Tight-binding analysis of the electronic structure of dilute bismide alloys of GaP and GaAs

Abstract

We develop an atomistic, nearest-neighbor sp 3 s * tight-binding Hamiltonian to investigate the electronic structure of dilute bismide alloys of GaP and GaAs. Using this model, we calculate that the incorporation of dilute concentrations of Bi in GaP introduces Bi-related defect states in the band gap, which interact with the host matrix valence band edge via a Bi composition dependent band anticrossing (BAC) interaction. By extending this analysis to GaBi x As 1−x , we demonstrate that the observed strong variation of the band gap (E g ) and spin-orbit-splitting energy ( SO ) with Bi composition can be well explained in terms of a BAC interaction between the extended states of the GaAs valence band edge and highly localized Bi-related defect states lying in the valence band, with the change in E g also having a significant contribution from a conventional alloy reduction in the conduction band edge energy. Our calculated values of E g and SO are in good agreement with experiment throughout the investigated composition range (x 13%). In particular, our calculations reproduce the experimentally observed crossover to an E g < SO regime at approximately 10.5% Bi composition in bulk GaBi x As 1−x . Recent x-ray spectroscopy measurements have indicated the presence of Bi pairs and clusters even for Bi compositions as low as 2%. We include a systematic study of different Bi nearest-neighbor environments in the alloy to achieve a quantitative understanding of the effect of Bi pairing and clustering on the GaBi x As 1−x electronic structure.

Impact of alloy disorder on the band structure of compressively strained GaBixAs1−x

“…The interaction between the resonant N states and the CBE of the host GaAs matrix then accounts for the observed rapid reduction in E g . It was proposed, 14 and later confirmed theoretically 2,15 that replacing As by Bi can introduce a similar BAC effect. Like N and As, Bi is also a group-V element, which lies below Sb in the periodic table.…”

“…III E, we consider the band edge alignment in compressively strained GaBi x As 1−x /GaAs samples. The band alignment at the GaBi x As 1−x /GaAs interface remains uncertain in the literature with reports suggesting that the conduction band offset is of type-I, 2,20,21 or type-II, 14 or nearly flat. 22 Our calculations support a type-I band alignment for all the samples considered.…”

“…These pairs and clusters introduce defect levels which lie above the isolated Bi state energy, E Bi , and which also interact with the valence band states. 2 In addition, isolated Bi atoms also see an increasingly disordered local environment, leading to an inhomogeneous broadening of the associated resonant defect level energies. We investigate here the effects of these two different types of disorder on the valence band structure of GaBi x As 1−x grown pseudomorphically on GaAs, using the sp 3 s * tight-binding model introduced in Ref.…”

“…Recent sp 3 s * tight-binding calculations which we have performed confirm the existence of such a band-anticrossing interaction, with the calculated variation of E g and of SO in excellent agreement with experiment. 2 Although the BAC model provides an accurate description of some of the key features in the band structure of highly mismatched alloys, it includes several critical simplifying assumptions. It assumes for instance in GaBi x As 1−x that each Bi atom introduces resonant defect levels with constant energy E Bi , and then treats the effect on the band structure in terms of the interaction between these states and the host matrix valence band.…”

“…There is increasing interest in the highly mismatched semiconductor alloy GaBi x As 1−x , both from a fundamental perspective [1][2][3][4] and also because of its potential device applications. [5][6][7][8] When a small fraction of As is replaced by Bi in GaAs, the energy gap E g decreases rapidly, by ≈90 meV when 1% of As is replaced by Bi.…”