Finite element method for electronic properties of semiconductor nanocrystals

Abstract

The finite element method (FEM) has been implemented in order to investigate the electronic structure of spherical quantum dots (SQDs) in an external magnetic field. The Schrödinger equation has been discretized by means of Galerkin’s weighted residue method with a nonuniform mesh of triangular elements. Unlike other approaches, the computational effort required to obtain converged results is independent of the strength of the magnetic field. Since the basis functions are given by strictly local polynomials in real space, FEM allows a controlled convergence of the solutions. The effects of the diamagnetic term on the energy levels and their reordering produced by state crossing for semiconductor metal oxide quantum dots in alkaline aqueous colloids, and CdTe SQDs embedded in a glass matrix, have been discussed. The efficiency and accuracy of FEM have been shown by its successful applications to a single SQD, two-coupled SQDs, and a hydrogenic impurity in SQDs.