Modeling a Nanowire Superlattice Using the Finite Difference Method in Cylindrical Polar Coordinates

Galeriu, C., Lew Yan Voon, L.C., Melnik, R.V.N. and Willatzen, M.

Computer Physics Communications,  157(2), 147--159, 2004


A new procedure for handling periodic boundary conditions within the finite difference method and in cylindrical polar coordinates is presented and applied to modeling a nanowire superlattice. The method is compared for accuracy and efficiency with two other formulations of the same problem: the finite difference method applied to a finite number of unit cells, and the exact solution of the equivalent Kronig-Penney model. The technique is then shown to reproduce a novel physical state, and is applied to an embedded nanowire for which there are no analytical solutions.