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-As 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