Bandgaps and band bowing in semiconductor alloys

The bandgap and band bowing parameter of semiconductor alloys are calculated with a fast and realistic approach. The method is a dielectric scaling approximation that is based on a scissor approximation. It adds an energy shift to the bandgap provided by the local density approximation (LDA) of the density functional theory (DFT). The energy shift consists of a material-independent constant weighted by the inverse of the high-frequency dielectric constant. The salient feature of the approach is the fast calculation of the dielectric constant of alloys via the Green function (GF) of the TB-LMTOs (tight-binding linear muffin-tin orbitals) in the atomic sphere approximation (ASA). When it is applied to highly mismatched semiconductor alloys (HMAs) like Zn Te_xSe_1?x, this method provides a band bowing parameter that is different from the band bowing parameter calculated with the LDA due to the bowing exhibited also by the high-frequency dielectric constant.     

Composition dependence of the optical properties and band structure of the zinc-blende ZnS1-xOx: a first principles study

We present first principles calculations of structural, electronic and optical properties of ZnS_1?xO_x in the zinc-blende phase. We employ the full potential linearized augmented plane wave method within the density functional theory in the generalized gradient approximation and Engel–Vosko generalized gradient approximation. Features such as the lattice constant, the bulk modulus and its pressure derivative are reported. The agreement between our calculated results and available experimental and theoretical data is generally good. Direct and indirect energy band gaps as a function of the oxygen composition in the material of interest are presented and discussed. The material under investigation is found to remain a direct band gap semiconductor over all the alloy composition range (0–1). Furthermore, the optical properties such as the dielectric function, the refractive index, the reflectivity and the electron loss energy have also been reported and analysed.     

Colour dielectric model of the proton

A model of the proton with its constituent quarks bound in a colour polarizable medium with dielectric constant varying as (a/r−b ²) from a fixed centre, is presented. The Dirac equation modified by the colour polarization is solved and the analytic expression for the wavefunction of the quarks obtained shows that quarks with higher energy lie closer to the fixed centre. The energy spectrum is equispaced without any continuum. A semiclassical approximation scheme yields closed orbits for quarks which have smaller size for higher energies and no orbits with size bigger than a certain maximum, thereby rendering the quarks permanently confined. The wavefunctions of the three quarks constituting the proton are used to calculate physical parameters of the proton such as its mass, charge radius and weak coupling constant which with suitable choice of the constantsa andb appearing in the dielectric constant agree fairly well with experimental results.     

Electronic and optical properties under pressure effect of alkali metal oxides

We report results of first-principles calculations for the electronic and optical properties under pressure effect of Li₂O, Na₂O, Ki₂O and Rb₂O compounds in the cubic antifluorite structure, using a full relativistic version of the full-potential augmented plane-wave plus local orbitals (FP-APW+lo) method based on density functional theory, within the local density approximation (LDA) and the generalized gradient approximation (GGA). Moreover, the alternative form of GGA proposed by Engel and Vosko (GGA-EV) is also used for band structure calculations. The calculated equilibrium lattices and bulk moduli are in good agreement with the available data. Band structure, density of states, and pressure coefficients of the fundamental energy gap are given. The critical point structure of the frequency dependent complex dielectric function is also calculated and analyzed to identify the optical transitions. The pressure dependence of the static optical dielectric constant is also investigated.     

Quantum chemical studies of the solvation of the hydroxide ion

Abstract

To understand and model the solvation of the hydroxide ion, OH(H₂O)^? _n clusters, n = 1?5, are studied using ab initio quantum chemical techniques, largely at the MP2 level of theory using a double zeta plus polarization functions basis extended by diffuse functions. Energies and vibrational frequencies, together with thermodynamic quantities such as enthalpies, entropies and Gibbs free energies, are computed. This permits comparison with experimental estimates of the successive thermodynamic changes associated with the reaction OH(H₂O)^? _n + H₂O → OH(H₂O)^? _n+1. The theoretical values are in good agreement with experiment. The free energy of hydration of OH^? is modelled by a composite discrete-continuum method where the effects of the first hydration shell (n = 3) are obtained from the gas phase cluster calculation, while the long-range effects are modelled using self consistent reaction field theory, namely by calculating the solvation energy of OH(H₂O)^? _n in a dielectric continuum. The best estimate of the solvation (free) energy at 298 K is ?84·5 kcal mol^?1, compared to the experimental value of ?102·8 kcal mol^?1.     

Electron-phonon interaction in polar solids with application to the tungsten bronzes

We investigate the interaction between electrons and lattice vibrations in polar solids taking into account their microscopic dielectric properties and constructing in a semi-phenomenological manner the nonlocal dielectric function, ?_GG'(q). The results of earlier, phenomenological theories, such as the Clausius-Mossotti formula for the macroscopic screening constant and Fröhlich's electron-phonon coupling parameter α are obtained from the RPA dielectric function when the dipole approximation is used to calculate the screening by the strongly localized valence electrons. For polar metals we also consider the screening by the free conduction electrons. We present and discuss the results of the screened electron-phonon interaction as a function of the phonon wavevector q for the sodium tungsten bronzes.     

Casimir amplitudes in a quantum spherical model with long-range interaction

A d-dimensional quantum model system confined to a general hypercubical geometry with linear spatial size L and “temporal size” 1/T ( T - temperature of the system) is considered in the spherical approximation under periodic boundary conditions. For a film geometry in different space dimensions , where is a parameter controlling the decay of the long-range interaction, the free energy and the Casimir amplitudes are given. We have proven that, if , the Casimir amplitude of the model, characterizing the leading temperature corrections to its ground state, is . The last implies that the universal constant of the model remains the same for both short, as well as long-range interactions, if one takes the normalization factor for the Gaussian model to be such that . This is a generalization to the case of long-range interaction of the well-known result due to Sachdev. That constant differs from the corresponding one characterizing the leading finite-size corrections at zero temperature which for is . Received 3 June 1999 and Received in final form 16 August 1999     

Theory of polar fluids. I

We examine a classical fluid composed of molecules which contain a polarizable electric dipole with finite permanent moment. The long-ranged dipolar and the short-ranged interactions are treated on a different footing by expanding relative to a reference system characterized by the absence of electrostatic interactions. Extensions of graph theoretical techniques developed in an earlier paper are used to analyse the pair distribution function and the dielectric constant. Reduction of the number of graphs and their complexity is effected by introducing renormalizations of the permanent moment and the polarizability. The analysis leads to the definition of a new function w(12), which is free of terms dependent on the shape of the sample. For polar, polarizable molecules the direct correlation function lacks translational invariance; its role as a basic quantity is ceded to w(12). The pair distribution function and the dielectric constant ε are expressed in terms of w(12) and two closely related functions. Attention is drawn to an unsolved problem in dielectric theory, and an alternative formula for ε is presented in the form of a conjecture. An approximation for ε is formulated for the case in which the short-ranged non-dipolar interactions are independent of the molecular orientations. A simplified version is solved analytically.     

Estimation of the influence of ionic dielectricity on the dynamic superconducting order parameter

We consider the influence of an ω-dependent ionic dielectric constant ?(ω) on the properties of a superconductor. Assuming that the pairing interaction is proportional to ?² we have solved the Eliashberg equations for this case, both for imaginary and real frequencies. The interaction potential depends on a coupling constant λ and on a longitudinal phonon frequency Ω. The dielectric constant is assumed to be independent of wavevector q, and to depend on frequency through the expression: ?(ω) = (ω² - ω²_long)/(ω² - ω²_trans), where ω_long, ω_trans are the frequencies of optical phonons of the dielectric. We find that along the imaginary frequency axis (but not for real frequencies) the weighted phonon propagator can be modeled by an appropriate choice of a cutoff frequency and an effective coupling constant. The influence of ?(ω) on T_c, the gap δ(ω), and the renormalization function Z(ω) are studied and it is found that these quantities increase significantly with the dielectric constant.     

Thermodynamics of the neutral Hubbard model

By use of Bogoljubov's variational principle the free energy of the neutral Hubbard model is calculated as a function of the total spinS _z . A transition from an antiferro-magnetic to a paramagnetic phase is found for all values of the coupling constantV ₀. The calculations are performed for the simple cubic and the body-centred cubic lattice; some numerical results are given for the transition temperature, the free energy, the sublattice magnetization, the transversal magnetic susceptibility and the response to a finite magnetic field.     

Structural,electronic and optical properties of Ca3Bi2: First-principles investigation

In this work by applying first principles calculations structural, electronic and optical properties of Ca₃Bi₂ compound in hexagonal and cubic phases are studied within the framework of the density functional theory using the full potential linearized augmented plane wave (FP-LAPW) approach. According to our study band gap for Ca₃Bi₂ in hexagonal phase are 0.47, 0.96 and 1?eV within the PBE-GGA, EV-GGA and mBJ-GGA, respectively. The corresponding values for cubic phase are 1.24, 2.08 and 2.14?eV, respectively. The effects of hydrostatic pressure on the behavior of the electronic properties such as band gap, valence bandwidths and anti-symmetry gap are investigated. It is found that the hydrostatic pressure increases the band widths of all bands below the Fermi energy while it decreases the band gap and the anti-symmetry gap. In our calculations, the dielectric tensor is derived within the random phase approximation (RPA). The first absorption peak in imaginary part of dielectric function for both phases is located in the energy range 2.0–2.5?eV which are beneficial to practical applications in optoelectronic devices in the visible spectral range. For instance, hexagonal phase of Ca₃Bi₂ with a band gap around 1?eV can be applied for photovoltaic application and cubic phase with a band gap of 2?eV can be used for water splitting application. Moreover, we found the optical spectra of hexagonal phase are anisotropic along E||x and E||z.     

Defect influence on charge transport in chalcogenide glasses

Abstract

Conductivity of chalcogenide glasses was measured as a function of temperature (290–340 K) and frequency (10^?4–10^?1 Hz). Frequency dependence of conductivity can be approximated by a power law G～ω^s (S < 1). The relaxation maximum of dielectric losses was found. The dielectric constant ? decreases with frequency rise. The obtained results are discussed in terms of the defect structure model.     

Colloidal dipolar interactions in 2D smectic-C films

We use a two-dimensional (2D) elastic free energy to calculate the effective interaction between two circular disks immersed in smectic-C films. For strong homeotropic anchoring, the distortion of the director field caused by the disks generates topological defects that induce an effective interaction between the disks. We use finite elements, with adaptive meshing, to minimize the 2D elastic free energy. The method is shown to be accurate and efficient for inhomogeneities on the length scales set by the disks and the defects, that differ by up to 3 orders of magnitude. We compute the effective interaction between two disk-defect pairs in a simple (linear) configuration. For large disk separations, D, the elastic free energy scales as ∼D ^-2, confirming the dipolar character of the long-range effective interaction. For small D the energy exhibits a pronounced minimum. The lowest energy corresponds to a symmetrical configuration of the disk-defect pairs, with the inner defect at the mid-point between the disks. The disks are separated by a distance that is twice the distance of the outer defect from the nearest disk. The latter is identical to the equilibrium distance of a defect nucleated by an isolated disk. Received 26 October 2001 and Received in final form 14 December 2001     

Static dielectric constant of disordered organic quasi one-dimensional conductors: Localization by defects

We have measured the low temperature dielectric constant ? of two similar quasi one-dimensional organic conductors, N-Me-iso Qn(TCNQ)₂ and Qn(TCNQ)₂. For N-Me-iso Qn(TCNQ)₂ below 10 K, ? is independent of temperature and is frequency independent in the range 5 × 10⁵ Hz to 9 × 10⁹ Hz, within the 50% experimental uncertainty. Thus we believe the low temperature microwave dielectric constant to be a good approximation of the static value in this salt. For Qn(TCNQ)₂ at low temperatures, the relation ? ∝ (c+c₀)^-2 holds, where c is the defect concentration and c₀ is an effective defect concentration of the nominally pure material. This relation is predicted by the model of interrupted metallic strands with energy spacings larger than kT, and it indicates that electrons are strongly localized by defects along the conducting chains.     

A relativistic coupled-cluster interaction potential and rovibrational constants for the xenon dimer

An accurate potential energy curve has been derived for the xenon dimer using state-of-the-art relativistic coupled-cluster theory up to quadruple excitations accounting for both basis set superposition and incompleteness errors. The data obtained is fitted to a computationally efficient extended Lennard-Jones potential form and to a modified Tang–Toennies potential function treating the short- and long-range part separately. The vibrational spectrum of Xe₂ obtained from a numerical solution of the rovibrational Schrödinger equation and subsequently derived spectroscopic constants are in excellent agreement with experimental values. We further present solid-state calculations for xenon using a static many-body expansion up to fourth-order in the xenon interaction potential including dynamic effects within the Einstein approximation. Again we find very good agreement with the experimental (face-centred cubic) lattice constant and cohesive energy.     

Order–disorder transformation of the O phase in Ti2AlNb alloys

The free energy of the O₂ (Ti₂AlNb) phase, based on the Gorsky–Bragg–Williams (G–B–W) approximation considering nearest-neighbour interactions, has been utilized to derive expressions for the transition and instability temperatures. The relations among the long-range order parameter, transformation temperatures and free energy as a function of the concentrations of Al and Nb have been established. The results are compared with those of earlier experimental and theoretical investigations.     

On the validity of the capillarity approximation in the rate theory of homogeneous nucleation

An Einstein model is used to calculate the internal vibrational free energy of approximately spherical fcc crystallites as a function of crystallite size at T/θ = 1. It is found that the free energy per surface atom does not become convergent until a size of about 3 × 10⁷ atoms is reached. The excess free energy at convergence is used to define the macroscopic surface tension for use in the capillarity approximation. The internal free energy of microcrystallites containing of the order of 100 atoms is fortuitously well described by the capillarity approximation. A good estimate of the total free energy of the microcrystallite (nucleus) is obtained from the capillarity approximation only by adding the contributions from free translation and rotation and the replacement partition function.     

Mode-coupling theory for the dynamics of tunnelling systems in dielectrics

A mode-coupling theory (MCT) is presented for the spin-boson model with a spectral density which accounts for a heat bath made up of lattice vibrations of a dielectric solid (superohmic dissipation). A usual decoupling approximation provides a set of non-linear integral equations which are solved both numerically by iteration on a computer and analytically by means of a frequency dependent ansatz for the memory functions. There is a transition to incoherent motion at a temperatureT ^* where the bare two-level energy is equal to the damping rate, in contradiction to results obtained previously from a path integral formulation. The discrepancy arises since in the MCT the relevant self-energy function does not exhibit a 1/z-pole atz=0. For tunnelling systems in dielectrics this yields a new relaxation mechanism due to incoherent tunnelling: the present results might require to modify some of the basic assumptions of the standard tunnelling model for dielectric glasses.     

The limitimg behaviour of the well width of a quantum two-dimensional metal–insulator transition

Metal–Insulator transition using an exact two-dimensional (2D) dielectric function is investigated for a shallow donor in an isolated well of a GaAs/Ga_1−xAl_sAs superlattice system within the effective mass approximation. Vanishing of the donor ionization energy as a function of well width and the donor concentration suggests that a phase transition is not possible even below a well width of 10 Å, supporting the scaling theory of localization. The effects of Anderson localization, exchange and correlation in the Hubbard model are included in a simple way. The relationship between the present model and the Mott criterion in terms of Hubbard model is also brought out. The critical concentration appears to be enhanced when a random distribution of impurities is considered. The limiting behaviour of the well width for a quantum 2D well is brought out. A simple expression is derived for a Mott constant in 2D, a*N_c^1/2 exp (9.86 exp (−L/a*))=0.123, where N_c is the critical concentration per area. Results are compared with the existing data available and discussed in the light of existing literature.