Generalization of the effective mass method for semiconductor structures with atomically sharp heterojunctions

Abstract

The Kohn-Luttinger envelope-function method is generalized to the case of heterostructures with atomically sharp heterojunctions based on lattice-matched layers of related semiconductors with zinc-blende symmetry. For electron states near the Γ point in (001) heterostructures the single-band effective-mass equation is derived, taking into account both the spatial dependence of the effective mass and effects associated with the atomically sharp heterojunctions. A small parameter is identified, in powers of which it is possible to classify the various contributions to this equation. For hole states only the main contributions to the effective Hamiltonian, due to the sharpness of the heterojunctions, are taken into account. An expression is derived for the parameter governing mixing of states of heavy and light holes at the center of the 2D Brillouin zone.

Strong photoluminescence caused by optical transitions between electron and hole Tamm-like interface states in ZnSe/BeTe heterostructures

“…According to ref. 17, the effect of boundary conditions associated with a sharp heterointerface can be included by adding to the Hamiltonian a point potential of the kind…”

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

“…However, if the effects caused by electron and hole scattering at the rapidly varying part of the interfacial potential are of main interest, we can neglect the corrections stipu lated by the nonparabolicity of the variance law [23][24][25]. The theory developed in [13][14][15]18] leads to the emergence of additional parameters in the effective Hamiltonian of the structure, which depend on the heterointerface properties. The presence of such parameters, which are lacking in bulk materials, is also shown in the context of the symmetry analysis in [16].…”

“…It is mentioned in [18] that the effective Hamilto nian for heterostructures grown in direction [001], along with corrections following from kp perturbation theory, contains additional summands, proportional to various degrees of (k z -), which is caused by the abrupt character of the heterojunction. The presence of such summands distinguishes the Hamiltonian found in [18] from those found in [10,11] for hetero structures with a smooth potential.…”

“…An impor tant result of the theory presented in [13][14][15]18] is estimation of the interfacial and kp corrections to the effective mass equation. It is shown that corrections conditioned by the coordinate dependence of the band parameters have the same order of smallness as kp corrections of the form (kp) 4 associated with the nonparabolicity of dispersion law.…”

“…Detailed analysis of the effective Hamiltonians for heterostructures in one or another form is performed in studies [2,[9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27]. In [12], the wave function of the heterostructure is sought in the form of expansion over the Bloch wave functions of the reference crystal.…”