Interpolation Methods and Position-Dependent Effective Mass for ViennaWD

Abstract

Modern nanoelectric devices typically require the combination of multiple materials in a highly layered structure. The complex geometries and interfaces are meticulously designed to optimize the electrical performance of such devices. Therefore, it is of utmost importance that simulation tools are able to model these structures and study the behavior of charge carriers at their various interfaces. Among the various available approaches to model the quantum electron transport problem, which are capable to describe such phenomena, the particle-based Wigner function approach, utilized by ViennaWD, stands out. Due to its representation in phase space, this method allows for the adoption of scattering models and analogies from semi-classical transport, thus retaining many classical concepts and notions. This provides important advantages for quantum mechanically simulating electron dynamics.A quantum-mechanical Wigner-based simulator should, therefore, be able to support (1) imported external quantities, such as the electric potential defined on arbitrary 2D grids, as well as (2) transport domains with different material parameters. These two aspects are represented by (1) an interpolation problem of mapping an externally generated quantity onto the ViennaWD grid structure and (2) the implementation of a position-dependent effective mass to capture the varying charge-carrier mobility in different transport domains. The means by which these two aspects can be introduced to the existing framework are assessed, and the optimal solution is implemented in ViennaWD.These additions to ViennaWD and their applicability to representative encountered data are evaluated with the help of various simulations. The developed interpolation mechanism is shown to capture a variety of different geometries, allowing for the import of diverse external quantities. Further, proof-of-concept simulations show that the effective mass functionality can be successfully implemented into ViennaWD, enabling the study of cutting-edge nanoelectric devices.