Damage formation and annealing studies of low energy ion implants ...

importance for many atomic collision problems, such as that of radiation damage in
solids. The purpose was to find a way of calculating the potential for any ion – target
combination. Using a calculation of the interatomic potential for about 500 ion – target
combinations, a function for the average potential could be produced.
2.2.1 Scattering cross section
The precise trajectories of the colliding particles depend on the impact parameter
and the interaction potential. This forms the basis of the quantitative calculation of the
probability of scattering through a specific angle and the rate of elastic energy loss as
the projectile particle passes through the solid target. The quantity of interest for both
these calculations is the so – called scattering cross – section (14, 15, 16). It is used as a
quantitative measure of the probability that an incident particle will be scattered by a
target atom at an angle θ into a solid angle Ω and comes from the work of Rutherford in
explaining the results of Geiger and Marsden on the scattering of alpha particles.
If a uniform parallel flux of ions is incident upon a stationary atom, ions at a
certain p will be scattered into a cone of half angle θ as shown in Figure 2.1. The plane
area defined by radii p and p + δp defines atoms that are scattered between angles θ and
θ + δθ. This area 2πpδp is known as the differential scattering cross section (dσ) for
scattering between impact parameter limits p and p + δp and scattering angles θ and θ +
δθ. However the solid angle (dΩ) included by the cones of half angle θ and θ + δθ is
equal to 2π sinθ δθ. The differential scattering cross section for scattering into unit solid
angle becomes:
dσ
pδp
σ ( θ ) = =
dΩ
sinθδθ
(2.5)
The value of the differential scattering cross section is given by:
1 2
σ = F⎢
2 ⎥
dΩ
⎣4E
sin ( θ / 2)
⎦
2
2
dσ
⎡ Z Z e ⎤
= g
(2.6)
( θ,
M , M )
where F is a function derived from the Moliere potential, given by (9, 10):
4
3
1
0.
042Z1Z
2
F = 1−
(2.7)
E
and g is a multiplication factor to account for the transformation from the centre of mass
to the lab frame of reference. The scattering yield will vary with the differential
scattering cross section. For conditions with a larger σ the scattering yield will therefore
also be larger. This has important consequences for MEIS analysis and the rate of
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