There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

The semiconductor ZnO has gained substantial interest in the research community in part because of its large exciton binding energy (60meV) which could lead to lasing action based on exciton recombination even above room temperature. Even though research focusing on ZnO goes back many decades, the renewed interest is fueled by availability of high-quality substrates and reports of p-type conduction and ferromagnetic behavior when doped with transitions metals, both of which remain controversial. It is this renewed interest in ZnO which forms the basis of this review. As mentioned already, ZnO is not new to the semiconductor field, with studies of its lattice parameter dating back to 1935 by Bunn [Proc. Phys. Soc. London 47, 836 (1935)], studies of its vibrational properties with Raman scattering in 1966 by Damen et al. [Phys. Rev. 142, 570 (1966)], detailed optical studies in 1954 by Mollwo [Z. Angew. Phys. 6, 257 (1954)], and its growth by chemical-vapor transport in 1970 by Galli and Coker [Appl. Phys. ...

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A comprehensive review of zno materials and devices

This article reviews the current status of lattice-dynamical calculations in crystals, using density-functional perturbation theory, with emphasis on the plane-wave pseudopotential method. Several specialized topics are treated, including the implementation for metals, the calculation of the response to macroscopic electric fields and their relevance to long-wavelength vibrations in polar materials, the response to strain deformations, and higher-order responses. The success of this methodology is demonstrated with a number of applications existing in the literature.

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Phonons and related crystal properties from density-functional perturbation theory

We present a comprehensive, up-to-date compilation of band parameters for the technologically important III–V zinc blende and wurtzite compound semiconductors: GaAs, GaSb, GaP, GaN, AlAs, AlSb, AlP, AlN, InAs, InSb, InP, and InN, along with their ternary and quaternary alloys. Based on a review of the existing literature, complete and consistent parameter sets are given for all materials. Emphasizing the quantities required for band structure calculations, we tabulate the direct and indirect energy gaps, spin-orbit, and crystal-field splittings, alloy bowing parameters, effective masses for electrons, heavy, light, and split-off holes, Luttinger parameters, interband momentum matrix elements, and deformation potentials, including temperature and alloy-composition dependences where available. Heterostructure band offsets are also given, on an absolute scale that allows any material to be aligned relative to any other.

Band parameters for III–V compound semiconductors and their alloys

The absolute energy positions of conduction and valence band edges were compiled for about 50 each semiconducting metal oxide and metal sulfide minerals. The relationships between energy levels at mineral semiconductor-electrolyte interfaces and the activities of these minerals as a catalyst or photocatalyst in aqueous redox reactions are reviewed. The compilation of band edge energies is based on experimental flatband potential data and complementary empirical calculations from electronegativities of constituent elements. Whereas most metal oxide semiconductors have valence band edges 1 to 3 eV below the H2O oxidation potential (relative to absolute vacuum scale), energies for conduction band edges are close to, or lower than, the H2O reduction potential. These oxide minerals are strong photo-oxidation catalysts in aqueous solutions, but are limited in their reducing power. Non-transition metal sulfides generally have higher conduction and valence band edge energies than metal oxides; therefore, valence band holes in non-transition metal sulfides are less oxidizing, but conduction band electrons are exceedingly reducing. Most transition-metal sulfides, however, are characterized by small band gaps (<1 eV) and band edges situated within or close to the H2O stability potentials. Hence, both the oxidizing power of the valence band holes and the reducing power of the conduction band electrons are lower than those of non-transition metal sulfides.

The absolute energy positions of conduction and valence bands of selected semiconducting minerals

The elastic constants of GaN have been determined using Brillouin scattering; in GPa they are: C11=390,  C33=398,  C44=105,  C66=123,  C12=145,  and   C13=106. Our values differ substantially from those quoted in the literature which were obtained from the determination of mean square displacement of atoms measured by x‐ray diffraction.

Elastic constants of gallium nitride

Gallium nitride was studied by Raman scattering and x-ray-absorption spectroscopy up to 60 GPa. A high-pressure structural phase transition was observed in gallium nitride at 47 GPa by means of Raman scattering and x-ray-absorption spectroscopy. We also report the direct determination of the bulk modulus ${\mathit{B}}_{0}$ of this compound (245 GPa). Gr\"uneisen parameters of the four observed phonon modes were established. The transition pressure is compared with existing calculations.

Raman scattering and x-ray-absorption spectroscopy in gallium nitride under high pressure.

The high-pressure behavior of optical phonons in wurtzite zinc oxide $(w\ensuremath{-}\mathrm{ZnO})$ is studied using room-temperature Raman spectroscopy and ab initio calculations based on a plane-wave pseudopotential method within the density-functional theory. The pressure dependence of the zone-center phonons ${(E}_{2},{A}_{1},$ and ${E}_{1})$ was measured for the wurtzite structure up to the $\mathrm{hexagonal}\ensuremath{\rightarrow}\mathrm{cubic}$ transition near 9 GPa. Above this pressure no active mode was observed. The only negative Gr\"uneisen parameter is that of the ${E}_{2}^{\mathrm{low}}$ mode. ${E}_{1}(\mathrm{LO})$ and (TO) frequencies increase with increasing pressure. The corresponding perpendicular tensor component of the Born's transverse dynamic charge ${e}_{T}^{*}$ is experimentally found to increase under compression like ${e}_{T}^{*}(P)=2.02+6.4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}P,$ whereas calculations give ${e}_{T}^{*}(P)=2.09--2.5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}P$ (in units of the elementary charge e, P in GPa). In both cases, the pressure variation is small, indicating a weak dependence of the bond ionicity with pressure. The pressure dependence of the optical mode energies is also compared with the prediction of a model that treats the wurtzite-to-rocksalt transition as an homogeneous shear strain. There is no evidence of an anomaly in the ${E}_{2}$ and ${A}_{1}$ mode behaviors before the phase transition.

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High-pressure Raman spectroscopy study of wurtzite ZnO

Pressure-induced coordination changes in crystalline and vitreous GeO2.

Using Brillouin scattering the three independent elastic stiffness constants cij of single‐crystal cubic boron nitride have been measured: c11=820, c12=190, and c44=480 GPa. The resulting bulk modulus, 400 GPa, is in reasonable agreement with two independent determinations obtained from x‐ray measurements in a diamond anvil cell. Using the bulk modulus it is found that the x‐ray results are best fitted with a value of dB/dP=3.0.

Alain Polian

Papers

Elastic constants of gallium nitride

Raman scattering and x-ray-absorption spectroscopy in gallium nitride under high pressure.

High-pressure Raman spectroscopy study of wurtzite ZnO

Pressure-induced coordination changes in crystalline and vitreous GeO2.

Elastic constants of boron nitride