TABLE OF CONTENTS With the increasing miniaturization of modern semiconductor devices, the application of kinetic Boltzmann-type equations to simulate the charge transport becomes mandatory, since the hydrodynamic models used for large devices lose their validities [Markowich et al. (1990)].
In this chapter, we propose a deterministic multigroup-WENO solver for the non-stationary two-dimensional Boltzmann-Poisson system for semiconductor devices. The multigroup approach, which is applied to determine the dependence of the electron distribution function on the electron wave vector, has been used with great success for investigating the particle transport in bulk semiconductors as illustrated in the previous chapters.
On the other hand, modern semiconductors devices are featured by changes of their composition on a short length scale. Hence, suitable numerical methods for dealing with the spatial dependence of the distribution function must be applied to cope, e.g., with abrupt changes in the doping concentration. Consequently, we combine our multigroup transport equations with a weighted essentially non-oscillatory (WENO) code [Jiang and Shu (1996)] for approximating the spatial derivatives in the diffusion term of the BTEs. We present an approach based on a multivalley-model for approximating the band structure of the considered semiconductor. In addition, we construct the transport equations in a way that they allow us to correctly describe the anisotropy of scattering mechanisms. In addition, the Poisson equations is coupled with the BTEs to determine the electric field strength in the device self-consistently.
In this section, we summarize the basic equations that constitute the Boltzmann-Poisson system for semiconductor...
