A Monte-Carlo Solution of the Wigner Transport-Equation

A generalized Monte Carlo method for the solution of the Wigner transport equation in semiconductor devices is proposed. The theoretical approach is based on the Wigner transport equation describing the time evolution of our electron-phonon system, and the Monte Carlo procedure is based on an iterative expansion of such an equation in powers of the various interaction coupling constants. In addition to a fully coherent description of the electron dynamics, the proposed approach allows us, in principle, to introduce in a quantum framework all the various interaction processes, such as electron-phonon, electron-impurity, and electron-electron scattering. Furthermore, boundary conditions, and therefore open systems, can be considered, as required for the analysis of semiconductor devices. Some numerical results are presented for a biased double-barrier structure with electron-phonon interaction.