Derivation of the effective-mass equation for a superlattice: A perturbational approach

We derive the effective-mass equation for a superlattice structure by considering the barrier as a perturbation of the bulk material in the well. The renormalization constants as well as the momentum matrix elements are allowed to vary with space in the resulting equation. Terms additional to the usual effective-mass equation are found by using second-order perturbation. They are shown to have little effect on the subband separation and are small on the scale of the energy gap. © 1992 The American Physical Society.