Ion implantation damages the silicon lattice and therefore produces high
point defect concentrations [Sig69], [Gib72], [Zie85],
[Hob88b], [Gil88], [Kim89]. After implantation, i.e. at the
beginning of the diffusion process, the dopants are primarily found at
interstitial sites. The concentration of the dopant interstitial pairs
is far from equilibrium.
In equilibrium the dopant interstitial pair concentration is in the
order of 
times the concentration of the substitutional dopants
, which comprises that the pair diffusivity 
is about
times the total (normal) diffusion coefficient 
.
The enormous supersaturation of dopant interstitial pairs leads to an
enhancement of diffusion. As the dopant point-defect pairs are dissolved via
, the enhanced diffusion slows down and reaches
normal diffusion as dopant point-defect pairs reach their
equilibrium values. The primary parameter to control the effect of the
transient enhanced diffusion is the reaction rate for .
The pair diffusion model described in Section 3.2.4 requires
three equations to be solved for each dopant and two additional equations
for the point defects. The model accounts for different charge states of the
diffusing species, and therefore we get an enormous number of charge state
reaction constants (
, 
) in addition to the diffusion
constants (
, 
), reaction constants (
, 
)
and equilibrium concentrations (
, 
) which are not
defined a priori.
To reduce this enormous number of parameters drastically we consider the
influence of non-equilibrium point defects just for those dopants which show
the most pronounced transient enhanced diffusion effect. Additionally, the
diffusion constants and reaction constants cannot be
chosen arbitrarily, as normal diffusion has to take place after
decay of the dopant point-defect pairs to their equilibrium
.
For simplicity, the pair diffusion mechanism and therefore the transient
enhanced diffusion effect is only taken into account for boron. For other
dopants, we apply Fair's diffusion model (see
Section 3.2.1). Since boron is known to diffuse mainly via
an interstitial mechanism, only the interstitial concentration and no vacancy
concentration is calculated. Thus, equations (3.2-59) -
(3.2-65) are solved for boron, and (3.2-66) -
(3.2-67) for other dopants. Remember that 
and 
are mean electric charges.
After implantation boron is primarily found on interstitial sites. We deduce
for the initial conditions for boron and boron interstitial pairs that only
a small part 
resides at substitutional sites and the major
part 
resides at interstitial sites (3.2-70).
The actual value of is rather uncritical for the diffusion
behavior (cf. page 
and Figure 3.7-15). The
implantation damage 
is more crucial. Hobler's
values [Hob88b] which are based on Monte Carlo
simulations seem to be to high by approximately a factor of 8 [Hob89],
[Pic91].
We apply zero flux boundary conditions for all dopants and dopant
interstitial pairs (3.2-71). For the interstitials the boundary
condition 
is frequently applied [Hei90], which
implicates an infinite surface recombination velocity for point defects. We
use a more realistic boundary condition (3.2-72) [Hu92a],
with a finite rate constant of the surface annihilation of excess
self-interstitials 
. This condition is not only more realistic,
but also allows larger time steps for the transient integration, and
therefore less CPU-time for the numerical solution.
