Derivation of 12- and 14-band<b>k</b>·<b>p</b>Hamiltonians for dilute bismide and bismide-nitride semiconductors

Abstract

Using an $sp^{3}s^{*}$ tight-binding model we demonstrate how the observed\nstrong bowing of the band gap and spin-orbit-splitting with increasing Bi\ncomposition in the dilute bismide alloy GaBi$_{x}$As$_{1-x}$ can be described\nin terms of a band-anticrossing interaction between the extended states of the\nGaAs valence band edge and highly localised Bi-related resonant states lying\nbelow the GaAs valence band edge. We derive a 12-band\n$\\textbf{k}\\cdot\\textbf{p}$ Hamiltonian to describe the band structure of\nGaBi$_{x}$As$_{1-x}$ and show that this model is in excellent agreement with\nfull tight-binding calculations of the band structure in the vicinity of the\nband edges, as well as with experimental measurements of the band gap and\nspin-orbit-splitting across a large composition range. Based on a tight-binding\nmodel of GaBi$_{x}$N$_{y}$As$_{1-x-y}$ we show that to a good approximation N\nand Bi act independently of one another in disordered\nGaBi$_{x}$N$_{y}$As$_{1-x-y}$ alloys, indicating that a simple description of\nthe band structure is possible. We present a 14-band\n$\\textbf{k}\\cdot\\textbf{p}$ Hamiltonian for ordered\nGaBi$_{x}$N$_{y}$As$_{1-x-y}$ crystals which reproduces accurately the\nessential features of full tight-binding calculations of the band structure in\nthe vicinity of the band edges. The $\\textbf{k}\\cdot\\textbf{p}$ models we\npresent here are therefore ideally suited to the simulation of the\noptoelectronic properties of these novel III-V semiconductor alloys.\n