Theory of the electronic and optical properties of dilute bismide alloys

Dilute bismide alloys, containing small fractions of bismuth (Bi), have recently attracted interest due to their potential for applications in a range of semiconductor devices. Experiments have revealed that dilute bismide alloys such as GaBixAs1−x, in which a small fraction x of the atoms in the III-V semiconductor GaAs are replaced by Bi, exhibit a number of unusual and unique properties. For example, the band gap energy (E g) decreases rapidly with increasing Bi composition x, by up to 90 meV per % Bi replacing As in the alloy. This band gap reduction is accompanied by a strong increase in the spin-orbit-splitting energy (ΔSO) with increasing x, and both E g and ΔSO are characterised by strong, composition-dependent bowing. The existence of a ΔSO > E g regime in the GaBixAs1−x alloy has been demonstrated for x ≳10%, a band structure condition which is promising for the development of highly efficient, temperature stable semiconductor lasers that could lead to large energy savings in future optical communication networks. In addition to their potential for specific applications, dilute bismide alloys have also attracted interest from a fundamental perspective due to their unique properties. In this thesis we develop the theory of the electronic and optical properties of dilute bismide alloys. By adopting a multi-scale approach encompassing atomistic calculations of the electronic structure using the semi-empirical tight-binding method, as well as continuum calculations based on the k•p method, we develop a fundamental understanding of this unusual class of semiconductor alloys and identify general material properties which are promising for applications in semiconductor optoelectronic and photovoltaic devices. By performing detailed supercell calculations on both ordered and disordered alloys we explicitly demonstrate that Bi atoms act as isovalent impurities when incorporated in dilute quantities in III-V (In)GaAs(P) materials, strongly perturbing the electronic structure of the valence band. We identify and quantify the causes and consequences of the unusual electronic properties of GaBixAs1−x and related alloys, and our analysis is reinforced throughout by a series of detailed comparisons to the results of experimental measurements. Our k•p models of the band structure of GaBixAs1−x and related alloys, which we derive directly from detailed atomistic calculations, are ideally suited to the study of dilute bismide-based devices. We focus in the latter part of the thesis on calculations of the electronic and optical properties of dilute bismide quantum well lasers. In addition to developing an understanding of the effects of Bi incorporation on the operational characteristics of semiconductor lasers, we also present calculations which have been used explicitly in designing and optimising the first generation of GaBixAs1−x-based devices.

Accelerating self-consistent field convergence with the augmented Roothaan-Hall energy function.

Based on Pulay's direct inversion iterative subspace (DIIS) approach, we present a method to accelerate self-consistent field (SCF) convergence. In this method, the quadratic augmented Roothaan-Hall (ARH) energy function, proposed recently by Høst and co-workers [J. Chem. Phys. 129, 124106 (2008)], is used as the object of minimization for obtaining the linear coefficients of Fock matrices within DIIS. This differs from the traditional DIIS of Pulay, which uses an object function derived from the commutator of the density and Fock matrices. Our results show that the present algorithm, abbreviated ADIIS, is more robust and efficient than the energy-DIIS (EDIIS) approach. In particular, several examples demonstrate that the combination of ADIIS and DIIS ("ADIIS+DIIS") is highly reliable and efficient in accelerating SCF convergence.

Spin three gauge theory revisited

We study the problem of consistent interactions for spin-3 gauge fields in flat spacetime of arbitrary dimension 3$">n>3. Under the sole assumptions of Poincaré and parity invariance, local and perturbative deformation of the free theory, we determine all nontrivial consistent deformations of the abelian gauge algebra and classify the corresponding deformations of the quadratic action, at first order in the deformation parameter. We prove that all such vertices are cubic, contain a total of either three or five derivatives and are uniquely characterized by a rank-three constant tensor (an internal algebra structure constant). The covariant cubic vertex containing three derivatives is the vertex discovered by Berends, Burgers and van Dam, which however leads to inconsistencies at second order in the deformation parameter. In dimensions 4$">n>4 and for a completely antisymmetric structure constant tensor, another covariant cubic vertex exists, which contains five derivatives and passes the consistency test where the previous vertex failed. © SISSA 2006.

Accurate ground-state potential energy surfaces of the C2H2–Kr and C2H2–Xe van der Waals complexes

Accurate ab initio intermolecular potential energy surfaces (IPES) have been obtained for the first time for the ground electronic state of the C 2H2-Kr and C2H2-Xe van der Waals complexes. Extensive tests, including complete basis set and all-electron scalar relativistic results, support their calculation at the CCSD(T) level of theory, using small-core relativistic pseudopotentials for the rare-gas atoms and aug-cc-pVQZ basis sets extended with a set of 3s3p2d1f1g mid-bond functions. All results are corrected for the basis set superposition error. The importance of the scalar relativistic and rare-gas outer-core (n.1)d correlation effects is investigated. The calculated IPES, adjusted to analytical functions, are characterized by global minima corresponding to skew T-shaped geometries, in which the Jacobi vector positioning the rare-gas atom with respect to the center of mass of the C2H2 moiety corresponds to distances of 4.064 and 4.229Å, and angles of 65.22° and 68.67° for C 2H2-Kr and C2H2-Xe, respectively. The interaction energy of both complexes is estimated to be -151.88 (1.817 kJ mol-1) and -182.76 cm-1 (2.186 kJ mol-1), respectively. The evolution of the topology of the IPES as a function of the rare-gas atom, from He to Xe, is also discussed. © 2012 Taylor and Francis.

The future of energy: are competitive markets and nuclear power the answer?

The inaugural lecture of Professor Stephen Thomas at the University of Greenwich, 4th February 2010. It examines whether further pursuit of competition in energy markets and expansion in the role of nuclear power can be the main elements in a policy to meet goals of security, sustainability and affordability.

Parameterisation of bivalve functional traits for mechanistic eco-physiological dynamic energy budget (DEB) models

Mechanistic models such as those based on dynamic energy budget (DEB) theory are emergent ecomechanics tools to investigate the extent of fitness in organisms through changes in life history traits as explained by bioenergetic principles. The rapid growth in interest around this approach originates from the mechanistic characteristics of DEB, which are based on a number of rules dictating the use of mass and energy flow through organisms. One apparent bottleneck in DEB applications comes from the estimations of DEB parameters which are based on mathematical and statistical methods (covariation method). The parameterisation process begins with the knowledge of some functional traits of a target organism (e. g. embryo, sexual maturity and ultimate body size, feeding and assimilation rates, maintenance costs), identified from the literature or laboratory experiments. However, considering the prominent role of the mechanistic approach in ecology, the reduction of possible uncertainties is an important objective. We propose a revaluation of the laboratory procedures commonly used in ecological studies to estimate DEB parameters in marine bivalves. Our experimental organism was Brachidontes pharaonis. We supported our proposal with a validation exercise which compared life history traits as obtained by DEBs (implemented with parameters obtained using classical laboratory methods) with the actual set of species traits obtained in the field. Correspondence between the 2 approaches was very high (>95%) with respect to estimating both size and fitness. Our results demonstrate a good agreement between field data and model output for the effect of temperature and food density on age-size curve, maximum body size and total gamete production per life span. The mechanistic approach is a promising method of providing accurate predictions in a world that is under in creasing anthropogenic pressure.

General rules for predicting where a catalytic reaction should occur on metal surfaces: A density functional theory study of C-H and C-O bond breaking/making on flat, stepped, and kinked metal surfaces

To predict where a catalytic reaction should occur is a fundamental issue scientifically. Technologically, it is also important because it can facilitate the catalyst's design. However, to date, the understanding of this issue is rather limited. In this work, two types of reactions, CH4 CH3 + H and CO C + 0 on two transition metal surfaces, were chosen as model systems aiming to address in general where a catalytic reaction should occur. The dissociations of CH4 - CH3 + H and CO --> C + O and their reverse reactions on flat, stepped, and kinked Rh and Pd surfaces were studied in detail. We find the following: First, for the CH4 Ch(3) + H reaction, the dissociation barrier is reduced by similar to0.3 eV on steps and kinks as compared to that on flat surfaces. On the other hand, there is essentially no difference in barrier for the association reaction of CH3 + H on the flat surfaces and the defects. Second, for the CO C + 0 reaction, the dissociation barrier decreases dramatically (more than 0.8 eV on Rh and Pd) on steps and kinks as compared to that on flat surfaces. In contrast to the CH3 + H reaction, the C + 0 association reaction also preferentially occurs on steps and kinks. We also present a detailed analysis of the reaction barriers in which each barrier is decomposed quantitatively into a local electronic effect and a geometrical effect. Our DFT calculations show that surface defects such as steps and kinks can largely facilitate bond breaking, while whether the surface defects could promote bond formation depends on the individual reaction as well as the particular metal. The physical origin of these trends is identified and discussed. On the basis of our results, we arrive at some simple rules with respect to where a reaction should occur: (i) defects such as steps are always favored for dissociation reactions as compared to flat surfaces; and (ii) the reaction site of the association reactions is largely related to the magnitude of the bonding competition effect, which is determined by the reactant and metal valency. Reactions with high valency reactants are more likely to occur on defects (more structure-sensitive), as compared to reactions with low valency reactants. Moreover, the reactions on late transition metals are more likely to proceed on defects than those on the early transition metals.

Free energy and molecular dynamics calculations for the cubic-tetragonal phase transition in zirconia

The high-temperature cubic-tetragonal phase transition of pure stoichiometric zirconia is studied by molecular dynamics (MD) simulations and within the framework of the Landau theory of phase transformations. The interatomic forces are calculated using an empirical, self-consistent, orthogonal tight-binding model, which includes atomic polarizabilities up to the quadrupolar level. A first set of standard MD calculations shows that, on increasing temperature, one particular vibrational frequency softens. The temperature evolution of the free-energy surfaces around the phase transition is then studied with a second set of calculations. These combine the thermodynamic integration technique with constrained MD simulations. The results seem to support the thesis of a second-order phase transition but with unusual, very anharmonic behavior above the transition temperature.

Effect of relaxation on the oxygen K-edge electron energy-loss near-edge structure in yttria-stabilized zirconia

The electron energy-loss near-edge structure (ELNES) at the oxygen K-edge has been investigated in a range of yttria-stabilized zirconia (YSZ) materials. The electronic structure of the three polymorphs of pure ZrO2 and of the doped YSZ structure close to the 33 mol %Y2O3 composition have been calculated using a full-potential linear muffin-tin orbital method (NFP-LMTO) as well as a pseudopotential based technique. Calculations of the ELNES dipole transition matrix elements in the framework of the NFP-LMTO scheme and inclusion of core hole screening within Slater's transition state theory enable the ELNES to be computed. Good agreement between the experimental and calculated ELNES is obtained for pure monoclinic ZrO2. The agreement is less good with the ideal tetragonal and cubic structures. This is because the inclusion of defects is essential in the calculation of the YSZ ELNES. If the model used contains ordered defects such as vacancies and metal Y planes, agreement between the calculated and experimental O K-edges is significantly improved. The calculations show how the five different O environments of Zr,Y,O, are connected with the features observed in the experimental spectra and demonstrate clearly the power of using ELNES to probe the stabilization mechanism in doped metal oxides.

The near-edge structure in energy-loss spectroscopy: many-electron and magnetic effects in transition metal nitrides and carbides

We investigate the ability of the local density approximation (LDA) in density functional theory to predict the near-edge structure in electron energy-loss spectroscopy in the dipole approximation. We include screening of the core hole within the LDA using Slater's transition state theory. We find that anion K-edge threshold energies are systematically overestimated by 4.22 +/- 0.44 eV in twelve transition metal carbides and nitrides in the rock-salt (B1) structure. When we apply this 'universal' many-electron correction to energy-loss spectra calculated within the transition state approximation to LDA, we find quantitative agreement with experiment to within one or two eV for TiC, TiN and VN. We compare our calculations to a simpler approach using a projected Mulliken density which honours the dipole selection rule, in place of the dipole matrix element itself. We find remarkably close agreement between these two approaches. Finally, we show an anomaly in the near-edge structure in CrN to be due to magnetic structure. In particular, we find that the N K edge in fact probes the magnetic moments and alignments of ther sublattice.

Magnetically quantized continuum distorted-wave theory in atomic and molecular collisions

The continuum distorted-wave eikonal initial-state (CDW-EIS) theory of Crothers and McCann (J Phys B 1983, 16, 3229) used to describe ionization in ion-atom collisions is generalized (G) to GCDW-EIS to incorporate the azimuthal angle dependence of each CDW in the final-state wave function. This is accomplished by the analytic continuation of hydrogenic-like wave functions from below to above threshold, using parabolic coordinates and quantum numbers including magnetic quantum numbers, thus providing a more complete set of states. At impact energies lower than 25 keVu(-1), the total ionization cross-section falls off, with decreasing energy, too quickly in comparison with experimental data. The idea behind and motivation for the GCDW-EIS model is to improve the theory with respect to experiment by including contributions from nonzero magnetic quantum numbers. We also therefore incidentally provide a new derivation of the theory of continuum distorted waves for zero magnetic quantum numbers while simultaneously generalizing it. (C) 2004 Wiley Periodicals, Inc.

Understanding the dehydrogenation mechanism of tetrahydrocarbazole over palladium using a combined experimental and density functional theory approach

The mechanism of the dehydrogenation of tetrahydrocarbazole to carbazole over palladium has been examined for the first time. By use of a combination of deuterium exchange experiments and density functional theory calculations, a detailed reaction profile for the aromatization of tetrahydrocarbazole has been identified and validated by experiment. As with many dehydrogenation reactions, the initial hydrogen abstraction is found to have the highest reaction barrier. Tetrahydrocarbazole has four hydrogens which can, in principle, be cleaved initially; however, the theory and experiment show that the reaction is dominated by the cleavage of the carbon hydrogens at the carbon atoms in positions 1 and 4. The two pathways originating from these two C-H bond cleavage processes are found to have similar reaction energy profiles and both contribute to the overall reaction.

R-matrix theory of electron molecule scattering

This paper presents an overview of R-matrix theory of electron scattering by diatomic and polyatomic molecules. The paper commences with a detailed discussion of the fixed-nuclei approximation which in recent years has been used as the basis of the most accurate ab initio calculations. This discussion includes an overview of the computer codes which enable electron collisions with both diatomic and polyatomic molecules to be calculated. Nuclear motion including rotational and vibrational excitation and dissociation is then discussed. In non-resonant energy regions, or when the scattered electron energy is not close to thresholds, the adiabatic-nuclei approximation can be successfully used. However, when these conditions are not applicable, non-adiabatic R-matrix theory must be used and a detailed discussion of this theory is given. Finally, recent applications of the theory to treat electron scattering by polyatomic molecules are reviewed and a detailed comparison of R-matrix calculations and experimental measurements for water is presented.

The 90-degree problem of scattering theory revisited: dynamical turbulence effects versus nonlinear effects

The 90° problem of cosmic-ray transport theory is revisited in this paper. By using standard forms of the wave spectrum in the solar wind, the pitch-angle Fokker–Planck coefficient and the parallel mean free path are computed for different resonance functions. A critical comparison is made of the strength of 90° scattering due to plasmawave effects, dynamical turbulence effects and nonlinear effects. It is demonstrated that, only for low-energy cosmic particles, dynamical effects are usually dominant. The novel results presented here are essential for an effective comparison of heliospheric observations for the parallel mean free path with the theoretical model results.

Electronic structure of the nitrogen-vacancy center in diamond from first-principles theory

The nitrogen-vacancy (NV) center is a paramagnetic defect in diamond with applications as a qubit. Here, we investigate its electronic structure by using ab initio density functional theory for five different NV center models of two different cluster sizes. We describe the symmetry and energetics of the low-lying states and compare the optical frequencies obtained to experimental results. We compute the major transition of the negatively charged NV centers to within 25–100 meV accuracy and find that it is energetically favorable for substitutional nitrogens to donate an electron to NV0. The excited state of the major transition and the NV0 state with a neutral donor nitrogen are found to be close in energy.