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 to include the exciton fine structure 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.
A theoretical investigation of the excess energy dissipation of highly excited photoinjected electrons in both wurtzite and zincblende GaN is presented. The calculations are performed by solving numerically coupled quantum transport equations for the carriers and the acoustic, transversal and longitudinal optical phonon in order to derive the evolution of their nonequilibrium temperatures, dubbed quasi-temperatures. It is shown that the electron energy dissipation is always faster in the wurtzite structure than in zincblende, both occurring in a subpicosecond time scale (< 0.2 ps).
We report a new biphasic crystalline wurtzite/zinc-blende homostructure in gallium nitride nanowires. Cathodoluminescence was used to quantitatively measure the wurtzite and zinc-blende band gaps. High resolution transmission electron microscopy was used to identify distinct wurtzite and zinc-blende crystalline phases within single nanowires through the use of selected area electron diffraction, electron dispersive spectroscopy, electron energy loss spectroscopy, and fast Fourier transform techniques. A mechanism for growth is identified.
The free-carrier screening of macroscopic polarization fields in wurtzite GaN/InGaN quantum wells lasers is investigated via a self-consistent tight-binding approach. We show that the high carrier concentrations found experimentally in nitride laser structures effectively screen the built-in spontaneous and piezoelectric polarization fields, thus inducing a ``field-free'' band profile. Our results explain some heretofore puzzling experimental data on nitride lasers, such as the unusually high lasing excitation thresholds and emission blue-shifts for increasing excitation levels.
Crystal morphologies are important for the design and functionality of devices based on low-dimensional nanomaterials. The equilibrium crystal shape (ECS) is a key quantity in this context. It is determined by surface energies, which are hard to access experimentally but can generally be well predicted by first-principles methods. Unfortunately, this is not necessarily so for polar and semipolar surfaces of wurtzite crystals. By extending the concept of Wulff construction, we demonstrate that the ECSs can nevertheless be obtained for this class of materials. For the example of GaN, we identify…
Zn in GaN forms an efficient radiative center and acts as a deep acceptor which can make the crystal insulating. Four different Zn-related centers have been by now identified, leading to light emission in the range between 1.8 eV and 2.9 eV. We present a first-principles investigation total energy and electronic structure calculations for Ga-substitutional and hetero-antisite N-substitutional Zn in wurtzite GaN, using ultrasoft pseudopotentials and a conjugate-gradient total energy minimization method. Our results permit the identification of the blue-light emission center as the substitutiona…
The piezoelectric (PZ) polarization effect enhances the phonon group velocity in wurtzite nitrides. This enhancement influences the phonon relaxation rates. We calculate the modified phonon relaxation rates in binary wurtzite nitrides (GaN, AlN and InN) by considering process like umklapp process, point defect, dislocation, boundary and phonon-electron scattering. The result will be useful to study the effect of PZ polarization on thermal conductivity of binary wurtzite nitrides (GaN, AlN and InN).
We report calculated, electronic and related properties of wurtzite and zinc blende gallium nitrides (w-GaN, zb-GaN). We employed a local density approximation (LDA) potential and the linear combination of atomic orbital (LCAO) formalism. The implementation of this formalism followed the Bagayoko, Zhao, and Williams (BZW) method, as enhanced by Ekuma and Franklin (BZW-EF). The calculated electronic and related properties, for both structures of GaN, are in good agreement with corresponding, experimental data, unlike results from most previous ab initio calculations utilizing a density function…
Based on the dielectric continuum model and transfer-matrix method, the completing polar optical phonon states in a wurtzite GaN-based superlattice (SLs) with arbitrary-layer complex bases are investigated. It is proved that $2^n$ types of phonon modes probably exist in a wurtzite nitride SL with $n$-layer complex bases. The analytical phonon states of these modes and their dispersive equations in the wurtzite GaN/Al$_{x}$Ga$_{1-x}$N SL structures are obtained. Numerical calculations on a three-layer GaN/Al$_{0.15}$Ga$_{0.85}$N/AlN complex bases SL are performed. Results reveal that there are …
Full optimization of quasiharmonic free energy with anharmonic lattice model: Application to thermal expansion and pyroelectricity of wurtzite GaN and ZnO
Selection rules are presented for electron-phonon scattering in GaN with the wurtzite crystal structure. The results are obtained for the interband scattering between the lowest conduction band ($Γ$-valley) and the second conduction band ($U$-valley). These selection rules are derived based on the original group-theoretical analysis of the crystal vibrations in GaN, which included detailed compatibility relations for all phonon modes.
We have confirmed the k-dependent spin splitting in wurtzite AlxGa1-xN/GaN heterostructures. Anomalous beating pattern in Shubnikov-de Haas measurements arises from the interference of Rashba and Dresselhaus spin-orbit interactions. The dominant mechanism for the k-dependent spin splitting at high values of k is attributed to Dresselhaus term which is enhanced by the Delta C1-Delta C3 coupling of wurtzite band folding effect.
Gallium nitride (GaN), a wide band-gap semiconductor, has been broadly used in power electronic devices due to its high electron mobility and high breakdown voltage. Its relatively high thermal conductivity makes GaN a favorable material for such applications, where heat dissipation is a major concern for device efficiency and long-term stability. However, in GaN-based transistors, where the active region can withstand extremely strong electric fields, the field effect on the thermal transport properties has drawn little attention so far. In this work, we apply first-principles methods to inve…
First-principles calculations of $e$-ph interactions are becoming a pillar of electronic structure theory. However, the current approach is incomplete. The piezoelectric (PE) $e$-ph interaction, a long-range scattering mechanism due to acoustic phonons in non-centrosymmetric polar materials, is not accurately described at present. Current calculations include short-range $e$-ph interactions (obtained by interpolation) and the dipole-like Fröhlich long-range coupling in polar materials, but lack important quadrupole effects for acoustic modes and PE materials. Here we derive and compute the lon…
First-principles full-potential linearized augmented plane wave (FLAPW) calculations are performed to clarify the role of the interface geometry on piezoelectric fields and on potential line-ups at the [0001]-wurtzite and [111]-zincblende GaN/Al junctions. The electric fields (polarity and magnitude) are found to be strongly affected by atomic relaxations in the interface region. A procedure is tested to evaluate the Schottky barrier in the presence of electric fields and used to show that their effect is quite small (a few tenths of an eV). These calculations assess the rectifying behaviour o…
A new mechanism (DeltaC1-DeltaC3 coupling) is accounted for the spin splitting of wurtzite GaN, which is originated from the intrinsic wurtzite effects (band folding and structure inversion asymmetry). The band-folding effect generates two conduction bands (DeltaC1 and DeltaC3), in which p-wave probability has tremendous change when kz approaches anti-crossing zone. The spin-splitting energy induced by the DeltaC1-DeltaC3 coupling and wurtzite structure inversion asymmetry is much larger than that evaluated by traditional Rashba or Dresselhaus effects. When we apply the coupling to GaN/AlN qua…
We present a study of the polarization properties of emission lines from single InGaN/GaN quantum dots (QDs). The QDs, formed by spinodal decomposition within ultra-thin InGaN quantum wells, are investigated using single-QD cathodoluminescence (CL). The emission lines exhibit a systematic linear polarization in the orthogonal crystal directions [1 1 -2 0] and [-1 1 0 0]--a symmetry that is non-native to hexagonal crystals. Eight-band k.p calculations reveal a mechanism that can explain the observed polarizations: The character of the hole(s) in an excitonic complex determines the polarization …
We report on lattice specific heat of bulk hexagonal GaN measured by the heat flow method in the temperature range 20-300 K and by the adiabatic method in the range 5-70 K. We fit the experimental data using two temperatures model. The best fit with the accuracy of 3 % was obtained for the temperature independent Debye's temperature $θ_{\rm D}=365$ {\rm K} and Einstein's temperature $θ_{\rm E}=880$ {\rm K}. We relate these temperatures to the function of density of states. Using our results for heat conduction coefficient, we established in temperature range 10-100 K the explicit dependence of…
Millikelvin magnetotransport studies are carried out on heavily $n$-doped wurtzite GaN:Si films grown on semi-insulating GaN:Mn buffer layers by metal-organic vapor phase epitaxy. The dependency of the conductivity on magnetic field and temperature is interpreted in terms of theories that take into account disorder-induced quantum interference of one-electron and many-electron self-crossing trajectories. The Rashba parameter $α_{\text{R}}\,=\,(4.5 \pm 1)$ meV$Å$ is determined, and it is shown that in the previous studies of electrons adjacent to GaN/(Al,Ga)N interfaces, bulk inversion asymmetr…
We study the linear and nonlinear optical properties of wurtzite GaN under c-axial stress field, using density functional theory calculations. The fully structural optimization at each c-axial strain was performed. The calculated dielectric functions show that tensile c-axial strain effectively improves the linear optical efficiency, especially for the band-edge transitions, and significantly increase the mobility of electrons in the conduction band. Second-order nonlinear optical susceptibilities show that the tensile c-axial strain will enhance the zero- and low-frequency nonlinear responses…
The accurate absolute surface energies of (0001)/(000-1) surfaces of wurtzite structures are crucial in determining the thin film growth mode of important energy materials. However, the surface energies still remain to be solved due to the intrinsic difficulty of calculating dangling bond energy of asymmetrically bonded surface atoms. In this study, we used a pseudo-hydrogen passivation method to estimate the dangling bond energy and calculate the polar surfaces of ZnO and GaN. The calculations were based on the pseudo chemical potentials obtained from a set of tetrahedral clusters or simple p…
Basal-plane stacking faults are an important class of optically active structural defects in wurtzite semiconductors. The local deviation from the 2H stacking of the wurtzite matrix to a 3C zinc-blende stacking induces a bound state in the gap of the host crystal, resulting in the localization of excitons. Due to the two-dimensional nature of these planar defects, stacking faults act as quantum wells, giving rise to radiative transitions of excitons with characteristic energies. Luminescence spectroscopy is thus capable of detecting even a single stacking fault in an otherwise perfect wurtzite…
Based on the full band electronic structure calculations, first we consider the effect of n-type doping on the optical absorption and the refractive index in wurtzite InN and GaN. We identify quite different dielectric response in either case; while InN shows a significant shift in the absorption edge due to n-type doping, this is masked for GaN due to efficient cancellation of the Burstein-Moss effect by the band gap renormalization. For high doping levels the intraband absorption becomes significant in InN. Furthermore, we observe that the free-carrier plasma contribution to refractive index…
In this paper we systematically analyze the electronic structures of polar and nonpolar wurtzite-InN/GaN quantum dots and their modification due to the quantum-confined Stark effect caused by intrinsic fields. This is achieved by combining continuum elasticity theory with an empirical tight binding model to describe the elastic and single-particle electronic properties in these nitride systems. Based on these results, a many-body treatment is used to determine optical absorption spectra. The efficiency of optical transitions depends on the interplay between the Coulomb interaction and the quan…
InGaN light-emitting diodes (LEDs) are more efficient and cost effective than incandescent and fluorescent lighting, but lattice mismatch limits the thickness of InGaN layers that can be grown on GaN without performance-degrading dislocations. In this work, we apply hybrid density functional theory calculations to investigate the thermodynamic stability, lattice parameters, and band gaps of wurtzite and zincblende quaternary BInGaN alloys. We find that the wurtzite phase is more stable and can be lattice-matched to GaN for BInGaN compositions containing up to ~30% boron. The lattice match with…
We present an $sp^3$ tight-binding model for the calculation of the electronic and optical properties of wurtzite semiconductor quantum dots (QDs). The tight-binding model takes into account strain, piezoelectricity, spin-orbit coupling and crystal-field splitting. Excitonic absorption spectra are calculated using the configuration interaction scheme. We study the electronic and optical properties of InN/GaN QDs and their dependence on structural properties, crystal-field splitting, and spin-orbit coupling.
Polaron binding energy and effective mass are calculated for semiconductors with wurtzite crystalline structure from the first order electron-phonon corrections to the self-energy. A recently introduced Frohlich-like electron-phonon interaction Hamiltonian which accounts for the LO and TO polarizations mixing due to the anisotropy is used in the calculation. The polaronic damping rates are evaluated for finite temperature. Numerical results are reported for GaN. It is shown that the electron-phonon coupling is strong enough to justify the necessity of the inclusion of second-order corrections.
Rocksalt ScN is a semiconductor with a small lattice mismatch to wurtzite GaN. Within the modern theory of polarization, ScN has a nonvanishing formal polarization along the [111] direction. As a result, we demonstrate that an interface between (0001) GaN and (111) ScN exihibts a large polarization discontinuity of $-$1.358 $\rm Cm^{-2}$. Interfaces between ScN and wurtzite III-nitrides will exhibit a high-density electron gas on the (000$\bar{1}$) GaN interface or a hole gas on the (0001) GaN interface, with carrier concentrations up to $8.5 \times 10^{14}$ cm$^{-2}$. The large polarization d…
An oversight of some previous density functional calculations of the band gaps of wurtzite and cubic InN and of wurtzite GaN by Rinke et al. [Appl. Phys. Lett. 89,161919, 2006] led to an inaccurate and misleading statement relative to limitations of density functional theory (DFT) for the description of electronic properties of these materials. These comments address this statement. In particular, they show that some local density approximation (LDA) calculations have correctly described or predicted electronic and related properties of these systems [Phys. Rev. B 60, 1563, 1999; J. Appl. Phys…
Using group theory and Kane-like $\mathbf{k\cdot p}$ model together with the Löwdining partition method, we derive the expressions of spin-orbit coupling of electrons and holes, including the linear-$k$ Rashba term due to the intrinsic structure inversion asymmetry and the cubic-$k$ Dresselhaus term due to the bulk inversion asymmetry in wurtzite semiconductors. The coefficients of the electron and hole Dresselhaus terms of ZnO and GaN in wurtzite structure and GaN in zinc-blende structure are calculated using the nearest-neighbor $sp^3$ and $sp^3s^\ast$ tight-binding models separately.
Accurate values for polarization discontinuities between pyroelectric materials are critical for understanding and designing the electronic properties of heterostructures. For wurtzite materials, the zincblende structure has been used in the literature as a reference to determine the effective spontaneous polarization constants. We show that, because the zincblende structure has a nonzero formal polarization, this method results in a spurious contribution to the spontaneous polarization differences between materials. In addition, we address the correct choice of "improper" versus "proper" piez…
The spontaneous polarization of wurtzite III-V nitrides XN (X=Al, Ga, In) and II-VI oxides YO (Y=Be, Zn) is investigated via first-principles computational methods. The modern treatment defines this quantity as the polarization difference between the investigated system and an appropriate reference state. We demonstrate that the trigonal structure can be used as a reference to determine the spontaneous polarization of wurtzite materials. We compare the current values with the widely-known zincblende results reported in the literature and find a very good agreement. It is shown that the electro…
We have derived consistent sets of band parameters (band gaps, crystal field-splittings, band gap deformation potentials, effective masses, Luttinger and EP parameters) for AlN, GaN, and InN in the zinc-blende and wurtzite phases employing many-body perturbation theory in the G0W0 approximation. The G0W0 method has been combined with density-functional theory (DFT) calculations in the exact-exchange optimized effective potential approach (OEPx) to overcome the limitations of local-density or gradient-corrected DFT functionals (LDA and GGA). The band structures in the vicinity of the Gamma-poin…
Binary III-N nitride semiconductors with wurtzite crystal structure such as GaN and AlN have been long used in many practical applications ranging from optoelectronic to telecommunication. The structurally related ZnGeN2 or ZnSnN2 derived from the parent binary compounds by cation mutation (elemental substitution) have recently attracted attention, but such ternary nitride materials are mostly limited to II-IV-N2 compositions. This paper reports on synthesis and characterization of zinc niobium nitride Zn2NbN3 - a previously unreported II2-V-N3 ternary nitride semiconductor. The Zn2NbN3 thin f…
Ground state properties of SiC, AlN, GaN and InN in the zinc-blende and wurtzite structures are determined using an ab initio scheme. For the self-consistent field part of the calculations, the Hartree-Fock program Crystal has been used. Correlation contributions are evaluated using the coupled-cluster approach with single and double excitations. This is done by means of increments derived for localized bond orbitals and for pairs and triples of such bonds. A comparison between the ground state energies of the zinc-blende and wurtzite structure is made: At the Hartree-Fock level, it turns out …
A multiband empirical tight-binding model for group-III-nitride semiconductors with a wurtzite structure has been developed and applied to both bulk systems and embedded quantum dots. As a minimal basis set we assume one s-orbital and three p-orbitals, localized in the unit cell of the hexagonal Bravais lattice, from which one conduction band and three valence bands are formed. Non-vanishing matrix elements up to second nearest neighbors are taken into account. These matrix elements are determined so that the resulting tight-binding band structure reproduces the known Gamma-point parameters, w…
A study of the mobility of n-doped wurtzite III-Nitrides is reported. We have determined the nonequilibrium thermodynamic state of the III-Nitrides systems, driven far away from equilibrium by a strong electric field, in the steady state, which follows after a very fast transient. The dependence of the mobility (which depends on the nonequilibrium thermodynamic state of the sample) on the electric field strength is derived, which decreases with the strength of electric field. We analyzed the contributions to the mobility arising out of the different channels of electron scattering, namely, the…
First-principles calculations are made for the primary pyroelectric coefficients of wurtzite GaN and ZnO. The pyroelectricity is attributed to the quasiharmonic thermal shifts of internal strains (internal displacements of cations and anions carrying their Born effective charges). The primary (zero-external-strain) pyroelectricity dominates at low temperatures, while the secondary pyroelectricity (the correction from external thermal strains) becomes comparable with the primary pyroelectricity at high temperatures. Contributions from the acoustic and the optical phonon modes to the primary pyr…
We are the first to report the frequency response and corresponding current density of a wurtzite phase Indium Nitride (InN)-based vertical configuration Gunn diode at 1 μm active length. Domain growths dynamics with respect to space and time, variation of domain velocity and the field outside the vicinity of the domain with respect to domain field have also been studied using the presented mathematical equations. It has been found that, InN-based Gunn diodes are capable to operate around 224 GHz with 691 kA/cm2 current density at 300 K. For comparison purpose, all these characteristics have b…
We have investigated the effect of piezoelectric (PZ) polarization property on group velocity of phonons in binary as well as in ternary wurtzite nitrides. It is found that with the presence of PZ polarization property, the phonon group velocity is modified. The change in phonon group velocity due to PZ polarization effect directly depends on piezoelectric tensor value. Using different piezoelectric tensor values recommended by different workers in the literature, percent change in group velocities of phonons has been estimated. The Debye temperatures and frequencies of binary nitrides GaN, Al…
A simple theoretical method for deducing the effective bond-orbital model (EBOM) of III-nitride wurtzite (WZ) semiconductors is presented. In this model, the interaction parameters for zinc-blende (ZB) structures are used as an initial guess for WZ structure based on the two-center approximation. The electronic band structure of III-nitride WZ semiconductors can hence be produced by utilizing this set of parameters modified to include effects due to three-center integrals and fitting with first-principles calculations. Details of the semi-empirical fitting procedure for constructing the EBOM H…
The spin relaxation time of electrons in GaAs and GaN are determined with a model that includes momentum scattering by phonons and ionized impurities, and spin scattering by the Elliot-Yafet, D'yakonov-Perel, and Bir-Aronov-Pikus mechanisms. Accurate bands generated using a long-range tight-binding Hamiltonian obtained from empirical pseudopotentials are used. The inferred temperature-dependence of the spin relaxation lifetime agrees well with measured values in GaAs. We further show that the spin lifetimes decrease rapidly with injected electrons energy and reach a local maximum at the longit…
Both hexagonal wurtzite and cubic zinc blend GaN phases were synthesized in GaAs by 50 keV N+ implantation at 400 deg C and subsequent annealing at 900 deg C for 15 min in N2 ambient. Crystallographic structural and Raman scattering studies revealed that GaN phases were grown for fluence above 2x1017 cm-2. Temperature-dependent photoluminescence study showed sharp direct band-to-band transition peak ~3.32 eV at temperature <= 200K. The intermediate bandgap value, with respect to ~3.4 eV for hexagonal and ~3.27 eV for cubic phases of GaN is an indicative for the formation of mixed hexagonal and…
The strain field of a dislocation emerging at a free surface is partially relaxed to ensure stress free boundary conditions. We show that this relaxation strain at the outcrop of edge threading dislocations in GaN{0001} gives rise to a piezoelectric volume charge. The electric field produced by this charge distribution is strong enough to dissociate free excitons at distances over 100 nm from the dislocation line. We evaluate the impact of this effect on cathodoluminescence images of dislocations.
We derive an energy-dependent decay-time distribution function from the multi-exponential decay of the ensemble photoluminescence (PL) of InGaN/GaN quantum dots (QDs), which agrees well with recently published single-QD time-resolved PL measurements. Using eight-band k.p modelling, we show that the built-in piezo- and pyroelectric fields within the QDs cause a sensitive dependence of the radiative lifetimes on the exact QD geometry and composition. Moreover, the radiative lifetimes also depend heavily on the composition of the direct surrounding of the QDs. A broad lifetime distribution occurs…
Nitride semiconductors are ubiquitous in optoelectronic devices such as LEDs and Blu-Ray optical disks. A major limitation for further adoption of GaN in power electronics is its low hole mobility. In order to address this challenge, here we investigate the phonon-limited mobility of wurtzite GaN using the ab initio Boltzmann transport formalism, including all electron-phonon scattering processes, spin-orbit coupling, and many-body quasiparticle band structures. We demonstrate that the mobility is dominated by acoustic deformation-potential scattering, and we predict that the hole mobility can…
In the effective-mass approximation, the step-like crystal potential of a wurtzite semiconductor heterostucture should be supplemented by Dirac delta-function heterointerface terms. They stem from the difference in the Bloch functions of the semiconductors and remain finite even for structures with graded chemical composition, where the terms are presented by a smeared Dirac delta function. We find these heterointerface potentials by employing the k*p method, and evaluate their strength from band-structure parameters of bulk materials. These potentials are weak for semiconductors compliant wit…
Machine learning is changing how we design and interpret experiments in materials science. In this work, we show how unsupervised learning, combined with ab initio modeling, improves our understanding of structural metastability in multicomponent alloys. We use the example case of Al-O-N alloys where the formation of aluminum vacancies in wurtzite AlN upon the incorporation of substitutional oxygen can be seen as a general mechanism of solids where crystal symmetry is reduced to stabilize defects. The ideal AlN wurtzite crystal structure occupation cannot be matched due to the presence of an a…
Stable partial dislocation complexes in GaN as charge carrier lifetime modifiers for terahertz device applications by molecular dynamics and first-principle simulations
V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine（乌克兰国家科学院V.拉什卡廖夫半导体物理研究所）；Educational Scientific Institute of High Technologies, Taras Shevchenko National University of Kyiv（基辅塔拉斯舍甫琴科国立大学高等技术教育科学研究所）；National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”（乌克兰国立伊戈尔·西科尔斯基基辅理工学院）；University of Rome “Tor Vergata”（罗马托维尔加塔大学）
