Enhancement of nonparabolicity effects in a quantum well

The effects of conduction-band nonparabolicity on the confinement energy and energy dispersion parallel to the layers for a GaAs quantum well are investigated with the use of an expression for the bulk conduction-band dispersion expanded to fourth order in k. The anisotropy of the conduction band is included. We derive some accurate analytical expressions for the perpendicular mass, which gives the confinement energy, and the parallel mass, which is relevant for motion along the quantum well. These masses explicitly depend on the confinement energy. We find that the nonparabolicity enhancement for the parallel mass is about three times stronger than for the perpendicular mass. We finally compare with some recent experimental results.