Effect of the nonparabolic mass on the electron confinement in arbitrarily shaped quantum wells

A numerical technique for the calculation of electron eigenstates in one-dimensional potential profiles has been improved by including the nonparabolicity of electrons and the material dependence of effective mass in heterostructures. The method is demonstrated for GaAs/${\mathrm{Al}}_{\mathit{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As quantum wells, showing its effectiveness and excellent agreement with experiment. It was found that the magnitude of the effective mass and the nonparabolicity have a significant influence on the confinement energy, especially for narrow wells.