Abstract
A numerical analysis of the hole energy spectrum and wave functions in a 2D (GaAs/AlAs) quantum wire (QWr) superlattice (SL) with arbitrary cross-section is presented. The intricate fourfold degenerate nature of valence band Г8 of the given materials is taken into account. The presented approach is based on a modified effective mass method, wherein the microscopic structure of the heterostructure and hole kp-interaction in the valence band are considered. It is shown that the solution of this problem in a k-representation is reduced to an eigenvalue problem for a matrix Hamiltonian. Superlattices of quantum wires with different cross-sections (square, circle, ellipse, and ring) are considered as an example. The influence of superlattice parameters on the hole energy spectrum is studied. Anti-crossing effects in the hole dispersion law are observed. For the hole ground and excited states, the wave function spatial distribution in the plane perpendicular to the QWr axis is also studied.
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