Quasiparticle band structure of AlN and GaN

Enhancing the photocatalytic efficiency of two-dimensional aluminum nitride materials through strategic rare earth doping

Two-dimensional (2D) materials demonstrate promising potential as high-efficiency photocatalysts. However, the intrinsic limitations of aluminum nitride (AlN), such as inadequate oxidation capacity, a high carrier recombination rate, and limited absorption of visible light, pose considerable challenges. In this paper, we introduce a novel co-doping technique with dysprosium (Dy) and carbon (C) on a 2D AlN monolayer, aiming to enhance its photocatalytic properties. Our first-principles calculations reveal a reduction in the bandgap and a significant enhancement in the visible light absorption rate of the co-doped Al24N22DyC2 structure. Notably, the distribution of the highest occupied molecular orbital and the lowest unoccupied molecular in proximity to Dy atoms demonstrates favorable conditions for carrier separation. Theoretical assessments of the hydrogen evolution reaction and oxygen evolution reaction activities further corroborate the potential of Al24N22DyC2 as a competent catalyst for photocatalytic reactions. These findings provide valuable theoretical insights for the experimental design and fabrication of novel, high-efficiency AlN semiconductor photocatalysts.

Origin of Structural Anomaly in Cuprous Halides

Cuprous halides (CuX; X = Cl, Br, or I) have been extensively investigated in the literature, but many of their fundamental properties are still not very well understood. For example, debate about their crystal stability, i.e., whether the ground-state structures of CuX are zinc-blende, still exists. By performing rigorous first-principles calculations for CuX using an accurate hybrid functional, we unambiguously demonstrate that CuX are indeed stable in the zinc-blende structure, but their accurate description requires careful treatment of the exchange interaction. Previous calculations based on local or semilocal density functionals underestimated the important contributions from exchange interactions and thus underestimated the energy separation between the unoccupied 4s and occupied 3d orbitals in Cu, resulting in an overestimation of the s-d coupling and the energy reduction of distorted CuX. Our study clarifies a long-standing and highly debated issue with regard to ground-state structures of CuX and advances the physics of phase stability and the importance of s-d coupling in semiconductors.

High Reflectivity AlN/Al1−xInxN Distributed Bragg Reflectors across the UV Regions by Sputtering

To improve the performance of III-nitride compound semiconductor-based optoelectronic devices, highly reflective distributed Bragg reflectors (DBRs) are a requirement. In this report, AlN and Al1−xInxN layers were first sputtered and characterized concerning their optical, structural and morphological properties. Ellipsometry measurements were used to determine the optical constants (refractive index, n and coefficient of extinction, k, in dependence of the wavelengths of the layers. The indium content of the Al1−xInxN film was investigated by X-ray photoelectron spectroscopy analysis. Subsequently, AlN/Al1−xInxN DBRs with high reflectivity spectra operating in the UV A, B and C were designed and fabricated on Si (111) and SiO2 substrates by radio frequency (RF) magnetron sputtering. The DBRs consist of an eight-pair AlN/Al0.84In0.16N at 235 nm, 290 nm and 365 nm with reflectances of 86.5%, 97.7% and 97.5% with FWHM of 45 nm, 70 nm and 96 nm, respectively. Atomic force microscopy analysis yielded a Root Mean Square (RMS) of 2.95 nm, implying that the DBR samples can achieve reasonable smoothness over a wide area. Furthermore, the impact of an annealing phase, which is frequently required during device growth, was investigated. Our findings indicate that AlN and Al1−xInxN are suitable materials for the fabrication of deep UV DBRs.

Realizing Effective Cubic-Scaling Coulomb Hole Plus Screened Exchange Approximation in Periodic Systems via Interpolative Separable Density Fitting with a Plane-Wave Basis Set

The GW approximation is an effective way to accurately describe the single-electron excitations of molecules and the quasiparticle energies of solids. However, a perceived drawback of the GW calculations is their high computational cost and large memory usage, which limit their applications to large systems. Herein, we demonstrate an accurate and effective low-rank approximation to accelerate non-self-consistent GW (G₀W₀) calculations under the static Coulomb hole plus screened exchange (COHSEX) approximation for periodic systems. Our approach is to adopt the interpolative separable density fitting (ISDF) decomposition and Cauchy's integral to construct low-rank representations of the dielectric matrix ϵ and self-energy matrix Σ. This approach reduces the number of floating point operations from O(Ne4) to O(Ne3) and requires a much smaller memory footprint. Two methods are used to select the interpolation points in ISDF, including the standard QR factorization with column pivoting (QRCP) procedure and the machine learning K-means clustering (K-means) algorithm. We demonstrate that these two methods can yield similar accuracy for both molecules and solids at much lower computational cost. In particular, K-means clustering can significantly reduce the computational cost of selecting the interpolation points by an order of magnitude compared to QRCP, resulting in an overall speedup factor of about ten times ISDF accelerated the static COHSEX calculations compared with conventional COHSEX approximation.

First-Principles Exploration of Hazardous Gas Molecule Adsorption on Pure and Modified Al60N60 Nanoclusters

In this work, we use the first-principles method to study in details the characteristics of the adsorption of hazardous NO₂, NO, CO₂, CO and SO₂ gas molecules by pure and heteroatom (Ti, Si, Mn) modified Al₆₀N₆₀ nanoclusters. It is found that the pure Al₆₀N₆₀ cluster is not sensitive to CO. When NO₂, NO, CO₂, CO and SO₂ are adsorbed on Al₆₀N₆₀ cluster’stop.b, edge.a_p, edge.a_h, edge.a_p andedge.a_h sites respectively, the obtained configuration is the most stable for each gas. Ti, Si and Mn atoms prefer to stay on the top sites of Al₆₀N₆₀ cluster when these heteroatoms are used to modify the pure clusters. The adsorption characteristics of above hazardous gas molecules on these hetero-atom modified nanoclusters are also revealed. It is found that when Ti-Al₆₀N₆₀ cluster adsorbs CO and SO₂, the energy gap decreases sharply and the change rate of gap is 62% and 50%, respectively. The Ti-modified Al₆₀N₆₀ improves the adsorption sensitivity of the cluster to CO and SO₂. This theoretical work is proposed to predict and understand the basic adsorption characteristics of AlN-based nanoclusters for hazardous gases, which will help and guide researchers to design better nanomaterials for gas adsorption or detection.

Precise radiative lifetimes in bulk crystals from first principles: the case of wurtzite gallium nitride

Gallium nitride (GaN) is a key semiconductor for solid-state lighting, but its radiative processes are not fully understood. Here we show a first-principles approach to accurately compute the radiative lifetimes in bulk uniaxial crystals, focusing on wurtzite GaN. Our computed radiative lifetimes are in very good agreement with experiment up to 100 K. We show that taking into account excitons (through the Bethe-Salpeter equation) and spin-orbit coupling is essential for computing accurate radiative lifetimes. A model for exciton dissociation into free carriers allows us to compute the radiative lifetimes up to room temperature. Our work enables precise radiative lifetime calculations in III-nitrides and other anisotropic solid-state emitters.

Theoretical study of nitride short period superlattices

Discussion of band gap behavior based on first principles calculations of electronic band structures for various short period nitride superlattices is presented. Binary superlattices, as InN/GaN and GaN/AlN as well as superlattices containing alloys, as InGaN/GaN, GaN/AlGaN, and GaN/InAlN are considered. Taking into account different crystallographic directions of growth (polar, semipolar and nonpolar) and different strain conditions (free-standing and pseudomorphic) all the factors influencing the band gap engineering are analyzed. Dependence on internal strain and lattice geometry is considered, but the main attention is devoted to the influence of the internal electric field and the hybridization of well and barrier wave functions. The contributions of these two important factors to band gap behavior are illustrated and estimated quantitatively. It appears that there are two interesting ranges of layer thicknesses; in one (few atomic monolayers in barriers and wells) the influence of the wave function hybridization is dominant, whereas in the other (layers thicker than roughly five to six monolayers) dependence of electric field on the band gaps is more important. The band gap behavior in superlattices is compared with the band gap dependence on composition in the corresponding ternary and quaternary alloys. It is shown that for superlattices it is possible to exceed by far the range of band gap values, which can be realized in ternary alloys. The calculated values of the band gaps are compared with the photoluminescence emission energies, when the corresponding data are available. Finally, similarities and differences between nitride and oxide polar superlattices are pointed out by comparison of wurtzite GaN/AlN and ZnO/MgO.

Mechanical, Thermodynamic and Electronic Properties of Wurtzite and Zinc-Blende GaN Crystals

For the limitation of experimental methods in crystal characterization, in this study, the mechanical, thermodynamic and electronic properties of wurtzite and zinc-blende GaN crystals were investigated by first-principles calculations based on density functional theory. Firstly, bulk moduli, shear moduli, elastic moduli and Poisson's ratios of the two GaN polycrystals were calculated using Voigt and Hill approximations, and the results show wurtzite GaN has larger shear and elastic moduli and exhibits more obvious brittleness. Moreover, both wurtzite and zinc-blende GaN monocrystals present obvious mechanical anisotropic behavior. For wurtzite GaN monocrystal, the maximum and minimum elastic moduli are located at orientations [001] and <111>, respectively, while they are in the orientations <111> and <100> for zinc-blende GaN monocrystal, respectively. Compared to the elastic modulus, the shear moduli of the two GaN monocrystals have completely opposite direction dependences. However, different from elastic and shear moduli, the bulk moduli of the two monocrystals are nearly isotropic, especially for the zinc-blende GaN. Besides, in the wurtzite GaN, Poisson's ratios at the planes containing [001] axis are anisotropic, and the maximum value is 0.31 which is located at the directions vertical to [001] axis. For zinc-blende GaN, Poisson's ratios at planes (100) and (111) are isotropic, while the Poisson's ratio at plane (110) exhibits dramatically anisotropic phenomenon. Additionally, the calculated Debye temperatures of wurtzite and zinc-blende GaN are 641.8 and 620.2 K, respectively. At 300 K, the calculated heat capacities of wurtzite and zinc-blende are 33.6 and 33.5 J mol^-1 K^-1, respectively. Finally, the band gap is located at the G point for the two crystals, and the band gaps of wurtzite and zinc-blende GaN are 3.62 eV and 3.06 eV, respectively. At the G point, the lowest energy of conduction band in the wurtzite GaN is larger, resulting in a wider band gap. Densities of states in the orbital hybridization between Ga and N atoms of wurtzite GaN are much higher, indicating more electrons participate in forming Ga-N ionic bonds in the wurtzite GaN.

Ultrafast Hot Carrier Dynamics in GaN and Its Impact on the Efficiency Droop

GaN is a key material for lighting technology. Yet, the carrier transport and ultrafast dynamics that are central in GaN light-emitting devices are not completely understood. We present first-principles calculations of carrier dynamics in GaN, focusing on electron-phonon (e-ph) scattering and the cooling and nanoscale dynamics of hot carriers. We find that e-ph scattering is significantly faster for holes compared to electrons and that for hot carriers with an initial 0.5-1 eV excess energy, holes take a significantly shorter time (∼0.1 ps) to relax to the band edge compared to electrons, which take ∼1 ps. The asymmetry in the hot carrier dynamics is shown to originate from the valence band degeneracy, the heavier effective mass of holes compared to electrons, and the details of the coupling to different phonon modes in the valence and conduction bands. We show that the slow cooling of hot electrons and their long ballistic mean free paths (over 3 nm at room temperature) are a possible cause of efficiency droop in GaN light-emitting diodes. Taken together, our work sheds light on the ultrafast dynamics of hot carriers in GaN and the nanoscale origin of efficiency droop.

Half-metallicity and ferromagnetism in penta-AlN2 nanostructure

We have performed a detailed first-principles study of the penta-AlN₂ nanostructure in the Cairo pentagonal tiling geometry, which is dynamically stable due to the absence of imaginary mode in the calculated phonon spectrum. The formation energy and the fragment cohesive energy analyses, the molecular dynamics simulations, and the mechanical property studies also support the structural stability. It could withstand the temperature as high as 1400 K and sustain the strain up to 16.1% against structural collapse. The slightly buckled penta-AlN₂ is found to be a ferromagnetic semiconductor. The strain of ~9% could drive the structural transition from the buckled to the planar. Interestingly, the strain of >7% would change the conducting properties to show half-metallic characters. Furthermore, it could be also used to continuously enhance the magnetic coupling strength, rendering penta-AlN₂ as a robust ferromagnetic material. These studies shed light on the possibilities in synthesizing penta-AlN₂ and present many unique properties, which are worth of further studying on both theory and experiment.

Design of defect spins in piezoelectric aluminum nitride for solid-state hybrid quantum technologies

Spin defects in wide-band gap semiconductors are promising systems for the realization of quantum bits, or qubits, in solid-state environments. To date, defect qubits have only been realized in materials with strong covalent bonds. Here, we introduce a strain-driven scheme to rationally design defect spins in functional ionic crystals, which may operate as potential qubits. In particular, using a combination of state-of-the-art ab-initio calculations based on hybrid density functional and many-body perturbation theory, we predicted that the negatively charged nitrogen vacancy center in piezoelectric aluminum nitride exhibits spin-triplet ground states under realistic uni- and bi-axial strain conditions; such states may be harnessed for the realization of qubits. The strain-driven strategy adopted here can be readily extended to a wide range of point defects in other wide-band gap semiconductors, paving the way to controlling the spin properties of defects in ionic systems for potential spintronic technologies.

Comparing LDA-1/2, HSE03, HSE06 and G₀W₀ approaches for band gap calculations of alloys

It has long been known that the local density approximation and the generalized gradient approximation do not furnish reliable band gaps, and one needs to go beyond these approximations to reliably describe these properties. Among alternatives are the use of hybrid functionals (HSE03 and HSE06 being popular), the GW approximation or the recently proposed LDA-1/2 method. In this work, we compare rigorously the performance of these four methods in describing the band gaps of alloys, employing the generalized quasi-chemical approach to treat the disorder of the alloy and to obtain judiciously the band gap for the entire compositional range. Zincblende InGaAs and InGaN were chosen as prototypes due to their importance in optoelectronic applications. The comparison between these four approaches was guided both by the agreement between the predicted band gap and the experimental one, and by the demanded computational effort (time and memory). We observed that the HSE06 method provided the most accurate results (in comparison with experiments), whereas, surprisingly, the LDA-1/2 method gave the best compromise between accuracy and computational resources. Due to its low computational cost and good accuracy, we decided to double the supercell used to describe the alloys, and employing LDA-1/2 we observed that the bowing parameter changed remarkably, only agreeing with the measured one for the larger supercell, where LDA-1/2 plays an important role.

Temperature dependence of the electronic structure of semiconductors and insulators

The renormalization of electronic eigenenergies due to electron-phonon coupling (temperature dependence and zero-point motion effect) is sizable in many materials with light atoms. This effect, often neglected in ab initio calculations, can be computed using the perturbation-based Allen-Heine-Cardona theory in the adiabatic or non-adiabatic harmonic approximation. After a short description of the recent progresses in this field and a brief overview of the theory, we focus on the issue of phonon wavevector sampling convergence, until now poorly understood. Indeed, the renormalization is obtained numerically through a slowly converging q-point integration. For non-zero Born effective charges, we show that a divergence appears in the electron-phonon matrix elements at q → Γ, leading to a divergence of the adiabatic renormalization at band extrema. This problem is exacerbated by the slow convergence of Born effective charges with electronic wavevector sampling, which leaves residual Born effective charges in ab initio calculations on materials that are physically devoid of such charges. Here, we propose a solution that improves this convergence. However, for materials where Born effective charges are physically non-zero, the divergence of the renormalization indicates a breakdown of the adiabatic harmonic approximation, which we assess here by switching to the non-adiabatic harmonic approximation. Also, we study the convergence behavior of the renormalization and develop reliable extrapolation schemes to obtain the converged results. Finally, the adiabatic and non-adiabatic theories, with corrections for the slow Born effective charge convergence problem (and the associated divergence) are applied to the study of five semiconductors and insulators: α-AlN, β-AlN, BN, diamond, and silicon. For these five materials, we present the zero-point renormalization, temperature dependence, phonon-induced lifetime broadening, and the renormalized electronic band structure.

Origin of 3.45 eV Emission Line and Yellow Luminescence Band in GaN Nanowires: Surface Microwire and Defect

The physical origin of the strong emission line at 3.45 eV and broadening yellow luminescence (YL) band centered at 2.2 eV in GaN nanowire (NW) has been debated for many years. Here, we solve these two notable issues by using state-of-the-art first-principles calculations based on many-body perturbation theory combined with polarization-resolved experiments. We demonstrate that the ubiquitous surface "microwires" with amazing characteristics, i.e., the outgrowth nanocrystal along the NW side wall, are vital and offer a new perspective to provide insight into some puzzles in epitaxy materials. Furthermore, inversion of the top valence bands, in the decreasing order of crystal-field split-off hole (CH) and heavy/light hole, results in the optical transition polarized along the NW axis due to quantum confinement. The optical emission from bound excitons localized around the surface microwire to CH band is responsible for the 3.45 eV line with E∥c polarization. Both gallium vacancy and carbon-related defects tend to assemble at the NW surface layer, determining the broadening YL band.

First-principles determination of defect energy levels through hybrid density functionals and GW

In this topical review, we discuss recent progress in electronic-structure methods for calculating defect energy levels in semiconductors and insulators. We concentrate mainly on two advanced electronic-structure schemes, namely hybrid density functional theory and many-body perturbation theory in the GW approximation. These two schemes go beyond standard density functional theory in the semilocal approximation providing a more realistic description of band gaps. In particular, we address important aspects underlying the GW scheme and highlight the correspondence between the defect levels as obtained in the various schemes. We further assess the quality of the band-edge positions determined with hybrid functionals and GW through the calculation of band-offsets at semiconductor heterojunctions and of ionization potentials at semiconductor surfaces.

Doping of AlGaN Alloys

Nitride-based device structures for electronic and optoelectronic applications usually incor-porate layers of AlxGa1−xN, and n- and p-type doping of these alloys is typically required. Experimental results indicate that doping efficiencies in AlxGa1−xN are lower than in GaN. We address the cause of these doping difficulties, based on results from first-principles density-functional-pseudopotential calculations. For n-type doping we will discuss doping with oxygen, the most common unintentional donor, and with silicon. For oxygen, a DX transition occurs which converts the shallow donor into a negatively charged deep level. We present experimental evidence that oxygen is a DX center in AlxGa1−xN for x>∼0.3. For p-type doping, we find that compensation by nitrogen vacancies becomes increasingly important as the Al content is in-creased. We also find that the ionization energy of the Mg acceptor increases with alloy composition x. To address the limitations on p-type doping we have performed a comprehensive investigation of alternative acceptor impurities; none of the candidates exhibits characteristics that surpass those of Mg in all respects.

Electronic and Optical Properties of the Group-III Nitrides, their Heterostructures and Alloys

Various aspects of the electronic structure of the group III nitrides are discussed. The relation between band structures and optical response in the vacuum ultraviolet is analyzed for zincblende and wurtzite GaN and for wurtzite A1N and compared with available experimental data obtained from reflectivity and spectroscopic ellipsometry. The spin-orbit and crystal field splittings of the valence band edges and their relations to exciton fine structure are discussed including substrate induced biaxial strain effects. The band-offsets between the III-nitrides and some relevant semiconductor substrates obtained within the dielectric midgap energy model are presented and strain effects which may alter these values are discussed. The importance of lattice mismatch in bandgap bowing is exemplified by comparing AlxGa1−xN and InxGa1−xN.

XPS Measurement of the SiC/AlN Band-Offset at the (0001) Interface

X-ray photoelectron spectroscopy is used to determine the band-offset at the SiC/AIN (0001) interface. First, the valence band spectra are determined for bulk materials and analyzed with the help of calculated densities of states. Core levels are then measured across the interface for a thin film of 2H-AIN on 6H-SiC and allow us to extract a band offset of 1.4 ±0.3 eV. The analysis of the discrepancies between measured peak positions and densities of states obtained within the local density approximation provides information on self-energy corrections in good agreement with independent calculations of the latter.

Photoemission Study of The Electronic Structure of Wurtzite Gan(0001) Surfaces

The surface electronic structure of wurtzite GaN (0001) (1 × 1) has been investigated using angle-resolved photoemission spectroscopy. Surfaces were cleaned by repeated cycles of N2 ion bombardment and annealing in ultra-high vacuum. A well-defined surface state below the top of the valence band is clearly observed. This state is sensitive to the adsorption of both activated H2 and O2, and exists in a projected bulk band gap, below the valence band maximum. The state shows no dispersion perpendicular or parallel to the surface. The symmetry of this surface state is even with respect to the mirror planes of the surface and polarization measurements indicate that it is of spz character, consistent with a dangling bond state.

Bulk and Surface Electronic Structure of GaN Measured Using Angle-Resolved Photoemission, Soft X-ray Emission and Soft X-ray Absorption

The electronic structure of thin film wurtzite GaN has been studied using a combination of angle resolved photoemission, soft x-ray absorption and soft x-ray emission spectroscopies. We have measured the bulk valence and conduction band partial density of states by recording Ga L- and N K- x-ray emission and absorption spectra. We compare the x-ray spectra to a recent ab initio calculation and find good overall agreement. The x-ray emission spectra reveal that the top of the valence band is dominated by N 2p states, while the x-ray absorption spectra show the bottom of the conduction band as a mixture of Ga 4s and N 2p states, again in good agreement with theory. However, due to strong dipole selection rules we can also identify weak hybridization between Ga 4s- and N 2p-states in the valence band. Furthermore, a component to the N K-emission appears at approximately 19.5 eV below the valence band maximum and can be identified as due to hybridization between N 2p and Ga 3d states. We report preliminary results of a study of the full dispersion of the bulk valence band states along high symmetry directions of the bulk Brillouin zone as measured using angle resolved photoemission. Finally, we tentatively identify a non-dispersive state at the top of the valence band in parts of the Brillouin zone as a surface state.

Theoretical Study of Native Point Defects in Aln and InN

We have studied native point defects in AlN and InN using density-functional calculations employing both the local-density and generalized gradient approximations for the exchange-correlation functional. For both materials we find that the nitrogen vacancy acts as a compensating center in p-type material. For AIN in the zinc-blende structure, the aluminum interstitial has an equally low formation energy as the nitrogen vacancy. For n-type material the aluminum vacancy is the dominant compensating center in AlN. For n-type InN, all defect formation energies are high.

An ab initio study of structural properties and single vacancy defects in Wurtzite AlN

The cell parameters, bulk moduli and electronic densities-of-states (DOS) of pure and vacancy defect AlN were computed using generalized-gradient approximation (GGA) and hybrid functional (B3LYP) computational methods within both plane wave-pseudopotential and localized Gaussian basis set approaches. All of the methods studied yielded cell parameters and bulk moduli in reasonable agreement with experiment. The B3LYP functional was also found to predict an optical band gap in excellent agreement with experiment. These methods were subsequently applied to the calculation of the geometry, defect state positions and formation energies of the cation (V(Al)) and anion (V(N)) single vacancy defects. For the V(Al) defect, the plane wave-pseudopotential predicted a significant retraction of the neighboring N away from the vacancy, while for the V(N) defect, only slight relaxations of the surrounding Al atoms towards the vacancy were predicted. For the computed DOS of both vacancy defects, the GGA methods yielded similar features and defect level positions relative to the valence band maximum, while the B3LYP method predicted higher separations between the defect levels and the valence and conduction bands, leading to higher energy occupied defect levels.