Previous: 4.1 Discretization
Up: 4.1 Discretization
Next: 4.1.2 Double Grid Discretization
In MINIMOS-NT
a Scharfetter-Gummel (SG) style discretization [Tan84]
was initially used for
the discretization of the six moments model.
Simulations using this variant of
the Scharfetter Gummel discretization
did not converge for closures with parameter 
.
In the literature there are several suggestions for discretizations which generalize and claim to improve on the Scharfetter-Gummel method. These were implemented and tried as a possible cure for the convergence problems. Methods of this kind which we studied are: Meinerzhagen's model [ME88], Forghieri's method [CAP+94] and variants thereof. All these methods can be unified in the framework of an optimal artificial diffusion method [TI95].
A variety of variants of Scharfetter-Gummel was implemented and tested laboriously, but the achieved improvements were minute. In the rare cases where the Newton solver converged, the results were of bad quality, showing traces of central differencing. We suspect that these are caused by interpolating quantities from the odd to the even grid and vice versa.
In Scharfetter-Gummel style discretization interpolation occurs
at the following steps:
First, the mobility 
is needed on the odd grid,
but depends on temperature 
which is defined on the even grid.
Secondly, the electric field 
which is naturally an odd
quantity is needed on the even grid in Equation 2.57.
Here the term
is defined on the odd grid,
but is
needed on the even grid.
Previous: 4.1 Discretization
Up: 4.1 Discretization
Next: 4.1.2 Double Grid Discretization