document: The validity of semi-classical boundary conditions for the WTE as introduced in [8] is a topic under vivid debate, especially after recent works which address the non-uniqueness and the symmetry properties of the Wigner function [27,28,46]. The numerical test cases presented therein are for symmetric potentials for which we cannot provide reliable, i.e. well-resolved, results due to the presence of singular terms in the steady state Wigner functions, see Section 4.3. Other recent studies demonstrate the convergence of the WTE calculations upon increasing the size of the simulation domain [44] as well as possible improvements by adapting the boundary distribution to the physical state of the active device region [47]. Despite their approximate nature we employ inflow/outflow boundary conditions here as well and demonstrate that accurate and physically valid results can be achieved for sufficiently large values of Lres. Due to the problematics with singular terms we present simulations only for non-zero bias voltages VDS≠0 V.
extractive_keyphrases: accurate and physically valid results adapting the boundary distribution convergence of the wte calculations increasing the size of the simulation domain numerical test cases other recent studies steady state wigner functions symmetric potentials
abstractive_keyphrases: employ inflow/outflow boundary conditions non-uniqueness and the symmetry properties of the wigner function present simulations only for non-zero bias voltages validity of semi-classical boundary conditions