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

3.2.2.5 Homogeneous model (Critical defects model)
The second model is based on ion irradiation causing a build up of defects
within the lattice (22-25). Once a certain critical defect density has been reached the
damaged crystal lattice collapses into an amorphous state. This is energetically
favourable because the free energy of amorphous Si is lower than that of highly
damaged crystalline Si. The number of defects increases with increasing fluence until a
point where the free energy of the defective crystalline phase exceeds that of amorphous
Si and a phase transformation into the amorphous state occurs.
This model for amorphisation is known as homogeneous amorphisation because
the amorphous Si is thought to nucleate as a result of an interaction among sufficient
number of defects produced within different collision cascades and distributed
homogeneously throughout the irradiated region. Homogeneous amorphisation is more
appropriate where irradiation produces low density cascades and simple defects, as is
the case with light ions at room or higher temperatures (24). The onset of amorphisation
would be expected to occur abruptly over a narrow range in dose, as has been found
experimentally (4). The transformation occurs when the defect concentration exceeds
about 1.15x10 22 cm -3 (4). The effect of dynamic annealing is to reduce the defect
density present compared to the number of defects produced and an increased
implantation dose would be required to for amorphisation at, for example, room
temperature compared to liquid nitrogen temperature where defects are frozen in (4).
3.2.2.6 Other models
A two stage nucleation limited model, is suggested because amorphisation
occurs preferentially at pre existing amorphous defects (26) or a/c interfaces (27-30).
This nucleation and growth (31) operates by the production of suitable amorphisation
sites, via the accumulation of residual defects to reach a certain type or density, which
then act as sinks for simple defects and produce the growth of the amorphous phase.
An energy spike is a term used to describe two similar types of collective effect,
i.e. displacement and thermal spikes. The production of interstitial – vacancy pairs, i.e.
the number of displaced atoms per cascade can be described using a modified version of
the Kinchin – Pease relationship (7, 32) using more realistic potentials (33)
kf ( E)
ν ( E)
=
(3.2)
E
d
40