Complex Absorbing Potential Formalism Accounting for Open Boundary Conditions Within the Wigner Transport Equation

Abstract

For the derivation of the Wigner Transport Equation an infinite computational domain is presumed. As a consequence, when considering a bounded computational domain as it is the case for numerical device modeling, several difficulties arise based on this assumption. Due to the inadequate inclusion of the boundary terms, the Wigner function inherently suffers from an artificial interference pattern. To address this aspect, a complex absorbing potential formalism, which is originally utilized for the numerical solution of the Schrodinger equation, is developed for the application onto the Wigner Transport Equation. As a result, the drift operator includes an additional term accounting for the finiteness of the computational domain reflecting open boundary conditions. The approach is discussed by means of a simple structured resonant tunneling diode and utilizing conventional finite difference schemes for a numerical solution of the Wigner Transport Equation. Additionally, the results are compared with a reference solution obtained by the Quantum Transmitting Boundary Method.