On the momentum resolution limit in solving the discrete Wigner transport equation

Abstract

The Wigner transport equation can take quantum-mechanical effects into account via the Wigner potential performing the non-local potential correlation. The discretization of the Wigner potential in the phase space makes the maximum correlation length finite and inversely proportional to the grid size (or resolution) in the momentum space (Δk). It has been known that the use of too small Δk leads to unphysical simulation results and there has been a lower bound called the momentum resolution limit for getting physically correct results. Here, we show that these numerical artifacts result from the abrupt regime change (quantum to classical or vice versa) across the contact between the simulated device and its boundary. We also demonstrate that its effect can be mitigated by introducing non-rectangular window functions to the Wigner potential.