Electron scattering and optical absorption at semiconductor surfaces

With the aid of a simple dielectric theory a discussion is given of the relation between the line shape observed on optical absorption due to interband transitions involving surface states and the corresponding electron energy-loss profile.     

Theory of defect complexes at semiconductor surfaces

We report calculations of deep levels associated with defect complexes at semiconductor surfaces. For the antistructure defect (As_Ga, Ga_As) at the (110) surface of GaAs, the results are qualitatively the same as the sum of those for the individual antisite defects As_Ga and Ga_As — a donor level and two acceptor levels within the band gap.     

The problem of the universal density functional and the density matrix functional theory

The analysis in this paper shows that the Hohenberg-Kohn theorem is the constellation of two statements: (i) the mathematically rigorous Hohenberg-Kohn lemma, which demonstrates that the same ground-state density cannot correspond to two different potentials of an external field, and (ii) the hypothesis of the existence of the universal density functional. Based on the obtained explicit expression for the nonrel-ativistic particle energy in a local external field, we prove that the energy of the system of more than two non-interacting electrons cannot be a functional of the inhomogeneous density. This result is generalized to the system of interacting electrons. It means that the Hohenberg-Kohn lemma cannot provide justification of the universal density functional for fermions. At the same time, statements of the density functional theory remain valid when considering any number of noninteracting ground-state bosons due to the Bose condensation effect. In the framework of the density matrix functional theory, the hypothesis of the existence of the universal density matrix functional corresponds to the cases of noninteracting particles and to interaction in the Hartree-Fock approximation.     

On the semiconductor energy gap in density functional theory

The non-existence of the functional derivative of the Hohenberg-Kohn functional at the ground-state density of a semiconductor earlier discussed in the literature^2,3 is analyzed. Arguments are given that this non-existence is not connected with the discontinuity of the (ordinary) derivative of the functional with respect to the particle number N as discussed by Perdew and Levy².     

Surface energy and relaxation effects at (111) semiconductor surfaces

A local orbital method is used to calculate the relaxed position of the unreconstructed (111) surface layer of atoms in a silicon or diamond crystal. The separation of the outermost layers decreases to about 40% of its bulk value and the surface energy is found to be about 1.0 eV per surface atom for silicon and 1.6 eV for carbon.     

Oxygen vacancies at oxide surfaces: ab initio density functional theory studies on vanadium pentoxide

The local electronic structure at the V₂O₅ (010) surface is studied by ab initio density functional theory (DFT) methods using gradient-corrected functionals (RPBE) where embedded clusters as large as V₂₀O₆₂H₂₄, representing one or two crystal layers of the substrate, are used as models. Results of local binding and charging of differently coordinated surface-oxygen sites as well as densities of states allow a characterization of the detailed electronic structure of the surface. Electronic and geometric details of surface-oxygen vacancies as well as hydrogen adsorption are studied by appropriate clusters. A comparison of the data, concerning vacancy energies, charging, geometric relaxation, and diffusion, shows sizeable variations between different oxygen sites and can give further insight into possible mechanisms of surface relaxation and reconstruction. Hydrogen is found to stabilize at all surface-oxygen sites forming surface-OH and H₂O species. As a result, the binding of surface oxygen with its vanadium neighbors is weakened. Therefore, the presence of hydrogen at the oxide surface facilitates oxygen removal and can contribute to the enhanced yield of oxygenated products near vanadia-based surfaces. Received: 10 April 2000 / Accepted: 25 July 2000 / Published online: 7 March 2001     

Theory of semiconductor surfaces

Three kinds of recent theories of the atomic and electronic structure of semiconductor surfaces are relevant to experiment. Self-consistent calculations have provided a firm basis for understanding covalent bonding at the surface. Realistic tight-binding models can study larger unit cells which commonly occur on reconstructed surfaces. Thermochernical analysis explains the atomic arrangements obtained by annealing clean covalent surfaces.     

Methylamine decomposition on nickel surfaces: A density functional theory study

The adsorption and decomposition of methylamine on Ni(1 1 1), Ni(1 0 0), stepped Ni(1 1 1), and nitrogen atom modified Ni(1 0 0) (denoted N–Ni(1 0 0)) have been studied with the DFT–GGA method using the periodic slab models. The initial scissions of C–H, N–H and C–N bond are considered. The adsorption energies under the most stable configurations for the possible species and the activation energies for the possible initial elementary reactions involved are obtained in the present work. Through systematic exploring of the kinetics mechanism of methylamine decomposition on these four surfaces, it is found that the reactivity of these surfaces decreased with the order of stepped Ni(1 1 1) > Ni(1 0 0) > Ni(1 1 1) > N–Ni(1 0 0). This indicates that the reactivity is related to the openness of the surface, and the presence of nitrogen atom reduces the reactivity of the Ni(1 0 0). For the three reactions, the barriers decreased with the order of C–N > N–H > C–H on Ni(1 1 1) and Ni(1 0 0), whereas they decreased with the order of C–N > C–H > N–H on stepped Ni(1 1 1) and N–Ni(1 0 0).     

Electron emission from insulator and semiconductor surfaces by multiphoton excitation below the optical damage threshold

The shape of acoustic pulses excited in crystalline silicon during absorption of Nd³⁺ YAG laser radiation was studied as a function of incident light intensity. It was revealed that the amplitude of the dilatation wave is saturated while the duration of the compression pulse is shortened. A theoretical model is suggested which explains the above experimental facts by a decrease in the time of Auger recombination for nonequilibrium carriers with an increase in their concentration for higher intensity of the optical excitation. The value of the Auger constant obtained from the experiment is 5×10^–31 cm⁶s^–1.     

Static correlated functionals for reduced density matrix functional theory

Based on recent progress on fermionic exchange symmetry we propose a way to develop new functionals for reduced density matrix functional theory. For some settings with an odd number of electrons, by assuming saturation of the inequalities stemming from the generalized Pauli principle, the many-body wave-function can be written explicitly in terms of the natural occupation numbers and the natural orbitals. This leads to an expression for the two-particle reduced density matrix and therefore for the correlation energy functional. This functional is tested for a three-electron Hubbard model where it shows excellent performance both in the weak and strong correlation regimes.     

Local approximation of the correlation energy functional in the density matrix functional theory

A local approximation formula of the correlation energy functional E(c) in terms of the first-order reduced density matrix (1-RDM) is presented. With the contracted Schr?dinger equation the principal dependence of E(c) on the natural occupation numbers n(i) is identified. Using the effective mass theory, E(c) is expressed as a functional of the local density and the local variable, J = SUM (i)[square root of (n(i)(1-n(i))] /phi(i)/(2), where phi(i) are the natural spin orbitals. This local approximation satisfies the homogeneous coordinate scaling relation, gives the exact result for a one-electron system, and is almost free from the exchange energy error. It reproduced about 90% of the correlation energies of atoms and molecules.     

A theory of excitation of a planar semiconductor optical waveguide using a diffraction grating: Single-scattering approximation

The problem of excitation of a totally reflecting planar optical waveguide using a coupling diffraction grating in the form of a periodic relief of the waveguide-layer thickness is solved within the single-scattering approximation. The polariton mode in the presence of a quantum well near the waveguide is considered. Based on the developed concepts, the following experimental features of the dependence of the intensity of radiation conducted in the waveguide layer on the angle of incidence of the excitation beam on the coupling diffraction grating are interpreted: the dependence on the mode number, the interference effects in the presence of two coupling diffraction gratings, and the influence of the lower substrate boundary on the thermal behavior of the waveguide structure.     

Quasiparticle spectrum and optical excitations of semiconductor surfaces

I investigated the spectra of well-ordered semiconductor surfaces within an ab-initio framework. Both the quasi-particle spectrum of electron and hole states and the optical differential reflectivity spectrum were addressed. As examples, I discuss the spectra of three surfaces: Si(111)-(2×1), hydrogenated H:Si(111)-(1×1), and Si adatom-terminated 6H-SiC(0001)-(×). I studied a number of physical features beyond the single-particle band-structure picture. In the case of Si(111)-(2×1), the dangling-bond surface states give rise to a surface exciton which dominates the differential reflectivity spectrum. In the case of 6H-SiC(0001)-(×), a Mott-Hubbard metal-insulator transition is observed. All calculations were performed within many-body perturbation theory, employing single- and two-particle Green functions. The solutions of the corresponding equations of motion yielded the observable excitations, i.e., single-particle electron and hole excitations, as well as bound and resonant electron-hole pair excitations. Received: 28 April 2000 / Accepted: 19 June 2000 / Published online: 7 March 2001     

Theoretical investigation of electronic and optical properties of andalusite within density functional theory

The electronic and optical properties of andalusite were studied by using quantum-mechanical calculations based on the density functional theory (DFT). The electronic structure shows that andalusite has a direct band gap of 5.01 eV. The complex dielectric function and optical constants, such as extinction coefficient, refractive index, reflectivity and energy-loss spectrum, are calculated. The optical properties of andalusite are discussed based on the band structure calculations. It is shown that the O-2p states and Al-3s states play a major role in optical transitions as initial and final states, respectively.     

Degenerate ground states and a fractional number of electrons in density and reduced density matrix functional theory

For a linear combination of electron densities of degenerate ground states, it is shown that the value of any energy functional is the ground state energy, if the energy functional is exact for ground state densities, size consistent, and translational invariant. The corresponding functional of kinetic and interaction energy is the linear combination of the functionals of the degenerate densities. Without invoking ensembles, it is shown that the energy functional of fractional number electrons is a series of straight lines interpolating its values at integers. These results underscore the importance of grand canonical ensemble formulation in density functional theory.     

Quantum field theory of optical birefringence phenomena

The inverse Faraday effect, in which a magnetization is induced in a solution through which is passed a polarized light beam of arbitrary ellipticity, is discussed on the basis of the S-matrix formulation of optical birefringence. It is shown that the Faraday effect and the inverse Faraday effect are topologically identical problems of diagrammatic perturbation theory and so it follows automatically that the magnetization should be proportional to the Verdet constant. The optical Faraday effect is the circular birefringence induced by an intense circularly polarized beam of light propagated colinearly with the weak measuring beam: the electric vector of the circularly polarized beam interacts with the molecule in a way that resembles the interaction of a static magnetic field. The interrelations of these two effects and the normal Faraday effect the self-rotation of the polarization ellipse of an intense beam are discussed.     

Charge transfer, double and bond-breaking excitations with time-dependent density matrix functional theory

Time-dependent density functional theory (TDDFT) in its current adiabatic implementations exhibits three remarkable failures: (a) completely wrong behavior of the excited state surface along a bond-breaking coordinate; (b) lack of doubly excited configurations; (c) much too low charge transfer excitation energies. These TDDFT failure cases are all strikingly exhibited by prototype two-electron systems such as dissociating H2 and HeH+. We find for these systems with time-dependent density matrix functional theory that: (a) Within previously formulated simple adiabatic approximations, the bonding-to-antibonding excited state surface as well as charge transfer excitations are described without problems, but not the double excitations; (b) An adiabatic approximation is formulated in which also the double excitations are fully accounted for.     

Critical phenomena at perfect and non-perfect surfaces

The effect of imperfections on surface critical properties is studied for Ising models with nearest-neighbour ferromagnetic couplings on simple cubic lattices. In particular, results of Monte Carlo simulations for flat, perfect surfaces are compared to those for flat surfaces with random, “weak” or “strong”, interactions between neighbouring spins in the surface layer, and for surfaces with steps of monoatomic height. Surface critical exponents at the ordinary transition, in particular ,are found to be robust against these perturbations. Received: 7 October 1997 / Accepted: 19 November 1997