Moreover, the LO scattering rate in the cubic approximation is valid regardless of the chosen point in the Brillouin zone [30]. Thus, the conventional cubic approximation and Price’s formulation for the scattering probabilities can be used, assuming that the phonons are three-dimensional [31]. The electron transition rate for polar optical interaction is: 2 − ω2 ) q2 πe2 (ωLO TO ε0 ε∞ V ωLO q 2 (q + q0 )2 1 1 ×Mi→f (qz ){Nopt (q) + ± } 2 2 ×δ(εf (k ) − εi (k) ± ωLO ),

Wi→f (k, k‘) =

(14)

where ∞ is the high frequency dielectric constant, ωLO is the LO-phonon frequency, ωTO is the TO phonon frequency and Nopt (q) is the LO-phonon number (occupancy). The electron screening is taken into account for the polar optical phonon scattering and the piezoelectric scattering. We have assumed long-wavelength diagonal screening derived from the matrix-random phase approximation [32]: q0 =

me2 fi (0), 2πε0 εs 2

(15)

i

where i is the subband index and fi (0) is the electron distribution function at the bottom of each subband. Integration of Eq. (9, 13, 14) over all possible final states k yields the integrated probability for the electron in the ith subband with wave vector k to be scattered into subband f per unit time. The integration is performed numerically, and the total scattering rates are tabulated for use in the Monte Carlo algorithm. Figure 3 shows the calculated scattering rates for the electrons in the first subband of Γ valley of AlGaN/GaN heterostructure. For the low energy electrons, the only energy dissipation channel is acoustic (deformation potential or piezoelectric) phonon emission. At a higher electron energy (higher than the LO-phonon energy), the LO-phonon emission prevails, and the main part of electron energy will by dissipated through LO-phonon emission. Small steps indicate intersubband transfer.

4

Monte Carlo Algorithm

Monte Carlo methods are the numerical methods based on random quantities [3]. Electron transport in semiconductors is treated in terms of realistic motion of one or a number of electrons in the external electric and magnetic fields. The motion is interrupted by scattering events. The duration of electron free flight between two successive collisions and the scattering mechanism responsible for the end of the free flight are selected stochastically

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M. Ramonas and A. Matulionis 14

10

polar optical emission 13

acoustic deformation potential

-1

Scattering rate (s )

10

polar optical absorption

12

10

acoustic piezoelectric 11

10

10

10

0.0

0.1

0.2

0.3

Electron energy (eV)

Figure 3: Scattering rates for the Γ valley first subband electrons in the AlGaN/GaN heterostructure at 300K. Scattering rates for acoustic deformation potential, acoustic piezoelectric, LO-phonon absorption and emission as functions of electron energy.

in accordance with the scattering probabilities associated with the microscopic process of interest. It is sufficient to simulate the motion of one electron when steady state homogeneous transport is under investigation. From the ergodicity one can assume that a long enough trajectory of the electron will provide with information about behavior of the entire electron gas. However, one cannot rely on the ergodicity of the system if the transport is not homogeneous or is not stationary. Thus, more general Ensemble Monte Carlo techniques were developed for considering nonhomogeneous systems or calculating the response to time-dependent electric and magnetic fields. For wurtzite-phase GaN, the conduction band minimum is located at the Γ point (Γ1 ). The lowest satellite valleys of the conduction band are at the U point that is two thirds on the way between the L- and M - symmetry points. The higher conduction band valleys are located at the Γ point (Γ3 ), at the M point, and at the K point. In the range of electric fields where the electron scattering into the upper valleys is negligible, a one-valley (Γ1 ) many-subband spherical parabolic model is employed for the scattering rate calculation and electron transport. When the physical system is defined, the next step is generation of the initial conditions for each electron under simulation. In the case of electron transport in a homogeneous material, only wave vector for each electron should be defined. Usually equilibrium Fermi–Dirac distribution function can be used to generate the initial electron velocities. If the nonequilibrium steady-state situation is simulated, the simulation time should be long enough to avoid the influence of initial conditions. Figure 4 shows the time dependence of electron drift velocity and LO-phonon population for the initial 5 ps. In order to avoid the undesirable effect of the transient on the average results, the transient part of the simulation is excluded from the statistics for a better convergence.


105

7

Velocity (10 cm/s)

2200

2.0 1.5

2100 Wvdr=0.3 ps

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AlGaN/AlN/GaN 300 K

0.5 0.0

0

1

2

3

4

2000

5

LO - phonon population (a.u.)

2300 Wph=1 ps

2.5

1900

Time (ps)

Figure 4: The time dependence of electron drift velocity (solid line, left axis) and LOphonon population (solid line, right axis) for the initial 5 ps of the electron motion in 30 kV/cm field. The dashed lines are the exponential function approximations with τph = 1 ps and τvdr = 0.3 ps. Reprinted with permission from [25]. Copyright (2005) by the American Physical Society.

In transport simulation, the uniform electric field is applied along the 2DEG channel, and the electron continuously changes its wave vector according to the classical relations of motion: k˙ = −eE. (16) In order to find the electron wave vector just before a scattering event, one should know the electron free-flight time. The free-flight time is evaluated using the Rees ”selfscattering” technique [3]. A fictitious ”self-scattering” is introduced, such that the total scattering probability (the sum of all real scattering probabilities plus self-scattering) is constant and equal to Γ ≡ τ0−1 . If the carrier undergoes a self-scattering, its state after the scattering event k is taken equal to its state before the event; the electron motion continues unperturbed as if no scattering at all have occurred. A random evenly distributed number r is used to generate the stochastic electron free flight ttr : ttr = −τ0 ln(1 − r). (17) During its free flight, the electron is moving according to the equation of motion (16). Thus, the electron wave vector k is known at the end of the free flight, and the scattering rates Wj (k) can be evaluated for each mechanism j. The probability of self-scattering will be a complement to the sum of all real scattering mechanisms represented by Γ. The scattering mechanism responsible for the end of the free flight must now be chosen among all those possible, according to the relative strength of different scattering mechanisms. An evenly distributed random number r is generated, and the product y = rΓ is compared with the successive sums of the Wj (k). The jth scattering mechanism is chosen if j is such that the first of the partial sums W1 , W1 + W2 , W1 + W2 + W3 , . . . is larger than y: y < W 1 + W2 + · · · + W j .

(18)

106


Once the scattering mechanism responsible for termination of the free flight is selected, the new electron state after the scattering event must be determined. For a true scattering, the electron state after the scattering event is generated stochastically, according to the differential cross-section of the selected jth scattering mechanism Wi→f (k, k‘). Since the differential cross-sections are complicated for electrons in a 2DEG, the rejection technique helps to find the electron state after the scattering event. The state after the scattering event is the initial state for the next free flight. Supposing that the electrons are considered independent, the motion of every electron is recorded, the history of each ith electron is subdivided into equal time intervals and all required data are collected at the end of each interval. The average value of quantity A(t) is defined as the ensemble average at time t over N electrons of the system [3] : A(t) =

1 Ai (t). N

(19)

i

The electron mean energy and drift velocity can be calculated, after Eq. (19). The spectral intensity of current fluctuations is related to a drift velocity autocorrelation function according to Wiener-Khintchine theorem: 4e2 n ∞ ζvα (t) cos(ωt)dt, (20) Sjα (ω) = V 0 where: ζvα (t) = vα (t1 )vα (t1 + t) − vα 2 ,

(21)

can be evaluated from the Monte Carlo simulation [33, 34]. The equivalent noise temperature or simply the noise temperature is defined as [2]: kB Tnα (ω) =

V Sjα (ω) , 4σαα (ω)

(22)

where Sjα (ω) is the spectral intensity of current fluctuations, α means ⊥ or , and σ⊥ and σ are the diagonal tensorial components of the small-signal conductances under bias in the directions transverse and longitudinal in respect to the bias. The required conductances are approximated by: σ⊥ = I/U,

(23)

σ = dI/dU,

(24)

and can be obtained from the calculated drift velocity dependence on the electric field. The Monte Carlo method is a semiclassical method: the electrons move according to classical laws, the scattering events are treated according to quantum mechanical transition probabilities. The electrons are fermions and must obey the Pauli exclusion principle: each k-space state can be occupied by two electrons at best, their spin quantum number must differ. The Fermi level in the heterostructure 2DEG channels for HEMTs is located above the bottom of the lowest subband, and, as a rule, the electron gas is degenerate.


107

In general, electron scattering probability from a state k to a state k can be expressed as: P (k, k ) = W (k, k )f (k)[1 − f (k )],

(25)

where W (k, k ) is the electron transition probability per unit time, and f (k) is the electron distribution function. The scattering probability is proportional to the probability f (k) that initial state is occupied and the probability [1 − f (k )] that the final state is unoccupied. The traditional Monte Carlo algorithm uses approximation f (k ) = 0. That is, it assumes that the electron gas is nondegenerate, and all final states are available. In general, the Pauli exclusion principle should be incorporated into Monte Carlo algorithm [35]. For calculation of the electron distribution in the momentum space, the plane of twodimensional electron wave vectors k is subdivided into cells of fixed area ∆k. Let us calculate either the time spent by the electrons in each cell or the number of electrons present in each cell at a given moment of time. The mean steady-state electron distribution function is proportional to the dwell time. However, the time-dependent electron distribution is available through counting the number of electrons n(k)∆k found at time t in the cell ∆k around k. The Ensemble Monte Carlo technique generates the electron distribution function that is known at each time step of the simulation and evolves with time. The algorithm proposed by Lugli and Ferry [36] easily includes the Pauli exclusion principle into the Ensemble Monte Carlo procedure. According to the standard Monte Carlo procedure no final state of the electron is needed in order to determine the duration of a free flight. Thus, the exclusion principle does not interfere the selection of the scattering mechanism responsible for the free flight termination. Once the final state is selected, f (k ) becomes known, and a random number between 0 and 1 can be used to accept or reject the transition. In the Ensemble Monte Carlo technique, the electron distribution function is expressed as a number of simulated electrons in each cell of the k-plane grid. The distribution function should be normalized to unity for the use in the proposed procedure. If the number of simulated electrons is N and n is the real electron density, the effective ”real” area S of the simulated heterostructure is S = N/n. The density of allowed wave vectors of one spin in k-space is (2π)2 /S. Every cell in the k-space grid can accommodate at most Nc electrons: Nc =

2SSc , (2π)2

(26)

where Sc is the area of the cell in the k-plane, and 2 accounts for the electron spin. The distribution function is normalized to unity by dividing the number of simulated electrons in each cell by Nc . The Nc must be sufficiently large. After the scattering event, the cell of the electron distribution function, corresponding to the final state of the electron is found. The normalized distribution function in the cell fc is compared with the random number r evenly distributed between 0 and 1. If r > fc the transition is accepted. If, instead, r < fc , the scattering event is treated as the self-scattering (it does not change electron wave vector). The distribution function is updated at the regular intervals, and the procedure is iterated until the probability of electron transitions into k state becomes proportional to the occupancy of that state.

108


5 Hot Phonons

0.6

0.4

n di phono

i stribut

on

The Ensemble Monte Carlo technique have been proposed to follow the time evolution of LO-phonon distribution function and evaluate modifications to the electron transport due to accumulation of hot phonons [37, 38]. For the Monte Carlo results on biased nitride 2DEG channels see [18, 22, 21, 25, 39]. In [18, 25], the time-dependent LO-phonon distribution, Nopt (q), is calculated by setting up a histogram hph (t) defined over the grid in the phonon wave-vector space q. In biased 2DEG channels, the applied electric field breaks the symmetry. As a consequence, a direction-independent integrated distribution hph (q) is not sufficient, and the full phonon distribution function hph (q) is considered.

0.2 0.0 -2 2

(10 qy

0

9

0

-1

m

)

2

-2

qx

-1 9

(1 0

m

)

Figure 5: The LO-phonon distribution function for AlGaN/AlN/GaN heterostructure at room temperature and 20 kV/cm electric field (applied in the x direction). Reprinted with permission from [25]. Copyright (2005) by the American Physical Society. At the beginning of the simulation, the mesh Nopt (t = 0) and the histogram hph (t = 0) are set to the equilibrium value given by Bose distribution function. Under the reasonable assumption of dispersionless LO phonons, Nopt (t = 0) is independent of the phonon wave vector. During the simulation, after each event of LO-phonon emission (absorption), ∆hph is added to (subtracted from) the corresponding cell of the histogram hph . The actual electron density ne and the number of simulated particles Nsim is taken into account as follows: 2π 2π 2π ne ∆hph = , (27) ∆qx ∆qy ∆qz Nsim Leff where ∆qx × ∆qy × ∆qz is the volume of the cell in the q space and Leff is the effective channel width. Due to low group velocity of the LO phonons, the launched phonons are assumed to remain in the 2DEG channel.


109

The excess LO phonons decay via anharmonic interaction into the zone-boundary phonons which weakly interact with electrons. Those phonons, in turn, decay into acoustic modes of the thermal bath. This complex phonon process, acts as an efficient sink of energy and momentum for the electron–LO-phonon subsystem. For a demonstration of hot-phonon effect on drift velocity the decay of nonequilibrium LO-phonon is treated in relaxation-time approximation. At fixed times i∆T , i = 1, . . . , M during the simulation (with ∆T shorter than the average LO-phonon scattering time), hph is updated through:

hph (i∆T ) = hph (i∆T ) − [hph (i∆T ) − hph (0)]

∆T , τph

(28)

where τph is the LO-phonon relaxation time (the lifetime with respect to their decay into other phonons). The LO-phonon lifetime can be determined experimentally or used as a fitting parameter in the Monte Carlo simulation. In framework of the discussed nitride channel model, the best agreement between Monte Carlo calculations and experimental results is obtained for τph =1 ps [25]. This value for the hot-phonon lifetime is in a good agreement with that obtained from Raman measurements [41]. The distribution Nopt (t) is refreshed at the end of each time step using the histogram hph . The rejection technique is used to avoid recalculation of electron–LO-phonon scattering rate at the end of each time step. The overall scattering rates are calculated at the beginning of the simulation. For convenience, the maximum value of the phonon distribution Nmax stands for the actual q-dependent LO-phonon distribution function Nopt (q) contained in the electron–LO-phonon scattering rate, Eq. (14). The non-physical artificial enhancement of the electron scattering rates due to Nmax is compensated through the following rejection technique. Once the final electron state after the scattering is known, the wave vector of the involved LO-phonon is determined. The random number r, evenly distributed between 0 and Nmax , is generated and compared with the phonon occupancy Nc of the cell associated with the wave vector of the involved phonon. If r < Nc , the transition is accepted, else the scattering event is treated as a self-scattering one. The computer time for taking care of the self-scattering events is more than compensated for by the simplification of the procedure. Figure 5 shows a cross-section of the simulated LO-phonon distribution function for AlGaN/AlN/GaN heterostructure at room temperature and 20 kV/cm electric field. The LO-phonon occupancy exceeds the equilibrium one in the limited q-plane area. Due to energy and momentum conservation the electrons cannot emit phonons with wave-vector values close to zero. The distribution of hot phonons is shifted in the direction of the applied electric field. Strong electron–LO-phonon interaction supports a streaming motion of lowenergy electrons. When a lucky electron reaches energy ε = ωLO , it shortly emits an LO phonon, returns to the state near ε ≈ 0 and repeats the acceleration and the LO-phonon emission many times. The emitted LO phonons are almost identical, they form a sharp peak at the corresponding q value. The peak is clearly resolved over the washed-out hot-phonon distribution (Fig. 5).

110


6

Velocity (10 cm/s)

10 8 6 4

AlGaN/GaN

2 0

0

5

10

15

20

Electric field (kV/cm)

Figure 6: Monte Carlo results for the electron velocity–field characteristics at 300 K ambient temperature without self-heating effect (line) and with self-heating effect included (triangles) [20]. Circles stand for the experimental data [22].

6

Drift Velocity

Heterostructure channels for high-power devices contain high electron densities and operate at high electrical fields applied along the channel. The dissipated power density exceeds tens W/mm, and the channel temperature exceeds the ambient temperature—channel selfheating takes place. In AlGaN/GaN channels, the current decreases with time passed after the step of electric field [19]. The results indicate that the electron drift velocity decreases as the Joule heat accumulates. The lattice temperature in the channel can be evaluated from the time-dependent noise power measurements [42]. The experimental dependence of the lattice temperature on the applied electric field for 0.5 µs voltage pulses [22] has been used for an illustration of the effect of Joule heat on the electron drift velocity through Monte Carlo simulation for AlGaN/GaN model with hot phonons taken into account [20]. Figure 6 presents the electron velocity–field characteristics at 300 K ambient temperature calculated without the self-heating effect (line) and with the self-heating effect included (triangles). The results indicate that the self-heating effect is weak at electric fields E 1) reflections are present. This is true for all samples

Structural Disorder in Cdsxse1-X Thin Film Probed by Microdiffraction …

149

and not only for the ternary compounds. Therefore, the structural features to which we should ascribe the lack of reflections are not related to alloying.

Fig.4. X-ray diffraction patterns of CdSxSe1-x obtained by integrating the intensity along the Debye rings. The intensity is plotted in a logaritmic scale. (a) CdS (x=1.0). (b) CdS0.6Se0.4 (x=0.6). (c) CdS0.4Se0.6 (x=0.4). (d) CdSe (x=0.0) The XRD patterns of CdS (dashed line) and CdSe (dotted line) generated from the reference data of the ICSD database are also shown below the corresponding experimental pattern.

Different attempts to simulate the lack of reflections in micro-diffraction spectra have been carried out. The measured spectra can not be described in terms of stacking fault obtained by considering a faulted cubic-hexagonal sequence, as we have tried by using the DIFFaX program [10]. In order to explain the features of the experimental diffraction pattern, a structural model was developed by using the CERIUS program [5]. In this model, a structural disorder was introduced in the a-b plane of the hexagonal cell.

150

V. Capozzi, G. Perna, S. Pagliara et al.

Fig. 5. XRD pattern of CdSe calculated on the basis of a disorder-model. The inset shows the model disordered structure as compared with the ordered wurtzite structure.

In the wurtzite crystal structure, shown in the inset of the Fig. 5, the vertexes of the hexagonal ring are alternatively occupied by either Cd or S,Se. The three Cd atoms lie in the bottom A plane at positions A1, A3, and A5, whereas the three S,Se atoms lie in the top plane, at positions B2, B4, and B6. In our model, we have assumed that because of disorder all the six lattice sites on each plane can be occupied by Cd or S (Se). Therefore, three new atoms are found in the bottom A plane, at positions A2, A4 and A6, whereas three new S,Se atoms are found in the top B plane at positions B1, B3 and B5. This structural change quenches the intensity of some reflections in the XRD pattern and allowed us to qualitatively reproduce the experimental data. In Fig 5 the experimental (dots) and the calculated (continuous line) XRD data for CdSe sample are shown. Although the simulated spectra do not closely fit some of the experimental reflections, it can be noticed that in the calculated pattern only the reflections detected in the experimental XRD pattern are reproduced.

Microraman Spectra Fig. 6 shows the room-temperature microraman spectra of the two investigated CdSxSe1-x films. From the point of view of Raman spectroscopy, the CdSxSe1-x alloy shows the two phonon modes characteristic of Cd-S and Cd-Se vibrations [11]. Thus two TO-LO pairs are expected, whose relative intensity and frequency characteristically depend on the composition. In the present study, only the LO modes are observed. These are the forbidden


151

LO modes which become allowed near resonance, when a major contribution to Raman scattering comes from the q-dependent intraband Frohlich term. Since this term contributes only to LO modes, only these modes are observed in such experimental conditions [12].

Fig.6. Microraman spectra of CdS0.6Se0.4 and CdS0.4Se0.6. In the inset, the LO2 CdS-like mode is shown, along with the two-lorentian fitting, yielding the broad ZE phonon mode at low wavenumbers.

Moreover, in the present set of samples only the Raman spectra of the mixed compounds are observed, because for these two samples only a near-resonant Raman scattering occurs, being the energy of the laser light (1.96 eV) close to their energy gap and off-resonance with respect to the pure CdS and CdSe gaps. The CdSe-like LO1 mode (at 205.8 cm-1 in CdS0.4Se0.6 and 201.0 cm-1 in CdS0.6Se0.4) and the CdS-like LO2 mode (at 284 cm-1 in CdS0.4Se0.6 and 290 cm-1 in CdS0.6Se0.4) are the most intense lines in the first order Raman spectra. The peak at 182.8 cm-1 is a plasma line of HeNe laser. Higher-order modes can be observed at larger wavenumbers. In particular, we observe the 2LO1-phonon mode (at 406.5 cm-1 in CdS0.4Se0.6 and 395 cm-1 in CdS0.6Se0.4), the 2LO2-phonon mode (at 567 cm-1 in CdS0.4Se0.6 and 576 cm-1 in CdS0.6Se0.4) the LO1+LO2phonon mode (at 486 cm-1 in CdS0.4Se0.6 and 488 cm-1 in CdS0.6Se0.4). Moreover, the Raman

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spectrum of the CdS0.6Se0.4 film is characterized by an intense line at 520 cm-1 due to the emission from the Si(111)-oriented substrate. This line is not observed in the CdS0.4Se0.6 sample because of the larger thickness with respect to that of the CdS0.6Se0.4 sample. The relative weight of LO1 and LO2 bands changes with S content. In fact, the increase of S fraction from 0.4 to 0.6 yields an increase of LO2 intensity with respect to LO1. Likewise, the frequency of the CdSe-like LO1 mode decreases with x, whereas the frequency of the CdSlike LO2 mode increases with x. The lineshapes of the LO2 phonon peaks are clearly asymmetric. This asymmetry has been observed earlier in other III-V and II-VI mixed semiconductors [12,13,14] and ascribed either to phonon confinement or disorder effects. The correct fitting of these peaks can be carried out if one assumes that in alloys the cohexistance of two Raman bands is expected: the relatively narrow bands at LO phonon frequency of the ternary compounds and a disorder activated, broad, band associated with the phonon density of states [15]. In fact, when disorder can not be neglected, defect-activated Raman scattering from all phonon modes is expected. The weight of this disorder-activated band in both CdS0.6Se0.4 and CdS0.4Se0.6 samples is remarkable. Therefore a deconvolution of the Raman bands was carried out by fitting the bands with the sum of two Lorentzian curves (inset of fig.6, [15]). One Lorentzian is ascribed to the zone-centre phonon contribution, whereas the other Lorentzian is ascribed to the zone-edge (ZE) phonon contribution [12], namely:

I(Ȧ) =

SLO SZE + 2 2 (Ȧ - ȦLO ) + (ī LO /2) (Ȧ - Ȧ ZE ) 2 + (ī ZE /2) 2

(4)

where SLO (SZE) is an amplitude factor relative to LO (ZE) phonon peak, ZLO (ZZE) is the frequency of the LO (ZE) mode, *LO and *ZE are the full width at half maximum of the LO (ZE) Lorentzian peak. In the inset of Fig. 6 the least-square fit of LO2 CdS-like mode with the two Lorentzian model (eq.4) to the experimental data is shown as continuous line, whereas the contributions of LO and ZE phonons are shown as dashed line and dotted line, respectively. As expected, the frequency of the LO2 mode increases with S content, as reported by Chang et al. [16] and S. Permagorov and A. Reznitsky [2]. The fit of CdSe-like phonon mode was not performed because of the presence of He-Ne ghost at 182.8 cm-1.

Luminescence Spectra The PL spectra of the CdSxSe1-x films at T=10K are shown in Fig. 7. All the samples present a narrow emission line in the higher energy region, corresponding to excitonic recombinations. The excitonic lines are centered at 2.540 eV, 2.110 eV, 1.993 eV and 1.820 eV for CdS, CdS0.6Se0.4, CdS0.4Se0.6 and CdSe, respectively. The emission bands at energies lower than the excitonic lines are due to radiative recombinations involving extrinsic defects located in the energy gap of the CdSxSe1-x films.


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Fig. 7. Photoluminescence spectra of the CdSxSe1-x ablated films, measured at the lattice temperature of (a) 10 K and (b) 300 K. The samples were photoexcited by the line 4579 Å of an Ar ion laser, with an exciting intensity of 80 W/cm2. In the inset (b), the dependence of the excitonic emission line on sulphur concentration x at room temperature is shown: the continuous line is a least square fit of experimental data to eq. (5). For each spectrum the relative sensitivity factor is indicated. Spectral resolution is 1 meV.

The excitonic peak shifts towards lower energies with decreasing the x fraction, due to the decrease of the fundamental energy gap with the sulfur content. Moreover, by raising T, the excitonic emission intensity decreases and an exponential tail appears on the high energy side of the excitonic peak (Fig. 7b), which is due to the thermal distribution of the excitons. The excitonic emission is even present at room temperature, where it is the most intense band of the PL spectra. Such a behaviour suggests the possibility of emission modulation by means

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of the CdSxSe1-x system, as illustrated in the inset of Fig. 7b, where the sulfur cotent dependence of the excitonic peak at room temperature is reported. The exciton energies XPL (dots) are well fitted (continuous line) by a quadratic relation: XPL(x) = XPLCdSe(1-x) + XPLCdSx –bx(1-x)

(5)

where b is the bowing parameter. The fitting parameters XPLCdSe = 1.741r0.009 eV and XPLCdS = 2.448r0.009 eV are in good agreement with the value of the A-type excitonic energy at room temperature for the CdSe and CdS single crystals, respectively [9]. An interesting result in Fig. 7 is the large PL efficiency of the CdS0.6Se0.4 film at low temperature. This result is due to the localized nature of the excitonic recombinations, related to the fluctuations of the local concentration in the solid solution: as a result, fluctuations in the periodic crystal potential occur and they act as potential wells for the carriers. Therefore, at the lowest temperatures the XPL line corresponds to radiative recombinations of excitons localized in potential wells. Consequently, the excitons have a reduced probability of diffusion into non radiative traps and the radiative recombination path is strongly enhanced. A similar PL enhancement is not observed in the spectrum of the CdS0.4Se0.6, because the exciton localization occurs only if the number of localized states is larger than the number of impurities and other structural defects [1]. It can be deduced that the CdS0.4Se0.6 film present a large number of impurities and defects, as also confirmed by the large PL efficiency related to intra-gap states (spectrum B of Fig. 7a). This finding is in agreement with the results of structural investigations which indicate that in CdS0.4Se0.6 disorder effects, detected as broadening both along and perpendicular to the Debye rings, are larger than in CdS0.6Se0.4. The excitonic emission from CdS and CdSe is also lower that that of CdS0.6Se0.4, because localization effects related to fluctuations of the local concentration do not occur in such binary compounds. The dependencies of the spectral position of the exciton line in CdSxSe1-x films as a function of the temperature (dots) are illustrated in Fig. 8. The red-shift of the excitonic levels when the temperature increases is related to the thermal expansion of the lattice and the temperature dependence of the electron-phonon interaction [17]. The experimental data of Fig. 8 for CdS, CdSe and CdS0.4Se0.6 are in good agreement with a model, introduced by Vina et al. [17], describing the thermal red-shift of the energy gap for typical semiconductors. The continuous lines in Fig. 8 are a fit of such model to the experimental data. The Vina model is represented by the following equation: X(T) = X(0) –2aBnB

(6)

where X(T) is the exciton energy at the temperature T, aB is the strength of the excitonphonon interaction and nB = [exp(T/T)-1]-1 is the Bose-Einstein statistical factor for phonon emission and absorption; T is a phonon temperature corresponding to an average phonon energy.


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Fig. 8. Temperature dependence of the exciton energy in CdSxSe1-x samples, as obtained from the analysis of the luminescence data. (a) CdSe (x=0.0). (b) CdS0.4Se0.6 (x=0.4). (c) CdS0.6Se0.4 (x=0.6). (d) CdS (x=1.0)

In contrast, the temperature dependence of the spectral position of the excitonic emission in CdS0.6Se0.4 follows the Vina model starting from a sufficiently high temperature (about 80 K), whereas it presents an anomalous behaviour at low temperature. In fact, a red-shift of the excitonic line is observed below 35 K, but a blue-shift is present when the temperature increases up to 80 K. The red-shift below 35 K can be due to a hopping process of the excitons among localized states in the low energy tail of the exciton level distribution, which takes place in a disordered semiconductor [18]. In fact, localized exciton can termally gain energy to relax into localized states at lower energy. Such a behaviour causes a red-shift of the maximum of the excitonic emission, because the peak of the localized excitonic distribution shifts to lower energy. In contrast, the blue-shift of the exciton line in the temperature range between 35 K and 80 K is related to the delocalization of the localized excitons as a consequence of the temperature increase. Thus, the density of the free excitons raises with temperature. Since free excitons have smaller binding energy than localized excitons, a blue-shift of the excitonic emission is observed. When the temperature is larger than 80 K, all the excitonic emission is due to free excitons and its spectral position follows the red-shift of the energy gap.

Conclusion In this study we have shown that X-ray microdiffraction is a powerful tool to probe structural disorder effects in thin films, otherwise missed by conventional T-2T XRD. In fact, the possibility to detect X-rays elastically scattered in a wide diffraction cone discloses several features that can give important information on disorder effects. For instance, it is observed that not all reflections expected from the hexagonal phase of the parent compounds are present in the diffraction pattern detected by the micro-diffractometer.

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According to the results of structural modelling, this finding is tentatively ascribed to disorder effects in the lattice planes parallel to the substrate. Unlike conventional T-2T X-ray diffraction which shows that the films grow in the hexagonal phase with the c-axis perpendicular to the substrate, microdiffraction patterns show that CdSxSe1-x layers do not grow in a perfect epitaxial habit, as can be observed from the analysis of the Debye rings. This effect is particularly evident in the samples closer to an equimolar concentration of Se and S. Moreover, the different broadening of the (002) reflections of the two films indicates that CdS0.6Se0.4 is less disordered than CdS0.4Se0.6. The method we propose is addressed to a class of materials (semiconductor alloys) whose structural properties are usually discussed in terms of reflection broadening of the T-2T conventional XRD patterns, and compliance with the Vegard's law [8]. We showed that when a larger portion of the reciprocal space is mapped, further structural features can be pointed out, which may suggest further disorder effects. Our attempt to justify the observed microdiffraction pattern, is based on symmetry considerations only. Additional work should be done on this issue, with, e.g., first-principle calculations of the total energy of our model system. This goes far beyond the scope of the present work. Nevertheless, our model catches the main feature of the pattern, namely the quenching of the reflections and suggest a direction for future work. In particular, it is known that X-ray diffraction probes the average crystal structure of the samples. A more local view of the structural features and related defects will be provided by EXAFS experiments. Finally, a correlation is found between microdiffraction and PL data. Also the Raman spectra are affected by structural disorder, whereas phonon confinement effects are not detectable. PL spectra of the films have been measured from 10 K up to 300 K. The exciton line recombination is well resolved in each film alloy up to room temperature. Only the PL spectrum of the CdS0.6Se0.4 film, at low temperature, shows an enhancement of PL efficiency, due to the compositional disorder (potential fluctuations) on a microscopic scale. In CdS0.4Se0.6 film, on the contrary, structural defects prevail over potential fluctuations which are held responsable for the exciton localization. The lineshape of the LO phonon structure in the microraman spectra is characterized by significant asymmetry and broadening induced by disorder. The data were fitted by using two Lorentzian bands. The weight of the disorder-activated band resulted to be large in both alloy samples.

Acknowledgements A. Iberl is greatly acknowledged for technical assistance during the microdiffraction experiments. We thank E. Depero for helpful and stimulating discussions about microdiffraction measurements. We are also grateful to A. Giardini and M. Ambrico for the fruitful scientific collaborations withthe "Istituto Materiali Speciali" of the C.N.R. of Tito Scalo (PZ), Italy. This work has been partially supported by “Progetto Finalizzato MSTAII”, CNR.


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References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18]

F.Firszt, Semicond. Sci. Technol. 12 (1997) 272 S. Permagorov and A. Reznitsky, J. Lumin. 52, 201 (1992) J. A. Van Vechten and T. K. Bergstresser, Phys. Rev. B 1, 3351 (1970) M. Ambrico, R. Martino, D. Smaldone, V. Capozzi, G. Lorusso, G. Perna, Giardini, and A. Mele, Mat. Res. Soc. Symp. Proc. Vol. 397, 125 (1996) Cerius2, Release 2.0; BIOSYM/Molecular Simulations H.P. Klug, L.E. Alexander: “X-ray Diffraction Procedures”, New York, Wiley, 1954. G. Perna, S. Pagliara, V. Capozzi, M. Ambrico, T. Ligonzo, Thin Solid Films 349, 220 (1999). L. Vegard, F. Zeit. Physik 5, 17 (1921). O. Madelung, M. Schulz, H. Wess (Eds.), Landolt-Bornstein Tables, vols. 17a and 17b, pag. 206, Springer, Berlin, 1982. Diffax, v.1.767, is computer program for calculating diffraction intensities from faulted crystals; M. M. J. Treacy, M. W. Deem (1992) N. Esser and J. Geurts in “Optical Characterization of Epitaxial Semiconductor Layers”, G. Bauer, W. Richter (eds.), Springer, Berlin, 1996, Chapt. 4 A. Ingale and K.C. Rustagi, Phys. Rev. B 58, 7197 (1998). H.C. Lin, J. Ou, C.H. Hsu, W.K. Chen and M.C. Lee, Solid State Comm. 107, 547 (1998). A. Fischer, L. Anthony, A.D. Compaan, Appl. Phys. Lett. 72, 1822 (1984). S. Pagliara, L. Sangaletti, L.E. Depero, V. Capozzi, G. Perna, Solid State Comm. 116, 115 (2000). R. K. Chang, J. M. Ralston, and D. E. Keating, Light Scattering Spectra of Solids (G. B. Wright, ed.) p. 369, Springer Verlag, New York (1969). L. Vina, S. Logothetidis, M. Cardona, Phys. Rev. B 30, 1979 (1984). V. Capozzi, K. Maschke, Phys. Rev. B 34, 3924 (1986).


ISBN 1-59454-920-6 c 2006 Nova Science Publishers, Inc.

Chapter 7

E LECTRODEPOSITION OF C U I N S E2 FOR P HOTOVOLTAIC C ELL A PPLICATION Shigeyuki Nakamura Department of Electrical and Electronic Engineering Tsuyama Natinal College of Technology Abstract This paper describes preparation of a ternary chalcopyrite semiconductor, copper indium diselenide (CuInSe2 :CIS), thin films as a light absorption layer for thin film solar cells by electrodeposition. This semiconductor is very attractive for an absorber material in the thin film solar cell because of its suitable bandgap and a large absorption coefficient. CuInSe2 has the bandgap of about 1.0 eV and the absorption coefficient of ∼ 105 cm−1 . The large absorption coefficient enables us to realize the thin film solar cell. Although the highest theoretical efficiency is obtained with the semiconductor whose bandgap is ranging from 1.4 to 1.5 eV, the bandgap of CIS can be enlarged up to 1.68 eV by adding Ga to form solid solution of Cu(Inx Ga1−x )Se2 (CIGS). Electrodeposition as a method for thin film semiconductor preparation is a good approach with respect to economic consideration. An important advantage of electrodeposition as a method for thin film preparation is that films with a large area can be prepared without a vacuum, using simple and low-cost equipments. However, conversion efficiencies ever reported for the cells fabricated by this method are considerably lower than those reported for the cells fabricated by other methods. One of the important problems for development of this technique is to control sample compositions. Understanding of deposition mechanisms of each species is essential in order to achieve higher controllability and reproducibility of film composition and then to improve performance of the photovoltaic cell prepared by electrodeposition. Moreover, an excellent morphology is also essential to achieve higher conversion efficiency. A poor morphology causes short-circuiting between the front and back electrodes. Voids and cracks in thin films degrade the conversion efficiency. On the basis of above mentioned, following subjects were studied. Electrodeposition of Cu-In-Se films has been studied with an aqueous solution containing CuCl2 , InCl3 and SeO2 , in terms of composition control of deposited films for the preparation of CuInSe2 . When a Si wafer is employed as a substrate, both the electrode potential dependence of In/Cu ratio in the film and a stirring effect on film composition are found to become small, compared with Mo substrate.

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Shigeyuki Nakamura This is explained by taking account of the existence of a space charge layer at the semiconductor surface. From the relationship between In/Cu or Se/Cu ratio in the bath and that in the deposited films, ratios of mass-transfer coefficients for In and Cu, k(In)/k(Cu) or for Se and Cu, k(Se)/k(Cu), have been obtained and their dependencies on deposition current density or stirring of the solution have been studied. The rate-determining step in the deposition process for each ion, “reaction-limited” or “diffusion-limited”, has been also discussed. By employing the stirring, a remarkable improvement, by a factor of 3, is attained for run-to-run and position-to-position fluctuation of the In/Cu ratio in the films. X-ray diffraction patterns show that CuInSe2 is contained in as-deposited films. In order to improve surface morphology, a revers bias is applied after electrodeposition in the same electrolyte. Pluse-plated electrodeposition was demonstrated for the same purpose. In order to improve crystallinity, as-deposited films were annealed in an inert atomosphere. Annealing effects on film properties, such as crystallinity, morphology and chemical composition, were investigated. Effects of Se concentration were also investigated. Excess Se is found to degrade controllability of composition and crystallinity. The conversion efficiency of 0.866 % (Voc=0.47 V, Isc=1.9 mA/cm2 , FF=0.533) is obtained with a chemical bath deposited CdS buffer layer on the electrodeposited CIS layer without any transparent conductive oxide layers. Preparation of CuInSe2 thin films with a bilayer structure by electrodeposition were studied. Change in a Cu/In ratio with depth is essential to obtain higher conversion efficiency. Thus, a new electrodeposition technique for preparing CuInSe2 thin films with controlled depth profile were developed. The CuInSe2 thin films with both Cu-rich and In-rich layers are deposited by changing substrate potential during electrodeposition.

1

Introduction

1.1 1.1.1

Background Advantages of Solar Cells

Necessity of Solar Cells Since Industrial Revolution, an amount of energy used has increased rapidly. This makes global environmental problems more serious recently. For example, excess CO2 results in global warming. Furthermore, conventional energy resources, such as fossil fuels, will be exhausted in the not-too-distant future. Therefore, we must develop and use alternative energy resources, especially our only long-term natural resource, the sun [1]. The solar cell is considered to be an attractive candidate for obtaining energy from the sun because it can convert sunlight directly to electricity with high conversion efficiency, can provide nearly permanent power at low operating cost, and is virtually free of pollution. Comparison with the amount of generated CO2 for each kind of power generation systems Figure 1.1 shows amount of generated CO2 for each kind of power generation systems [2]. One can see that the amount of generated CO2 for the solar cell is less than

Electrodeposition of CuInSe2 for Photovoltaic Cell Application

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Figure 1.1: Amount of generated CO2 for each kind of power generation systems. that for an oil power plant by a factor of 1/14. The solar cell plants no longer generate CO2 once they have been built. This is the main motivation to develop the solar cell. Transition of an annual yield for solar cells Figure 1.2 shows a transition of an annual yield for solar cells from 1995 to 2003 [3]. It has increased rapidly, especially in Japan, and such an increase is accelerated recently. This is due to the subsidy policy for residences, which began in 1994. Most of these cells consist of silicon. As the silicon is indirect semiconductor, an absorption coefficient is in the order of 103 cm−1 . Hence, a thickness of 300 to 500 micron is required for the crystalline silicon solar cell to absorb sun light sufficiently. Thus, a large amount of high purity single or large-grained polycrystalline silicon is required to fill demand. A large amount of energy is also required to fabricate the silicon solar cell. It is well known that silicon is an abundant material. However, there will be a possibility that we run short of high-purity silicon for solar cells because quantity of off-glade silicone used for fabricating the Si solar cells separated from the semiconductor glade standard silicone is restricted [4]. Transition of solar cell costs Figure 1.3 shows the transition of the costs for the system production and electricity generation of solar cells in Japan [5]. A BOS (balance of system), inverter and indirect costs has decreased drastically while a cell cost has not been reduced so much. It is, therefore, important to reduce the cell cost in order to decrease an overall solar cell system cost. EPT The solar cell is one of clean energy resources and one of indexes for cleanness is an energy pay-back time (EPT). The EPT is defined as the time that an amount of energy generated by a solar cell is equal to an amount of energy used to make the cell. Table 1.1 shows the calculated EPTs for some yield assumptions [6]. The EPTs are estimated to be

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Figure 1.2: The transition of an annual yield for the solar cell.

Figure 1.3: The transition of cost for the solar cell. 1.5 to 2.4 y for poly-crystalline Si cells, 1.1 to 2.2 y for amorphous Si cells and 1.1 to 1.7 y for CdTe cells. The EPT becomes shorter as the annual yield increases. An EPT for thin film cells is expected to be lower than that for crystalline Si solar cells.


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Table 1.1: The energy pay-back time (year) Annual yield MW 10 30 100 1.1.2

Poly-crystalline Si 2.4 2.2 1.5

Amorphous Si 2.2 1.7 1.1

CdS/CdTe 1.7 1.4 1.1

Thin Film Solar Cells

Advantages of thin film solar cells A thin film solar cell seems to be the most attractive to overcome such problems because it requires smaller amount of materials compared with the crystalline silicon solar cell. A thickness of the thin film solar cell is as thin as 10 micron or less. If the thickness of the silicon cell and that of the thin film solar cell are assumed to be 300 micron and 5 micron, respectively, the amount of materials for the thin film cell can be reduced by a factor of 1/60. Therefore, the production energy, amount of materials and cost for the cell can be cut down drastically by introducing the thin film cell [7]. Absorption coefficient The most important parameter for the thin film solar cell is an absorption coefficient. If the absorption coefficient is higher, the cell with the thinner thickness can be used. Figure 1.4 shows absorption coefficients for several semiconductor candidates for the thin film solar cell as a function of photon energy [8]. The absorption coefficient for c-Si is also shown in this figure for comparison. As the semiconductor materials, such as CuInSe2 , GaAs, CdTe and a-Si, have the larger absorption coefficients, they are suitable for an absorption layer of the thin film solar cell [8]. The film thickness of several micron is sufficient to absorb sun light, as shown in Table 1.2, where absorption length L = 1/α (α: absorption coefficient) [9]. On the contrary, since the crystalline silicon has the smaller absorption coefficient, the thickness of 300 micron or more is required to absorb the sun light sufficiently. Table 1.2: Comparison of the absorption lengths for different semiconductors materials Materials FeS2 CuInSe2 CuInS2 GaAs CdTe a-Si c-Si

Absorption lengths µm 0.02 0.3 1.0 1.5 2.0 2.0 300

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Figure 1.4: The absorption coefficients for several semiconductors 1.1.3 CuInSe2 and Related Material Thin Film Solar Cells History Among semiconductors which are candidates for the thin film solar cells, a research for copper indium diselenide (CuInSe2 ) and related materials, such as CuInS2 and Cu(Inx Ga1−x )Se2 (CIGS), is the most progressive. A mono-crystalline CuInSe2 /CdS hetero-junction solar cell with an efficiency of 5 % has been developed in 1974 at Bell Lab. for the first time [10]. In 1975, the efficiency has risen up to 12 % [11]. Recently, the efficiency of solar cells based on CIGS thin films, whose bandgap is more suitable than that of CuInSe2 , has reached 19.2 % with a small area (less than 1 cm2 ) [12]. The CIGS layer for this cell was prepared by so called “three stage process” with an MBE (Molecular Beam Epitaxy) apparatus. An efficiency of 14.2 % for the CIGS solar cell with a module aperture-area of 900 cm2 has been achieved by Showa Shell Sekiyu [13]. The CIGS layer of this cell was prepared by selenization of a sputtered metal precursor. The basic properties of CuInSe2 will be detailed in next chapter. Electrodeposition as a CuInSe2 thin film preparation method For such absorber materials, one of the most important problems is to reduce cell costs. The CIGS layers for the high efficiency cells described above are prepared by the co-evaporation or selenization methods. However, these methods require expensive equipment, such as ultra high vacuum chambers. Furthermore, the co-evaporation method is hard to apply for preparing large area cells. The selenization method needs an annealing process with a highly toxic H2 Se gas. These weaknesses result in high manufacturing costs. On the contrary, electrodeposition as a method for thin film semiconductor preparation is a good approach with respect to economic consideration. An important advantage of electrodeposition as the method for thin film preparation is that films with a large area can be prepared without a vacuum, using


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simple and low-cost equipment. Electrodeposition will be detailed in chapter 3. This paper describes preparation of ternary chalcopyrite semiconductor, i.e. CuInSe2 , as a light absorption layer for the thin film solar cell by electrodeposition. Progress in research for CuInSe2 thin film preparation by electrodeposition In 1983, electrodeposition of CuInSe2 thin films were demonstrated by Bhattacharya for the first time [14]. The deposition solution contained In3+ of 0.018 M, Cu+ of 0.018 and SeO2 of 0.025 M as well as triethanolamine of 0.006 vol.% and NH3 of 0.007 vol.%. The films were deposited on SnO2 :F coated glass substrates at –0.7 V vs a saturated calomel electrode (SCE) at a room temperature and at pH of about unity. The solution was stirred during the deposition. Film compositions were not analyzed, but X-ray diffractograms of the post-annealed films (1 h at 600 o C under Ar) showed many of the reflections of the chalcopyrite phase. In 1996, his group achieved an efficiency of 8 % using electrodeposited Cu-In precursors followed by selenization in a vacuum chamber [15]. The efficiency of 9.4 % was attained in the same year by co-deposition of Cu-Se and In-Se followed by physical vapor deposition (PVD) of Cu, In and Se to adjust final composition [16]. Fernandez et al. carried out co-electrodeposition of Cu,In and Se, followed by selenizing as-deposited films by chemical vapor transport by gas method [17]. From the photoelectrochemical charactrization, energetic characterization and AES depth profile results, they concluded that their films have a p type bulk because of the Se-rich composition and an n type surface becasue of the In-rich composition. This group raised up an efficiency to 9.8 % [18] and 13.7 % [19] in 1998. The 9.8 % cell was prepared by adjusting composition by In, Ga and Se evaporation on electrodeposited Cu-In-Se precursors, while the 13.7 % cell was prepared from electrodeposited Cu-In-Ga-Se precursors followed by In, Ga and Se evaporation for final composition adjustment. They achieved an efficiency of 15.4 %, which is the highest one for the electrodeposited CIGS based thin film solar cells, in 2000 [20, 21]. Depth profile of CuInSe2 thin films grown by the electrodeposition technique was analyzed by Calixto et al [22]. A new CIGS electrodeposition bath based on a buffer solution so that the stability of the electrodeposition process is enhanced without metal oxides or hydroxides precipitation were developed by Bhattacharya et al [23]. They reported an efficiency of 9.4 % in that paper. These cells above mentioned require evaporating elements to adjust final composition. Thus, they are developing the process without the PVD [24]. Shih et al. have produced photovoltaic cells with a single absorbing layer with a conversion efficiency of 4 % in 1987 [25] and 5.2 % in 1989 [26]. They measured a refractive index [27] and a minority carrier diffusion length [28] of electrodeposited CuInSe2 thin films. They have achieved an efficiency of 7 % in 1995 [28]. Guillén et al. have investigated an electrical [29] and optical [30] properties, namely effects of thermal and chemical treatments on a composition and a crystal structure [31], reaction pathways to CuInSe2 from electrodeposited precursors [32] and an improved selenization method [33]. Raffaelle et al. have characterized an electrodeposited CuInSe2 nano-scale multilayer by scanning tunneling microscopy [34]. They have fabricated the heterojunction by electrodeposition of CdS films on electrodeposited CuInSe2 films [35] and prepared CIGS thin films from electrodeposited CuInSe2 /Cu-Ga multilayer precursors [36]. Other interesting studies for the electrodepositon of CuInSe2 are as follows. Selenization of electrodeposited Cu-In precursors was studied by Kim et al[37, 38]. Kampmann

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et al. have reported large area electrodeposited CIGS thin film solar cells. The best efficiency of 4.8 % was obtained with a cell area of 80 cm2 [39]. An efficiency of 9 % has been achieved with the cell prepared by selenization of electrodeposited Cu-In-Ga stacked layers on a Cu substrate [40]. Ganchev et al. have studied electrodeposition processes and structural and optical porerties [41, 42]. Kumar et al. have studied selenization of electrodeposited Cu-In precursors [43]. A new selenization process with Se[(EtO)2 PS2 ]2 was studied by Fritz et al [44]. Formation of CuInSe2 and Cu(In,Ga)Se2 films by electrodeposition and vacuum annealing treatment was studied by Zhang et al [45]. Kois et al. have reported a partial phase diagram for electrodeposition of CuInSe2 [46]. Another unique and interesting research has been reported by Chaure et al [47]. They have prepared p-i-n type CuInSe2 multilayer solar cells by electrodeposition. They deposited various types of CuInSe2 thin films potentiostatically in an aqueous solution containing 0.002M CuSO4 , 0.004M In2 (SO4 )3 and 0.004M H2 SeO3 with Cu:In:Se ratio of 1:2:2. Small samples with an area of 100mm2 were grown at different cathodic potentials (0.3 ∼ 1.2 V vs a saturated Ag/AgCl reference electrode) from the same electrolyte to evaluate different properties of the layers. Four-layer n-n-i-p photovoltaic cells (glass/FTO/n-CdS/n-CIS/i-CIS/p-CIS/Au) with back contact area of 0.031 cm2 (2mm diameter dots) were fabricated. Prior to metal contacting, the cell structures were annealed at 450 o C for 8 ∼ 10 min in selenium atmosphere and etched in KCN solution to remove any Cu-Se phases. Compositional analysis by an X-ray fluorescent spectrometer (XRF) revealed that at lower cathodic potential range up to 0.70 V, a Cu- and Se-rich layer was obtained. As the cathodic potential increases, an indium content also increases and the composition of copper and selenium decreases in the film. Near stoichiometric CuInSe2 material is obtained at higher cathodic potentials in the range varying from 0.90 to 1.00 V. They have investigated the electrical conductivity type of the layers by photoelectrochemical characterization using a 0.01M CuSO4 solution. The polarity of the open-circuit voltage produced by illuminated solid/liquid junction provides the information on electrical conductivity type. The material grown at cathodic potentials of 0.30 ∼ 0.65 V showed a p-type (positive photovoltage) conductivity due to more copper and selenium deposition. At higher cathodic potentials (0.65 ∼ 0.85 V), indium incorporation into the films increases. Also such potentials reduce the incorporation of the amount of copper and selenium resulting in a zero open-circuit voltage for the compensated intrinsic material. As the cathodic potential increases further (0.85 ∼ 1.20 V), indium inclusion increases and the photovoltage becomes negative due to appropriate n-type doping of the material. Further increase of the cathodic voltage causes production of metallic layers due to the deposition of indium. It is, therefore, possible to obtain n+ materials at high cathodic potentials (above 1.20 V) and p+ materials at low cathodic potentials (below 0.3 V). They also fabricated photovoltaic devices using n-, i- and p-type CuInSe2 materials, which were deposited at 1.00, 0.75 and 0.60 V, respectively, on glass/FTO/n-CdS substrates. The dark and illuminated I-V characteristics of configuration glass/FTO/n-CdS/n-CIS/i-CIS/p-CIS/Au shows the rectification factor at 1 V of > 104 , the diode quality factor of n=1.43 and the potential barrier height of φb = 1.10 eV. The best cell parameters measured under AM 1.5 condition were Voc of 410 mV, Jsc of 36 mA/cm2 and F.F. of 0.45. For more than decade, Lincot et al. have studied systematically reaction mechanisms involved in electrodeposition of CuInSe2 thin films and prepared solar cells base on them


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[48-58]. This group reported the deposition mechanisms including a behavior of a Cu-Se system in the presence of In3+ [49], a phase diagram [50], transport mechanisms of each specimen [51], relations between physical properties and deposition conditions [52]. They found that if In3+ in the solution is excess, the film composition is controlled by the Se4+ /Cu2+ flux ratio (α) arriving at the electrode [49]. While, if In3+ concentration is not sufficiently high, the electrodeposition process is limited by diffusion of all the three ions. Consequently, the film composition is determined by both flux ratios α and β, where β is the In3+ /Cu2+ flux ratio [51]. They also attempted to prepare solar cells based on electrodeposited CuInSe2 . An efficiency of 0.9 % was obtained in 1992 with Se annealing [48]. Introduction of high pressure Se anneal in a closed chamber with two zone furness, in which temperatures of the substrate and Se are controlled independently, enables them to obtain higher efficiency of the cells. Efficiencies of 5.6 % [53] and 6.5 % [54] were obtained in 1994 using high pressure Se annealing [55]. Detailed properties of 6.5 % cell such as relationship between a cell performance and film compositions [56], photoluminescences, photoelectrochemical characteristics, sintering mechanisms, structural properties, morphologies, transport properties and device analysis [57] were investigated. Recently, they have reported the highest efficiency of 10.2 % for electrodeposited CIGS based solar cell [58]. Nomura et al. have prepared CuInSe2 and CIGS thin films by DC and pulse-plated electrodeposition [59-63]. An efficiency of 1.49 % was obtained for a DC electrodeposited CuInSe2 based solar cell. In the case of the pulse-plated electrodeposition, they concluded that films with a stoichiometric composition and a smooth surface has been achieved by controlling applied pulses with a duty cycle θ of 33 % and a cathode potential during “ONtime” of –0.7 V vs SCE with annealing temperature of 400 o C and annealing duration of 90 min.

1.2

Objective of This Study

To reduce the cost for manufacturing solar cells, a low cost manufacturing method by which the cell with the large area can be prepared must be developed. This study aim to establish the electrodeposition technique as a ternary chalcopyrite semiconductor thin film preparation method. For this purpose, dominant factors which affect compositions in the films as well as controllability, reproducibility and rate determination step for each ion were investigated because the film compositions much influence the film properties, such as conductivity, crystallinity and grain size, and conseqently cell performance. As-deposited films are annealed in various atmosphere to improve film crystallinity. Morphology must be improved to fabricate solar cells because the poor morphology causes short-circuit of a front and back electrodes. Photovoltaic properties of the electrodeposited CuInSe2 based thin film solar cell are also discussed. Moreover, a new electrodeposition technique to control compositional depth profile of the film was proposed. This research is believed to be helpful to establish electrodeposition as the thin film semiconductor preparation method.

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Basic Properties of CuInSe2 and Solar Cell Structure

To obtain high efficiency solar cells, understanding physical properties of CuInSe2 is basically requiered. Thus, this chapter describes basic properties of CuInSe2 , i.e. crystallographic properties, a phase diagram and electric properties including defect physics. Solar cell structure as well as band structure of CuInSe2 solar cells are also shown. Crystallography Eighteen ternary AI BIII CVI 2 chalcopyrite semiconductors where A = Cu, Ag, B = Al, Ga, In and C = S, Se, Te are known. The crystal structure of chalcopyrite is shown in Fig. 2.1 as well as a zindblende structure. It can be systematically constructed starting from a cubic face centered structure, which is a cubic close-packed structure [64]. By arranging two face centered cubic units shifted 1/4 in order along a cubical diagonal, the diamond structure is obtained. The zincblende structure can be derived when the each unit of the cubic face centered structure in the diamond structure is occupied regularly with two different kinds of atoms, i.e. anion and cation, as shown in Fig. 2.1 (a). Finally, the chalcopyrite structure can be obtained by doubling the zincblende unit cell along the c-axis and filling the lattice sites according to the following: The anions remain at their sites and every cation site is occupied regularly by each of the two kinds of cations, e.g. Cu and In, as shown in Fig. 2.1 (b). Consequently, each C anion, which configure a cubic face centered structure, is coordinated by two A and two B cations and each cation is tetrahedrally coordinated by four anions. The observed structural features for real chalcopyrite compounds are slightly different from those obtained theoretically from this construction rules because of two basic chemical bonds A-C and B-C with generally unequal bond lengths RAC = RBC . This unequality propose the following two unique properties of chalcopyrite, compered with zincblende: First, the unit cell is tetragonally distorted with a distortion parameter η = c/2a = 1. Second, the anions are displaced from the ideal tetrahedral site u0 = 1/4 by an amount u, where u is called “u parameter” and

Figure 2.1: Crystal structure of zincblende (left) and chalcopyrite (right).


169

expressed as

2 − R2 1 RAC BC + . (2.1) 4 a2 The lattice constants and bandgap of CuInSe2 are summarized in table 2.1 [65]. Note that the distortion parameter η = c/2a is slightly larger than unity.

u=

Table 2.1: The lattice constants and the bandgap of CuInSe2 . a [nm] 0.579

c [nm] 1.160

c/2a 1.0017

bandgap (eV) 1.04

Figure 2.2: Cu2 Se-In2 Se3 pseudo-binary phase diagram. Phase diagram The presence of secondary phases in the bulk of the material critically influence structural, optical and electrical properties of chalcopyrite thin films. In most cases, the presence of Cu-rich and In-rich secondary phases deteriorates the device performance and should therefore be eliminated or limited at least. In this regard, phase diagram gives us useful information in regard to the occurrence of different secondary phases during film deposition. The available phase information for the CuInSe2 system is largely limited to the Cu2 Se-In2 Se3 pseudo-binary phase diagram. Fig 2.2 shows the Cu2 Se-In2 Se3 pseudo-binary phase diagram of CuInSe2 [66]. According to this phase diagram, various compounds (e.g. Cu2 In4 Se7 , Cu3 In5 Se9 , CuIn3 Se5 , Cu5 In5 Se8 ) can occur in this ternary system. The homogeneity ranges deduced from X-ray diffraction studies at room temperature are indicated below the break in the temperature axis. The γ, γ and γ regions represent distinct phases associated with the compounds CuInSe2 , Cu2 In4 Se7 and CuIn3 Se5 , respectively. The sphalerite phase CuInSe2 (δ phase) is stable only at temperatures higher than 810 ◦ C, whereas the chalcopyrite structure (γ phase) is stable

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from room temperature up to 810 ◦ C. In other words, an order-disorder phase transition (γ → δ) occur at 810 ◦ C [67]. The chalcopyrite single phase, CuInSe2 , extends from the stoichiometric composition of 50 mol.% In2 Se3 to the In-rich composition of about 55 mol.% In2 Se3 . The corresponding Cu/In atomic ratio for single phase CuInSe2 lies between 1.0 and 0.82. In case where the Cu/In atomic ratio is greater than 1.0, the materials are expected to contain secondary phases of Cu2 Se while for the Cu/In atomic ratio of less than 0.82 the materials are expected to contain secondary phases of the type Cu2 In4 Se7 and CuIn3 Se5 [66].

Figure 2.3: Resistivity, type of conductivity and carrier density as a function of Cu/In ratio. Electrical Properties and defect physics Conductivities of p-type and n-type are obtained for Se-rich (or Cu-rich) and Se-poor (or In-rich) CuInSe2 material, respectively, in both thin film and single crystalline forms because CuInSe2 has native defects, such as vacancies and antisites, which dominate electrical properties, such as a conductivity type, p or n, and a resistivity, or it contains secondaly phases as writen above. Fig. 2.3 shows a resistivity, a type of conductivity and a carrier density as a function of Cu/In ratio


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Table 2.2: Summary of calculated native defect formation energies and defect levels. point defects V0Cu V− Cu V0In V− In V2− In V3− In Cu0In Cu− In Cu2− In In2+ Cu In+ Cu In0Cu Cu+ i Cu+ i VSe

formation energies (eV) 0.80 0.63 3.04 3.21 3.62 4.29 1.54 1.83 2.41 1.85 2.55 3.34 2.04 2.88 2.40

defect levels (eV)

type

Ev + 0.03

acceptor

Ev + 0.17 Ev + 0.41 Ev + 0.67

acceptor acceptor acceptor

Ev + 0.29 Ev + 0.58

acceptor acceptor

Ec − 0.34 Ec − 0.25

donor donor

Ec − 0.20 Ec − 0.08

donor donor

[68, 69, 70]. The resistivity of CuInSe2 is drastically changed with Cu/In ratios by a factor of 106 . Cu-rich CuInSe2 shows a low resistivity because it is a complex of CuInSe2 and low resitivity Cu2−x Se. On the other hand, In-rich CuInSe2 has a high resistivity probably due to compensation of donors and acceptors. Stoichiometric and Cu-rich CuInSe2 show generally p-type conductivity and In-rich n-type. Zunger et al. and Wasim calculated native defect formation energies and defect energy levels by first principle calculation [71, 72, 73]. These are summarized in Table 2.2, where Vα , αβ and αi represent vacancies of α atom, α atom in β site and α interstitial, respectively. In Fig. 2.4, thier predicted defect transition levels are compared with experimental data [72]. From these results, Cu vacancies, which is a shallow acceptor whose level is 30 meV above the valence band edge, are found to be easy to form. The results also show V In and CuIn defects act as aceptors while InCu and Cui defects donors. Moreover, they reported that the structurel tolerance to large off-stoichiometry in CuInSe2 is explained by the unusual stability of (2V0Cu + In0Cu ) defect pair whose formation energy is as low as –6.1 eV/pair when there is a astrong interaction between the components of the defect pairs. This low formation energy explains the existence of the ”Orderd Defect Compuounds” (ODC) ,such as CuIn5 Se8 , CuIn3 Se5 , Cu2 In4 Se7 and Cu3 In5 Se9 . They also concluded that the electrically benign nature of the structural deffects is explained in terms − of the electronic passivation of the In2+ Cu by VCu . Structure of CuInSe2 thin film solar cells Figure 2.5 shows a cross sectional schematic representation of a CuInSe2 -based solar cell. Cell preparation starts with the deposition of a Mo back contact on glass, followed by fabrication of a p-type ternary chalcopyrite absorber, a high resistivity CdS or other weakly n-type buffer layer, bi-layer with undoped ZnO and n-type transparent conductor (usually Al doped ZnO or ITO (Indium Tin Oxide)) shown as

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Figure 2.4: Defect transition energy levels from (a) their thory and (b) experiments.

Figure 2.5: Schematic representation of a cross section for the CuInSe2 solar cell. TCO in Fig. 2.5, metal grids and a antireflection coating (not shown in Fig. 2.5) [74]. Typical band structure of the CuInSe2 -based solar cell is shown in Fig. 2.6 [75, 76, 77]. In this figure, ∆Ec and ∆Ev denote a conduction and valence band offsets at the CIS and


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Figure 2.6: Schematic representation of a band structure for the CuInSe2 solar cell. CdS interface, respectively. Results of simulation show that ∆Ec which act as a barier for photo-excited electron hardly influence cell performance if ∆Ec is less than 0.4 eV [78]. Nelson et al. have reported ∆Ec and ∆Ev are about 0.4 [79] and 0.8 eV [80], respectively. High efficiency CuInSe2 solar cells have a Cu-poor surface, resulting in a surface composition of CuIn3 Se5 . The n-type surface material produce type inversion at the surface of absorber. This leads to a shift of the regime p=n into the absorber and hence away from the defect rich CdS/CIS interface resulting in a reduced recombination rate. In addition, the grading of the valence band close to the surface provides a transport barrier for holes which reduce the hole density at the interface and hence decrease the interface recombination rate [76].

3 3.1

Experimental Details Electrodeposition

Electrodeposition is one of methods to deposit metal and semiconductor thin films. It is almost the only one method to obtain such films at a room temperature and a nomal pressure. It is based on an electrochemical reduction reaction of ions on a cathode substrate surface in an electrolyte. This section describes the basics of electrodeposition [81, 82, 83]. 3.1.1 Theory Electrodeposition of metallic films (commonly known as electroplating) has long been known and used for preparing metallic mirrors and a corrosion-resistant surface, and so on [81]. Electrodeposition process can be divided into the following three steps: (1) Ions are provided from a bulk of an electrolyte. (2) Adatoms are generated by discharging electrons from a cathode to ions. (3) Adatoms diffuse on the crystal surface and incorporated into

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the crystal. The first process is mainly due to diffusion of the ions from the bulk of the electrolyte to the substrate surface. The second one is interpreted as reduction reactions of ions at the substrate surface. The third process is the same as that of vapor phase crystal growth, such as evaporation. The redox potential Er for a electronation reaction, M z+ + ze− = M, is given by Er = E0 +

RT ln[M z+ ], zF

(3.1)

(3.2)

where M z+ : activity of a metal ion (az+ M /aM ), z: ionic charge, M : deposited metal, E0 : standard electrode potential, R: gas constant, T : absorute temperature, F : Faraday’s constant. If the reaction starts by applying voltage between a cathode and an anode, metal ions, M z+ , accept electrons from the cathode and metal M deposits on the surface of the cathode. Consequently, a concentration difference of ions between the bulk of the electrolyte and an adjacent area of the cathode surface arises because of decreasing ion concentration near the cathode. This difference is the driving force to provide the ions from the bulk to the cathode surface by diffusion. An overpotential, η, which is an electrodeposition driving force, has a relationship with a difference of chemical potentials between equilibrium and under deposition (∆µ) and this relationship is given by η = E − Er =

∆µ , zF

(3.3)

where E is the cathode potential during the deposition. According to Stern’s model, an electrode-electrolyte interface can be divided into two parts: One is a compact double layer known as the Helmholtz double layer adjacent to the electrode and the other is a diffuse layer known as the Gouy-Chapman layer. Figure 3.1 shows potential and ion distributions around the cathode surface. A potential varies linearly and exponentially with distance in the Helmholtz layer and the diffuse layer, respectively, as shown in Fig. 3.1. The Helmholtz double layer can be divided into an inner and outer planes. The inner Helmholz plane (IHP) is adjacent to the electrode surface and consists of completely oriented water dipoles and contact-adsorbed ions. These layers are shown in Fig. 3.2. In aqueous electrolytes, the cations react rather strongly with the water molecule, and their inner hydration sphere is retained. This limits their closest distance of approach. They are usually separated from the cathode by approximately one or two water molecules. On the other hand, anions interact weakly with water, and their closest distance of approach could correspond to direct contact. The outer Helmholtz plane (OHP) consists of solvated ions at the closest distance of approach from the electrode surface. In the diffuse layer, there is a difference between concentration of anions and that of cations. Outside of the diffuse layer is the bulk of electrolyte, and the distribution of anions and cations is not changed whether potential is applied or not. In the case of alloy, Mp Nq is deposited by a eutectoid reaction as shown in Eqs.3.4 and 3.5, M m+ + me− = M, N n+ + ne− = N (3.4)


Figure 3.1: Potential and ion distributions.

Figure 3.2: Helmholz double layer.

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Shigeyuki Nakamura pM + qN = Mp Nq ,

(3.5)

and electrodeposition potentials for each component are as follows; ∗ + Er,M = EM

RT ln[M m+ ] mF

(3.6)

RT (3.7) ln[N n+ ] nF ∗ : standard electrode potentials for each element in the alloy and are and EN ∗ + Er,N = EN

∗ where EM given by

RT ln(aM ) mF RT ∗ o ln(aN ) = EN + EN nF and aN : activity in the alloy. E is given by ∗ o = EM + EM

where aM

E = Er,M + ηM = Er,N + ηN

(3.8) (3.9)

(3.10)

where ηM and ηN : overpotential of each element. This indicates that a difference between redox potentials for each element is equal to a difference between overpotentials. The difference of redox potentials is usually too large to be compensated by difference in concentrations for each ion. On the other hand, under electrodeposition, a concentration of metal ion adjacent to the electrode surface, Cs , is smaller than a bulk concentration, C0 . At Cs = 0, a velocity of electrodeposition reaches critical level and increase no more even if a potential veries more negative. A critical diffusion current id is given by id = nF DC0 /δ

(3.11)

where D: diffusion constant, δ: diffusion layer thickness (i.e. diffusion limited). For the current higher than id , the cathode potential should be jumped to a more negative value. Thus, co-electrodeposition is carried out under the condition of a sufficiently negative cathode potential to deposit the less noble metal with the concentration of the noble metal ion lowered until the deposition current for the noble metal reaches critical. For example, electrodeposition of ZnSe is explained as follows [83]. Figure 3.3 shows a typical current-potential curve for electrodepositon of ZnSe. In the case of the solution concentration of [H2 SeO3 ][Zn2+ ], elemental Se begins to deposit at the potential of Er,Se = 0.159V. ZnSe begins to deposit at Er,Zn +∆EZn = −0.159V when the deposition rate of elemental Se reaches critical and the potential is shifted more negative. However, since the ZnSe deposition is limited by diffusion of H2 SeO3 , the current reaches critical again when the cathode potential becomes more negative (from -0.159 to -0.962 V). At the further negative potential of Er,Zn = −0.962V, a deposition of elemental Zn results in a Zn composition increase in the deposited material. Thus, single phase ZnSe is deposited between –0.159 and –0.962 V.


177

Figure 3.3: Theoretical current-voltage curve for electrodeposition of ZnSe. 3.1.2

Experimental Apparatus

Electrodeposition was carried out potentiostatically or galvanostatically in an aqueous solution using a standard three electrode cell. Figure 3.4 shows a schematic representation of the electrodeposition cell. A titanium or moribudium sheet was used as a cathode substrate electrode, a carbon rod as an anode counter electrode and a standard calomel electrode (SCE) or a Ag/AgCl electrode (SSE) as a reference electrode. The substrates were ultrasonically cleaned in organic solvents. If necessary, substrates were etched in acidic solutions, a pH value was controlled by adding dilute acidic solution and a solution was stirred by a magnetic stirrer. Detail electrodeposition conditions will be shown in each section.

3.2

Annealing and Evaluation Methods

The highest efficiencies of electrodeposited CuInSe2 based thin film solar cells are lower than that of evaporated or sputtered ones because quality of electrodeposited films is generally poor. The film resistivity is higher because of smaller grain size due to a deposition condition of high overpotential corresponding to a highly supersaturated vapor condition for the vapor-phase growth. For this reason, all of researchers have reported that a thermal process such as annealing is necessary to improve film quality [83]. In general, crystallinity, grain size and adhesion of the film is improved by the annealing. An annealing apparatus consisting of a electric furnace and a quartz tube with gas line of N2 is used in this work. Annealing temperatures were varied from 250 to 600 o C and annealing time from 30 min to 120 min. Detailed annealing conditions will be shown later. Composition, crystallinity, surface morphology, cross-sectional morphology and compositional depth profile of as-deposited and annealed films were evaluated by an electron

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Figure 3.4: The electrodeposition cell. probe microanalyzer (EPMA), an X-ray diffraction (XRD), a scanning electron microscope (SEM) and an X-ray photoelectron spectroscope (XPS), respectively.

4 4.1

Electrodeposition of CuInSe2 Layers and Their Solar Cell Application Introduction

This chapter describes electrodeposition of Cu-In-Se films prepared with an aqueous solution containing CuCl2 , InCl3 and SeO2 in terms of composition control of deposited films for the preparation of CuInSe2 [84, 85]. Taking account of the abscondence of Se element from deposited layers during post-annealing, the preparation of Cu-In-Se layers with an excess Se content has been studied using a solution with a high Se content. An important problem for the development of this technique is to control sample compositions because they affect film properties which influence cell performance very much, as shown in section 2. Understanding of deposition mechanisms of each species is essential in order to achieve higher controllability and reproducibility of film composition and then to improve performances of CuInSe2 solar cells prepared by electrodeposition. Crystallinity of as-deposited films has also been described. In general, electrodeposited films must be annealed to improve their crystallinities [86]. Thus, effects of annealing on compositions, morphologies and crystallinities were investigated. Solar cells based on electrodeposited CIS thin films are fabricated with a chemicalbath-deposited n-CdS buffer layer on the CIS layer without a transparence conductive layer such as Al-doped ZnO or ITO [86]. The best efficiency of 0.87 % is obtained with the electrodeposited CuInSe2 thin film.


4.2

179

Relationship between Compositions in the Films and That in the Baths

It is reasonable for us to consider that the compositions in the films are affected by that in the baths. For composition control of deposited films, it is preferable that there is a simple relation between them. For example, the compositions in the films are proportional to that in the baths and proportionality constants are not affected by other parameters. Moreover, it is preferable that, for example, a In/Cu ratio is not affected by a Se concentration. On the basis of above, relationships between compositions in the films and that in the baths are investigated. Figure 4.1 shows relationships between Se/Cu ratios in the films, α, and those in the source baths, [Se(IV)]/[Cu(II)]. Deposition conditions are summarized in Table 4.1. One can see that for the wide range of current density (∼10 mA/cm2 ), a linear relationship is held between these values. Under the assumption that all the Se(IV) and Cu(II) ions arriving at the electrode are involved in the deposited film, a ratio of mass-transfer coefficients for Se and Cu, k(Se)/k(Cu) is obtained as a ratio of α to [Se(IV)]/[Cu(II)] [87]: k(Se)/k(Cu) =

α . [Se(IV)]/[Cu(II)]

(4.1)

In this case, a constant k(Se)/k(Cu) value (∼ 0.65) is obtained for the wide range of current density when no stirring is employed. Figure 4.2 shows relationships between In/Cu ratios in the films, β, and those in the source baths, [In(III)]/[Cu(II)]. The deposition condition is the same as Table 4.1. A linear relation is held between them only for a low current density (therefore, a noble electrode potential) and for a solution with a low solute concentration. Using the same assumption as the case for k(Se)/k(Cu), a ratio of mass-transfer coefficients for In and Cu, k(In)/k(Cu) is obtained as follows: β k(In)/k(Cu) = . (4.2) [In(III)]/[Cu(II)] The ratio increases as the current density increases as shown later. Table 4.1: Deposition conditions No.1 Substrate material Source materials and their concentrations Composition ratio in the baths A pH value of solution A solution temperature Substrate potentials Current densities Deposition duration Stirring

Mo Cu: CuCl2 : 0.05mM In: InCl3 : 1.0mM Se: SeO2 : 0 ∼ 1.0mM Cu:In:Se = 1∼5:20:20 2.0 20 o C −0.5 ∼ −2.2 V vs SCE 1.0 ∼ 10 mA/cm2 9 ∼ 90 min. 90rpm (if necessary)

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Shigeyuki Nakamura

15

&A

10

1mA/cm2 3 5 10

5

0

10

20

[Se(IV)]/[Cu(II)] Figure 4.1: Relationships between Se/Cu ratio in the film, α, and those in the source bath, [Se(IV)]/[Cu(II)].

&B

4

1mA/cm2 3 5 10

2

0

10

20

[In(III)]/[Cu(II)] Figure 4.2: Relationships between In/Cu ratio in the film, β, and those in the source bath, [In(III)]/[Cu(II)].

4.3

Relationship between the In/Cu Ratio in the Film and Se(IV) Concentration in the Bath

In general, deposition rates of each element (Cu, In and Se) are competitive. Thus, if a deposition rate of one element (e.g. Se) increases, that of other elements (Cu and In) must decrease under a constant current density. If rates of the decrease for these elements


181

15 [In(III)]/[Cu(II)]=20 2 mA/cm2 pH:1.0 pH:2.0

&B

10

5

0

10 [Se(IV)]/[Cu(III)]

20

Figure 4.3: Relationships between In/Cu ratio in deposited film, β, and Se/Cu ratio in the source bath, [Se(IV)]/[Cu(ll)]

Composition [at%]

100

Cu In Se

50

0 0

10 [Se(IV)]/[Cu(II)]

20

Figure 4.4: Dependence of the composition for each element on the Se concentration in the source-bath are same, there is no problem in terms of composition control. However if not, some complications, such as an In/Cu ratio in the film depends on a Se bath concentration, arise for composition controlling. In this electrodeposition system, the Se concentration in the bath was found to influence the In/Cu ratios in the films as follows. Figure 4.3 shows the relationship between the In/Cu ratios in the films, β, and Se(IV) concentrations in the baths. Deposition conditions are summarized in Tabel 4.2. As seen in Fig. 4.3, β decreases drastically and then becomes constant as [Se(IV)]/[Cu(II)] increases. This result shows

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In/Cu ratio in the films

4

2 With stirring Without stirring

0

−1

−2

−3

Deposition potential vs SCE [V] Figure 4.5: Variation in In/Cu ratio in film by stirring on Mo substrate

Se/Cu in the films

15

10

5 Without stirring With stirring 0 −1 −2 −3 Deposition potential vs SCE [V]

Figure 4.6: Variation in Se/Cu ratio in film by stirring that the Se/Cu ratio in the source bath is also one of the important factors to control the In/Cu ratio in a deposited film. To investigate origin for this dependence, a composition dependence of each element on Se concentrations is examined. Figure 4.4 shows the dependence of the composition for each element on the Se concentrations in the source bath. The figure shows that a composition of In is much effected by Se concentration while that of Cu is hardly influenced. As a result, this dependence is found to be mainly due to a decrease in the In deposition rate with increasing the Se concentration in the bath.


183

Table 4.2: Deposition conditions No.2 Substrate material Source materials and concentration Composition ratio in the baths A pH value of solution A solution temperature Substrate potentials Current densities Deposition durations Stirring

Mo Cu: CuCl2 : 0.05mM In: InCl3 : 1.0mM Se: SeO2 : 0 ∼ 1.0mM Cu:In:Se = 1:20:0∼20 2.0 20 o C −0.5 ∼ −2.2 V vs SCE 1.0 ∼ 10 mA/cm2 9 ∼ 90 min. 90rpm (if necessary)

k(Se)/k(Cu), k(In)/k(Cu)

0.8 k(Se)/k(Cu)−NS

0.6 k(Se)/k(Cu)−S

0.4 k(In)/k(Cu)−NS

0.2

0

k(In)/k(Cu)−S

5

10

Current Density [mA/cm2] Figure 4.7: k(Se)/k(Cu) and k(In)/k(Cu) with (-S) and without (-NS) stirring of the solution as a function of current density.

4.4

Rate-Determination Step and Stirring Effects

From effects of stirring of the solution during the deposition on film compositions or ratios of mass-transfer coefficients, generally, one can get useful information about rate-determining steps of electrodeposited species. Influences of the solution stirring on the film compositions and its controllability are shown in Figs. 4.5 and 4.6. The stirring of the solution during the deposition decreases in both In/Cu and Se/Cu ratios in deposited films. This seems to be due to the enhanced deposition rate of Cu by the stirring because a rate-determining step for Cu is “diffusion-limited” as described later. It is noted that a deposition rate of a diffusion-limited species is independent of a electrode potential and, therefore, the rate does not increase even if a total deposition current increases by applying

184

Shigeyuki Nakamura

In/Cu ratio in film

6 Without stirring 4

2 With stirring

0 −1 −2 −3 Deposition potential vs SCE [V]

In/Cu ratio in the films

Figure 4.8: Maximum and minimum values of In/Cu ratio for nine specimens prepared with and without stirring.

4

2

0

Mo p−Si

−2 −4 Substrate potential vs SCE [V]

Figure 4.9: Substrate potential dependences on film compositions. Comparison with a Si and Mo substrate. a more negative potential. On the contrary, a deposition rate of a reaction-limited species increases with a deposition current. There is a general tendency that a rate-determining step changes from “reaction-limited” to “diffusion-limited” when a deposition current density increases. Figure 4.7 shows k(Se)/k(Cu) and k(In)/k(Cu) with and without the stirring as a function of a deposition current density. Both k(Se)/k(Cu) and k(In)/k(Cu) values in Fig. 4.7 are


In/Cu tatio in the films

4

185

p−Si substrate With stirring Without stirring

2

0

−2

−4

Substrate potential vs SCE [V] Figure 4.10: Variation in In/Cu ratios in the films on the Si substrate by stirring. smaller than those reported for the sulfate-based solution [87, 88]. A remarkable reduction of the k(Se)/k(Cu) and the k(In)/k(Cu) at a low current density by the stirring shows that the deposition rate of Cu(II) is most influenced by the stirring, compared with other species. Since the diffusion-limited process is mainly affected by the stirring, it is reasonable to consider that the deposition reaction of Cu(II) is diffusion-limited in the wide range of current density (1-10 mA/cm2 ) even under the stirring condition. The k(Se)/k(Cu) values without stirring are independent of a current density, as shown in Fig. 4.7. This result shows that the supply of both elements is diffusion-limited when no stirring is employed. When the solution is stirred, k(Se)/k(Cu) values at low current densities (

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