Impurities in Semiconductors: Solubility, Migration and Interactions

440 Pages·2004·9.447 MB·English

by  Victor I. Fistul

IMPURITIES IN
SEMICONDUCTORS:
SOLUBILITY,
MIGRATION, AND
INTERACTIONS
© 2004 by CRC Press LLC
IMPURITIES IN
SEMICONDUCTORS:
SOLUBILITY,
MIGRATION, AND
INTERACTIONS
Victor I. Fistul
CRC PR ESS
Boca Raton London New York Washington, D.C.
© 2004 by CRC Press LLC
TF1658_discl Page 1 Friday, December 19, 2003 9:50 AM
Library of Congress Cataloging-in-Publication Data
Fistul, V.I. (Viktor Ilich), 1927(cid:150)
Impurities in semiconductors : solubility, migration, and interactions / V.I. Fistul ; translated
by L.N. Smirnova.
p. cm.
Includes bibliographical references and index.
ISBN 0-415-30831-3 (alk. paper)
1. Semiconductor doping. 2. Semiconductors (cid:151) Impurity distribution. 3. Semiconductors
(cid:151) Diffusion. 4. Solubility. I. Title.
QC611.6.D6F57 2004
537.6¢22 (cid:151) dc22 2003067460
This book contains information obtained from authentic and highly regarded sources. Reprinted material
is quoted with permission, and sources are indicated. A wide variety of references are listed. Reasonable
efforts have been made to publish reliable data and information, but the author and the publisher cannot
assume responsibility for the validity of all materials or for the consequences of their use.
Neither this book nor any part may be reproduced or transmitted in any form or by any means, electronic
or mechanical, including photocopying, micro(cid:222)lming, and recording, or by any information storage or
retrieval system, without prior permission in writing from the publisher.
The consent of CRC Press LLC does not extend to copying for general distribution, for promotion, for
creating new works, or for resale. Speci(cid:222)c permission must be obtained in writing from CRC Press LLC
for such copying.
Direct all inquiries to CRC Press LLC, 2000 N.W. Corporate Blvd., Boca Raton, Florida 33431.
Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are
used only for identi(cid:222)cation and explanation, without intent to infringe.
Visit the CRC Press Web site at www.crcpress.com
' 2004 by CRC Press LLC
No claim to original U.S. Government works
International Standard Book Number 0-4153-0831-3
Library of Congress Card Number 2003067460
Printed in the United States of America 1 2 3 4 5 6 7 8 9 0
Printed on acid-free paper
© 2004 by CRC Press LLC
Preface

Every century bears its own name in History, characterizing its principal
achievement. We do not know yet what name our descendants will give to
the 20th century. It may be called the nuclear age, owing to the discovery
and application of nuclear power. Or, it may be called the age of space
flights, because man has overcome the Earth’s gravity to go into space and
has even visited the Moon. But there is another possible name which might
as well be given to the 20th century—the age of electronics! The time that
has elapsed since the invention of the radio is a period of major
achievements in solid state electronics which has filled up every “pore” of
our life. No progress would ever have been possible in nuclear technology,
space flights or other technologies without electronics. Electronics, in turn,
directly depends on high quality semiconductor materials. Nature has
supplied us with very few semiconductor substances, such as germanium,
silicon, selenium, and tellurium, whereas other commonly used materials of
the III–V and II–VI groups and more complex compounds (III –VI and III –
2 3 2
IV–VI) are man-made.
All semiconductor materials, both natural and synthesized, require much
effort for their production in a perfect (defect-free) crystalline state with a
negligible background of foreign impurities. Such impurities contaminate the
crystal in an uncontrollable or poorly controllable way. On the other hand,
all remarkable properties of semiconductors, that paved the way for modern
solid state electronics, are due not only to their purification but also to a
well-controlled doping dosage.
Today we have at our disposal a nearly complete list of impurities
suitable for doping basic semiconductors. This circumstance permits sys-
tematization of properties of various semiconductor–impurity systems in one
book. However, I did not intend to write a reference book, because fairly
complete and good reference books have already been published. A good
illustration is the world-known work Numerical Data and Functional Rela-
tionship in Science and Technology. New Series Ed. K. Hellwey and
O. Madelung. Berlin: Springer–Verlag, 1984. V. 17, pp. 652. No doubt it is
important to know the properties of a semiconductor doped with an impurity
in a definite concentration. For practical applications, it is more important,
© 2004 by CRC Press LLC
however, to know the techniques, procedures, and external effects which can
help us to control the distributions of impurity atoms over various crystal
positions. This control is the key to a wide controllable application of
impurities, whose potentialities are still far from being exhausted.
It was my primary aim to draw the attention of researchers and engineers
to impurities which have not yet found a wide application in semiconductor
technology: d-, f-, isovalent, and other types of impurities. I had another aim,
too. It seems important to me that the western reader should be introduced to
the research done in this area of physics by scientists in the former Soviet
Union. I hope this gap will be filled after the publication of this book.
The author’s philosophy will inevitably show itself in the material
presentation, and the reader may not agree with some of my judgments.
Besides, because of the extensive character of the problem, some of its
aspects have been left aside, for example, the interaction of impurities with
dislocations and stacking faults, or the state and behavior of adsorbed
impurities. I hope, however, that this book will appear useful even in its
present format. I would be very happy if it could eventually find its place
among the books by such outstanding researchers as F.A. Kroger of the
Philips Laboratory in Endhoven, R.A. Swalin of the University of Minne-
sota, A.G. Milnes of the Carnegie–Mellon University, or V.M. Glazov of the
Moscow Institute for Electronics Technology.
I would like to express my sincere gratitude to the many people who have
stimulated the evolution of my thinking as a scientist and, sometimes, as a
human being. Among them are the much lamented professors
R.N. Rubinshtein, D.N. Nasledov, and Yu.V. Shmartzev. My gratitude also
goes to my numerous colleagues who are presently working actively in
physics—professors B.V. Tzarenkov, F.A. Gimelfarb, V.M. Koshkin,
D.G. Andrianov, M.G. Milvidsky, N.S. Rytova, S.V. Bulyarsky, P.M. Grin-
shtein, B.L. Oksengendler, and K.A. Kikoin.
I want to thank the translator of this book L.N. Smirnova, Ph.D., who has
brilliantly overcome numerous translation difficulties, and M.A. Smirnova
for the camera-ready preparation of the book.
Finally, I am very grateful to the Publisher for their effort in publishing
this book.

© 2004 by CRC Press LLC
CONTENTS

Preface

1 The Semiconductor–Impurity System
1.1 The Semiconductor Crystal as a Thermodynamic System
1.2 Thermodynamic Descriptions of Impurity Solubility
1.3 General Characteristics of Impurity Centers
Reference s

2 Impurity Behavior in Semiconductors
2.1 Hydrogen-Like Impurities
2.2 Impurities with Partly Filled Electron Shells
(d- and f-Impurities)
2.3 Amphoteric Impurities
2.3.1 General concept s
2.3.2 Carrier thermodynamics in semiconductors with
amphoteric impurities
2.3.3 Amphoteric impurity distribution in elemental
semiconductors
2.3.4 Amphoteric impurity distribution in semiconductor
compounds
2.3.5 Data on amphoteric impurity states and behavior
2.3.6 Amphoteric excitons bound by d-impurities
2.3.7 Dissociative amphoteric impurities
2.3.8 Cation–anion amphoteric impurities in semiconductor
compounds
2.4 Isovalent Impurities
2.4.1 General concepts
2.4.2 Empirical models of isovalent impurities
2.4.3 Physicochemical behavior of the host–IVI system
2.4.4 Possible mechanisms of the isovalent impurity effect
2.4.5 Isovalent doping effects
2.5 Volatile Impurities
2.5.1 Hydrogen
2.5.2 Oxygen
© 2004 by CRC Press LLC
2.5.3 Carbon
2.5.4 Nitrogen
References

3 Impurity Solubility in Semiconductors
(A Macroscopic Approach)
3.1 Retrograde Solubility of Impurities
3.2 Solubility of Hydrogen-Like Impurity Atoms in
Germanium and Silicon
3.3 Hydrogen-Like Impurity Solubility in AIIIBV Compounds
3.4 Solubility of Deep Impurities
3.4.1 Solubility of AIV semiconductors
3.4.2 Solubility in semiconductor compounds
3.5 Solubility of Amphoteric Impurities
3.5.1 A thermodynamic analysis
3.5.2 Solubility of dissociative amphoteric impurities
3.5.3 Solubility of cation–anion impurities in
semiconductor compounds
References

4 Microscopic Analysis of Impurity Solubility in Semiconductors
4.1 Dissolution Enthalpy Calculation by Weisser’s Method
4.1.1 Site solubility
4.1.2 Interstitial solubility
4.2 Dissolution Enthalpy in the Pseudo-Alloy Model
4.3 Weisser’s Modified Solubility Theory
4.3.1 Interstitial d-atom solubility
4.3.2 Site solubility of d-atoms
4.4 Solubility of Interstitial f-Atoms in Silicon
4.5 On Solubility Theory for Semiconductor Compounds
4.6 Comparison with Experimental Data
4.7 Quantum Chemical Calculation of Dissolution Enthalpy
4.7.1 Formulation of the quantum chemical problem
4.7.2 The dissolution model for a substitutional impurity
4.7.3 Quantum chemical calculations of impurity solubility
4.7.4 Perspectives of the quantum chemical method
References

5 Impurity Interactions in Semiconductors
5.1 Types of Impurity Interactions
5.2 Statistical Interaction
β
5.2.1 Configuration entropy of a lattice with N sites
β
and N vacancies
V
© 2004 by CRC Press LLC
5.2.2 A lattice with several defect types
5.2.3 A lattice with structural elements in several positions
5.2.4 The arrangement of complexes
5.2.5 The arrangement of electrons and holes
5.3 Charge Interaction
5.4 Potential Interaction
5.5 Defect Interaction in a Regular Approximation
5.6 Interaction Leading to Complexation
5.7 Defect Ionization in Solids
References

6 Associations of Impurity Atoms
6.1 Ion Pairs
6.1.1 Point ions
6.1.2 Ions with a fixed radius
6.1.3 Ion pairing manifestation in semiconductor properties
6.2 Polytropic Impurities
6.3 Complexation Thermodynamics in a Semiconductor
Compound
6.4 Impurity–Vacancy Complexes in AIIIBV Compounds
6.5 Impurity–Vacancy Complexes in Silicon
6.6 Impurity Syneresis
6.7 Combined Complexation
6.8 Indirect Ion–Ion Interaction
6.9 Applied Aspects of Complexation
6.9.1 Deep center content versus growth temperature and
free electron concentration
6.9.2 Homogeneity region width in AIIIBV compounds
References

7 Impurity Kinetics in Semiconductors
7.1 Impurity Migration Energy
7.2 Microscopic Theory of Impurity Kinetics
7.3 Dissociative Diffusion of Impurities
7.4 Kinetic Effects in Subsurface Layers
7.5 Diffusion Profiles of Interacting Impurities
7.5.1 General principles
7.5.2 Impurity interactions in terms of thermodynamics
of irreversible processes
7.5.3 Impurity interactions in terms of a model approach
7.5.4 Diffusion theory for immobile complexes
References

© 2004 by CRC Press LLC
8 Impurity Migration in the Formation of Mobile Complexes
8.1 Diatomic Complexes: Formation and Decomposition
8.2 Diffusion Model for Mobile Complexes
8.3 Solution of Diffusion Equations for Various Boundary
Conditions
8.3.1 Sequential diffusion
8.3.2 Simultaneous diffusion
8.3.3 Interdiffusion
8.3.4 The allowance for the finite front thickness
8.3.5 The physics of impurity diffusion with interactions
8.4 Diffusion Theory Versus Experiment
8.4.1 Chemical diffusion of phosphorus into silicon
8.4.2 Radiation-stimulated P diffusion into uniformly
O -doped silicon
2
8.4.3 Fe redistribution in B and P diffusion-doped silicon
Referceens

© 2004 by CRC Press LLC
Chapter 1

The Semiconductor–Impurity System

1.1 THE SEMICONDUCTOR CRYSTAL AS A
THERMODYNAMIC SYSTEM

A semiconductor crystal doped with impurities is usually regarded as a solid
solution, in which the semiconductor is the solvent and the ensemble of im-
purity atoms is the solute.
Sites and interstices in a crystal lattice serve as positions for various
structural units—atoms and vacancies. A chemical potential can be ascribed
only to these units.
A perfect crystal consists only of intrinsic (host) atoms and stoichiomet-
ric vacancies occupying intrinsic sites in the crystal lattice. Any deviation
from crystal perfection is known as a defect, and the process that has brought
it into life is termed defect formation. In the generally accepted classification
[1], impurities and vacancies are referred to as point defects. In this book, the
word “vacancy” will be used only for nonstoichiometric vacancies formed
after a host atom has left its site.
Normally, point defects are considered to be distributed between two
phases—the crystal and its ambient. The former is taken to be an entity,
without subdividing it into the variety of positions provided for impurity
atoms. This is because a common impurity can usually occupy only one kind
of position in a crystal lattice in a wide temperature range, irrespective of
other point defects, intrinsic or impurity-type. One exception is amphoteric
impurities, which can simultaneously occupy different positions in a lattice
© 2004 by CRC Press LLC