Simple calculations of confinement states in a quantum well

Abstract

A simple and unified description of conduction- and valence-band confinement states in a quantum well is developed. In particular, the lowest confinement states in GaAs/${\mathrm{Ga}}_{1\mathrm{-}\mathrm{x}}$ ${\mathrm{Al}}_{\mathrm{x}}$As (0≤x≤1) are accurately described. From a detailed comparison with a much more involved, 20-band, tight-binding description, the accuracy is estimated to be better than a few percent in the confinement energies. The description is easily numerically implemented.