Electronic miniband formation in a two-dimensional semiconductor superlattice

A system of periodically arranged uniform rods has been investigated, regarded as a twodimensional superlattice. The assumed arrangement of rods within a supercell allows one to express the two-dimensional effective potential as a sum of two terms depending only on either x or y coordinate. The structure consists of two square lattices of square rods embedded in the matrix material. Rods in one lattice act as potential barriers for electrons, and those in the other as potential wells. The separation of the effective potential is shown not to imply Hamiltonian separation in the envelope function approximation. The energy spectra of the conduction band are computed for the numerical solution as well as for the analytical one, the latter wrongly assuming the separation of the Hamiltonian. The band structures computed in the two cases differ in band position and width.