arXiv subjects

Christopher A. Broderick

Publications and source records attributed to Christopher A. Broderick.

At least 19 recordsLinked to original sources

arXiv2024

First-principles theory of direct-gap optical emission in hexagonal Ge and its enhancement via strain engineering

The emergence of hexagonal Ge (2H-Ge) as a candidate direct-gap group-IV semiconductor for Si photonics mandates rigorous understanding of its optoelectronic properties. Theoretical predictions of a "pseudo-direct" band gap, characterized by weak oscillator strength, contrast with a claimed high radiative recombination coefficient $B$ comparable to conventional (cubic) InAs. We compute $B$ in 2H-Ge from first principles and quantify its dependence on temperature, carrier density and strain. For unstrained 2H-Ge, our calculated spontaneous emission spectra corroborate that measured photoluminescence corresponds to direct-gap emission, but with $B$ being approximately three orders of magnitude lower than in InAs. We confirm a pseudo-direct- to direct-gap transition under $\sim 2$\% [0001] uniaxial tension, which can enhance $B$ by up to three orders of magnitude, making it comparable to that of InAs. Beyond quantifying strong enhancement of $B$ via strain engineering, our analysis suggests the dominance of additional, as-yet unquantified recombination mechanisms in this nascent material.

cond-mat.mtrl-sci↗

arXiv2023

Theory and optimisation of radiative recombination in broken-gap InAs/GaSb superlattices

We present a theoretical analysis of mid-infrared radiative recombination in InAs/GaSb superlattices (SLs). We employ a semi-analytical plane wave expansion method in conjunction with an 8-band $\mathbf{k} \cdot \mathbf{p}$ Hamiltonian to compute the SL electronic structure, paying careful attention to the identification and mitigation of spurious solutions. The calculated SL eigenstates are used directly to compute spontaneous emission spectra and the radiative recombination coefficient $B$. We elucidate the origin of the relatively large $B$ coefficients in InAs/GaSb SLs which, despite the presence of spatially indirect (type-II-like) carrier confinement, are close to that of bulk InAs and compare favourably to those calculated for mid-infrared type-I pseudomorphic and metamorphic quantum well structures having comparable emission wavelengths. Our analysis explicitly quantifies the roles played by carrier localisation (specifically, partial delocalisation of bound electron states) and miniband formation (specifically, miniband occupation and optical selection rules) in determining the magnitude of $B$ and its temperature dependence. We perform a high-throughput optimisation of the room temperature $B$ coefficient in InAs/GaSb SLs across the 3.5 -- 7 $μ$m wavelength range, quantifying the dependence of $B$ on the relative thickness of the electron-confining InAs and hole-confining GaSb layers. This analysis provides guidance for the growth of optimised SLs for mid-infrared light emitters. Our results, combined with the expected low non-radiative Auger recombination rates in structures having spatially indirect electron and hole confinement, corroborate recently observed high output power in prototype InAs/GaSb SL inter-band cascade light-emitting diodes.

cond-mat.mtrl-sci↗

arXiv2022

Electronic and optical properties of Si$_{x}$Ge$_{1-x-y}$Sn$_{y}$ alloys lattice-matched to Ge

We present a combined experimental and theoretical analysis of the evolution of the near-band gap electronic and optical properties of Si$_{x}$Ge$_{1-x-y}$Sn$_{y}$ alloys lattice-matched to Ge and GaAs substrates. We perform photoreflectance (PR) and photoluminescence (PL) measurements on Si$_{x}$Ge$_{1-x-y}$Sn$_{y}$ epitaxial layers grown via chemical vapour deposition, for Si (Sn) compositions up to $x =$ 9.6% ($y =$ 2.5%). Our measurements indicate the presence of an indirect fundamental band gap, with PL observed $\approx$ 200-250 meV lower in energy than the direct $E_0$ transition identified by PR measurements. The measured PL is Ge-like, suggesting that the alloy conduction band (CB) edge is primarily derived from the Ge L-point CB minimum. Interpretation of the PR and PL measurements is supported by atomistic electronic structure calculations. Effective alloy band structures calculated via density functional theory confirm the presence of an indirect fundamental band gap, and reveal the origin of the observed inhomogeneous broadening of the measured optical spectra as being alloy-induced band hybridisation occurring close in energy to the CB edge. To analyze the evolution of the band gap, semi-empirical tight-binding (TB) calculations are employed to enable calculations for large supercell sizes. TB calculations reveal that the alloy CB edge is hybridized in nature, consisting at low Si and Sn compositions of an admixture of Ge L-, $Γ$- and X-point CB edge states, and confirm that the alloy CB edge retains primarily Ge L-point CB edge character. Our experimental measurements and theoretical calculations confirm a direct transition energy close to 1 eV in magnitude for Si and Sn compositions $x =$ 6.8 - 9.6% and $y =$ 1.6 - 2.2%.

cond-mat.mtrl-sci↗

arXiv2021

Raman spectroscopy of group-IV Ge$_{1-x}$Sn$_{x}$ alloys: theory and experiment

Ge$_{1-x}$Sn$_{x}$ alloys are a promising candidate material to realise direct-gap group-IV semiconductors for applications in Si-compatible electronic and photonic devices. Here, we present a combined theoretical and experimental analysis of Raman spectroscopy in Ge$_{1-x}$Sn$_{x}$ alloys. We describe liquid-vapour-solid growth and structural characterisation of Ge$_{1-x}$Sn$_{x}$ ($x \leq 8$%) nanowires displaying high crystalline quality, and investigate the structural and vibrational properties of the nanowires using Raman spectroscopy. Our theoretical analysis is based on a fully analytic anharmonic valence force field (VFF) potential, which describes exactly - i.e. without recourse to numerical fitting - the second-order elastic constants, third-order bulk modulus, selected second- and third-order inner elastic constants and, as a consequence, the zone-centre transverse optical phonon mode frequency and its hydrostatic and axial strain dependence. We compute bulk elastic properties via density functional theory to parametrise the VFF potential for Ge$_{1-x}$Sn$_{x}$ alloys, and apply the VFF potential to explicitly compute the Raman spectra of realistic, disordered Ge$_{1-x}$Sn$_{x}$ alloy supercells. Our atomistic theoretical calculations quantitatively capture: (i) the evolution of the measured Raman spectra with Sn composition $x$, (ii) demonstrate explicitly that the presence of short-range alloy disorder can significantly impact the shift coefficients $a$ and $b$ that respectively describe the dependence of the Raman shift on Sn composition and pseudomorphic strain, (iii) elucidate the origin of the so-called "disorder activated" mode identified in previous experimental investigations, and (iv) allow for detailed atomic-scale interpretation of measured Raman spectra. Overall, our analysis provides insight relevant to the characterisation of this emerging material system.

cond-mat.mtrl-sci↗

arXiv2021

Fully analytic valence force fields for the relaxation of group-IV semiconductor alloys: elastic properties of group-IV materials calculated from first principles

Si$_{y}$Ge$_{1-x-y}$(C,Sn,Pb)$_{x}$ alloys have attracted significant attention as a route to achieve a direct-gap group-IV semiconductor. Using density functional theory (DFT) - employing local density approximation and hybrid Heyd-Scuzeria-Ernzerhof exchange-correlation functionals - we compute the lattice parameters, relaxed and inner elastic constants, and internal strain (Kleinman) parameters for elemental (diamond) group-IV materials and zinc blende IV-IV compounds. Our DFT calculations support a little-known experimental re-evaluation of the $α$-Sn elastic constants, and contradict a recent prediction of dynamic instability in selected IV-IV compounds. DFT-calculated structural and elastic properties are used in conjunction with a recently derived analytical parametrisation of a harmonic valence force field (VFF) [Phys. Rev. B 100, 094112 (2019)] to obtain a complete set of VFF potentials for Si$_{y}$Ge$_{1-x-y}$(C,Sn,Pb)$_{x}$ and Si$_{x}$Ge$_{1-x}$ alloys. The analytical parametrisation exactly reproduces the relaxed elastic constants and Kleinman parameter without recourse to numerical fitting, allowing for accurate and computationally inexpensive lattice relaxation. The accuracy of the VFF potentials is demonstrated via comparison to the results of DFT supercell relaxation for (i) ordered Si (Ge) alloy supercells containing a substitutional C, Ge (Si), Sn or Pb impurity, where comparison is also made to a model analytical VFF, and (ii) disordered Si$_{x}$Ge$_{1-x}$ alloy supercells. The VFF potentials we present enable accurate and computationally inexpensive relaxation of large-scale supercells representing bulk-like group-IV alloys or group-IV heterostructures, providing input to first principles or empirical electronic structure calculations, and enabling structural analysis and calculation of strain fields in heterostructures for device applications.

cond-mat.mtrl-sci↗

arXiv2021

Impact of band-anticrossing on band-to-band tunneling in highly-mismatched semiconductor alloys

We theoretically analyse band-to-band tunneling (BTBT) in highly-mismatched, narrow-gap dilute nitride and bismide alloys, and quantify the impact of the N- or Bi-induced perturbation of the band structure -- due to band-anticrossing (BAC) with localised impurity states -- on the electric field-dependent BTBT generation rate. For this class of semiconductors the assumptions underpinning the widely-employed Kane model of direct BTBT break down, due to the strong band edge nonparabolicity resulting from BAC interactions. Via numerical calculations based on the Wentzel-Kramers-Brillouin approximation we demonstrate that BAC leads, at fixed band gap, to reduced (increased) BTBT current at low (high) applied electric fields compared to that in a conventional InAs$_{1-x}$Sb$_{x}$ alloy. Our analysis reveals that BTBT in InN$_{x}$As$_{1-x}$ and InAs$_{1-x}$Bi$_{x}$ is governed by a field-dependent competition between the impact of N (Bi) incorporation on (i) the dispersion of the complex band linking the valence and conduction bands, which dominates at low field strengths, and (ii) the conduction (valence) band edge density of states, which dominates at high field strengths. The implications of our results for applications in avalanche photodiodes and tunneling field-effect transistors are discussed.

cond-mat.mtrl-sci↗

arXiv2020

Impact of stoichiometry and strain on Ge$_{1-x}$Sn$_{x}$ alloys from first principles calculations

We calculate the electronic structure of germanium-tin (Ge$_{1-x}$Sn$_{x}$) binary alloys for $0 \leq x \leq 1$ using density functional theory (DFT). Relaxed alloys with semiconducting or semimetallic behaviour as a function of Sn composition $x$ are identified, and the impact of epitaxial strain is included by constraining supercell lattice constants perpendicular to the [001] growth direction to the lattice constants of Ge, zinc telluride (ZnTe), or cadmium telluride (CdTe) substrates. It is found that application of 1% tensile strain reduces the Sn composition required to bring the (positive) direct band gap to zero by approximately 5% compared to a relaxed Ge$_{1-x}$Sn$_{x}$ alloy having the same gap at $Γ$. On the other hand, compressive strain has comparatively less impact on the alloy band gap at $Γ$. Using DFT calculated alloy lattice and elastic constants, the critical thickness for Ge$_{1-x}$Sn$_{x}$ thin films as a function of $x$ and substrate lattice constant is estimated, and validated against supercell DFT calculations. The analysis correctly predicts the Sn composition range at which it becomes energetically favourable for Ge$_{1-x}$Sn$_{x}$/Ge to become amorphous. The influence of stoichiometry and strain is examined in relation to reducing the magnitude of the inverted (``negative'') $Γ_{7}^{-}$-$Γ_{8}^{+}$ band gap, which is characteristic of semimetallic alloy electronic structure. Based on our findings, strategies for engineering the semimetal-to-semiconductor transition via strain and quantum confinement in Ge$_{1-x}$Sn$_{x}$ nanostructures are proposed.

cond-mat.mtrl-sci↗

arXiv2020

Magneto-optical determination of the carrier lifetime in coherent Ge(1-x)Sn(x)/Ge heterostructures

We present a magneto-optical study of the carrier dynamics in compressively strained Ge(1-x)Sn(x) films having Sn compositions up to 10% epitaxially grown on blanket Ge on Si (001) virtual substrates. We leverage the Hanle effect under steady-state excitation to study the spin-dependent optical transitions in presence of an external magnetic field. This allowed us to obtain direct access to the dynamics of the optically-induced carrier population. Our approach singled out that at cryogenic temperatures the effective lifetime of the photogenerated carriers in coherent Ge(1-x)Sn(x) occurs in the sub-ns time scale. Supported by a model estimate of the radiative lifetime, our measurements indicate that carrier recombination is dominated by non-radiative processes. Our results thus provide central information to advance the fundamental understanding of carrier kinetics in this novel direct-gap group-IV material system. Such knowledge can be a stepping stone in the quest for the implementation of Ge(1-x)Sn(x)-based functional devices.

physics.optics↗

arXiv2020

Electronic properties of type-II GaAs$_{1-x}$Sb$_{x}$/GaAs quantum rings for applications in intermediate-band solar cells

We present a theoretical analysis of the electronic properties of type-II GaAs$_{1-x}$Sb$_{x}$/GaAs quantum rings (QRs), from the perspective of applications in intermediate band solar cells (IBSCs). We outline the analytical solution of Schrödinger's equation for a cylindrical QR of infinite potential depth, and describe the evolution of the QR ground state with QR morphology. Having used this analytical model to elucidate general aspects of the electronic properties of QRs, we undertake multi-band $\textbf{k} \cdot \textbf{p}$ calculations -- including strain and piezoelectric effects -- for realistic GaAs$_{1-x}$Sb$_{x}$/GaAs QRs. Our $\textbf{k} \cdot \textbf{p}$ calculations confirm that the large type-II band offsets in GaAs$_{1-x}$Sb$_{x}$/GaAs QRs provide strong confinement of holes, and further indicate the presence of resonant (quasi-bound) electron states which localise in the centre of the QR. From the perspective of IBSC design the calculated electronic properties demonstrate several benefits, including (i) large hole ionisation energies, mitigating thermionic emission from the intermediate band, and (ii) electron-hole spatial overlaps exceeding those in conventional GaAs$_{1-x}$Sb$_{x}$/GaAs QDs, with the potential to engineer these overlaps via the QR morphology so as to manage the trade-off between optical absorption and radiative recombination. Overall, our analysis highlights the flexibility offered by the QR geometry from the perspective of band structure engineering, and identifies specific combinations of QR alloy composition and morphology which offer optimised sub-band gap energies for QR-based IBSCs.

cond-mat.mtrl-sci↗

arXiv2019

Electronic structure evolution in dilute carbide Ge$_{1-x}$C$_{x}$ alloys and implications for device applications

We present a theoretical analysis of electronic structure evolution in the highly-mismatched dilute carbide group-IV alloy Ge$_{1-x}$C$_{x}$. For ordered alloy supercells, we demonstrate that C incorporation strongly perturbs the conduction band (CB) structure by driving hybridisation of $A_{1}$-symmetric linear combinations of Ge states lying close in energy to the CB edge. This leads, in the ultra-dilute limit, to the alloy CB edge being formed primarily of an $A_{1}$-symmetric linear combination of the L-point CB edge states of the Ge host matrix semiconductor. Our calculations describe the emergence of a "quasi-direct" alloy band gap, which retains a significant admixture of indirect Ge L-point CB edge character. We then analyse the evolution of the electronic structure of realistic (large, disordered) Ge$_{1-x}$C$_{x}$ alloy supercells for C compositions up to $x = 2$%. We show that short-range alloy disorder introduces a distribution of localised states at energies below the Ge CB edge, with these states acquiring minimal direct ($Γ$) character. Our calculations demonstrate strong intrinsic inhomogeneous energy broadening of the CB edge Bloch character, driven by hybridisation between Ge host matrix and C-related localised states. The trends identified by our calculations are markedly different to those expected based on a recently proposed interpretation of the CB structure based on the band anti-crossing model. The implications of our findings for device applications are discussed.

cond-mat.mtrl-sci↗

arXiv2019

First principles analysis of electronic structure evolution and the indirect- to direct-gap transition in Ge$_{1-x}$Pb$_{x}$ group-IV alloys

We present a theoretical analysis of electronic structure evolution in the group-IV alloy Ge$_{1-x}$Pb$_{x}$ based on density functional theory. For ordered alloy supercells we demonstrate the emergence of a singlet conduction band (CB) edge state, suggesting the emergence of a direct band gap for Pb compositions as low as $x \approx 1$%. However, application of hydrostatic pressure reveals Pb-induced hybridisation, with the CB edge state in a Ge$_{63}$Pb$_{1}$ ($x = 1.56$%) supercell retaining primarily indirect (Ge L$_{6c}$) character. For an ordered Ge$_{15}$Pb$_{1}$ ($x = 6.25$%) supercell we find that the CB edge has acquired primarily direct (Ge $Γ_{7c}$) character, confirming the presence of an indirect- to direct-gap transition. The importance of alloy disorder is highlighted by investigating the impact on the electronic structure of the formation of a nearest-neighbour Pb-Pb pair. Having established the importance of short-range disorder, we analyse the electronic structure evolution as a function of $x$ using a series of 128-atom special quasi-random structures (SQSs). Our calculations reveal a strong reduction (increase) of the band gap (spin-orbit splitting energy), by $\approx 100$ meV ($\approx 40$ meV) per % Pb replacing Ge. We find an indirect- to direct-gap transition occurring in a narrow composition range centred about $x \approx 7$%, close to which composition we calculate that the alloy becomes semimetallic. Further analysis suggests that long-range order introduced by Born von Karman (supercell) boundary conditions leads to overestimated energy splitting of the Ge L$_{6c}$-derived CB states in the 128-atom SQSs. Accounting for these finite-size effects, we expect a direct band gap to emerge in Ge$_{1-x}$Pb$_{x}$ for $x \gtrsim 3 - 4$%.

cond-mat.mtrl-sci↗

arXiv2019

Comparison of first principles and semi-empirical models of the structural and electronic properties of Ge$_{1-x}$Sn$_{x}$ alloys

We present and compare three distinct atomistic models -- based on first principles and semi-empirical approaches -- of the structural and electronic properties of Ge$_{1-x}$Sn$_{x}$ alloys. Density functional theory calculations incorporating Heyd-Scuseria-Ernzerhof (HSE) and modified Becke-Johnson (mBJ) exchange-correlation functionals are used to perform structural relaxation and electronic structure calculations for a series of Ge$_{1-x}$Sn$_{x}$ alloy supercells. Based on HSE calculations, a semi-empirical valence force field (VFF) potential and $sp^{3}s^{\ast}$ tight-binding (TB) Hamiltonian are parametrised. Comparing the HSE, mBJ and TB models, and using the HSE results as a benchmark, we demonstrate that: (i) mBJ calculations provide an accurate first principles description of the electronic structure at reduced computational cost, (ii) the VFF potential is sufficiently accurate to circumvent the requirement to perform first principles structural relaxation, and (iii) TB calculations provide a good quantitative description of the alloy electronic structure in the vicinity of the band edges. Our results also emphasise the importance of Sn-induced band mixing in determining the nature of the conduction band structure of Ge$_{1-x}$Sn$_{x}$ alloys. The theoretical models and benchmark calculations we present inform and enable predictive, computationally efficient and scalable atomistic calculations for disordered alloys and nanostructures. This provides a suitable platform to underpin further theoretical investigations of the properties of this emerging semiconductor alloy.

cond-mat.mtrl-sci↗

arXiv2018

Optical properties of metamorphic type-I InAs$_{1-x}$Sb$_{x}$/Al$_{y}$In$_{1-y}$As quantum wells grown on GaAs for the mid-infrared spectral range

We analyse the optical properties of InAs$_{1-x}$Sb$_{x}$/Al$_{y}$In$_{1-y}$As quantum wells (QWs) grown by molecular beam epitaxy on relaxed Al$_{y}$In$_{1-y}$As metamorphic buffer layers (MBLs) using GaAs substrates. The use of Al$_{y}$In$_{1-y}$As MBLs allows for the growth of QWs having large type-I band offsets, and emission wavelengths $> 3$ $μ$m. Photoluminescence (PL) measurements for QWs having Sb compositions up to $x = 10$\% demonstrate strong room temperature emission up to 3.4 $μ$m, as well as enhancement of the PL intensity with increasing wavelength. To quantify the trends in the measured PL we calculate the QW spontaneous emission, using a theoretical model based on an 8-band $\vec{k} \cdot \vec{p}$ Hamiltonian. The theoretical calculations, which are in good agreement with experiment, identify that the observed enhancement in PL intensity with increasing wavelength is associated with the impact of compressive strain on the QW valence band structure. Our results highlight the potential of type-I InAs$_{1-x}$Sb$_{x}$/Al$_{y}$In$_{1-y}$As metamorphic QWs to address several limitations associated with existing heterostructures operating in the mid-infrared, establishing these novel heterostructures as a suitable platform for the development of mid-infrared light-emitting diodes.

cond-mat.mtrl-sci↗

arXiv2018

Impact of disorder on the optoelectronic properties of GaN$_y$As$_{1-x-y}$Bi$_x$ alloys and heterostructures

We perform a systematic theoretical analysis of the nature and importance of alloy disorder effects on the electronic and optical properties of GaN$_{y}$As$_{1-x-y}$Bi$_{x}$ alloys and quantum wells (QWs), using large-scale atomistic supercell electronic structure calculations based on the tight-binding method. Using ordered alloy supercell calculations we also derive and parametrise an extended basis 14-band \textbf{k}$\cdot$\textbf{p} Hamiltonian for GaN$_{y}$As$_{1-x-y}$Bi$_{x}$. Comparison of the results of these models highlights the role played by short-range alloy disorder -- associated with substitutional nitrogen (N) and bismuth (Bi) incorporation -- in determining the details of the electronic and optical properties. Systematic analysis of large alloy supercells reveals that the respective impact of N and Bi on the band structure remain largely independent, a robust conclusion we find to be valid even in the presence of significant alloy disorder where N and Bi atoms share common Ga nearest neighbours. Our calculations reveal that N- (Bi-) related alloy disorder strongly influences the conduction (valence) band edge states, leading in QWs to strong carrier localisation, as well as inhomogeneous broadening and modification of the conventional selection rules for optical transitions. Our analysis provides detailed insight into key properties and trends in this unusual material system, and enables quantitative evaluation of the potential of GaN$_{y}$As$_{1-x-y}$Bi$_{x}$ alloys for applications in photonic and photovoltaic devices.

cond-mat.mtrl-sci↗

arXiv2018

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 $μ$m on InP substrates

We present a theoretical analysis and optimisation of the properties and performance of mid-infrared semiconductor lasers based on the dilute bismide alloy In$_{x}$Ga$_{1-x}$As$_{1-y}$Bi$_{y}$, grown on conventional (001) InP substrates. The ability to independently vary the epitaxial strain and emission wavelength in this quaternary alloy provides significant scope for band structure engineering. Our calculations demonstrate that structures based on compressively strained In$_{x}$Ga$_{1-x}$As$_{1-y}$Bi$_{y}$ quantum wells (QWs) can readily achieve emission wavelengths in the 3 -- 5 $μ$m range, and that these QWs have large type-I band offsets. As such, these structures have the potential to overcome a number of limitations commonly associated with this application-rich but technologically challenging wavelength range. By considering structures having (i) fixed QW thickness and variable strain, and (ii) fixed strain and variable QW thickness, we quantify key trends in the properties and performance as functions of the alloy composition, structural properties, and emission wavelength, and on this basis identify routes towards the realisation of optimised devices for practical applications. Our analysis suggests that simple laser structures -- incorporating In$_{x}$Ga$_{1-x}$As$_{1-y}$Bi$_{y}$ QWs and unstrained ternary In$_{0.53}$Ga$_{0.47}$As barriers -- which are compatible with established epitaxial growth, provide a route to realising InP-based mid-infrared diode lasers.

cond-mat.mtrl-sci↗

arXiv2017

Valence band-anticrossing in GaP$_{1-x}$Bi$_{x}$ dilute bismide alloys: giant bowing of the band gap and spin-orbit splitting energy

Using spectroscopic ellipsometry measurements on GaP$_{1-x}$Bi$_{x}$/GaP epitaxial layers up to $x = 3.7$% we observe a giant bowing of the direct band gap ($E_{g}^Γ$) and valence band spin-orbit splitting energy ($Δ_{\textrm{SO}}$). $E_{g}^Γ$ ($Δ_{\textrm{SO}}$) is measured to decrease (increase) by approximately 200 meV (240 meV) with the incorporation of 1% Bi, corresponding to a greater than fourfold increase in $Δ_{\textrm{SO}}$ in going from GaP to GaP$_{0.99}$Bi$_{0.01}$. The evolution of $E_{g}^Γ$ and $Δ_{\textrm{SO}}$ with $x$ is characterised by strong, composition-dependent bowing. We demonstrate that a simple valence band-anticrossing model, parametrised directly from atomistic supercell calculations, quantitatively describes the measured evolution of $E_{g}^Γ$ and $Δ_{\textrm{SO}}$ with $x$. In contrast to the well-studied GaAs$_{1-x}$Bi$_{x}$ alloy, in GaP$_{1-x}$Bi$_{x}$ substitutional Bi creates localised impurity states lying energetically within the GaP host matrix band gap. This leads to the emergence of an optically active band of Bi-hybridised states, accounting for the overall large bowing of $E_{g}^Γ$ and $Δ_{\textrm{SO}}$ and in particular for the giant bowing observed for $x \lesssim 1$%. Our analysis provides insight into the action of Bi as an isovalent impurity, and constitutes the first detailed experimental and theoretical analysis of the GaP$_{1-x}$Bi$_{x}$ alloy band structure.

cond-mat.mtrl-sci↗

arXiv2014

Investigation of the anisotropic electron g factor as a probe of the electronic structure of GaBi$_{x}$As$_{1-x}$/GaAs epilayers

The electron Landé 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 photoluminescence 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.

cond-mat.mtrl-sci↗

arXiv2013

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

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-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 $\textbf{k}\cdot\textbf{p}$ 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 $\textbf{k}\cdot\textbf{p}$ 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 $\textbf{k}\cdot\textbf{p}$ models we present here are therefore ideally suited to the simulation of the optoelectronic properties of these novel III-V semiconductor alloys.

cond-mat.mtrl-sci↗