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To close the system of equations the highest order moment has to be expressed as a function of the lower order moments. For the numerical properties of the six moments model - especially for robustness - this is an extremely critical issue. In this chapter we review different methods from the literature and propose a new solution to the closure problem.
First, the use of cumulants instead of moments for the description of the
distribution function [WSYM98] leads to a generalized Gaussian closure.
Second, the maximum entropy principle in the diffusion approximation was
applied to solve the closure problem. A third alternative is the use of polynomial approximations
which are popular in higher order statistics.
Finally, the closure relations proposed in
[GKGS01] are considered, where the
sixth moment is modeled as a function of the variance
and the kurtosis of the
distribution function using a real number 
as parameter.
In the latter case the closure problem is reduced to the
choice of . This indeterminacy can be eliminated by requiring
consistency with bulk Monte Carlo data.
Previous: 2.3.5 Hierarchy of Equations
Up: II. Nanoscale CMOS Simulation
Next: 3.1 Cumulant Closure