A Finite Difference Scheme Solving the Boltzmann–Poisson System for Semiconductor Devices

The Boltzmann equation describing electron flow in semiconductor devices is considered. The collision operator models the scattering processes between free electrons and phonons in thermal equilibrium. The doping profile and the self-consistent electric field are related by the Poisson equation. The coupled system is solved by using a simple numerical scheme based on finite differences. Hydrodynamical variables are obtained by integrating the distribution function. Numerical results are shown for a one-dimensional n+−n−n+ silicon diode.