Effect of nonparabolicity in GaAs/Ga1−xAlxAs semiconductor quantum wells

We investigate the effect of nonparabolicity in various bands of bulk semiconductors on the electronic-subband-edge energies in quantum wells. We compare the results from different versions of the model originally proposed by Bastard. We show that their efficacy in yielding the correct quantum-well energy levels for the conduction band can be characterized in terms of two parameters, namely, the effective mass $m^{\mathrm{*}}$ and the nonparabolicity parameter γ. We have performed this comparison of the models for a number of well widths for GaAs/${\mathrm{Ga}}_{1\mathrm{-}\mathrm{x}}$ ${\mathrm{Al}}_{\mathrm{x}}$As quantum-well structures using the results from an eight-band second-order k⋅p Hamiltonian, in a transfer-matrix method derived earlier, as the benchmark. We confirm the observation made earlier that band nonparabolicity actually raises the lowest conduction-band energy level of the quantum well by a small amount while lowering the higher energy levels.