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.

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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.

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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 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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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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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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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).

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