Discretization techniques for the efficient solution of the eigenvalue problem in heterostructures

Abstract

SUMMARYA systematic development of efficient discretization schemes for the numerical evaluation of the eigenvalues of the single-band effective mass equation that describes the motion of electrons in an ideal periodic crystal is presented. The approach presented makes use of the translational symmetry of the crystal lattice and utilizes the quantum mechanical properties of the momentum operator as the generator of spatial translation. Boundary conditions satisfied at the heterointerfaces are explicitly incorporated in the discretization procedure and the effects of this approach in overall accuracy are evaluated by studying a prototype quantum well heterostructure.