Modeling a nanowire superlattice using the finite difference method in cylindrical polar coordinates

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.