Study of Ion Scattering Process by the Method of Binary Collision Approximation

International Journal of Trend in Scientific Research and Development, Volume 1(4), ISSN: 2456-6470
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Study of Ion Scattering Process by the Method of Binary Collision
Approximation
Kutliev
Uchkun Otoboevich
Department of Physics, faculty of
Physic and mathematics of
Urgench State University,
Urgench, Uzbekistan
Karimov
Muxtor Karimberganovich
Department of Physics, faculty of
Physic and mathematics of
Urgench State University,
Urgench, Uzbekistan
Narimonov
Nurbek Davronbekovich
Student of Physics Department,
faculty of Physics and
mathematics of Urgench State
University, Urgench, Uzbekistan
ABSTRACT
In this paper presents the computer simulation method
based on binary collision approximation for a study of
low energy (E 0 = 1-15 keV) ion collisions on the
surface of a solid and of the accompanying effect like
namely scattering. The peculiarities of the process of
correlated small angle scattering of 1–5 keV Ne Ar
ions by the Cu(100) single-crystal surfaces have been
investigated by computer simulation. It has been
shown that under these conditions the inelastic energy
losses become predominant over the elastic ones.
KEYWORDS: computer simulation; atomic
collisions; ion scattering;
INTRODUCTION
Understanding the outermost atomic layer is
extremely helpful for understanding heterogeneous
catalysts. In a mixed metal system such as platinum-
gold, the composition of the outer surface, while
dependent upon the bulk composition, can differ
radically from that composition. The ultimate driving
force is thermodynamics, which means that the metal
with the lowest surface energy will tend to segregate
to the surface. However the attainment of this
thermodynamic equilibrium may be limited by kinetic
factors determined by the precise history of the
sample including temperature and environment.
A commonly used surface analysis technique is X-ray
photoelectron spectroscopy (XPS). XPS gives very
useful chemical information but the composition is
averaged over a dozen or so atomic layers and does
not immediately provide information for the
outermost atomic layer which, of course, is the place
where catalysis occurs.
Low-energy ion scattering (LEIS), also known as ion
scattering spectroscopy (ISS), has the unique property
that it does give the composition of the outer atomic
surface, precisely the atoms that largely determine the
catalyst's activity and selectivity. Correlation of this
with chemical information from XPS gives a more
complete picture of a catalyst system, enabling the
development of a suitable model of the surface.
In LEIS measurements, ions of known mass and
energy are directed at a sample surface where they
collide with surface atoms. Such collisions are
‘billiard-ball’ in nature, and the resultant energy of the
scattered ion can provide information about its
collision partner. When the scattering angle is fixed
(and narrowly defined) there is a direct relationship
between the resultant ion energy and the mass of the
surface atom. There is a time-dependent probability of
neutralisation by the electrons in the surface which
means that only the incident ions scattered from the
outer surface contribute to the signal. As a result of
these effects, LEIS provides a single-atomic-layer
mass spectrum of a material's surface.
Low Energy Ion Scattering spectroscopy is the non-
destructive technique that analyzes the
compositional depth profile of the sample with
the atomic depth resolution (3 Å) using medium
energy (~15 keV) ion. The energy of scattered ion is
decreased depending on the target elements and the
depth. The detector measures the scattered ion energy
with the 10-3 energy resolution (ΔE/E), resulting in
the compositional depth profile of the sample
with the 3 Å depth resolution. In addition, atomic
structure of crystal array is analyzed by a channeling
method. LEIS is an excellent tool for the analysis of
the surface and the interface of the ultra thin film and
nano-materials of 5~200 Å scale. The concentration
and the type of the radiation defects being formed
depend upon the experimental conditions and

International Journal of Trend in Scientific Research and Development, Volume 1(
significantly influence the particles’ trajectories and
their angular and energy distributions, as well as the
number of scattered particles. Moreover, there is a
correlation between the defect type, the blocking
angles of the reflected beam and the energy
distributions of the scattered particles, which allows
the determination of the defect type and its surface
concentration [1-3]. For the analysis of the first one or
two atomic top layers of a solid, noble gas ions with
primary energies between about 0.5 and 10 keV are
very well suited. This is due to their comparatively
large scattering cross sections (of the order of
1018
cm2
/sr) and due to the effective neutralization of
ions that penetrate into the sample. Thus, the detection
of scattered ions provides a powerful tool for surface
analysis that is exclusively sensitive to the outermost
atomic layers. The method is known in the literature
as “ion scattering spectroscopy” (ISS) [4].
While LEIS is best known for the ability to give a
quantitative element analysis of the outermost atomic
layer, it is also capable of giving static (non
destructive) depth profiles over the outermost 5
nm of a sample. The peaks in the LEIS spectrum are
caused by scattering from surface atoms (i.e., the
outermost atomic layer). The background is due to
scattering by heavier atoms, such as gold, from deeper
layers. LEIS are surface sensitive due to the use of
noble gas ions. Though these particles scatter from
deeper layers as well as the surface, the noble gas ions
are neutralized as soon as they penetrate the sample,
making them undetectable. However, a very small
fraction of the neutrals that are scattered from deeper
layers are re-ionized as they leave the sample. This
fraction is small enough that it doesn't significantly
interfere with the signal from the surface atoms, but
large enough to give rise to a background that can be
interpreted and used for subsequent determination of
overlayer thickness [5-7].
In this paper, we present possibility using of binary
collision method for a study of LEIS.
Computational method and discussion
The theoretical investigation of atomic collision
processes in crystals caused by ion irradiation is
usually done using computer simulation, because real
physical conditions (e.g., surfaces, interaction
potential, interfaces) can be taken into account much
easier than it is possible by using analytical methods
International Journal of Trend in Scientific Research and Development, Volume 1(4), ISSN:
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significantly influence the particles’ trajectories and
ar and energy distributions, as well as the
number of scattered particles. Moreover, there is a
correlation between the defect type, the blocking
angles of the reflected beam and the energy
distributions of the scattered particles, which allows
nation of the defect type and its surface
3]. For the analysis of the first one or
two atomic top layers of a solid, noble gas ions with
primary energies between about 0.5 and 10 keV are
very well suited. This is due to their comparatively
large scattering cross sections (of the order of
sr) and due to the effective neutralization of
ions that penetrate into the sample. Thus, the detection
of scattered ions provides a powerful tool for surface
ve to the outermost
atomic layers. The method is known in the literature
as “ion scattering spectroscopy” (ISS) [4].
While LEIS is best known for the ability to give a
quantitative element analysis of the outermost atomic
ng static (non-
destructive) depth profiles over the outermost 5–10
nm of a sample. The peaks in the LEIS spectrum are
caused by scattering from surface atoms (i.e., the
outermost atomic layer). The background is due to
gold, from deeper
layers. LEIS are surface sensitive due to the use of
noble gas ions. Though these particles scatter from
deeper layers as well as the surface, the noble gas ions
are neutralized as soon as they penetrate the sample,
le. However, a very small
fraction of the neutrals that are scattered from deeper
ionized as they leave the sample. This
fraction is small enough that it doesn't significantly
interfere with the signal from the surface atoms, but
to give rise to a background that can be
interpreted and used for subsequent determination of
In this paper, we present possibility using of binary
Computational method and discussion
theoretical investigation of atomic collision
processes in crystals caused by ion irradiation is
usually done using computer simulation, because real
physical conditions (e.g., surfaces, interaction
potential, interfaces) can be taken into account much
sier than it is possible by using analytical methods
[8]. The simulation used in our calculations to
construct the trajectories of the ions or projectile
scattered by target atoms is based on the binary
collision approximation [9] with two main
assumptions: only binary collisions of ions within
target atoms or between two target atoms are
considered, and the path in which a projectile goes
between collisions is represented by straight
segments (Figure 1.). In the binary collision model,
particles move along straight
representing asymptotes to their trajectories in
laboratory system, and one determines not a particle
trajectory but rather the difference between the angles
characterizing the initial and final directions of
motion. While this approach permits one to cut the
required computer time (compared with direct
integration of the equations of motion), it also entails
a systematic error due to the fact that over short
segments of path, the real ion trajectory differs from
the asymptotes used to replace the former.
For the description of the particle interactions, the
repulsive Biersack–Ziegler–Littmark (BZL) potential
[10] with regard to the time integral was used. The
BZL approximation for the screening function in the
Thomas–Fermi potential takes into account the
exchange and correlation energies, and the so
“universal” potential obtained in this way shows good
agreement with experiment over a wide range of
interatomic separations.
Figure 1. scheme of the binary collision
approximation.
Elastic and inelastic energy losses have been summed
along trajectories of scattered ions. The inelastic
energy losses ε (E 0, p) were regarded as local
depending on the impact parameter
into the scattering kinematics. These losse
calculated on the basis of Firsov model modified by
Kishinevsky [11] and contain direct dependence on
the impact parameter:
), ISSN: 2456-6470
285
[8]. The simulation used in our calculations to
construct the trajectories of the ions or projectile
scattered by target atoms is based on the binary
collision approximation [9] with two main
: only binary collisions of ions within
target atoms or between two target atoms are
considered, and the path in which a projectile goes
between collisions is represented by straight-line
segments (Figure 1.). In the binary collision model,
along straight-line segments,
representing asymptotes to their trajectories in
laboratory system, and one determines not a particle
trajectory but rather the difference between the angles
characterizing the initial and final directions of
is approach permits one to cut the
required computer time (compared with direct
integration of the equations of motion), it also entails
a systematic error due to the fact that over short
segments of path, the real ion trajectory differs from
s used to replace the former.
For the description of the particle interactions, the
Littmark (BZL) potential
[10] with regard to the time integral was used. The
BZL approximation for the screening function in the
ential takes into account the
exchange and correlation energies, and the so-called
“universal” potential obtained in this way shows good
agreement with experiment over a wide range of
1. scheme of the binary collision
Elastic and inelastic energy losses have been summed
along trajectories of scattered ions. The inelastic
) were regarded as local
depending on the impact parameter p and included
into the scattering kinematics. These losses have been
calculated on the basis of Firsov model modified by
] and contain direct dependence on

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286
where v and E r are the velocity and energy of relative
atomic motion, Z 1 is a greater, and Z 2 the smaller of
the atomic numbers, and r 0 is in units of Å.
The expressions for the ion Ei energy after binary
collision, taking into account inelastic losses, can be
written as follows [12]:
where f = [1 – (1 + μ)/με(E 0, p)/E 0]; θi and θr are the
angles of ion and recoil scattering in the laboratory
system of coordinate; E 0 is initial energy of
impinging ion; p is impact parameter, andμ = m 2/m 1.
Estimating the accuracy of models for various values
of the impact parameter in the low-energy range, it is
necessary to notice that in a small impact parameter
region (p < 0.5 Å), it is more preferable to use the
Kishinevsky model; however, in the region of large
impact parameters, all three models give
approximately the same results, and they are useful
even when the energy E 0 ~ 100 eV. The above-
mentioned models were checked experimentally more
than once.
One way to learn about the scattering ion or recoil
inside a target is by computer simulation. The binary
collision (BC) simulation method accomplishes this,
using the binary collision approximation (BCA) to
calculate the paths of the particles in the cascade.
The simulation starts with a scattering ion of specified
velocity and position. This is followed through a
series of inelastic binary collisions, i.e collisions
including only two particles. Between the collisions
the particles travel in straight line segments, which are
the asymptotes of the paths of the particles in the
laboratory system. If the energy a particle receives in
a collision is larger than some threshold value, it is
included in the cascade. To simulate the development
of the cascade in time, the simulation follows the
current fastest particle. When the energy of a particle
falls below some threshold value, or e.g. when it
escapes from the target, the particle is excluded from
the cascade.
The collisions are considered to be composed of a
quasielastic part and a separate electron excitation
(inelastic) part. The quasielastic part is governed by a
repulsive pair potential. The inelastic energy loss may
be continuous and dependent on the traveled path
length, or discontinuous and occurring only at the
moment of collision between primary and secondary.
The ion scattering simulation program used in the
present work is similar by structure to the well-known
MARLOWE program and based on the binary
collision approximation. But in the case of the solid
phase, the binary interaction gets distorted by the
influence of neighboring atoms and multiple
collisions. It is impossible to calculate inelastic energy
losses in this case without exact knowledge of the
trajectory of scattering ions. For their calculation, it is
necessary to perform computer simulation of ion
scattering and channeling in a single crystal. A
parallel, uniform, mono-energetic ion beam impinges
on an impact area on the surface of a crystal. The
angle of incidence of primary ions ψ was counted
from a target surface. It is assumed that the incident
beam is of small density; so, the ions of the beam do
not hit twice at the same place. The impact area
covers an elementary cell in the transverse plane of
channel axis. The number of incident particles is 4 ×
104. The shape of the target area is chosen such that
by translating it, one could cover the entire surface of
the crystal. Successive multiple scattering of ions
from atoms in the rows lying along the principal
crystallographic axes is followed in a special search
procedure to find the next lattice atom or atoms with
which the projectile will interact, with impact
parameters for all target atoms forming the walls of a
channel calculated for each layer in the crystallite.
Around the colliding target atom, the coordinates of
the nearest neighbor atoms are consistently set
according to the crystal structure of the target. For
each set of atoms, the following conditions are
checked: (i) it should be at the front part of the ion
movement, relatively to a crossing point of
asymptotes of the projectile movement directions
before and after collision; (ii) the ion impact
parameter should be less than p lim (p lim is the
impact parameter corresponding to the scattering
angle of 0.05°); (iii) among colliding atoms, it should
be the first in turn p 1, p 2, p 3… on the consecutive
collisions. After each collision, the scattering angle,
energy, and the new movement direction of the
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International Journal of Trend in Scientific Research and Development, Volume 1(
channeled ion are determined. It is checked if the
projectile is still moving in the given channel.
In order to consider simultaneous and nearly
simultaneous collisions of a particle with the atoms of
the adjacent chains, the special procedure was
proposed in [13] was used. So-called simultaneous
collisions which occur if a projectile has a
symmetrical position, and which can collide with
more than one target atom at the same time, are
approximated by successive binary collisions. The
program allowed the consideration of main
peculiarities in channeled particle distribution
depth, such as collision-by-collision details of
trajectories, flux-peaking, and difference in specific
energy losses for random and channeled trajectories.
The number of incident ions is 4 × 10
particle is incident on a reset, pure surfac
incident ions and the recoil atoms were followed
throughout their slowing-down process until their
energy fell below a predetermined energy: 25 eV was
used for the incident ions, and the surface
energy was used for the knock-on atoms. The
simulations were run with the crystal atoms placed
stationary at the equilibrium lattice sites.
The initial energy of incident ions was varied from 0.5
to 10 keV, a grazing angle of incidence
from the target surface was 3–30°, and an azimuth
angle of incidence φ realized by rotating the target
around its normal and counted from the
direction was 0–180°. The polar scattering
angle θ was counted from the primary beam direction,
the polar escape angle δ––from the target surface, and
the azimuthal scattering angle φ––from the incidence
plane.
Fig.2 shows schematically a surface semichannel and
the target area on it, and identifies the angles used in
the computation. The aiming points filled a rectangle
whose sides were divided into 50 and 200 segments in
the beam incidence plane (I coordinate) and in the
perpendicular direction (J coordinate), respectively.
Thus, the number of incident ions is 2x10
of incidence of the ion beam relative to the surface
was changed in the range ψ = 5 - 200, on azimu
angle of incidence the ion beam was directed along
the axis of surface semichannel or atomic row, polar
and azimuth scattering angles have been marked in δ
and φ, respectively.
International Journal of Trend in Scientific Research and Development, Volume 1(4), ISSN:
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channeled ion are determined. It is checked if the
l moving in the given channel.
In order to consider simultaneous and nearly
simultaneous collisions of a particle with the atoms of
the adjacent chains, the special procedure was
called simultaneous
a projectile has a
symmetrical position, and which can collide with
more than one target atom at the same time, are
approximated by successive binary collisions. The
program allowed the consideration of main
peculiarities in channeled particle distribution with
collision details of
peaking, and difference in specific
energy losses for random and channeled trajectories.
The number of incident ions is 4 × 104. Each new
particle is incident on a reset, pure surface. The
incident ions and the recoil atoms were followed
down process until their
energy fell below a predetermined energy: 25 eV was
used for the incident ions, and the surface-binding
on atoms. The
mulations were run with the crystal atoms placed
stationary at the equilibrium lattice sites.
The initial energy of incident ions was varied from 0.5
to 10 keV, a grazing angle of incidence ψ counted
30°, and an azimuth
realized by rotating the target
around its normal and counted from the <100>
180°. The polar scattering
was counted from the primary beam direction,
from the target surface, and
from the incidence
Fig.2 shows schematically a surface semichannel and
the target area on it, and identifies the angles used in
s filled a rectangle
whose sides were divided into 50 and 200 segments in
the beam incidence plane (I coordinate) and in the
perpendicular direction (J coordinate), respectively.
Thus, the number of incident ions is 2x104. The angle
beam relative to the surface
, on azimu-thal
angle of incidence the ion beam was directed along
the axis of surface semichannel or atomic row, polar
and azimuth scattering angles have been marked in δ
The dependence of =f(J) on the Ne
bombardment of the surface Cu(100)<100> at the
E0=5 keV, ψ=50 was received(Fig.3).
Figure 2. Scheme of ion scattering by a surface
semichannel and target area located on it.
the coordinates of the impact points along and
transverse to the semichannel
determining the number of incidence ions.
From dependency is seen that she consists of three
groups of the scattered particles. The First group form
the ions, diffused with surrface layer. This effect
reveals itself on distance until 0,
0 100 200 300
-3
-2
-1
0
1
2
3
4
II
I
,degree
Figure.3. The dependence of
E0=5 keV, ψ=50
.
In this case the ions scattered from atomic chain and
around them. The II group pertains to the ions which
scattered from both surface atomic chains. At the end
of dependence we can observe that the ions scattered
at the range azimuthal scattering angle
a group of particles which
channel
), ISSN: 2456-6470
287
=f(J) on the Ne+ ions
of the surface Cu(100)<100> at the
was received(Fig.3).
Scheme of ion scattering by a surface
semichannel and target area located on it. I and J are
the coordinates of the impact points along and
transverse to the semichannel axis, respectively,
determining the number of incidence ions.
From dependency is seen that she consists of three
groups of the scattered particles. The First group form
the ions, diffused with surrface layer. This effect
reveals itself on distance until 0,64 Å.
400 500
III
x0,00252 A
Ne
+
, =5
0
E0
=5 keV,
Cu(100)<100>
Figure.3. The dependence of =f(J) on the Ne+
ions
In this case the ions scattered from atomic chain and
around them. The II group pertains to the ions which
scattered from both surface atomic chains. At the end
of dependence we can observe that the ions scattered
ering angle φ=10
. This is
which scattered from semi

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288
Conclusions
The opportunity of using of binary collision
approximation at the study of ion scattering has been
described. A unique property of the LEIS technique
with the binary collision approximation is that it can
selectively analyze the atomic composition of the
outermost atoms. The received initial results show
that the this method are interesting at the analyzing of
surface structure.
Acknowledgement
The data used here to illustrate the image processing
were recorded during calculation funded by the
Agence Science and Technolgy Republic of
Uzbekistan (Grants No.OT-F2-65).
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Study of Ion Scattering Process by the Method of Binary Collision Approximation