Wurtzite GaN Crystals Research Articles

Introduction of localized spin-state transitions in the optical absorption spectrum of Cr-doped GaN

Using a hybrid density functional, we study the electronic, magnetic, and neutral excitations of the paradigmatic Cr-doped GaN solid. Our results indicate that the $\ensuremath{\approx}1$% doped wurtzite GaN crystal retains the semiconducting nature of the host, associated with a magnetic moment of 3 ${\ensuremath{\mu}}_{B}$. As a consequence of Cr doping, additional hybridized bands are formed within the intrinsic band gap of GaN, leading to a considerable band gap narrowing by 1.4 eV and low-energy optical transitions. Our results indicate dark Cr $d\text{\ensuremath{-}}d$ transitions at very low energy (0.5--0.7 eV), followed by bright transitions in the visible energy range (1.8--2.2 eV). Characterization of the electron-hole pairs suggests that the latter originates from the internal transitions among hybridized ${\mathrm{Cr}}_{d}\text{--}{\mathrm{N}}_{p}$ states. With the existence of these additional optical features within the visible energy window, one can expect an enhancement to the photoelectric conversion efficiency of GaN upon Cr doping, in addition to applications in spintronics.

Mean Free Path–Thermal Conductivity Accumulation Calculations for Wurtzite Gallium Nitride: Two Approaches

ABSTRACT Understanding the mean free path distribution of the dominant heat carriers is very important in determining the ballistic to diffusive heat transport transition in nanoscale devices. This is true for the high electron mobility transistors made from GaN where both the thickness of the buffer layer and localized heating causing ballistic-diffusive heat transfer may complicate the transport properties needed to describe the device thermal response. In this work, we obtain the mean free path–thermal conductivity relation of phonons in bulk wurtzite GaN crystals using two different, ab-initio-based calculations. While the Vienna Ab-initio Simulation Package (VASP) is used in both approaches at the initial stage, the first method does not calculate the third-order force constants (FCs) and approximates the anharmonicity with a single fitting parameter in determination of discrete phonon properties thermal conductivity and relaxation time, while the second method uses third-order force constants directly. Results show that the third-order FCs are important in modeling the contribution of high-frequency optical phonons with relatively short MFPs, to the thermal conductivity of the material. Yet these effects are more significant at high temperatures and at samples without crystallographic disorders, and they can be omitted while modeling the real samples at low temperatures.

Influence of Pressure on the Mechanical and Electronic Properties of Wurtzite and Zinc-Blende GaN Crystals

The mechanical and electronic properties of two GaN crystals, wurtzite and zinc-blende GaN, under various hydrostatic pressures were investigated using first principles calculations. The results show that the lattice constants of the two GaN crystals calculated in this study are close to previous experimental results, and the two GaN crystals are stable under hydrostatic pressures up to 40 GPa. The pressure presents extremely similar trend effect on the volumes of unit cells and average Ga-N bond lengths of the two GaN crystals. The bulk modulus increases while the shear modulus decreases with the increase in pressure, resulting in the significant increase of the ratios of bulk moduli to shear moduli for the two GaN polycrystals. Different with the monotonic changes of bulk and shear moduli, the elastic moduli of the two GaN polycrystals may increase at first and then decrease with increasing pressure. The two GaN crystals are brittle materials at zero pressure, while they may exhibit ductile behaviour under high pressures. Moreover, the increase in pressure raises the elastic anisotropy of GaN crystals, and the anisotropy factors of the two GaN single crystals are quite different. Different with the obvious directional dependences of elastic modulus, shear modulus and Poisson’s ratio of the two GaN single crystals, there is no anisotropy for bulk modulus, especially for that of zinc-blende GaN. Furthermore, the band gaps of GaN crystals increase with increasing pressure, and zinc-blende GaN has a larger pressure coefficient. To further understand the pressure effect on the band gap, the band structure and density of states (DOSs) of GaN crystals were also analysed in this study.

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.

Fabrication of GaN hexagonal cones by inductively coupled plasma reactive ion etching

There is a growing demand for the patterning of gallium nitride for light extraction/absorption to improve the performance of photoelectric devices. In this paper, hexagonal cones were fabricated on Ga-polar GaN substrates using the inductively coupled plasma reactive ion etching method. It was found that the etch rate of different crystal faces could be altered by changing the ratio of BCl3 to Cl2 in the reactive gas mixture, which enabled hexagonal cone structures to be fabricated on the wurtzite GaN crystal. The mechanism of the GaN hexagonal cone formation was analyzed based on physical sputtering and chemical reaction, wherein the physical sputtering by heavy radicals assisted the bond breaking and the chemical erosion by Cl radicals that preferentially etched specific crystal planes. The hexagonal cones can be used on light-emitting diodes, photovoltaic devices, and for site control of quantum dots.

Electron band bending of polar, semipolar and non-polar GaN surfaces

The magnitudes of the surface band bending have been determined by X-ray photoelectron spectroscopy for polar, semipolar, and non-polar surfaces of wurtzite GaN crystals. All surfaces have been prepared from crystalline GaN samples grown by the hydride-vapour phase epitaxy and separated from sapphire substrates. The Ga 3d core level peak shifts have been used for band bending determination. Small band bending magnitudes and also relatively small difference between the band bendings of the surfaces with opposite polarity have been found. These results point to the presence of electron surface states of different amounts and types on surfaces of different polarity and confirm the important role of the electron surface states in compensation of the bound surface polarity charges in wurtzite GaN crystals.

First-principles study of migration mechanisms and diffusion of carbon in GaN

Carbon related defects are readily incorporated in GaN due to its abundance during growth both with MBE and CVD techniques. Employing first-principles calculations we compute the migration barrier of neutral carbon interstitials in the wurtzite GaN crystal. The Minimum Energy Path (MEP) and the migration barriers of these defects are obtained using the Nudged Elastic Band (NEB) method with the climbing image modification (CI-NEB). In addition, the Dimer method is used to verify the results. The results yield a quantitative description of carbon diffusion in the crystal allowing for the determination of the most probable migration paths.

Polarity of GaN with polar {0001} and semipolar , , orientations by x-ray photoelectron diffraction

Abstract

Dependence on pressure of the refractive indices of wurtzite ZnO, GaN, and AlN

We have measured both the ordinary and extraordinary refractive index of $m$-plane cuts of wurtzite ZnO, GaN, and AlN single crystals at room temperature and as a function of hydrostatic pressure up to 8 GPa. For that purpose we have developed an alternative optical interference method, called bisected-beam method, which leads, in general, to high contrast interference fringes. Its main feature, however, is to be particularly suitable for high pressure experiments with the diamond anvil cell, when the refractive index of the sample is low and similar to that of diamond and/or the pressure transmitting medium, as is the case here. For all three wide-gap materials we observe a monotonous decrease of the ordinary and extraordinary refractive indices with increasing pressure, being most pronounced for GaN, less marked for ZnO, and the smallest for AlN. The frequency dependence of the refractive indices was extrapolated to zero energy using a critical-point-plus-Lorentz-oscillator model of the ordinary and extraordinary dielectric function. In this way, we determined the variation with pressure of the electronic part (no-phonon contribution) of the static dielectric constant ${\ensuremath{\varepsilon}}_{\ensuremath{\infty}}$. Its volume derivative, $r=d\phantom{\rule{0.16em}{0ex}}ln{\ensuremath{\varepsilon}}_{\ensuremath{\infty}}/d\phantom{\rule{0.16em}{0ex}}lnV$, serves as single scaling coefficient for comparison with experimental and/or theoretical results for other semiconductors, regarding the pressure effects on the dielectric properties. We have obtained an ordinary/extraordinary average value $\overline{r}$ of 0.49(15) for ZnO, 1.22(9) for GaN, and 0.32(4) for AlN. With the values for the ordinary and extraordinary case being within experimental uncertainty, there is thus no apparent change in dielectric anisotropy under pressure for these wurtzite semiconductors. Results are discussed in terms of the pressure-dependent electronic band structure of the materials.

Hexagonal GaN microdisk with wurtzite/zinc-blende GaN crystal phase nano-heterostructures and high quality zinc-blende GaN crystal layer

We revealed that a hexagonal GaN microdisk exhibiting lasing action at a wavelength of approximately 390 nm has peculiar crystal structures consisting of wurtzite (WZ)/zinc-blende (ZB) GaN crystal phase nano-heterostructures and a high-quality ZB GaN crystal layer. Upon transmission electron microscopy measurement, 5–20 monolayer ZB GaN nanocrystals were observed in the WZ GaN crystals in the microdisk, and approximately 250-nm-thick ZB crystals with no dislocations were observed in the upper part of the microdisk. The result indcates that the optical gain of the lasing action at a wavelength of approximately 390 nm is based on ZB GaN crystals.

Quantum size effect on the luminous properties of excitonic states in a quasi-one-dimensional wurtzite GaN nanowire: Two-parameter variational approach

In order to reflect the anisotropic confined situations of quasi-one-dimensional (Q1D) wurtzite nanowires (NWs) in axial and radial directions and wurtzite GaN crystal, a two-parameter variational approach is brought forward and applied to investigate luminous properties of excitonic states in wurtzite NW systems. Numerical calculations on a GaN NW are performed. The quantum size effect on the excitonic binding energies of ground states, the ground state energies as well as the emission spectra is analyzed in detailed. Both the light hole excitons and heavy hole excitons in wurtzite NWs are taken in account. The calculated excitonic binding energies in the wurtzite GaN NWs are far larger than those in cubic GaAs-based quantum wires with the same radius. This is mainly ascribed to the large effective masses of electron and hole and relatively small dielectric constants in GaN material. The excitons emission wavelengths calculated here qualitatively agree with recent experimental results of exciton luminous spectra in Q1D GaN NWs. This confirmed the reasonability and reliability of the present theoretical scheme and numerical results. The numerical results also show that the two-parameter variational approach is reasonable and necessary for the description of excitonic states in Q1D wurtzite GaN NWs.

Synthesis Porous GaN by Using UV-assisted Electrochemical Etching and Its Optical Studies

The PL of porous GaN sample shows higher intensity with smaller FWHM and red-shifting relative to the as-grown sample. The energy gap for porous GaN sample was smaller compare to the as-grown sample. The SEM surface image of UV-assisted electrochemical etching process is shown a shape and size of pore which was formed on the surface of the GaN, therefore the shape of pores formed was in spherical shape. The size of the pores formed has diameter as small as 85 nm. Two PL peaks were observed in the as-grown and porous GaN sample. For the as-grown GaN, the higher peak was observed at “361.946 nm” and the other at “723.739 nm” which is in UV and red luminescence region respectively. The FWHM is “8.198 nm” at “361.946 nm”. For the porous GaN, the higher peak was observed at “364.235 nm” and at “728.039 nm”, so their FWHM are “4.244 nm” and “8.926 nm” respectively. The peaks of porous sample were red-shifted at “2.289 nm and 4.30 nm” respectively compare to the peaks of the as-grown GaN. PL intensity of the porous samples was observed to be increased. Raman peaks representative to the wurtzite GaN crystal, namely E 2 (low) at 142.426 cm -1 , E 2 (high) at 568.771 cm -1 , and A 1 (LO) at 736.769 cm -1 were clearly observed.

Spatial distribution of defects and the kinetics of nonequilibrium charge carriers in GaN wurtzite crystals doped with Sm, Eu, Er, Tm, and supplementary Zn impurities

By analyzing time-resolved and steady-state photoluminescence spectra, it is established that the spatial distribution of rare-earth ion dopants in wurtzite GaN crystals doped with Sm, Eu, Er, or Tm is governed by the type and concentration of defects in the initial semiconductor matrix as well as by the type of the impurity (its capacity for segregation). Doping with multicharged rare-earth impurities and additionally introduced Zn impurity leads to an intensification of emission. The effect of intensification of emission in the case of n-and p-GaN crystals is considered with the use of the model of isoelectronic traps.

Ab initio calculations on nuclear quadrupole interactions of 69,71Ga and 14N nuclei in GaN of ionic crystal

This paper presents the results of our calculation of nuclear quadrupole coupling constant (NQCC) of 69,71Ga and 14N on wurtzite GaN crystal using the Hartree-Fock Roothaan Molecular Cluster procedure. We employed Ga 4N 4H 18 cluster as well as the (GaN 4) 9− and the (NGa 4) 9+ clusters surrounded by 1160 external Ga 3+ and N 3− ions in 15 Å radius lattice to simulate the covalent bonding and ionic bonding among the constituent atoms in the solid-state system and to calculate the electronic structure and the associated nuclear quadrupole interaction properties of 14N and 69,71Ga. The nuclear quadrupole coupling constant (NQCC) e 2 qQ/h for 69Ga with a value of its Q as 0.168 barns was found to be 2.98 MHz in the (GaN 4) 9− cluster and 34.43 MHz in the Ga 4N 4H 18 cluster. The e 2 qQ/h for the 14N in the (NGa 4) 9+ cluster representing the ionic bonding was found to be 0.0303 MHz using the nuclear quadrupole moment of 14N nucleus as 0.0193 barns. The calculated NQI parameters from the (GaN 4) 9− and the (NGa 4) 9+ clusters agree well with the experimental values indicating the existence of the significant ionic bonding between the constituent atoms in the solid-state system.

On the upper limit of thermal conductivity GaN crystals

The maximal value of thermal conductivity κ max of the perfect wurtzite GaN crystal containing isotopes of natural abundance is estimated. Our upper limit of κ = 4800 W/K m at T max = 32 K is smaller than that calculated by Liu and Balandin κ = 6000 W/K m and higher than that obtained by Slack et al. κ = 3750 W/K m . The phenomenological dependence κ ∝ T − 1.43 obtained by Mion et al. for the temperature interval 300–450 K is extended to 200–300 K. For temperatures higher than T max the best fitting of our experimental data to Callaway’s formula is obtained for Grueneisen’s constant equal to γ = 1.35 .

Sensitization of luminescence of wurtzite GaN crystals doped with Eu and the additionally introduced Zn impurity

A possibility to increase the intensity of intracenter transitions of the Eu ion in GaN crystals is investigated via introduction of the additional impurity to vary the local environment of the rare-earth ion. Wurtzite p-GaN crystals were initially doped with Mg and then with Eu. The introduction of the additional Zn impurity leads to a significant increase in the photoluminescence intensity in the range 3580–4250 A and the long-wavelength spectral range 5400–6237 A. This phenomenon can be attributed to the manifestation of sensitization of luminescence of optically active intracenter f-f transitions of the Eu3+ ion due to the introduction of the additional impurity, which promotes the formation of complexes of the rare-earth ion with a large capture cross-section of charge carriers.

Structural analysis of (Ga,Mn)N epilayers and self-organized dots using MeV ion channeling

Rutherford backscattering (RBS) and particle-induced X-ray emission (PIXE) experiments were performed on (Ga,Mn)N epilayers and self-organized dots grown by plasma-assisted MBE. The combined channeling RBS and Mn PIXE experiments were performed on Ga 0.949 M 0.051 N epilayer, which was confirmed to be of pure diluted phase by X-ray diffraction (XRD) in our previous study, in order to check the presence of Mn atoms in the interstitial site in wurtzite crystal. The axis scan around and axes and the plane scan around (1010) plane revealed that almost all the Mn atoms were in the substitutional site of wurtzite GaN crystal. For self-organized dots of (Ga,Mn)N grown on AlN by MBE, the PIXE spectra were measured and the Mn composition in the dot layer was estimated from the ratio of emission intensity of Mn and Ga K α lines. At a result, it was found that the Mn composition in the dots was higher by two or three times than that in thick epilayers grown with the addition of the same amount of Mn flux.

Theory of magneto-optical properties of excitons in GaN

The magnetoexciton spectrum of wurtzite-type GaN in high magnetic field parallel to the crystal $c$ axis is studied theoretically. The magnetic field dependence of the interband absorption spectra for various polarizations of light is obtained by solving the multisubband exciton equation in the Landau orbitals representation using the Lanczos reduction technique. Our theoretical model takes into account the hexagonal symmetry of the wurtzite GaN crystal and includes the coupling between different valence subbands. It is shown that the proposed method consistently reproduces experimental data in the wide range of magnetic fields. By comparing our results with experimental data we were able to estimate the valence band Luttinger constant $\ensuremath{\kappa}\ensuremath{\approx}0.35$.

Thermoelectric effects in wurtzite GaN and AlxGa1−xN alloys

We have investigated theoretically the thermoelectric effects in wurtzite GaN crystals and AlxGa1−xN alloys. The electron-transport model includes all dominant energy-dependent electron-scattering mechanisms, such as charged dislocation and ionized impurity scattering, polar optical phonon, deformation potential, and piezoelectric acoustic-phonon scattering. The results of the calculation show that GaN-based alloys may have some potential as thermoelectric materials at high temperature. It was found that the thermoelectric figure-of-merit for bulk GaN at T=300K is about 0.0017 while it can reach 0.2 in the thermally resistive Al0.4Ga0.6N alloy at T=1000K. The obtained results agree well with available experimental data. The developed calculation procedure can be used for the optimization of the thermoelectric properties of GaN alloys. The proposed integration of the GaN high-power microwave and optoelectronic devices with the active thermoelectric cooling implemented on the same material system can improve the device performance.

Full-band Monte Carlo study on free electron laser induced impact ionization in wurtzite GaN

We have conducted a computational investigation of electron motion in wurtzite GaN crystal under intense mid-infrared irradiation by a free electron laser, and studied effects of polar-optical-phonon scatterings on electron heating processes.