Numerical aspects of a Godunov-type stabilization scheme for the Boltzmann transport equation

Abstract We discuss the numerical aspects of Boltzmann transport equation (BE) for electrons in semiconductor devices, which is stabilized by Godunov’s scheme. The k-space discretized with a grid based on total energy to suppress spurious diffusion stationary case. Band structures arbitrary shape can be handled. In case, discrete BE yields always nonnegative distribution functions and corresponding system matrix has only eigenvalues positive real parts (diagonally dominant matrix) resulting an excellent stability. transient this property upper limit time step ensuring stability CPU-efficient forward Euler scheme function. Similar Monte-Carlo (MC) method, solved together Poisson (PE), where steps PE are split into shorter BE, performed at minor additional computational cost. Thus, similar MC approach matrix-free solution memory CPU intensive large systems linear equations avoided. properties demonstrated silicon nanowire NMOSFET, I–V characteristics, small-signal admittance parameters switching behavior simulated without strong scattering. damping introduced (upwind) found negligible technically relevant frequency range. inherent asymmetry upwind results error very scattering that alleviated finer direction.