2.3 Closure Relations for the Scattering Operator

In general the terms involving the scattering operator cannot be expressed as a simple function of, for instance, the parabolic moments . Here we use a macroscopic relaxation time approximation for the closure which gives the system of moment equations a structure resembling the drift diffusion system.

In a deliberate way the scattering integral stemming from an observable is modeled as

Here denotes the moment from the equilibrium solution. A discussion on the validity of this approximation is given in [Lun00]. Note that the odd equilibrium moments vanish and hence the expression simplifies in this case.

- 2.3.1 Even Moments: Relaxation Times
- 2.3.2 Odd Moments: Mobilities
- 2.3.3 Analytical Mobility and Relaxation Times
- 2.3.4 Consistency with Bulk Monte Carlo Results
- 2.3.5 Hierarchy of Equations

R. Kosik: Numerical Challenges on the Road to NanoTCAD