Effects of band nonparabolicity on two-dimensional electron gas

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Abstract
Energy band nonparabolicity is present in the majority of materials used in heterojunctions, quantum wells, and superlattices. In the present work we derive a simplified dispersion relation for electrons using the k⋅p model. We demonstrate that this dispersion relation can account for nonparabolicity in both narrow and wide gap isotropic semiconductors. We then calculate the carrier effective mass and densities of states for both two‐ and three‐dimensional electron systems. Finally, we derive a simple analytical relation between the carrier concentration and the Fermi energy in a nonparabolic two‐dimensional electron gas. Agreement with a numerical model is demonstrated, while the traditional, parabolic approximation results in a large error. The simplicity of the new approximation allows an intuitive understanding of the nonparabolicity effect in two‐dimensional systems. Therefore, the new approach should be useful for design, characterization, and modeling of quantum semiconductor devices with nonparabolic energy bands.