A three-dimensional solver of the Schrödingerequation in momentum space for the detailed simulation ofnanostructures

Abstract

We propose a simple method for computing the single-particleeigenfunctions in nanostructures with three-dimensionalconfinement. The proposed procedure transfers the problem to the momentum space, solves an eigenvalue equation on a reduced wavevectors space and then transfers the solution back to thereal space. We show that in such a way it is possible to obtainthe eigenvectors and eigenvalues corresponding to lower energieswith significant improvement in computing time and memoryrequirements with respect to numerical methods in the coordinatespace. The method can be applied to structures with inhomogeneouseffective mass and can easily include the full band structure.We have tested the code on typical confining potentials ofnanostructures, in order to show the advantages and possiblelimitations of the proposed method.