Implementation of the Wigner-Boltzmann transport equation within particle Monte Carlo simulation

In this paper, we detail the main numerical issues of the Monte Carlo method developed to solve the Wigner-Boltzmann transport equation and simulate the quantum transport in semiconductor nanodevices. In particular, we focus on the boundary conditions regarding the injection of particles and the limits of integration for the calculation of the Wigner potential which are of crucial importance for the physical correctness of simulation results. Through typical examples we show that this model is able to treat correctly purely quantum coherent and semi-classical transport situations as well. It is finally shown that to investigate devices operating in mixed quantum/semi-classical regimes and to analyze the transition between both regimes, this approach takes advantage of its full compatibility with Boltzmann algorithm.