On the Nonphysical Solutions to the Wigner Equation Used in Electronic Transport

The Wigner transport equation is gaining traction as a useful tool for modeling quantum electronic transport in semiconductors. However, nonphysical results are known to occur in numerical implementations and are often related to violation of the Heisenberg uncertainty principle when finite-difference techniques are employed. In this study, we analyze the role of boundary conditions in the behavior of the solutions to the Wigner equation for the example of a finite-sized one-dimensional nanostructure with a potential barrier in the middle and connected to reservoirs of charge. We discuss the cases in which artefacts occur and propose a boundary condition scheme that alleviates potential issues stemming from charge injection into a finite-sized simulation domain.