Numerical simulation of two-dimensional electron transport in cylindrical nanostructures using Wigner function methods

We have constructed a lattice Wigner–Weyl code to expand the Buot–Jensen algorithm to calculation of electron transport in two-dimensional cylindrically symmetric structures. Almost all of the numerical simulations to date have dealt with the restricted problem of one-dimensional transport. In real devices, electrons are not confined to a single transport 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.