The fitting of an idempotent density matrix to x-ray structure factors is discussed. If the density matrix is identified with a single Slater determinant of orbitals, then a model wave function can be recovered, enabling the computation of two-electron properties as well as the usual one-electron properties derived from the electron density. Hence this approach is potentially superior to the usual multipole expansion used in charge-density analysis, although the current formalisms are only useful for molecular crystals of very small molecules. A procedure is described, and applications to one theoretical example (methylamine) and one experimental example (formamide) are presented.

We present an expression, obtained by following the principles of the effective medium theory (EMT), to compute average dielectric properties of mixtures of random ellipsoids. We show that our formulation is quite general and includes former expressions, valid only for dilute mixtures, as particular cases; moreover it gives accurate predictions when compared with experimental measurements in the whole range of filling factors. The expression can be extended to mixtures of irregularly shaped particles with very little loss of accuracy. Also, our equation is suitable to be used with anisotropic samples. The equation requires an additional parameter, which amounts to a percolation threshold, to the parameters usually employed to describe a binary mixture in EMT, namely, the dielectrical functions of the components and the filling factor. This parameter contains information about the geometry of the particle packing, and approximate values have been found by numerical simulation of different arrangements of spheres in a matrix. Reflectance IR spectra have been measured on pressed pellets of particles of LiF, MgO, α-${\mathrm{Fe}}_2$${\mathrm{O}}_3$, and ${\mathrm{MgAl}}_2$${\mathrm{O}}_4$ and compared with the spectra predicted by the expression presented in this paper, and other previous formulations.

Based on conventional electronegativity arguments, gold–alkali-metal compounds are expected to be among the most ‘‘ionic’’ of metallic compounds. The concepts of ionicity and charge transfer are difficult to quantify. However, the changes in bonding in the 50/50 Au–alkali-metal systems between the elemental metals and the compounds are so severe that observations can readily be made concerning their character. The results, as obtained from self-consistent electronic-structure calculations, lead to the apparently odd observation that the electron density at the alkali-metal sites in the compound increases significantly and this involves high l componennts in the charge density. This increase, however, can be attributed to Au-like orbitals spatially overlapping the alkali-metal sites. In a chemical sense, it is reasonable to consider the alkali-metal transferring charge to these Au orbitals. While normally the difference in heats of formation between muffin-tin and full-potential calculations for transition-metal–transition-metal and transition-metal–main-group (e.g., Al) compounds having high site symmetry are small, for the gold–alkali-metal systems, the changes in bonding in the compounds cause differences of ∼0.5 eV/atom between the two classes of potential. Any serious estimate of the electronic structure in these systems must account for these aspherical bonding charges. The origin of the semiconducting behavior of the heavy-alkali-metal Au compounds is shown to arise from a combination of the Au-Au separations and the ionic character of the compounds; the light-alkali-metal Au compounds, with their smaller Au-Au separations, do not have a semiconducting gap. Core-level shifts and isomer shifts are also briefly discussed.

The electronic structures of the chalcopyrite-type ${\mathrm{CuFeS}}_2$ and ${\mathrm{CuAl}}_{0.9}$${\mathrm{Fe}}_{0.1}$${\mathrm{S}}_2$ are studied by x-ray photoemission (XPS), resonance photoemission, Auger-electron, optical reflectance, and electron-energy-loss (EELS) spectroscopies. The Fe 3d-derived states are revealed by the valence-band XPS spectra and the Fe 3p core resonance photoemission spectra. The spectra are analyzed by configuration-interaction calculation on the ${\mathrm{FeS}}_4$ cluster model; the analysis yields the S 3p→Fe 3d charge-transfer energy Δ close to zero, indicating strong covalency between the Fe 3d and S 3p orbitals. This situation is reflected upon the reduced Fe magnetic moment and the high Neel temperature of ${\mathrm{CuFeS}}_2$. The S 3p→Fe 3d charge-transfer excitation is resolved in the optical reflectance and EELS spectra, which explains the larger binding-energy tails of the core-level photoemission spectra of ${\mathrm{CuFeS}}_2$. The Cu 3d two-hole bound state is studied through the Cu ${\mathit{L}}_3$${\mathit{M}}_{4,5}$${\mathit{M}}_{4,5}$ Auger and Cu 3p core resonance photoemission spectra, from which the effective Coulomb energy ${\mathit{U}}_{\mathrm{eff}}$${(}^1$G) between the two holes and the Cu 3d→4sp promotion energy ${\mathrm{\Delta }}_{\mathit{d}\mathrm{-}\mathit{s}\mathit{p}}$ are evaluated. The Cu 2p core XPS spectrum of ${\mathrm{CuFeS}}_2$ has revealed a mixing of the ${\mathit{d}}^9$ (‘‘${\mathrm{Cu}}^{2+}$’’) configuration into the formally monovalent Cu. This is interpreted as due to the Cu 3d–Fe 3d hybridization mediated by the S 3sp valence states.

We have calculated the electronic structure, photoelectron spectra, and magnetic moments for the UPdSn compound. The electronic structure and photoelectron spectra (x-ray photoemission spectroscopy) were calculated using both itinerant as well as localized 5f states (using both an ${\mathit{f}}^2$ and ${\mathit{f}}^3$ configuration). By comparing our calculated results with experimental data we argue that the localized ${\mathit{f}}^2$ configuration is likely to be the most appropriate description for UPdSn.

Angle-resolved photoemission spectra of the (100) and (110) faces of ${\mathrm{TiO}}_2$ have been recorded in the photon-energy range from 18 to 47 eV. These normal emission data have been analyzed on the basis of direct transitions into free-electron-like final states, yielding valence-band dispersion relations, E(k), along the high-symmetry Δ and Σ lines of the bulk Brillouin zone. Polarization selection rules are derived for the appropriate nonsymmorphic space group, which are used to identify the symmetries of the valence bands. Empirical dispersion relations are compared with the results of a band-structure calculation, which employed an ab initio atomic orbital-based method. While there is reasonable agreement overall, for a Δ-line empirical band at about 1.2 eV below the valence-band maximum (${\mathit{E}}_{\mathrm{vbm}}$) there is no counterpart in the calculated bulk band structure. This discrepancy may be related to a ${\mathrm{TiO}}_2$(100) surface resonance predicted to lie 1.5 eV below ${\mathit{E}}_{\mathrm{vbm}}$.

Photoinduced absorption data for polyaniline films in two forms, emeraldine base (EB) and emeraldine salt (ES), are presented and discussed. Electrochemically synthesized films were excited with laser pulses of large intensity (the energy ≃2 eV, the pulse duration ≃8 ps, the pulse energy up to 10 mJ/${\mathrm{cm}}^2$). Optical spectra of the EB and ES films in the temperature range from 298 to 363 K are also studied. The polymer film is presumed to be a three-dimensional (3D) system of long finite conjugated fragments of polymer chains. Considering each fragment integrally and taking into account the electronic polarization energy (≃1.5 eV) for a charge in the film, the 3D model of a charge-transfer exciton is proposed. The low-energy absorption of EB and ES and the electronc processes in photoexcited films are interpreted within the framework of the proposed model, avoiding the commonly adopted approach of an isolated polymer chain.

The insulating oxide ${\mathrm{NaCuO}}_2$ has been studied by x-ray photoemission spectroscopy and subsequent cluster-model analysis. It is found that the ${\mathit{d}}^8$→${\mathit{d}}^9$L charge-transfer energy (L:ligand hole) is negative and the ground state is dominated by the ${\mathit{d}}^9$L configuration. Using the Anderson impurity model, it is shown that strong 3d-ligand hybridization opens a band gap for a negative charge-transfer energy. This band gap corresponds to charge fluctuations mainly of the p-p type, ${\mathit{d}}^9$L+${\mathit{d}}^9$L→${\mathit{d}}^9$+${\mathit{d}}^9$${\mathit{L}}^2$, with a considerable mixture of d character into the p states, and not of the conventional Mott-Hubbard (d-d) type nor of the charge-transfer (p-d) type. The magnitude of the gap is strongly affected by the geometrical arrangement of metal-oxygen local units, giving a natural explanation for the difference between the insulating ${\mathrm{NaCuO}}_2$ and metallic ${\mathrm{LaCuO}}_3$. The electronic structures of ${\mathrm{Fe}}^{4+}$ and ${\mathrm{Ni}}^{3+}$ oxides and their insulating versus metallic behaviors, which are expected to resemble those of the ${\mathrm{Cu}}^{3+}$ oxides, are also discussed. To generalize the above conclusions, a modification of the metal-insulator boundaries in the Zaanen-Sawatzky-Allen diagram is proposed to include compounds with small or negative charge-transfer energies.

The simplified version of the Hubbard model, obtained by allowing hoppings between all pairs of sites, is studied for a finite number L of lattice sites, by using the theory of representations of the symmetric group ${\mathit{S}}_{\mathit{L}}$. The secular problem splits into sets of equations where each set refers to a different representation of ${\mathit{S}}_{\mathit{L}}$. The dimension of the secular problem is enormously reduced. Analytic expressions are found for the eigenvalues ${\mathit{E}}_{\pm }$ corresponding to the identical representation and it is conjectured that ${\mathit{E}}_{+}$ is the highest eigenvalue. Some previous results of van Dongen and Vollhardt on the thermodynamic limit of the model are confirmed and the limit for large U is briefly discussed.

We present band-structure and cluster-model calculations of ${\mathrm{LaCoO}}_3$ in the low-spin phase. The purpose of these calculations is to contrast and complement the results and conclusions of recent spectroscopic studies. The total density of states (DOS) is compared to the photoemission spectrum; the agreement is very good except for the many-body satellites which appear at higher binding energies. The unoccupied O p DOS reproduces fairly well the O 1s x-ray-absorption spectrum; the main discrepancy appears in the Co 3d region and is attributed to core-hole effects. The ground state predicted by the cluster-model calculation is highly covalent and contains mainly 62% of ${\mathit{t}}_{2\mathit{g}}^6$${(}^1$${\mathit{A}}_1$) and 36% of ${\mathit{t}}_{2\mathit{g}}^6$${\mathit{e}}_{\mathit{g}}$${(}^2$E)L. The first (one-electron) removal state has more 3${\mathit{d}}^6$L than 3${\mathit{d}}^5$ character whereas the first addition state is almost completely dominated by the 3${\mathit{d}}^7$ state. This means that low-spin ${\mathrm{LaCoO}}_3$ is in the charge-transfer regime and the optical band gap is of the p-d type. The Co 3d contribution to the photoemission spectrum calculated with the cluster-model reproduces not only the leading peaks but also the many-body satellites. The main drawback in this case is the absence of the spectral weight coming from the O 2p bands.

A method for calculating both the valence- and high-lying conduction-band structure of a solid is developed. The basis functions are linear-muffin-tin orbitals with multiple orbitals per angular momentum channel corresponding to different energies. In contrast to the conventional paneling method, our method treats the valence and conduction bands on an equal footing so that the wave functions are orthogonal, which avoids the nonorthogonality problem when calculating transition-matrix elements between occupied and unoccupied states and the discontinuity in the band structure. An empty-lattice test reproduces the free-electron band up to at least 50 eV. The method is applied to nickel and a comparison with a different approach based on a modified linear augmented-plane-wave method is made.

We have studied resonance Raman scattering tuned to the ${\mathrm{\sigma }}_{\mathit{g}}$→${\mathrm{\sigma }}_{\mathit{u}}$ hole transition of the self-trapped excitons (STE’s) in alkali halides. The Raman spectrum is characterized by a sharp line of 137 ${\mathrm{cm}}^{\mathrm{-}1}$ in NaBr, 361 ${\mathrm{cm}}^{\mathrm{-}1}$ in NaCl, and 139 ${\mathrm{cm}}^{\mathrm{-}1}$ in RbI. Each line has been assigned to the stretching vibration of the halogen molecular ion (${\mathit{X}}_2^{\mathrm{-}}$) composing the STE. Comparison of the Raman frequencies with those of ${\mathit{V}}_{\mathit{K}}$ and H centers obtained by similar measurements indicates that the frequency of the STE in NaBr coincides with that of the ${\mathit{V}}_{\mathit{K}}$ center, while those in NaCl and in RbI are almost identical to the frequencies of the H centers. These results provide evidence that the ${\mathit{X}}_2^{\mathrm{-}}$ of the STE in NaBr occupies two adjacent halogen sites and the ${\mathit{X}}_2^{\mathrm{-}}$ of the STE in NaCl and in RbI occupies a single halogen site.

A transferable tight-binding model for silicon is found by fitting the energies of silicon in various bulk crystal structures and examining functional parametrizations of the tight-binding forms. The model has short-range radial forms similar to the tight-binding Hamiltonian of Goodwin, Skinner, and Pettifor but can be utilized in molecular dynamics with a fixed radial cutoff for all structural configurations. In addition to a very good fit to the energy of Si in different bulk crystal structures the model describes very well the elastic constants, defect-formation energies for vacancies and interstitials in crystalline silicon, the melting of Si, and short-range order in liquid silicon. Results for phonon frequencies and Grüneisen constants in c-Si are also presented.

From electrical resistivity and Hall coefficient measurements below 3 K on slightly reduced, semiconductive rutile single crystals with oxygen deficiencies ${\mathit{O}}_{\mathit{d}}$ between 3.7×${10}^{18}$/${\mathrm{cm}}^3$ and 5.5×${10}^{19}$/${\mathrm{cm}}^3$, it is concluded that the electrical conduction takes place by means of a defect-level permutation conduction mechanism involving Ti interstitial donors. In the range of 3.7×${10}^{18}$/${\mathrm{cm}}^3$≤${\mathit{O}}_{\mathit{d}}$≤2×${10}^{19}$/${\mathrm{cm}}^3$ the electrical resistivity decreases with increasing ${\mathit{O}}_{\mathit{d}}$, while in the range of 2×${10}^{19}$/${\mathrm{cm}}^3$≤${\mathit{O}}_{\mathit{d}}$≤5.5×${10}^{19}$/${\mathrm{cm}}^3$ it increases with increasing ${\mathit{O}}_{\mathit{d}}$. Values of ${\mathit{O}}_{\mathit{d}}$ between 8×${10}^{18}$/${\mathrm{cm}}^3$ and 2×${10}^{19}$/${\mathrm{cm}}^3$ correspond to the so-called intermediate concentration range of the impurity (defect) conduction, but the transition to metallic-type conduction does not occur because of a change in the defect structures, i.e., the formation of planar defects and the clustering of Ti interstitial donors at higher oxygen deficiencies.

Carrier relaxation and LO-phonon dynamics are investigated in GaAs crystals illuminated by picosecond laser pulses. It is evidenced that an overshoot of the LO-phonon quasitemperature above the electron quasitemperature can occur in the absence of intervalley scattering. This effect is ascribed to the screening of the polar optical interaction.

We present room-temperature ellipsometric measurements of the dielectric function of ${\mathrm{Zn}}_{\mathit{x}}$${\mathrm{Cd}}_{1\mathrm{-}\mathit{x}}$Se single-crystal films grown on (001)GaAs in the 1.5–6.0-eV energy region x ranging from 0 to 1. We identify the ${\mathit{E}}_0$, ${\mathit{E}}_0$+${\mathrm{\Delta }}_0$, ${\mathit{E}}_1$, ${\mathit{E}}_1$+${\mathrm{\Delta }}_1$, and ${\mathit{E}}_2$ threshold energies using the CdSe band structure calculated with a nonlocal empirical pseudopotential method. We find that the contact exciton effect has to be included in the calculated dielectric function of CdSe in order to obtain good agreement with our measurements. A compositon-dependent critical-point analysis of the ${\mathit{E}}_1$ and ${\mathit{E}}_1$+${\mathrm{\Delta }}_1$ structures has been performed. We also find that the spin-orbit-splitting band gap ${\mathrm{\Delta }}_1$(x), the linewidths, and the excitonic angles are about maximum at x=0.5, which we attribute to the statistical fluctuation of the alloy composition. Finally, the ${\mathit{E}}_1$ and ${\mathit{E}}_1$+${\mathrm{\Delta }}_1$ critical-point amplitudes cannot be understood by the one-electron approximation, confirming the existence of strong excitonic effects.

The density of vacancylike defects, produced in silicon by hydrogen implantation at 15.5 keV and surviving to successive isochronal annealings, has been measured by means of a slow positron beam. The results show that the number of defects acting as positron traps is a small fraction of the Frenkel pairs produced by implantation. This number decreases, increases again, and eventually disappears after annealing at increasing temperatures. The mean depth of the positron traps in as-implanted samples is smaller than the mean depth of vacancies predicted by computer simulations, but reaches, and in some cases surpasses, this limit after annealing. A minimum in the number of the positron traps occurs around 350 °C when the number of displaced silicon atoms, produced by hydrogen agglomeration, is at maximum. Further annealing increases the number of traps, until at high temperatures, above 700 °C, all the traps disappear. This complicated behavior is interpreted as the result of several concomitant effects: the formation of vacancylike defects during implantation, their partial annealing below 350 °C, an initial passivation of the traps caused by hydrogen followed by a reactivation stage, and the formation of thermally stable hydrogen complexes.

We present a detailed analysis of photoreflectance (PR) spectra of semiconductors using complex Airy functions and their derivatives. We demonstrate that photoreflectance spectra can be treated in terms of a single complex Airy function with an energy-dependent broadening parameter. We show analytically and numerically that this complex Airy PR treatment is functionally equivalent within field conditions appropriate for PR to the model of R. N. Bhattacharya, H. Shen, P. Parayanthal, F. H. Pollak, T. Coutts, and A. Aharoni [Phys. Rev. B 37, 4044 (1988)], where the effects of gradient electric field and non-flat-band modulation are treated explicitly. The equivalence occurs because the field gradient and non-flat-band modulation effects are included in our model in the energy dependence of the phenomenological broadening parameter ${\mathrm{\Gamma }}^{\mathrm{*}}$=(${\mathrm{\Gamma }}_0$/ħθ)exp[δ(ħω-${\mathit{E}}_{\mathit{g}}$)], where ħω is the photon energy, ${\mathit{E}}_{\mathit{g}}$ is the band-gap energy, ${\mathrm{\Gamma }}_0$ is the nominal broadening at the band-gap energy, and δ is a parameter directly proportional to the electric-field gradient and modulation between two finite fields. The major utility of our model is that a single effective layer can be treated instead of a more computationally intensive laminar model.

We apply our complex Airy model to bulk semiconductors such as GaAs, InP, and ${\mathrm{In}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As. In the photoreflectance spectra of these semiconductors, our model considers three distinct but convolved features at ${\mathit{E}}_0$ which represent the light- and heavy-hole valence bands and an exciton-impurity feature below ${\mathit{E}}_0$. At ${\mathit{E}}_0$+${\mathrm{\Delta }}_0$ our model considers two features which are related to the spin-orbit-split valence band and a second state just below this critical point. For GaAs, we determined from our PR modeling that the band-gap energy for these films was 1.422±0.003 eV, which agreed, within experimental error, with the band-gap energy measured by room-temperature photoluminescence. A feature was found below the ${\mathit{E}}_0$ gap in the GaAs samples with energies ranging from 3 to 4 meV below the band gap, which is similar to excitonic binding energies in this material system.

A below-critical-point feature was evident in one GaAs sample at 11 meV below the ${\mathit{E}}_0$+${\mathrm{\Delta }}_0$ transition. Also, in GaAs we determined the ratio of light and heavy interband effective masses, ${\mathrm{\mu }}_{\mathrm{LH}}$/${\mathrm{\mu }}_{\mathrm{HH}}$, to be 0.6865, which is in good agreement with values determined in previous studies. For bulk InP the band-gap energy was determined to be 1.340±0.003 eV, which agreed, within experimental error, with the band-gap energy determined from PL. Below-critical-point features were also found for InP with energies of 4.0 and 3.5 meV below the ${\mathit{E}}_0$ and ${\mathit{E}}_0$+${\mathrm{\Delta }}_0$ transitions, respectively. For both GaAs and InP, the surface electric fields determined from the ${\mathit{E}}_0$ and ${\mathit{E}}_0$+${\mathrm{\Delta }}_0$ critical points were in agreement within experimental error. For ${\mathrm{In}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As on InP films near lattice-matched conditions, the complex Airy line shape was applied to both intermediate electric field (Franz-Keldysh oscillations) and low-field-like PR spectra illustrating the utility of the complex Airy functional analysis in fitting both simple and complicated PR responses. We found that the band-gap energy from the PR spectral fits to those determined from photoluminescence measurements agreed within experimental error for these ${\mathrm{In}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As films.

First- and second-order Raman scattering has been studied in epitaxial AlAs grown by solid-source molecular-beam epitaxy. A strong resonant enhancement of dipole-forbidden one-LO and intrinsic two-LO-phonon scattering is observed for excitation at the band-gap energy ${\mathit{E}}_0$. Maxima in the second-order Raman spectrum for excitation both at and below the ${\mathit{E}}_0$ gap resonance are assigned to contributions from various critical points of the Brillouin zone. Published data of ab initio calculations of the AlAs phonon dispersions are found to be in good agreement with the measured frequency positions of the second-order Raman bands. In highly carbon-doped p-type AlAs layers the local vibrational mode of the carbon acceptor (${\mathrm{C}}_{\mathrm{As}}$) is observed at about 635 ${\mathrm{cm}}^{\mathrm{-}1}$.

We extend our previous analysis of the ultrafast laser-induced instability of the diamond structure of semiconductors by including longitudinal optical-phonon distortions in addition to the instability of the transverse acoustic phonons. Generally, longitudinal optical distortions enhance the instability of the transverse acoustic phonons, increasing the kinetic energy of the atoms and the final lattice temperature. These phonons make a transition to a centrosymmetric structure of GaAs with metallic properties possible. We present results for the time dependence of the instability of Si for the case where 15% of the valence electrons have been excited into the conduction band. Thus, already 100 fsec after the excitation of the plasma the atoms are displaced about 1 Å from their equilibrium position and their kinetic energy has increased to approximately 0.4 eV. Collisions between the atoms then lead to a rapid melting of the crystal. These results are in good agreement with recent experiments performed on Si and GaAs.