Derivation of 12- and 14-bandk·pHamiltonians for dilute bismide and bismide-nitride semiconductors

Abstract

Using an sp 3 s * 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 GaBixAs1−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 k · p Hamiltonian to describe the band structure of GaBixAs1−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 GaBixNyAs1−x−y we show that to a good approximation N and Bi act independently of one another in disordered GaBixNyAs1−x−y alloys, indicating that a simple description of the band structure is possible. We present a 14-band k · p Hamiltonian for ordered GaBixNyAs1−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 k · p models we present here are therefore ideally suited to the simulation of the optoelectronic properties of these novel III-V semiconductor alloys.

Novel Dilute Bismide, Epitaxy, Physical Properties and Device Application

“…Structural and electronic properties of InPBi alloys have been systematically investigated by Lu et al [73] using the first-principle calculations. The alloys with seven different configurations are considered and the formation energy is studied to investigate the relative stability.…”

Highly mismatched III–V semiconductor alloys applied in multiple quantum well photovoltaics

“…In additional, the interaction between the subsititutional N and Bi atoms in the supercells is smaller than 1 eV [1], which means that the effects of N-and Bi-related impurity states on the electronic structure are decoupled. Therefore, the N-and B-related BAC interactions in the band structure of host matrix can be treated separately.…”

“…The band structures of these high mismatched alloys can be explained in terms of the Band Anti-Crossing (BAC) model [1] which was developed to describe the pressure and composition dependent bandgap behaviour of the HMAs. The band gap bowing in dilute nitride alloys has been well explained by a two-level BAC model.…”

GaAs-based dilute bismide semiconductor lasers: Theory vs. experiment

“…Our theoretical description of the GaBi x As 1−x band structure is based upon a 12-band k·p Hamiltonian, which we have derived directly using atomistic supercell calculations [6]. This extended basis Hamiltonian directly incorporates Bi composition dependent interactions between the valence band edge states of the GaAs host matrix, and localised Bi-related impurity states.…”

“…This extended basis Hamiltonian directly incorporates Bi composition dependent interactions between the valence band edge states of the GaAs host matrix, and localised Bi-related impurity states. This model has been parametrised directly on the basis of ordered alloy supercell calculations [6], and we have more recently refined and constrained the Bi-related band structure parameters by comparing the band offsets and transition energies calculated using the 12-band model to the results of polarisation-resolved photovoltage measurements on a series of GaBi x As 1−x /(Al)GaAs QW laser structures [7].…”