Wurtzite Semiconductors Research Articles

Tight-binding study of the optical properties of GaN/AlN polar and nonpolar quantum wells

The electronic structure of wurtzite semiconductor superlattices (SLs) and quantum wells (QWs) is calculated by using the empirical tight-binding method. The basis used consists of four orbitals per atom (sp3 model), and the calculations include the spin–orbit coupling as well as the strain and electric polarization effects. We focus our study on GaN/AlN QWs wells grown both in polar (C) and nonpolar (A) directions. The band structure, wave functions and optical absorption spectrum are obtained and compared for both cases.

Anisotropy of the momentum matrix element, dichroism, and conduction-band dispersion relation of wurtzite semiconductors

By comparison of calculated imaginary parts of the ordinary and extraordinary dielectric functions of wurtzite semiconductors near the band gap with experimental results, we demonstrate that the interband matrix elements ${E}_{P}^{\ensuremath{\parallel}}$ and ${E}_{P}^{\ensuremath{\perp}}$ of the momentum operator parallel and perpendicular to the optic axis are different. ${E}_{P}^{\ensuremath{\parallel}}$ exceeds ${E}_{P}^{\ensuremath{\perp}}$ and their ratio increases along the series CdSe, CdS, ZnO. The $u$ parameters of GaN, InN, and AlN suggest that the ${E}_{P}^{\ensuremath{\parallel}}/{E}_{P}^{\ensuremath{\perp}}$ ratio should increase along this series as well. We also determined the conduction-band dispersion relation and nonparabolicity, as well as the effective mass, as a function of electron concentration and wave vector for GaN, ZnO, CdS, and CdSe. In addition, optical response due to transitions into exciton-phonon complexes was observed and analyzed. We conclude that up to about ten phonons may participate in such absorption processes in ZnO.

Spin-orbit coupling and crystal-field splitting in the electronic and optical properties of nitride quantum dots with a wurtzite crystal structure

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.

Spontaneous Emission and Characteristics of Staggered InGaN Quantum-Well Light-Emitting Diodes

A novel gain media based on staggered InGaN quantum wells (QWs) grown by metal-organic chemical vapor deposition was demonstrated as improved active region for visible light emitters. Fermi's golden rule indicates that InGaN QW with step-function like In content in the well leads to significantly improved radiative recombination rate and optical gain due to increased electron-hole wavefunction overlap, in comparison to that of conventional InGaN QW. Spontaneous emission spectra of both conventional and staggered InGaN QW were calculated based on energy dispersion and transition matrix element obtained by 6-band k middotp formalism for wurtzite semiconductor, taking into account valence-band-states mixing, strain effects, and polarization-induced electric fields. The calculated spectra for the staggered InGaN QW showed enhancement of radiative recombination rate, which is in good agreement with photoluminescence and cathodoluminescence measurements at emission wavelength regime of 425 and 500 nm. Experimental results of light-emitting diode (LED) structures utilizing staggered InGaN QW also show significant improvement in output power. Staggered InGaN QW allows polarization engineering leading to improved luminescence intensity and LED output power as a result of enhanced radiative recombination rate.

Lattice dynamics of wurtzite and rocksalt AlN under high pressure: Effect of compression on the crystal anisotropy of wurtzite-type semiconductors

Raman spectra of aluminum nitride (AlN) under pressure have been measured up to $25\phantom{\rule{0.3em}{0ex}}\mathrm{GPa}$, i.e., beyond the onset of the wurtzite-to-rocksalt phase transition around $20\phantom{\rule{0.3em}{0ex}}\mathrm{GPa}$. The experimental pressure coefficients for all the Raman-active modes of the wurtzite phase are reported and compared to those obtained from ab initio lattice dynamical calculations, as well as to previous experimental and theoretical results. The pressure coefficients of all the Raman-active modes in wurtzite-type semiconductors (AlN, GaN, InN, ZnO, and BeO), as well as the relatively low bulk modulus and phase transition pressure in wurtzite AlN, are discussed in the light of the pressure dependence of the structural crystal anisotropy in wurtzite semiconductors. On pressure release, AlN partially returns to the wurtzite phase below $1.3\phantom{\rule{0.3em}{0ex}}\mathrm{GPa}$ but the presence of a rocksalt phase in AlN was observed at pressures as low as $1.3\phantom{\rule{0.3em}{0ex}}\mathrm{GPa}$, as evidenced by comparing the experimental Raman spectra to calculated one- and two-phonon densities of states of the rocksalt phase.

Origin of the hot phonon effect in group-III nitrides

Lifetimes of the zone-center ${A}_{1}(\mathrm{LO})$ and higher-${E}_{2}$ modes in group-III-nitride wurtzite semiconductors have been calculated by employing a theoretical treatment of three-phonon and four-phonon processes based on realistic phonon dispersion curves and an elastic continuum model for crystal anharmonicity. The hot phonon effect observed in GaN and InN has been identified to originate from the ineffectiveness of these modes to decay into two or three lower frequency optical modes. This effect is predicted to be significantly reduced in AlGaN and AlInN alloys. Explanations have been forwarded for the observations that the lifetime of the LO mode strongly depends on photoexcited carrier density in GaN and that it follows a weak temperature dependence in $\mathrm{Al}\mathrm{Ga}\mathrm{N}∕\mathrm{Ga}\mathrm{N}$.

Type-II InGaN-GaNAs quantum wells for lasers applications

We present a visible III-nitride gain medium based on type-II InGaN-GaNAs quantum well (QW), employing thin dilute-As (∼3%) GaNAs layer. The utilization of GaNAs layer shifts the hole confinement to the center of the type-II QW, which significantly reduces the charge separation effect. The optical gain and spontaneous recombination rate of the type-II InGaN-GaNAs QW are analyzed and compared with those of conventional InGaN QW emitting in the blue regime (λ∼450nm), using six-band k.p formalism for energy dispersion of the III-nitride wurtzite semiconductor. The use of type-II QW leads to significant improvement in the optical gain and spontaneous recombination rate.

Band structure and optical properties of wurtzite semiconductor nanotubes

We develop a comprehensive theoretical model for the band structure of single-crystal faceted nanotubes of wurtzite semiconductors based on the tight-binding approach. We focus on the GaN nanotube grown along the [0001] direction and surrounded by the equivalent surfaces ${1\overline{1}00}$. We first calculate the band structure of the wurtzite slab of finite thickness grown along the axis $[1\overline{1}00]$. We show that dangling bonds on two surfaces of the slab cause surface bands, which form the conduction and valence bands of the slab. Analyzing the symmetry of the single-crystal faceted nanotubes, we conclude that their band structure can be calculated from that of the slab with the help of cyclic boundary conditions. We show that the spectrum of the nanotubes depends both on the thickness of nanotube walls and on the radius. We further study the absorption coefficient of the nanotubes. We demonstrate that, with decreasing wall thickness, the contribution of surface states to the absorption spectrum becomes more pronounced.

Optical anisotropy in [hkil]-oriented wurtzite semiconductor quantum wells

An 8×8 band edge potential matrix of the [hkil]-oriented wurtzite Hamiltonian is developed and applied to explore optical anisotropy in [hkil]-oriented wurtzite semiconductor quantum wells. The wave-vector-dependent optical matrix elements are expressed entirely in terms of Hamiltonian matrix elements, thus avoiding the requirement to introduce any additional optical parameters. To accommodate the noncubic symmetry of the wurtzite lattice, spinor rotation is taken into account when performing the calculations for different crystal orientations. The optical matrix elements are formulated and calculated for both the real finite-barrier-height case and the approximate infinite-barrier-height case. It is found that giant anisotropy of the optical matrix elements appears in the [101¯0]- and [101¯2]-oriented well planes.

Variational Calculations of Donor Binding Energy in Rectangular Wurtzite Aluminium Gallium Nitride / Gallium Nitride Quantum Wires

AbstractWe present variational calculations of donor binding energy in rectangular wurtzite aluminium gallium nitride / gallium nitride quantum wires. We explicitly take into account the effect of spontaneous and piezoelectric polarization on the energy levels of donors in quantum wires. Wurtzite structure nitride semiconductors have spontaneous polarization even in the absence of externally applied electric fields. They also have large piezoelectric polarization when grown as pseudomorphic layers. The magnitude of both polarization components is of the order of 1013 electrons per cm2, and has a non-trivial effect on the potential profile seen by electrons. Due to the large built-in electric fields resulting from the polarization discontinuities at heterojunctions, the binding energies of donors is a strong function of the position inside the quantum wire. The potential profile in the 0001 direction can vary by as much as 1.5eV due to polarization effects for vertical dimensions of the quantum wire up to 20 angstroms. The probability density of electrons tends to concentrate near the minimum of the conduction band profile in the 0001 direction. Donors located close to this minimum tend to have a larger concentration of electron density compared to those located closer to the maximum. As a consequence, the binding energy of the former are higher compared to the latter. We use Lorentzian variational wavefunctions to calculate the binding energy as a function of donor position. The confinement potential enhances the binding by a factor of about 3 compared to donors in bulk nitride semiconductors, from about 30 meV to about 90 meV. The variation of binding energy with position is calculated to be more than 50% for typical compositions of the quantum wire regions. Our calculations will be useful for understanding device applications involving n-type doped nitride semiconductor quantum wires.

Structural Effects of Transition Metal Oxide Calcinations on Wurtzite Type Semiconductors That are Ferromagnetic at Room Temperature

AbstractGallium nitride powders and zinc oxide powders were each calcined with a few weight percent of copper oxide and/or magnesium oxide either in air or N2. Powder X-ray diffractometry, transmission electron microscopy, energy dispersive X-ray spectroscopy, and electron energy loss spectroscopy were performed in order to observe calcination induced structural effects on these wurtzite type semiconductors. We note that our earlier magnetic results on Cu doped GaN are qualitatively consistent with recent first principle calculations [Wu et al., Appl. Phys. Lett. 89 (2006) 62505].

Interrelation of structural and electronic properties inInxGa1−xN∕GaNquantum dots using an eight-bandk∙pmodel

We present an eight-band $\mathbf{k}∙\mathbf{p}$-model for the calculation of the electronic structure of wurtzite semiconductor quantum dots (QDs) and its application to indium gallium nitride $({\mathrm{In}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{N})$ QDs formed by composition fluctuations in ${\mathrm{In}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{N}$ layers. The eight-band $\mathbf{k}∙\mathbf{p}$-model accounts for strain effects, piezoelectricity and pyroelectricity, and spin-orbit and crystal-field splitting. Exciton binding energies are calculated using the self-consistent Hartree method. Using this model, we studied the electronic properties of ${\mathrm{In}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{N}$ QDs and their dependence on structural properties, i.e., their chemical composition, height, and lateral diameter. We found a dominant influence of the built-in piezoelectric and pyroelectric fields, causing a spatial separation of the bound electron and hole states and a redshift of the exciton transition energies. The single-particle energies as well as the exciton energies depend heavily on the composition and geometry of the QDs.

Surface states of wurtzite semiconductor nanowires with identical lateral facets: A transfer-matrix approach

The focus of this paper is to investigate systematically surface states of semiconductor nanowires of wurtzite crystals with identical lateral surfaces. We first calculate the surface spectrum of a semi-infinite crystal. Then, using cyclic boundary conditions, we calculate the quantized spectrum of the surface states in nanowires. We find that the spectrum of the nanowire surfaces consists of a number of quantized levels inside the band gap. We further study absorption coefficients due to dipole transitions between the surface states in such nanowires. We demonstrate that such transitions lead to absorption above the fundamental band edge transition. Our calculations also show that the absorption coefficient induced by the transitions between the surface states depends weakly on the light polarization.

Electronic structure of ZnO wurtzite quantum wires

The electronic structure and optical properties of ZnO wurtzite quantum wires with radius R >= 3 nm are studied in the framework of six-band effective-mass envelope function theory. The hole effective-mass parameters of ZnO wurtzite material are calculated by the empirical pseudopotential method. It is found that the electron states are either two-fold or four-fold degenerate. There is a dark exciton effect when the radius R of the ZnO quantum wires is in the range of [3,19.1] nm (dark range in our model). The dark ranges of other wurtzite semiconductor quantum wires are calculated for comparison. The dark range becomes smaller when the |Delta(so)| is larger, which also happens in the quantum-dot systems. The linear polarization factor of ZnO quantum wires is larger when the temperature is higher.

Wavefunction engineering of layered wurtzite semiconductors grown along arbitrary crystallographic directions

The electronic band structure of wurtzite semiconductor heterostructures is investigated theoretically using the envelope function k ⋅ P formalism. We use a Lagrangian formulation for the valence bands so that the order of the derivatives appearing in the multiband description is explicitly specified when Schrödinger’s equations for the envelope functions are generated through the application of the principle of least action. The issues of derivative operator ordering and boundary conditions at material interfaces are examined in detail. The theoretical results are presented for arbitrary growth directions and the spin–orbit interaction is taken into account. This is of interest, for example, in treating A -plane wurtzite heterostructures such as GaN/AlGaN quantum wells grown on R -plane sapphire. Strain effects are included using a general rotation method that diagonalizes strain and is appropriate for pseudomorphic wurtzite structures in any allowed orientation. It is shown that inversion asymmetry in the valence band leads to shifts in the band-edge energies in the [ 11 2 ¯ 0 ]-grown quantum wells. The finite element method is used with the Lagrangian for the composite layered semiconductor structure in order to obtain the energy eigenvalues for multi-quantum well systems. Calculations for quantum wells and superlattices are presented.

Ultrafast shift and injection currents observed in wurtzite semiconductors via emitted terahertz radiation

Shift and injection currents are generated in the wurtzite semiconductors CdSe and CdS at 295K using above-band-gap (ℏω>Eg) femtosecond pulses and detected via the emitted terahertz radiation; the optical beams are normally incident on samples with the optic axis in the plane of the surface. For optical intensities up to 75MWcm−2 (or carrier density <1018cm−3) the terahertz radiation amplitude shows the expected linear dependence and also varies with optical polarization and sample orientation consistent with the third-rank tensors that govern the current generation processes in the wurtzite structure. The largest shift currents are generated along the optical axis for light polarized along that axis. In CdSe with ℏω=1.80eV (690nm), the electron shift distance is ∼40% of the 0.25nm bond length and the peak current density is 5kAcm−2 for an optical intensity of 10MWcm−2; for CdS the corresponding experiment at ℏω=3.0eV (410nm) gives a shift distance ∼80% of the 0.26nm bond length with a peak current density of 50kAcm−2 for an incident intensity of 75MWcm−2. For injection current produced in CdSe with circularly polarized 690nm excitation, electrons are injected with an average speed of 9kms−1; this is ∼3% of the group velocity for electrons excited with the same energy. The corresponding values for CdS excited at 410nm are 20kms−1 and 2%. From the temporal characteristics of the terahertz emission for injection currents in CdS we deduce that the electron momentum scattering time is <100fs, consistent with mobility studies.

Large electromechanical response in ZnO and its microscopic origin

The electromechanical coefficient ${d}_{33}$ of wurtzite ZnO is determined by direct first-principles density functional calculations which are performed for solids under finite electric fields. Our theoretical ${d}_{33}$ value of $12.84\phantom{\rule{0.3em}{0ex}}\mathrm{pC}∕\mathrm{N}$ turns out to be in good agreement with experiment. This electromechanical response in ZnO (which is the largest among the known tetrahedral semiconductors) is found to originate from the strong coupling between strain and polarization, namely, a notably large $\ensuremath{\beta}$ parameter. We further show that the electromechanical response in wurtzite semiconductors bears a previously unknown resemblance to the polarization rotation mechanism in ferroelectric $\mathrm{Pb}(\mathrm{Zn}\mathrm{Nb}){\mathrm{O}}_{3}\ensuremath{-}\mathrm{Pb}\mathrm{Ti}{\mathrm{O}}_{3}$ and $\mathrm{Pb}(\mathrm{Mg}\mathrm{Nb}){\mathrm{O}}_{3}\ensuremath{-}\mathrm{Pb}\mathrm{Ti}{\mathrm{O}}_{3}$ single-crystal solid solutions. Our results demonstrate that, different from what is commonly believed, the main effect of electric fields in wurtzite semiconductors is not to elongate the polar chemical bonds, but to rotate those bonds that are non-collinear with the polar axis. This finding also suggests that the electromechanical response in wurtzite materials is governed mainly by the ease of bond bending, which may provide an useful scheme for designing better piezoelectric semiconductors with enhanced performance.

Spin of valence-band holes in wurtzite semiconductors

Spin polarization properties of a ballistic hole in wurtzite semiconductors are analyzed using the concept of spin surface. It is shown that, in general, the spin surface in a three-dimensional spin space has the shape of spheroid whose minor/major axis and orientation depend on a relative strength of the spin-orbit and crystal-field interactions as well as on the hole wave vector direction and length. Analytical expressions for the spin surfaces of heavy-mass, light-mass, and split-off bands were found for two experimentally important cases, when the hole wave vector is parallel and perpendicular to the hexagonal axis. For an arbitrary direction of the wave vector the numerical results are presented which show that the spin surface remains the spheroid in this case as well. However, the surface transforms to a line or sphere at small and large wave vectors. The properties of the spin surfaces are illustrated for valence band parameters of GaN, where the crystal field dominates in the band-edge splitting.

Electronic structure of wurtzite quantum dots with cylindrical symmetry

This paper presents a six-band k∙p theory for wurtzite semiconductor nanostructures with cylindrical symmetry. Our work extends the formulation of Vahala and Sercel [Phys. Rev. Lett. 65 239 (1990)] to the Rashba-Sheka-Pikus Hamiltonian for wurtzite semiconductors, without the need for the axial approximation. Comparisons of our formulation for studying the electronic structure of wurzite quantum dots with the conventional formulation are given.

Hole spin surfaces in wurtzite semiconductors

Spin properties of holes in the wurtzite semiconductors, when the hole with a given wave vector ballistically propagates in either heavy-, light-mass or crystal-field split-off band, are considered. Analytical solutions for an averaged hole spin are found for two important cases, when the hole wave vector is parallel and perpendicular to the hexagonal axis. Shapes of the spin surfaces are presented for these cases. It is shown that the surfaces, in general, are spheroids. However, depending on the wave vector magnitude and valence band parameters, the surfaces may also be spheres or line-shaped. The properties of the spin surfaces are illustrated for parameters of the wurtzite GaN, where the crystal field dominates in the splitting of the valence band.