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

energy Ed causing the target atom to be displaced. Any energy transferred exceeding Ed
becomes the resulting kinetic energy of this so-called primary recoil atom, which moves
away from the ion track into the lattice. Primary recoil atoms with sufficient energy are
able to displace further atoms, producing secondary recoil atoms, which in turn can
create higher order recoils. This process continues, creating a collision cascade. The ion
will continue travelling through the material, creating more primary recoil atoms along
its path until all its energy is dissipated.
The energy deposition density is much higher for heavy ions compared to light
ones. This difference results in the damage build up proceeding in a very different
fashion for heavy and light ions, and is a critical factor for amorphous zone and layer
formation. In this section the collision cascades of heavy ions are first described,
followed by light ions, highlighting the differences. Different models for amorphisation,
i.e. heterogeneous and homogeneous amorphisation, appropriate for heavy and light
ions respectively, are described in the following sections, along with a brief summary of
other relevant models and damage effects.
The amount of energy transferred in a collision is impact parameter dependent,
with maximum transfer for a head on collision, and decreasing with increasing impact
parameter. The average energy transfer is dependent on the scattering cross section (18).
Heavy ions, with a larger scattering cross section are more likely to undergo collisions,
and the average energy transfer is therefore higher for heavy ions (18). The mean free
path for an energetic particle between collisions λd is given by
λ 1
d = (3.1)
Nσ
where N is the atomic lattice density and σ is the scattering cross section, given in
equation 2.6. Since σ is proportional to Z1 2 it follows that the mean free path for a heavy
ion is much shorter than for a light ion. It is in fact of the order of an interatomic
spacing. A heavy ion therefore generates another displacement almost immediately after
the first, causing the energy deposition density to be much higher for heavy ions than
with light ones. Since primary recoils are created close together along the ion track, the
individual cascades tend to overlap with their neighbours and the final result would be a
giant collision cascade containing all the overlapping individual cascades. As the ion
energy decreases along its path, its scattering cross section increases causing collisions
closer together. The rate of energy deposition increases along the ion path, until towards
the end of the ion path where the ion energy is low and correspondingly the total energy
transferred to recoils is also low. The resulting collision cascade is therefore ellipsoidal
in shape (18), as shown schematically in Figure 3.5 a). A heavy ion, such as As, hitting
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