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

constant value along the exit path compared to the inward path. Using the surface
approximation method, the two constant values of the stopping powers are taken as the
value that would occur at the surface and immediately after scattering, i.e. the value of
dE/dx corresponding to the beam energy and corresponding to the beam energy
multiplied by the kinematic factor.
The value of the inelastic energy loss can be read off an inelastic energy loss
curve or calculated from a function of the curve. In Figure 4.3 a plot of the inelastic
energy loss of He in Si is given, with the constant values of the stopping power on the
inward and exit paths indicated for scattering off Si following scattering through 70.5°.
The constant value does deviate slightly from the instantaneous stopping power. Despite
these simplifications the surface approximation is reasonably accurate over small
depths.
Inelastic energy loss (eV/Ang)
21
20
19
18
He in Si
(dE/dx) out
KE 0
75 80 85 90 95 100 105
Energy (keV)
The final energy of an ion after scattering from a depth ∆z inside the sample is
given by accounting for all the inelastic and elastic energy loss processes. Using
(dE/dx)in as the rate of inelastic energy loss on the way in, the energy lost on the inward
path is simply (dE/dx)in multiplied by the path length (∆z/cosθ1). Before a scattering
event the ion has energy E1, which is E0 minus the energy lost along the inward path. E1
is multiplied by the kinematic factor K, to give the energy after the collision E2. On the
outward path the amount of energy lost inelastically is the rate of inelastic energy loss
69
(dE/dx) in
Figure 4.3 Graph of the inelastic energy loss rates, indicating how the energy loss values
used in the surface approximation (blue lines) differs slightly from reality (green lines).
E 0