Fourier transform-based k·p method: An approach to meshless modeling of low-dimensional heterostructures

Abstract

Among methods modeling electronic structures of low dimensional heterostructures, such as first principles, tight binding, k·p, etc., the multiband k·p method is the most effective for low dimensional systems with a big compilation of atoms such as quantum dots. Numerical implementation like the finite difference method and the finite element method engages differential or integral process and thus requires a 3D-space mesh. In our developed Fourier transform-based k·p method (FTM), both Hamiltonian matrix and envelope functions are formulated in Fourier domain. The analytical Fourier transform of the 3D shape function of the object can be adopted such that meshing 3D space is avoidable in retrieving eigen solutions of k·p equations. Both the kinetic part and the strain have been incorporated in the Hamiltonian equation. The FTM demonstrates advantage on controlling spurious solutions due to its inborn cut-off process, whereas incorporation of Burt-Foreman operator ordering further enhances the merit.