Electron-phonon relaxation and excited electron distribution in gallium nitride

We develop a theory of energy relaxation in semiconductors and insulators highly excited by the long-acting external irradiation. We derive the equation for the non-equilibrium distribution function of excited electrons. The solution for this function breaks up into the sum of two contributions. The low-energy contribution is concentrated in a narrow range near the bottom of the conduction band. It has the typical form of a Fermi distribution with an effective temperature and chemical potential. The effective temperature and chemical potential in this low-energy term are determined by the intensity of carriers' generation, the speed of electron-phonon relaxation, rates of inter-band recombination and electron capture on the defects. In addition, there is a substantial high-energy correction. This high-energy 'tail' covers largely the conduction band. The shape of the high-energy 'tail' strongly depends on the rate of electron-phonon relaxation but does not depend on the rates of recombination and trapping. We apply the theory to the calculation of a non-equilibrium distribution of electrons in irradiated GaN. Probabilities of optical excitations from the valence to conduction band and electron-phonon coupling probabilities in GaN were calculated by the density functional perturbation theory. Our calculation of both parts of distribution function in gallium nitride shows that when the speed of electron-phonon scattering is comparable with the rate of recombination and trapping then the contribution of the non-Fermi 'tail' is comparable with that of the low-energy Fermi-like component. So the high-energy contribution can affect essentially the charge transport in the irradiated and highly doped semiconductors.Comment: 15 pages, 6 figure

An efficient method for energy levels calculation using full symmetry and exact kinetic energy operator: Tetrahedral molecules

A simultaneous use of the full molecular symmetry and of an exact kinetic energy operator (KEO) is of key importance for accurate predictions of vibrational levels at a high energy range from a potential energy surface (PES). An efficient method that permits a fast convergence of variational calculations would allow iterative optimization of the PES parameters using experimental data. In this work, we propose such a method applied to tetrahedral AB4 molecules for which a use of high symmetry is crucial for vibrational calculations. A symmetry-adapted contracted angular basis set for six redundant angles is introduced. Simple formulas using this basis set for explicit calculation of the angular matrix elements of KEO and PES are reported. The symmetric form (six redundant angles) of vibrational KEO without the sin(q)−2 type singularity is derived. The efficient recursive algorithm based on the tensorial formalism is used for the calculation of vibrational matrix elements. A good basis set convergence for the calculations of vibrational levels of the CH4 molecule is demonstrated

First fully ab initio potential energy surface of methane with a spectroscopic accuracy

Full 9-dimensional ab initio potential energy surfaces for the methane molecule are constructed using extended electronic structure coupled-cluster calculations with various series of basis sets following increasing X cardinal numbers: cc-pVXZ (X = 3, 4, 5, 6), aug-cc-ACVXZ (X = 3, 4, 5), and cc-pCVXZ-F12 (X = 3, 4). High-order dynamic electron correlations including triple and quadrupole excitations as well as relativistic and diagonal Born-Oppenheimer breakdown corrections were accounted for. Analytical potential functions are parametrized as non-polynomial expansions in internal coordinates in irreducible tensor representation. Vibrational energy levels are reported using global variational nuclear motion calculations with exact kinetic energy operator and a full account of the tetrahedral symmetry of CH4. Our best ab initio surface including above-mentioned contributions provides the rms (obs.-calc.) errors of less than 0.11 cm−1 for vibrational band centers below 4700 cm−1, and ∼0.3 cm−1 for all 229 assigned experimentally determined vibrational levels up to the Icosad range <7900 cm−1 without empirically adjusted parameters. These results improve the accuracy of ab initio methane vibrational predictions by more than an order of magnitude with respect to previous works. This is an unprecedented accuracy of first-principles calculations of a five-atomic molecule for such a large data set. New ab initio potential results in significantly better band center predictions even in comparison with best available empirically corrected potential energy surfaces. The issues related to the basis set extrapolation and an additivity of various corrections at this level of accuracy are discussed

Theoretical hot methane line lists up to T=2000 K for astrophysical applications

The paper describes the construction of complete sets of hot methane lines based on accurate ab initio potential and dipole moment surfaces and extensive first-principle calculations. Four line lists spanning the [0–5000] cm−1 infrared region were built at T = 500, 1000, 1500, and 2000 K. For each of these four temperatures, we have constructed two versions of line lists: a version for high-resolution applications containing strong and medium lines and a full version appropriate for low-resolution opacity calculations. A comparison with available empirical databases is discussed in detail for both cold and hot bands giving a very good agreement for line positions, typically 10−29 cm mol−1. These new lists are expected to be quantitatively accurate with respect to the precision of available and currently planned observations of astrophysical objects with improved spectral resolution

Hole-phonon relaxation and photocatalytic properties of titanium dioxide and zinc oxide: first-principles approach

This is an open access article distributed under the Creative Commons Attribution License.First-principles calculations for the temporal characteristics of hole-phonon relaxation in the valence band of titanium dioxide and zinc oxide have been performed. A first-principles method for the calculations of the quasistationary distribution function of holes has been developed. The results show that the quasistationary distribution of the holes in TiO2 extends to an energy level approximately 1 eV below the top of the valence band. This conclusion in turn helps to elucidate the origin of the spectral dependence of the photocatalytic activity of TiO2. Analysis of the analogous data for ZnO shows that in this material spectral dependence of photocatalytic activity in the oxidative reactions is unlikely.The authors acknowledge financial support from the Spanish MICINN (Grant no. FIS2010-19609-C02-01), the Departamento de Educacíon del Gobierno Vasco, the University of the Basque Country (Grant no. GIC07-IT-366-07), and the Presidium of the Ural Branch of Russian Academy of Sciences (Grant no. 12-U-3-1001).Peer Reviewe

First theoretical global line lists of ethylene (12C2H4) spectra for the temperature range 50-700 K in the far-infrared for quantification of absorption and emission in planetary atmospheres

We present the construction of complete and comprehensive ethylene line lists for the temperatures 50−700 K based on accurate ab initio potential and dipole moment surfaces and extensive first-principle calculations. Three lists spanning the [0−6400] cm-1 infrared region were built at T = 80, 160, and 296 K, and two lists in the range [0−5200] cm-1 were built at 500 and 700 K. For each of these five temperatures, we considered possible convergence problems to ensure reliable opacity calculations. Our final list at 700 K was computed up to J = 71 and contains almost 60 million lines for intensities I > 5 × 10-27 cm/molecule. Comparisons with experimental spectra carried out in this study showed that for the most active infrared bands, the accuracy of band centers in our theoretical lists is better on average than 0.3 cm-1, and the integrated absorbance errors in the intervals relevant for spectral analyses are about 1−3%. These lists can be applied to simulations of absorption and emission spectra, radiative and non-LTE processes, and opacity calculations for planetary and astrophysical applications