Derivation of 12- and 14-band $\text{k}\cdot \text{p}$ Hamiltonians for dilute bismide and bismide-nitride semiconductors

Abstract

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

Accepted for publication in Semiconductor Science and Technology

References in corpus (3)

• Band engineering in dilute nitride and bismide semiconductor lasers
• Impact of alloy disorder on the band structure of compressively strained GaBiAs
• 12-band $\text{k}\cdot \text{p}$ model for dilute bismide alloys of (In)GaAs derived from supercell calculations

Cited by in corpus (11)

• Impact of alloy disorder on the band structure of compressively strained GaBiAs
• 12-band $\text{k}\cdot \text{p}$ model for dilute bismide alloys of (In)GaAs derived from supercell calculations
• Investigation of the anisotropic electron g factor as a probe of the electronic structure of GaBi${}_x$As${}_{1-x}$/GaAs epilayers
• Impact of disorder on the optoelectronic properties of GaN${}_y$As${}_{1-x-y}$Bi${}_x$ alloys and heterostructures
• Electronic bandstructure and optical gain of lattice matched III-V dilute nitride bismide quantum wells for 1.55 $\mu$m optical communication systems
• Theory and design of In${}_x$Ga${}_{1-x}$As${}_{1-y}$Bi${}_y$ mid-infrared semiconductor lasers: type-I quantum wells for emission beyond 3 $\mu$m on InP substrates
• Large-scale atomistic simulations demonstrate dominant alloy disorder effects in GaBi${}_x$As${}_{1-x}$/GaAs multiple quantum wells
• An ab initio based approach to optical properties of semiconductor heterostructures
• Towards low-loss telecom-wavelength photonic devices by designing GaBi${}_x$As${}_{1-x}$/GaAs core$-$shell nanowires
• Tunable band-gap and isotropic light absorption from bismuth-containing GaAs core$-$shell and multi$-$shell nanowires
• Influence of Bi Alloying on GaAs Valence Band Structure