At least some of the parameters in the model equations (3.2-59) -
(3.2-69) are well established, namely the dopant
diffusivities . For the interstitial diffusivity
and equilibrium
concentration
we take literature values ([Tan85],
[Bro87], [Nic89]). For the other parameters (
,
,
,
and
) we have additional conditions.
When the equilibrium between boron, boron interstitial pairs and
interstitials is established, normal diffusion
() has to
take place. Then, the effective diffusion coefficient
of
the total boron concentration
can be equated to the well known
literature values
(cf. Table 3.2-1).
A somewhat toilsome derivation [Hei91a] yields (3.2-75) for the
effective diffusion coefficient . Its comparison with the
literature value (3.2-74) gives us additional relations for the
product
, and thus reduces the number of
free parameters. These relations depend on the local concentrations
and
and are therefore solved for
in
the program code, rather than modeling the products explicitly.
Likewise, the annihilation rate and the generation rate
of the dopant point-defect pairs cannot be modeled completely individually.
At point defect equilibrium the generation term
(3.2-62)
vanishes. Then the ratio of the concentration of boron at interstitial
sites
to the concentration of boron at substitutional sites
assumes its equilibrium value
. A reaction rate
determines how fast this equilibrium is approached. We model the two
parameters
and
rather than the rates
and
directly; they are calculated from (3.2-78).
The decay of the transient diffusion enhancement shows a pronounced
temperature dependence. Whilst transient diffusion enhancement lasts about
one second at it can take several hundred seconds at
.
For boron the activation energy for the RTA-effect, and thus for
, is
approximately
according to Michel's experiments [Mic89].
In consideration of the relations (3.2-74) - (3.2-78)
four adjustable model parameters remain. (1) The reaction rate
which determines the velocity of the reaction
. (2) The ratio
which determines the percentage of the boron concentration residing on
interstitial sites in the point defect equilibrium state. (3) A guess for
the boron interstitial pair diffusivity
in order to separate the
products
which are given by (3.2-74) -
(3.2-77). Note, that the diffusion behavior is primarily determined
by the product
. And (4) the Frenkel-pair constant
. The model parameters are given in Table 3.2-7.