Numerical Simulation of Two Dimensional Electron Transport in a Circularly Symmetric Cylindrical Nanostructure using Wigner Function Methods

TL;DR

This paper develops a 2D Wigner function simulation method for electron transport in cylindrical nanostructures, incorporating self-consistent Coulomb interactions and parallel processing, advancing beyond traditional 1D models.

Contribution

It introduces a lattice Wigner-Weyl code for 2D electron transport in cylindrical structures, extending previous 1D approaches with self-consistent Poisson coupling and parallel computation.

Findings

Numerical simulations show consistent results with theoretical expectations.

The method effectively models 2D electron transport in cylindrical nanostructures.

Parallel processing enables efficient computation of complex 2D problems.

Abstract

We have constructed a lattice Wigner-Weyl code that generalizes the Buot-Jensen algorithm to the calculation of electron transport in two-dimensional circular-cylindrically symmetric structures, where the Wigner function equation is solved self-consistently with the Poisson equation. Almost all of the numerical simulations to date have dealt with the restriction of the problem to one dimensional transport. In real devices, electrons are not confined to a single dimension and the coulombic potential is fully present and felt in three dimensions. We show the derivation of the 2D equation in cylindrical coordinates as well as approximations employed in the calculation of the four-dimensional convolution integral of the Wigner function and the potential. We work under the assumption that longitudinal transport is more dominant than radial transport and employ parallel processing techniques. The total transport is calculated in two steps: (1) transport the particles in the longitudinal direction in each shell separately, then (2) each shell exchanges particles with its nearest neighbor. Most of this work is concerned with the former step: A 1D space and 2D momentum transport problem. Time evolution simulations based on these method are presented for three different cases. Each case lead to numerical results consistent with expectations. Discussions of future improvements are discussed.