This article is cited in 9 papers

Semiconductor structures, low-dimensional systems, quantum phenomena

Effective Hamiltonians for heterostructures based on direct-gap III–V semiconductors. The $kp$ perturbation theory and the method of invariants

G. F. Glinskii, M. S. Mironova

Saint Petersburg Electrotechnical University "LETI"

Abstract: A sequential procedure for obtaining effective $kp$ Hamiltonians for arbitrary heterostructures based on direct-gap semiconductors with identical lattice parameters is suggested. The heterostructure potential is described with the help of characteristic functions $f_l(\mathbf a)$, which indicate atom substitution in sublattice $l$ of the reference crystal in unit cell $\mathbf a$. The $kp$ perturbation theory for heterostructures, which takes into account the scattering effects of charge carriers on the additional local potential that emerges due to atom substitution, is developed. A method of constructing the corresponding effective $kp$ Hamiltonians by the method of invariants, which takes into account the microscopic symmetry of interfaces, is suggested. Along with the band parameters, the obtained Hamiltonians contain additional parameters, which have no analogs in bulk materials. The derivation of the effective Hamiltonians of bands $\Gamma_1$, $\Gamma_6$, $\Gamma_{15}$, and $\Gamma_8$ in heterostructures based on cubic III–V semiconductors with atom substitution in one sublattice is given as an example.

Received: 17.07.2013
Accepted: 10.04.2014

 English version: Semiconductors, 2014, 48:10, 1324–1334

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