Computer Simulation of Ion-Solid Interactions

302 Pages·1991·8.028 MB·English

by  Dr. Wolfgang Eckstein (auth.)

Springer Series in Materials Science 10
Springer Series in Materials Science
Advisors: M. S. Dresselhaus . H. Kamimura . K. A. Muller
Editors: U. Gonser· A. Mooradian· R. M. Osgood· M. B. Panish . H. Sakaki
Managing Editor: .fl. K. V. Lotsch
Chemical Processing with Lasers 11 Mechanisms
By D. Bauerle of High Temperature
Superconductivity
2 Laser-Beam Interactions with Materials Editors: H. Kamimura and A. Oshiyama
Physical Principles and Applications
By M. von Allmen 12 Dislocation Dynamics and Plasticity
ByT. Suzuki, S. Takeuchi,
3 Laser Processing and H. Yoshinaga
of Thin Films and Microstructures
Oxidation, Deposition and Etching 13 Semiconductor Silicon
of Insulators Materials Science and Technology
By!. W. Boyd Editors: G. Harbeke and M. J. Schulz
4 Microclusters 14 Graphite Intercalation Compounds I
Editors: S. Sugano, Y. Nishina,
Structure and Dynamics
and S. Ohnishi
Editors: H. Zabel and S. A. Solin
5 Graphite Fibers and Filaments
15 Crystal Chemistry of
By M. S. Dresselhaus, G. Dresselhaus,
High Tc Superconducting Copper Oxides
K. Sugihara,!. L. Spain,
By B. Raveau, C. Michel, M. Hervieu,
and H. A. Goldberg
and D. Groult
6 Elemental and Molecular Clusters
16 Hydrogen in Semiconductors
Editors: G. Benedek, T. P. Martin,
By S. J. Pearton, M. Stavola,
and G. Pacchioni
and J. W. Corbett
7 Molecular Beam Epitaxy
17 Ordering at Surfaces and Interfaces
Fundamentals and Current Status
Editors: A. Yoshimori, T. Shinjo,
By M. A. Herman and H. Sitter
and H. Watanabe
8 Physical Chemistry of, in and on Silicon
By G. F. Cerofolini and L. Meda 18 Graphite Intercalation Compounds II
Editors: S. A. Solin and H. Zabel
9 Tritium and Helium-3 in Metals
ByR. Lasser 19 Laser-Assisted Microtechnology
By S. M. Metev and V. P. Veiko
10 Computer Simulation
oflon-Solid Interactions 20 Microcluster Physics
By W. Eckstein ByS. Sugano
Wolfgang Eckstein
Computer Simulation
of Ion-Solid Interactions
With 104 Figures
Springer-Verlag
Berlin Heidelberg New York
London Paris Tokyo
Hong Kong Barcelona
Budapest
Dr. Wolfgang Eckstein
Max-Planck-Institut flir Plasmaphysik
Boltzmannstrasse 2
W-8046 Garching, Fed. Rep. of Germany
Series Editors: Prof. R. M. Osgood
Microelectronics Science Laboratory
Department of Electrical Engineering
Columbia University
Seeley W. Mudd Building
New York, NY 10027, USA
Prof. Dr. U. Gonser M. B. Panish, Ph. D.
Fachbereich 1211 AT&T Bell Laboratories,
Werkstoffwissenschaften 600 Mountain Avenue,
Universitat des Saarlandes Murray Hill, NJ 07974, USA
W-6600 Saarbrucken, Fed. Rep. of Germany
Prof. H. Sakaki
A. Mooradian, Ph. D.
Institute of Industrial Science,
Leader of the Quantum Electronics Group, MIT, University of Tokyo,
Lincoln Laboratory, P. O. Box 73 7-22-1 Roppongi, Minato-ku,
Lexington, MA 02173, USA Tokyo 106, Japan
Managing Editor: Dr. Helmut K. V. Lotsch
Springer Verlag, Tiergartenstrasse 17
W-6900 Heidelberg, Fed. Rep. of Germany
ISBN-13 :978-3-642-73515-8 e-ISBN-13: 978-3-642-73513-4
DOl: 10.1007/978-3-642-73513-4
Library of Congress Cataloging-in-Publication Data. Eckstein, Wolfgang, 1935 - Computer simulation of ion
solid interactions / Wolfgang Eckstein. p. cm. -(Springer series in materials science; v. 10) Includes bibliographical
references and index. ISBN-13:978-3-642-735l5-8 1. Collisions (Nuclear physics) - Computer simulation.
2. Solids-Effect of radiation on-Computer simulation. I. Title. II. Series. QC794.6.C6E25 1991 539.7'57-
dc20 91-14991
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Preface
This book deals with computer simulation of the processes that occur when
projectiles hit the surface of an amorphous, crystalline or polycrystalline solid.
Only atomic particles, neutral or charged, are considered as possible projectiles.
The word "ion" appearing in the title reflects the fact that charged atomic particles
are most often used experimentally, although neutral atoms would show the same
effects in most cases. The main processes treated here are the penetration of
atomic particles into the target, back scattering from and transmission through
the target, the removal of target atoms due to sputtering and the creation of
damage in the target. The general theme could alternatively be described as
atomic collisions in solids and at the surface.
All these processes have many applications, for example, for implantation
in semiconductors. Scattering processes are important in surface chemical and
structural analysis. Sputtering is used for the production of thin films, in surface
analysis techniques and surface cleaning procedures. The processes of sputtering,
backscattering and implantation are of crucial importance at the walls of plasma
machines for fusion, and indeed in all plasma apparatus. The damage caused by
atomic particles in the materials used for nuclear reactors is another vital topic.
This monograph presents the physics required for a study of the relevant col
lision processes by means of computer simulations. Two approaches, the binary
collision approximation and the molecular dynamics model, are discussed, as
well as interaction potentials and inelastic energy losses. The main results in the
various areas mentioned above and an extensive overview of the literature up
to 1990 are provided. Therefore this book can be used as an introduction to the
field for advanced students of physics with suitable mathematical and physical
background knowledge. It will also be welcomed by researchers as a source of
detailed information about previous investigations.
Garching
May 1991 W. Eckstein
v
Acknowledgements
The proposal that I write this book came from Professor Dose. I thank him for
this opportunity and for his encouragement and support. The scientific advice
from M.T. Robinson, V. Dose, V. Molchanov, E. Mashkova, and M. Rou is
greatly appreciated. 1. Giber, 1. Laszlo, W. Moller and M. Saler read parts of the
manuscript and thus helped to clarify some topics and erase many typing errors.
1. Laszlo provided Fig. 2.9. K. Ertl's support in connection with the TJY( system
is gratefully acknowledged. I also wish to express my thanks to Mrs. Daube
for typing parts of the manuscript, to Mrs. Sombach for producing most of the
figures, to Mrs. Beirer and Mrs. Brands for the preparation of the glossy prints,
and to G. Venus and my son Klaus for help in organizing the references. I am
grateful to Dr. Lotsch for providing the opportunity to publish this book with
Springer-Verlag.
Last but not least I am very grateful to my family for their patience and
support during the work on this book.
VII
Contents
1. Introduction 1
2. The Binary Collision Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.1 Laboratory System ................................... 4
2.2 Centre-of-Mass System ............................... 6
2.3 Relations Between Laboratory
and Centre-of-Mass Systems ........................... 7
2.4 Energy Transfer ..................................... 11
2.5 Classical Scattering Theory ............................ 11
2.6 Asymptotic Trajectories ............................... 14
2.7 Detennination of the Scattering Angle
and the Time Integral ....... . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.8 Limitations of the Binary Collision Approximation ........ 26
2.9 Limitations of the Classical Mechanics Treatment ........ . 30
3. Classical Dynamics Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.1 Newton's Equations .................................. 33
3.2 Integration of Newton's Equations ...................... 35
3.2.1 Central Difference Scheme ..................... 36
3.2.2 Average Force Method ......................... 36
3.2.3 Euler-Cauchy Scheme ......................... 36
3.2.4 Predictor-Corrector Scheme ..................... 37
3.2.5 The VerIet Scheme ............................ 37
3.2.6 Nordsieck Method ............................ 38
3.3 The Time Step, Bookkeeping .......................... 39
4. Interaction Potentials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
4.1 Screened Coulomb Potentials .......................... 40
4.2 The Born-Mayer Potential ............................. 45
4.3 Attractive Potentials .................................. 52
4.4 Combined Potentials ................................. 54
4.5 Empirical Potentials .................................. 56
4.6 Embedded Atom Method .............................. 58
4.7 Analytical Methods .................................. 59
4.8 Comparison of Potentials ............................. 60
IX
5. Inelastic Energy Loss .......... . . . . . . . . . . . . . . . . . . . . . . . . . . 63
5.1 Local Electronic Energy Loss .......................... 64
5.2 Continuous Electronic Energy Loss ..................... 66
5.3 Comparison ........................................ 72
6. Thermal Vibrations and Specific Energies . . . . . . . . . . . . . . . . . . 73
6.1 Thermal Vibrations .................................. 73
6.2 Specific Energies .................................... 78
6.2.1 Cutoff Energy ................................ 78
6.2.2 Displacement Energy .......................... 78
6.2.3 Bulk Binding Energy .......................... 79
6.2.4 Surface Binding Energy ........................ 79
7. Programs Based on the BCA Model . . . . . . . . . . . . . . . . . . . . . . . 83
7.1 Random Target Structures ............................. 83
7.2 Monte Carlo Programs ................................ 89
7.3 Crystalline Targets ................................... 90
7.4 Lattice Programs .................................... 90
7.5 TRIM.SP and TRIDYN ............................... 92
7.5.1 TRIM.SP. . . . .. . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . 92
7.5.2 TRIDYN .................................... 99
7.6 MARLOWE. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
8. Programs Based on the Classical Dynamics Model ........... 108
8.1 Stable, Metastable and Quasi-Stable Programs ............ 108
8.2 Classical Dynamics Programs .......................... 109
9. Trajectories 111
10. Ranges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
10.1 Definitions ......................................... 121
10.2 Literature 125
10.3 Examples 135
11. Backscattering 142
11.1 Definitions 142
11.2 Literature 144
11.3 Examples 157
12. Sputtering .............................................. 169
12.1 Definitions ......................................... 169
12.2 Negative Binomial Distribution ........................ 170
12.3 Literature .......................................... 172
12.4 Examples .......................................... 175
x
13. Radiation Damage ....................................... 219
13.1 Definitions ......................................... 219
13.2 Component Analysis ................................. 221
13.3 Fuzzy Clustering .................................... 222
13.4 Literature .......................................... 224
13.5 Examples .......................................... 225
Abbreviations Used in the Tables 237
Constants 239
References 241
Subject Index 271
Author Index 279
XI
1. Introduction
This book discusses the interaction of energetic particles with solids. The parti
cles may be neutral atoms or ions, which may hit a solid from outside or may
start inside the solid. Particles arriving from outside the solid are usually termed
projectiles. The adjective "energetic" indicates that the particle energy ranges
from the e V to the Me V region. If a projectile penetrates a solid target it will be
scattered due to collisions with target atoms, which lead to an elastic energy loss
and to a change in direction. In addition, the projectiles suffer an inelastic energy
loss due to collisions with electrons. Finally, when the projectiles have lost all
their energy, they are deposited somewhere in the target. Other possibilities are
that the projectiles are backscattered after some collisions or that they are trans
mitted, if the target is thin enough. The processes mentioned are well known
under the names implantation, ranges, backscattering or reflection, and transmis
sion. So far the projectiles have been discussed, but that is only one part of the
process. The elastic energy lost by a projectile in a collision is transferred to a
target or recoil atom, which itself collides with other target atoms and so forth.
In this way the projectile creates what is called a cascade. Target atoms may
acquire a kinetic energy large enough to escape from the solid, a process called
sputtering. If the target atom is removed from the surface where the projectile
hits the solid, the process is named backward sputtering, to distinguish it from
transmission sputtering, where the target atom is removed from the other side of
a thin foil. In a crystal target, atoms can be removed from their lattice sites to
come to rest at an interstitial site and to leave behind a vacancy. These kinds of
processes are known as radiation damage created by particle bombardment.
All the processes mentioned can be studied by following a projectile and the
recoils through a solid target step by step. A full cascade may involve many
atoms and a large number of steps, depending on the energy of the projectile.
To get reasonable statistics for calculated values many projectile histories have
to be considered, which can be achieved by simulating the trajectories of all the
moving particles in a solid. Two main methods are used, the classical dynamics
approach and the binary collision approximation, which will be discussed in
Chaps. 2 and 3 respectively.
The first computer simulation of the movement of atoms of a small crys
tallite dates back to a publication by Alder and Wainwright [1.1] over 30 years
ago. At about the same time, Monte Carlo simulations using the binary collision
approximation were started by Bredov et al. [1.2] to study penetration and by
Goldman et al. [1.3] to study sputtering. The application of computer simulation