New Research on Semiconductors

NEW RESEARCH ON SEMICONDUCTORS

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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– Schr¨odinger 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.

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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

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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

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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.

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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

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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.

Crystal Growth of Ternary and Quaternary Alloy Semiconductors by Rotational…

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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.

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

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.

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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.

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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.

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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

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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).

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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.

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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

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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%).

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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,

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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

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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.

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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.

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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.

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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.

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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.

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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)

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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)

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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.

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

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

Crystal Growth of Ternary and Quaternary Alloy Semiconductors by Rotational…

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.

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

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
Acknowledgment The authors wish to thank Profs T.Sukegawa and A. Tanaka for the four-crystal X-ray diffractometry, Prof.S.Fuke and Mr.K.Kuwabara for SIMS, Prof..K.Murakami for scanning electron microscopy, Mr.T.Koyama and Mr.K.Katuno for EPMA. We also thank Mr.Y.Momose for preparing the growth ampoules. This research was supported in part by a Grant-in-Aid for International Scientific Program and by a part of Grand Research for Space Utilization promoted by NASDA and Japan Space Forum.

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References [1] K.Nakajima, T.Kusunoki and C.Takenaka, J. Crystal Growth 113 (1991) 485. [2] T.Hibiya, H.Watanabe, H.Matsumoto and N.Iwata, J. Electrochem. Soc. 134 (1987) 981. [3] K.J.Bachmann, F.A.Thiel, H.Schreiber, Jr., and J.J.Rubin, J.Electron.Mater. 9 (1980) 445. [4] M.Ohmukai, H.Naito, M.Okuda and K.Kurosawa, J. Crystal Growth 152 (1995) 247. [5] K.J.Bachmann, F.A.Thiel and S.Ferris. J. Crystal Growth 43 (1978) 752. [6] V.K.Dixit, Bhavtosh Bansal, V.Venkataraman, H.L.Bhat and G.N.Subbanna, Appl.Phys.Lett 81(2002)1630. [7] R.Singh, A.F.Witt and H.C.Gatos, J.Electrochem. Soc. 121 (1974) 380. [8] K.M.Kim, J. Crystal Growth 44 (1978) 403. [9] A.M.Jean-Louis, B.Ayrault and J.Vargas, Phys. Status Solidi 34 (1969) 341. [10] K.Nakajima, T.Kusunoki and K.Otsubo, J. Crystal Growth 173 (1997) 42. [11] S.Kodama, Y.Furumura, K.Kinoshita, H.Kato and S.Yoda, J.Crystal Growth 208 (2000) 165. [12] H.Sheibani, S.Dost, S.Sakai and B.Lent, J.Crystal Growth 258 (2003) 283. [13] M.Kumagawa, H.Oka, N.V.Quang and Y.Hayakawa, Jpn. J. Appl. Phys. 19 (1980) 753. [14] Y.Hayakawa, Y.Sone, K.Tatsumi and M.Kumagawa, Jpn. J. Appl. Phys. 21 (1982) 1273. [15] Y. Hayakawa and M.Kumagawa, Jpn. J. Appl. Phys. 22 (1983) 206. [16] Y.Hayakawa, Y. Sone, F. Ishino and M.Kumagawa, Jpn. J. Appl. Phys. 22 (1983) 1069. [17] Y.Hayakawa and M.Kumagawa, Crystal Res. Technol. 20 (1985) 3. [18] Y.Hayakawa and M.Kumagawa, Jpn. J. Appl. Phys. 24 Suppl. 24-1 (1985) 166. [19] T.Tsuruta,Y.Hayakawa and M.Kumagawa, Jpn.J.Appl.Phys. 27 Suppl.27-1 (1988) 47. [20] T.Tsuruta,Y.Hayakawa and M.Kumagawa, Jpn.J.Appl.Phys.28 Suppl.28-1 (1989) 36. [21] T.Tsuruta,Y.Hayakawa and M.Kumagawa, Jpn.J.Appl.Phys. 31 Suppl.31-1 (1992) 23. [22] M.Kumagawa, T.Tsuruta, N.Nishida, J.Ohtsuki, K.Takahashi, S.Adachi and Y.Hayakawa, Cryst.Res.Technol. 29 (1994) 1037. [23] M.Kumagawa, M.Tamaki and Y.Hayakawa, Jpn.J.Appl.Phys. 26 (1987) 180. [24] Y.Hayakawa, M.Nagura and M.Kumagawa, Semicond.Sci.Technol. 3 (1988) 372. [25] M.Nelson. RCA Rev. 24 (1963) 603. [26] M.Kumagawa, T.Ozawa and Y.Hayakawa, Appl. Surface Sci. 33/34 (1988) 611. [27] T.Ozawa, Y.Hayakawa and M.Kumagawa, J.Crystal Growth 109 (1991) 212. [28] T.Ozawa, Y.Hayakawa and M.Kumagawa, J. Crystal Growth 115 (1991) 728. [29] T.Ozawa, Y.Hayakawa, K.Balakrishnan, F.Ohonishi, T.Koyama and M.Kumagawa, J. Crystal Growth 229 (2001) 124. [30] Y.Hayakawa, M.Ando, T.Matsuyama, E.Hamakawa, T.Koyama, S.Adachi, K.Takahashi, V.G.Lifshits and M.Kumagawa, J.Appl.Phys. 76 (1994) 858. [31] T.Ozawa, Y.Hayakawa, K.Balakrishnan, F.Ohonishi, T.Koyama and M.Kumagawa, J.Crystal Growth 229 (2001) 124. [32] Y.Hayakawa, T.Ozawa, M.Haris and M.Kumagawa, J.Crystal. Growth (2005) in press. [33] T.Ozawa, N.Ishigami,Y.Hayakawa, K.Koyama and M.Kumagawa, Computer Modeling in Engineering & Sciences,10 (2000) 1.

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[34] T.Ozawa, Y.Hayakawa, K. Balakrishnan and M.Kumagawa, J.Crystal Growth 237-239 (2002) 1692. [35] B.Joukoff and A.M.Jean-Louis, J.Crystal Growth 12 (1972) 169. [36] P.Görnert, Crystal Research and Technology 15 (1980) 627. [37] A.N.Danilewsky and K.W.Benz, J. Crystal Growth 106 (1990) 273. [38] K.Nakajima, J.Crystal Growth 144 (1991) 633. [39] L.Pauling, The Nature of the Chemical Bond (Cornell University Press, Ithaca, NY,1960), p.72 [40] P.D.Shewmon, Diffusion in Solids (McGraw-Hill, New York, 1963) 29. [41] D.L. Kendall and R.A.Huggins, J. Apply.Phys. 40 (1969) 2750.

In: New Research on Semiconductors Editor: Thomas B. Elliot, pp. 31-67

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

Chapter 2

FORMATION OF GROWN-IN MICRODEFECTS IN DISLOCATION-FREE SILICON MONOCRYSTALS V.I. Talanin*, I.E. Talanin 1

Institute of State & Municipal Government, Zhukovskii str. 70B, 69002 Zaporozhye, Ukraine

Abstract The paper 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. ɋooling-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 selfinterstitials, 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 *

E-mail address: [email protected]

32

V.I. Talanin and I.E. Talanin 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.

Keywords: grown-in microdefects, mechanism of formation, intrinsic point defects, oxygen, carbon, oxygen-vacancy aggregates, carbon-interstitial aggregates, physical classification.

Introduction In the modern world the magnification of industrial production is impossible without electronics engineering. Material basis of electronics engineering it is dislocation-free silicon monocrystals. Search of other materials and assimilation of their production it’s only adding to silicon. Achievements reached in the area of hyper pure silicon single crystals growing highlighted the further problem to study the peculiarities of the defect formation in such a perfect structure medium. It becomes of great importance now as microelectronics turned to megabit and gigabit integrated circuits fabricated by submicron-level technologies. Successful fabrication of high-quality single crystals and device structures with controlled and predictable parameters depends substantially on how a point defect ensemble is controlled. The structure imperfections named as grown-in microdefects are formed during hightemperature growing and further cooling of dislocation-free single Si crystals. Presently, any local lattice imperfection from a few tens angstroms to few micrometers is deemed as grownin microdefect. According to the generally accepted geometry (size) classification the grownin microdefects belong to the transient class of defects between point and linear ones. Complex of problems which are decided during modern researches in the field of physics, chemistry, material, both technology of semiconducting silicon and structures on it basis is huge. The problem of grown-in microdefects in dislocation-free silicon monocrystals is central in this complex. In particular from our view point the solution of a grown-in microdefects problem is a key to a solution of a problem of thermal donors and thermal acceptors formation in monocrystalline silicon. First data of etching pits in dislocation-free single Si crystals refer to the late sixties of last century [1]. A.J.R. de Kock introduced fist classification for empty etching pits, having identified them as clusters. According to size of etching pits he divided clusters into two types: Ⱥ-clusters (Ⱥ-microdefects) and ȼ-clusters (ȼ-microdefects) [2, 3]. It should be noted that till the late seventies the grown-in microdefects have been studied in small-scale FZ-Si crystals (26 to 30 mm in diameter). It was established that Ⱥ-microdefects observed in FZ-Si single crystals of 30 mm in diameter had a striated distribution at growth rate V = 1 to 3.5 mm/min and B-microdefects had a striated distribution at V d 4.5 mm/min [4]. When Ⱥ-

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33

microdefects size increased up to a certain limit (about 40 Pm at V = 1 mm/min), dislocations appear at single silicon crystals [5]. It was shown that fluctuation in temperature and presence of impurities (especially, carbon [6, 7] and oxygen [8, 9]) are basic factors responsible for the mechanism of Ⱥ- and ȼ-microdefects formation. When crystals are grown at sufficiently high rates, a new type of microdefects was observed as uniform distribution and could be identified as dim regions after preferential etching and decoration [10]. These defects were classified as C- or D-microdefects depending on the their macrodistribution images. Both types were visualized at the regions with uniform defect distribution of high density and, according to the authors of the paper [10], differed from each other by a distribution geometry. The uniform D-microdefects distribution is focused in the form of a “channel” in the central part of the crystal. Currently “Cmicrodefects” often referred to as “V-distribution” (or “V-band”) and “W-distribution” (or “W-band”). However C-microdefects are also observed as rings or circles of irregular shape located at the most extensively cooled parts of the crystal. Therefore the term “Cmicrodefects” has a general meaning. In small-scale silicon crystals grown by Czochralski method (CZ-Si) A-, B- and Dmicrodefects, identical to defects in FZ-Si, were also observed using preferential etching technique [11, 12]. Undoped or low-doped single crystals of 50 mm in diameter, which were grown at V d 1 mm/min, contain Ⱥ- ɢ ȼ-microdefects in a striated distribution. Furthermore, at V ~ 1 mm/min Ⱥ- and ȼ-microdefects are formed in concentrations comparable to their concentrations in silicon single crystals grown by floating-zone melting method. At rate of V t 2 mm/min the Ⱥ- and ȼ-microdefects generation is fully suppressed. It should be noted that a discrepancy in classifying D-microdefects emerged. As stated above, first the term “D-microdefects” was introduced in 1977 by Sheikhet et all [10] for grown-in microdefects in FZ-Si (V = 6 mm/min), which have uniform distribution in the form of a “channel” in the central part of the crystal. Quite possible, Roksnoer did not know of the paper [10] and in 1981 determined as D-microdefects such defects, which are generated also as uniform distribution in the form of a “channel” in the central part of the crystal FZ-Si (but at V = 7 to 8 mm/min) [13]. On the basis of X-ray topography results coupled with copper decoration, researchers in [13] made an assumption that the D-microdefects in FZ-Si are vacancy-type. It must be allowed for that in the theoretical model of the formation mechanism of microdefects in FZ-Si [14] Voronkov defines D-microdefects in accordance with classification [13]. The fact that uniform distribution of D-microdefects in the form of a “channel” in the central part of the crystal (in accordance with classification [10]) is not observed in CZ-Si makes the confusion in classification worse. Therefore, most authors still use a definition “D-microdefects” in accordance with [13]. Nevertheless, we believe that in the context of history and experimental results as for grown-in microdefects origin, such a definition of D-microdefects is erroneous.

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Fig.1. Grown-in microdefects in FZ-Si and CZ-Si crystals, selective etching: a) A-microdefects (FZ-Si, V = 2 mm/min), plane (112); b) B-microdefects (FZ-Si, V = 4 mm/min), plane (111); c) D-microdefects (FZ-Si, V = 6 mm/min), plane (111); d) A-microdefects and (I+V)-microdefects (CZ-Si, V = 2.5 mm/min), plane (112); e) (I+V)-microdefects (FZ-Si, V = 8 mm/min), plane (111); f) C-microdefects (FZ-Si), plane (112).

What grounds are for such a conclusion? Later, using the transmission electron microscopy (TEM) we established that in FZ-Si crystals at V = 6 mm/min only interstitialtype defects are generated, while at V = 7 to 8 mm/min in FZ-Si crystals the interstitial-type and vacancy-type defects co-exist simultaneously [4, 15, 16]. Furthermore, we showed

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35

experimentally that at Vcrit a 6.5 mm/min in accordance with ratio V/G (where V is a crystal growth rate; G is an axial temperature gradient) the mode of FZ-Si crystal growth is changing (from interstitial-type into vacancy-interstitial type and vise versa) [4, 15]. Thus, two quite different types of grown-in microdefects having uniform distribution were referred the same as to D-microdefects. Here we use the classification, which historically was first and more comprehensive [10]. Based on the classification [10] and TEM research results we define in this paper the grown-in microdefects in FZ-Si (V = 7 to 8 mm/min) having uniform distribution in the form of a “channel” in the central part of the crystal as “(I+V)microdefects” [4, 15, 16]. On Fig.1 the macrodistribution pictures of main kinds grown-in microdefects in FZ-S and CZ-Si crystals are represented. New types of grown-in microdefects are observed in large-scale silicon crystals (over 100 mm in diameter). In particular, presently thermal oxidation typically leads to a ring-shaped distribution in plane (111) of so-called “oxidation-induced stacking faults”, OSF-ring [17, 18]. Researches in a growth rate influence on a distribution of grown-in microdefects in single CZ-Si crystals of 150 mm in diameter revealed that OSF-ring is observed in crystals grown at a moderate growth rate (0.7 to 0.8 mm/min), and absent in crystals grown at growth rates 0.4 mm/min and 1.1 mm/min [19]. As is shown, stacking faults are formed around the plate-like oxygen precipitates [18]. When evaluating future trends in growing crystals of 300 mm and 400 mm in diameter [20], it should be noted that required growth rate decreasing (up to 0.55 mm/min for the crystal of 300 mm in diameter, which is twice less comparing to the crystal of 200 mm in diameter) below the critical rate in order to diminish the thermal stress in the crystal makes the task to fabricate ingots without OSF-ring rather complicated. Outside OSF-ring the interstitial dislocation loops (A-microdefects) are observed [21, 22]. Inside OSF-ring there are defects, which according to observation techniques were named as FP-defects (flow pattern defects), COP-defects (crystal-originated particles) and LST-defects (light-scattering tomography defects) [23]. As is shown, all these defects are different forms of the same defect presentation obtained by various techniques, i.e. vacancy complexes, which are formed inside OSF-ring [24]. With the use of TEM the form and size of LST-defects were determined (100 to 300 nm) [25, 26]. Although TEM observation fails to determine the sign of the defect-induced lattice imperfection, on the basis of a smaller content of oxygen in the center of the defect as compared to the periphery and defect contrast image, was assumed that LST-defects constitute microvoids, i.e. they are vacancy-type. This enabled researchers to interpret all the defect types, identified by different techniques, as a one type of defects identical to D-microdefects in FZ-Si and CZ-Si, formed as a result of homogenous nucleation [25-28]. Unfortunately, these results strengthened the erroneous opinion among researchers that D-microdefects in FZ-Si and CZ-Si crystals are microvoids. It is generally assumed that depending on V/G ratio only interstitial-type dislocation loops (A-microdefects) or only microvoids (D-microdefects) are formed in large-diameter crystals. It is clear and simple approaches as in particular large microdefects either interstitial-type (A-microdefects) or vacancy-type (microvoids) considerably affect both electrophysical and mechanical properties of single-crystal silicon and discrete devices and integrated circuits. However, we believe such an approach is exceptionally technological because it does not allow for the physical nature of defect formation in the dislocation-free single crystal silicon. There are several models of grown-in microdefects formation differing from each other both initial physical concept and level of validity. Every model is based on types and origin of dominating point defects in the growing crystal, which then are transformed into microdefects

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V.I. Talanin and I.E. Talanin

during cooling. Basic models of grown-in microdefects formation include the following: equilibrium interstitial-type model [7], non-equilibrium interstitial-type model [29], local melting model (drop model) [30], vacancy-type model [31], vacancy-interstitial type model [32, 33] and recombination-diffusion model [14, 27]. At present the recombination-diffusion model is the most well-grounded and optimal from the point of its quality. It is distinguished by compiling basics of other models. Furthermore, as many researchers acknowledged, it is convenient and plain to divide the grown-in microdefects simply to A-microdefects and microvoids on the basis of V/G ratio. The point is that V/G ratio allows correlating the lattice imperfection with the thermal growth conditions. Adjusting thermal growth conditions one can calculate the crystal defect structure. Voronkov’s common model is based on the following: 1) there is a fast recombination between intrinsic point defects at temperatures close to melting point; 2) there are areas with only interstitial-type (A- and B-microdefects) or only vacancy-type microdefects (microvoids or D-microdefects); 3) there is a critical parameter Ccrit = V/G. When V/G < Ccrit, self-interstitial atoms dominate in the crystal (interstitial-type crystal growth) and when V/G > Ccrit, vacancies prevail in the crystal (vacancy-type crystal growth). The effect of V/G ratio is reversible and repeatable: reduce V/G – and find A-microdefects and no microvoids; increase V/G – and find microvoids and no A-microdefects. To apply this criterion one should measure or calculate the value of G. However this model does not allow for the affect of impurities (except for oxygen) and does not reflect a real physical nature of formation processes of the grown-in microdefects in silicon single crystals. Recently, Voronkov reported he took into consideration the other impurities in addition to oxygen, which effect the formation of microdefects [34]. He suggested that V/G ratio is shifted by impurities. Some impurities, such as oxygen, nitrogen, and hydrogen, trap vacancies and cause a downward shift in the critical V/G ratio (and also a fast increase in the fraction of trapped vacancies). Other impurities, like carbon, trap selfinterstitial, and cause an upward shift in the critical V/G ratio (and also an increase in the fraction of impurity interstitials) [34]. The drawbacks of the existing classification (and the drawbacks of the theoretical models based upon it) are in that it does not provide any information about the sign of lattice imperfection, which depends on the microdefect type. The sign of defect-induced lattice imperfection (often defined as the microdefect origin) bears an implicit information of the defect chemical composition. At the same time it allows to determine the mechanisms, through which the grown-in microdefects form and transform. It was exactly the absence of this parameter that caused confusion in identification and classification of D-microdefects in FZ-Si and CZ-Si.

1

Experimental

The comprehensive study aiming to reveal the mechanism of the grown-in microdefects formation and transformation is required to solve the problem of the defect formation in dislocation-free single crystal silicon. Following this way, we have been researching the distribution images and images of individual properties (size, form, sign of lattice imperfection) of grown-in microdefects in FZ-Si and CZ-Si crystals, which were grown at different thermal conditions. Special attention was drawn to study the FZ-Si crystals, which are hyper pure crystals (most of them have contents of oxygen and carbon less than

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37

5·1015 cm-3). The principal objective of study was to distinguish the operative body (basis) of the mechanism of the grown-in microdefects formation, effecting which (i.e. changing in thermal growth conditions, doping, thermal processing) one can control the process of defect formation in the dislocation-free single crystal silicon. We have conducted a series of experiments with the FZ-Si and CZ-Si using preferential etching and transmission electron microscopy. The silicon crystals of 30 mm (FZ-Si) and 50 mm (CZ-Si) in diameter were studied. These diameters were chosen because all the known types of the grown-in microdefects are formed in crystals of such diameters when thermal conditions of crystal growth vary. FZ-Si crystals were not doped, oxygen and carbon concentrations were less than 5˜1015 cm-3, the number of passes varied from 2 to 10, U = (2…4)˜103 :˜cm. Concentration of the electrically active impurities were less than 1012 cm-3. CZ-Si n-type crystals were with U = 10…50 :˜cm, oxygen concentration ~ (4…7)˜1017 ɫm-3, carbon ~ (5…7)˜1016 ɫm-3. The crystals were grown at constant growth rates ranging from 1 to 9 mm/min (for FZ-Si) and 0.5 to 3 mm/min (for CZ-Si). Several crystals were obtained under specially programmed growth rate change. To freeze-in the initial stages of formation of grown-in microdefects we conducted quenching of crystals. To study the reasons of formation of microdefects the crystals were subjected to special thermal processing. Furthermore, to confirm the influence of oxygen on formation of microdefects, the experiments with intentional doping of crystals by oxygen were conducted. The oxygen doping was carried out from a gas phase at adding the steams of H2O2 to the growth chamber. Sirtl etch was used to identify microdefects of different types and their distribution images. The inside-outside contrast method, black-white contrast method and defocused darkfield image method (2.5D) were used to determine the sign of lattice imperfection. Electron microscope with 100 kV acceleration voltage was employed that excludes radiation defect infusion [35, 36]. To avoid contamination of the surface by alkali atoms and hydrogen (which are known to penetrate while etching to a depth of several micrometers), the samples for the TEM study were not subjected to that procedure. Knowing the etch pattern for a certain silicon wafer, one can rather exactly cut the samples for the TEM study from a selected place of a near-by wafer, thus the identity of microdefects distribution over the cross-section of both wafers being ensured.

2 2.1

Results Scheme Formation and Transformation Mechanism of Grown-in Microdefects in Silicon Single Crystals

Large number of crystals studied (more 60 ingots FZ-Si and more 20 ingots CZ-Si), which were obtained under various thermal growth conditions, enabled us to make a schematic representation of the microdefect distribution in FZ-Si and CZ-Si under the changing crystal growth rate (Fig.2).

38

V.I. Talanin and I.E. Talanin

Fig 2. Schematic formation and transformation mechanism of microdefects in silicon single crystals, plane (112): a – FZ-Si crystal ‡ 30 mm; b – CZ-Si crystal ‡ 50 mm; Vcrit, Vcrit 2 – crystal growth rates defined experimentally, at which the vacancy-type microdefects appear (disappear), mm/min; Vr – crystal growth rate, at which the remelting phenomenon is suppressed; Vcrit 1 – crystal growth rate calculated theoretically, at which vacancy-type microdefects appear while the interstitial-type defects disappear (according to Voronkov’s model), mm/min.

As one can see in Fig.2a, with gradual increase of growth rate, one type of microdefects in FZ-Si crystals is replaced progressively with the other type. A-microdefect large swirls are replaced with smaller swirls of B-microdefects. After the rate Vr reaches a certain value (at which the remelting phenomenon is suppressed) B-microdefects are replaced with uniform Dmicrodefects distribution. For FZ-Si we determined the adjusted value of rate Vr to be ~ 4.5 mm/min. Our study results showed that above a certain critical growth rate Vcrit the (I+V)microdefects (defect-free region on Fig.2a) begin to appear in crystals, while before Vcrit only D-microdefects could be detected. If V > 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)2˜exp(-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.

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

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 4.5˜1013 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

V.I. Talanin and I.E. Talanin

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

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

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

V.I. Talanin and I.E. Talanin

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.

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

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 Ÿ˜cm, which were vacuum-grown at V = 6 mm/min. Oxygen and carbon concentration was determined by infrared absorption spectrum and amounted to: <

46

V.I. Talanin and I.E. Talanin

1˜1016 cm-3 for oxygen and 1.6˜1016 cm-3 for carbon. Authors [15, 53] observed the Dmicrodefects electron-microscopic images of two types: having regular (periodic) and irregular (amorphous) structure (Fig. 6). Microprecipitates of SiO2 amorphous phase produce the amorphous image [53]. From our point of view, the regular structure belongs to SiC microprecipitates. Both types of D-microdefects revealed are of interstitial-type. Hence, two independent TEM study techniques (amplitude contrast and direct lattice resolution) established the interstitial nature of D-microdefects while being of two types in the crystal. TEM studies of crystals with B-microdefects (FZ-Si, V = 4 mm/min) showed the same defects of white-black contrast of image as for the crystals with D-microdefects. However, Bmicrodefects size ranges within 15 to 50 nm, having concentration a1010cm-3. Zero contrast line is often displayed as broken line. The white-black contrast imaging and 2.5D methods were used to define the physical nature of B-microdefects. We established that all theses defects induce the compressive strain in the crystal, i.e. they are of interstitial type [4, 16]. Geometry of a certain part of B-microdefects emerged under conditions deviating from dynamic image. In this case B-microdefects look like plates having at planes {111} projection a square and diamond shapes (Fig.7d). Either diamond diagonal lines or square sides are parallel to the diffraction vector g ( 220) . Hence, such defects have cuts in directions [100] or [110] and lie in planes {100}.

Fig.6. D-microdefects in FZ-Si (V = 6 mm/min), TEM (direct solution of crystalline lattice): a) recurring structure; b) amorphous structure.

It should be noted that the agglomerations in planes {100} with cuts along the directions [110] have been observed in CZ-Si crystals and identified as SiO2 precipitates [8, 54]. This agglomerates has an amorphous structure and they represent SiO2 amorphous phase [8, 15]. They may be considered as a model of edge dislocation interstitial loops with Burgers vector b 1 / 2[100] [8]. The generation and growth of such agglomerations caused by the oxygen precipitation induce the strong compression of silicon lattice. Relieving from compression results in the prismatic extruding of the interstitial-type dislocation loops (A-microdefects) [4, 55]. Furthermore, SiO2 precipitates growing causes the oversaturation of solid-state solution of silicon intrinsic interstitials and leads to A-microdefects occurrence [4, 7, 56, 57]. Hence, A-microdefects generation is associated with the generation and growth of precipitates (i.e. primary grown-in microdefects). Our TEM studies prove that (I+V)-microdefects, D(C)-

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

47

microdefects and B-microdefects should be referred to as the primary grown-in microdefects. Besides, two forms of D(C)-microdefects existence and size nearness and similar contrast of electron-microscopic images enable us to presume they are uniform distributed small-size Bmicrodefects. TEM studies of crystals with Ⱥ-microdefects (FZ-Si, V = 2 mm/min) were carried out with the use of electronic microscope JEM-1000 [58]. A-microdefects physical nature has been analyzed by the inside-outside contrast method [59]. The dislocation interstitial loops with Burgers vector b

1 / 2[110] were revealed lying in planes {110} and {111} (Fig.7a,b).

The loop size increases as the crystal growth rate slows down. In some cases dislocation lines of loops were decorated with residual oxygen and carbon impurities. These experiments quite well match the earlier obtained results of Ⱥ-microdefects study [29, 57]. It should be pointed to that it was recently shown the Ⱥ-microdefects in CZ-Si crystals are also interstitial type dislocation loops [21, 60]. As is reported, the vacancy microvoids were not observed in smallscale FZ-Si and CZ-Si crystals.

Fig. 7. TEM imaged A-microdefects and B-microdefects in FZ-Si: a) A-microdefects, light field,

g

s  0;

b) A-microdefects,

g

(022) ,

( 2 20) , dark field, s | 0 ; d) B-microdefects, g

light field,

s  0;

g

(022) ,

c) B-microdefects,

( 202) , dark field, s ! 0 .

48

V.I. Talanin and I.E. Talanin

Our experimental results in studying the physical nature of grown-in microdefects illustrate the entire interrelation of their generation and further growth with the presence of carbon and oxygen impurities in the silicon crystal. It is worth to emphasize, this interrelation is revealed experimentally in hyper pure undoped silicon single crystals, where carbon and oxygen concentration is less than 5˜1015 cm-3. So, the study of so-called “oxygen-free” FZ-Si crystals is of much importance. A background oxygen impurity is an important factor influencing the formation mechanism of the grown-in microdefects. And a carbon background impurity is as important as above, especially for FZ-Si [4, 16]. For instance, we showed in CZ-Si that the points with maximum carbon concentration and the points with maximum density of microdefects coincide [40]. However, if microdefects concentration is considered as a function of carbon concentration in different CZ-Si crystals, the relationship will be a bit different. Then, as carbon content increases to 5˜1016 ɫm-3, the concentration of the grown-in microdefects oscillates. When carbon concentration exceeds 5˜1016 cm-3, the concentration of microdefects tends to rise as carbon concentration rises. Apparently, when carbon concentration is below 5˜1016 ɫɦ-3, oxygen impurities are more important in the formation of microdefects. After doping by oxygen from a gas phase, D-microdefects are formed and concentration of B-microdefects is increased [16]. Comparing FZ-Si crystals with CZ-Si crystals one can see the changes in distribution images of grown-in microdefects. This is related to both the change in thermal growth conditions of the crystal and a much greater concentration of carbon and oxygen impurities (with the latter being especially important). However the formation mechanism of the grownin microdefects in CZ-Si will allow two independent directions in which the supersaturated solid solution of the point defects is relaxed. The study of the nature of the grown-in microdefects in CZ-Si proves that the processes responsible for their formation are similar to those in FZ-Si. So, the recombination process of intrinsic point defects in FZ-Si and CZ-Si singlecrystals near the crystallization front is hindered due to the recombination barrier. Vacancies and self-interstitials find out drains in the form of background oxygen and carbon impurities. Consequently, in the context of physical nature of defect formation in real small-scale crystals the Voronkov’s theoretical model fails to be consistent. Considering a concept of entropy barrier and a factor of simultaneous self-diffusion of vacancies and self-interstitials [45], we may reason in this way contrary to the theory of Voronkov that there is a recombination barrier [4]. Experimental results of TEM studies and heterogeneous formation mechanism of the grown-in microdefects prove the theoretical considerations of Hu, Sirtl [32, 33] and Gosele [45] to be true.

2.4

Interaction of Grown-in Microdefects with Radiation Defects

On efficiency of interaction of vacancies or self-interstitials entered by J-rays with microdefects of a concrete type is possible also to judge about a nature of microdefects. We investigated of ingot of FZ-Si with U | 100 :˜cm grown in vacuum with variable growth rate (V = 1.0; 3.0; 6.0 mm/min). From this crystals were cut of samples which contained approximately identical amounts of technological impurities but various concentration and types of grown-in microdefects. Depending on a kind of macrodistribution pictures of microdefects these crystals were saw as three groups. The measurement of W was conducted

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

49

by a phase method and the informations about concentration of carriers n0 are obtained from measurements of Hall factor. The performances of these crystals are indicated in table 2. Table 2 – The crystal performances Group I II III

Type of defect D Ⱥ+ȼ Ⱥ

Growth rate, mm/min 6 3 1

Size, Pm 0,01 0,1…1 up to 20

Concentration, cm-3 1˜1013 1,7˜105 5˜102

W, Ps 90…130 50…120 90…120

n0, cm-3 5,5˜1013 5,1˜1013 6,0˜1013

The informations about sizes and concentration of grown-in microdefects are obtained with the help of transmission electronic microscopy. The form of defects and sign of a strain of a silicon crystalline lattice correspond to experimental results of paragraph 2.3. In crystals, investigated by us, the authors of Ref. [61] analyzed the dependence of lifetime of unmain carriers (W) and concentration of main carriers (n0) from temperature (Ɍ = 100…400 Ʉ) and also dependences of W on a level of excitation of unmain carriers (J = 'n/n0 =10-4…100) which were obtained before and after an exposure by various streams J-quantum ɋɨ60. The experimental results have shown that in all crystals at exposure the Ecentres will be effectively formed and through their levels the recombination of unmain carriers happens. However, degree of a radiation modification of life-time was unequal in crystals which were irradiated with the same stream J-quantum. From the analysis of doses temperature dependences (Wf) the factors ɄW of a radiation modification of life-time (ɄWF = 1/Wf – 1/W0, where F - fluens of J-quantum, W0 - life-time before exposure) were determined. These factors are shown in Tab. 3. In Tab. 3 the calculated rates of introduction ((K = dM/dF, where M - concentration of radiation defects) of E-centres (Kȿ) and centres Ci-Cs (Kɋ) are shown also. Table 3 – The value of factors ɄW and rates of introduction Kȿ and Kɋ [61]. Group I II III

Type of defect D Ⱥ+ȼ Ⱥ

ɄW, cm2˜s-1 1,2˜10-10 (4…6)˜10-11 (5…13)˜10-11

Kȿ, cm-1 4,0˜10-4 (1…4)˜10-4 (1…4)˜10-4

Kɋ, cm-1 5,2˜10-4 (8…5)˜10-4 (8…5)˜10-4

The modification of ɄW can be stipulated only by decreasing K, as a nature and parameters of defects (for example, the factors of grab of electrons and holes on levels of radiation defects) were identical in crystals of all three groups. The analysis of temperature dependences of Hall factor has shown that the rate of introduction of E-centres (Kȿ) correlates with value ɄW [61]. From our view point, the reason of a decreasing of a rate of E-centers introduction in crystals II and III groups is a presence of drains for generated vacancies. Such defects can be agglomerates or precipitates of self-interstitials both background impurities of oxygen and carbon which the compression of matrix. Due to this they effectively seize free vacancies and it results in a decrease of a rate of introduction of secondary radiation defects vacancy-type (including E-centres and, therefore, factors ɄW). Under our judgement, difference of factors Ʉt

50

V.I. Talanin and I.E. Talanin

from a sample to sample (their sizes was 1,5u2u13 mm3) is a corollary of striated distribution of grown-in microdefects on crystals volume. The intensive grab of vacancies results in increasing of life-time of self-interstitials and, therefore, increasing of a rate of introduction of interstitial-type defects. Really, the experiment has shown that simultaneously with a decrease of Kȿ was observed incresing of a introduction rate of complexes Ci-Cs (Kɋ). These complexes poses a level ȿ2 = ȿɫ – 0.17 eV. In difference in crystals of I groups happened a minor decrease of Kȿ and Kɋ [61]. It can mean that in crystals of I groups are present the drains for vacancies and for self-interstitials.

2.5

Transformation of Grown-in Microdefects

During production of semiconducting devices the initial monocrystals or the silicon structures are subjected to sequential technological operations. Their thermal processing happens which results in origin of additional defects and also to transformation of initial defects. Therefore, from our view point, it was necessary to establish the correlation of grown-in microdefects in initial substrates both defects of epitaxy structures and mechanisms with the help of which the initial microdefects are transformed to defects of actual area of structures. We investigated semiconducting structures obtained by a method conversion epitaxy. The essence of a method consists in a sedimentation on high-resistance (as a rule dislocation-free) silicon substrate of high-doped (defective) epitaxy stratum with consequent two-sided chemical-machining processing of wafers up to a necessary thickness. In a conversion structure a working (instrument) stratum is the substrate and basic (contact) - epitaxy film. It is necessary to mark, that long effect of high temperatures and origin of thermal-mechanical stresses stipulate a sharp decrease of structural perfection of a substrate and the denseness of dislocations in her reaches of values ~ 103…106 ɫɦ-2. Therefore, greatest interest for us is study of the factors which determine formation of dislocations in a substrate in epitaxy process. For researches we used substrates made from FZ-Si grown with rates 2.0; 3.0; 6.0; 8.0 mm/min. A part of substrates subjected to heat treatment in hydrogen atmosphere at Ɍ # 1453 K within 3 hours. Such imitation of a temperature mode of epitaxy growth allows precisely to reveal transformation of an initial defective structure of a substrate. On other part of substrates in separate process were formed the epitaxial stratums. TEM-research of thermal-treatment substrates on base of monocrystals obtained with rates 2…8 mm/min reveal defects of black-white contrast in dynamic conditions. Under our judgement, it testifies to continuously going process of defect formation at thermal effect on crystal. In result TEM-researches of thermal-treatment substrates with initial D-microdefects (at V = 6 mm/min) are fixed increasing of size of microdefects up to 10…14 nm and also availability of defects with force contrast of a complicated type (Fig. 8a). The concentration of such large microdefects at centre of crystal is unsignificantly reduced with increase of crystal growth rate. In substrates from monocrystals obtained at V = 8 mm/min the dislocations in a central part of substrates practically are absent. The processes of direct epitaxial growth and thermal imitation of epitaxy result in formation at centre of a wafer of the 600-s dislocations with a Burgers vector b 1 / 2[110] are in planes {111} (Fig. 8b).

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

51

Fig.8. Defects in substrata after epitaxial growth: a) FZ-Si (V = 6 mm/min), TEM, light field, g ( 220) ; b) FZ-Si (V = 2 mm/min), TEM, light field, g ( 220) .

The processes of transformation of initial grown-in microdefects and defects which arise during epitaxial growth are similar. The main mechanism of formation of dislocations in a working stratum of conversion structures is stipulated by process of transformation of initial grown-in microdefects. We see the following sequence of stages of interstitial microdefects transformation: D-microdefects o B-microdefects o A-microdefects. The growth of Amicrodefects stimulates formation of dislocations. Hence, in process of epitaxial growth the initial defective structure essentially varies. The growth of A-microdefects results in formation of dislocations in volume of crystals. At the same time B-microdefects are transformed in dislocation loops (A-microdefects) with consequent formation of dislocations. D-microdefects grow and are transformed in Bmicrodefects. The formation of dislocations in samples with D-microdefects is hampered as the process of transformation is limited by a diffusion of intrinsic point defects and uncontrollable impurities. Obtained during epitaxial experiments the datas about transformation of small-sized microdefects in larger allow to assume that D-microdefects are an initial stage of formation A-microdefects, i.e. interstitial dislocation loops. For clarification of this position we have conducted experiments on heat treatment of crystals [4, 16, 40]. Two monocrystals FZ-Si were obtained: one from them grown at V = 6 mm/min and in the certain instant the growth stayed during 60 mines and other crystal grown at V = 6 mm/min and then was cutted on four parts (cylinders). Each from four parts was bisected on a plane {112}. One half of each cylinder was subjected to etching for revealing distribution of microdefects and appropriate second halves was subjected thermal processing during 60 mines in vacuum at temperatures 1073, 1173, 1273, 1373 K accordingly. During a stop of growth in crystal all known types of interstitial microdefects were formed. Each from these types is characteristic usually of crystals obtained at the certain growth rates (Fig.9a). Here they are present at one crystal and this fact allows to explain their emerging only by thermal processing. The stop of crystal growth can be considered as a modification of actual temperature conditions of crystal growth. The crystall in points located below place of a stop during the certain time receives additional processing at various temperatures.

52

V.I. Talanin and I.E. Talanin

Fig.9. Defects in FZ-Si crystal with intermediate stop of growth in the course 60 min: a) selective etching, plane (112); b) A-microdefects, form, TEM,

g

g

(02 2) , light field, s

0 ; c) defects of complicated

( 2 20) , light field, s ! 0 .

TEM-research of crystal areas with A-microdefects (near to a place of a stop of growth) is shown availability of interstitial dislocation loops with size 2…20 nm. The dislocation line of loops hardly decored by background impurities because of additional heat treatment (Fig. 9b). In the field of crystal with (A + B)-microdefects are detected defects of complicated form (Fig. 9c). Such defects represent the intermediate form between A-microdefects and Bmicrodefects. In the field of crystal with B-microdefects the interstitial-type defects with sizes 20…60 nm emerge. In the field of crystal with D-microdefects the interstitial-type defects with black-white contrast with sizes up to 15 nm are detected. TEM-research of the second crystal shown that the heat treatment is accompanied by redistribution of defects and increasing of their sizes. Heat treatment at 1173 K increases the sizes of D-microdefects up to 10…12 nm. In crystals treated at 1373 K were observed defects such as "sockets" with force contrast and sizes 50…100 nm (Fig. 10a).

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

53

Fig.10. Defects in crystals after of thermal treatment: a) FZ-Si (V = 6 mm/min, T =1373 K, t = 60 min, vacuum), TEM, hydrogen), TEM,

g g

( 2 20) ,

light field; b) FZ-Si (V = 6 mm/min, T = 1373 K, t = 180 min,

( 2 20) , light field; c) defects in the ring D(C)-microdefects CZ-Si (V = 2.5

mm/min, T = 1373 K, t = 600 min, vacuum), TEM,

g

(22 0) , light field; d) defects inside the ring

D(C)-microdefects CZ-Si (V = 2.5 mm/min, T = 1373 K, t = 600 min, vacuum), TEM,

g

(22 0) ,

light field;

Then the FZ-Si grown with various rates were investigated (2.0; 3.0; 6.0; 8.0 mm/min) and subjected to heat treatment within three hours at the temperature of ~ 1373 K in atmosphere of hydrogen. After heat treatment everywhere there are defects of black-white contrast in dynamic conditions. In a comparison with grown-in D-microdefects the size of defects in treatment crystals is increased up to 12…15 nm. Furthermore, the defects with force contrast as "sockets" (Fig. 10a) or more complicated form (Fig. 10b) with sizes up to 300…700 nm will be formed. Thus, during thermal processings the sizes of defects are increased and defects with force contrast are emerged. It testifies to a continuity of defect formation process and transformation of initial microdefects at thermal effect on crystal. The defects with force contrast can be sources of interstitial dislocation loops. It is necessary to mark, that the same defects were revealed in FZ-Si crystals (V = 3 mm/min) and were interpreted as Bmicrodefects [29]. From our view point, these defects are an intermediate stage of development of defects between B- and A-microdefects.

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V.I. Talanin and I.E. Talanin

Processing procedures lead to the transformation of the grown-in microdefects. As a result, secondary defects are formed. The transformation of the grown-in microdefects in course of processing (e.g. thermal treatment or ion-implantation) provides information about the relaxation process of the supersaturated solid solution of point defects. Single crystal of CZ-Si, 50 mm in diameter, grown at V = 2.5 mm/min, was subjected to vacuum thermal treatment at 1373 K for 600 min. In the region of the OSF-ring (in non-processed CZ-Si it was the ring of D-microdefects), using TEM, we identified black-white contrast defects with sizes of 10 to 20 nm and defects having a strong strain contrast (precipitates) with sizes of 300 to 600 nm (Fig.10c). Inside OSF-ring the complex-shaped defects we are observed with sizes of 700 to 900 nm (Fig.10d). Further, two phosphorus-doped CZ-Si crystals of 80 mm in diameter were grown at growth rates V = 0.6 mm/min (U = 18…30 :cm) and V = 2 mm/min (U = 7…10 :cm). The crystals were subjected to thermal treatment in the growing vessel at 923 K for 60 min in the ambient air medium. We studied the distribution of microdefects in three areas located at the "top", "middle" and "bottom" of the crystals before and after thermal treatment. Table 4 summarizes the measurement results of defect density and carbon and oxygen concentrations. Table 4 – Density of microdefects and concentration of background impurities in crystals before and after thermal treatment (Ɍ = 923 K, t = 60 min) Growth rate, mm/min

2.0 ("top") 2.0 ("middle") 2.0 ("bottom") 0.6 ("top") 0.6 ("middle") 0.6 ("bottom")

Oxygen concentration, cm-3

Carbon concentration, cm-3

centre

rim

centre

rim

3.7˜1017 3.4˜1017 3˜1017 3.8˜1017 3.5˜1017 3.7˜1017

3.2˜1017 3˜1017 2.8˜1017 1.9˜1017 2.9˜1017 1.8˜1017

4.8˜1016 7.9˜1016 1.5˜1017 4.6˜1016 5.9˜1016 8.6˜1016

5˜1016 7.6˜1016 1.6˜1017 4.5˜1016 5.3˜1016 8.9˜1016

Microdefects density in plane (111), cm-2 before thermal processing centre rim 2.3˜104 2.8˜104 2.8˜104 2.7˜104 4 2.3˜10 2.9˜104 4 2.6˜10 1.9˜104 4 1.8˜10 2.8˜104 4 2.6˜10 2.8˜104

after thermal processing centre rim 3.9˜104 4.9˜104 4˜104 3.2˜104 5 2.5˜10 4˜104 4 4.5˜10 1.1˜105 4 4.4˜10 5˜104 5 3˜10 9.6˜104

Carbon concentration increases towards the bottom part of the crystal. After thermal treatment the etching pit sizes become smaller and the swirl distribution in the bottom part of the crystal disappears. In CZ-Si crystals grown at V = 0.6 mm/min we identified big etching pits (~ 103 ɫm-2) after thermal treatment, which were absent in crystals grown at V = 2 mm/min. Consequently, the view of microdefects distribution changes due to thermal treatment: the concentration of microdefects and their size increase steeply and the swirl distribution disappears in the bottom part of the crystal where carbon concentration is higher. CZ-Si initial defect structure change due to ion-implantation was the subject of second series of experiments. CZ-Si crystal had the grown-in microdefects of a certain type. CZ-Si crystal of 50 mm in diameter had striated distribution of A- and B-microdefects in the region with a growth rate V = 0.5 mm/min; striated distribution of B-microdefects in the region with a growth rate V = 1 mm/min. In the region with a growth rate V = 2.5 mm/min we used the area with both interstitial-type and vacancy-type microdefects.

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

55

It needs to be noted that first two crystal growth regions indicate no substantial difference (crystals with A- and B-microdefects and crystals with B-microdefects), so we will denote them as the crystal with (A+B)-microdefects. Let us denote the crystal growth region with V = 2.5 mm/min as the crystal with (I+V)-microdefects. We may compile experimental results obtained by TEM observation into three groups. The first group results cover samples not subjected to annealing after ion-implantation (I); the second group covers the samples subjected to annealing at 923 K (II); the third group covers the samples subjected to annealing at 1123 K (III). The study of group (I) samples with (A+B)-microdefects revealed the following (Fig.11a): a) small-scale defects with sizes ranging 6 to 20 nm at concentration of 5u(108…109) cm-3; b) precipitates of regular (square-shaped, rhomb-shaped) and irregular shape with sizes ranging 30 to 100 nm; c) dislocation loops with sizes ranging 30 to 150 nm. The concentration of precipitates amounted to 3u(108…109) cm-3 and the concentration of dislocation loops was 4u(108…109) cm-3. Imperfections of the similar type were found in samples with (I+V)-microdefects, but their sizes were two-three times smaller. At the same time, the concentration of precipitates and concentration of dislocation loops were one order of magnitude smaller than those in the samples with (A+B)-microdefects.

Fig.11. Defects in CZ-Si after of ion implantation: a) arsenic implantation without annealing, TEM, dark field,

g

g

( 2 20) ;

( 2 20) ;

b) arsenic implantation and annealing at 923 K, TEM, dark field,

c) antimony implantation and annealing at 923 K, TEM, dark field,

arsenic implantation and annealing at 1123 K, TEM, dark field,

g

( 2 20) .

g

( 2 20) ;

d)

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V.I. Talanin and I.E. Talanin

The study of group (II) samples with (A+B)-microdefects revealed the following (Fig.11b,c): a) b) c) d) e)

small-scale defects with sizes ranging 4 to 20 nm; precipitates with sizes ranging 30 to 100 nm; dislocation loops with sizes 20 to 40 nm; straight dislocation segments being angled to surface (111); hexagonal formations with dimensions 160u80 nm to 600u240 nm.

Group (II) samples contain higher concentration of small-scale defects, precipitates and dislocation loops by one to two orders of magnitude as compared to those of group (I). The concentrations of dislocations and hexagonal formations are ~ 107 cm-3. Apparently, these formations represent hexagonal stacking faults [38]. In group (II) samples with (I+V)microdefects the concentrations of all the imperfections observed were smaller by one to two orders of magnitude, while the straight dislocation segments were not found. The study of group (III) samples with (A+B)-microdefects revealed the following (Fig.11d): a) b) c) d) e)

small-scale defects with sizes ranging 4 to 20 nm; precipitates with sizes ranging 30 to 130 nm; dislocation loops with sizes ranging 40 to 100 nm; straight dislocation segments; hexagonal formations.

The concentration of small-scale defects, precipitates and dislocation loops in samples of group (III) decreases by one to two orders of magnitude as compared to samples of group (II). Precipitates often occur as plate-like formations in the shape of square, rhombus or rectangle. In samples of group (III) with (I+V)-microdefects the concentrations of all the imperfections observed were one to two orders of magnitude smaller, while the straight dislocation segments were not found. Obtained experimental results analysis shows that in course of ion-implantation and further technological annealing, CZ-Si grown-in microdefects growth and transformation occur, following by relaxation of the supersaturated solid solution of point defects. The structural imperfections transformation is as follows: grown-in microdefects + point defects o dislocation loops ҙҏprecipitates o plate-like formations + dislocations. Processing (ion-implantation, thermal treatment) leads to generating the supersaturated solid solution of point defects. The initial grown-in microdefects facilitate the subsequent decomposing of this solution. This process leads to the transformation of the initial microdefects and the appearance of new imperfections. Low-temperature annealing of implanted CZ-Si at 923 K induces dislocations and hexagonal stacking faults. However, such defects have not been found in implanted CZ-Si not subjected to thermal treatment. Seemingly, low-temperature annealing entails a process when some impurity atoms transit from lattice sites into interstitial ones [62]. The decrease in the defects concentration during annealing at 1123 K may be explained both by the decomposition of the oversaturated ‘silicon-impurity’ solid solution and by the diffusion process of the intrinsic point defects.

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

57

The prismatic punch out mechanism induces the formation of dislocation loops, while their growth is connected with self-interstitials emitted by the growing precipitates. Ion-implantation to CZ-Si obtained by vacancy-interstitial-type growth indicates the general direction of the defect formation mechanism. The supersaturated solid solution of point defects is forming in course of implantation and consists of arsenic atoms, native point defects and background impurity atoms of carbon and oxygen. Other researchers in [63] point to that in such a case the SiAs complex generation is more energy favorable, while the VAs2 complex generation is not proved experimentally [62]. SiAs complex generation is accompanied by the process when free vacancies are absorbed by the interstitial-type microdefects. Thus, both interstitial-type microdefects grow emitting self-interstitial atoms of silicon that results in their excess number. Self-interstitials interact with the vacancy-type microdefects, which during transformation change their sign of imperfection from the vacancy-type to the interstitial-type. Therefore, the mechanisms and processes of formation, growth and transformation of grown-in microdefects in FZ-Si and CZ-Si crystals are identical. During growth of crystals the continuous process of transformation of an initial defective structure happens.

3

Conclusion

3.1

Formation Mechanism of the Grown-in Microdefects

From our point of view the experiments with hyper pure FZ-Si are of especial importance. It was these experiments that allowed us to suggest the heterogeneous formation mechanism of the grown-in microdefects [4]. Its basic principles can be outlined as follows: í í

í

recombination of intrinsic point defects at crystallization temperature is hindered because of recombination barrier; background impurities of oxygen and carbon participate in the process of defect formation as nucleation centers, and consequently participate in the processes of further growth and transformation of grown-in microdefects; cooling-induced decomposition of the oversaturated solid solution of point defects in silicon follows two mechanisms: vacancy-type and interstitial-type.

For the vacancy mechanism theoretically only vacancy aggregation and joint vacancyimpurity aggregation are possible. Vacancy-impurity aggregation begins earlier than a vacancy aggregation. Interstitial atoms of oxygen are very mobile, and therefore the formation of complexes is stimulated by leaving interstitial oxygen in positions of substitution Os: Oi + VSi o Os o 2Os + 3Os +…+ nOs. At lower temperature, Os can be formation centers of microprecipitates of oxygen. When microprecipitates are formed, there is a surplus of volume and one vacancy will be consumed by a growing precipitate for each two oxygen atoms precipitated. The absorption of vacancies and impurities by growing microdefects results in a decreased concentration of vacancies in

58

V.I. Talanin and I.E. Talanin

comparison with oxygen concentration. As a result precipitates begin to absorb oxygen without participation of vacancies, their sizes are increased and then the type of a strain around them varies from vacancy (tensile) to interstitial (compressive). The full transition boundary can be determined from the relation V/G. Thus, the parameter Ccrit does not describe a change in condition of growth mode (interstitial or vacancy). This parameter describes conditions of the vanishing (emerging) of microdefects of a vacancy type as a result of diffusion and interaction of point defects during cooling of the crystal. The centers of nucleation in a base of interstitial atoms of oxygen exist also for the interstitial mechanism. However, here a catalytic role is played by carbon atoms. The oversaturation of interstitial atoms of silicon results in the appearance of complexes [CsISi]: Cs + ISi l [CsISi]. The decrease of the critical radius [CsISi] nuclei and the acceleration of a diffusion Cs occur here. Thus, agglomerates [CsISi] are formed. Furthermore, during supersaturation of ISi co-precipitation of Oi and Cs may occur. Thus, for the formation of B-microdefects: ISi + Cs o [CI] + Oi o ȼ-microdefects. The growth of interstitial microdefects results in a significant decrease of the concentration of interstitial atoms of silicon. It creates conditions for precipitations of impurities. In this case the formation of particles of impurity phase is accompanied by the generation of self-interstitial atoms in positions between knots of the lattice. Thus two types of interstitial microdefects are formed: as interstitial congestion (drains for interstitial atoms of silicon) and as impurity precipitates (sources of these atoms). Therefore, the vacancy-oxygen aggregation occurs in the vacancy-interstitial mode of crystal growth when the oversaturated solid-state solution of vacancies is decomposed and the vacancy-carbon aggregation occurs when the oversaturated solid-state solution of intrinsic silicon interstitials is decomposed. At a certain critical value of V/G ratio both independent mechanisms (vacancy-type and interstitial-type) result in generation of D-microdefects. These D-microdefects are uniform distributed small-size ȼ-microdefects, which are further transformed into Ⱥ-microdefects. At the interstitial-type crystal growth mode the growth of precipitates facilitate the oversaturation in self-interstitials and induce the homogeneous nucleation of interstitial clusters (interstitial-type dislocation loops, i.e. A-microdefects). In general, A-microdefects are formed during B-microdefect transformation both through the mechanism of prismatic extruding or through the condensation of silicon intrinsic interstitials. For vacancy-type mechanism: 1) nOi + VSi o n(VO2) o vacancy-type microdefects. 2) n(VO2) + Oi +…+ nOi o n[(VnOn) + ISi] o D-microdefects. For interstitial-type mechanism: 1) ɋs + ISi o (CsISi) o D-microdefects. 2) (CsISi) + Oi o n[(CsISi) + Oi] o B-microdefects.

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

59

3) B-microdefects + ISi o A-microdefects. Thus, follows that regardless of the growth method of dislocation-free silicon singlecrystals, the interstitial-type and vacancy-type microdefects are arisen during the crystals cooling below the temperature of crystallization, and then transformed into interstitial-type microdefects. Further transformation of interstitial-type microdefects follows the scheme: Dmicrodefects o ȼ-microdefects o Ⱥ-microdefects. When the oversaturated solid-state solution of intrinsic point defects is decomposed the background oxygen and carbon impurities present themselves as nucleation centers of grown-in microdefects and participate in their further growth and transformation. We consider the suggested mechanism as the “core” of formation mechanism of defects. To change the “core” (i.e. to control decomposition of the oversaturated solid solutions of point defects) is possible as follows: -

to vary thermal growth conditions (growth rate, temperature gradients at the phase boundary, cooling rate); to adjust the condition of the native point defects ensemble in the crystal by employing various external factors (doping, radiation, etc.); to subject the grown single crystals to different kinds of thermal processing.

The heterogeneous mechanism of grown-in microdefects formation describes in the whole the defect structure of small-scale FZ-Si and CZ-Si crystals. From our viewpoint this heterogeneous mechanism is works in case of large-scale crystals FZ-Si and CZ-Si. Although new type of grown-in microdefects, namely vacancy microvoids, appear in such crystals. We believe the vacancy microvoids are as secondary defects as A-microdefects. They appear due to change in growth conditions for large-scale FZ-Si and CZ-Si crystals.

3.2

Grown-in Microdefects in Large-Diameter Silicon Crystals

In small-scale crystals under changing thermal growth conditions the grown-in microdefects of any type except for microvoids are appeared. Adjusting the thermal growth conditions in large-scale crystals shows that dislocation-free growth is available within the limited range of growth rate. From Fig.12 one can see that above is existence conditions for ring of D(C)microdefects (often called as ring OSF-defects), for A-microdefects outside the ring of D(C)microdefects and for (I+V)-microdefects inside the ring of D(C)-microdefects. Recently the authors [64] have used the X-ray diffuse scattering method to detect both interstitial-type and vacancy-type defects coexisting at CZ-Si vacancy-interstitial-type growth. This experimental results reveal that in large-scale CZ-Si the cooling-induced decomposition of the oversaturated solid solution of point defects follows two mechanisms: vacancy-type and interstitial-type. Then why do microvoids appear in large-scale crystals, but not in small-scale crystals?

60

V.I. Talanin and I.E. Talanin

Fig.12. Schematic large-diameter silicon crystals, plane (112).

It was defined that microvoids are forming and growing at the temperature range ~ 1373 to 1343 K and the oxide film on their side-walls is growing at the temperature range a 1323…1173 K [65-67]. Here, microvoids have been forming in the large-diameter crystals under conditions of vacancy-interstitial-type growth, which is characterized by relatively fast growth rates, lesser curvature of crystallization front and a small temperature gradient. Under such growth conditions, at a certain cooling stage as thermal conditions change it is quite possible that the pure vacancy agglomeration will prevail over oxygen-vacancy one. Vacancy agglomeration will result in forming single or dual-type microvoids and their thermodynamic equilibrium shape will be octahedral [14]. As is well-known, single microvoids are formed under a relatively rapid cooling rate and a small oxygen concentration, and dual-type microvoids are formed under a relatively slow cooling rate and a large oxygen concentration while the oxide film is growing on side-walls of microvoids and hinders further growth of dual microvoids [67]. As established by [65], short-time thermal processing (during from 15 minutes at Ɍ = 1373 K) induces microvoids to diminish their size steeply and to change the structure and, what is more important, precipitates are revealed. It is determined, that small voids are first to diminish and disappear and then large voids of dual microvoids [65]. Thorough observations make it clear that the process of microvoid size diminishing begins in the area between two voids [67]. Hence, the process of the microvoid formation runs at the expense of the process of vacancy agglomeration on the nucleation centers during crystal cooling. Nucleation centers may be either agglomerates of oxygen-vacancy type or agglomerates of carbon-interstitial type that are formed at higher temperatures. Under certain thermal growth conditions of largescale silicon crystals the vacancy oversaturation becomes a prevailing factor to precipitate vacancies on oxygen-vacancy and carbon-interstitial aggregates. Above assertion is verified by the experimental fact that there is an oxygen in certain microvoids and a carbon in other microvoids [68]. Paper [67] is a direct support to the heterogeneous formation mechanism of grown-in microdefects in large-scale crystals [4]. Therefore, we may establish a fact that octahedral microvoids and interstitial-type A-microdefects are secondary defects.

3.3

Physical Classification of the Grown-in Microdefects

Silicon single crystals contain a noticeable number of growth impurities (doping or background) that engender the complex systems like “semiconductor-impurity” to be created in crystals. Under certain conditions (temperature, impurity concentration) such systems become the decomposing solid solutions. As their intrinsic point defects not having drains, the impurities are actively involved in the decomposition of solid solution of the point

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61

defects. As is seen from experimental results of our study the main and determining factor when the decomposition of solid solution of the point defects in semiconductor silicon concerned is the formation of primary defects either in the form of oxygen-vacancy aggregates (identified here as SiO2 microprecipitates) or carbon-interstitial aggregates (identified here as SiC micro-precipitates). Heterogeneous nature of defects nucleation determines in substance the further defect formation mechanism in semiconductor silicon. As effective drains in the form of dislocations are not available, the decomposition of solid solution of the point defects entails the intensive formation of structure from secondary strains, which are agglomerates of intrinsic point defects. Nature of secondary defects is established by low equilibrium density of the intrinsic point defects as well as by the value and sign of the misfit volume, which accompany the formation of new phase. Consequently, the decomposition of solid solution of the point defects is first and foremost distinguished for the generation of secondary defects when the new phase particle is growing. The generation is defined by the atom volume difference between the matrix and precipitate. At that, the secondary defects are mostly localized as agglomerates close to precipitates. As our study of hyper pure CZ-Si and FZ-Si crystals shows the secondary defects revealed in them are interstitial-type Ⱥ-microdefects (interstitial dislocation loops) and vacancy-type octahedral microvoids. Consequently, the lattice imperfection can be defined by not only new phase particles having insignificant total volume due to low impurity solubility in silicon, but by secondary defects. They diffuse to a distance of few micrometers from the new phase particles that generated them, spread over the total volume of crystal and make a problem for its use in future. Primary and secondary grown-in microdefects existing in silicon single crystals gives us an opportunity to introduce a new classification. Such a classification must include all known grown-in microdefects and proceed from the kinematics of defect formation which is defined by the heterogeneous formation mechanism of the microdefects. From our point of view, such classification may avoid discrepancy in letter designations and concepts that constitute a problem in understanding the grown-in microdefects in dislocation-free silicon, which originates from existing practice to assign a letter designation to a microdefect of a certain type. At the same time a classification must reveal the physical nature of defect formation and be simple and coherent. So, on the basis of heterogeneous formation mechanism of the grown-in microdefects and introduced concepts of primary and secondary grown-in microdefects we may develop a new physical classification (Fig.13). It follows from the assumption that the primary oxygenvacancy and carbon-interstitial agglomerates formed on impurity centers are the motive force of defect formation. Under certain thermal conditions of crystal growth the process of defect formation entails the generation of secondary defects (agglomerates of intrinsic point defects). In this case the oxygen-vacancy and carbon-interstitial agglomerates (B-, D- and I+Vmicrodefects) turn to be the primary grown-in microdefects and the agglomerates of intrinsic point defects turn to be the secondary grown-in microdefects (Ⱥ-microdefects and vacancy microvoids). To form some type of grown-in microdefects or other it depends on adjusting the thermal conditions of crystal growth. We think this classification is simple and reflects the physical nature of the defect formation mechanism in dislocation-free silicon single crystals. Fig.13 outlines the physical classification posed as described above.

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Fig.13. Schematic illustration (physical classification) of the grown-in microdefects based on the heterogeneous mechanism of their formation and transformation: I – interstitial-type agglomerates, V – vacancy-type agglomerates; C – carbon, O – oxygen, i – self-interstitials, v - vacancies

In addition to the physical classification, Fig.13 depicts the universal heterogeneous formation mechanism of the grown-in microdefects in semiconductor silicon crystals of different diameters. Recombination of intrinsic point defects at about crystallization temperature is hindered because of recombination barrier. Cooling-induced decomposition of the oversaturated solid solution of point defects in silicon follows two mechanisms: vacancytype and interstitial-type. Background impurities of oxygen and carbon are involved in the process of defect formation as nucleation centers, and consequently participate in the processes of further growth and transformation of the grown-in microdefects. As nucleation centers for oxygen-vacancy aggregates serve the areas of contraction close to oxygen interstitial atoms the redundant vacancies and other oxygen interstitial atoms are directed towards them. As nucleation centers for carbon-interstitial aggregates serve the areas of strain around of carbon substitutions, the redundant intrinsic interstitial atoms and oxygen interstitial atoms are directed towards them. Such agglomerates growth results in the formation of (I+V)- microdefects. The latter are primary microdefects, which are formed near the crystallization front. However, V-microdefects are not referred to microvoids. They are oxygen-vacancy agglomerates (SiO2 microprecipitates). Growth and transformation of (I+V)microdefects gives rise to formation of the secondary defects (A-microdefects) [16]. In real small-scale crystals the microvoids are not formed. Increasing the crystal diameter leads to an abrupt change of thermal growth conditions as compared to small-scale crystals. Adjusting thermal growth conditions as well as crystal doping allow controlling the formation mechanism and growth of vacancy-type and interstitial-type defects under conditions of vacancy-interstitial-type growth. This results in the defect size and shape change and give an advantage to vacancy agglomeration over oxygen-vacancy agglomeration. The process leads to the formation of the secondary defects, namely microvoids. Hence, there are secondary defects of two types in large-scale crystals (A-microdefects and microvoids). However, the basic principles (i.e. “core”) of the heterogeneous mechanism suggested for the grown-in microdefects formation in FZ-Si and CZ-Si remain unchanged.

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Above mechanism is alternative to assumptions of Voronkov while not denying the importance of V/G ratio and mathematical tool of Voronkov’s model. V/G ratio characterizes the conditions when vacancy microdefects appear (disappear). But non-critical approach to the Voronkov’s model leads to that the “elephants” (A-microdefects and microvoids) can hide the genuine cause and distort the physical nature of the defect formation in dislocation-free silicon single crystals.

3.4

Formation Mechanisms of the Secondary Grown-in Microdefects

By the formation mechanism the defects can be divided into two groups: strain-type and coagulation-type. To the strain-type secondary defects we can refer the dislocation loops. They are formed by the prismatic punching-out that is a rather common mechanism of defect generation, which activates under a large difference between the precipitate atomic volume and matrix atomic volume and is independent of its sign. To the coagulation-type secondary defects we can refer the defects of two types. The defects of first type in the form of complete interstitial dislocation loops appear by way of combining the redundant silicon interstitial atoms located near the precipitates into clusters predominantly in directions {111} and {110}. We can suggest that the coagulation mechanism of the secondary defects generation activates at relatively small strain levels near the precipitates when the value of elastic strain is insufficient to induce the shear dislocation loop. The motive force for such secondary defects to grow may be undersaturation with vacancies that gone to relieve the elastic strain near the precipitates. Contrary to above defects the motive force for secondary defects of other type is oversaturation with vacancies. The oversaturation results in generating the single and dualtype octahedral voids near the precipitates. Low growth rates for a crystal of certain diameter combined with a large curvature of crystallization front and a large axial temperature gradient are crucial parameters affecting the formation of interstitial dislocation loops (A-microdefects) by employing the strain and coagulation mechanisms of the secondary defects formation. At the same time high growth rates for a crystal of certain diameter combined with a small curvature of crystallization front and a small axial temperature gradient bring out to the formation of octahedral microvoids by employing the coagulation formation mechanism of the secondary defects. In view of that during further high-temperature processing the dislocation loops tend to continue to grow, the silicon crystals should be grown under vacancy-interstitial mode because the defect structure at this growth stage is very much controlled either by adjusting the thermal growth conditions or by doping with special dopant impurity (nitrogen, hydrogen) and additional thermal processing. So, as the formation of the microdefect of any type is connected with carbon and oxygen impurities, which are present in the crystal, and also with varying the crystal growth conditions, it is worthwhile to notice that the defect formation may be affected both by selecting the optimal thermal conditions of growth and by improving the quality of raw material for silicon single crystals. To conclude it should be denoted that the heterogeneous formation mechanism of the grown-in microdefects make it possible to explain the experimental results observed during the microdefect study of dislocation-free silicon single crystals, in particular, how the striated distribution of A- and B-microdefect is generated and suppressed, how impurities affect the nucleation and growth processes of interstitial and vacancy-type microdefects, and thermal

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growth conditions of the microdefects formation [69, 70]. It is arguable that such a mechanism reflects as complete as possible the processes that take place in dislocation-free silicon single crystals during the crystal growth and cooling. Results of numerous experiments prove this to be correct. The special importance of the heterogeneous mechanism of formation and transformation of grown-in microdefects consists in following: he allows to understand the defect formation processes in small-scale and large-scale crystals of FZ-Si and CZ-Si. On base of heterogeneous mechanism of grown-in microdefects formation it is possible to create a data base on defects in wafers of monocrystalline silicon. In a basis of the heterogeneous mechanism of grown-in microdefects formation there are processes of disintegration of solid solutions of intrinsic point defects on impurity centres. Therefore, this mechanism assumes the participation in defect formation process other impurities (for example, nitrogen, iron, dopant impurities etc.) and impurity centres.

4

Summary

1. It is established and proved experimentally the heterogeneous formation and transformation mechanism of the grown-in microdefects in dislocation-free silicon single crystals, which use completely new approaches: í

í

í í

concentrations of vacancies and intrinsic interstitial silicon atoms at the crystallization front near the melting point are comparable, recombination of intrinsic defects are hindered at high temperatures; the decomposition of the oversaturated solid-state solution of point defects during the silicon cooling below the crystallization temperature follows two independent mechanisms: vacancy-type and interstitial-type; the driving force of the defect formation is initial oxygen-vacancy agglomerates and carbon-interstitial agglomerates formed on impurities centers; the reigning feature of decomposition of the oversaturated solid-state solution of point defects is the generation of secondary defects (agglomerates of intrinsic point defects), which accompanies a new phase growth (the primary defects).

2. Depending on growth conditions (in particular V/G ratio) dislocation-free silicon monocrystals grow in vacancy-interstitial and interstitial modes of growth. 3. The technological effects result in a modification of volumetric distribution and transformation of grown-in microdefects. In particular, irrespective of a crystal growth method the transformation of interstitial microdefects happens under the following scheme: D-microdefects o B-microdefects o A-microdefects. 4. At a certain thermal growth conditions the aggregation of point defects under vacancyinterstitial-type or interstitial type growth mode in the course of crystal cooling may cause the secondary defects occurrence around primary oxygen-vacancy and carbon-interstitial aggregates, namely vacancy octahedral microvoids and interstitial-type dislocation loops, accordingly.

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5. The physical classification of grown-in microdefects based on the heterogeneous mechanism of grown-in microdefects formation in semiconductor silicon is proposed.

References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10]

[11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25]

Abe, T.; Samizo, T.; Marujama S. Jpn. J. Appl. Phys. 1966, vol, 5, p. 458. Kock de, A.J.R. J. Electrochem. Soc. 1971, vol, 118, p. 1851. Kock de, A.J.R.; Roksnoer, P.J.; Boonen, P.G.T. J. Cryst. Growth 1974, vol, 22, p. 311. Talanin, V.I.; Talanin, I.E.; Levinzon, D.I. Cryst. Res. & Technol. 2002, vol, 37, p. 983. Bernewitz, L.J.; Kolbesen, B.O.; Mayer, K.R.; Shuh, G.E. Appl. Phys. Lett. 1974, vol, 25, p. 277. Kolbesen, B.O.; Muhlbauer, A. Sol. State Electr. 1977, vol, 25, p. 1561. Foll, H.; Gosele, U.; Kolbesen, B.O. J. Cryst. Growth 1977, vol, 40, p. 90. Bourret, A.; Thibault-Desseaux, J.; Seidman, D.N. J. Appl. Phys. 1984, vol, 55, p. 825. Voronkov, V.V.; Milvidskii, M.G. Kristallographya 1988, Vol, 33, p. 471. Veselovskaya, N.V.; Sheikhet, E.G.; Neimark, K.N.; Falkevich, E.S. In Rost i legirovanie polyprovodnikovych kristallov i plenok; Ed. Alexandrov, L.N.; (Nauka: Novosibirsk, Russia), 1977; Vol. 2, pp. 284-287. Kock de, A.J.R.; Stacy, W.T.; Wijgert van de, W.M. Appl. Phys. Lett. 1979, vol, 34, p. 611. Kock de, A.J.R.; Wijgert van de, W.M. J. Cryst. Growth 1980, Vol, 49, p. 718. Roksnoer, P.J.; Boom van den, M.M.B. J. Cryst. Growth 1981, vol, 53, p. 563. Voronkov, V.V. J. Cryst. Growth 1982, vol, 59, p. 625. Sitnikova, A.A.; Sorokin, L.M.; Talanin, I.E.; Sheikhet, E.G.; Falkevich, E.S. Phys. Stat. Sol. (a). 1985, vol, 90, p. K31. Talanin, V.I.; Talanin, I.E.; Levinzon, D.I. Semicond. Sci. & Technol. 2002, vol, 17, p. 104. Shimizu, H.; Munakata, C.; Honma, N.; Aoki S.; Kosaka, Y. Jpn. J. Appl. Phys. 1992, vol, 31, p. 1817. Harada, K.; Tanaka, H.; Watanabe T.; Furuya, H. Jpn. J. Appl. Phys. 1998, vol, 37, p. 3194. Sadamitsu, S.; Umeno, S.; Koike, Y.; Hourai, M.; Sumita S.; Shigematsu, T. Jpn. J. Appl. Phys. 1993, vol, 32, p. 3675. Ammon von, W.; Dornberger E.; Hansson, P.O. J. Cryst. Growth 1999, vol, 198-199, p. 390. Furukawa, J.; Tanaka, H.; Nakada, Y.; Ono N.; Shiraki, S. J. Cryst. Growth 2000, vol, 210, p. 26. Puzanov N.I.; Eidenzon, A.M. J. Cryst. Growth 1994, vol, 137, p. 642. Umeno, S.; Yanase, Y.; Hourai, M.; Sano, M.; Shida Y.; Tsuya, H. Jpn. J. Appl. Phys. 1999, vol, 38, p. 5725. Umeno, S.; Okui, M.; Hourai, M.; Sano M.; Tsuya, H. Jpn. J. Appl. Phys. 1997, vol, 36, p. L591. Kato, M.; Yoshida, T.; Ikeda Y.; Kitagawara, Y. Jpn. J. Appl. Phys. 1996, vol, 35, p. 5597.

66

V.I. Talanin and I.E. Talanin

[26] Nishimura, M.; Yoshino, S.; Motoura, H.; Shimura, S.; Mchedlidze T.; Hikone, T. J. Electrochem. Soc. 1996, vol, 143, p. L243. [27] Voronkov V.V.; Falster, R. J. Cryst. Growth 1998, vol, 194, p. 76. [28] Voronkov V.V.; Falster, R. J. Cryst. Growth 1999, vol, 198-199, p. 399. [29] Petroff P.M.; Kock de, A.J.R. J. Cryst. Growth 1975, vol, 30, p. 117. [30] Chikawa J.; Shirai, S. J. Cryst. Growth 1977, vol, 39, p. 328. [31] Vechten van, J.A. Phys. Rev. B 1978, vol, 17, p. 3197. [32] Hu, S.M. J. Vac. Sci. and Technol. 1977, vol, 14, p. 17. [33] Sirtl, E. In Semiconductor silicon; Ed. Huff, R.; Burgess, R.R.; (Electrochem. Soc.: Princeton), 1977; pp. 4-17. [34] Voronkov V.V.; Falster, R. J. Electrochem. Soc. 2002, vol, 149, p. G167. [35] Pasemann, M.; Werner, P. Phys. Stat. Sol. (a) 1979, vol, 54, p. 179. [36] Pasemann, M.; Werner, P. Phys. Stat. Sol. (a) 1980, vol, 58, p. K1. [37] Okui, M.; Nishimoto, M. J. Cryst. Growth 2002, vol, 237–239, p. 1651. [38] Ravi, K.V.; Varker, C.J. J.Appl. Phys. 1974, vol, 45, p. 272. [39] Neimark, K.N.; Sakharov, B.A.; Chulitskii, B.F.; Osovskii, M.I. In Kremnii i Germanii; Eds: Falkevich, E.S.; Levinzon, D.I.; (Metallurgia: Moskow, Russia), 1970; Vol. 2, pp. 32-37. [40] Talanin, V.I.; Talanin, I.E. Phys. Stat. Sol. (a) 2003, vol, 200, p. 297. [41] Wilkens, M.; Foll, H. Phys. Stat. Sol. (a) 1978, vol, 49, p. 555. [42] Mitchell, J.B.; Bell, W.L. Acta Met. 1976, vol, 24, p. 147. [43] Seeger, A.; Frank, W.; Gosele, U. In Radiation effects in semiconductors; Eds: Urli, N.B.; Corbett, J.W.; Conference series N 46; (Inst. of Phys.: Bristol, London), 1979; pp. 148-157. [44] Gosele, U.; Frank, W.; Seeger, A. J. Appl. Phys. 1980, vol, 23, p. 361. [45] Gosele, U.; Frank, W.; Seeger, A. Solid State Commun. 1983, vol, 45, p. 31. [46] Dzelme, J.; Ertsinsh, I.; Zapol, B.; Misiuk, A. Phys. Stat. Sol. (a) 1999, vol, 171, p. 197. [47] Fedina, L.; Gutakovskii, A.; Aseev, A.; Landujt van, J.; Vanhellemont, J. Phys. Stat. Sol. (a) 1999, vol, 171, p. 147. [48] Fedina, L.; Gutakovskii, A.; Aseev, A. Cryst. Res. & Technol. 2000, vol, 35, p. 775. [49] Tognato, R. Phys. Stat. Sol. (a) 1986, vol, 98, p. K133. [50] Pizzini, S. Phys. Stat. Sol. (a) 1999, vol, 171, p. 123. [51] Katerbau, K.H. Phys. Stat. Sol. (a) 1976, vol, 38, p. 463. [52] Ohr, S.M. Phys. Stat. Sol. (a) 1976, vol, 38, p. 553. [53] Sitnikova, A.A.; Sorokin L.M.; Sheikhet, E.G. Fizika Tverdogo Tela 1987, vol, 29, p 2623. [54] Tan, T.Y.; Tice, W.K. Phil. Mag. 1976, vol, 34, p. 615. [55] Bender, H. Phys. Stat. Sol. (a) 1984, vol, 86, p. 245. [56] Matsushita, Y.; Kishino, S.; Kanamori, M. Jpn. J. Appl. Phys. 1980, vol, 19, p. L101. [57] Foll, H.; Kolbesen, B.O. J. Appl. Phys. 1975, vol, 8, p. 319. [58] Sitnikova, A.A.; Sorokin, L.M.; Talanin, I.E.; Malyshev, K.L.; Sheikhet, E.G.; Falkevich, E.S. Fizika Tverdogo Tela 1986, vol, 28, p 1829. [59] Foll, H.; Wilkens, M. Phys. Stat. Sol. (a) 1975, vol, 31, p. 519. [60] Iida, S.; Aoki, Y.; Sugita, Y.; Abe, T.; Kawata, H. Jpn. J. Appl. Phys. 2000, vol, 39, p. 6130.

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[61] Kolkovskii, I.I.; Latyshenko, V.F.; Sheikhet, E.G.; Shusha, V.V. Fizika i technika polyprovodnikov 1986, vol, 21, p. 1821. [62] Popov, V.P.; Dvurechenskii, A.V.; Kashnikov, B.P.; Popov, A.I. Phys. Stat. Sol. (a) 1986, vol, 94, p. 569. [63] Terrasi, A.; Rimini, E.; Raineri, V. Appl. Phys. Lett. 1998, vol, 73, p. 2633. [64] Byblik, V.T.; Zotov, N.M. Kristallographya 1997, vol, 42, p. 1103. [65] Itsumi, M. J. Cryst. Growth 2002, vol, 237-239, p. 1773. [66] Yanase, Y.; Nishihata, H.; Ochiai, T.; Tsuya, H. Jpn. J. Appl. Phys. 1998, vol, 37, p. 1. [67] Ueki, T.; Itsumi, M.; Takeda, T.; Yoshida, K.; Takaoka, A.; Nakajima, S. Jpn. J. Appl. Phys. 1998, vol, 37, p. L771. [68] Ueki, T.; Itsumi, M.; Takeda, T. Jpn. J. Appl. Phys. 1999, vol, 38, p. 5695. [69] Talanin, V.I.; Talanin, I.E.; Levinzon, D.I. Crystallography Reports 2004, vol, 49, p. 188. [70] Talanin,V.I.; Talanin, I.E. Defect & Diffusion Forum 2004, vol, 230-232, p.177.

In: New Research on Semiconductors Editor: Thomas B. Elliot, pp. 69-94

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

Chapter 3

LASER-INDUCED PHASE TRANSFORMATION IN NANOCRYSTALLINE SILICON THIN FILMS R. H. Buitrago1, 2* and S. B. Concari1** 1

Departamento de Física, Facultad de Ingeniería Química (UNL), Stgo. del Estero 2829 (3000), Santa Fe, Argentina 2 Instituto de Desarrollo Tecnológico para la Industria Química (CONICET-UNL), Güemes 3450 (3000), Santa Fe, Argentina

Abstract 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 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 this chapter 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 *

E-mail address: [email protected] E-mail address: [email protected]

**

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R. H. Buitrago and S. B. Concari 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.

1

Introduction

In spite of the fact that this chapter deals with nanocrystalline silicon thin films, some features of crystalline silicon used as a basic photovoltaic material are discussed first. The composition, flow rate and pressure of the reactant gases, the substrate temperature and doping concentration are the most important variables in the PECVD, the preparation technique used in the present study to deposit the films. For selected values of those variables two set of samples of films were chosen to study the laser-induced phase transformation processes in nanocrystalline silicon. Phase transformation processes of the films are better understood if the crystalline structure, composition and other morphological, optical and electrical properties of them are well known. Being that these properties are strongly dependent on the preparation conditions, as we said before, for this reason, a complete characterization of these properties for nanocrystalline silicon thin films are also presented in this chapter.

2

Silicon as a Photovoltaic Material

Photovoltaic research and market have been first focused on crystalline silicon, since the first solar cell was developed at Bell Laboratories in 1954. Although others materials have also been explored, there is still great interest in crystalline silicon, because it has the most developed technology as well as its abundance on the earth surface. Relative cost of photovoltaic system compare to hydrocarbon energies sources is the actual challenger. During the 80th a great research effort was dedicated to develop the amorphous silicon thin film solar cells, due to it potential low relative cost. The goals prices were reached and companies started to produce amorphous modules, but latter the modules showed a degradation process when were exposed to sun. This problem known as Staebler-Wronski effect (Staebler and Wronski, 1977) is controlled through a multijuncture system, which turns the photovoltaic module price up, equivalent or more than the single-crystal silicon one. Since the middle of 90th decade, the group of Neuchâtel at Swisserland (Meier et al., 1994) proved that microcrystalline silicon could be used as a absorber layer in a pin solar cell, obtaining efficiencies higher than 7 %, and presenting two very important properties: a) it was stable under light soaking and b) it could be produce using the same equipment used for amorphous silicon thin films. After that microcrystalline or nanocrystalline silicon thin film have converted in the most promising new material to make thin film solar cells.

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The optimization of the photovoltaic materials is essential for improving the solar cells conversion efficiency. To this aim, the knowledge of structural and physical properties of the materials plays a relevant role, and many groups of researchers are advocated to this task. In last years silicon prepared in thin films with micro or nano-structure (grain size between 3 and 50 nm) has been investigated by He et al., 1994; Meier et al., 1998; Tzolov et al, 1997 and Houben et al., 1998, among others. Not only for applications on sensors and transistors (TFT), but also for certain quantum effects such as the band gap blue shift, photoluminiscence and visible electroluminiscence and resonant tunnelling. These last properties have possible application in opto-electronic devices (Chen et al., 1996). The present interest on silicon thin films is evident from the great amount of research reports on silicon thin films (amorphous, polymorphous and micro or nanocrystalline) presented at the 20th International Conference on Amorphous and Microcrystalline Semiconductors (ICAMS) held at Campos do Jordao (Brasil) at August, 20031. The improvements in the deposition techniques and conditions as well as the optimization of structural and other physical properties are the scope of great research in this area.

3

Silicon Phases

Besides crystalline (Si-I) and amorphous (a-Si) faces present at normal temperature and pressure, there are other ten known Silicon faces: Si-II, with metallic structure (ȕ-Sn), Si-III, with eight atoms in the primitive cell in a center cubic structure (bcc or bc8) and Si-IV, with four atoms in the primitive cell in an hexagonal diamond structure (hd, wurtzita-type) (Needs and Mujica, 1995; Crain et al., 1994); Si-V, with simple hexagonal structure (sh) (Hu and Spain, 1984); Si-VI, with a non yet known structure (initially assigned a double hexagonal packed structure: dhcp); Si-VII, with hexagonal packed structure (hcp) (Needs and Mujica, 1995); Si-VIII y Si-IX, with tetragonal structure (Zhao et al., 1986); Si-X, face center cubic structure (fcc) and Si-XI, with orthorhombic center cubic structure named as Imma (McMahon and Nelmes, 1993); SiXII, with rombohedric structure (r8) (Crain et al., 1994). These structural faces are present in Silicon when it is under high pressure. Faces II, V, VI y XI are stables faces at high pressure, while the rest of the faces are meta-stable ones. In general all the preparation techniques use Hydrogen-diluted silane as a reactant gas to deposit hydrogenated nanocrystalline Silicon (nc-Si:H) thin films. The amount of Hydrogen bounded to silicon in the amorphous tissue as well as in the grain boundaries of the nanocrystallites, depends on the dilution grade and both influence the growth rate, the grain size and the residual stress in the films. Usually nanocrystalline Silicon thin films deposited by PECVD have great residual compression stress because the differences in thermal expansion coefficient of both Silicon and substrate. So many stable and meta-stable crystalline faces may be present in these films. That it follows is a brief description of the faces involved in the transformation faces processes of intrinsic and p-doped nanocrystalline Silicon thin films. Si-III is a crystalline form with distortion tetrahedral bonds and primitive cell length a = 6.64 Å. This Silicon face is very well known as a meta-stable one, present in Silicon under 1

A summary of the ICAMS 2003 made by Christian Godet (2003) is at the web site: http://www.upicardie.fr/labo/lpmc/ GDRCarbone/documents/ICAMS_2003_ReportCG.rtf

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de-pressurization processes in the range 10 – 13 GPa (100 –130 kbar). Kobliska and Solin (1972) have studied this face in polycrystalline Silicon obtained by hydrostatic pressure of face I up to 12 GPa and then relaxing to normal pressure. They have calculated the following Raman scattering lines for this face at 478 cm-1, 433 cm-1, 403 cm-1, 397 cm-1 and 181 cm-1 and identified experimentally the 463 cm-1, 433 cm-1, 416 cm-1 and 384 cm-1 ones with a maximum error of 3 cm-1. Such lines are appreciably wide (mean height wide, MHW § 15 cm-1). This fact is attributed by the authors to the very high residual tensions in the surface. Others researchers have assigned to this face wave number of scattering Raman at 432 cm-1, 412 cm-1, 382 cm-1 and 163 cm-1 (Kailer et al., 1997). Si-IV is a meta-stable face with wurtzita type in layers structure. This face has been detected in re-cristalization processes of Si-III face (Wentorf and Kasper, 1963) and in depressurization processes of Si-I (Kailer et al., 1997; Piltz et al., 1995; Gogotsi et al., 1999). This face presents a Raman scattering signal at 511 cm-1 (Kailer et al., 1997). The hexagonal diamond structure of this face have a bonded energy slightly greater than the diamond structure (~ 0,01 eV per atom). Si-XII is a meta-stable phase that has been first reported by Crain et al. (1994). It consists of a rhombohedral diamond structure (r8) with eight atoms in the primitive cell. The density of this phase is higher than any of the tetrahedral forms of Silicon due to non-bonded neighbors’ separation in r8, which is substantially shorter than those of the other forms. This reduction in next-near neighbors distance is achieved through important local deviations from tetrahedral bonding, making the r8 phase the most structurally distorted crystalline tetrahedral form of silicon. As Piltz et al. (1995) have pointed out, the importance of the r8 structure is further increased by the presence of add fold bonded rings, which are known to greatly affect electronic properties. Distance between atoms in Si-XII is 3.32 Å in (111) direction with a primitive cell length a = 5.609 Å (Crain et al., 1994). This face is not a distorted bc8 face but a different one. Besides the six atoms, it has rings of five atoms and it is the tetrahedral crystalline more structurally distorted form of Silicon. This face has been detected in de-pressurization processes of Silicon at pressure of 8.2 GPa and it predominates over face III at pressure superior than 7 GPa (Crain et al., 1994). Gogotsi et al. (1999) have identified positions of TO scattering Raman for Si-XII (r8) at 514 cm-1, 440 cm-1,350 cm-1, 337 cm-1,234 cm-1,183 cm1 ,179 cm-1. This values are in great agreement with those calculated by Piltz et al. (1995). The phase-transformation processes induced by compressive stress in bulk Silicon have been studied through microindentation using diamond tools (Lucazeau and Abello, 1999; Kailer et al., 1997), by micro-cutting (Gogotsi et al., 1999; Tanikella et al., 1996), and by hydrostatic tests (Crain et al., 1994; Piltz et al., 1995). Such crystallographic studies have established that, for pressures up to 10 GPa, single-crystal silicon structures (c-Si) identified as a phase I (dc) are transformed totally into metallic phase II (ȕ-Sn). As pressure is being slowly reduced to 9.3 GPa, phase XII (r8) starts to form, maintaining itself, down to a pressure of 2.6 GPa. Reducing the pressure even more, phase XII is partially transformed into phase III (bc8), which at pressures smaller than 1.6 Gpa transforms to phase I. If the process of depressurization is slow, phases XII, III and I can coexist at normal pressure. Similar studies of phase-transformation processes in silicon thin films have not been reported. Intermediate order in tetrahedrally coordinated silicon thin films has been recently investigated by Tsu et al. (2003), and Sundae-Meya et al. (2001), but in other experiments of

Laser-Induced Phase Transformation in Nanocrystalline Silicon Thin Films

73

crystallization of silicon thin films with laser excimer beam, no phases other than I and amorphous have been detected. In addition, Sundae-Meya et al. found that higher irradiation power and higher initial hydrogen concentration both lead to films with decreased crystalline size. It is generally accepted that structural disorder of the Silicon network is influenced by the Hydrogen concentration. It is also well known that the correlations between the Hydrogen content and the degree of disorder depend strongly on the preparation method. In addition to the neutralization of Si dangling bonds, the hydrogenation induces rearrangement of the Si–Si bonding, so differences in phase transformation are expected for different contents of Hydrogen in the films.

4 4.1

Nanocrystalline Silicon Thin Films Preparation Technologies

There are available many different techniques to deposit microcrystalline silicon. As was mentioned before the deposition is achieved by diluting silane in Hydrogen, issues on this research include mainly how to break the Hydrogen bonds, in both silane and Hydrogen, obtaining more free radicals and less ions. The most developed technique is the Plasma Enhanced Chemical Vapor Deposition (PECVD), using excitation frequencies within 13 to 120 MHz (Kroll et al., 1996), the use of high frequency have the goal of increasing the deposition rates. Between the others techniques that compete with PECVD may be mentioned the Hot Wire or Catalytic Chemical Vapor Deposition (HW-CVD) (Koh et al., 1995), the High Pressure Depletion (HPD) (Kondo et al., 2001), and RF Hybrid Thermal Plasma Chemical Vapor Deposition (TPCVD) (Eguchi et al., 1994). By the Plasma Enhanced Chemical Vapor Deposition (PECVD) technique has been possible to obtain polycrystalline material formed by grains of dimensions smaller than 20 nm, imbibed in an amorphous matrix that has been denominated polymorphous as well as microcrystalline or nanocrystalline silicon (Roca i Cabarrocas et al., 1998; Matsuda, 1983). The reactive gas concentration to prepare the intrinsic material as well as the doping gases are variables of the deposition process that influence greatly on properties of the material. One of the most used gas is silane (SiH4) highly diluted in Hydrogen, Helium and/or Argon. By using the PECVD technique, crystalline fractions close to 100 % have been reported in intrinsic nc-Si:H (Siebke et al., 1998; Zhou et al., 1997), p-type (Rubino et al., 1993), and n type (Nakahata et al., 1998; VČprek et al., 1991). The plasma contains much different ions and neutral radicals generated by collisions between electrons and molecules. These ones, in turn, produce secondary reactions while they move to the substrate. All the species contained in typical reactors plasma reach the substrate. Most part of the film in formation is finished with Hydrogen, and no SiH3 radicals are taken. So these radicals present great superficial mobility, to find sites energetically favorable, a necessary condition for the growing of a high quality material (Guha et al., 2000). Others radicals such as SiH2 can be incorporated directly at the surface with a high sticking coefficient. Presence of these and others heavy radicals in the plasma leads to a poor microcrystalline structure of the film. Nanocrystalline Silicon thin films have some advantage related to amorphous silicon and the use of its technology, yet at the industry level. It presents greater photon optic absorption

74

R. H. Buitrago and S. B. Concari

in the range 1 to 3 eV, compared with crystalline silicon. Such property makes this material a promising one for factoring devices based on the photoemission effect of silicon. When crystallites size is reduced to a few nanometers, some convenient properties are obtained for applications in optics and electrical thin films devices, multijunctions and p-i-n solar cells. The presence of the –B2H5 group and the Hydrogen bounded to silicon in the bulk as well as in the grain boundaries of the nanocrystallites, depends on the dilution grade and both influence the growth rate, the grain size and the residual stress in the films.

4.2

Characterization Techniques

To characterize nanocrystalline thin films many physical methods can be used. We choose the most standard ones. Lateral dark conductivity, measured in a cryostat in the temperature range of 25 to 160 C, X-ray diffraction of low angle at room temperature, Infra Red spectrometry on a single crystal silicon substrate, Atomic-Force Microscopy (AFM) to examine the surface structure, Transmission Electron Microscopy (TEM) which gives information on crystalline phases present in the films, and finally Raman scattering spectroscopy. The latter is a straightforward and very sensitive method of examining crystalline structures (Lucazeau and Abello, 1997; Campbell and Fauchet, 1986; Lengsfeld et al., 2000) and phase transformations (Gogotsi et al., 1999; Tanikella et al., 1996) of thin solid films, as well as, a non-destructive way of monitoring stress in those films (Lucazeau and Abello, 1997; Gogotsi et al., 1999; Paillard et al., 2001). However, compressive or tensile stress, grain size, phonon confinement and temperature effects can lead to a misinterpretation of the Raman spectra of these microcrystalline materials (Viera et al., 2001).

4.3

Preparation Conditions

Nanocrystalline silicon thin films study in this chapter were deposited on Corning 7059 glass by PECVD in a capacitive-type radio frequency reactor working at 50 MHz. The 20 cm diameter electrodes were 1.35 cm apart from each other. The reactant gas used was SiH4 containing B2H6 highly diluted in H2. Silane concentration is defined as:

C ( SiH 4 )

Q( SiH 4 ) x 100 [%] Q( SiH 4 )  Q( H 2 )

(1)

with Q(SiH4) and Q(H2) being the flow of silane and Hydrogen gases, respectively. Diborane concentration in the reactant gas was established by partial pressure relationship as a mixture prepared previously, as:

C(B2 H 6 )

p( B2 H 6 ) x 10 6 [ppm] p(B2 H 6 )  p(SiH 4 )

(2)

with p(B2H6) and p(SiH4) being the partial pressure of diborane and silane gases, respectively.

Laser-Induced Phase Transformation in Nanocrystalline Silicon Thin Films

75

We analyze here experimental results of two series of samples of intrinsic and doped films respectively. The samples were prepared with a different dilution of Hydrogen in the reactant gas. The applied RF power, the total mixture gas flow, the gas pressure, and the substrate temperature were 110 mW cm-2, 40 sccm, 60 Pa, and 150 qC, respectively. For the doped films the total mixture gas flow was 6 %, and the substrate temperature was 140 qC, with the same other experimental conditions. C(B2H6) was varied in the range 25 ppm to 10000 ppm. The nomenclature used to identify the intrinsic samples is the following: “IN” being N = 2, 3, 4, 5, 6, according to the value of silane concentration used in the deposition. Doped samples are identified as “PM x 10 5” being M the diborane flow related to the total gas flow evaluated as M = C(B2H6) x 10 -6 x Q(SiH4) [%], that was in the range of 1.5 x 10 -4 % to 6.0 x 10 -2 %. To analyse the structure of as-deposited thin films, we collected micro Raman spectra at low power density (<1 kWcmí2) with a triple Jobin-Yvon T64000 spectrometer equipped with a liquid-N2-cooled charged coupled device camera. We used the 514.5 nm line of an Arion laser for excitation in a backscattering geometry. A 10X lens provided an apparent spot size of about 10–25 µm. Spectral resolution was 0.5 cmí1. A multichannel Ar laser TRS-600SZ-P with an excitation wavelength of 514.5 nm of a photometric Raman spectrometer was used to induce phase transformation. Power density of the laser beam was ~100 kW cmí2, penetration length ~0.5 µm and the spatial resolution was 1 µm. All spectra were obtained using a 0.5 cmí1 step.

5

Characterization of the Nanocrystalline Silicon Thin Films

In this section a brief report of the results of electrical measurements, AFM, TEM, X-ray and IR studies as well as optical measurements of the nanocrystalline silicon thin films prepared by PECVD are presented. Thickness of the films measured from transmittance spectra was in the range 400 nm to 660 nm and 360 nm to 820 nm for intrinsic and doped films respectively.

5.1

Electrical Measurements

All the intrinsic films studied present an activated dark conductivity (ıd) as a function of the inverse of temperature. The obtained values of curves of ıd versus Tí1 in the temperature range of 300–450 K, are shown in Figure 1. The great difference in the ıd value of samples I6 and I5 shows an onset from amorphous to microcrystalline material. The values of dark conductivity at room temperature are close to those obtained by Asano (1990), Siebke et al. (1998) and by the Neuchâtel group (Meier et al., 1997).

76

R. H. Buitrago and S. B. Concari

-2

10

-3

I3 I2 I4

-4

I5



-1

Vd (: cm )

10 10

-5

10

-6

10

-7

10

-8

a

10

-9

10

I6

2,2

2,4

2,6

2,8

3,0

3,2

3,4

-1

1000/T (K )

0

10

P3000 P4500

-1

10

P750

-2

10

P180 P100

-3

-1

Vd (: cm)

-1

10

-4

10

-5

P60

10

-6

10

-7

10

P6000 P30 P15

b

-8

10

2,2

2,4

2,6

2,8

3,0

3,2

3,4

-1

1000/T (K ) Figure 1. Dark conductivity vs T –1 for (a) intrinsic (from Concari and Buitrago, 2003) and (b) p-doped (from Concari, 2004) nc-Si:H films

Light incident slightly enhances the conductivity of the intrinsic nc-Si-H thin films. Photoconductivity of these samples is very low but stable under standard illuminating conditions (ıph > 10 -3 :-1 cm-1). Photoconductivity of sample I6 is quite similar to one of an amorphous material. It is 104 times the dark conductivity (ıph = 7 x 10 -5 :-1 cm-1). Values of ıd at room temperature and activation energy (Ea) are displayed en Figure 2. Both ıd and Ea values of intrinsic films are in a broad range as C(SiH4) varies from 6 % to 2 %.

Laser-Induced Phase Transformation in Nanocrystalline Silicon Thin Films

a

-2

10

77

0.7

-3

10

0.6

-4

0.5

-5

10

-6

0.4

-7

0.3

10 10

EA (eV)

Vd (: cm)

-1

10

-8

10

0.2

-9

10

0.1 2

3

4

5

6

Silane flow (%) 0.8

b

0

10

0.7

-1

10

-2

0.6

-3

0.5

-4

0.4

-5

0.3

-6

0.2

-7

0.1

-8

0.0

10 10 10 10 10 10

0.00

0.01

0.02

0.03

0.04

0.05

Ea (eV)

Vd (: cm)

-1

10

0.06

Diborane flow (%) Figure 2. Dark conductivity at room temperature (Ŷ) and activation energy measured at 300–450 K (o) for (a) intrinsic and (b) p-doped nc-Si:H films (from Concari et al., 2003)

Also dark conductivity of doped films is strongly dependent on doping. Lightly doped nanocrystalline silicon gives a low activation energies corresponding to n-type semiconductor material (see Figure 2). As doping increases, the Fermi level moves down to the center of the gap, corresponding to compensate nanocrystalline films, which have the lowest ıd and the largest Ea. Increasing further more the diborane flow, the activation energy decreases and the films become to a p-type semiconductor, reaching the maximum ıd and the minimum Ea for the sample P3000. The electric transport behavior of this film corresponds to a crystalline material, with large grain size, so the influence of the presence of a grain boundary barrier in the sample P3000 is neglectable. For diborane concentration larger than 5000 ppm, the amount of boron is such that induces a higher disorder instead of a better crystallization process as before, moving back ıd and Ea to lower and higher values respectively.

78

5.2

R. H. Buitrago and S. B. Concari

AFM and TEM Studies

The influence of silane dilution in hydrogen on grain size could be studied by AFM. Figure 3 shows the AFM images of the samples I2 and I6, taken in the same conditions and having the same scales. When the silane is diluted in Hydrogen the resulting material has a better defined structure, with increasing coalescence for decreasing silane flow. The bilayer morphology difference may be stated by the value of the root mean square (RMS) roughness: 6.0 nm for I6 and 8.5 nm for I2. As the thickness of all the samples is around 400–650 nm, the difference of the RMS values may be attributed to the difference in the grain size.

a

b 2 nm ȝm

Figure 3. 2d and 3d AFM pictures of the intrinsic films surface (a) I2 (from Concari and Buitrago, 2003) and (b) I5

The effect of the diborane flow on the coalescence of p-doped nc-Si:H:B films can be seen in the AFM images of Figure 4. The bilayer morphology difference may be stated by the value of the root mean square (RMS) roughness presented in Table I. For doping up to 5000 ppm the grain size increases with boron doping (see Table I) but for a greater diborane concentration it results in films with small crystallites.

Laser-Induced Phase Transformation in Nanocrystalline Silicon Thin Films

79

Figure 4. AFM pictures of the p-doped films surface (a) P15, (b) P3000 and (c) P6000 (from Concari and Buitrago, 2004)

TEM measurements indicate that nc-Si:H films are a heterogeneous mixture of an amorphous matrix and crystallites, the grain size of the later growing with Hydrogen dilution. Micrograph and its corresponding transmission electron diffractogram of sample I3 are shown in Figure 5 as example. Select area electron diffraction showed the presence of sharp spots, including (111), (220) and (311) reflections. The spots are place on rings corresponding to the amorphous matrix. The presence of the spots clearly indicated that the nacrocrystallites had the long-range order needed to establish such crystalline diffraction. The first ring indicates preferential growth in the (111) direction and the small size of the crystallites. Micrograph shows nanocrystallites of ~ 10 to 20 nm. Similar TEM diffractograms result for the intrinsic samples I2, I4 and I5 (Concari and Buitrago, 2003).

80

R. H. Buitrago and S. B. Concari

Figure 5. Bright field planar TEM and select area diffraction pattern of sample I3 (adapted from Concari and Buitrago, 2003)

Table I. Root mean square (RMS) roughness, mean height (h), and crystalline volume fraction (Xc) of p-doped nc-Si:H films (From Concari and Buitrago, 2003). Sample P15 P60 P180 P750 P3000 P4500 P6000

C(B2H6) (ppm) 25 104 312 1250 5000 7500 10000

RMS (nm) 4.6 4.3 4.9 5.2 9.1 5.5 1.7

h (nm) 12 13 11 16 26 17 7

Xc 0.52 0.37 0.40 0.56 0.82 0.70 0.12

Laser-Induced Phase Transformation in Nanocrystalline Silicon Thin Films

5.3

81

X-ray and IR Studies

The IR spectra were not well defined due to the thickness of the samples. Peaks at 2100 and 2200 cmí1 were not resolved, and the 650 cmí1 peak presents an interference with oxygen signal which was probably adsorbed at the surface. In Figure 6 are plotted the absorption IR spectra of the intrinsic sample. In spite of this difficulty, from absorption peak at 2200 cm-1 the Hydrogen content can be obtained. I6 sample has a higher concentration of Hydrogen estimated to 8 %. The rest of the intrinsic samples oscillate around 5 %. Doped samples have Hydrogen content less than 10 %.

I2

Absorbance (a.u.)

I3 I5 I6

a

500

1000

1500

2000

2500

3000

-1

Wavenumber (cm )

P0 P180

Absorbance (a.u.)

P3000 P4500 P6000

b

500

1000

1500

2000

2500

3000

-1

Wavenumber (cm ) Figure 6. Infrared spectra of the (a) intrinsic and (b) p-doped nc-Si:H films

82

R. H. Buitrago and S. B. Concari

Intensity (a.u.)

X-ray spectrum of the I2 surface sample shown in Figure 7 presents a peak at 28º, as well as the less resolute spectrum of sample I6. The peak at this angle accounts for a preferential growing in a (111) plane.

I2

I6

22

24

26

28

30

32

34

36

38

o

2T( )

Figure 7. X-ray diffraction spectra obtained by subtracting the spectrum of substrate material for samples I2 and I6

5.4

Raman Studies

Intensity (a. u.)

Figure 8 shows the micro-Raman scattering spectra of the as-deposited intrinsic films at room temperature. A semi-quantitative measurement of the crystalline volume fraction XC can be obtained from the deconvolution of the Raman TO phonon band into components of amorphous, nanocrocrystalline and crystalline. These peaks are fitted with Lorentzian curves centered at ~480 cmí1, 510–514 cmí1 and ~520 cmí1, respectively.

I2 I3 I4 I5 I6 c-Si 350

400

450

500

550

600

650

-1

Raman shift (cm ) Figure 8. Micro-Raman scattering spectra obtained at ~1kW/cm2 and three successive expositions of 20 s from intrinsic nc-Si:H films (from Concari and Buitrago, 2003). Spectrum of c-Si is included at the bottom as reference

Laser-Induced Phase Transformation in Nanocrystalline Silicon Thin Films

83

In order to obtain XC, the differences in the Raman cross sections should also be taken into account. The following equation is used:

XC

Ic Ic  SIa

(3)

where Ic is the total microcrystalline and crystalline peak area, Ia is the amorphous peak area and S is the relative integrated Raman scattering cross-section for c-Si to a-Si. We have used the data S = 1, 13 obtained at 2.4 eV by Tsu et al. (1982). Values of XC calculated with Equation 3 are shown in Table I and Table II for doped and intrinsic films respectively. These results are in agreement with dark conductivity, TEM, IR and AFM data reported above. Equation 3 is used by other authors taking S not as the integrated Raman scattering crosssection for c-Si to a-Si, but as a correction to the crystallite size (Schropp and Zeman, 1998; Bustarret et al., 1988). For the estimated grain size of our samples, volume fraction calculated with both methods differs by 25 %. Table II. Crystalline volume fraction (Xc) and grain size (d) of intrinsic nc-Si:H films Sample

C(SiH4) (%)

Xc

d (nm)

I2

2

0.95

15

I3

3

0.95

15

I4

4

0.90

12

I5

5

0.18

10

I6

6

0.04

9

In Figure 8 it can also be appreciated that, while the concentration of silane in the mixture of reactive gases decreases, the peak at 520 cmí1 (phase Si-I) grows. The broad one at 480 cmí1, due to the amorphous phase, shifts to higher frequencies and decreases until disappearing at high Hydrogen dilution. Structural disorder of the silicon network is influenced by the Hydrogen concentration of the reactant gases because the neutralization of the dangling bonds as well as the induced rearrangement of the Si-Si bonds while deposition occurs. So the sample I2 is expected to be the most crystalline and the I6 the less one. The values of Xc shown in Table I and II evidence these expectations were right. The low deposition rate for the samples I2, I3 and I4 favors the coalescent growing of the nanocrystallites leading to a predominating crystalline phase. The grain size (d) was obtained from the low frequency shift ('Z) of the TO signal of cSi from the value 520 cm-1 by the relation

d

§ B · 2S ¨ ¸ © 'Z ¹

1/ 2

(4)

where B = 2 cm-1 nm2 (He et al., 1994). Values of d for the intrinsic films are shown in Table II. As Sundae-Meya et al. (2001) have stated, the greater Hydrogen concentration, the minor grain size of the films.

84

R. H. Buitrago and S. B. Concari

The empiric relation of Dey et al. (2000) between angle deviation ('ș) of Silicon atom 2 bonds and the middle height width (ī) of the dispersion Raman amorphous phase peak can be used too. With a Lorentzian fitting of amorphous Raman peak the value 'ș | 6q was obtained for simple I6 and 'ș < 3q for the others intrinsic samples confirming the amorphous and nanocrystalline structure respectively. In spite of the low deposition temperature, high diborane concentration in the reactant gases induces a high value of crystalline fraction (Xc > 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

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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 (*)

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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

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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.

References Asano, A. Appl. Phys. Lett. 1990, 56 (6) 533 Bustarret, E.; Hichicha, H. A.; Bunei, M. Appl. Phys. Lett.1988, 52 (20) 1675 Campbell, I. H.; Fauchet, P. M. Sol. Stat. Comm. 1986, 58 (10) 739 Cerqueira, M. F.; Ferreira, J. A. J. Mater. Process. Tech. 1999, 92–3, 235 Chen K.; Qin, H.; Huang, X.; Ikuta, K.; Matsuda, A.; Tanaka, K. J. 0f Non-Crystalline Solids. 1996, 198-200, 891 Cicala, G.; Capezzuto P.; Bruno, G. Thin Solid Films. 1999, 337, 59 Concari, S. B. Buitrago, R. H.; Gutiérrez, M. T.; Gandía, J. J. J. Appl. Phys. 2003, 94 (5) 2417-2422, Concari, S. B.; Buitrago, R. H. J. Non-Cryst. Solids. 2004, 338-340, 192 Concari, S. B.; Buitrago, R. H. Semicond. Sci. Technol. 2003, 18, 1 Concari, S. B. Doctoral Thesis. Universidad Nacional de Rosario: Argentina. 2004 Crain, J.; Ackland, G. J.; Maclean, J. R.; Piltz, R. O.; Hatton, P. D.; Pawley, G. S. Phys. Rev. B 1994-I, 50 (17) 13043 Danesh, P.; Pantchev, B.; Grambole, D.; Schmidt, B. J. Appl. Phys. 2001, 90 (6) 3065 Danesh, P.; Savatinova, I.; Toneva, A.; Liarokapis, E. J. Non-Cryst. Solids. 1996, 204, 265 Dey, S.; Roy, Ch.; Pradhan, A.; Varma, S. J. Appl. Phys. 2000, 87 (3) 1110 Diehl, F.; Scheib, M.; Schröder B.; Oechsner, H. J. Non-Cryst. Solids. 1998, 227-230, 973 Eguchi, E.; Sata, S.; Tosida, T. Appl. Phys. Lett. 1994, 64, 58 Godet, C. (2003). ICAMS 2003. Compte-rendu établi pour le GDR 2449. http://www.upicardie.fr/labo/lpmc/GDRCarbone/documents/ICAMS_2003_ReportCG.rtf Gogotsi, Y.; Baek, C.; Kirscht, F. Semic. Sci. Technol., 1999, 14 (10) 936. Erratum. Semic. Sci. Technol. 1999, 14 (11) 1019 Guha, S.; Yang, J.; Banerjee, A. Prog. Photovolt. Res. Appl. 2000, 8, 141 He, Y.; Yin, Ch.; Cheng, G.; Wang, L.; Liu, X. Appl. Phys. 1994, 75, 797 Hernández-Rojas, J. L.; Lucia, M. L.; Martil, I.; González-Díaz, G.; Santamaría, J.; SánchezQuesada, F. Appl. Optics. 1992, 31, 1606 Hishikawa, Y. J. Appl. Phys. 1987, 62, 3150 Houben, L.; Luysberg, M.; Hapke, P.; Vetterl, O.; Finger, F.; Carius, R.; Wagner, H. J. NonCryst. Solids. 1998, 227-230, 896 Hu, J. Z.; Spain, I. L. Solid State Commun. 1984, 51, 263 Kailer, A.; Gogotsi, Y. G.; Nickel, K. G. J. Appl. Phys. 1997, 81 (7) 3057 Kalkan, A. K.; Fonash, S. Mat. Res. Soc. Symp. Proc. 1997, 467, 319 Kobliska, R. J.; Solin, S. A. Phys. Rev. Lett. 1972, 29 (11) 725 Koh, J.; Ferlautto, A. S.; Rovira, P. J.; Wronski, C. R.; Collins, R. W. Appl. Phys. Lett. 1995, 75, 2295 Kondo, M.; Susuki, S.; Nasuno, Y.; Matsuda. A. Mat. Res. Symp. Proc. 2001, l664, A4.3.1 Kroll, U.; Meier, J.; Shah, A.; Mikhailov, J.; Weber, K. J. Appl. Phys. 1996, 80, 4971 Lengsfeld, P.; Nickel, N. H.; Fuhs, W. Appl. Phys. Lett. 2000, 76 (13) 1680 Lucazeau, G.; Abello, L. J. Mater. Res. 1997, 12 (9) 2262

94

R. H. Buitrago and S. B. Concari

Matsuda, A. J. Non-Cryst. Solids. 1983, 50-60, 767 McMahon, M. I.; Nelmes, R. J. Phys. Rev B 1993, 47, 8337 Meier, J.; Dubail, S.; Cuperus, J.; Kroll, U.; Platz, R.; Torres, P.; Anna Selvan, J. A; Permnet, P.; Beck, N.; Pellaton Vaucher, N.; Hof, Ch.; Fischer, D.; Keppner H.; Shah, A. J. NonCryst. Solids. 1998, 227-230, 1250 Meier, J.; Fluckiger, R.; Keppner, H.; Shah, A. Appl. Phys. Lett. 1994, 65 (7) 860 Nakahata, K.; Niida, A.; Kamiza, T.; Fortmann, C. A.; Shimitzu, I. Thin Solid Films. 1998, 337, 45 Needs, R.J.; Mujica, A. Phys. Rev. B 1995, 51 (15) 9652 Paillard, P.; Puech, P.; Sirvin, R. J. Appl. Phys. 2001, 90 (7) 3276 Piltz, R. O.; Maclean, J. R.; Clark, S. J.; Ackland, G. J.; Hatton, P. D.; Crain, J. Phys. Rev. B 1995, 52 (6) 4072 Richter, H.; Wang, Z. P.; Ley, L. Solid State Commun. 1981, 39 625 Roca i Cabarrocas, P.; Hamma, S.; Sharma, S. N.; Viera, G.; Bertrán, E.; Costa, J. J. NonCryst. Solids. 1998, 227-230, 871 Rubino, A.; Addonizio, M. L.; Conte, G.; Nobile, G.; Terzini, E.; Madan, A. Mat. Res. Soc. Symp. Proc. 1993, 297, 509 Scholten, A. J.; Akimov, J. I. J. Non-Cryst. Solids. 1993, 164-166, 923 Schropp, R. E. I.; Zeman, M. Amorphous and microcrystalline silicon solar cells. Modelling, Materials and Device Technology; Kluwer Academic Publishers: London, U.K., 1998; 49 Siebke, F.; Yata, S.; Hishikawa, Y.; Tanaka, M. Jpn. J. Appl. Phys. 1998, 37, 1730 Spanakis, E.; Stratakis, E.; Tzanetakis, P.; Fritzsche, H.; Guha, S.; Yang, J. ICAMS 19. 2001 Staebler, D. L.; Wronski, C. R. Appl. Phys. Lett. 1977, 31, 292 Street, R. A. Hydrogenated Amorphous Silicon; Cambridge University Press: Cambridge, U.K., 1991 Sundae-Meya, A.; Gracin, D.; Dutta, J.; Vlahovic, B.; Nemanich, R. J. Mat. Res. Soc. Symp. Proc. 2001, 664, 691 Swanepoel, R. J. Phys. E.: Sci. Instrum. 1983, 16, 1214 Tanikella, B. V.; Somasekhar, A. H.; Sowers, A. T.; Nemanich, R. J.; Scattergood, R. O. Appl. Phys.Lett. 1996, 69 (19) 2870 Tsu, D. V.; Chao, B. S.; Jones, S. J. Sol. En. Mat. Sol. Cel. 2003, 78 (1-4) 115 Tzolov, M.; Finger, F.; Carius, R; Hapke, P. J. J. Appl. Phys. 1997, 81 (11) 7376 VČprek, S.; Sarott, F. J. Non Cryst. Solids. 1991, 137-138, 733 Viera, G.; Huet, S.; Boufendi, L. J. Appl. Phys. 2001, 90 (8) 4175 Wentorf, R. H.; Kasper, J. S. Science. 1963, 139, 338 Zhao, Y. X.; Buheler, F.; Sites, J. R.; Spain, I. L. Solid State Commun. 1986, 59, 679 Zhou, J. H.; Ikuta, K.; Yasuda, T.; Umeda, T.; Yamasaki, S. Appl. Phys. Lett., 1997, 71 (11) 1534

In: New Research on Semiconductors Editor: Thomas B. Elliot, pp. 95-121

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– Schr¨odinger 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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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].

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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 Shr¨odinger–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 Shr¨odinger 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 Schr¨odinger 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 , π
2 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 Schr¨odinger 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 Shr¨odinger 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 Shr¨odinger 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 Shr¨odinger equation is adjusted to receive a vanishing electron wavefunction in the other barrier. The Poisson equation is discretized the same way as the Shr¨odinger 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.

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

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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

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(a) AlGaN/GaN 300K

(b)

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AlGaN/AlN/GaN 300K

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Energy (eV)

Energy (eV)

0.8 0.6 0.4

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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 Shr¨odinger–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–Shr¨odinger 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-Shr¨odinger 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

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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)

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

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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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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.

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

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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)

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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.

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

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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.

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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.

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

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).

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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 <5 kV/cm. At higher electric fields, the self-heating reduces the electron drift velocity, and the electron velocity tends to saturate at the electric fields lower as compared with those in absence of the self-heating. The experimental results (circles) are close to the simulation data obtained with the self-heating taken into account. In the following, we shall discuss the results obtained under conditions of negligible channel self-heating. The corresponding experimental current–field characteristics are available for voltage pulses lasting 1–10 ns [20, 21, 25, 43]. In particular, the results for AlGaN/AlN/GaN channels indicate that the self-heating effect is negligible in the field range up to 100 kV/cm when the pulse duration is 150 ns (Fig. 7, closed triangles). An example of Monte Carlo simulation of the electron drift velocity for AlGaN/GaN heterostructure is illustrated in Figure 8 [18]. The simulation shows that electron gas de-

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Figure 7: The current dependence on applied electric field for AlGaN/AlN/GaN heterostructure at 300 K lattice temperature. The voltage-pulse duration: 1 ns (open squares), 0.15 µs (closed triangles), 2 µs (open triangles) [43]. Reprinted with permission from [25]. Copyright (2005) by the American Physical Society.

generacy and hot phonons influence the electron drift velocity. When the degeneracy is neglected, the electron drift velocity (Fig. 8, dashes) exceeds that obtained for the complete model (solid line). The absolute increase is the highest at the intermediate electric fields (∼ 4 kV/cm). Since the electron mean-energy increases with field, the degeneracy effect tends to decrease as the electric field increases. As a result, the drift velocity curves calculated with and without considering the degeneracy tend to merge at high fields. When the hot-phonon effect is neglected, the calculated drift velocity (dots) exceeds considerably the experimental data (circles) and the simulation results for the complete model (solid line). The Pauli exclusion principle can affect the drift velocity because some scattering events are forbidden due to occupancy of the final states. This means that the electron scattering probability is lower everywhere when the degeneracy is taken into account. Thus, it is easier for a low-energy electron to acquire the velocity component in the drift direction. Supposing that this effect prevailed, the drift velocity would increase. However, since more electrons gain enough energy sufficient for optical phonon emission, the number of LOphonon emission events increases despite of the reduced scattering probability, and more electrons return back into the low-energy region. The net effect on the drift velocity is difficult to predict as it depends on many circumstances (electron density, lattice temperature, optical phonon energy, electric field). The Monte Carlo simulation for AlGaN/GaN at 300 K lattice temperature leads to a lower drift velocity when the degeneracy is taken into account (Fig. 8, dashes). This result can be explained in terms of angular dependence of final electron states after events of LO-phonon emission. The statistics for the angles between the electric field and the final electron velocity vector at 5 kV/cm electric field are collected and shown in Figure 9. Small angles are most frequent if the degeneracy is neglected (open circles). When the Pauli principle is included, the small-angle scattering rate reduces dramatically (cf. closed and open circles).

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Figure 8: Monte Carlo results for the electron velocity–field characteristics at 300 K. Solid line takes into account electron gas degeneracy and hot-phonon effects (τph = 1 ps), dashed line neglects degeneracy and includes hot phonons, and doted line includes degeneracy and neglects hot phonons. Open circles stand for the experimental results. Reprinted with permission from [18]. Copyright (2005) by the IOP Publishing Ltd.

Figure 10 gives a schematic reasoning for the enhanced probability for large-angle scattering events. Since the final states for the small-angle scattering are occupied (k ), the electrons are forced to be scattered at large angles (k ), and this implies a strong negative contribution to the drift velocity. The Monte Carlo simulation shows that accumulation of hot phonons has an effect on the electron drift velocity at high electric fields. The explanation is as follows. The enhanced occupancy of the involved phonon states (Fig. 5) supports a stronger scattering of electrons. Indeed, the scattering due to LO-phonon absorption increases because of hot-phonon reabsorption, and the scattering due to LO-phonon emission increases due to stimulated emission. This explains the reduction in the drift velocity when hot phonons are taken into account (cf. dots and solid line in Fig. 8). The stronger is applied electric field, the more pronounced is the hot-phonon effect. In response to a step of applied electric field the electron drift velocity overshoots its steady-state value if the hot phonons are taken into account (Fig. 11, solid line). Indeed, it takes time for the hot-phonon population to build up and reach the steady state. During this time, the electron–LO-phonon scattering rate gradually increases. As a result, the drift velocity passes the maximum value and decreases down to its steady-state value. Without the hot-phonon effect, the electron drift velocity overshoot is almost absent in this range of electric fields (Fig. 11, dashes). The transients of electron drift velocity and hot-phonon population can be approximated by exponential functions (Fig. 4, dashed lines). The electron drift velocity reaches the steady-state value faster (τvdr = 0.3 ps) than the LO-phonon occupancy (τph = 1 ps). In the linear situation, the relaxation times should coincide. However, the considered electron– hot-phonon processes are essentially nonlinear when the electron gas degeneracy and hot-

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Figure 9: Monte Carlo simulation data for the angle between the electric field and the electron velocity after a scattering event. Open circles - without Pauli exclusion principle, full circles - with Pauli exclusion principle. Reprinted with permission from [18]. Copyright (2005) by the IOP Publishing Ltd.

phonon effects are included. As a result, the electron drift velocity relaxes faster than the hot-phonon population.

7

Electron Temperature and Noise Temperature

The electron temperature in the biased 2DEG channel is evaluated through simulation of the electron energy distribution functions. In absence of hot phonons for biased semiconductors with strong electron–LO-phonon interaction, the simulated electron energy distribution function has a kink near the LO-phonon energy [40]. The electrons with energy, higher than the LO-phonon energy, quickly emit LO-phonons and appear in the low-energy region. The electron-temperature approximation fails. Hot phonons support a strong energy exchange between the electron and the LO-phonon subsystems. This, together with a weak interaction of hot phonons with the thermal bath, forms a nearly isolated hot-electron–hot-phonon subsystem [22]. Under a steady-state, the particles of the subsystem reach a near-equilibrium state at the elevated (hot) temperature that differs from the lattice temperature and the ambient temperature. Here the lattice temperature means the temperature of acoustic phonons strongly coupled with the thermal bath. The electron distribution functions for the first three subbands of the AlGaN/AlN/GaN heterostructure are presented in Fig. 12 (symbols). In the first subband, the 2DEG is degenerate (circles): the occupancy of low-energy electron states is close to unity. The reabsorption of hot phonons have nearly washed out the kink near the LO-phonon energy. The simulated functions can be fitted with a Fermi–Dirac distribution function (Fig. 12, solid lines). The fitting is good. Two parameters can be extracted from the fitting: the electron temperature and the Fermi energy. The same values for the electron temperature and the Fermi energy suit each subband.

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k’’

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k

Figure 10: Electron distribution and possible electron states after LO-phonon emission. Solid line is the Fermi energy, dots stand for the possible final states. Reprinted with permission from [18]. Copyright (2005) by the IOP Publishing Ltd.

This close proximity of the hot-electron–hot-phonon subsystem to the equilibrium at the elevated temperature is essential for electric fluctuations [44]. Hot-electron velocity fluctuations cause noise in all directions in the 2DEG plane. In addition to this source, a great variety of noise sources is agitated in the bias direction. For example, any resistance fluctuation modulates the bias current and generates a modulation-type excess noise in the bias direction. The modulation-type sources cause no noise in an isotropic 2DEG in the transverse direction to the current. In the electron-temperature approximation, the effective temperature of electron gas Te has to be substituted for the absolute temperature T0 into the Nyquist theorem in order to account for the chaotic motion of hot electrons enhanced by the applied electric field. For brevity, let us call this source the hot-electron ”thermal” noise. In an isotropic 2DEG, the hot-electron ”thermal” noise is the only source of noise acting in the direction transverse to the mean current. Thus, the transverse noise temperature equals the electron temperature [2]: Tn⊥ = Te (29) The modulation-type sources of the excess noise appear in the bias direction together with the hot-electron ”thermal” noise: Tn = Te [1 + C(Te )]

(30)

where Tn is the longitudinal noise temperature, C(Te ) is the correction term that takes into account the noise sources acting in the bias direction only. Real-space-transfer noise, intervalley transfer noise, impact ionization noise are examples of modulation-type sources

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important at high electric fields at microwave frequencies. In the range of subthreshold fields for these sources, the main correction goes for electron-temperature fluctuations. The noise temperature anisotropy due to the electron-temperature fluctuations has been recently treated theoretically for a biased degenerate 2DEG [45]. These inevitable fluctuations cause resistance fluctuations if the current–voltage dependence is not linear. Thus, the associated noise appears in the bias direction together with the hot-electron ”thermal” noise. Figure 13 presents some results of Monte Carlo simulation of the noise temperature anisotropy [44]. For the chosen AlGaN/AlN/GaN model, the hot-electron ”thermal” noise and the electron-temperature fluctuations are the only sources of noise in the considered range of supplied power. When the hot-phonon effect is not included into the Monte Carlo Simulation (closed squares), the longitudinal noise temperature is considerably higher as compared with the transverse noise temperature. The accumulation of hot phonons causes an essential reduction of the anisotropy (open squares). These results suggest that the electron temperature can be obtained from the experimental data on the longitudinal noise temperature with a better than 10 % accuracy in the range of fields where real-space transfer, intervalley transfer and other similar sources of noise do not manifest themselves. Since there is no anisotropy at equilibrium, the obtained very low anisotropy of the noise temperature supports the idea that the mentioned strong electron–hot-phonon interaction and the weak coupling with the thermal bath are responsible for formation of the quasi-isolated hot-electron–hot-phonon subsystem where the hot electrons and the hot phonons are almost at equilibrium at the elevated (hot-electron) temperature [44]. Figure 14 presents the noise temperature for the 2DEG channels in AlGaN/GaN and AlGaN/AlN/GaN heterostructures as a function of the applied electric field [25]. In AlGaN/GaN, the main sources of noise are caused by the thermal motion of the electrons, by the electron-temperature fluctuations, and by the electron sharing [46]. At electric fields up to 7 kV/cm, the noise temperature is nearly the same for AlGaN/GaN and AlGaN/AlN/GaN heterostructures. In this range of fields, the electrons are confined in the GaN in both het-

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Figure 12: The simulated hot-electron distribution functions for AlGaN/AlN/GaN heterostructure at 300 K lattice temperature and 10 kV/cm applied electric field. Circles, squares, and triangles stand for the first, second, and third subband, respectively. The solid lines are fitted Fermi–Dirac distribution functions. Estimated electron temperature is Te = 590 K. Reprinted with permission from [25]. Copyright (2005) by the American Physical Society.

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Figure 13: Monte Carlo simulation of dependence of noise temperature anisotropy on supplied electric power: hot-phonon accumulation taken into account (open squares) and hot phonons neglected (closed squares)[44].

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Figure 14: The experimental results for field-dependent hot-electron longitudinal noise temperature at 10 GHz frequency at 300 K temperature for AlGaN/GaN (open squares, left axis) and AlGaN/AlN/GaN (open circles, left axis) heterostructures. The solid lines guide the eye. The closed triangles (right axis) represent the electron temperatures evaluated from the Monte Carlo results. The vertical bars indicate errors. Reprinted with permission from [25]. Copyright (2005) by the American Physical Society.

erostructures. At a higher electric field, the difference appears: the electron sharing starts, and the additional noise source due to electron sharing emerges in the AlGaN/GaN heterostructure (Fig. 14, open squares). The AlN barrier prevents electron penetration into AlGaN barrier, and the noise due to electron sharing is absent at electric fields under investigation (Fig. 14, open circles). The Monte Carlo results on the electron temperature (triangles) are close to the experimental results on the longitudinal noise temperature [25].

8

Power Dissipation

The dissipated power can be directly evaluated during the Monte Carlo simulation. After each electron scattering event, the change of electron energy during the scattering event is recorded. The total energy change is normalized to the simulated electron number and the simulated time of the electron motion. The results for AlGaN/AlN/GaN are shown as closed triangles in the Fig. 15. Under the steady-state conditions, the power received from the applied electric field equals the power dissipated by the electrons. The experimental results on the supplied power are in a good agreement with the Monte Carlo results on the dissipated power. This indicates that the main scattering mechanisms responsible for the power dissipation are included into the Monte Carlo model. The only fitting parameter is the LO-phonon lifetime. The best agreement is obtained for the hot-phonon lifetime τph = 1 ps.

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9

Conclusion

Monte Carlo simulation of channel self-heating, hot-phonon accumulation and electron gas degeneracy on electron drift velocity is studied for nitride 2DEG channels at room temperature. The degeneracy reduces the electron drift velocity at low and moderate electric fields, and this effect is mainly caused by the angular dependence of the scattering rate: the electrons moving at a small angle to the electric field direction prefer to be scattered at a large angle. Hot phonons and self-heating reduce electron drift velocity at high electric fields due to increased phonon scattering. Under conditions of negligible self-heating, the investigation of microwave noise shows that AlN interbarrier prevents the hot-electron penetration into the adjacent AlGaN barrier. Simulation results indicate that hot phonons slow down the hot-electron power dissipation. A reasonable agreement with the experimental data is obtained when electron gas degeneracy and hot-phonon effect are included into Monte Carlo simulation. Electron temperature and power dissipation measurements yield a more reliable estimate of the hot-phonon lifetime as compared with current–voltage measurements. Accumulation of hot phonons reduces the anisotropy of hot-electron noise temperature. Therefore, the electron temperature can be obtained from the measured longitudinal noise temperature in the electric field range where the electron sharing effect is not present.

Acknowledgements This work has been partly funded by the US Office of Naval Research through ONR Award No. N00014-03-1-0558 monitored by Dr. Colin Wood, the Lithuanian National Foundation

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for Science and Education (Contract No. C-33/2005), and the European Commission within the Network of Excellence ”SINANO” (IST-506844).

References [1] Morkoc¸, H. Nitride Semiconductors and Devices; Springer: Heidelberg, 1999. [2] Hartnagel, H. L.; Katilius, R., & Matulionis A. Microwave Noise in Semiconductor Devices; John Wiley & Sons: New York, 2001. [3] Jacoboni, C.; Lugli, P. The Monte Carlo Method for Semiconductor Device Simulation; Springer: Wien, 1989. [4] Laux, S. E.; Fischetti, M. V. Monte Carlo Device Simulation: Full Band and Beyond; Kluwer: Boston, 1991. [5] Moglestue, C. Monte Carlo Simulation of Semiconductor Devices; Chapman and Hall: London, 1993. [6] Shah, J. In Spectroscopy of Nonequilibrium Electrons and Phonons; Shank, C. V., & Zakharchenya, B. P.; Ed.; North Holland: Amsterdam, 1992; pp 57-112. [7] Kash, J. A. ibid.; pp 113-168. [8] Lugli, P. ibid.; pp 1-56. [9] Ambacher, O.; Foutz, B.; Smart, J.; Shealy, J. R.; Weimann, N. G.; Chu, K.; Murphy, M.; Sierakowski, A. J.; Schaff, W. J.; Eastman, L. F.; Dimitrov, R; Mitchell, A., & Stutzmann M. J. Appl. Phys. 2000, 87, 334-344. [10] Wraback, M.; Shen, H.; Carrano, J. C.; Collins, C. J.; Campbell, J. C.; Dupuis, R. D.; Schuman, M. J., & Ferguson, I. T. Appl. Phys. Lett. 2001, 79, 1303-1305. [11] Wraback, M.; Shen, H.; Rudin, S.; Bellotti, E.; Goano, M.; Carrano, J. C.; Collins, C. J.; Campbell, J. C., & Dupuis, R. D. Appl. Phys. Lett. 2003, 82, 3674-3676. [12] Eastman, L. F.; Tilak, V.; Kaper, V.; Smart, J.; Thompson, R.; Green, B.; Shealy, J. R., & Prunty, T. Phys. Status Solidi A 2002, 194, 433-438. [13] Mishra,U.K. In 62nd Device Research Conference Digest;(IEEE Cat. No. 04TH8724), 2004, pp 3. [14] Eastman, L. F. In Proc. 29th WOCSDICE; Cardiff, Wales, 2005; pp 57-58. [15] Mishra, U. K. ibid.; pp 107-110. [16] Vertiatchikh, A.; Schaff, W. J., & Eastman L. F. In International Symposium on Compound Semciconductors; (IEEE Cat. No. 03TH8675), 2003, pp 53-54.

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[17] Oxley, C. H., & Uren, M. J IEEE Trans. Electron Dev. 2005, ED-52, 165-169. [18] Ramonas, M.; Matulionis, A., & Rota, L. Semicond. Sci. Technol. 2003, 18, 118-124. [19] Gaska, R.; Osinsky, A.; Wang, J. W., & Shur, M. IEEE Trans. Electron Dev. Lett. 1998, 19, 89-91. [20] Ardaraviˇcius, L.; Matulionis, A.; Liberis, J.; Kiprijanovic, O.; Ramonas, M.; Eastman, L. F.; Shealy, J. R., & Vertiatchikh, A. Appl. Phys. Lett. 2003, 83, 4038-4040. [21] Barker, J. M.; Ferry, D. K.; Goodnick, S. M.; Koleske, D. D.; Allerman, A., & Shul, R. J. J. Vac. Sci. Technol. B 2004, 22, 2045-2050. [22] Matulionis, A.; Liberis, J.; Matulionien˙e, I.; Ramonas, M.; Eastman, L.F.; Shealy, J. R.; Tilak, V., & Vertiatchikh, A. Phys. Rev. B 2003, 68, 035338. [23] Gokden, S.; Balkan, N., & and Ridley, B. K. Semicond. Sci. Technol. 2003, 18, 206-211. [24] Ridley, B. K.; Schaff, W. J., & Eastman L. F. J. Appl. Phys. 2004, 96, 1449-1502. [25] Ramonas, M.; Matulionis, A.; Liberis, J.; Eastman, L. F.; Chen, X.; Sun, Y.-J. Phys. Rev. B 2005, 71, 075324. [26] Chu, R. M.; Zhou, Y. G.; Zheng, Y. D.; Han, P.; Shen, B., & Gu, S. L. Appl. Phys. Lett. 2001, 79, 2270-2272. [27] Ridley, B. K. Rep. Prog. Phys. 1991, 54, 169-256. [28] Kolnik, J.; Oguzman, I. H.; Brennan, K. F.; Wang, R.; Ruden, P. P., & Wang, Y. J. Appl. Phys. 1995, 78, 1033-1038. [29] Ridley, B. K.; Foutz, B. E., & Eastman, L. F. Phys. Rev. B 2000, 61, 16862-16869. [30] Bulutay, C.; Ridley, B. K., & Zakhleniuk, N. A. Phys. Rev. B 2000,62, 15754-15763. [31] Price, P. J. Ann. Phys. 1981, 133, 217-239. [32] Goodnick, S. M.; Lugli, P. Phys. Rev. B 1988, 38, 10135-10138. [33] Reggiani, L.; Kuhn, T., & Varani, L. Appl. Phys. A 1992, 54, 411-427. [34] Adams, J. G.; Tang, T. IEEE Electron Device Letters 1992, 13, 378-380. [35] Bosi, S.; Jacoboni, C. J. Phys. C 1976, 9, 315-319. [36] Lugli, P.; Ferry, D. K. IEEE Trans. Electron Dev. 1985, ED-32, 2431-2437. [37] Lugli, P.; Jacoboni, C.; Reggiani L., & Kocevar, P. Appl. Phys. Lett. 1987, 50, 1251-1253. [38] Mickevicius, R., & Reklaitis, A. Solid State Communications 1987, 64, 1305-1308.

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[39] Ramonas, M., & Matulionis, A. Semicond. Sci. Technol. 2004, 19, S424-S426. [40] Paulaviˇcius. G.; Mitin, V. V., & Bannov N. A. J. Appl. Phys. 1997, 82, 5580-5588; [41] Shi, L.; Ponce, F. A., & Menendez, J. Appl. Phys. Lett. 2004, 84, 3471-3473. [42] Ardaraviˇcius, L.; Liberis, J.; Matulionis, A.; Eastman, L. F.; Shealy, J. R., & Vertiatchikh, A. Phys. Stat. Sol.(a) 2004, 201, 203-206. [43] Ardaraviˇcius, L.; Ramonas, M.; Kiprijanovic, O. Liberis, J.; Matulionis, A.; Eastman, L. F.; Shealy, J. R.; Chen, X., & Sun, Y. J.Phys. Stat. Sol. (a) 2005, 202, 808-811. [44] Matulionis, A.; Liberis, J., & Ramonas, M. AIP Conf. Proc 2005, CP780, 105. [45] Katilius, R. Phys. Rev. B 2004, 69, 245315. [46] Matulionis, A., & Liberis, J. IEE Proc.-Circuits Devices Syst. 2004, 151, 148-154.

In: New Research on Semiconductors Editor: Thomas B. Elliot, pp. 123-142

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

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 Laboratory of Excited State Processes, Chang Chun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences, 130033,P.R.China

Abstract In this paper, 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 9.95ȍ·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

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Y. M. Lu, D. Z. Shen, J. Y. Zhang et al. 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.

1

Introduction

For some time now there has been a great deal of attention in wide band-gap semiconductors, in particular there is strong commercial desire to produce efficient and lasting blue-light emitting diodes (LEDs) and short-wavelength laser diodes (LDs). World-wide research efforts were initially focused on ZnSe and its alloys[1,2], but recently, GaN based technologies have progressed more rapidly[3]. These developments have culminated in the demonstration of room-temperature (RT) operating green-blue as well as blue LD structure[46]. ZnO, as an oxide, is another wide band semiconductor material with a direct band gap of 3.37eV at RT[7]. It is superior over nitrides and selenides in chemical and thermal stability and in resistance to chemical attack and oxidation. It has a high exciton binding energy of 60 meV[8], which in principle should allow efficient excitonic lasing mechanisms to operate at RT. Ultraviolet (UV) stimulated emission and lasing have been extensively reported in ZnO microcrystallite thin films[9] and its quantum well structure[10]. To realize these device applications, an important issue is to fabricate both high-quality p-type and n-type ZnO films. However, like most wide band-gap semiconductors, ZnO has the “asymmetric doping” limitation, i.e., it can be an easily doped high-quality n-type, but it is difficult to dope p-type. This is due to the existent of some problems such as its self-compensating effect, deep acceptor level, and low solubility of the acceptor dopant. For the realization of p-type ZnO, it is necessary to grow high crystalline quality ZnO thin film. Therefore, the extensive researches were reported on the growth of ZnO thin films by various growth techniques including magnetron sputtering [11], chemical vapor deposition (CVD) [12], and plasmamolecular beam epitaxy (P-MBE) [13]. However, it has hardly been obtained for the preparation of high quality ZnO thin films. This is due to that insufficient supply of oxygen during growth results in the formation of many structural defects such as oxygen vacancies (VO) or Zn interstitials (Zni) in ZnO films [14,15]. On the other hand, the 18% lattice mismatch between ZnO and Al2O3 substrate[13,16] will strongly influence the structural, optical and electrical properties of ZnO thin films. So far, many researches on the growth of high-quality ZnO thin films are reported, including accommodation of II/VI ratio [14, 17], post-deposition annealing [15,18], low-temperature buffer layers [16, 19], MgO buffer layers [17, 20] and polarity control [18, 21]. Although high temperature growth has revealed the improvement of ZnO crystal quality[20], the systemic study on effects of growth temperature on optical and electrical properties of ZnO grown directly on Al2O3 substrates have been not reported. In this paper, the influence of growth temperature on ZnO film quality grown on Al2O3 substrates was investigated by the measurements of optical and electrical properties. The result indicates that the crystalline quality of ZnO films was improved with increasing growth temperature. The unintentionally doped ZnO usually shows n-type conduction, which is related to either presents of native donor defects, such as O vacancies (VO) or Zn interstitials (Zni) [22]. These native defects have been demonstrated that they have lower formation energy than other acceptor defects (O interstitials or Zn vacancies VZn) whether in Zn rich condition or not

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[15]. For Compensation of these native defects, all of the common group V elements, i.e., N[23], P[24] and As[25], have been used to make p-type ZnO. In particular, N was established as being the more soluble group-V impurity. The theory predicts that N is a better candidate in current research for p-type doping of ZnO [26]. Under proper conditions, it is expected to form nitrogen substitution in the oxygen site (NO), which is a single shallow acceptor [27]. However, surprising behavior was uncovered: Doping with N2O or N2 source led to n-type, not p-type conduction [28-30], while doping with an NO2 or NO source without the use of plasma led to p-type behavior successfully by MOVCD technology [31,32]. This is due to the difficult for breaking N2 bond, so the (N2)O was easily formed, which is a shallow double donor. For NO molecules, it is more easily to provide single-N atoms. (N2)O centers are difficult to be formed due to the tiny probability of the process of two N atoms arriving simultaneously at the same site on the growth surface [27]. In this work, we successfully prepared p-type ZnO thin films by P-MBE using NO as both O source and N dopant. The significant difference between our experiment and reports [31] is that the N-O bond was broken by an r.f. atomic source before the molecules arrived to the substrate. In an optimum growth temperature, it is found that the p-type ZnO films can be prepared easily by activated NO doping and the results have good repeatability. Additionally, compared to direct NOdoping [31], the use of activated NO can decrease distinctly the growth temperature for ptype ZnO thin films. Although many groups reported to have successfully made p-type ZnO by using group V elements, such as N[23], P[24], As[25] and so on, the hole concentration or mobility was too low to meet the demands of device fabrication. We should also mention here that there is a ptype ZnO with lower resistivity using NO as dopant. However, there is still no progress in homo-junction based ZnO p-n diodes. So far, only two results of ZnO p-n homo-junction with weak bluish-white light emission and weak white-violet emission were reported [33,34]. To take the advantage of ZnO, many researchers tried to use ZnO heterojunction devices, including p-n heterojunction such as n-ZnO/p-transparent oxide semiconductor (pSrCu2O2[35], p-ZnRu2O[36], Cu2O[37]), n-ZnO/diamond[38] and n-ZnO/p-Si[39], and MIS diode with insulator formed by N+ ion implantation[40]. Among numerous candidates, GaN is with the same crystal structure as that of ZnO and with similar band gap energy at room temperature (ZnO 3.37 eV, GaN 3.4 eV). Due to the accessibility of high quality p-type GaN, it starts to draw great attention for the fabrication of ZnO heterojunction. Stronger emission has been observed in n-ZnO/p-GaN heterojunction, although the emission of the p-GaN still plays dominant role in the EL spectra [41] due to the large density of electrons injected into the p-GaN layer. Recently, Ya. I. Alivov [42] reported the use of AlGaN as the hole injection layer in the ZnO heterojunction to effectively block the electron, resulting in the successful observation of the exciton emission originated from the ZnO. Since the epitaxially grown ZnO is intrinsically n-type with high electron concentration, it is difficult to make ZnO p-i-n heterostructure with the recombination region in the ZnO layer. In this paper, we make use of the high resistivity characteristic of the nitrogen-doped ZnO to design and fabricate p-i-n heterojunction. By inserting the insulating N-doped ZnO layer between the n-ZnO and the pGaN layers, the electrons and holes are believed to be blocked inside the N-doped ZnO. In the EL spectra, the near ultraviolet emission band was observed at room temperature for the p-i-n structure, which is different from the blue emission for the p-n junction samples. The recombination mechanism will also be discussed based on the comparison between the PL, EL and absorption spectra.

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Experiments

Al2O3 substrate was cleaned by acetone and methanol for 10 min, respectively, and then etched by solution of H2SO4:H3PO4=3:1 for 10 min, followed by a rinse in deionized water and dried by the high-pure(5N) nitrogen gas. The chemical cleaned substrates were degassed at 650 in ultrahigh vacuum atmosphere (<1×10-6 Pa) for about 30 min. A Knudsen effusion cell is used to evaporate elemental zinc with 99.9999% purity. Atomic oxygen is activated from ultrapure O2 gas (99.999%) by an rf-plasma source with an electrostatic ion trap operated at 500V. Before growth, the substrate that mounted on a molybdenum holder using indium as solder was treated by O-plasma at 650 for 30 min, which is expected to remove surface contaminant and produce oxygen terminated Al2O3 (0001) surface[13]. During growth, the Zn source flux and O2 partial pressure in the growth chamber are kept at 4×10-5 Pa and 6×10-3 Pa, respectively. The growth temperature of ZnO film was varied between 350°C and 700 °C. For the growth of p-type ZnO films, two gas sources were used, respectively, i.e., N2 (99.9999%) + O2 (99.9999%), and NO(99.99%). Zn beam pressure is fixed at 4×10-4 Pa and the substrate temperature was kept at 400 °C. The thicknesses of all the samples are about 200-400 nm. The growth process was monitored by in-situ RHEED. For the growth of the p-i-n heterojunction using MBE, Mg doped p-type GaN grown on c-plane sapphire by metal organic chemical vapor deposition (MOCVD) served as the substrate. The hole concentration and mobility, determined by Hall effect measurement, were p=2.7 1017cm-3 and ȝ=5.1cm2 V-1S-1. The epilayers were consisted of 20nm insulating ZnO followed by 200 nm n-type ZnO. In order to grow the insulator layer of p-i-n structure, N2 gas was introduced into the growth chamber through the same r.f. plasma as that of the oxygen. The as-grown ZnO showed n-type conductivity (n=2 1018cm-3, U=0.6ȍcm) in our samples due to the intrinsic donor defects, such as Zni or VO3. Just like previous reports [40,43], nitrogen doped ZnO showed high resistivity characteristics (U=4650ȍcm). To make ohmic contact, indium electrode was fabricated on the n-type ZnO film by soldering at 300 0C for 10 min. Ohmic contact to p-type GaN was made by thermal evaporation of Ni/Au and thermal anneal at 4000C for 15min in oxygen gas. The quality of the grown samples was characterized by the Rigaku Company O/max-RA X-ray system, D/Max 2400 double crystal diffractometer at 40 kV and 98 mA and VG ESCALABMK XPS system. The surface morphology was analyzed by the measurement of atomic force microscope (AFM). The optical properties of all samples were studied by absorption and photoluminescence (PL) spectra. UV absorption spectra were measured using the SHIMADZU UV-3101 PC spectrophotometer. A JY63 Micro Raman spectrometer was employed for PL measurement. The luminescence was detected by a charged-coupled device (CCD) detector. The 325nm line of a He-Cd laser was used as the excitation source. The liquid-nitrogen cooling system was used in conjunction with the sample stage to cool a sample down to 80K. The temperature was controlled by the TMS94 from 80K to room temperature. The ZnO/GaN diodes were excited by pulse current in forward bias with the pulse width of 0.2ms and repetition frequency of 160Hz. The EL spectra were measured using a grating monochromater of Model Spex 1404 with an RCA-C31034 cooled photomultiplier. The electrical properties of as-grown samples were measured by the Hall system of LakeShore Company with Model 7707 at the field strength of 3200 Gauss.

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Results and Discussion Growth of High Quality ZnO Thin Filmes

Fig.1 shows the RHEED patterns of the substrate exposed to O-plasma at 650 for 30 min and the samples grown at 350 , 550 and 650 , respectively. After plasma treatment, the substrate gives a streaky pattern (Fig.1a), which indicates a well-ordered and flat Al2 O3 surface. For the grown samples, RHEED results exhibit different patterns with the changing of growth temperature, as seen in Fig.1b~Fig.1d. At growth temperature of 350 , a spotty pattern indicates a rough surface consisting of ZnO crystallites. When the growth temperature increases to 550 , a elongated spotty pattern was observed. While at high temperature (above 650 ), sharp streaky RHEED patterns show the formations of the smooth ZnO surfaces. Y. Chen et al. [44] had reported a gradual change of the RHEED patterns from streak to spotty during the growth stages for ZnO film, which was due to the transition of the epitaxial growth mode from 2D nucleation to 3D nucleation. Compared to our results, the RHEED patterns reveals that the growth mode changes from 3D to 2D with increasing growth temperature.

(a)

(b)

.

(c)

(d)

Fig.1. The RHEED patterns of Al2O3 substrate treated by O-plasma (a) and ZnO thin films grown at 350 (b), 550 (c) and 650 (d).

To understand the effect of the growth temperature on surface morphology, the ZnO thin film surfaces were analyzed by AFM measurements. Fig.2 shows the 2ȝm×2ȝm surface roughness images of the samples grown at 350 , 450 , 550 and 650 , respectively. With increase of the growth temperature, the root-mean-square (RMS) roughness of ZnO samples gradually decreased from 6.5 nm to 3.4 nm. The change of the surface roughness indicates the difference of the epitaxial growth mode, in which the formation of 2D growth is easy at high temperature. The growth mode dependent on the growth temperature can be clearly seen by the measurements of the mean crystal grain sizes. At the growth temperatures of 350 and 450 , the mean crystal grain sizes are in range of 20-25 nm and 25-30 nm, respectively. Be close to growth temperature of 550 , the crystal grain size is more than 100nm. For growth temperature of 650 , the crystal grain size becomes upwards of 200nm. The temperature dependence of the grain size can be explained by the migration and the diffusion of the

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reactants. At low temperature, the zinc and oxygen atoms can be absorbed easily on the substrate surface and diffuse into the nucleation sites to form ZnO film. However, the lower migration and diffusion rates will lead to 3D nucleation. In this case, ZnO epilayer has a small crystal grain size and a rough surface. With the increasing temperature, the enhancement of the atomic migration ability results in the increasing of the grain size and the decreasing of the surface roughness. This evolution reveals a transition of the growth mode from the 3D growth to 2D growth with increasing growth temperature. The 2D growth would be preferable for the growth of high-quality ZnO films[45].

(a)

(b)

(c)

(d)

Fig.2 AFM images of ZnO thin films grown at (a)350 , (b)400 ,(c)550

and (d)650 .

Table 1 The crystal quality and optoelectrical properties of the ZnO samples grown on Al2O3 substrates at different temperatures. Growth temperature of samples 350 400 450 500 550 600 650

FWHMs of ZnO (002) differaction peaks 0.84867 0.79063 0.77077 0.61130 0.47916 0.44731 0.29392

Intensity ratio of UV emission and visible emission 0.36 1.68 2.96 6.10 10.86 43.20 82.70

Carrier concentration 1.06×1019/cm3 1.92×1018/cm3 1.87×1018/cm3 9.80×1017/cm3 9.19×1016/cm3 8.16×1016/cm3 7.66×1016/cm3

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X-ray diffraction spectra of the ZnO films give only diffraction peak of ZnO (00·l) orientation, indicating the formation of wurtzite structural ZnO with a preferential orientation. In X-ray rocking curve spectra of ZnO (002) diffraction peak, the full width at half maximum (FWHM) decreases from 088˚ to 0.20˚ with increasing growth temperature from 350°C to 650 °C, as is shown in Table 1. While at 700 , the FWHM becomes up to 0.78°. Fig.3 shows the PL spectra of all as-grown samples at RT. As is clearly seen in Fig.3, the main features of the PL spectra are similar for all samples. A strong ultraviolet (UV) emission and a weak visible emission in the PL spectra are observed. The UV emission is considered to be from free exciton emission, which will be identified by the temperature-dependent PL spectra discussed below. The visible emission located at around 2.500eV is usually associated with intrinsic defects such as oxygen vacancies (VO) [15]. As the growth temperature increases from 350 to 650 , the FWHM of UV emission band becomes narrow and relative intensity of the visible emission decreases, indicating the improvement of the ZnO thin film quality with increasing growth temperature. Table 1 gives the integral intensity ratio of UV emission and visible emission. For the ZnO films grown at 350 and 400 , the energy positions of UV emission peaks are located at 3.357 eV and 3.341 eV, respectively. The blue-shifts are observed by comparing with other samples grown in temperature range of 450 ~650 , in which positions of the UV peaks are located at about 3.295 eV. When the growth temperature is 700 , the FWHM of the UV emission band becomes broad and the intensity of the visible emission increases, as seen in Fig.3h. We note that UV emission peak at 700 shows a noticeable red-shift (>80meV). At high temperature, because of the reevaporation of surface atoms and the mismatch of thermal expansion coefficient lead to high density of structural defects and misfit dislocations formed in ZnO films. It is suggested that the UV emission peak at 3.212eV is related to the bound excitons due to these defects as deep centers. The above results indicate that the quality of ZnO thin film at 700 is relatively poor.

(a) (b)

PL Intensity (a.u.)

(c)

(d) (e) (f) (g) (h)

2.4

3.0 Energy(eV)

3.6

Fig.3 The PL spectra at RT of ZnO thin films grown at (a)350, (b)400, (c) 450, (d)500, (e) 550, (f) 600, (g) 650 and (h)700 .

The room temperature electrical properties of ZnO films grown at different temperatures were measured by the four-probe van der Pauw method. Based on these measurements, all samples show n-type characteristics. The room temperature carrier concentration as function of the growth temperature was shown in Table 1. As the growth temperature was increased

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from 350 to 650 , the carrier concentration decreases from 1.06 ×1019 /cm3 to 7.66 ×1016 /cm3. At growth temperature of 700 , the carrier concentration increases to N=8.5 ×1018 / cm3. Joshy Jose et al. reported that the grain boundary would influence carrier concentration [46]. Because the defects can be very easily concentrated in the grain boundary, the sample of smaller grain size has a high carrier concentration. With the growth temperature increase, the changing of carrier concentration with that of the intensity of the visible emission related to oxygen vacancy [12]. The oxygen vacancy is considered to be an intrinsic donor in ZnO. However, if only oxygen vacancy density affect electrical properties, the measured carrier concentration is quite surprising. S.B.Zhang et al.[12] had proposed that interstitial Zn (Zni) as another donor would play an important role in the electrical properties, because the Zni level is shallower than the level of oxygen vacancy [12]. Zn atoms absorbed on the substrate surface need enough thermal activated energy to take the lattice sites. A low growth temperature will lead to the formation of Zni with higher density in ZnO films. In this case, the Zn atoms diffused into interstitial sites will act as shallow donors. This means that the coexistence of oxygen vacancy and Zni defects will influence the carrier concentration. With increasing temperature, these crystal defects contributing to the carrier concentration are decreased due to the enhancement of the atomic diffusion ability. However, the formation of thermal defects with high density will result in the increasing of carrier concentration at high temperature. In the optimum growth condition(650 ), the carrier concentration has a minimum of N=7.66 ×1016 / cm3 which is closed to that of bulk ZnO[47]. E2 3.378eV a)

intensity(a.u)

E1 3.392eV

E 3 3 .3 5 8 e V in te n s ity (a .u )

b)

3 .2 0

3 .2 5

3 .3 0 3 .3 5 3 .4 0 e n e r g y (e V )

Fig.4 The PL spectra of the ZnO thin films grown at 350

3 .4 5

and 650

3 .5 0

measured from 82K to 300K.

In order to investigate the origin of UVE peak at RT, dependence of the PL spectra on the temperature was measured for all samples. Fig.4 gives the measured results of the samples grown at 350 and 650 . At the temperature of 82K, PL spectrum of the sample grown at 350 shows that two UV emission peaks labeled E1 and E2 were located at 3.378eV and 3.392eV, respectively. For the sample grown at 650 , only one UVE peak E3 at 3.358eV was

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observed at 82 K. With increasing temperature, the integral intensity ratio of E1 to E2 increases and the E2 peak disappears around 170K. The temperature dependence of the integrated PL intensity can be expressed by the following equation [48] I0

I (T )

1  A exp( 

(1)

'E ) kBT

where 'E is the thermal activation energy, k B is the Boltzman constant, I 0 is the emission intensity at 0K, T is the thermodynamic temperature and A is a contains ratio of opticalcollection efficiencies and effective degeneracy between the unbound and bound states. The experimental data can be fitted by using the equation (1), as shown in Fig.5 with the solid lines and broken lines, 'E values of the bands E1, E2 and E3 are 63meV, 20meV and 58meV, respectively. In Ref.49, the free exciton binding energy of bulk ZnO is about 60meV, which is approximately equal to the 'E values of the bands E1 and E3. Therefore, the origin of the bands E1and E3 was considered to be from the free exciton recombination. The excitons bound to neutral donor in ZnO have been reported [49], in which the binding energy of the bound exciton was about 20 meV. We suggest that the band E2 observed in the range of low temperature is from donor-bound-exciton transition.

P L In t e g r a t e In t e n s it y (a .u .)

Experimental data of E2 peak Experimental data of E1 peak Theoretical fit of E2 peak Theoretical fit of E1 peak

(a)

E x p e r im e n ta l d a ta o f E 3 p e a k T h e o r e t ic a l f it o f E 3 p e a k

(b) 2

4

6

8

10

12

14

-1

1 0 0 0 /T (K )

Fig.5 The fitting curve of PL intensity as a function of measured temperature of ZnO thin films grown at 350 and 650 .

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The AFM images have revealed that the mean crystal grain sizes become small with decreasing growth temperature. It is known that small grain size will lead to the quantum confinement effect. An expression for the shift of energy gap ( 'E g ) due to the quantum confinement effect is given by [50] 'E g | E g 0 

h 2S 2 P 2d 2



1.8e 2 Hd

where E g 0 is the energy gap for bulk materials, d is the particle size,

(2)

1

1 1  ( m e and me mh

P

m h being the electron and hole effective masses, respectively), and

H

is the dielectric

constant. For ZnO, the effective masses of electrons and holes are 0.38 m0 and 1.80 m0[51], respectively, and the dielectric constant is 8.75. For the ZnO, the equation (2) can be expressed as follows: 'Eg | 75.885d 2 (nm)2  1.902d 1(nm)

(3)

By the measurement of AFM, the mean crystal grain sizes of the samples grown at 350 and 400 are about 23 and 27nm, respectively. Using equation (3), the calculated Eg values are 60 and 34meV, respectively. Because the UVE peak at RT is identified to be from the recombination of free exciton, the energy change of band gap should be equal to that of UV emission peak. From Fig.3, we obtain that the blue shifts of UV emission peaks for the samples grown at 350 and 400 are 60meV and 44 meV, respectively. These results are in agreement with the above calculated values.

B

Preparation of the p-type ZnO

Table 2 gives the ZnO samples grown by using different gas source. Sample A is the N-doped ZnO thin films using radical N2. The N2 and O2 are separated to two different plasma chambers. The typical N-doped ZnO thin films using radical N2 has a low carrier concentration 2.5×1014cm-3 and a high resistivity 900ȍ.cm. Although the radical N2 can be incorporated into the ZnO films and compensate the native donor defects resulting in the trends toward to p-type, the attempts to obtain p-type ZnO by employing radical N2 are failed, as reported in Ref. [52-54]. Sample B is the ZnO thin films prepared by employing the radical NO. Hall effect measurement results indicate that sample B shows p-type conduction with a high net hole carrier concentration (NA-ND) of 1.2×1018 cm-3 and lower resistivity of 9.95ȍ.cm. The hole carrier concentration varies from 1.0×1015 to 1.2×1018 cm-3 under the different preparing condition, such as growth temperature, flow rate of NO, for the p-type ZnO. The sample C, undoped ZnO thin films, shows typical n-type conduction with the carrier concentration of 2.74×1019cm-3 and a lower resistivity of 0.043ȍcm. The n-type conduction in native ZnO films is generally accepted arose from either oxygen VO or Zni because they have low formation energy either in O-rich or Zn-rich conditions [52].

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Intensity (a.u)

Al2O3(006)

ZnO(002) A B

C 25

30

35

40

45

50

55

60

65

70

75

2T(Deg.)

Fig.6 XRD spectra of N-doped ZnO using radical N2 (A), radical NO (B), and undoped ZnO sample (C).

Table 2 The prepared conditions and electronic properties of N-doped using radical N2(Sample A) ,radical NO(Sample B),and undoped ZnO (Sample C). FO2 and FNO represent the flow rate of O2 and NO, respectively. Sample

Gas

FO2*

FNO*

Carrier type

N2

0.1

1.0

B

NO

0

1.0

C

O2

1.0

0

Mobility

ȍ.cm

cmV-1s-1

n

24.60

0.89

1.43×1016

p

9.95

0. 53

1.26×1018

0.043

5.34

2.74×1019

(sccm) (sccm) A

Resistivity

n

Carrier

concentration(cm-3)

The crystalline structures of as-grown samples were investigated by XRD spectra, as shown in Fig.6. Besides the diffraction peak of Al2O3(006), only one peak related to wurtzite structural ZnO(002) can be observed for all samples, which located at 34.40º. Although nitrogen as dopant source for p-type ZnO thin film was usually found to increase the tensile force and lattice constants for the N-doped ZnO [55], however, obvious change in d value was not observed in our work. When radical N2 gas or radical NO gas was used for growth of N-doped ZnO, the intensity of the diffraction peak of ZnO (002) is significantly reduced, and FWHM is relatively broad comparing with the undoped ZnO thin film (sample C). The FWHM of ZnO(002) diffraction peak is 0.34°for sample A, 0.25°for sample B and 0.15°for sample C. The broadening of N-doped ZnO(002) peak should be attributed to the defects related to incorporation of N in the films, as observed by Li et al.[31].

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Absorption intensity(a.u.)

RT

Radical N 2 doped ZnO Radical NO doped ZnO Undoped ZnO

400

500

600

Wavelength(nm)

Fig.7 Absorption spectra of N-doped ZnO using radical N2 (A), radical NO (B), and undoped ZnO sample (C).

Fig.7 shows the absorption spectra for N-doped ZnO and undoped ZnO thin films. It is obvious that the absorption intensity of N-doped ZnO thin films is smaller than that of the undoped ZnO thin films. The sample C shows a very sharp absorption edge. While the N doped ZnO thin films show a much mild absorption edge. Similar result was also observed by Garces et al. [56] and Li et al. [31], which is concluded that subbandgap levels associated with N doping present in the band-gap of ZnO. p-type ZnO thin films undoped ZnO thin films

9000

DAP FE

Intensity(a.u.)

DAP-1LO D0X

6000 DAP-2LO 3000 FE-1LO

FE

FE-2LO 0 3.0

3.1

3.2

3.3

3.4

Energy (eV) Fig.8 Photoluminescence spectra of N-doped and undoped ZnO samples.

Fig.8 is the photoluminescence (PL) spectra of p-type and undoped ZnO thin films measured at 77K. The near-band-gap emission of the sample A is not detectable. The UV emission of the undoped ZnO (sample C) consists of free exciton band at 3.377eV, neutraldonor-bound-exciton (D0X) band at 3.360eV and replica lines of free exciton with first and

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second-longitudinal optical (LO) phonon at 3.313eV and 3.240eV, respectively [57]. While in the p-type ZnO (sample B), beside emission of free exciton at 3.377eV, three peaks located at 3.267eV, 3.197eV and 3.124eV were found. These peak positions depend on the N concentration. Similar result has been observed by Tamura et.al in their work [58], in which the peak at 3.267eV is assigned to donor-acceptor pair (DAP) transition. Three peaks have equal energy spacing of about 70meV, which is in good agreement with the energy of LO phonon of ZnO. This implies that the peaks at 3.197eV and 3.124eV are the first and secondLO phonon replica of DAP, respectively. The energetic position (EDAP) of DAP transition can be calculated by the following equation [23]:

EDAP

E gap  ED  E A 

e2 4SHr

(4)

where Egap, ED and EA are the energy of band gap, the binding energy of donor and the binding energy of acceptor, respectively. e is the dielectric constant, and r is the pair separation. The pair separation r can be very roughly estimated by letting ~( 3 / 4 S N A ) 1/3. The NA=ND + 1.2×1018cm-3, and which is estimated to be in the range of 1019-1020 cm-3. The dielectric constant of ZnO is 8.3, the donor binding energy is known to be about 60meV and the energy gap at 77K is Egap =3. 437eV [59,60]. Thus, EA§168-234meV can be obtained, which is similar with the reported value of EA=165±40meV [61]. O*

Radical NO

st

nd

N 2*(1 )

N 2*(2 )

O*

Intensity(a.u.)

N* N*

Radical N 2 N* 300

400

500

600

700

N* 800

Wavelength(nm)

Fig.9 The optical emission spectra of radical NO (a) and nitrogen (b).

To explain the formation mechanism of p-type ZnO, the optical emission spectra (OES) of the radical N2 and radical NO are investigated. Fig.9 shows the OES of radical NO and N2, respectively. The OES spectrum of NO is dominated by the emission peaks of atomic oxygen (O*) located at 777 nm and 841 nm originating from 3p5P-3s5S0 and 3p3P-3s3S0 transitions, and emission of atomic nitrogen (N*) located at 744 and 821nm from 3S4 P-3P4S0 and 3S4 P3P4 P0 transitions, respectively [56]. Further, a very weaker emission peaks of radical

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nitrogen moleculars (N2*) originating from the second positive (C3 Ȇu-B3 Ȇg) and first positive (B3 Ȇu-A3 Ȉu+) transition were also observed in the wavelength regions of ultraviolet and visible light [26]. While the OES of radical N2 is dominated by the emission peaks of second positive and first positive transition (N2*). Namely, the chemical species in radical NO and radical N2 are different, this may be the reason for the difference in electrical propertied of N doping ZnO by the two dopants. Although the NO acceptors were formed by radical N2 doping, however, in the same times, the (N2)O were also introduced and which compensated the NO acceptors because the radical N2 is consisting of more N2* than radical NO. Based on the above depictions, the produce of N* seems to be responsible for p-type conduction of ZnO thin films in our work. It is also reported that p-type ZnO was prepared using NO in Ref.31 and Ref.32. The success in the p-type ZnO by N-doping indicates that the NO is a good dopant to fabricate p-type ZnO.

C

Fabrication of the ZnO/GaN pn Heterojunction LED

Fig.10 shows the current-voltage curve of the n-ZnO/i-ZnO/p-GaN heterojunction by solid line and the inset figure gives the schematic diagram of the device structure. The heterojunction diode exhibited rectifying I-V characteristics. In Fig.8, the dash line presents the current-voltage curve of p-GaN/n-ZnO p-n heterojunction. We found that p-i-n heterojunction has larger resistance than p-n heterojunction from I-V curves. This maybe come from the existence of high resistivity N-doped ZnO layer. And current-voltage curve of p-i-n heterojunction showed turn on voltage of ~3.3eV very close to RT band gap of ZnO.

In

1.5

Current (mA)

n-type ZnO i-ZnO 1.0 p-type GaN

Ni/Au

0.5

0.0 p-n heterojunction p-i-n heterojunction -0.5

-1.0 -20

-15

-10

-5

0 5 Voltage (V)

10

15

20

Fig.10 RT current–voltage characteristics of the fabricated diodes composed of n-ZnO/p-GaN and nZnO/i-ZnO/p-GaN heterojunctions. The inset is the schematic diagram of the p-i-n heterojunction device.

EL spectra of the n-ZnO/i-ZnO/p-GaN and n-ZnO/p-GaN heterojunction at room temperature are shown in Fig.10. From the EL spectra, very broad emission band centered at 430nm was observed for p-GaN/n-ZnO heterojunction. This is consistent with the reported result in GaN pn junctions, in which the emission was attributed to the Mg levels in p-GaN

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[41]. To understand the reason why the luminescence originates from the GaN layer in nZnO/p-GaN heterojunction, we have examined the band structure of the heterojunction. If we simply take the band offset of the GaN/ZnO heterojunction given by the Anderson model[62], the conduction band offset (ǻEc) and the valence band offset (ǻEv) are given by

F ZnO  FGaN

(5)

Eg ZnO  'E C  Eg GaN

(6)

'EC 'EV

in which the EgZnO and EgGaN are the band gaps of ZnO and GaN, respectively, ȤZnO and ȤGaN are the electron affinities of ZnO (4.35 eV)[63] and GaN (4.2 eV)[64], respectively. The calculated result gives the conduction band offset of ǻEc=0.15 eV and similar valence band offset of ǻEV=0.12 eV. Namely, the electrons in ZnO and holes in GaN will overcome almost equal barrier to realize the carrier injection. In this work, electron concentrations of n-type ZnO are 1018 cm-3 and hole concentration of p-type GaN are 1017 cm-3, and considering of the mobility of the electrons is much bigger than that of the holes, the electrons will be injected much easier into p-type GaN than holes into ZnO, resulting in the observation of the electroluminescence originating from GaN layer. However, the emission of the p-i-n heterojunction is different from that of the p-n junction. There appears a near ultraviolet peak at about 400 nm in the EL spectra of the forward biased LED. For the p-i-n heterojunction, the emission peak shows obvious blue-shift and narrowing, as seen in Fig.11. This indicates that the emission intensity near ultraviolet region increases and the blue emission at 430 nm becomes weak. The weak tail in the blue region is possibly due to the recombination of the excess electrons injected into the p-GaN layer, similar to the p-n junction. This implies that the blue emission at 430 nm originating from GaN layer is strongly suppressed in the p-i-n heterojunction. 800 700 600

500

400

300

430nm 400nm

EL intensity (a.u.)

p-i-n heterojunction p-n heterojunction

1.5

2.0

2.5

3.0

3.5

4.0

4.5

Energy (eV)

Fig.11. The EL spectra of the heterojunction LEDs with the solid line for the n-ZnO/i-ZnO/p-GaN junction and dashed line for the n-ZnO/p-GaN junction.

Y. M. Lu, D. Z. Shen, J. Y. Zhang et al.

-2

Absorption coefficient D (x10 cm )

138

undoped ZnO nitrogen doped ZnO

2

1.0

0.5

Normalized PL intensity (a.u.)

10

1.0 0.8 0.6 0.4 0.2 0.0 2.0

2.5

3.0

3.5

Energy (eV)

0.0

3.0

3.2

3.4

Energy (eV)

Fig.12 Square plot of the absorption coefficient as a function of photon energy for the undoped ZnO film and ZnO: N film grown on C-plane sapphire. The inset shows the RT PL spectra of different samples as indicated.

We attribute the ultraviolate emission to the nitrogen doped ZnO layer sandwiched between the n-ZnO and p-GaN. In order to investigate the properties of this layer, both nitrogen doped ZnO and undoped ZnO thin films were grown on c-Al2O3 substrate. Fig.12 shows the absorption spectra of the above two samples at room temperature. Optical band gap (Eg) and absorption coefficient (Į) can be expressed by the following equation[65]

D (hQ )

A (hQ  Eg )1 2

(7)

where hȣ is the photon energy, A* is a constant independent of photon energy. Following this relationship, the band gaps of the ZnO: N and undoped ZnO thin films are subtracted from the plot of Į2 as a function of the incident photon energy by extrapolating the linear part of the curve to intercept the energy axis. As shown in Fig.10, the optical band gap of ZnO: N becomes narrower than that of undoped ZnO thin film with the difference of about 90 meV due to the formation of the nitrogen impurity band. Masanobu Futshara et al have also observed similar phenomena in their woks [66]. The room temperature PL spectra were also shown in the inset. The emission peak for the N-doped sample shows obvious redshift comparing with that of the undoped ZnO thin film, which is consistent with the optical bandgap narrowing observed in the absorption spectra. When N-doped ZnO was inserted into heterostructure, the injected carriers inclucing electrons from n-type ZnO layer and the holes from p-type GaN layer will be blocked and recombine inside the ZnO: N layer. The energy diagram of the p-i-n heterojunction is shown in Fig. 13. By comparing the EL spectra of the p-i-n heterojunction and the PL spectra of the insulating ZnO thin film, we can also come to the conclusion that the EL emission in near-ultraviolet region originating from the i-ZnO layer in the device. We noted that the energy position of the emission peak exhibits a slight shift between the EL spectrum of the p-i-n heterojunction and the PL spectrum of N doped ZnO film. This is interpreted as the co-existence of the GaN related emission located at the

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lower energy side (blue region) in the p-i-n heterojunction. A small quantity of electrons still get across the i-ZnO layer and are inject into p-GaN region, resulting in weak blue emission from the GaN layer. Further optimized growth conditions and device structure of the heterojunction are in progress. Vacuum level

Ȥ=4.20eV

Ȥ=4.35eV Eg=3.40eV

Eg=3.37eV n-type ZnO

i-ZnO

p-type GaN

Fig.13 The band diagram of the p-GaN/i-ZnO/n-ZnO heterojunction.

4

Conclusions

The optical and electrical properties of ZnO thin films grown at different temperature by PMBE were investigated. The influence of growth temperature on the quality of ZnO film prepared by P-MBE is investigated. At growth temperature of 350 , ZnO crystallites with a rough surface was formed by 3D epitaixal growth. With the growth temperature increase, the roughness of ZnO films gradually decreases and the crystal grain size becomes large. The growth mode changes from the 3D growth to 2D growth as the growth temperature increases above 650 . For the samples grown below 650 , the UV emission band at RT is identified to be from free exciton transition. The blue shift of the samples grown at lower growth temperatures is attributed to the quantum confinement effect due to smaller crystal grain sizes. At the growth temperature of 700 , the UV emission peak at 3.212eV is considered to be related to the excitons bound to neutral donor. The PL spectra and Hall effect measurements show that the crystal quality of ZnO thin films was improved with increasing the growth temperature. The p-type ZnO thin films were grown using radical NO as nitrogen and oxygen sources by P-MBE technology. The absorption spectra show the presence of subbandgap levels associated with N doping. The p-type ZnO has a minimum resistivity of 9.95 : ˜ cm and hole concentration of 1.2×1019cm-3. From OES of radical NO and radical N2, It was found that the atomic N from radical NO is responsible for p-type ZnO and the N-O complex is possible to be a shallow donor in the ZnO thin films.. The success in the N-doped p-type ZnO demonstrated that it is the feasibility to use radical NO source as N dopant.

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We have fabricated p-GaN/i-ZnO/n-ZnO heterojunction LEDs by plasma-enhanced molecular beam epitaxy, in which nitrogen doped ZnO was introduced as the insulator layer. Diode like I-V characteristic has been observed under forward bias. RT EL spectrum shows strong emission at near-ultraviolet region without the deep center related luminescence. By comparison with the p-n heterojunction and PL spectra of ZnO, it is confirmed that the origin of the emission comes from the insulating ZnO layer rather than usually observed to come from the p-GaN.

Acknowledgment This work was supported by the “863” High Technology Research Program in China, under Grant No 2001AA31112, the Innovation Project of Chinese Academy of Sciences, the National Natural Science Foundation of China under Grant No 69896260 and No 69977019, and the Program of Hundred Talents of Chinese Academy of Sciences.

References [1] V. Nurmikko, R. L. Gunshor, Proc. Int. Symp. on Blue Laser and Light Emitting Diodes. Chiba University, 1996 p.3 [2] H. Morkoc, S. Strne, G. B. Gao, M. E. Lin, B. Sverdlov, J. Appl. Phys. 1994, 76, 1363 [3] S. Nakamura, Proc. Int. Symp. on Blue Laser and Light Emitting Diodes. Chiba University, 1996 p.119 [4] S. Y. Myong, S. J. Baik, C. H. Lee, W. Y. Cho, K. S. Lim, Japan.J. Appl. Phys. 1997, 35, L56 [5] Yamada, W. Wenas, M. Yoshino, M. Konagai, K. Takahashi, Japan. J. Appl. Phys. 1991, 30, 1152 [6] S. Kohiki, M. Nishitani, T. Wada, T. Hirao, Appl. Phys. Lett. 1994, 64, 2876 [7] Klingshirn, Phys. Stat. Sol. (b) 1975, 71, 547 [8] G. Thomas, J. Phys. Chem.Solids 1960, 15, 86 [9] Z. K. Tang, G. K. L. Wong, P. Yu, M. Kawasaki, A. Ohtomo, H. Koinuma, Y. Segawa, Appl. Phys. Lett. 1998, 77, 3270 [10] T. Kakino, C. H Chia, Nguan, T. Tuan, H. D. Sun, Y. Segawa, M. Kawasaki, A. Ohtomo, K. Tamura, H. Koinuma, Appl. Phys. lett. 2000, 77, 975 [11] R. Ondo-Ndong, F. Pascal-Delannoy, A. Boyer, A. Giani, A.Foucaran, Mater. Sci. and eng. B 2003, 97, 68 [12] K. Haga, T. Suzuki, Y. Kashiwaba, H. Watanabe, B. P. Zhang, Y. Segawa, Thin solid films 2003, 433, 131 [13] H. J. Ko, Y. Chen, S. K. Hong, T. Yao, J. Crystal Growth 2000, 209, 816. [14] Kobayashi, O. F. Sankey, J. D. Dow, Phys.Rev.B 1983, 28, 946 [15] S. B. Zhang, S. H. Wei, Alex Zunger, Phys.Rev.B 2001, 63, 075205 [16] Y. Chen, D. M. Bagnall, H. J. Koh, K. T. Park, K. J. Hiraga, Z. Q. Zhu, T. Yao, J. Appl. Lett. 1998, 84, 3912 [17] H. J. Ko, T. Yao, Y. Chen, S. K. Hong, J. Appl. Phys. 2002, 92, 4354 [18] R. J. Lad, P. D. Funkenbusch, C. R. Aita, J. Vac. Sci. Technol. 1980, 17(4), 808

Researches of Growth and Device Based on ZnO by Plasma Assisted …

141

[19] H. J. Ko, Y. F. Chen, S. K. Hong, T. Yao, J. Cryst. Growth 2000, 209, 819 [20] Y. F. Chen, H. J. Ko, S. K. Hong, T. Yao, Appl. Phys. Lett. 2000, 76, 559 [21] S. K. Hong, T. Hanada, H. J. Ko, Y. F. Chen, T. Yao, D. Imai, K. Araki, M. Shimohara, Appl. Phys. Lett. 2000, 77, 3571 [22] . C. H. Park, S. B. Zhang, S. H. Wei, Phys. Rev. B 2002, 66, 073202 [23] C. Look, D. C. Reynolds, C. W. Litton, R. L. Jones, D. B. Eason, G. Cantwell, Appl. Phys. Lett. 2002, 81, 1830 [24] K. K. Kim, H. S. Kim, D. K. Hwang, J. H. Lim, S. J. Park, Appl. Phys. Lett. 2003, 83, 63 [25] Y. R. Ryu, T. S. Lee, H. W. White, Appl. Phys. Lett. 2003, 83, 87 [26] C. Lee, Y. S. Kim, Y. G. Jin, K. J. Chang, Phys. Rev. B 2001, 64, 085120 [27] Y. Yan, S. B. Zhang, Phys. Rev. Lett. 2001, 86, 5723 [28] X. L. Guo, H. Tabata, T. Kawai, J. Cryst. Growth 2002, 237–239, 544 [29] X. Wang, S. Yang, J. Wang, M. Li, X. Jiang, G. Du, X. Liu, R. P. H. Chang, J. Cryst. Growth 2001, 226, 123 [30] K. Iwata, P. Fons, A. Yamada, K. Matsubara, S. Niki, J. Cryst. Growth 2000, 209, 526 [31] X. Li, Y. Yan, T. A. Gessert, C. D. Hart, C. L. Perkins, D. Young, T. J. Coutts, Electrochemical and Solid-State Letters, 2003, 6 (4), C56 [32] W. Z. Xu, Z. Z. Ye, T. Zhou, B. H. Zhao, L. P. Zhu, J. Y. Huang, J. Cryst. Growth 2004, 265,133 [33] X. L. Guo, J. H. Choi, H. Tabata, T. Kawai, Jpn. J. Appl. Phys. 2001, 40, L177 [34] T. Aoki, Y. Hatanaka, D. C. Look, Appl. Phys. Lett. 2000, 76, 3257 [35] H. Ohta, K. Kawamura, M. Orita, M. Hirano, N. Sarukura, H. Hosono, Appl. Phys. Lett. 2000, 77, 475 [36] H. Ohta, H. Mizoguchi, M. H. Narushima, T. Kamiya, H. Hosono, Appl. Phys. Lett. 2003, 82, 823, [37] S. Ishizuka, K. Suzuki, Y. Okamoto, M. Yanagita, T. Sakurai, K. Akimoto, N. Fujiwara, H. Kobayashi, K. Matsubara, S. Niki, Phys. Stat. Sol. (c) 2004, 1, 1067 [38] X. Wang G. W. Yang, H. W. Liu, Y. H. Han, J. F. Luo, C. X. Gao, G. T. Zou, Appl. Phys. Lett 2004, 84, 2427 [39] S. Jeong, J. H. Kim, S. Im, Appl. Phys. Lett 2004, 83, 2946 [40] Ya. I. Alivov, D. C. Look, B. M. Ataev, M. V. Chukichev, V. V. Mamedov, V. IZinenko, Yu. A. Agafonov, A. N. Pustovit, Solid-State Electronics 2004, 48, 2343 [41] Ya. I. Alivov, J. E. Van Nostrand, D. C. Look, M. V. Chukichev, B. M. Ataev, Appl. Phys. Lett. 2003, 83, 2943 [42] Ya. I. Alivov, E. V. Kalinina, A. E. Cherenkov, D. C. Look, B. M. Ataev, A. K. Omaev, M.V Chukichev, D. M. Bagnall, Appl. Phys. Lett. 2003, 83, 4719 [43] X. L. Guo, H. Tabata, T. Kawai, J. Cryst. Growth 2002, 237-239, 544 [44] Y. Chen, H. J. Ko, S. K. Hong, T. Yao, Appl. Phys. Lett. 2000, 76, 559. [45] Vigué, C. Deparis, P. Vennéguès, S. Vézian, M. Laügt, P. Lorenzini, C. Morhain, F. Raymond, J. Guion,, .P. Faurie, Phys. Stat. Sol.(b) 2002, 229, 931 [46] Joshy Jose, M. Abdul Khadar, Materials Science and Engineering A 2001, 304-306, 810 [47] S. Cho, J. Ma,Y. Kim, Y. Sun, G. K. L. Womg, Appl. Phys. Lett. 1999, 75, 2761 [48] Kyu-hyun Bang, D. K. Hwang, M. C. Jeong, K. S. Sohn, J. M. Myoung Solid State Communications 2003, 126, 623 [49] L. E. Brus, J. Chem. Phys. 1984, 80, 4403 [50] K. Hümmer, Phys. Stat. Sol. 1973, 56, 249

142

Y. M. Lu, D. Z. Shen, J. Y. Zhang et al.

[51] S. Jiang, H. Jung, K. Ploog, J. Appl. Phys. 1988, 64, 1371 [52] Y. G. Wang, S. P. Lau, X. H. Zhang, H. W. Lee, H. H. Hng, B. K. Tay. Journal of Cryst.Grwoth. 2003, 252, 265 [53] C. Lee, Y. S. Kim, Y. G. Jin, K. J. Chang, Physica B 2001, 308-310, 912 [54] Y. Sato, S. Sato, Thin Solid Films 1996, 281-282, 445 [55] J. D. Ye, S. L. Gu, S. M. Zhu, T. Chen, L. Q. Hu, F. Qin, R. Zhang, Y. Shi, Y. D. Zheng, J. Cryst. Growth 2002, 243, 151 [56] N. Y. Garces, N. C. Giles, L. E. Halliburton, G. Cantwell, D. B. Eason, D. C. Reynolds, D. C. Look, Appl. Phys. Lett. 2002, 80, 1334 [57] J. Ko, Y. F. Chen, K. Miyajima, A. Yamamoto, T. Goto, Appl. Phys. Lett. 2000, 77, 537 [58] K. Tamura,T. Makino, A. Tsukazaki, M. Sumiya, S. Fuke, T. Furumochi, M. Lippmaa, C. H. Chia, Y. Segawa, H. Koinuma, M. Kawasaki, Solid State Comminications 2003, 127, 265 [59] C. Look, Mater. Sci. Eng. B 2001, 80, 383 [60] D. C. Reynolds, D. C. Look, B. Jogai, C. W. Litton, T. C. Collins, W. Harsch, G. Cantwell, Phys. Rev. B 1998, 57, 12151 [61] Zeuner, H. Alves, D. M. Hofmann, B. K. Meyer, A. Hoffmann, U. Haboeck, M. Strassburg, M. Dworzak, Phys. Status Solidi B 2002, 234, R7 [62] G. Milnes, D. L. Feucht, Heterojunctions and metal-semiconductor Junctions( Academic, New York, 1972) [63] J. A. Aranovich, D. G. Golmayo, A. L. Fahrenbruch, R. H. Bube, J. Appl. Phys. 1980, 51, 4260 [64] D. Qiao, L. S. Yu, S. S. Lau, J. M. Redwing, J. Y. Lin, H. X. Jiang, J. Appl. Phys. 2000, 87, 801 [65] J. Tauce, optical properties if solid ed F Abeles( Amserdam: North-Holland) P277 [66] M. Fyutsuhara, K. Yoshioka, O. Takai. Thin Solid Films 1998, 317, 322

In: New Research on Semiconductors Editor: Thomas B. Elliot, pp. 143-157

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

Chapter 6

STRUCTURAL DISORDER IN CDSXSE1-X THIN FILM PROBED BY MICRODIFFRACTION AND OPTICAL SPECTROSCOPIES V. Capozzi(1), G. Perna(1), S. Pagliara(2) and L. Sangaletti(2) (1)

Dipartimento di Scienze Biomediche, Università di Foggia, Via L. Pinto, 71100 Foggia, Italy (2) Dipartimento di Matematica e Fisica, Università Cattolica, Via dei Musei 41, 25121 Brescia, Italy

Abstract 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 T-2T diffractometers. The Xray spectra measured by using conventional T-2T diffractometer have shown that the CdSxSe1x 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.

Introduction Ternary compounds of II-VI semiconductors are largely used in optoelectronic devices due to the possibility of controlling of the lattice costant and the energy gap by modulating the relative composition of binary compounds. CdSxSe1-x ternary alloys, in particular, are mostly

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important in the production of the devices such as laser diodes and light emitting diodes operating in the visible region according to the band gap modulation obtained by varying the sulphur concentration (x) [1]. Besides these appealing applications, the semiconductor solid solution provides a good system for the study of the effect of disorder on the optical properties of solids. In solid solution formed by isoelectronic substitution the disorder is usually weak, permitting easy comparison of the optical spectra of the ternary compounds with those of the binary semiconductors. As a rule, the atoms in such solutions keep, in average, the regular positions so that the long range order exists and samples with perfect crystal habit can be grown. Moreover, the isoelectronic alloying does not change the nature of the chemical bonding so that the main features of the band structure are preserved. The random distribution of substitutional atoms over the possible crystal sites results in fluctuations of the local electronic density, producing the corresponding fluctations in the periodic crystal potential [2]. The most simple theorical model for the description of the solid solutions is the so-called virtual crystal approximation [3]; it gives a satisfactory picture of compositional dependence of the band energy positions and the lattice costant values in solid solutions, but this approximation does not take into account the disorder at all (e.g., bond and lattice distortion due to the different atomic size). Indeed, for the study of the broadening of the electronic states, models with explicit consideration of disorder should be used. This is known for optical spectroscopy studies [2], where suitable functions are considered in the deconvolution of data to account for electronic states induced by disorder. Likewise, excitonic lines in alloys are larger than those of binary compounds. Disorder in solid solutions can have various forms. In ternary compounds with substitutional disorder, because of the difference of lattice costants of the binary compounds, the atoms can be shifted from the exact symmetry positions which will produce strong local stresses and will give an additional contribution to the atomic potential. Microscopic stresses due to the bond length mismatch can be partially relaxed through formation of intrinsic structural defects such as vacancies and interstitials [2]. The maximum defect concentration is expected for equimolar compositions. Stacking faults may also appear; this type of disorder can lead to structural phase transition at some intermediate composition [2]. In the present work we report X-ray diffraction, microdiffraction, microraman, and photo-luminescence (PL) measurements of CdSxSe1-x alloy films deposited on Si (111)oriented substrates by laser ablation, in order to study the microscopic nature of substitutional and structural disorder.

Experimental The investigated CdSxSe1-x films were deposited by laser ablation technique on Si(111)oriented substrate, starting from stoichiometric and high purity (99,999%) cold pressed target of CdS and CdSe powder. The substrate temperature was optimized at 400°C as discussed in [4]. A pulsed Kr-F laser operating at 248 nm, with a repetition rate of 10 Hz, and a pulse width of 18 nsec, was used as sublimation source. Laser fluence was optimized at 10 J/cm2.

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The deposition chamber was evacuated by a turbomolecular pump and the residual pressure, before the deposition, was about 10-6 torr. Conventional T-2T X-ray diffraction spectra were measured by using the Cu-KD radiation (O = 1.5406 Å) of a Siemens D5000 diffractometer. Microdiffraction patterns have been collected with a Bruker D8 Discover diffractometer equipped with an area detector (General Area Dtector Diffraction System: GADDS) and a Co KD X-ray source (KD1=1.789007 Å, KD2=1.792892 Å). The minimum size of the X-ray beam is 50 Pm. For the present experiment a collimator for the X-ray beam was used, which yielded a 100 Pm diameter X-ray spot on the sample surface. Microraman spectra were collected by a Dilor Labram spectrograph with a He-Ne laser (632 nm, output power=14 mW). The spectrometer was confocally coupled with a microscope (100X objective, N.A. = 0.9) which allowed us to collect Raman spectra with a spatial resolution of about 1 Pm. For the PL measurements, the samples were mounted into a He closed-cycle cryostat, whose temperature could be varied from 10 to 300 K. They were illuminated in a direction forming a 45° angle with respect to the normal to the film surface, by using the 4579 Å line of a cw Ar-ion laser. The emission light was collected along a direction perpendicular to the laser beam and analysed by a double grating spectrometer (line dispersion of 1 meV/mm). The signal, detectd by a GaAs cooled photomultiplier, was recorded using photon counting techniques. The film quality was controlled by the width of the PL excitonic lines. Structural modeling and simulations have been performed by using the CERIUS program on an IBM RISC system 6000 workstation [5].

Results and Discussion X-ray Diffraction Measurements X-ray spectra of the four CdSxSe1-x films (x = 0, 0.4, 0.6, 1) deposited on Si(111)-oriented substrates are shown in Fig. 1. All peaks refer to the (002)-orientation of the film corresponding to the hexagonal phase, with the c-axis perpendicular to the film layers. The diffraction peak shifts towards larger angles with increasing x, indicating that the lattice constant decreases with the sulphur concentration. The grain dimension D, calculated by the Debye-Scherrer relationship [6], are reported in Table 1.The lattice plane distance dhkl (hkl are the Miller indices) can be determined by means of the Bragg equation: dhkl = mO/2sinT

(1)

where m is the diffraction order O=1.5406 Å and T is the Bragg diffraction angle. The obtained values are reported in Table 1. The lattice parameter c can be calculated according to the following equation [7]:

1 4 h 2 +k 2 +hk l2 = + 2 d2 3 a2 c

(2)

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Table 1. Full width at half maximum (FWHM) of the XRD peak of the CdSxSe1-x deposited on Si(111)-oriented substrate; average grain dimension (D), as deduced from the DebyeSchrerrer equation [6]; lattice plains distance (d), as obtained from the Bragg equation; values of the lattice parameter c, obtained from eq. (3).

CdS CdS0.6Se0.4 CdS0.4Se0.6 CdSe

FWHM (0) 0.159± 0.002 0.201± 0.002 0.282±0.002 0.188± 0.001

D (nm) 47.5± 0.5 40.6± 0.4 29.0±0.2 43.1± 0.3

d(002) (Å) 3.36± 0.01 3.42± 0.01 3.45± 0.02 3.51± 0.01

c (Å) 6.72±0.01 6.84± 0.01 6.90± 0.01 7.01± 0.01

Fig. 1. X-ray spectra of the CdSxSe1-x films deposited on Si(111)-oriented substrates. Each peak refers to the (002)-orientation of the crystal domains. In the inset, the lattice papameters c of the CdSxSe1-x in the hexagonal phase are shown for each film, as calculated from eq. (2).

The obtained c values (reported in Table 1) follow quite well Vegard’s rule [8], which assumes a linear dependence of c on the composition x, according to: c(x) = x˜cCdS + (1-x)˜cCdSe

(3)

The continuous straight line, in the inset of Fig. 1, is a least square fit of the c data to eq. (3). The c values obtained from the fit (cCdS = 6.72 r 0.01 Å and cCdSe = 6.98 r 0.01 Å) are in good agreement with the literature values of the corresponding bulk materials [9].

Microdiffraction Measurements The microdiffraction patterns collected from the CdSxSe1-x samples with the GADDS system are shown in Fig.2 a-d.

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Unlike conventional T-2T diffraction, the area detector allowed us to sample a large solid angle of the diffraction cone and thus to detect all the reflections at once from the sample. Therefore, in addition to the reflections already detected with the conventional diffractometer, other reflections are detected by the two-dimensional detector. The point-like spots detectable in all patterns are ascribed to the Si(111) substrate, whereas the larger spots are ascribed to the thin film alloy. In agreement with the data of conventional T-2T diffraction, a broadening perpendicular to the Debye ring (i.e. the FWHM of the reflection) is found. This effect, ascribed to structural disorder, is larger in CdS0.4Se0.6 (Fig. 2-c) than in CdS0.6Se0.4 (Fig. 2-b).

Fig.2. Microdiffraction patterns of the CdSxSe1-x films deposited on Si (111)-oriented substrates. The bright spots are ascribed to reflections from the Si substrate, whereas the broad spots are the reflections of the CdSxSe1-x hexagonal phase.(a) CdS (x=1.0). (b) CdS0.6Se0.4 (x=0.6). (c) CdS0.4Se0.6 (x=0.4). (d) CdSe (x=0.0)

While the broadening perpendicular to the Debye ring is important to evaluate the structural disorder, the broadening along the Debye rings is important to achieve information about the texture of the film. The broadening of the spots along the Debye ring, i.e. along the azimuthal angle

I, is shown in Fig. 3, where the intensity of the 103 reflection is plotted vs.

I This broadening indicates that deviations from the perfect epitaxy are present, i.e., a small random angle may be found between the c-axis and the axis normal to the substrate. The largest deviations occur in CdS0.4Se0.6. These deviations indicate that a different degree of orientation of the microcrystallites along the a and b crystallographic directions exists. It is rather important to relate this effect to the sample thickness. In fact a degradation of the epitaxy may occur for the thicker samples. The sample thickness was measured with a profilometer and the results are 0.747 Pm, 3.138 Pm, 0.663 Pm and 1.950 Pm for CdS, CdS0.4Se0.6, CdS0.6Se0.4 and CdSe, respectively.

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Fig.3. Intensity of microdiffraction spots of theCdSxSe1-x films measured along one of the Debye rings. The drawing shown in the inset defines the azimuthal I angle along which the intensity of the 103 reflection has been plotted.(a) CdS (x=1.0). (b) CdS0.6Se0.4 (x=0.6). (c) CdS0.4Se0.6 (x=0.4). (d) CdSe (x=0.0)

As can be observed, the CdS0.4Se0.6 film is thicker than CdS0.6Se0.4. Indeed, a broader peak of the intensity profile measured along the Debye ring is observed for CdS0.4Se0.6 (Fig.3, thicker solid line) with respect to CdS0.6Se0.4 (Fig.3, dotted line). When the binary sample is compared with the ternary sample (e.g. CdS vs. CdS0.6Se0.4) one can realize that, in spite of the similar thickness (0.747 Pm and 0.663 Pm, respectively), the ternary sample shows a larger peak of the intensity profile. This indicates that not only thickness affects the deviation from epitaxy but also the disorder induced by alloying. Fig. 4 shows the XRD patterns obtained by performing an integration of the diffracted intensity along the Debye rings. Several reflections of the hexagonal phase are identified, along with some reflections of the Si substrate, indicated with asterisks. The following reflections have been identified: (002), (004), (102), (103), (104). All of them can be ascribed to the hexagonal phase of CdS-Se. Moreover, the broadening is observed for each of the mentioned diffraction lines. As expected, for all the reflections an increase of the 2T angle with x is observed, accounting for the progressive contraction of the lattice parameters in the CdS sample with respect to that of CdSe. In conventional T-2T diffraction, only the 00l reflections of the hexagonal phase are expected. The area detector allows us to map a larger volume of the reciprocal space and, in principle, all the reflections from the hexagonal phase must be present. However, it is rather important to observe that some reflections of the hexagonal phase are missing. In particular, only the 00l (l = 2, 4) and the 10l (l > 1) reflections are present. This is true for all samples

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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.

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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

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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).

In: New Research on Semiconductors Editor: Thomas B. Elliot, pp. 159-207

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

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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]. Guill´en 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).

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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)

Electrodeposition of CuInSe2 for Photovoltaic Cell Application

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.

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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.

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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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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

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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.

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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

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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

Electrodeposition of CuInSe2 for Photovoltaic Cell Application

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 (<5mA/cm2 ) are decreased and show a current density dependence, while those at high current densities are not changed by stirring and still show no significant dependence on change in the current density. This suggests that the rate-determining step for Se(IV) deposition at a low current density is changed from “diffusion” to “reaction” by employing the stirring. The increase in k(In)/k(Cu) without stirring with increasing current density shows that the deposition of In(III) is reaction-limited at a low current density (< 5 mA/cm2 ). Even when the stirring is employed, the deposition of In(III) at a high current density (∼10 mA/cm2 ) is diffusion-limited, as seen in Fig. 4.7. From the above, the rate-determining step for each ion is summarized in Fig. 4.11 The k(In)/k(Cu) at the high current density (< 5[mA/cm2 ]) under no-stirring condition can not be calculated because the β is not proportional to [In(III)/Cu(II)] under such condition. Marked improvement of controllability and uniformity for film composition is achieved by employing the stirring. Figure 4.8 shows a fluctuation of In/Cu ratios in the films with and without stirring. Nine specimens were prepared for the EPMA analysis from three thin film samples deposited under the same conditions. Each sample with an area of 1 cm2 was divided into three specimens. The maximum and minimum composition data for nine specimens are plotted in Fig. 4.8 as a function of electrode potentials. As can be seen in

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Fig. 4.8, reproducibility and uniformity of the film composition are improved by employing the stirring. For a film with an In/Cu ratio of about unity, the fluctuations with and without stirring are about 7 and 21 %, respectively. Thus, the reproducibility of the In/Cu ratios in the film is improved by a factor of 3 by employing the stirring.

4.5

Dependences on Substrate Materials of Film Compositions

This section describes dependences on substrate materials, semiconductor or metal, of film compositions. Figure 4.9 shows the dependences of In/Cu ratios in the films on substrate potentials, deposited on a p-Si and Mo substrates. This figure indicates that the substrate potentials less influence compositional variations of the films deposited on the p-Si substrate than on the Mo. Moreover, the dependence of compositions in the films deposited on the Si substrate with or without stirring on the substrate potentials is shown in Fig. 4.10. Compared with that of films on the Mo substrate shown in Fig. 4.5, the stirring less influence the compositional variation for the p-Si substrate. To investigate causes of the difference, energy band diagrams at the interface between the p-Si substrate and a electrolyte are considered. In general, the energy band is bent at the interface as shown in Fig. 4.12 (a). For this bending, a space charge layer whose charge distribution is polarized is formed at the semiconductor surface, resulting in the potential drop. When a negative bias is applied as shown in Fig. 4.12 (b), the almost voltage is applied at the space charge layer. Figure 4.13 shows potential distributions for the case of a Mo (a) and Si (b) substrates. In the potential distributions, an available potential for deposition is the potential applied at the Helmholz layer. In the case of the Mo substrate, almost substrate potential is considered to be applied to the Helmholz layer. Hence, a variation of the potentials applied to the Helmholz layer according to a change in the substrate potential results in a variation of the film compositions. On the contrary, in the case of the p-Si substrate, the potential is considered to be preferentially applied to the space charge layer rather than the Helmholz layer. A variation of the substrate potential is, therefore, consumed as the

Figure 4.11: Summery of the rate-determining step.

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187

Figure 4.12: Energy level diagram for an interface between p-Si and the electrolyte. No bias (a) and negative bias (b). variation of the potential applied to the space charge layer. Consequently, the composition change becomes small because the variation of the potentials applied to the Helmholz layer becomes smaller than that of the potentials applied to the substrate. Moreover, the reason why the stirring hardly influence compositions of films for the Si substrate is considered that a rate determination step of Cu ion is not diffusion-limited due to a noble effective potential for the Si substrate and, consequently, Cu ions are sufficiently supplied to the substrate surface from the bulk of the electrolyte.

4.6

Crystallinity of As-Deposited Films

Figure 4.14 shows XRD patterns of as-deposited films with different In/Cu ratios. CuInSe2 was found to be contained in as-deposited films from the figure. The copper-rich and stoichiometry films have no secondly phases while the In-rich film contains an elemental indium. Peaks from elemental Se was not observed although as-deposited films contain excess Se, as described above. This indicates that excess Se in these films is of amorphous phase. These broad peaks from the CuInSe2 show that these films have poor crystallinity. Thus, in order to improve crystallinity, an annealing process is needed. Details of post-annealing effects will be described later.

4.7

Surface Morphology and its Improvement

Surface morphology is one of important factors for high efficiency solar cells. In this section, surface morphologies of Se rich samples are discussed [86]. The film and solution compositions are summarized in Table 4.3. Figure 4.15 shows surface morphologies of samples with different Se compositions. The figure denotes that both samples has rough surface. However there are some differences

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Figure 4.13: Potential distributions for the case of the Mo (a) and Si (b) substrates. between them, especially, in grain sizes, i.e., the sample B has a larger grain than the sample A. The largest grain size in sample B is about 10 µm. The sample B is superior to sample A in terms of the grain size. However, a morphological improvement is required because even the morphology of the sample B has not sufficient quality in uniformity for

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189

Table 4.3: Compositions in the films and those in the solutions for morphology investigations. Sample No. A B

Solution compositions Cu:In:Se 1:20:20 1:5:5

Film compositions In/Cu Se/(Cu+In) 0.97 4.42 0.78 1.92

the solar cell application. One can also see gaps between each grain even in the sample B. In general, substrate potentials dominate both film compositions and morphologies in electrodeposition. In this case, first priority is film compositions when the potentials are decided. Thus, the potentials are not optimized in terms of the surface morphologies. Hence, electrochemical etching is attempted to improve surface morphologies by applying reverse biases. It is expected to uniform a film thickness and to reduce a surface roughness because the electrochemical etching preferentially occurs from the tip of the rough surface. Figure 4.16 shows a morphological comparison before (a) and after (b) etching. The figure shows the surface-roughness of the etched sample is improved. It also seems that the gaps between each grain decrease. Thus, the electrochemical etching is found to be effective to improve the surface morphology. To enhance effects of the reverse bias, pulse-plated electrodepositon is proposed. Namely, each forward and reverse bias are applied periodically in sufficiently short time compared with a deposition duration. Here, let’s call a period for which the forward bias is applied to a substrate “ON-time” and the reverse bias “OFF-time”. Influences of substrate potentials and duty ratios on surface morphologies are investigated. The duty ratio is defined as a time ratio between ‘ON-time” and “OFF-time”. Figure 4.17 shows surface morphologies of the films deposited with various duty ratios and potentials for “ON-time” and “OFF-time”. The deposition conditions as well as In/Cu ratios in the films

Figure 4.14: XRD patterns of the as-deposited films.

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Figure 4.15: Surface morphologies of samples with different Se compositions. The bar denotes 50 µm.

Figure 4.16: Surface morphology of (a) an etched film and (b) an as-deposited film. The bar denotes 10 µm. are summarized in Table 4.4. By comparing Figs.4.17 (a), (b) and (c), grain sizes are found to become larger and a ratio where large grains are included increases with a decrease in the duty ratios. However, differences in size between the largest and smallest grains become larger with an increase in the duty ratios. Uniformity in the grain sizes is not improved by decreasing duty ratios. The figures also show a decrease in roughness with an increase in reverse bias potentials (for example, see Figs.4.17 (c), (e) and (g)). The results indicate that by applying the reverse bias with appropriate duty ratios the surface morphologies are improved.

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Figure 4.17: Surface morphologies of the films deposited by pulse-plated electrodeposition with various duty ratios and potentials. The bar denotes 50 µm.

4.8

Effects of Annealing on Se Excess Films

Electrodeposited CuInSe2 films must be annealed to improve their crystallinities because as-deposited films have poor crystallinity, as shown in previous section. Taking account

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of the abscondence of Se element from deposited layers during the annealing, as-deposited Cu-In-Se films have Se-rich compositions, as described above. Thus, effects of the excess Se on annealed film properties, such as compositions, crystallinities and morphologies, must be investigated. In this investigation, samples with a similar Cu/In ratio and a different Se/(Cu+In) ratio are used. Samples with very (Se/(Cu+In)=3.0∼7.0) and slightly (1.2∼3.0) excess Se are labeled A and B, respectively. Annealing temperatures are varied from 150 ∼ 550 o C. The samples are annealed for 30 min in N2 flow of 200 ml/min [86]. . Change in compositions Figure 4.18 shows a change in compositions before and after annealing at 400 o C. In/Cu ratios of sample B hardly change with annealing while those of sample A become larger. This suggests that Cu-Se compounds with lower vapor pressure which are produced by a reaction between Cu and excess Se evaporate. Figure 4.19 and 4.20 show variations of Se/(Cu+In) and In/Cu ratios as a function of annealing temperature, respectively. The Se/(Cu+In) ratios of sample A drastically decrease with an increase in the temperature, while, those of sample B hardly change. In/Cu ratios of both sample A and B do not change so much. Crystallinity Figures 4.21 and 4.22 show XRD patterns of annealed sample A and B, respectively. The figures indicate that sample B is superior to A because FWHM and peak intensities of sample B are smaller and higher than those of sample A, respectively. Peaks from Se are observed at 150 o C and disappeared at 250 o C for both samples. At 450 o C, In O and other unknown peaks are observed. Thus, 400 o C is found to be the most 2 3 appropriate temperature for annealing electrodeposited CuInSe2 thin films. Morphology Figures 4.23 (a) and (b) show surface morphologies of sample A and B, respectively, annealed at 400 o C which is the best temperature for crystallinity. Sample A has very rough surface probably due to Se and/or Cu-Se evaporation. The surface of sample B is smoother than that of sample A. Table 4.4: Deposition conditions and compositions of pulse-plated electrodeposition.

“OFF-time” Pot. (V) 0

+0.1

+0.5

Fig. No. “ON-time” Pot. (V) In/Cu ratios Fig. No. “ON-time” Pot. (V) In/Cu ratios Fig. No. “ON-time” Pot. (V) In/Cu ratios

Duty 100 % (D.C.) 90 % (a) (b) –1.5 –1.5 0.78 0.60 (d) –2.0 0.81 (f) –2.0 0.81

50 % (c) –2.25 0.81 (e) –2.5 1.06 (g) –3.0 0.98

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193

These results indicate that too excess Se is undesirable for film qualities, e.g. composition, crystallinity and morphology.

4.9

Cell Performance

As shown in section 2, general CuInSe2 solar cells have a CdS and TCO layers. However, in this study, a TCO layer is not deposited because deposition conditions for the TCO layer is not established [86]. The cell structure fabricated is Mo/CIS/CdS/Au. The CdS buffer layer is generally prepared by a chemical bath deposition method as follows [89, 90]. Electrodeposited CIS thin films are dipped in an aqueous solution containing CdCl2 of 1mM, NH4 Cl of 5mM and (NH2 )2 SC of 7.5 mM for 60 min at 60 o C. A pH of solution is maintained to 9.5 by adding aqueous ammonium. A film thickness and a resistivity of CdS layer are estimated to be 273 nm and 105 Ωcm, respectively. Figure 4.24 shows current-voltage curves under a dark and light conditions. A power-voltage curve is also shown in the figure. The curves show rectification and this indicates that a pn junction is formed. From the curve under the light condition, following cell properties are obtained: a Voc of 0.47 V, an Isc of 1.9 mA/cm2 , a fill factor (FF) of 0.533 and a conversion efficiency η of 0.866 %. However, the conversion efficiency is very low, compared with the highest one. Therefore, further investigation and development are required to obtain higher conversion efficiency.

4.10

Conclusion

In/Cu ratios in the annealed films

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 . Dependences of compositions in the films on bath compositions, current density, substrate potential and presence of stirring are investigated. As a result, for 6

4 Sample A

2 Sample B

0

1 2 3 In/Cu ratios in the as−deposited films

Figure 4.18: Change in compositions before and after annealing.

Shigeyuki Nakamura Se/(Cu+In) ratios in the annealed films

194 6

Sample A

4

2

0 0

Sample B

200 400 Annealing temperature (oC)

In/Cu ratios in the annealed films

Figure 4.19: Variation of Se/(Cu+In) ratios as a function of annealing temperature.

1

0.5 Sample A Sample B 0 0

200 400 Annealing temperature(oC)

Figure 4.20: Variation of In/Cu ratios as a function of annealing temperature. the wide range of current density (∼10 mA/cm2 ), a linear relationship is found to be held between β and [Se(IV)]/[Cu(II)] while such relation is held between α and [In(III)]/[Cu(II)] only for a low current density (therefore, a noble electrode potential) and for a solution with a low solute concentration. Not only the In/Cu ratio in the bath but also the Se concentration is found to be affected the In/Cu ratios in the films. Under the assumption that all the Se(IV), In(III) and Cu(II) arriving at the electrode are involved in deposited films, the ratios of the mass-transfer coefficients k(Se)/k(Cu) and k(In)/k(Cu) has been obtained. From their dependencies on deposition current density and stirring of the solution, the rate-determining step for each species in the deposition process has been discussed. The reproducibility

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Figure 4.21: XRD patterns of annealed sample A as a function of annealing temperature.

Figure 4.22: XRD patterns of annealed sample B as a function of annealing temperature. and uniformity of In/Cu ratio in the film is improved by a factor of 3 by employing the stirring. X-ray diffraction patterns show that CuInSe2 is contained in as-deposited films. Morphologies of as-deposited films can be improved by applying reverse bias after deposition or by pulse-plated electrodeposition, as well as annealing. Excess Se is undesirable for film qualities, such as composition, crystallinity and morphology. The I-V curve shows that pn junction is formed and the efficiency of the cell is 0.87 %.

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Figure 4.23: Surface morphologies of sample A and B annealed at 400 o C. The bar denotes 50 µm.

Figure 4.24: I-V and P-V curves.

5

New Electrodeposition Technique for Controlling Depth Profile of CuInSe2 Thin Films

It is known that the efficiency of CuInSe2 -based solar cells can be improved using a composition that can be modulated to be In-rich near the pn junction interface. In this work, a new electrodeposition technique for preparing CuInSe2 thin films with controlled depth profile was developed. CuInSe2 thin films having a bilayer structure, that is, films with the Cu-rich and In-rich layers, were successfully deposited from one electrolyte only by changing the substrate potential during electrodeposition.

Electrodeposition of CuInSe2 for Photovoltaic Cell Application

5.1

197

Introduction

By introducing the so called “bi-layer” method to prepare CuInSe2 layers, an efficiency larger than 10 % was attained for the first time [91]. The bilayer structure was fabricated by sequential vacuum evaporation, that is, a Cu-rich layer was deposited first, and then subsequently, an In-rich layer was deposited on the Cu-rich layer, resulting in films with two layers, i.e., the Cu-rich and In-rich layers. The reason for the better performance of the bilayer structure is as follows. The composition of CuInSe2 thin films affects the electric and structural properties, as described in section 2 (page 170). Cu-rich films have a low resistivity, which causes short circuiting in the pn-junction, and a large grain size, which leads to a large diffusion length and is desirable for solar cell application. On the other hand, In-rich films have a high resistivity and a small grain size. Thus, the composition near the pn-junction interface should be In-rich to prevent short circuiting, and the rest should be Cu-rich to enhance diffusion length. That is, in order to obtain a high-efficiency cell, the compositional depth profile is one of the most important factors. However, there are a very few reports on the compositional depth profile of electrodeposited CIS thin films [92, 93, 94]. Moreover, conversion efficiencies ever reported for the cells fabricated by electrodeposition are considerably lower than that for the cells fabricated by other methods. Although Bhattacharya et al. reported the highest efficiency of 15.4 % by this method, a physical vapor deposition (PVD) was needed to adjust the final composition [92]. Guimard et al. have reported a conversion efficiency of 9.1 % without PVD [95]. As described above, an important problem for the development of this technique is the control of the composition ratio including depth profile. Some authors have investigated the compositional depth profiles of the CuInSe2 thin films prepared by electrodeposition [92, 93, 94]. Calixto and Sebastian have reported that the concentration of Cu is higher than that of In at the initial, and then the Cu concentration decrease with deposition time, resulting in CuInSe2 films with the Cu-poor surface and the Cu-rich bulk [93]. Although this profile is desirable, the properties, such as a thickness of Cu-poor layer and compositions of each layer, are uncontrollable by their method. Friedfeld et al. have reported the two step electrodeposition method for forming a Cu-Ga/CuInSe2 bilayer [94]. A high surface content of Ga and a low bulk content form the graded bandgap. They use two types of electrolyte: one containing Cu and Ga ions and the other Cu, In and Se ions. However, the electrodeposition method using two types of electrolyte seems to be a little cumbersome because the substrates must be transferred. Chaure et al. have prepared p-i-n type CuInSe2 multilayer solar cells by electrodeposition, as shown in section 1.1.3 [96]. However, they have not mentioned the compositional depth profile of their multilayer. One of the causes for low efficency of electrodeposited CIS thin film solar cells is considered not to be optimized in the compositional depth profile. Thus, new electrodeposition technique to control the compositional depth profile must be developed. This section describes a new technique for forming CuInSe2 films with a bilayer structure by electrodeposition [97, 98]. The Cu-rich and In-rich layers were deposited from one electrolyte by changing the substrate potential during the deposition. Composition controlled bilayer CuInSe2 thin films were prepared very easily by this method.

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Shigeyuki Nakamura Table 5.1: Standard redox potentials. Chemical reactions Cu(II) + 2e− → Cu In(III) + 3e− → In H2 SeO3 + H+ → Se + 3H2 O

5.2

Standard redox potentials vs. SHE (V) 0.342 −0.338 0.74

Experiments

Cu, In and Se were electrodeposited from a bath containing 1 mM CuCl2 , 5-7 mM InCl3 and 3-5 mM SeO2 using a conventional three electrode electrochemical cell and a potentiostat at room temperature. Substrate potentials were –0.5 V vs the Ag/AgCl reference electrode for the deposition of the Cu-rich layer and –0.8 V for the deposition of the In-rich layer. These values were selected by considering the standard redox potentials of Cu, In and Se, as shown in Table 5.1. Conventional D.C. electrodeposition for depositing the single-layer films was carried out at –0.5 V and –0.8 V to determine the bath composition for the bilayer film deposition. A 1 cm2 Ti sheet and a carbon rod were used as a substrate and a counter electrode, respectively. Each deposition time was determined by the amount of electric charge measured using a coulombmeter: first step 0.75 C and second step 1.0 C. As-deposited films were evaluated by an electron prove micro-analyzer (EPMA) for overall chemical compositions and an X-ray photoelectron spectroscope (XPS) for the depth-profile. Surface morphology was observed by a scanning electron microscope (SEM).

5.3

Results and Discussion

Preliminary experiments were carried out to determine the bath composition. Table 5.2 shows the deposition conditions and composition results measured by EPMA for the singlelayer deposition. From these results, the Cu- and In-rich films were found to be obtained at –0.5 V and –0.8 V, respectively, from the solution containing 1 mM CuCl2 , 5 mM InCl3 and 3 mM SeO2 . Thus, these values were selected for the bilayer deposition. Table 5.3 shows overall compositions of the bilayer films prepared at –0.5 V and –0.8 V measured by EPMA. Slightly In-rich and/or stoichiometric films were obtained under this condition. Figure 5.1 shows the depth-profile of the bilayer film deposited under the same conditions described above. The bottom of the film is found to be Cu-rich and the top In-rich. The bilayer CuInSe2 films were obtained by this method. However, the surface seems to be Cu-rich. This remarkably differ from the evaporated films, which have In-rich surface [99]. The thickness of the top (In-rich) layer was about 0.3 µm and the overall thickness larger than 1 µm. The differences between the compositions prepared at –0.8 V shown in Table 5.2 (Cu/In=0.85) and Fig. 5.1 (0.1) is probably due to the Cu concentration decrease in the electrolyte because of the deposition of the Cu-rich layer as the first step of the bilayer deposition, which leads to a decrease in Cu/In ratio at the second step. The insufficient calibration in the quantitative analyses using the EPMA and the XPS is considered one of the causes of such differences.

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Table 5.2: Electrodeposition conditions and film compositions of preliminary experiments. Bath comp. Cu In 1 5 5 1 1 7 7 1 1 5 5 1

mM Se 5 5 5 5 3 3

Pot. V -0.5 -0.8 -0.5 -0.8 -0.5 -0.8

Film comp. Cu In 31.41 4.23 25.56 12.25 26.73 10.67 21.03 16.36 30.46 14.77 25.92 23.94

% Se 64.36 62.20 62.60 62.61 54.77 50.14

Film comp. Cu/In Se/(Cu+In) 7.42 1.81 2.09 1.65 2.50 1.67 1.29 1.67 2.06 1.21 1.08 1.01

Table 5.3: Overall compositions of electrodeposited bilayer thin films. Bath comp. Cu In 1 5 5 1 1 5

mM Se 3 3 3

Pot. V 1st 2nd -0.5 -0.8 -0.5 -0.8 -0.5 -0.8

Film comp. Cu In 25.20 27.22 24.45 28.83 25.38 24.67

% Se 47.58 46.72 49.94

Film comp. Cu/In Se/(Cu+In) 0.93 0.91 0.85 0.88 1.03 1.00

Figure 5.2 shows the morphology of the bottom (Cu-rich) and top (In-rich) layers prepared at –0.5 V and –0.8 V, respectively. The top layer was peeled to observe the bottom layer. The Cu-rich layer has isolated crystallites or grains of 1 to 3 µm in size, while the In-rich layer has a smooth surface. However, grain boundaries were not observed definitively and some cracks existed in the In-rich layer.

Figure 5.1: Composition depth profile of electrodeposited bilayer film measured by XPS.

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Figure 5.2: Surface morphology of bottom (Cu-rich:left) and top (In-rich:right) layers. The bars denote 10 µm.

5.4

Summary

In summary, the bilayer CuInSe2 films is successfully deposited by changing substrate potential during electrodeposition. Further crystallographic, electrical, optical and crosssection morphological investigations are needed to establish this method as the CuInSe2 thin film preparation method. A post-deposition annealing may be required to improve film property, such as crystallinity and grain size. For convenience, the ternary compound was deposited in this study. However, as a high efficiency is generally obtained using a quaternary chalcopyrite compound solar cell, the preparation of Ga-containing films must be studied. On the basis of the present technique, it may also be possible to obtain a graded composition profile, which is more effective in improving the solar cell efficiency than the step profile.

6 6.1

Conclusion Summary of this Work

Electrodeposition is studied as a low cost thin film semiconductor preparation method. Ternary chalcopyrite semiconductor thin films, that is, copper indium diselenide (CuInSe2 ) is prepared by this method. This is a promising material as an absorber layer for thin film solar cells because of its suitable bandgap and a large absorption coefficient. For ternary materials, composition controlling is essential to obtain high efficiency thin film

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solar cells because properties of this material are sensitive to its composition. Thus, electrodeposition conditions including bath compositions, substrate potentials, substrate materials, current densities, pH of solution and presence of stirring on film properties such as film compositions, crystallinity, surface and cross-sectional morphologies and cell performances are investigated. The results of this work are summarized as follows. • For the wide range of current density, Se/Cu ratios in the films are proportional to those in the source baths. On the other hand, a linear relation is held between In/Cu ratios in the films and those in the source baths only for low current densities and for solutions with low solute concentrations. • The In/Cu ratios in the films decrease drastically and then become constant as the Se(IV) concentrations in the baths increase, and consequently, it is found 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. • The rate-determining step for Cu is “diffusion-limited” under all condition in this work. • The rate-determining step for Se deposition at low current densities is changed from “diffusion-limited” to “reaction-limited” by employing stirring. • The deposition of In(III) is reaction-limited at low current densities. • When a solution is stirred, the deposition of In(III) changes from “reaction-limited” to “diffusion-limited” with an increase in the current density. • Reproducibility of the In/Cu ratios in the films is improved by a factor of 3 by stirring. • Difference in potential distribution between metal and semiconductor substrates causes difference in composition of the films. • A reverse bias and pulse-plated electrodeposition are effective to improve a surface morphology of the films. • Excess Se degrades the controllability of composition and the crystallinity. • The conversion efficiency of 0.866 % (Voc=0.47 V, Isc=1.9 mA/cm2 , FF=0.533) is obtained. • CuInSe2 thin films with the bilayer structure, i.e. the Cu-rich and In-lich layers, are successfully deposited by changing substrate potential during electrodeposition.

6.2

Suggestion for Future Works

In this work, ternary chalcopyrite semiconductor thin films were successfully deposited by electrodeposition. However, the efficiency of the cell is very low (< 1%). For the cell fabrication, an n-type semiconductor, such as CdS or ZnS, as a buffer layer and a transparent conductive layer, such as ITO (indium tin oxide) or FTO (F doped SnO2 ), must be deposited on a electrodeposited CuInSe2 layer. Hence, deposition conditions for these layers must be

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optimized. Moreover, one of the causes for the low efficiency seems to be existence of cracks and voids in the films. Thus, to obtain crack and void free thin films, surface and cross-sectional morphology must be investigated in more detail. Improvement of surface properties as well as that of bulk crystal is also important. The “bi-layer” CuInSe2 films were successfully deposited by changing substrate potential during electrodeposition. However, further crystallographic, electrical, optical and cross-section morphological investigations are needed to establish this method as the CuInSe2 thin film preparation method. A post-deposition annealing may be required to improve film properties, such as crystallinity and grain size. For convenience, the ternary compound was deposited in this study. However, as the higher efficiency is generally obtained with quaternary chalcopyrite compound Cu(Inx Ga1−x )Se2 (CIGS), the preparation of Ga containing film must be studied. Furthermore, it is also important to attempt to obtain graded composition profile by gradually changing potential profile.

References [1] S. M. Sze: Physics of Semiconductor Devices 2nd edition: John Wiley & Sons (1981) 790. [2] Central Research Institute of Electric Power Industry News No.338 (2000) http://criepi.denken.or.jp/jp/pub/news/pdf/den338.pdf [in Japanese]. [3] Solar Systems No.96 (2004) 46 [in Japanese]. [4] M. Konagai Ed. Basic and application of thin film solar cells Ohmsha (2001) 3 [in Japanese]. [5] Photovoltaic Power Generation Technology Research Association Homepage http://www.pvtec.or.jp/PVTEC [in Japanese]. [6] New Energy and Industrial Technology Development Organization (NEDO) report http://www.nedo.go.jp/nedata/14fy/01/h/0001h008.htm (2000) [in Japanese]. [7] NEDO Database Japanese].

http://www.nedo.go.jp/nedata/14fy/01/g/0001g002.htm

[in

[8] M. Konagai Ed. Basic and application of thin film solar cells Ohmsha (2001) 6 [in Japanese]. [9] A. Ennaoui, S. Fiechter, Ch. Pettenkofer, N. Alonso-Vante, K. B¨uker, M. Bronold, Ch. H¨opfner, H. Tributsch: Solar Energy Materials and Solar Cells 29 (1993) 289-370. [10] S. Wagner, J. L. Shay, P. Migliorato and H. M. Kasper: Appl. Phys. Lett. 24 (1974) 434. [11] J. L. Shay, S. Wagner and H. M. Kasper: Appl. Phys. Lett. 27 (1975) 89. [12] H. S. Ullal: Tech. Dig. 14th International Photovoltaic Science and Engineering Conference, Bangkok, Thailand (2004) 417.

Electrodeposition of CuInSe2 for Photovoltaic Cell Application

203

[13] M. Konagai: Tech. Dig. 14th International Photovoltaic Science and Engineering Conference, Bangkok, Thailand (2004) 657. [14] R. N. Bhattacharya J. Electrochem. Soc. 130 (1983) 2040. [15] A. M. Fernandez, P. J. Sebastian, R. N. Bhattacharya, R. Noufi, M. Contreras and A. M. Hermann: Semicond. Sci. Technol. 11 (1996) 964-967. [16] R. N. Bhattacharya, A. M. Fernandez, M. A. Contreras, J. Keane, A. L. Tennant, K. Ramanathan, J. R. Tuttle, R. Noufi and A. M. Hermann: J. Electrochm. Soc, 143 (1996) 854-858. [17] A. M. Fernandez, P. J. Sebastian, M. E. Calixto, S. A. Gamboa and O. Solorza: Thin Solid Films 298(1997)92-97. [18] M. E. Calixto, R. N. Bhattacharya, P. J. Sebastian, A. M. Fernandez, G. A. Gamboa and R. Noufi: Solar Energy Materials and Solar Cells 55 (1998) 23-29. [19] R. N. Bhattacharya, W. Batchelor, J. E. Granata, F. Hasoon, H. Wiesner, K. Ramanathan, F. Keane and R. Noufi: Solar Energy Materials and Solar Cells 55 (1998) 83-94. [20] R. N. Bhattacharya, W. Batchelor, K. Ramanathan, M. A. Contreras, T. Moriarty Solar Energy Materials and Solar Cells 63 (2000) 367-374. [21] R. N. Bhattacharya, J. F. Hiltnerb, W. Batchelora, M. A. Contrerasa, R. N. Noufia and J. R. Sitesb: Thin Solid Films 361-362 (2000) 396-399. [22] M. E. Calixto and P. J. Sebastian: Solar Energy Materials and Solar Cells 63 (2000) 335-345. [23] R. N. Bhattacharya and M. A. Fernandez: Solar Energy Materials and Solar Cells 76 (2003) 331-337. [24] M. E. Calixto, P. J. Sebastian, R. N. Bhattacharya and R. Noufi: Solar Energy Materials and Solar Cells 59 (1999) 75-84. [25] I. Shih and C. S. Qiu: Conf. Rec. 19th PVSC New Orleans, LA (1987) 1291. [26] C. X. Qiu and I. Shin: Can. J. Phys 67 (1989) 444. [27] S. N. Qiu, C. X. Qui and I. Shih: Materials Letters 17 (1993) 190-191. [28] S. N. Qiu, L. Li, C. X. Qui, I. Shih and C. H. Champness: Solar Energy Materials and Solar Cells 37(1995)389-393. [29] C. Guill´en and J. Herrero: Proc. 11th EC Photovol. Solar Energy Conf. (1992) 815-817. [30] C. Guill´en and J. Herrero: Solar Energy Materials and Solar Cells 43 (1996) 47-57. [31] C. Guill´en and J. Herrero: J. Electrochm. Soc. 141 (1994) 225-230.

204

Shigeyuki Nakamura

[32] C. Guill´en and J. Herrero: J. Electrochm. Soc, 142 (1995) 1834-1838. [33] C. Guill´en and J. Herrero: J. Electrochm. Soc, 143 (1996) 493-498. [34] R. P. Raffaelle, J. G. Mantovani and R. Friedfeld: Solar Energy Materials and Solar Cells 46(1997) 201-208. [35] R. P. Raffaelle, H. Forsell, T. Potdevin, R. Friedfeld, J. G. Mantovani, S. G. Bailey, S. M. Hubbard, E. M. Gordon and A. F. Fepp: Solar Energy Materials and Solar Cells 57(1999) 167-178 [36] R. Friedfeld, R. P. Raffaelle and J. G. Mantovani: Solar Energy Materials and Solar Cells 58 (1999) 375-385. [37] Y. H. Kim, Y. E. Lee, H. J. Kim and J. Song: Conf. Rec. 1st World Conf. Photovol. Energy Conv. (1994) 202-205. [38] Y. E. Lee, H. J. Kim, Y. J. Kim, K. K. Lee, B. H. Choi, K. H. Yoon and J. S. Song: J. Electrochm. Soc, 141 (1994) 558-561. [39] A. Kampmann, V. Sittinger, J. Rechid and R. Reineke-Koch: Thin Solid Films 361-362 (2000) 309-313. [40] J. Rechid, R. Thyen, A. Raitzig, S. Wulff, M. Mihhailova, K. Kalberlah and A. Kampmann: Abst. Tech. Prog. 3rd World Conference on Photovoltaic Energy Conversion Osaka, Japan (2003) 2LN-C-02. [41] M. G. Ganchev and K. D. Kochev: Solar Energy Materials and Solar Cells 31 (1993) 163-170. [42] N. Stratieva, E. Tzvetkova, M. Ganchev, K. Kochev and I. Tomov: Solar Energy Materials and Solar Cells 45(1997) 87-96. [43] S. R. Kumar, R. B. Gore and R. K. Pandey: Solar Energy Materials and Solar Cells 26 (1992) 149-158. [44] H. P. Fritz and P. Chatziagorastou: Thin Solid Films, 247(1994) 129-133. [45] L. Zhang, F. D. Jiang and J. Y. Feng: Solar Energy Materials and Solar Cells 80 (2003) 483-490. [46] Julia Kois, Sergei Bereznev, Mare Altosaar and Enn Mellikov: Abst. Tech. Prog. 3rd World Conference on Photovoltaic Energy Conversion Osaka , Japan (2003) 4P-B4-29. [47] N. B. Chaure, J. Young, A. P. Samantilleke and I. M. Dharmadasa: Solar Energy Materials and Solar Cells 81 (2004) 125-133. [48] L. Thouin, J. F. Guillemoles, S. Massaccesi, R. Ortega, P. Cowache, S. RouquetteSachez, D. Lincot and J. Vedel: Proc. 11th EC Photovol. Solar Energy Conf. Montreux Switzerland (1992) 866.

Electrodeposition of CuInSe2 for Photovoltaic Cell Application

205

[49] L. Thouin, S. Massaccesi, S. Sanchez and J. Vedel: J. Electroanal. Chem. 374 (1994) 81-88. [50] L. Thouin, J. F. Guillemoles, S. Massaccesi, R. Ortega. Borges, S. Sachez, P. Cowache, D. Lincot and J. Vedel: Solid State Phenomena 37-38 (1994) 527-532. [51] L. Thouin and J. Vedel: J. Electrochem. Soc. 142 (1995) 2996-3001. [52] J. Vedel, L. Thouin and D. Lincot: J. Electrocham. Soc. 143 (1996) 2173-2180. [53] J. F. Guillemoles, P. Cowache, S. Massaccesi, L. Thouin, S. Sachez, D. Lincot and J. Vedel: Adv. Mater. 6 (1994) 379-381. [54] D. Lincot, J. F. Guillemoles, P. Cowache, S. Massaccesi, L. Thouin, K. Fezzaa, F. Boisivon and J. Vedel: Conf. Rec. 1st World Conf. Photovol. Energy Conv. (1994) 136-139. [55] J. F. Guillemoles, A. Lusson, P. Cowache, S. Massaccesi, J. Vedel and D. Lincot: Adv. Mater. 6 (1994) 376-379. [56] J. F. Guillemoles, R. Diaz, P. Cowache, L. Thouin, D. Lincot and J. Vedel: Preprint of the 13th European Photovol. Solar Energy Conf. Nice, France (1995) [57] J. F. Guillemoles, P. Cowache, A. Lusson, S. Massaccesi, K. Fezzaa, F. Boisivon, J. Vedel and D. Lincot: J. Appl. Phys. 79 (1996) 7293-7302. [58] D. Guimard, N. Bodereau, J. Kurdi, J. F. Guillemoles, D. Lincot, P. P. Grand, M. BenFarrah, S. Taunier, O. Kerrec and P. Mogensen: Abst. Tech. Prog. 3rd World Conference on Photovoltaic Energy Conversion Osaka, Japan (2003) 2P-D3-58. [59] Y. Sudo, S. Endo and T. Irie: Jpn. J. Appl. Phys. Vol. 32 (1993) 1562-1567. [60] T. Matsuoka, Y. Nagahori and S. Endo: Jpn. J. Appl. Phys. 33 (1994) 6105-6110. [61] S. Endo, Y. Nagahori and S. Nomura: Jpn. J. Appl. Phys. 35 (1996) L1101-L1103. [62] S. Nomura, K. Nishiyama, K. Tanaka, M. Sakakibara, M. Ohtsubo, N. Furutani and S. Endo :Jpn. J. Appl. Phys. 37 (1998) 3232-3237. [63] S. Nomura and S. Endo Ternary and Multinary Compound in the 21st Century IPAP Books 1 (2001) 131-136. [64] T. Riedle: Ph.D Thesis, Technical University Berlin (2002) 4 [65] N. Yamamoto Ed.: Novel Functional Semiconductors IPC (1989) 19 [in Japanese]. [66] M. L. Feartheiley: Solar Cells 16 (1986) 91. [67] N. Yamamoto Ed. : Novel Functional Semiconductors IPC (1989) 157 [in Japanese]. [68] J. Bougnot, S. Duchemin and M. Savelli: Solar Cells 16 (1986) 221.

206

Shigeyuki Nakamura

[69] V. K. Kapur, P. Singh, M. V. Choudary, F. M. Auno, L. Elyash and S. Meised: Proc. 17th IEEE Photovol. Specealists Conf. (1984) 777. [70] R. Noufi, R. Axton, C. Heffington and S. K. Deb: Appl. Phys. Lett. 45 (1984) 668. [71] A. Zunger, S. B. Zhang and S-H. Wei: Proc. 16th IEEE photoboltaic Specialists Conf. (1997) 313-318. [72] S. B. Zhang, S-H. Wei and A. Zunger: Physical Review B, 57 (1998) 9642-9656. [73] S. M. Wasim: Solar Cells 16 (1986) 289-316. [74] M. Kemell: Dr Thesis, University of Helsinki (2003) 20. [75] U. Rau and H. W. Shock: Appl. Phys. A69 (1999) 131-147. [76] T. Dullweber, G. Hanna, U. Rau and H. W. Shock: Tech. Dig. 11th International Photovoltaic Science & Engineering Conference (1999) 85-86. [77] M. Konagai Ed.: Basic and application of thin film solar cells Ohmsha (2001) 187 [in Japanese]. [78] M.Ruckh, D.Schmid and H.W.Schock, J. Appl. Phys. 76 (1994) 5945. [79] S-H. Wei and A. Zunger: Appl.Phys, Lett. 63 (1993) 2549. [80] A. J. Nelson, C. T. Schwerdtfeger, S-H. Wei, A. Zunger, D. Rioux, R.Patel and H.Hochst: Appl. Phys. Lett. 62 (1993) 2557. [81] P. K. Pandey, S. N. Sahu, S. Chandra: Handbook of Semiconductor Electrodeposition Marcel Dekker, Inc. (1996). [82] I. Ohno and S. Haruyama, Jap. J. Materia Japan (1991) 735-742 [in Japanese]. [83] I Ohno: Oyo Buturi 64 (1995) 798-802 [in Japanese]. [84] S. Nakamura, S. Sugawara, A. Hashimoto and A. Yamamoto: Tech. Dig. 9th International Photovoltaic Science & Engineering Conference, Miyazaki, Japan P-I-D-51 (1996) 387-388. [85] S. Nakamura, S. Sugawara, A. Hashimoto and A. Yamamoto: Solar Energy Materials and Solar Cells, 50 (1998) 25-30. [86] S. Sugawara: Master Thesis, Fukui University (1997). [87] L. Thouin and J. Vedel: J. Electrochem. Soc., 142 (1995) 2996. [88] L. Thouin, S. Massaccesi, S. Sanchez, and J. Vedel. J. Electroanal. Chem., 374 (1994) 81. [89] T. Nakanishi and K.Ito: Solar Energy Materials and Solar Cells 35 (1994) 171-178.

Electrodeposition of CuInSe2 for Photovoltaic Cell Application

207

[90] S. Kuranouch, T. Nakazawa, A. Ashida and N.Yamamoto: Solar Energy Materials and Solar Cells 35 (1994) 185-191. [91] R. A. Mickelsen, W. S. Chen, Y. R. Hsiao and V. E. Lowe: IEEE Trans. Electron Devices, 31 (1984) 542. [92] R. N. Bhattacharya, W. Batchelor, K. Ramanathan, M. A. Contreras and T. Moriarty: Solar Energy Materials and Solar Cells 63 (2000) 367-374. [93] M. E. Calixto and P. J. Sebastian, Solar Energy Materials and Solar Cells 63 (2000) 335-345. [94] R. Friedfeld, R. P. Raffaelle and J. G. Mantovani, Solar Energy Materials and Solar Cells 58 (1999) 375-385. [95] D. Guimard, D. Lincot, J. Guillemoles, S. Taunier, P. Mogensen, N. Bodereau, J. Kurdi, P. P. Grand O.Kerrec and M. Benfarrah: Abst. Tech. Prog. 3rd World Conf. Photovol. Energy Conv. Osaka (2003) 34. [96] N. B. Chaure, J. Young, A. P. Samantilleke and I. M. Dharmadasa: Solar Energy Materials and Solar Cells 81 (2004) 125-133. [97] S. Nakamura: Tech. Dig. 14th International Photovoltaic Science and Engineering Conference, Bangkok, Thailand, P-138 (2004) 611-612. [98] S. Nakamura: Jpn. J. Appl. Phys. 44 (2005) 1939-1940. [99] D. Schmid, M. Ruckh, F. Grunwald and H. W. Schock: J. Appl. Phys. 73 (1993) 2902.

INDEX A accommodation, 124 accounting, 148 accumulation, ix, 95, 97, 108, 112, 115, 116, 118 accuracy, 98, 115 acetone, 126 acoustic microscopy, vii activation, 76, 77, 84 activation energy, 76, 77, 84 adhesion, 177 adjustment, 165 affect, 28, 35, 36, 63, 72, 111, 130, 167, 178 aggregates, viii, 31, 32, 60, 61, 62, 64 aggregation, viii, 31, 57, 58, 64 algorithm, 103, 107 alloys, 2, 124, 143, 144, 152, 156 alternative, 4, 63, 160 alternative energy, 160 alters, 100 ambient air, 54 ammonium, 193 amplitude, 45, 46, 152 anisotropy, 115, 116, 118 annealing, 55, 56, 124, 164, 166, 167, 177, 178, 187, 192, 193, 194, 195, 200, 202 Argentina, 69, 93 argon, 39 ash, 101 assimilation, 32 assumptions, 63, 161 asymmetry, 85, 90, 91, 152, 156 atomic force, 126 atomic force microscope, 126 atoms, viii, x, 18, 21, 22, 31, 36, 37, 40, 41, 42, 43, 56, 57, 58, 62, 63, 64, 71, 72, 88, 98, 123, 125, 128, 129, 130, 144, 150, 168 attention, 36, 124, 125

availability, 50, 52 averaging, 102

B backscattering, 75 bandgap, xi, 138, 159, 164, 169, 197, 200 barriers, 97, 98 baths, 179, 181, 183, 201 behavior, 77, 104, 125, 167 bending, 186 benign, 171 bias, x, xi, 97, 100, 106, 114, 115, 123, 126, 140, 160, 186, 187, 189, 190, 195, 201 binding, 124, 131, 135, 155 binding energy, 124, 131, 135, 155 bismuth, 4, 5, 6, 17, 19, 20, 21, 22, 27, 28 body, 37, 101 Boltzmann constant, 98, 131 bonding, 72, 73, 144 bonds, 19, 71, 73, 83, 84 boundary value problem, 98 breakdown, vii

C calculus, 89 calibration, 198 candidates, 125, 163, 164 carbon, viii, 31, 32, 33, 36, 37, 39, 45, 46, 47, 48, 49, 54, 57, 58, 59, 60, 61, 62, 63, 64, 177, 198 carbon atoms, viii, 31, 58 carrier, x, 105, 123, 129, 130, 132, 137, 165, 170 cation, 99, 168 cell, xi, 42, 70, 71, 72, 98, 107, 108, 109, 126, 149, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 171, 172, 173, 177, 178, 189, 193, 195, 197, 198, 200, 201

210

Index

CH3COOH, 5 channels, ix, 95, 96, 97, 106, 108, 110, 115, 118 charge migration, vii chemical bonds, 168 chemical vapor deposition, 124 China, 123, 140 classification, viii, 32, 33, 35, 36, 38, 39, 41, 45, 61, 62, 65 clean energy, 161 clusters, 32, 44, 58, 63 CO2, 160, 161 coagulation, 63 collisions, 73, 101, 103 compensation, 171 competition, 42 complement, 105 compliance, 156 complications, 181 components, vii, 24, 28, 82, 106, 171 composition, vii, xi, 1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21, 22, 27, 28, 36, 70, 143, 144, 146, 150, 159, 160, 165, 166, 167, 170, 173, 176, 178, 179, 181, 182, 185, 186, 187, 193, 195, 196, 197, 198, 200, 201, 202 compounds, 98, 143, 144, 149, 151, 152, 154, 155, 168, 169, 192 computation, 101 concentration, ix, x, xi, 2, 5, 11, 13, 37, 41, 42, 45, 46, 48, 49, 50, 54, 55, 56, 57, 58, 60, 69, 70, 73, 74, 75, 77, 78, 81, 83, 84, 89, 123, 125, 126, 128, 129, 130, 132, 133, 135, 137, 139, 144, 145, 153, 154, 156, 160, 167, 174, 176, 179, 181, 182, 183, 194, 197, 198 concrete, 48 condensation, 58 conduction, 97, 104, 124, 125, 132, 136, 137, 172 conductivity, ix, 24, 70, 74, 75, 76, 77, 83, 86, 89, 91, 92, 96, 126, 166, 167, 170, 171 conductor, 171 configuration, 41, 42, 166 confinement, ix, 74, 85, 90, 95, 99, 132, 152, 156 confusion, 33, 36 conservation, 101, 109 construction, 168 contaminant, 126 contamination, 37 context, 33, 48 continuity, 3, 28, 53 control, xi, 28, 37, 59, 124, 159, 167, 178, 179, 181, 182, 193, 197, 201 convergence, 104 conversion, xi, xii, 50, 51, 71, 159, 160, 165, 193, 197, 201

cooling, viii, 5, 31, 32, 36, 40, 41, 57, 58, 59, 60, 64, 126 copper, xi, 33, 159, 164, 166, 187, 200 correlation, x, 50, 85, 143, 156 corrosion, 173 costs, 161, 164 coupling, 96, 102, 103, 115 crack, 202 critical value, 58 crystal growth, viii, 3, 7, 9, 21, 31, 35, 36, 37, 38, 39, 40, 43, 44, 47, 50, 51, 55, 58, 61, 63, 64 crystallinity, xi, 160, 167, 177, 187, 191, 192, 193, 195, 200, 201, 202 crystallisation, 39 crystallites, viii, 69, 74, 78, 79, 127, 139, 199 crystallization, viii, 31, 39, 40, 41, 42, 43, 48, 57, 59, 60, 62, 63, 64, 73, 77, 91 crystals, vii, viii, 1, 2, 3, 5, 6, 7, 8, 9, 10, 11, 16, 17, 18, 21, 22, 23, 25, 26, 27, 28, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 57, 59, 60, 61, 62, 63, 64, 87, 91, 99, 103, 157 CVD, 73, 124

D database, 149 decay, 96, 97, 109 decomposition, viii, 31, 56, 57, 59, 60, 61, 62, 64 defects, viii, 31, 32, 33, 34, 35, 38, 39, 41, 43, 44, 45, 46, 49, 50, 51, 52, 53, 54, 55, 56, 57, 59, 60, 61, 62, 63, 64, 124, 125, 126, 129, 130, 132, 133, 152, 154, 156, 170, 171 definition, vii, 33, 43 deformation, 41, 102, 103, 104 degenerate, ix, 95, 98, 106, 113, 115 degradation, ix, 69, 70, 147 degradation process, 70 demand, 161 density, xi, 33, 45, 48, 54, 61, 72, 75, 84, 85, 96, 97, 99, 100, 102, 107, 108, 110, 111, 125, 129, 130, 144, 152, 155, 160, 170, 173, 179, 180, 183, 184, 185, 193, 194, 201 deposition, ix, xi, 69, 71, 73, 75, 83, 84, 124, 145, 159, 160, 165, 166, 167, 169, 171, 174, 176, 177, 178, 179, 180, 182, 183, 184, 185, 186, 189, 193, 194, 195, 197, 198, 200, 201, 202 deposition rate, ix, 69, 73, 83, 180, 182, 183, 184, 185 deposits, 174 desire, 124 detachment, 40 detection, 19

Index deviation, 84, 148 dielectric constant, 98, 102, 103, 132, 135 diffraction, xi, 15, 18, 45, 46, 79, 80, 129, 133, 145, 147, 148, 149, 155, 156, 157 diffusion, xi, 3, 22, 28, 36, 42, 43, 48, 51, 56, 58, 127, 128, 130, 154, 160, 165, 167, 174, 176, 183, 184, 185, 187, 197, 201 diffusion process, 22, 56 diffusion rates, 128 diodes, 96, 124, 125, 126, 136, 144 dislocation, viii, 31, 32, 35, 36, 37, 39, 43, 45, 46, 47, 50, 51, 52, 53, 55, 56, 57, 58, 59, 61, 63, 64 disorder, x, 73, 77, 83, 143, 144, 147, 148, 149, 150, 152, 154, 155, 156, 170 dispersion, 84, 85, 88, 145 distribution, vii, viii, ix, 1, 3, 26, 27, 28, 31, 32, 33, 35, 36, 37, 38, 39, 40, 44, 45, 48, 50, 51, 54, 63, 64, 85, 91, 95, 97, 98, 100, 103, 104, 107, 108, 109, 113, 114, 116, 144, 153, 155, 174, 186, 201 distribution function, ix, 95, 100, 103, 104, 107, 108, 109, 113, 116 domain, 19, 20 donors, 32, 98, 130, 171 dopants, 136 doping, 37, 48, 59, 60, 62, 63, 70, 73, 77, 78, 89, 96, 99, 124, 125, 134, 136, 139, 166 duration, 11, 103, 107, 110, 111, 167, 179, 189

E earth, 70 effusion, 126 elastic deformation, viii, 32 electric charge, 198 electric field, ix, 95, 96, 99, 105, 106, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118 electrical conductivity, 166 electrical fields, 110 electrical properties, viii, ix, 69, 70, 124, 126, 129, 130, 139, 169, 170 electricity, 160, 161 electrodeposition, xi, xii, 159, 160, 164, 165, 166, 167, 173, 174, 176, 177, 178, 181, 189, 191, 192, 195, 196, 197, 198, 200, 201, 202 electrodes, xi, 74, 159, 167 electroluminescence, x, 123, 137 electrolyte, 166, 174, 186, 196, 197, 198 electro-migration, vii electron density distribution, 98 electron diffraction, 79 electron microscopy, viii, 28, 31, 41 electron state, 101, 106, 109, 111, 113, 114

211

electrons, ix, 49, 73, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 106, 107, 109, 111, 112, 113, 114, 115, 117, 118, 125, 132, 137, 138, 139, 173, 174 electroplating, 173 emission, vii, x, 97, 102, 103, 104, 108, 109, 111, 112, 114, 123, 124, 125, 128, 129, 130, 131, 132, 134, 135, 136, 137, 138, 139, 140, 145, 152, 153, 154, 155 entropy, 41, 42, 43, 48 epitaxial growth, vii, 50, 51, 127 equilibrium, ix, 21, 36, 42, 43, 60, 61, 70, 92, 100, 101, 102, 104, 108, 109, 113, 114, 115, 174 equipment, 70, 85, 164, 165 etching, viii, 11, 31, 32, 33, 34, 37, 38, 44, 45, 51, 52, 54, 189 European Commission, 119 evacuation, 4 evaporation, 164, 165, 174, 192, 197 evidence, x, 83, 90, 91, 143 evolution, 108, 128 EXAFS, 156 excitation, x, 49, 73, 75, 126, 143 exciton, x, 123, 124, 125, 129, 131, 132, 134, 135, 139, 154, 155, 156 exclusion, 106, 107, 111, 113 experimental condition, 75, 151 exponential functions, 112 exposure, 49, 89, 90 expression, 42, 132

F fabrication, vii, 32, 125, 171, 201 failure, vii Fermi level, 77, 100, 101, 106 fermions, 106 film thickness, 163, 189, 193 films, vii, ix, x, xi, xii, 69, 70, 71, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 91, 92, 123, 124, 125, 126, 128, 129, 130, 132, 133, 139, 140, 143, 144, 145, 146, 147, 148, 150, 152, 153, 154, 156, 159, 160, 164, 165, 166, 167, 173, 177, 178, 179, 181, 182, 183, 185, 186, 187, 189, 191, 192, 193, 194, 195, 196, 197, 198, 200, 201, 202 flight, 103, 105, 106, 107 fluctuations, ix, 95, 106, 114, 115, 144, 154, 156, 186 fluid, 24, 25 fossil, 160 France, 205 free radicals, 73

212

Index

G gallium, 2, 13, 16, 17, 18, 19, 20, 21, 22, 28, 99 generation, viii, 32, 33, 39, 42, 46, 48, 57, 58, 61, 63, 64, 96, 104, 160, 161 goals, 70 gold, 3, 4, 7 grading, 173 grain boundaries, 71, 74, 199 grains, 73, 85, 190, 199 grids, 172 groups, 48, 49, 50, 55, 63, 71, 125 growth, vii, viii, x, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 18, 21, 22, 23, 24, 25, 26, 27, 28, 31, 32, 35, 36, 37, 38, 39, 40, 42, 43, 44, 45, 46, 48, 50, 51, 52, 54, 56, 57, 58, 59, 60, 62, 63, 64, 71, 74, 79, 87, 91, 123, 124, 125, 126, 127, 128, 129, 130, 132, 133, 139, 174, 177 growth modes, 42, 43 growth rate, 3, 11, 12, 13, 14, 15, 28, 32, 35, 37, 38, 39, 40, 43, 44, 45, 48, 51, 54, 59, 60, 63, 71, 74 growth temperature, x, 13, 21, 22, 123, 124, 125, 126, 127, 128, 129, 130, 132, 139

H heat, 2, 14, 15, 28, 50, 51, 52, 53, 97, 110 heat transfer, 15, 28 heating, ix, 88, 89, 91, 95, 97, 100, 110, 118 height, 42, 72, 80, 84, 86, 88, 89, 91, 166 histogram, 108, 109 homogeneity, 169 hot carrier effects, vii hydrogen, ix, 36, 37, 50, 53, 63, 69, 73, 78, 84 hydrogenation, 73

I identification, 36, 41 identity, 37 imitation, 50 impurities, vii, viii, 1, 3, 31, 33, 36, 37, 47, 48, 49, 51, 52, 54, 57, 58, 59, 60, 62, 63, 64, 154 inclusion, 166 indicators, vii indices, 145 indium, xi, 2, 3, 8, 9, 10, 11, 12, 13, 14, 15, 18, 19, 20, 22, 27, 28, 126, 159, 164, 166, 187, 200, 201 industry, 73 inelastic, 101

influence, vii, x, 11, 13, 35, 37, 71, 73, 74, 77, 78, 104, 111, 123, 124, 130, 139, 167, 169, 173, 178, 181, 186, 187 initial state, 106, 107 input, 101 instability, 13, 14 integrated circuits, 32, 35 integration, 101, 103, 148 intensity, 18, 19, 89, 92, 106, 129, 130, 131, 133, 134, 137, 138, 147, 148, 149, 150, 152, 153 interaction, 48, 58, 87, 101, 102, 103, 109, 113, 115, 154, 171 interactions, 101 interest, ix, 50, 69, 70, 71, 85, 96, 104 interface, vii, 2, 5, 6, 8, 11, 13, 14, 15, 16, 17, 18, 22, 24, 25, 26, 27, 97, 99, 100, 101, 173, 174, 186, 187, 196, 197 interference, 81 interpretation, 45 interval, 26, 106 inversion, 173 ionization, 114 ions, 19, 73, 167, 173, 174, 179, 187, 197 IR spectra, 81 iron, 64 irradiation, 12, 73 Italy, 143, 156 iteration, 98 I-V curves, 136

J Japan, 1, 28, 140, 161, 204, 205, 206

K kinetic equations, 96 kinetics, vii knots, 58 knowledge, viii, 69, 71, 102

L laser ablation, x, 143, 144 lattice parameters, 148 laws, 106 lead, 54, 73, 74, 84, 91, 101, 128, 129, 130, 132, 144 LED, 136 lens, 75 lifetime, 49, 97, 109, 117, 118 light conditions, 193 light emitting diode, x, 123

Index light scattering, 85 limitation, 124 linear dependence, 146 liquid phase, 2 Lithuania, 95 localization, x, 143, 154, 156 low temperatures, 41, 42 luminescence, x, 123, 126, 137, 140, 143, 144, 155 lying, 47

M magnetic field, 2, 103, 104 manufacturing, 164, 167 market, 70 mass, xi, 2, 13, 15, 19, 28, 98, 100, 102, 160, 179, 183, 194 matrix, 49, 61, 63, 73, 79, 97, 101, 103 measurement, vii, 16, 17, 19, 48, 54, 82, 126, 132 melt, vii, viii, 1, 2, 3 melting, 2, 17, 33, 36, 39, 43, 64 melting temperature, 43 metal organic chemical vapor deposition, 126 methanol, 126 microdefects, viii, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65 microelectronics, 32 microscope, 12, 37, 44, 47, 145, 178, 198 microvoid, 60 migration, vii, 127, 128 minority, 165 misfit dislocations, 129 mobility, 73, 96, 125, 126, 137 MOCVD, 126 mode, x, 35, 50, 58, 63, 64, 103, 123, 127, 128, 139, 151, 152 modeling, 145 models, 35, 36, 96, 144 modules, 70 mole, 21 molecular beam, vii, x, 123, 124, 140 molecular beam epitaxy, 124 molecules, 73, 125, 174 molybdenum, 126 momentum, 96, 101, 107, 109 monitoring, vii, 74 Monte Carlo method, 103, 106 morphology, xi, 15, 78, 126, 127, 159, 160, 167, 177, 187, 188, 189, 190, 193, 195, 198, 199, 200, 201, 202 motion, 3, 5, 97, 103, 104, 105, 106, 109, 114, 115, 117

213

motivation, 161

N nanocrystals, 92 needs, 55, 164 neglect, 85 network, viii, 69, 73, 83 nitrides, 98, 102, 124 nitrogen, x, 4, 36, 63, 64, 99, 123, 125, 126, 133, 135, 136, 138, 139, 140 nitrogen gas, 4, 126 noise, vii, ix, 90, 95, 96, 97, 106, 110, 114, 115, 116, 117, 118 nonequilibrium, ix, 95, 96, 104, 109 nucleation, x, 35, 57, 58, 59, 60, 61, 62, 63, 123, 127, 128 nuclei, 58 numerical analysis, 25

O observations, 15, 60 oil, 161 optical properties, 126, 142, 144 optimization, 71 organic solvents, 177 orientation, 15, 129, 145, 146, 147 output, vii, 1, 3, 145 oxides, 165 oxygen, viii, x, 31, 32, 33, 35, 36, 37, 39, 46, 47, 48, 49, 54, 57, 58, 59, 60, 61, 62, 63, 64, 81, 123, 124, 125, 126, 128, 129, 130, 132, 135, 139

P parameter, viii, 31, 36, 58, 100, 109, 117, 145, 146, 154, 163, 168, 169 particles, 35, 58, 61, 108, 113 passivation, 171 pathways, 165 permittivity, 98, 102 pH, 165, 177, 179, 181, 183, 193, 201 phase diagram, 5, 13, 166, 167, 168, 169 phase transformation, ix, 69, 70, 73, 74, 75, 85, 86, 87, 88, 89, 91 phonons, ix, 85, 95, 96, 97, 101, 102, 103, 108, 109, 110, 111, 112, 113, 115, 116, 118, 152 phosphorus, 54 photoemission, 74 photoluminescence, x, 123, 126, 134, 143 photovoltaic cells, 2, 165

214

Index

physical properties, 71, 167, 168 physics, vii, 32, 168, 170 PL spectrum, 130, 138 Planck constant, 102 plants, 161 plasma, x, 73, 123, 124, 125, 126, 127, 132, 140, 151 PM, 75 point defects, viii, 31, 32, 35, 36, 41, 42, 43, 44, 48, 51, 54, 56, 57, 58, 59, 60, 61, 62, 64, 171 Poisson equation, 97, 98, 100 polarity, 124, 166 polarization, 98, 99, 102 pollution, 160 poor, xi, 8, 73, 129, 159, 167, 170, 173, 177, 187, 191, 197 population, 100, 104, 105, 112, 113 power, vii, ix, 1, 3, 73, 75, 85, 86, 87, 88, 89, 90, 92, 95, 96, 97, 110, 115, 116, 117, 118, 145, 160, 161, 193 precipitation, 22, 39, 46, 58, 165 prediction, vii preparation, vii, ix, xi, 69, 70, 71, 73, 124, 159, 164, 165, 167, 171, 178, 193, 200, 202 pressure, ix, 24, 69, 70, 71, 72, 74, 75, 89, 126, 145, 167, 173, 192 prices, 70 principle, 106, 107, 111, 113, 124, 148, 156, 171 probability, 101, 102, 103, 105, 107, 111, 112, 125, 154 probe, 129, 155, 178 production, 32, 50, 144, 161, 163, 166 program, 145, 149, 157 proportionality, 179 pulse, 3, 11, 12, 13, 28, 110, 111, 126, 144

118, 127, 129, 131, 135, 144, 155, 166, 179, 185, 194, 201 reactant, 70, 71, 74, 75, 83, 84 reaction mechanism, 166 reasoning, 112 recombination, viii, 31, 36, 41, 42, 48, 49, 57, 62, 64, 125, 131, 132, 137, 154, 156, 173 rectification, 166, 193 redistribution, 52, 100 redshift, 138 reduction, 72, 112, 115, 173, 174, 185 reflection, x, 41, 143, 147, 148, 156 refraction index, 84 refractive index, 165 relationship, xi, 8, 48, 74, 138, 145, 160, 167, 174, 179, 181, 194 relationships, 179 relaxation, 54, 56, 96, 100, 109, 112 relaxation process, 54 relaxation times, 112 relevance, 44, 45 reliability, vii resistance, 50, 114, 115, 124, 136 resolution, 45, 46, 75, 145, 153 resources, 160, 161 returns, 109 room temperature, x, 74, 75, 76, 77, 88, 89, 91, 92, 101, 108, 109, 118, 123, 125, 129, 138, 153, 154, 156, 165, 169, 170, 173, 198 root-mean-square, 127 roughness, 78, 80, 84, 101, 127, 128, 139, 189, 190 Russia, 65, 66

Q

sample, xi, 17, 50, 76, 77, 79, 80, 81, 82, 83, 86, 87, 88, 89, 91, 92, 126, 130, 132, 133, 134, 135, 138, 145, 147, 148, 150, 152, 159, 178, 185, 188, 189, 192, 195, 196 sampling, 89, 91, 92 satellite, 104 scattering, ix, 35, 59, 72, 74, 82, 83, 85, 86, 87, 88, 90, 91, 95, 97, 100, 101, 102, 103, 104, 105, 106, 107, 109, 111, 112, 113, 117, 118, 151, 152 secondary radiation, 49 sedimentation, 50 seed, vii, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 15, 16, 17, 18, 19, 21, 22, 23, 24, 25, 26, 27, 28 seeding, 4, 7 segregation, 2, 5, 17, 21, 27, 28 selecting, 63 selenium, 166

quantum confinement, x, 123, 139 quantum well, 97, 98, 100, 124 quartz, 3, 7, 14, 23, 24, 177

R radiation, 37, 44, 49, 145 radio, 74 radius, 25, 58 Raman spectra, x, 74, 75, 85, 86, 88, 89, 92, 143, 145, 151 Raman spectroscopy, ix, 69, 150 range, viii, 1, 2, 3, 11, 22, 23, 39, 59, 60, 72, 74, 75, 76, 79, 84, 85, 92, 96, 100, 104, 110, 112, 115,

S

Index self, viii, ix, 22, 31, 32, 36, 41, 42, 43, 48, 49, 50, 57, 58, 62, 95, 97, 98, 99, 100, 101, 102, 105, 107, 109, 110, 118, 124 self-consistency, 100 semiconductor, vii, xi, 60, 61, 62, 65, 77, 96, 124, 125, 142, 144, 155, 156, 159, 160, 161, 163, 164, 165, 167, 173, 186, 200, 201 semiconductors, vii, 1, 2, 66, 98, 103, 113, 124, 143, 144, 152, 154, 163, 164, 168 sensitivity, 19, 153 sensors, 71 separation, 2, 72, 135 series, 37, 54, 66, 75, 92 shape, 8, 13, 15, 23, 33, 41, 44, 55, 56, 60, 62 sharing, 115, 117, 118 shear, 63 sign, viii, 31, 35, 36, 37, 41, 44, 45, 49, 57, 61 silane, ix, 69, 71, 73, 74, 75, 78, 83, 86 silicon, viii, ix, 31, 32, 33, 35, 36, 37, 38, 40, 42, 43, 46, 48, 49, 50, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 69, 70, 71, 72, 73, 74, 75, 77, 83, 84, 85, 89, 91, 92, 94, 161, 163 simulation, vii, ix, 3, 95, 96, 100, 101, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 115, 116, 117, 118, 173 single crystals, vii, viii, 1, 2, 5, 27, 28, 31, 32, 33, 36, 38, 40, 48, 59, 60, 61, 63, 64, 92, 154 SiO2, viii, 31, 39, 46, 61, 62 sites, 2, 56, 73, 128, 130, 144, 150, 168 solar cells, ix, xi, 69, 70, 71, 74, 94, 159, 161, 162, 163, 164, 165, 166, 167, 168, 171, 173, 177, 178, 187, 193, 196, 197, 200, 201, 202, 206 solid solutions, 59, 60, 144 solubility, 61, 124 Spain, 71, 93, 94 species, xi, 73, 136, 159, 178, 183, 184, 185, 194 spectroscopy, 19, 74, 144 spectrum, x, 45, 82, 86, 87, 88, 91, 123, 124, 135, 138, 140, 152, 153, 154, 156 speed, 3, 5, 15 spin, 106, 107 stability, 165, 171 stages, 37, 39, 51, 127 statistics, 98, 104, 111 steel, 86, 87, 91 stoichiometry, 171, 187 strain, 44, 45, 46, 49, 54, 58, 62, 63, 100 streams, 49 strength, 102, 105, 126, 154 stress, vii, 35, 71, 72, 74, 89, 91, 92 structural defects, 101, 124, 144, 154, 156 subsidy, 161 substitution, 57, 125, 144

215

substrates, x, 50, 123, 124, 126, 128, 143, 144, 145, 146, 147, 165, 166, 177, 186, 188, 197, 201 sulfur, 153, 154 sulphur, 144, 145, 153 Sun, 120, 121, 140, 141 supply, 8, 124, 185 suppression, 39 surface structure, 74 surplus, 57 Switzerland, 204 symbols, 102, 113 symmetry, x, 104, 108, 143, 144, 156 systems, 60, 104, 160, 161

T technical assistance, 156 technology, vii, ix, 32, 69, 70, 73, 125, 139 tellurium, 11 temperature, viii, ix, x, 2, 3, 4, 5, 6, 7, 9, 11, 13, 14, 15, 16, 18, 22, 23, 24, 25, 26, 27, 28, 31, 32, 33, 35, 39, 40, 41, 42, 49, 50, 51, 53, 56, 57, 59, 60, 62, 63, 64, 69, 70, 71, 74, 75, 82, 84, 85, 86, 88, 89, 91, 92, 95, 97, 98, 99, 100, 101, 106, 110, 111, 113, 114, 115, 116, 117, 118, 123, 124, 125, 126, 127, 128, 129, 130, 131, 136, 139, 144, 145, 150, 153, 154, 155, 156, 167, 169, 174, 179, 183, 192, 194, 195 temperature annealing, 56 temperature dependence, 49, 131, 154, 155 tension, ix, 69 Thailand, 202, 203, 207 theory, 42, 43, 48, 125 thermal activation, 131 thermal activation energy, 131 thermal evaporation, 126 thermal oxidation, 35 thermal stability, 124 thermal treatment, 45, 53, 54, 56 thin films, ix, x, xi, xii, 69, 70, 71, 72, 73, 74, 75, 76, 85, 86, 92, 123, 124, 125, 127, 128, 129, 130, 131, 132, 134, 136, 138, 139, 143, 155, 159, 160, 164, 165, 166, 167, 169, 173, 178, 192, 193, 196, 197, 199, 200, 201, 202 time, 9, 22, 36, 42, 49, 50, 51, 55, 60, 61, 63, 86, 89, 90, 91, 92, 97, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 112, 115, 117, 124, 161, 163, 164, 165, 177, 189, 192, 197, 198 tin, 201 tin oxide, 201 tissue, viii, 69, 71, 86 titanium, 177 total energy, 117, 156

216

Index

trajectory, 104 transformation, viii, ix, 31, 32, 36, 38, 39, 41, 50, 51, 53, 54, 56, 57, 58, 59, 62, 64, 69, 70, 71, 72, 89, 90, 91, 92 transformation processes, 70, 72 transformations, 88, 91 transistor, 96 transition, ix, 58, 69, 84, 85, 91, 102, 103, 106, 107, 109, 127, 128, 131, 135, 136, 139, 144, 161, 162, 170, 171, 172 transition rate, 102, 103 transitions, 85, 107, 135 transmission, viii, 31, 34, 37, 49, 79 transmission electron microscopy, 37 transmittance spectra, 75, 84 transport, ix, 14, 77, 95, 96, 100, 101, 103, 104, 105, 108, 165, 167, 173 trend, 13 trial, 98 tunneling, 165

U Ukraine, 31 ultrasonic vibrations, vii, 1, 2, 3 uniform, viii, 2, 3, 8, 13, 27, 28, 32, 33, 35, 38, 39, 44, 45, 47, 58, 105, 189 UV, x, 123, 124, 126, 128, 129, 130, 132, 134, 139 UV absorption spectra, 126

variable(s), 48, 70, 73, 86 variation, 186, 187 vector, 25, 45, 46, 47, 50, 108, 109, 111 velocity, 3, 24, 25, 28, 96, 97, 102, 104, 105, 106, 108, 109, 110, 111, 112, 113, 114, 115, 118, 176 vibration, vii, 1, 2 viscosity, 24

W water, 126, 174 wave number, 72 wave vector, 102, 103, 104, 105, 107, 109 weak interaction, 113 web, 71 weight ratio, 19 wide band gap, 96 work, 100, 118, 125, 133, 135, 136, 137, 140, 144, 156, 177, 196, 201 workstation, 145

X XPS, 126, 178, 198, 199 X-ray diffraction (XRD), x, 8, 9, 10, 11, 18, 27, 28, 74, 82, 91, 129, 133, 143, 144, 145, 146, 148, 149, 150, 155, 156, 160, 169, 178, 187, 189, 192, 195

Y V vacancies, viii, 31, 36, 40, 41, 42, 43, 48, 49, 50, 57, 58, 60, 62, 63, 64, 124, 129, 144, 170, 171 vacuum, xi, 45, 48, 51, 53, 54, 126, 159, 164, 165, 166, 197 valence, 137, 171, 172, 173 validity, 35, 96 values, 16, 19, 27, 38, 39, 40, 50, 70, 72, 75, 76, 77, 78, 83, 84, 92, 96, 99, 101, 109, 113, 131, 132, 144, 145, 146, 179, 184, 185, 198 vapor, 165, 174, 177, 192, 197

yield, 98, 118, 161, 162, 163

Z zinc, 126, 128 ZnO, x, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 171, 178