Controlling the crystal phase and lattice mismatch of semiconductors offers a powerful route to engineer electronic and optical properties of heterostructures. As a consequence, semiconductors in the wurtzite phase are increasingly sought after, superseding the thermodynamically favored cubic zinc blende phase. Empirical atomistic modeling, required for large scale simulations of heterostructures and their properties, relies heavily on valence force field (VFF) methods to find the equilibrium atomic positions in an alloy. For zinc blende crystals, VFF models are well-established. In the case of wurtzite, VFF parameters are frequently adopted without rigorous analysis, despite subtle but critical differences from the zinc blende structure. Such an approach can compromise accuracy in describing material properties, since the structural differences between zinc blende and wurtzite directly influence electronic and optical characteristics. Based on the analytical VFF model by Tanneret al(2019Phys. Rev. B100094112), and using structural similarities between wurtzite and [111]-oriented zinc blende crystals, we guide the development of a wurtzite VFF without introducing additional parameters. Our framework utilizes analytic expressions and minimization routines to project zinc blende models onto wurtzite systems. Beyond elastic tensors, we train the model to reproduce bond length asymmetries and band gaps by using output of the VFF model in density functional theory (DFT) electronic structure calculations. Applied to wurtzite III-N compounds and BN, the model accurately reproduces targeted observables but also properties it has not been trained on, including the internal parameteru. We further validate the model on highly mismatched alloys such as (B,Ga)N and (B,In,Ga)N, exhibiting good agreement between VFF and DFT results when using identical supercells in these calculations.

In this work, we report on recent results in understanding and addressing the issue of interface smearing in high-aluminum content AlGaN/AlGaN heterostructures. On the one hand, the growth of high-crystal quality AlGaN by metal-organic vapor phase epitaxy requires the use of high temperatures, but, on the other hand, this may lead to alloy intermixing between barrier and channel layers, which smoothens out the polarization contrast and severely degrades or even completely destroys the 2-dimensional electron gas (2DEG). We show that x-ray diffraction analysis can be used as a nondestructive way to assess the sharpness of the interface, and that improved growth schemes can be successfully used to achieve high-quality 2DEG, as confirmed by contactless resistivity measurements. In particular, sheet resistivities around 2500 Omega/square were demonstrated for AlN/Al0.75Ga0.25N, consistent with the best-reported values in the literature.

Non-radiative Auger-Meitner recombination processes in III-nitride based optoelectronic devices operating in the visible spectral range have received significant attention in recent years as they can present a major contribution to the efficiency drop at high temperatures and carrier densities. However, insight into these recombination processes is sparse for III-N devices operating in the ultraviolet wavelength window. In this work we target the temperature dependence of the Auger-Meitner recombination rate in (Al,Ga)N/AlN quantum wells by means of an atomistic electronic structure model that accounts for random alloy fluctuations and connected carrier localisation effects. Our calculations show that in the low temperature regime both the non-radiative Auger-Meitner and radiative recombination rate are strongly impacted by alloy disorder induced carrier localisation effects in these systems. The influence of alloy disorder on the recombination rates is reduced in the high temperature regime, especially for the radiative rate. The Auger-Meitner recombination rate, however, may still be more strongly impacted by alloy disorder when compared to the radiative rate. Our calculations show that while on average radiative recombination slightly increases with increasing temperature, the Auger-Meitner recombination process may, on average, slightly decrease in the temperature range relevant to the thermal efficiency drop (thermal droop). This finding suggests that the considered Auger-Meitner recombination process is unlikely to be directly responsible for the thermal efficiency drop observed experimentally in (Al,Ga)N/AlN quantum well based light emitting devices. Thus, different non-radiative processes, external to the active region, may be the underlying cause of thermal droop in (Al,Ga)N wells.

Aluminium Gallium Nitride ($(\text{Al}, \text{Ga}) \mathrm{N})$ is an ideal material for light emitting devices in the UV spectral range. However, these devices still suffer from low external quantum efficiencies, particularly in the deep-UV range. A contributor to the low external quantum efficiency is low light extraction efficiency (LEE), which is tightly linked to the valence band structure of (Al,Ga)N quantum wells. Theoretical studies that account for alloy disorder-induced valence band mixing effects in these structures are sparse. Here, we utilise an atomistic multiband tight-binding model to gain insight into the degree of optical polarisation in (Al,Ga)N quantum well systems. Special attention is paid to the impact of Al content, well width and carrier density in the wells.

Despite considerable advancements, high electron mobility transistors (HEMTs) based on gallium nitride (GaN) channels remain largely limited to power applications below 650 V. For higher power demands, the ultra-wide bandgap semiconductor alloy aluminum gallium nitride, (Al,Ga)N, has emerged as a key contender for next-generation HEMTs. In this simulation study, we show that Al-rich AlxGa1−xN-channel HEMTs (with x ≥ 0.5) outperform the GaN-channel counterparts at and above room temperature, across all Al compositions, x. This contrasts with recent theory reports, which suggest that only AlxGa1−xN HEMTs with high Al content (x ≥ 0.85) offer comparable performance to GaN-channel devices. Unlike previous assumptions of a constant two-dimensional electron gas (2DEG) density across the entire composition range x, we show that the 2DEG density is highly sensitive to both the Al content and thickness of the individual layers in a HEMT structure. We demonstrate that the superior performance of Al-rich (Al,Ga)N-channel HEMTs is driven by a competing effect between 2DEG density and electron mobility. This work challenges the assumptions of prior studies, which can result in a significant under or overestimation of the potential of high Al content HEMTs. The insights gained from our work provide a comprehensive understanding of the trade-offs between device and material parameters, thus helping to guide the design of future Al-rich (x = 0.5–1.0) AlxGa1−xN-channel HEMTs for high-power applications.

Aluminum gallium nitride [(Al,Ga)N] presents an ideal platform for designing ultraviolet (UV) light emitters across the entire UV spectral range. However, in the deep-UV spectral range (<280 nm) these emitters exhibit very low quantum efficiencies, which in part is linked to the light-polarization characteristics of (Al,Ga)N quantum wells (QWs). In this study, we provide insight into the degree of optical polarization of (Al,Ga)N QW systems operating across the UV-C spectral range by means of an atomistic multiband electronic structure model. Our model not only captures the difference in valence-band ordering in AlN and GaN but it also accounts for alloy-disorder-induced band-mixing effects originating from random alloy fluctuations in (Al,Ga)N QWs. The latter aspect is often not captured in widely employed continuum-based models. The impact of alloy disorder on the electronic structure is studied in terms of Urbach-tail energies, which reflect the broadening of the valence-band density of states due to carrier-localization effects. We find that especially in wider wells, Urbach-tail energies are reduced with increasing carrier densities in the well, highlighting that alloy-disorder-induced carrier-localization effects in (Al,Ga)N QWs are also tightly linked to electrostatic built-in fields. Our calculations show that for QWs designed to emit at the longer-wavelength end of the UV-C spectrum, carrier density and well width are of secondary importance for their light-emission properties, meaning that one observes mainly transverse electrical polarization. However, for (Al,Ga)N QWs with high Al contents, we find that both well width and carrier density will impact the degree of optical polarization. Our calculations suggest that wider wells will increase the degree of optical polarization and may therefore be an option to improve the light-extraction efficiency in deep-UV light emitters.

UV emitters based on the semiconductor alloy aluminium gallium nitride, (Al,Ga)N, have attracted significant interest in recent years due to their potential for optoelectronic devices. To guide the design of such devices with improved efficiencies, theoretical frameworks based on so-called k.p methods have found widespread application in the literature. Given that k.p models are empirical in nature, parameters such as effective masses or crystal field splitting energies of (Al,Ga)N alloys have to be provided as input from first-principles calculations or experiment. Although these parameters are available for GaN and AlN, detailed information on their composition dependence is sparse. Here, we address this question and provide (Al,Ga)N band parameters for widely used k.p Hamiltonians. We start from density functional theory (DFT) to sample the electronic structure of (Al,Ga)N alloys over the full composition range. The k.p parameters are treated as free parameters to reproduce the DFT data. For GaN and AlN the parameters extracted here agree well with literature values. When turning to the composition dependence of the k.p parameters, our calculations show that most parameters deviate significantly from a linear interpolation of the GaN and AlN values, an approximation widely made in the literature. Moreover, to describe changes in the band parameters with Al content, composition dependent bowing parameters have to be considered for an accurate description of the DFT data. Finally, our analysis also provides initial insight into consequences of the nonlinear composition dependence of the k.p parameters for the electronic structure of (Al,Ga)N alloys. We find that in particular the band ordering is affected by the nonlinear evolution of the crystal field splitting energy with composition, an important aspect for the light polarization characteristics of high Al content (Al,Ga)N alloys.

Aluminium gallium nitride (Al,Ga)N alloys and heterostructures are used in the development of UV light emitting devices, and can emit at energies extending into the UV-C spectral range. In the UV-C wavelength window and thus at high AlN content, devices exhibit poor quantum efficiencies. In order to aid the development of these devices, simulation techniques which capture the essential physics of these materials and heterostructures should be used. Due to a change in band ordering in a quantum well at compositions close to Al _0.75 Ga _0.25 N, special attention should be given to the treatment of valence band states in device simulation. In this work we develop a hybrid single band effective mass model which is informed by degree of optical polarization data obtained from atomistic multi-band calculations. Overall, the hybrid single band effective mass model is benchmarked against tight-binding electronic structure calculations. To do so a confining energy landscape is extracted from the tight-binding model and used as input for the single band effective mass calculations. Moreover, the extracted tight-binding energy landscape is transferred to a drift-diffusion model, allowing therefore for a multi-scale study of transport properties of a single (Al,Ga)N quantum well embedded in a p-i-n junction. Our results show that wider wells lead to a lower turn-on voltage due to a reduction of the band gap, but the internal quantum efficiency of these wells is lower than in narrower wells. Alloy disorder leads to carrier localization and an uneven distribution of recombination within the quantum well plane, which gives rise to percolation currents. A comparison of results with ‘pure’ band simulations shows that when TE emission dominated, the heavy hole mass is a good approximation. In contrast, where band mixing was strong between heavy hole and split-off bands the mass from the split off band was very effective.

Aluminium gallium nitride alloys are used for developing light emitting diodes operating in the UV part of the electromagnetic spectrum. These devices suffer from a low efficiency. To gain insight to this question we develop a 3-D modified drift-diffusion model which takes into account both alloy disorder effects and valence band mixing, and investigate the device efficiency. Results show that the current injection efficiency is strongly influenced by the chosen doping profile.

UV emitters based on the semiconductor alloy aluminium gallium nitride, (Al,Ga)N, have attracted significant interest in recent years due to their potential for optoelectronic devices. To guide the design of such devices with improved efficiencies, theoretical frameworks based on so-called k.p methods have found widespread application in the literature. Given that k.p models are empirical in nature, parameters such as effective masses or crystal field splitting energies of (Al,Ga)N alloys have to be provided as input from first-principles calculations or experiment. Although these parameters are available for GaN and AlN, detailed information on their composition dependence is sparse. Here, we address this question and provide (Al,Ga)N band parameters for widely used k.p Hamiltonians. We start from density functional theory (DFT) to sample the electronic structure of (Al,Ga)N alloys over the full composition range. The k.p parameters are treated as free parameters to reproduce the DFT data. For GaN and AlN the parameters extracted here agree well with literature values. When turning to the composition dependence of the k.p parameters, our calculations show that most parameters deviate significantly from a linear interpolation of the GaN and AlN values, an approximation widely made in the literature. Moreover, to describe changes in the band parameters with Al content, composition dependent bowing parameters have to be considered for an accurate description of the DFT data. Finally, our analysis also provides initial insight into consequences of the nonlinear composition dependence of the k.p parameters for the electronic structure of (Al,Ga)N alloys. We find that in particular the band ordering is affected by the nonlinear evolution of the crystal field splitting energy with composition, an important aspect for the light polarization characteristics of high Al content (Al,Ga)N alloys.

Deep UV (Al,Ga)N-based light emitters exhibit very low quantum efficiencies when compared to UV emitters at longer wavelengths. To improve the efficiencies of e.g. (Al,Ga)N-based light emitting diodes, theory and simulation can help to guide the device design. The theoretical framework underlying device simulations is often based on drift-diffusion models coupled with a self-consistent Schrodinger-Poisson equation solver. To achieve accurate and predictive models, understanding the composition dependence of material input parameters is of central importance. We target the composition dependence of k center dot p parameters in AlxGa(1-x)N alloys by using density functional theory (DFT) to obtain effective band structures from alloy disordered supercells. Building on these effective band structures, a numerically efficient fitting scheme based on the Sobol-sequence method is employed to extract effective electron masses, m(e)(x), Luttinger-like parameters A(i)(x), with i = 1 ... 6, and crystal field splitting energy, Delta(CF), as a function of Al content, x, in the system. Our calculations reveal that for m(e)(x) a linear interpolation of the GaN and AlN values provides a good description of the DFT data. However, for A(i)(x) and Delta(CF)(x) this simple approximation breaks down and we find that composition dependent bowing parameters are required to describe effective DFT band structures accurately.

Understanding Auger recombination in (In,Ga)N-based quantum wells is of central importance to unravelling the experimentally observed efficiency 'droop' in modern (In,Ga)N light emitting diodes (LEDs). While there have been conflicting results in the literature about the importance of non-radiative Auger recombination processes for the droop phenomenon, it has been discussed that alloy fluctuations strongly enhance the Auger rate. However, these studies were often focused on bulk systems, not quantum wells, which lie at the heart of (In,Ga)N-based LEDs. In this study, we present an atomistic analysis of the carrier density dependence of the Auger recombination coefficients in (In,Ga)N/GaN quantum wells. The model accounts for random alloy fluctuations, the connected carrier localisation effects, and carrier density dependent screening of the built-in polarisation fields. Our studies reveal that at low temperatures and low carrier densities the calculated Auger coefficients are strongly dependent on the alloy microstructure. However, at elevated temperatures and carrier densities, where the localised states are starting to be saturated, the different alloy configurations studied give (very) similar Auger coefficients. We find that over the range of carrier densities investigated, the contribution of the electron-electron-hole related Auger process is of secondary importance compared to the hole-hole-electron process. Overall, for higher temperatures and carrier densities, our calculated total Auger coefficients are in excess of 10(-31) cm(6) s(-1) and may reach 10(-30) cm(6) s(-1), which, based on current understanding in the literature, is sufficient to result in a significant efficiency droop. Thus, our results are indicative of Auger recombination being an important contributor to the efficiency droop in (In,Ga)N-based light emitters even without defect-assisted processes.

The electronic structure of highly mismatched semiconductor alloys is characterized by carrier localization and strongly influenced by the local alloy microstructure. First-principles calculations can deliver valuable quantitative insight, but their associated computational expense limits alloy supercell size and imposes artificial long-range ordering, which can produce misleading results. The empirical tight-binding method (ETBM) provides a transparent approach to investigate large-scale supercells on an atomistic level, to quantitatively predict the electronic structure of semiconductor alloys. Here, we overview key aspects and considerations for establishing ETBMs. Additionally, we discuss and highlight, given that the ETBM matrix elements are described in the language of overlaps between localized atomic orbitals, that ETBMs have proven highly successful in analyzing the impact of localized and resonant impurity states, as well as disorder, on the optoelectronic properties of highly mismatched alloys. The ETBM continues to provide valuable insight for emerging material systems, including two-dimensional materials, perovskites and their heterostructures, and provides a framework to address technologically relevant questions including the importance of short-range disorder for loss mechanisms such as non-radiative Auger–Meitner recombination. Moreover, the ETBM furnishes a quantitative basis for continuum models such as k⋅p or localization landscape theories, allowing to explicitly incorporate disorder effects in nanostructures to underpin predictive device-level analysis.

Semiconductor alloys are at the heart of many optoelectronic devices. Among these alloys there are many prominent materials in which the virtual crystal approximation breaks down, including both highly-mismatched alloys such as GaAs1−xNx, and also the III-N alloys, (Al,Ga, In)N, where the difference in energy gap between InN and AlN is more than twice that between any of the more conventional III-V alloys. For such alloys one needs to describe the electronic structure taking atomic-scale disorder effects explicitly into account. Density functional theory can give some insight, but the limited supercell size that can be treated imposes artificial long-range ordering that can give misleading results. This has mandated the development of predictive empirical atomistic methods such as tight-binding and empirical pseudopotential models for large-scale calculations to quantitatively predict electronic and optical properties. Such atomistic models are, however, computationally too expensive for full device simulation, which then requires continuum models. But conventional continuum models are not sufficiently accurate for many disordered systems. Various quantum approaches have therefore been developed to overcome this challenge. These include explicitly incorporating random composition fluctuations into one- or multi-band k·p models, or the explicit introduction of localized states in the Hamiltonian, giving a band-anticrossing model to describe, e.g., the impact of N resonant defect levels on the band structure of GaAs1−xNx. Device simulations based, e.g., on the drift-diffusion model require semi-classical approaches that quantitatively treat disorder. We describe how the recently developed localization landscape method is addressing this question. Having overviewed the impact of disorder, we exemplify its effects by considering III-N alloys and heterostructures, where disorder effects play an increasingly important role as one moves from (Al,Ga)N to (In,Ga)N and then to (Al,In)N.

In this work, we study the impact that random alloy fluctuations have on the distribution of electrons and holes across the active region of a (In,Ga)N/GaN multi-quantum well based light emitting diode (LED). To do so, an atomistic tight-binding model is employed to account for alloy fluctuations on a microscopic level and the resulting tight-binding energy landscape forms input to a drift-diffusion model. Here, quantum corrections are introduced via localization landscape theory and we show that when neglecting alloy disorder our theoretical framework yields results similar to commercial software packages that employ a self-consistent Schroedinger-Poisson-drift-diffusion solver. Similar to experimental studies in the literature, we have focused on a multi-quantum well system where two of the three wells have the same In content while the third well differs in In content. By changing the order of wells in this multicolor quantum well structure and looking at the relative radiative recombination rates of the different emitted wavelengths, we (i) gain insight into the distribution of carriers in such a system and (ii) can compare our findings to trends observed in experiment. Our results indicate that the distribution of carriers depends significantly on the treatment of the quantum well microstructure. When including random alloy fluctuations and quantum corrections in the simulations, the calculated trends in the relative radiative recombination rates as a function of the well ordering are consistent with previous experimental studies. The results from the widely employed virtual crystal approximation contradict the experimental data. Overall, our work highlights the importance of a careful and detailed theoretical description of the carrier transport in an (In,Ga)N/GaN multi-quantum well system to ultimately guide the design of the active region of III-N-based LED structures.

Tailoring the electronic and optical properties of nitride‐based alloys for optoelectronic device applications in the ultraviolet and red spectral range has attracted significant attention in recent years. Adding boron nitride (BN) to indium gallium nitride (In,Ga)N alloys can help to control the lattice mismatch between (In,Ga)N and GaN and may thus allow to reduce strain‐related defect formation. However, understanding of the impact of BN on the electronic properties of III‐N alloys, in particular the influence of experimentally observed boron atom clustering, is sparse. This work presents first‐principles calculations investigating the electronic properties of highly mismatched (B,In)N alloys with boron contents between 2% and 7%. Special attention is paid to the impact of the alloy microstructure. While the results show that the lattice constants of such alloys largely agree with lattice constants determined from a Vegard approximation, the electronic structure strongly depends on the local boron atom configuration. For instance, if boron atoms are dispersed throughout the structure and are not sharing nitrogen atoms, the band gap of (B,In)N alloys is largely unaffected and stays close to the gap of pristine InN. However, in the case of boron atom clustering, i.e., when boron atoms are sharing nitrogen atoms, the band gap can be strongly reduced, often leading to a metallic state in (B,In)N alloys. These strong band gap reductions are mainly driven by carrier localization effects in the valence band. Our calculations thus show that the electronic structure of (B,In)N alloys strongly depends on the alloy microstructure and that boron atom clustering plays an important role in understanding the electronic and optical properties of these emerging materials.

The internal quantum efficiency of (In,Ga)N/GaN quantumwells cansurpass 90% for blue-emitting structures at moderate drive currentdensities but decreases significantly for longer emission wavelengthsand at higher excitation rates. This latter effect is known as efficiency"droop" and limits the brightness of light-emittingdiodes (LEDs) based on such quantum wells. Several mechanisms havebeen proposed to explain efficiency droop including Auger recombination,both intrinsic and defect-assisted, carrier escape, and the saturationof localized states. However, it remains unclear which of these mechanismsis most important because it has proven difficult to reconcile theoreticalcalculations of droop with measurements. Here, we first present experimentalphotoluminescence measurements extending over three orders of magnitudeof excitation for three samples grown at different temperatures thatindicate that droop behavior is not dependent on the point defectdensity in the quantum wells studied. Second, we use an atomistictight-binding electronic structure model to calculate localization-enhancedradiative and Auger rates and show that both the corresponding carrierdensity-dependent internal quantum efficiency and the carrier densitydecay dynamics are in excellent agreement with our experimental measurements.Moreover, we show that point defect density, Auger recombination,and the effect of the polarization field on recombination rates onlylimit the peak internal quantum efficiency to about 70% in the resonantlyexcited green-emitting quantum wells studied. This suggests that factorsexternal to the quantum wells, such as carrier injection efficiencyand homogeneity, contribute appreciably to the significantly lowerpeak external quantum efficiency of green LEDs.

We present a theoretical study on the impact of alloy disorder on carrier transport and recombination rates in an (Al,Ga)N single quantum well based LED operating in the deep UV spectral range. Our calculations indicate that alloy fluctuations enable ‘percolative pathways’ which can result in improved carrier injection into the well, but may also increase carrier leakage from the well. Additionally, we find that alloy disorder induces carrier localization effects, a feature particularly noticeable for the holes. These localization effects can lead to locally increased carrier densities when compared to a virtual crystal approximation which neglects alloy disorder. We observe that both radiative and non-radiative recombination rates are increased. Our calculations also indicate that Auger-Meitner recombination increases faster than the radiative rate, based on a comparison with a virtual crystal approximation.

We show the importance of using a thermodynamically consistent flux discretization when describing drift–diffusion processes within light emitting diode simulations. Using the classical Scharfetter–Gummel scheme with Fermi–Dirac statistics is an example of such an inconsistent scheme. In this case, for an (In,Ga)N multi quantum well device, the Fermi levels show an unphysical hump within the quantum well regions. This result originates from neglecting diffusion enhancement associated with Fermi–Dirac statistics in the numerical flux approximation. For a thermodynamically consistent scheme, such as the SEDAN scheme, the humps in the Fermi levels disappear. We show that thermodynamic inconsistency has far reaching implications on the current–voltage curves and recombination rates.

Boron (B) containing III-nitride materials, such as wurtzite (wz) (B, Ga)N alloys, have recently attracted significant interest due to their ability to tailor the electronic and optical properties of optoelectronic devices operating in the visible and ultraviolet spectral range. However, the growth of high quality samples is challenging and B atom clustering is often observed in (B, Ga)N alloys. To date, a fundamental understanding of the impact of such clustering on the electronic and optical properties of these alloys is sparse. In this work, we employ density functional theory (DFT) in the framework of the meta-generalized gradient approximation [modified Becke Johnson (mBJ) functional] to provide insight into this question. We use mBJ DFT calculations, benchmarked against state-of-the-art hybrid functional DFT, on (B, Ga)N alloys in the experimentally relevant B content range of up to 7.4%. Our results reveal that B atom clustering can lead to a strong reduction in the bandgap of such an alloy, in contrast to alloy configurations where B atoms are not forming clusters, thus not sharing nitrogen (N) atoms. We find that the reduction in bandgap is linked mainly to carrier localization effects in the valence band, which stem from local strain and polarization field effects. However, our study also reveals that the alloy microstructure of a B atom cluster plays an important role: B atom chains along the wz c axis impact the electronic structure far less strongly when compared to a chain formed within the c-plane. This effect is again linked to local polarization field effects and the orbital character of the involved valence states in wz BN and GaN. Overall, our calculations show that controlling the alloy microstructure of (B, Ga)N alloys is of central importance when it comes to utilizing these systems in future optoelectronic devices with improved efficiencies.