As already mentioned, some works explicitly assume a particular interpolation of the
generalized concentration between two grid points, for instance an exponential variation. No
such assumption was necessary to calculate the fluxes in the presented discretization.
Nonetheless, the resulting interpolation is needed in some cases and will be investigated in
this section.
First, a variable upper boundary is used in the definite integral
(3.51)

(3.69) 
which evaluates to

(3.70) 
By using eqn. (3.52) the coefficient is found to be

(3.71) 
A normalization of to the range can be achieved by using the substitution

(3.72) 
where is called growth function [8, p.156]. Inserting
eqn. (3.71) and eqn. (3.72) into
eqn. (3.70) yields
the expression for the growth function

(3.73) 
A graph of this function with as parameter is depicted in Fig. 3.5.
The curves in the upperleft region are obtained for
and vice
versa.
M. Gritsch: Numerical Modeling of SilicononInsulator MOSFETs PDF