The Observation of Atomic Collisions in Crystalline Solids

288 Pages·1968·23.873 MB·English

by  R.S. NELSON (Eds.)

SERIES DEFECTS IN CRYSTALLINE SOLIDS
Editors:
S. AMELINCKX
R. GEVERS
J. NIHOUL
Studiecentrum voor kernenergie, Mol,
and
University of Antwerpen Belgium
Vol. 1
R. S. NELSON: THE OBSERVATION OF ATOMIC COLLISIONS
IN CRYSTALLINE SOLIDS
N O R T H - H O L L A ND P U B L I S H I NG C O M P A N Y - A M S T E R D AM
THE OBSERVATION
OF ATOMIC COLLISIONS IN
CRYSTALLINE SOLIDS
R. S. NELSON
Atomic Energy Research
Establishment
Harwell
1968
N O R T H - H O L L A ND PUBLISHING C Ο Μ PA Ν Y - A M S Τ Ε R DA M
Publishers:
North-Holland Publishing Company - Amsterdam
Sole distributors for the Western Hemisphere:
Wiley Interscience Division
John Wiley and Sons, Inc. - New York
© North-Holland Publishing Company - Amsterdam - 1968
No part of this i$stfè may be reproduced in any form, by print, photoprint, microfilm
or any other means without written permission from the publisher.
Library of Congress Catalog Card Nr. 68-58532
Printed in The Netherlands
Dedicated to my son Paul
PREFACE
This book is intended to present a critical account of the more important experi-
ments which have provided the basis for a better understanding of atomic
collision phenomena in crystalline solids. The significance of the regular nature
of the crystal lattice on atomic collision processes is stressed as this has played
a major part in furthering our knowledge. Collisions have been divided into
two artificial regimes; primary collisions which deal with the interaction of the
incident particles with the solid, and secondary collisions which deal with those
events which occur as a result of lattice atoms recoiling from primary encounters.
Although the book is intended principally for the experimentalist some simple
theoretical models have been introduced, the reader is referred to the companion
monograph by Dr. Chr. Lehmann for a more sophisticated theoretical treat-
ment.
It is hoped that the book will provide a useful introduction to the subject
of atomic collisions in solids for the post-graduate research student, as well as
providing a collection of the most important experimental data for established
scientists actively engaged in the field. It is also intended to provide a back-
groundfor the technologist engaged in such fields as the ion implantation doping
of semiconductors.
I would like to extend my thanks to my colleagues at Harwell and to many
other scientists throughout the worldfor allowing me to use their results, without
which the book could not have been written. Finally I would like to express my
deepest thanks to my wife for her encouragement throughout, and especially
for her part in preparing the manuscript.
1 INTRODUCTION
The interaction of energetic ions with solids has aroused scientific
curiosity ever since the experimental physicist was first provided with beams
of charged particles. However, the advent of nuclear energy together with
the associated problems of radiation damage have provided a new impetus
to the whole field of atomic collisions. In 1942, E. P. Wigner first recognised
that energetic neutrons and fission fragments resulting from the nuclear
fission process would cause lattice atoms to be displaced from their normal
equilibrium positions, and this in turn might lead to serious technological
effects (Wigner, 1946). A plethora of theoretical and experimental studies on
radiation effects soon followed, but it was not until the late fifties that any
real progress was made in the details of the atomic collision events respon-
sible for radiation damage. An exact calculation of the rate of production of
displaced atoms in a solid during heavy particle irradiation is extremely
complex and statistical calculations must involve simplifying assumptions.
One of the most fundamental assumptions in early theories was to regard the
solid as a structureless medium and to take no account of its regular nature.
The inadequacy of this simplification was first realised by R. H. Silsbee
(1957) who pointed out that the transference of energy and momentum
between atoms in a crystalline solid might be strongly influenced by the well
ordered nature of its lattice. He recognised that an ordered atomic array
would impose a directional correlation between successive collisions and
that energy and momentum would be focused into those directions consisting
of close-packed rows of atoms. This concept was an important step forward
in our understanding of the dynamics of radiation damage and has been the
inspiration for numerous theoretical and experimental investigations.
1
2 INTRODUCTION [1
Other fields which have been responsible for the furtherance of our
understanding of atomic collisions are those of mass spectrometry, ion
bombardment and nuclear physics; inasmuch as experimentalists must know
something of the ranges and collision cross-sections of their bombarding
particles. In each case, early theories relating to the rate of energy loss or
stopping of these particles in solids completely neglected the regular nature of
the crystalline lattice, and it was not until 1963 that its importance was
recognised. This led to the phenomenon known as channelling, which is the
steering of fast particles between the open crystallographic planes and
channels of the crystal lattice so that their trajectories are constrained to
move in regions of low atomic density. This phenomenon has provided a
very fruitful field of research and has been exploited both for its scientific
and industrial applications.
In this book we shall be mainly concerned with the influence of the
regular nature of the crystal lattice on atomic collision phenomena. Em-
phasis will be placed on experiment as the sophisticated theoretical con-
siderations will be dealt with in detail by Chr. Lehmann in another mono-
graph in the same series.
References
Silsbee, R. H., 1957, J. Appl. Phys. 28, 1246.
Wigner, E. P., 1946, J. Appl. Phys. 17, 857.
General bibliography
Behrisch, R., 1964, Ergeb. Exakt. Naturw. 35, 295.
Billington, D. S. and J. M. Crawford, 1961, Radiation Damage in Solids (Princeton Univ.
Press, Princeton).
Carter, G. and J. S. Colligen, 1968, Ion Bombardment of Solids (Heinemann, London).
Chadderton, L. T., 1964, Radiation Damage in Crystals (Methuen, London).
Dienes, G. J. and G. H. Vineyard, 1957, Radiation Effects in Solids (Interscience, New
York).
Kaminsky, M., 1965, Atomic and Ionic Impact Phenomena on Metal Surfaces (Springer-
Verlag, Berlin).
Seitz, F. and J. S. Koehler, 1956, Solid State Phys. 2, 307.
Thompson, M. W., 1969, Defects and Radiation Damage in Metals (Cambridge Uni-
versity Press, Cambridge).
THE INTERACTION
2 OF RADIATION
WITH MATTER
2.1. Introduction
The interaction of radiation with matter is a complex phenomenon and
for this reason it is convenient to create two somewhat artificial stages in the
collision processes responsible for radiation damage; these we shall call
primary and secondary collisions respectively (fig. 2.1)
Primary collisions deal with the interaction of the incident particles
with the solid, and these may be neutrons, protons, heavier charged particles
or electrons. These collisions are of two basic types which can be identified
by the details of the energy transfer occurring in the collision. If the total
SECONDARY COLLISIONS
* PRIMARY COLLISIONS
Fig. 2.1. The interaction of an incident particle with a solid showing the primary collision,
and subsequent secondary collisions.
3
4 THE INTERACTION OF RADIATION WITH MATTER [2,§2
kinetic energy of the participating particles is conserved, then the collision
is said to be "elastic", whereas if some fraction of the total kinetic energy
is converted into another form, such as electron excitation, and is absorbed,
the collision is said to be "inelastic". In general, both types of collision occur
simultaneously during the passage of fast particles through a solid. However,
in practical cases, either one or the other is dominant as we shall see later.
Secondary collisions deal with those events which occur as a result of
lattice atoms recoiling from primary encounters. In the majority of cases,
primary recoils have energies well into the tens of kiloelectron volts and
initiate a cascade of atomic collisions. It is the spreading of this cascade
which is largely responsible for radiation damage inasmuch as whenever an
atom receives an energy greater than a certain threshold, it will be ejected
from its normal lattice site. This threshold is called the "displacement
energy" and is in most cases of the order of 25 eV. However, this will be
dealt with in more detail later.
2.2 Primary collisions
2.2.1. NEUTRONS
Fast neutrons from a nuclear reactor have no charge and interact
directly with the nuclei of the atoms of the solid. These collisions are per-
fectly elastic and recoiling atoms maintain their neutrality by taking their
electron clouds with them. The scattering is assumed to be isotropic inasmuch
E-T(E)
T^T(E)
Fig. 2.2. An elastic hard-sphere collision between a neutron and a nucleus.
as every possible energy transfer from zero to the maximum is equally
probable.
Consider the neutron-atom collision illustrated in fig. 2.2. Both the
neutron and the atomic nucleus can be assumed to behave as perfectly hard
spheres with a uniquely defined total collision cross-section given by σ = nR2,
η
where R is the distance of closest approach. In most cases σ varies between
η
2, §2] PRIMARY COLLISIONS 5
1 and 10 barns (1 barn = 10" 24 cm2). By simple application of the laws of
the conservation of energy and momentum, it is easily shown that the
maximum transferable energy is:
4M M £
n 2 = ΠΕ, (2.1)
(M + M )2
n 2
where M is the neutron mass, M is the mass of the nucleus, Ε is the incident
n 2
neutron energy and T{E) is the energy transferred to the nucleus in a
collision with a neutron of energy E. In the case of neutron collisions, M = 1
n
and as M increases, Π approaches 4/M , as can be seen from the curve
2 2
represented in fig. 2.3. Further as all collisions are equally probable, the
average energy transferred is simply:
f(E) = ±T (£). (2.2)
m
If there are N atoms per unit volume, the number of primary collisions
0
per unit length of neutron track is Ν σ and we can therefore define a "mean
0 η
I/M
2
Fig. 2.3. The maximum energy transfer Π between a neutron and an atom of mass M2
plotted as a function of Ι/Λ/2.
free-path" between collisions equal to
Λ=1/(Ν σ ). (2.3)
0 η
Taking typical values for N = 1023 atoms cm"3 and σ = 5 barns, the
0 η
average distance between primary collisions turns out to be of the order of a
few centimetres and is a distinguishing feature of this type of interaction.
2.2.2. FAST CHARGED PARTICLES
Unlike neutrons, fast charged particles interact with the lattice through