Quasiparticle Band Gap Research Articles

First-principle calculations of optical properties of wurtzite AlN and GaN

The imaginary part of the dielectric function of wurtzite AlN and GaN has been calculated in the long wavelength limit, using two different first-principle electronic structure methods. The first method is a full-potential linearized augmented plane wave method and the second is a full-potential linear muffin-tin orbital method. From the Kramers–Kronig dispersion relations the real part of the dielectric function has been obtained, taking into account a quasi-particle band-gap correction according to Bechstedt and Del Sole. Absorption due to optical phonons is treated as a delta function in the imaginary part of the dielectric function. Both the longitudinal as well as the transverse components of the dielectric function are presented, showing that the anisotropy is small in these materials. Although we use different correlation potentials in the two methods, the results are similar. We compare our calculated dielectric functions with spectroscopic ellipsometry and reflectance spectra measurements.

On the laser ignition and initiation of explosives

Energetic materials are conventionally ignited by the application of heat to some part of an explosive target. This is most often provided by a flame or by electrical heating using a resistive wire. The material responds by thermally heating and starting a burning zone, which spreads out from the ignition point generating gas. In some cases this zone can accelerate (due to the effect of this gas) into a reactive shock wave, termed detonation. Lasers are used in a variety of applications to thermal heat a range of materials, and thus seem an obvious candidate to trigger chemical reaction in energetic ones. A light pulse offers several advantages over an electrical one, since it may be delivered down a path both immune to electrical effects and chemically stable. Thus, the triggering of safety apparatus (such as the firing of bolts on aircraft exits) represents a major thrust in the development of laser–triggered explosive devices. The energy of the pulse may be used in one of two ways to achieve these effects. In the first, the laser is shone directly upon the chemical medium, which absorbs the light at discrete wavelengths. In the second, it is used to vaporize a metallic flyer that is launched to impact on a target creating a high–pressure zone. Either mechanism starts the required reaction. However, when the pulse is delivered directly to the material, detonation is found to proceed immediately with no transition via burning. This makes the process inexplicable using present concepts. This review will address a range of the experiments conducted and theories developed for this novel field. However, it should be emphasized that the fundamental mechanisms remain to be fully explained making the application both academically stimulating as well as industrially important.

A two-dimensional hot-spot mixer model for phonon-cooled hot electron bolometers

A hot spot model for superconducting hot electron bolometers is presented based on a two-dimensional heat transport equation for electrons and phonons including heat trapping due to quasiparticle bandgap gradients. Skin effect concentrates the RF heating in lateral regions of the bridge and the bias current in the center. A reduction in conversion gain compared to a one-dimensional hot spot model is explained by the RF and bias heating profiles not being identical. An experimentally verified increase of the IF bandwidth from 3.5 GHz to 8 GHz when increasing bias voltage is predicted. IV curves, gain and noise are in very good agreement with measurements.

All-electron projector-augmented-waveGWapproximation: Application to the electronic properties of semiconductors

The so-called $\mathrm{GW}$ approximation (GWA) based on an all-electron full-potential projector-augmented-wave method (PAW) has been implemented. For the screening of the Coulomb interaction W three different plasmon-pole model dielectric function models have been tested, and it is shown that the accuracy of the quasiparticle energies is not sensitive to the details of these models. For the decoupling of the valence and core electrons two different schemes produced quasiparticle energies that differ on average by less than 0.1 eV for Si. This method has been used to study the quasiparticle band structure of some small, medium, and wide-band-gap semiconductors: Si, GaAs, AlAs, InP, ${\mathrm{Mg}}_{2}\mathrm{Si},$ diamond, and the insulator LiCl. Special attention was devoted to the convergence of the self-energy with respect to both the $\mathbf{k}$ points in the Brillouin zone and to the number of reciprocal-space $\mathbf{G}$ vectors. The most important and surprising result is that although the all-electron GWA improves considerably the local-density approximation electronic structure of semiconductors, it does not always provide the correct energy band gaps for small- and medium-band-gap semiconductors as originally inferred from pseudopotential GWA calculations. The discrepancy between the all-electron and pseudopotential quasiparticle band gaps is mainly traced back to differences between the exchange-correlation matrix elements obtained by the two methods.

Quasiparticle Energy Calculations on II(Zn)-VI(O, S, Se) and III(Al,Ga)-V(N) Semiconductors in the Wurtzite Structure

Quasiparticle energies of AlN, GaN, ZnO, ZnS and ZnSe in the wurtzite structure have been calculated by the GW approximation with a full random phase approximation dielectric matrix instead of using plasmon pole approximation. The linear muffin tin orbital basis was used for this work and the d orbitals of the Zn and Ga atoms were treated as valence state explicitly in every case. The calculated quasiparticle band gaps and the semicore levels by the GW method are in good agreements with the experimental values. The electronic energy levels of these five systems calculated using the local density, GW and Hartree-Fock approximations were compared systematically.

Ab initioprediction of the electronic and optical excitations in polythiophene: Isolated chains versus bulk polymer

We calculate the electronic and optical excitations of polythiophene using the GW (G stands for one-electron Green function, W for the screened Coulomb interaction) approximation for the electronic self-energy, and include excitonic effects by solving the electron-hole Bethe-Salpeter equation. Two different situations are studied: excitations on isolated chains and excitations on chains in crystalline polythiophene. The dielectric tensor for the crystalline situation is obtained by modeling the polymer chains as polarizable line objects, with a long-wavelength polarizability tensor obtained from the ab initio polarizability function of the isolated chain. With this model dielectric tensor we construct a screened interaction for the crystalline case, including both intra- and interchain screening. In the crystalline situation both the quasiparticle band gap and the exciton binding energies are drastically reduced in comparison with the isolated chain. However, the optical gap is hardly affected. We expect this result to be relevant for conjugated polymers in general.

Ab InitioCalculation of the Electronic and Optical Excitations in Polythiophene: Effects of Intra- and Interchain Screening

We present an ab initio calculation of the electronic and optical excitations of an isolated polythiophene chain as well as of bulk polythiophene. We use the $\mathrm{GW}$ approximation for the electronic self-energy and include excitonic effects by solving the electron-hole Bethe-Salpeter equation. The inclusion of interchain screening in the case of bulk polythiophene drastically reduces both the quasiparticle band gap and the exciton binding energies, but the optical gap is hardly affected. This finding is relevant for conjugated polymers in general.

Band gaps and quasiparticle energy calculations on ZnO, ZnS, and ZnSe in the zinc-blende structure by theGWapproximation

We have calculated the quasiparticle band gaps of ZnO, ZnS, and ZnSe in zinc-blende structure within the GW approximation using a full random-phase approximation dielectric matrix. The linear muffin-tin orbital basis was used for this calculation and the $3d$ orbitals of the Zn atom were treated as valence band in every case. The calculated band gaps are 3.59, 3.97, and 3.10 eV for ZnO, ZnS, and ZnSe, respectively. The gaps of ZnS and ZnSe are in good agreement with the experimental values and so is the gap of ZnO if we compare it with the experimental optical gap of wurtzite ZnO.

Structural and electronic properties of composite B x C y N z nanotubes and heterojunctions

The structure, stability and electronic properties of composite BxCyNz nanotubes and related heterojunctions have been studied using both ab initio and semi-empirical approaches. Pure BN nanotubes present a very stable quasi particle band gap around 5.5-6.0 eV independent of the tube radius and helicity. The bottom of the conduction bands is controlled by a nearly-free-electronn state localized inside the nanotube, suggesting interesting properties under doping. In the case of nanotubes with BC2N stoichiometry, we show that in the thermodynamic limit the system is driven towards segregation of pure C and BN sections. This demixing significantly affects the electronic properties of such materials. The same process of segregation into BC3 islands is evidenced in the case of B-doped carbon nanotubes. These spontaneous segregation processes lead to the formation of quantum dots or nanotube heterojunctions. In particular, C/BN superlattices or isolated junctions have been investigated as specific examples of the wide variety of electronic devices that can be realized using such nanotubes.

Structural properties and quasiparticle band structure of zirconia

We report ab initio calculations of the structural and quasiparticle properties of ${\mathrm{ZrO}}_{2}$, otherwise known as zirconia. The plane-wave pseudopotential method is used to compute the structural properties of the cubic, tetragonal, and monoclinic phases of zirconia. Oxygen vacancies in the cubic phase are also studied using a supercell approach. The structural parameters, including all internal degrees of freedom of all phases, are relaxed. Excellent agreement is achieved with experiment and with other ab initio calculations available. We compute the quasiparticle band gaps within Hedin's $\mathrm{GW}$ approximation using the method of Hybertsen and Louie, and confirm that the quasiparticle approach can be successfully applied to transition-metal oxides if the core-valence overlap is small. We predict the fundamental gap of pure cubic, tetragonal, and monoclinic zirconia to be 5.55 eV, 6.40 eV, and 5.42 eV, respectively. Within the $\mathrm{GW}$ approximation, the oxygen vacancy state in the cubic phase is found to be nondegenerate, fully occupied, and well separated from the valence and conduction bands, positioned 2.1 eV below the conduction band edge.

Pseudogap formation in the symmetric Anderson lattice model.

We present self-consistent calculations for the self-energy and magnetic susceptibility of the 2D and 3D symmetric Anderson lattice Hamiltonian, in the fluctuation exchange approximation. At high temperatures, strong f-electron scattering leads to broad quasiparticle spectral functions, a reduced quasiparticle band gap, and a metallic density of states. As the temperature is lowered, the spectral functions narrow and a pseudogap forms at the characteristic temperature $T_x$ at which the width of the quasiparticle spectral function at the gap edge is comparable to the renormalized activation energy. For $T << T_x $, the pseudogap is approximately equal to the hybridization gap in the bare band structure. The opening of the pseudogap is clearly apparent in both the spin susceptibility and the compressibility.

Quantum Monte Carlo study of density-functional theory for a semiconducting wire.

We use diffusion quantum Monte Carlo (DQMC) techniques to obtain accurate estimates of the components of the Kohn-Sham effective potential of density-functional theory for a model semiconductor, and the corresponding components of the energy functional, by determining the local potential which, when filled with noninteracting electrons, reproduces the DQMC electron density. The results are compared with the widely used local-density approximation. There is a large deviation in the exchange-correlation potential, a slight deviation in the electron density, but a very small deviation in the total energy and its components. We also use DQMC techniques to calculate the quasiparticle band gap, and hence the discontinuity \ensuremath{\Delta} in the exchange-correlation potential on the addition of an electron.

Calculated quasiparticle band gap of beta -C3N4.

The quasiparticle electronic band structure of ${\mathrm{C}}_{3}$${\mathrm{N}}_{4}$ carbon nitride in the \ensuremath{\beta}-${\mathrm{Si}}_{3}$${\mathrm{N}}_{4}$ structure is calculated using the GW approximation. The indirect band gap is predicted to be 6.4\ifmmode\pm\else\textpm\fi{}0.5 eV and the minimum direct gap is found to be at \ensuremath{\Gamma} with a value of 6.75 eV. A plane-wave local-density-approximation band structure is also presented.

Investigating exact density-functional theory of a model semiconductor.

Using the diffusion quantum Monte Carlo method, we calculte the ground-state density and energy, and the quasiparticle band gap, of a model semiconductor. The exchange-correlation potential of density-functional theory (DFT), ${\mathit{V}}_{\mathrm{xc}}$(r), is obtained using optimization techniques. From this we calculate the DFT functionals ${\mathit{E}}_{\mathrm{sc}}$ and ${\mathit{T}}_{\mathit{s}}$ and the DFT band gap for various external potentials and compare the results with the local-density approximation (LDA). Whereas energies are found to be very accurate in the LDA, and the density reasonably good, we find large differences in the shape of ${\mathit{V}}_{\mathrm{xc}}$(r).

Model dielectric matrices for quasiparticle self-energy calculations.

A computationally simple model for the full static dielectric matrices is proposed for use in self-energy calculations to obtain quasiparticle energies and band gaps. The screening hole around an added electron at a given point in the crystal is approximated by the screening response of a homogeneous medium determined by the local density. The resulting approximation to the screening potential includes the crucial part of the local fields. When used with the previously developed self-energy approach, quasiparticle energies and band gaps in good agreement with experimental results are obtained for diamond, Si, and Ge.