2.1 The Boltzmann Poisson System

The Boltzmann equation is a semiclassical equation and describes the time-dependent position and momentum of electrons and holes in semiconductors. To describe the interaction between electrons the BTE is coupled with the Poisson equation.

To simplify the (3+3)-dimensional equation additional assumptions are made. Using cylinder symmetry the equation can be reduced to (1+2) dimensions. Further simplifications in the framework of the diffusion approximations are defined.