Band-offset ratio dependence on the effective-mass Hamiltonian based on a modified profile of the GaAs-AlxGa1xAs quantum well

Tsung L. Li and Kelin J. Kuhn
Phys. Rev. B 47, 12760 – Published 15 May 1993
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Abstract

This paper suggests a simple permutation scheme to construct the Hermitian Hamiltonian utilized in the effective-mass equation, introduces a smoothed profile to more accurately model heterojunctions, and illustrates the dependence of the band-offset ratio of a GaAs-AlxGa1xAs quantum well on the particular Hermitian Hamiltonian used in the calculation. The permutation scheme produces the BenDaniel and Duke Hamiltonian, the Bastard Hamiltonian, the Zhu and Kroemer Hamiltonian, and a Hamiltonian termed the redistributed Hamiltonian in this paper. The heterojunction is modeled by an error function rather than a step function to more accurately model the material transition region at the interface between the two materials. The 11 heavy-hole (HH) transition energy obtained by BenDaniel and Duke Hamiltonian with a particular band-offset ratio is reproduced by utilizing non-BenDaniel and Duke Hamiltonians with appropriate band-offset ratios. This process is repeated for BenDaniel and Duke Hamiltonian band-offset ratios varying from 0.5 to 0.8, and then proceeds to 11 light-hole (LH), 22 HH, and 22 LH transitions. It is found that the Hamiltonian dependence of the band-offset ratio is significant.

  • Received 3 December 1992

DOI:https://doi.org/10.1103/PhysRevB.47.12760

©1993 American Physical Society

Authors & Affiliations

Tsung L. Li and Kelin J. Kuhn

  • Department of Electrical Engineering, FT-10, University of Washington, Seattle, Washington 98195

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Vol. 47, Iss. 19 — 15 May 1993

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