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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 $\mu$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., Comment: Published version

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.

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 $\alpha$-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.

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.

(Si)GeSn semiconductors are finally coming of age after a long gestation period. The demonstration of device quality epi-layers and quantum-engineered heterostructures has meant that tunable all-group IV Si-integrated infrared photonics is now a real possibility. Notwithstanding the recent exciting developments in (Si)GeSn materials and devices, this family of semiconductors is still facing serious limitations that need to be addressed to enable reliable and scalable applications. The main outstanding challenges include the difficulty to grow high crystalline quality layers and heterostructures at the desired Sn content and lattice strain, preserve the material integrity during growth and throughout device processing steps, and control doping and defect density. Other challenges are related to the lack of optimized device designs and predictive theoretical models to evaluate and simulate the fundamental properties and performance of (Si)GeSn layers and heterostructures. This Perspective highlights key strategies to circumvent these hurdles and bring this material system to maturity to create far-reaching new opportunities for Si-compatible infrared photodetectors, sensors, and emitters for applications in free-space communication, infrared harvesting, biological and chemical sensing, and thermal imaging.

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.

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 Schr\"{o}dinger'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.

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 ($\Gamma$) 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.

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 $\Gamma_{7c}$) 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 $x \gtrsim 3 - 4$%.

Using a valence force field model based on that introduced by Martin, we present three related methods through which we analytically determine valence force field parameters. The methods introduced allow easy derivation of valence force field parameters in terms of the Kleinman parameter $\zeta$ and bulk properties of zincblende and diamond crystals. We start with a model suited for covalent and weakly ionic materials, where the valence force field parameters are derived in terms of $\zeta$ and the bulk elastic constants $C_{11}$, $C_{12}$, and $C_{44}$. We show that this model breaks down as the material becomes more ionic and specifically when the elastic anisotropy factor $A = 2C_{44}/(C_{11}-C_{12}) > 2$. The analytic model can be stabilised for ionic materials by including Martin's electrostatic terms with effective cation and anion charges in the valence force field model. Inclusion of effective charges determined via the optical phonon mode splitting provides a stable model for all but two of the materials considered (zincblende GaN and AlN). A stable model is obtained for all materials considered by also utilising the inner elastic constant $E_{11}$ to determine the magnitude of the effective charges used in the Coulomb interaction. Test calculations show that the models describe well structural relaxation in superlattices and alloys, and reproduce key phonon band structure features.

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.

We investigate the elastic properties of selected zincblende III-V semiconductors. Using hybrid functional density functional theory we calculate the second and third order elastic constants, and first and second-order internal strain tensor components for Ga, In and Al containing III-V compounds. For many of these parameters, there are no available experimental measurements, and this work is the first to predict their values. The stricter convergence criteria for the calculation of higher order elastic constants are demonstrated, and arguments are made based on this for extracting these constants via the calculated stresses, rather than the energies, in the context of plane-wave-based calculations. The calculated elastic properties are used to determine the strain regime at which higher order elasticity becomes important by comparing the stresses predicted by a lower and a higher order elasticity theory. Finally, the results are compared with available experimental literature data and previous theory., Comment: 15 pages, 7 figures

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 $> 3$ $\mu$m. Photoluminescence (PL) measurements for QWs having Sb compositions up to $x = 10$\% demonstrate strong room temperature emission up to 3.4 $\mu$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.

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 $\mu$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., Comment: Submitted version

A three-dimensional ordered and self-organized semiconductor system emitting highly-polarized light in the yellow-orange visible range (580-650 nm) is presented, comprising self-assembled in-plane AlInP wires vertically stacked in regularly-spaced columns. More than 200 wires per column without detectable defect formation could be stacked. Theoretical simulations and temperature-dependent photoluminescence provided a benchmark to engineer multilayered structures showing internal quantum efficiency at room temperature larger than comparable quantum wells emitting at similar wavelengths. Finally, proof-of-concept light emitting diodes (LED) showed a high degree of light polarization and lower surface parasitic currents than comparable quantum well LEDs, providing an interesting perspective for high-efficiency polarized yellow-orange light emitting devices.

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., Comment: 29 pages, 11 figures

We present a detailed theoretical analysis of the electronic structure of $c$-plane InGaN/GaN quantum wells with indium contents varying between 10\% and 25\%. The electronic structure of the quantum wells is treated by means of an atomistic tight-binding model, accounting for variations in strain and built-in field due to random alloy fluctuations. Our analysis reveals strong localisation effects in the hole states. These effects are found not only in the ground states, but also the excited states. We conclude that localisation effects persist to of order 100~meV into the valence band, for as little as 10\% indium in the quantum well, giving rise to a significant density of localised states. We find, from an examination of the modulus overlap of the wave functions, that the hole states can be divided into three regimes of localisation. Our results also show that localisation effects due to random alloy fluctuations are far less pronounced for electron states. However, the combination of electrostatic built-in field, alloy fluctuations and structural inhomogeneities, such as well-width fluctuations, can nevertheless lead to significant localisation effects in the electron states, especially at higher indium contents. Overall, our results are indicative of individually localised electron and hole states, consistent with the experimentally proposed explanation of time-dependent photoluminescence results in $c$-plane InGaN/GaN QWs.

We derive first- and second-order piezoelectric coefficients for the zinc-blende III-V semiconductors, {Al,Ga,In}-{N,P,As,Sb}. The results are obtained within the Heyd-Scuseria-Ernzerhof hybrid-functional approach in the framework of density functional theory and the Berry-phase theory of electric polarization. To achieve a meaningful interpretation of the results, we build an intuitive phenomenological model based on the description of internal strain and the dynamics of the electronic charge centers. We discuss in detail first- and second-order internal strain effects, together with strain-induced changes in ionicity. This analysis reveals that the relatively large importance in the III-Vs of non-linear piezoelectric effects compared to the linear ones arises because of a delicate balance between the ionic polarization contribution due to internal strain relaxation effects, and the contribution due to the electronic charge redistribution induced by macroscopic and internal strain.

We present an atomistic description of the electronic and optical properties of $\text{In}_{0.25}\text{Ga}_{0.75}$N/GaN quantum wells. Our analysis accounts for fluctuations of well width, local alloy composition, strain and built-in field fluctuations as well as Coulomb effects. We find a strong hole and much weaker electron wave function localization in InGaN random alloy quantum wells. The presented calculations show that while the electron states are mainly localized by well-width fluctuations, the holes states are already localized by random alloy fluctuations. These localization effects affect significantly the quantum well optical properties,leading to strong inhomogeneous broadening of the lowest interband transition energy. Our results are compared with experimental literature data., Comment: 14 pages, 10 figures

The electron Land\'e 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.

Large-supercell tight-binding calculations are presented for GaBi$_{x}$As$_{1-x}$/GaAs single quantum wells (QWs) with Bi fractions $x$ of 3.125% and 12.5%. Our results highlight significant distortion of the valence band states due to the alloy disorder. A large full-width-half-maximum (FWHM) is estimated in the ground state interband transition energy ($\approx$ 33 meV) at 3.125% Bi, consistent with recent photovoltage measurements for similar Bi compositions. Additionally, the alloy disorder effects are predicted to become more pronounced as the QW width is increased. However, they are less strong at the higher Bi composition (12.5%) required for the design of temperature-stable lasers, with a calculated FWHM of $\approx$ 23.5 meV at $x$=12.5%., Comment: Accepted for publication in Applied Physics Letters

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., Comment: Accepted for publication in Semiconductor Science and Technology

We present a theory of local electric polarization in crystalline solids and apply it to study the case of wurtzite group-III nitrides. We show that a local value of the electric polarization, evaluated at the atomic sites, can be cast in terms of a summation over nearest-neighbor distances and Born effective charges. Within this model, the local polarization shows a direct relation to internal strain and can be expressed in terms of internal strain parameters. The predictions of the present theory show excellent agreement with a formal Berry phase calculation for random distortions of a test-case CuPt-like InGaN alloy and InGaN supercells with randomly placed cations. While the present level of theory is appropriate for highly ionic compounds, we show that a more complex model is needed for less ionic materials, in which the strain dependence of Born effective charges has to be taken into account. Moreover, we provide ab initio parameters for GaN, InN and AlN, including hybrid functional values for the piezoelectric coefficients and the spontaneous polarization, which we use to accurately implement the local theory expressions. In order to calculate the local polarization potential, we also present a point dipole method. This method overcomes several limitations related to discretization and resolution which arise when obtaining the local potential by solving Poisson's equation on an atomic grid. Finally, we perform tight-binding supercell calculations to assess the impact of the local polarization potential arising from alloy fluctuations on the electronic properties of InGaN alloys. In particular, we find that the large upward bowing with composition of the InGaN valence band edge is strongly influenced by local polarization effects. Furthermore, our analysis allows us to extract composition-dependent bowing parameters for the energy gap and valence and conduction band edges.

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 models 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 $\textbf{k}\cdot\textbf{p}$ 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.

We present a quantum mechanical approach to calculate broadening of plasmonic resonances in metallic nanostructures due to collisions of electrons with the surface of the structure. The approach is applicable if the characteristic size of the structure is much larger than the de Broglie electron wavelength in the metal. The approach can be used in studies of plasmonic properties of both single nanoparticles and arrays of nanoparticles., Comment: 9 pages

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.

Highly mismatched semiconductor alloys such as GaNAs and GaBiAs have several novel electronic properties, including a rapid reduction in energy gap with increasing x and also, for GaBiAs, a strong increase in spin orbit- splitting energy with increasing Bi composition. We review here the electronic structure of such alloys and their consequences for ideal lasers. We then describe the substantial progress made in the demonstration of actual GaInNAs telecomm lasers. These have characteristics comparable to conventional InP-based devices. This includes a strong Auger contribution to the threshold current. We show, however, that the large spin-orbit-splitting energy in GaBiAs and GaBiNAs could lead to the suppression of the dominant Auger recombination loss mechanism, finally opening the route to efficient temperature-stable telecomm and longer wavelength lasers with significantly reduced power consumption., Comment: 27 pages, 11 figures

The addition of dilute concentrations of bismuth (Bi) into GaAs to form GaBiAs alloys results in a large reduction of the band gap energy Eg accompanied by a significant increase of the spin-orbit-splitting energy (delta_SO), leading to an Eg < delta_SO regime for ~10% Bi composition which is technologically relevant for the design of highly efficient photonic devices. The quaternary alloy GaBiNAs offers further flexibility for band gap tuning, because both nitrogen and bismuth can independently induce band gap reduction. This work reports sp3s* tight binding and 14-band k.p models for the study of the electronic structure of GaBiAs and GaBiNAs alloys. Our results are in good agreement with the available experimental data., Comment: 2 pages, 1 figure

III-V growth and surface conditions strongly influence the physical structure and resulting optical properties of self-assembled quantum dots (QDs). Beyond the design of a desired active optical wavelength, the polarization response of QDs is of particular interest for optical communications and quantum information science. Previous theoretical studies based on a pure InAs QD model failed to reproduce experimentally observed polarization properties. In this work, multi-million atom simulations are performed to understand the correlation between chemical composition and polarization properties of QDs. A systematic analysis of QD structural parameters leads us to propose a two layer composition model, mimicking In segregation and In-Ga intermixing effects. This model, consistent with mostly accepted compositional findings, allows to accurately fit the experimental PL spectra. The detailed study of QD morphology parameters presented here serves as a tool for using growth dynamics to engineer the strain field inside and around the QD structures, allowing tuning of the polarization response., Comment: 8 pages, 6 figures; accepted for publication in IOP Nanotechnology journal

We develop an atomistic, nearest-neighbor sp3s* 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 anti-crossing (BAC) interaction. By extending this analysis to GaBiAs we demonstrate that the observed strong variation of the band gap Eg and spin-orbit-splitting (SO) energy 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 Eg also having a significant contribution from a conventional alloy reduction in the conduction band edge energy. Our calculated values of Eg and SO are in good agreement with experiment throughout the investigated composition range x less than 13%. In particular, our calculations reproduce the experimentally observed crossover to an Eg < SO regime at approximately 10.5% Bi composition in bulk GaBiAs. 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 GaBiAs electronic structure., Comment: 14 Pages, 13 Figures, Accepted for publication in PRB

We generalize the concept of nonlinear periodic structures to systems that show arbitrary spacetime variations of the refractive index. Nonlinear pulse propagation through these spatiotemporal photonic crystals can be described, for shallow nonstationary gratings, by coupled mode equations which are a generalization of the traditional equations used for stationary photonic crystals. Novel gap soliton solutions are found by solving a modified massive Thirring model. They represent the missing link between the gap solitons in static photonic crystals and resonance solitons found in dynamic gratings., Comment: 3 figures, submitted

Propagation, transmission and reflection properties of linearly polarized plane waves and arbitrarily short electromagnetic pulses in one-dimensional dispersionless dielectric media possessing an arbitrary space-time dependence of the refractive index are studied by using a two-component, highly symmetric version of Maxwell's equations. The use of any slow varying amplitude approximation is avoided. Transfer matrices of sharp nonstationary interfaces are calculated explicitly, together with the amplitudes of all secondary waves produced in the scattering. Time-varying multilayer structures and spatiotemporal lenses in various configurations are investigated analytically and numerically in a unified approach. Several new effects are reported, such as pulse compression, broadening and spectral manipulation of pulses by a spatiotemporal lens, and the closure of the forbidden frequency gaps with the subsequent opening of wavenumber bandgaps in a generalized Bragg reflector.