Effect of nonparabolicity in GaAs/<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">Ga</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn><mml:mi mathvariant="normal">−</mml:mi><mml:mi mathvariant="normal">x</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">Al</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="normal">x</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math>As semiconductor quantum wells

Abstract

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 \ensuremath{\gamma}. We have performed this comparison of the models for a number of well widths for GaAs/${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$${\mathrm{Al}}_{\mathrm{x}}$As quantum-well structures using the results from an eight-band second-order k\ensuremath{\cdot}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.

Keywords

Affiliated Institutions

• Worcester Polytechnic Institute US
• Massachusetts Institute of Technology US

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