The electron Lande g factor ($g^{*}$) is investigated both experimentally and theoretically in a series of GaBi$_{x}$As$_{1-x}$/GaAs strained epitaxial layers, for bismuth compositions up to $x = 3.8$%. We measure $g^{*}$ via time-resolved photolumin
escence spectroscopy, which we use to analyze the spin quantum beats in the polarization of the photoluminescence in the presence of an externally applied magnetic field. The experimental measurements are compared directly to atomistic tight-binding calculations on large supercells, which allows us to explicitly account for alloy disorder effects. We demonstrate that the magnitude of $g^{*}$ increases strongly with increasing Bi composition $x$ and, based on the agreement between the theoretical calculations and experimental measurements, elucidate the underlying causes of the observed variation of $g^{*}$. By performing measurements in which the orientation of the applied magnetic field is changed, we further demonstrate that $g^{*}$ is strongly anisotropic. We quantify the observed variation of $g^{*}$ with $x$, and its anisotropy, in terms of a combination of epitaxial strain and Bi-induced hybridization of valence states due to alloy disorder, which strongly perturbs the electronic structure.
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 GaBi$_{x}$As$_{1-x}$ can be described in terms of a band-anti
crossing 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 $textbf{k}cdottextbf{p}$ 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 $textbf{k}cdottextbf{p}$ 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 $textbf{k}cdottextbf{p}$ models we present here are therefore ideally suited to the simulation of the optoelectronic properties of these novel III-V semiconductor alloys.
Incorporation of bismuth (Bi) in dilute quantities in (In)GaAs has been shown to lead to unique electronic properties that can in principle be exploited for the design of high efficiency telecomm lasers. This motivates the development of simple model
s of the electronic structure of these dilute bismide alloys, which can be used to evaluate their potential as a candidate material system for optical applications. Here, we begin by using detailed calculations based on an $sp^{3}s^{*}$ tight-binding model of (In)GaBi$_{x}$As$_{1-x}$ to verify the presence of a valence band-anticrossing interaction in these alloys. Based on the tight-binding model the derivation of a 12-band $textbf{k}cdottextbf{p}$ Hamiltonian for dilute bismide alloys is outlined. We show that the band structure obtained from the 12-band model is in excellent agreement with full tight-binding supercell calculations. Finally, we apply the 12-band model to In$_{0.53}$Ga$_{0.47}$Bi$_{x}$As$_{1-x}$ and compare the calculated variation of the band gap and spin-orbit-splitting to a variety of spectroscopic measurements performed on a series of MBE-grown In$_{0.53}$Ga$_{0.47}$Bi$_{x}$As$_{1-x}$/InP layers.
The incorporation of bismuth (Bi) in GaAs results in a large reduction of the band gap energy (E$_g$) accompanied with a large increase in the spin-orbit splitting energy ($bigtriangleup_{SO}$), leading to the condition that $bigtriangleup_{SO} > E_g
$ which is anticipated to reduce so-called CHSH Auger recombination losses whereby the energy and momentum of a recombining electron-hole pair is given to a second hole which is excited into the spin-orbit band. We theoretically investigate the electronic structure of experimentally grown GaBi$_x$As$_{1-x}$ samples on (100) GaAs substrates by directly comparing our data with room temperature photo-modulated reflectance (PR) measurements. Our atomistic theoretical calculations, in agreement with the PR measurements, confirm that E$_g$ is equal to $bigtriangleup_{SO}$ for $textit{x} approx$ 9$%$. We then theoretically probe the inhomogeneous broadening of the interband transition energies as a function of the alloy disorder. The broadening associated with spin-split-off transitions arises from conventional alloy effects, while the behaviour of the heavy-hole transitions can be well described using a valence band-anticrossing model. We show that for the samples containing 8.5% and 10.4% Bi the difficulty in identifying a clear light-hole-related transition energy from the measured PR data is due to the significant broadening of the host matrix light-hole states as a result of the presence of a large number of Bi resonant states in the same energy range and disorder in the alloy. We further provide quantitative estimates of the impact of supercell size and the assumed random distribution of Bi atoms on the interband transition energies in GaBi$_{x}$As$_{1-x}$. Our calculations support a type-I band alignment at the GaBi$_x$As$_{1-x}$/GaAs interface, consistent with recent experimental findings.
