A parallel deterministic solver for the Schrödinger–Poisson–Boltzmann system in ultra-short DG-MOSFETs: Comparison with Monte-Carlo

We present a parallel deterministic solver for the Boltzmann–Schrödinger–Poisson system for partially-confined DG-MOSFETs. Our 2D model uses a dimensional coupling: the electrons behave as particles along the longitudinal dimension, and as waves along the transverse dimension. In Ben Abdallah et al. (2009) the authors validated, in a simplified setting, the solver for the eigenproblems. In this paper we have focused on obtaining physically accurate results by introducing a realistic Si conduction band and electron–phonon interactions. We have switched from Cartesian to elliptic variables for the wave vector, and consequently radically rebuilt the time integrator. The code has been parallelized following a domain-decomposition approach. The results have been compared to those given by a Monte-Carlo solver.