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

zero temperature on a fixed uniform positive background with overall charge neutrality.
A fast charged particle entering the system brings about a polarisation of the medium
which causes energy absorption. The interaction of the charged particle on the
homogeneous electron gas is a small perturbation. It is worth mentioning that this work
forms part of a comprehensive theory of energetic ions often referred to as LSS theory
(23). The electronic stopping power is dependant on the colliding atoms but varies
linearly with velocity for low energies. In addition to the electronic stopping power LSS
theory gives a universal nuclear stopping power and allows the range to be calculated. A
more detailed treatment of LSS theory is beyond the scope of this thesis.
2.3.2 Summary of General trends in the inelastic energy loss curve
The rate of inelastic energy loss is dependant on the ion energy, and can be
considered to consist of two different velocity regimes. The maximum of the stopping
curve lies in the general vicinity of the ‘Thomas – Fermi’ velocity given by Z1 2/3 v0 (v0 is
the Bohr velocity and, v0 = e 2 / ħ = 2.2x10 8 cm/s) and is usually somewhat above it.
This provides a convenient reference point. Starting with fast moving particles the
stopping cross section increases with decreasing velocity because the particle spends
more time in the vicinity of the atom. The stopping is found to be inversely proportional
to the energy. As the energy decreases towards the maximum (dE/dx)e increases less
rapidly with falling energy E, and eventually turns around and starts to decrease. For
low velocities the stopping is found to be proportional to E 0.5 (24). These aspects are
illustrated in Figure 2.3 below for the electronic stopping powers of He and H ions in
Si.
23