We discuss the Mott-Hubbard transition in light of the Hubbard model in infinite dimensions with special emphasis on the finite-temperature aspects of the problem. We demonstrate that the Mott transition at finite temperatures has a first-order character. We determine the region where metallic and insulating solutions coexist using second-order perturbation theory and we draw the phase diagram of the Hubbard model at half filling with a semicircular density of states. We discuss the lessons learned from the present treatment of the Hubbard model and the connection to other approximation schemes and to experiments on transition-metal oxides.

Hole-doped ${\mathrm{Sr}}_{1+\mathit{x}}$${\mathrm{La}}_{1\mathrm{-}\mathit{x}}$${\mathrm{FeO}}_4$ (0≤x≤0.3) samples were prepared, and electrical transport, magnetic properties and ${}_{}{}^{57}{}_{}{}^{}\mathrm{Fe}$ Mössbauer spectra of the resulting materials were measured. The results were compared with those of hole-doped charge-transfer (CT) insulators. The antiferromagnetic Néel temperature decreased from ∼ 350 to ∼150 K on going from x=0 to 0.3, and dc electrical resistivity at room temperature decreased from ∼${10}^3$ Ω cm for x=0 to ∼${10}^0$ Ω cm for x=0.3. The heavily doped samples showed semiconducting behavior even for x=0.3. Seebeck voltage measurements demonstrated that all the samples were p-type semiconductors. Although the changes in the magnetic properties upon doping were qualitatively similar to the CT insulators such as (La,Sr${)}_2$${\mathrm{CuO}}_4$ and (La,Sr${)}_2$${\mathrm{NiO}}_4$, the changes in the electrical-transport properties upon doping differed from those in the CT insulators. The origin of these differences is discussed with reference to the changes in the electronic structure upon doping.

The electronic structure of ${\mathrm{K}}_2$${\mathrm{NiF}}_4$-type ${\mathrm{Sr}}_{1+\mathit{x}}$${\mathrm{La}}_{1\mathrm{-}\mathit{x}}$${\mathrm{FeO}}_4$ compounds (0≤x≤0.3) was studied by ultraviolet-photoemission and x-ray-absorption spectroscopies. Resonant photoemission measurements demonstrated that although the satellite feature of ${\mathrm{Sr}}_{1\mathrm{-}\mathit{x}}$${\mathrm{La}}_{1\mathrm{-}\mathit{x}}$${\mathrm{FeO}}_4$ was attributed to ${\mathit{d}}^4$ final states, the whole valence band was constructed from well mixed Fe 3d and O 2p states. It was suggested that the parent ${\mathrm{Sr}}_{1+\mathit{x}}$${\mathrm{La}}_{1\mathrm{-}\mathit{x}}$${\mathrm{FeO}}_4$ compound is intermediate between Mott-Hubbard and charge-transfer insulators. O K-edge and Fe K-edge x-ray-absorption measurements showed that hole bands composed of O 2p and Fe 3d character were formed in the original conduction-band edge upon hole doping, while the valence-band structure obtained by nonresonant photoemission measurements did not change. Changes in the electrical and magnetic properties were correlated with those in electronic structure.

Expressions for the generalized Friedel sum rule are derived which are applicable as a condition for charge neutrality at defects in metallic systems. These defects include the thoroughly studied substitutional impurity as well as the poorly explored interstitial impurity and an atom at the saddle-point position between two vacancies, being typical for substitutional electromigration. The expressions are derived starting from Lloyd’s formula for the density of states of an arbitrary collection of scattering potentials.

An expression is derived for the electron density of states of an arbitrary collection of scattering potentials, described with respect to another, related collection of scatterers. This latter system, serving as a reference system, replaces free space, being the reference system for Lloyd’s formula. The expression is very similar in form compared with the original expression. It contains the system t-matrix defined with respect to the reference system. The generalized Lloyd formula is very useful in describing defects in dilute alloys. The derivation is accomplished by evaluating the trace operation in the formal density-of-states expression in the r representation, by integrating over all space explicitly, and by using a generalized form of the equality due to Jacobs and Zaman.

Multiple-scattering theory, as it is applicable to metallic systems, is generalized systematically compared with the usual formulation. The generalization refers to the reference system, which conventionally is free space, but which can be chosen to be much more general. For example, in describing a binary alloy, a defect in a metal, or a finite impurity-cluster model for the latter system, the reference system may be an average medium, the unperturbed metallic host system, or the finite host cluster, respectively. Applications are indicated for the generalized Friedel sum rule, the local density of states, and the transition probability of a Bloch electron. A state in a system is shown to be built up of properly generalized incoming and outgoing waves.

A linear combination of a few Gaussian functions of variable widths and anisotropy was used as a trial function for ${\mathit{D}}^0$ centers in bulk crystals and in parabolic quantum wells in the presence of a magnetic field. The same types of functions with an additional correlation factor were then used for ${\mathit{D}}^{\mathrm{-}}$ ions in the bulk and in parabolic quantum wells. All integrals including the electron-electron interaction were calculated analytically. The results obtained for the bulk are very accurate for ${\mathit{D}}^0$ centers and quite close to the experimental data for ${\mathit{D}}^{\mathrm{-}}$ ions in GaAs. The impurities in parabolic quantum wells were not yet experimentally investigated but the present results indicate that even in the case of a uniform spatial distribution they should lead to well-defined infrared absorption maxima.

We have observed that the infrared-active stretching modes of hydrogen in device-quality a-Si:H films are redshifted as the temperature increases. Over the range of temperatures studied, 100–600 K, the shift is approximately linear with temperature, 0.035 ${\mathrm{cm}}^{\mathrm{-}1}$ ${\mathrm{K}}^{\mathrm{-}1}$, and shows a totally reversible behavior. We have established that changes in the polarization of the material, via changes of the dielectric constant with temperature, can lead to small shifts, but cannot explain the magnitude of the experimentally observed effect. We compare our results with a similar observation made on well defined hydrogen-terminated Si surfaces. In that case, the shift was attributed to the coupling of the hydrogen stretching motion with lower-frequency phonons. We propose that an analogous coupling mechanism is present in the a-Si:H structure.

Using the method of selective excitation of the exciton luminescence in ${\mathrm{Cd}}_{1\mathrm{-}\mathit{x}}$${\mathrm{Mn}}_{\mathit{x}}$Te epilayers we have measured energies of localized magnetic polarons (LMP’s) for alloys with manganese mole fractions x≤0.34. The suppression of the LMP energy has been studied in external magnetic fields and with temperature increase. Polaron formation times and exciton lifetimes have been measured by time-resolved photoluminescence. We have found that in alloys with x<0.17 the polaron formation process is interrupted by exciton recombination and, as a result, the LMP does not reach its equilibrium energy. This dynamical effect on the polaron energy together with the strong sensitivity of the LMP formation to the conditions of primary exciton localization causes the absence of the LMP formation in layers with x<0.1. Antiferromagnetic clustering of Mn ions, which leads to the spin-glass phase formation at low temperatures, affects the polaron energy and results in the increasing stability of LMP’s against suppression by temperature increase and magnetic fields. In ${\mathrm{Cd}}_{1\mathrm{-}\mathit{x}}$${\mathrm{Mn}}_{\mathit{x}}$Te with x>0.20 a considerable part of the polaron energy is controlled by the input of clusters of antiferromagnetically coupled Mn spins located in the nonuniform molecular field of localized excitons. The comparison of the exciton Zeeman splitting and the LMP magnetic-field suppression provides insight into the internal structure of LMP’s.

Thermal emission of electrons and holes from the ${\mathrm{Fe}}^{2+}$-${\mathrm{Fe}}^{3+}$ level in ${\mathrm{In}}_{0.53}$${\mathrm{Ga}}_{0.47}$As is investigated in detail. Iron is found to act as a recombination center in this material, since majority carrier emission is observed in n- and in p-type layers. The interaction of the Fe level with free carriers is strongly localized, resulting in statistical distributions of the apparent activation energy and the electron and hole capture cross sections due to the statistical distribution of the occupancy of the cation sites by indium and gallium ions. A detailed general model for carrier capture and emission of a recombination center in a ternary alloy as observed by deep-level transient spectroscopy (DLTS) is developed. The mean energy position of ${\mathrm{Fe}}^{2+}$-${\mathrm{Fe}}^{3+}$ is determined as 0.39±0.02 eV above the valence-band edge. This value agrees perfectly with the prediction of the internal reference rule. The electron and hole capture cross sections are distributed over nearly two orders of magnitude, causing a shift of the DLTS peaks with filling pulse width and nonexponential refilling of the traps. The mean values at 250 K are ${\mathrm{\sigma }}_{\mathit{n}}$=8±5×${10}^{\mathrm{-}18}$ ${\mathrm{cm}}^2$ and ${\mathrm{\sigma }}_{\mathit{p}}$=2±1×${10}^{\mathrm{-}17}$ ${\mathrm{cm}}^2$ for the electron and hole capture cross sections, respectively.

We present here extensive numerical simulations on electron transport in an impurity-band model for a doped semiconductor in the presence of site-diagonal disorder and long-range Coulomb interactions. The primary question we address is, what is the role of the finite-temperature particle-hole distribution on the conductance? At T=0, we find a soft Coulomb gap of the form ρ(${\mathit{E}}_{\mathit{F}}$)∼‖E-${\mathit{E}}_{\mathit{F}}$${\mathrm{\Vert }}^{1.17}$ for d=2 and ρ(${\mathit{E}}_{\mathit{F}}$)∼‖E-${\mathit{E}}_{\mathit{F}}$${\mathrm{\Vert }}^{2.38}$ for d=3. An analysis of the distribution of particles and holes at T=0 reveals that sites with small excitation energies in the ground state are segregated into particle and hole clusters of varying radii. The role of such clusters in the transport process is examined. It is observed that the conductance calculated within single-particle transport theory obeys the expected granular metal law of σ=${\mathrm{\sigma }}_0$ exp[-(${\mathit{T}}_0$/T${)}^{1/2}$] in d=2,3 when the T=0 ground-state configuration of the particles and holes is used to compute the conductance. At finite temperature, we find that the Coulomb gap fills in as ρ(${\mathit{E}}_{\mathit{F}}$)∼${\mathit{T}}^{\mathit{d}\mathrm{-}1}$. However, we observe that the conductance is activated, σ=${\mathrm{\sigma }}_0$ exp(-${\mathit{T}}_{\mathit{a}}$/T), even at very low temperatures when the finite-temperature distribution of particles and holes is used to compute the conductance in d=3. Only slight deviations from ${\mathit{T}}^{\mathrm{-}1/2}$ were observed in d=2. Our results suggest then that the precise origin of the σ=${\mathrm{\sigma }}_0$ exp[-(${\mathit{T}}_0$/T${)}^{1/2}$] law for the conductance in strongly correlated systems is unclear. The relevance of our findings to experiments on doped magnetic semiconductors which observe activated as opposed to ${\mathit{T}}^{\mathrm{-}1/2}$ transport is discussed.

A detailed theoretical study of impact-ionization-related transport phenomena in ${\mathrm{SiO}}_2$ thin films is presented. The Boltzmann transport equation is integrated by the Monte Carlo method using acoustic-phonon-scattering rates derived from photoinduced electron transmission experiments. It is shown that these empirical scattering rates necessitate the inclusion of impact ionization at fields F>${\mathit{F}}_{\mathrm{th}}^{\mathrm{ii}}$=7 MV/cm because phonon scattering alone can no longer stabilize the electron energy distribution below the ionization energy of 9 eV. However, even above ${\mathit{F}}_{\mathrm{th}}^{\mathrm{ii}}$, acoustic-phonon scattering is found to considerably delay the heating of electrons, leading to a wide dark space in which impact ionization cannot take place or is strongly reduced. Therefore, the electron multiplication factors m(F,${\mathit{t}}_{\mathrm{ox}}$) decrease rapidly with decreasing oxide thickness, ${\mathit{t}}_{\mathrm{ox}}$, for ${\mathit{t}}_{\mathrm{ox}}$<30 nm. These predictions are shown to be consistent with results of several high-field transport experiments in silicon–silicon-dioxide device structures. The calculated electron energy distributions develop high-energy tails which extend beyond the band-gap energy at fields larger than ${\mathit{F}}_{\mathrm{th}}^{\mathrm{ii}}$, as observed by vacuum emission experiments. The calculated impact-ionization coefficients are found to be in good agreement with values derived from experiments.

The hole generation factors m-1 quantitatively agree with substrate hole-current to channel-current ratios measured by the carrier separation technique in n-channel field effect transistors with gate oxide thicknesses ${\mathit{t}}_{\mathrm{ox}}$≥25 nm. The field and thickness dependence of the measured positive charge buildup (hole trapping) near the Si/${\mathrm{SiO}}_2$ interface can be quantified in terms of impact ionization in the oxide film. The calculated carrier multiplication, however, cannot fully account for the substrate hole currents and the hole trapping measured in thinner oxides, ${\mathit{t}}_{\mathrm{ox}}$≤20 nm, indicating that another mechanism, likely related to hole injection from the anode, becomes the dominant source for hole currents in thin oxides. Dielectric breakdown of thin ${\mathrm{SiO}}_2$ films on silicon is reevaluated on the bases of all of these findings. It is proposed that time-dependent breakdown is the result of cumulative degradation of the oxide near its interfaces caused by impact ionization and by hot-electron-induced hydrogen release together. This ansatz is shown to yield a good understanding for the oxide field and thickness dependence of the interface-state generation and of the charge to breakdown. Since impact ionization is strongly suppressed in thin films, ${\mathit{t}}_{\mathrm{ox}}$<25 nm, degradation and time-dependent breakdown appear to be largely caused by hydrogen release and its subsequent secondary reactions in these thin films.

The coupled plasmon–longitudinal-optical-phonon modes of a degenerate inhomogeneous electron or hole gas in a bulk compound semiconductor are studied. The interaction of a point charge with these coupled modes is derived in the random-phase approximation for both the carriers and the phonons in a form which is appropriate for treating inhomogeneous carrier systems. An integral equation governing the interaction of a static point charge with these coupled modes is derived which has the same form as that in the case of a point-charge interacting with plasmons alone but in which the parameters are modified by the coupling to phonons. As a specific example, these results are used to study the binding of the coupled plasmon-phonon modes to point charges in degenerate compound semiconductors, and it is found that such bound states will exist only at very low carrier densities.

We report results on the relaxation of deposition-induced nonequilibrium state and steady-state defect density in undoped hydrogenated amorphous silicon (a-Si:H). The relaxation was studied by monitoring the change of dark conductivity and photoconductivity as a low-substrate-temperature film undergoes thermal annealing. It is found that the time dependence of the relaxation follows a stretched-exponential time law, as observed in the relaxation of the nonequilibrium state induced by various treatments. It is found that the time constant ${\mathrm{\tau }}_{\mathit{R}}$ and stretched exponent β derived from the relaxation is thermally activated with an activation energy of about 0.94 eV and is given by β≊T/273 K, respectively. In addition, it is found that the defect density in the steady state is about 2.6×${10}^{16}$ ${\mathrm{cm}}^{\mathrm{-}3}$, and independent of temperature, inconsistent with that expected in the thermal equilibrium theory.

Besides the known tetrahedral ${\mathrm{Mn}}_4^0$ cluster, a second Mn cluster is observed by electron paramagnetic resonance in high-resistivity silicon doped with manganese. The spectrum shows trigonal symmetry. The analysis of the fine structure and the hyperfine structure suggests that the spectrum is due to a cluster consisting of four Mn ions forming a tetrahedron, [${\mathrm{Mn}}_{3\mathit{i}}^0$-${\mathrm{Mn}}_{\mathit{i}}^{\mathit{x}}$], where the fourth ${\mathrm{Mn}}^{\mathit{x}}$ ion gives rise to the trigonal symmetry. Most likely it is either a ${\mathrm{Mn}}^{\mathrm{-}}$ ion at an interstitial site or a ${\mathrm{Mn}}^{+}$ ion at a substitutional site. The [${\mathrm{Mn}}_{3\mathit{i}}^0$-${\mathrm{Mn}}_{\mathit{i}}^{\mathrm{-}}$] cluster model is favored. The observed S=11/2 ground-state manifold is the result of the dominant exchange coupling between the electronic spins of the four Mn constituents. The coordination of four ions in a tetrahedron seems to be an energetically preferred state during the formation of bigger clusters in the silicon lattice.

We have performed infrared absorption, continuous-wave photoluminescence, and nanosecond photoluminescence decay measurements to characterize stain-etched porous silicon. Stain-etched porous silicon samples were prepared by etching boron-doped crystalline silicon wafers in a solution of HF:${\mathrm{HNO}}_3$:${\mathrm{H}}_2$O with ratios of 1:5:10 by volume. The dependence of continuous-wave photoluminescence intensity upon temperature and excitation energy has been studied. We have also investigated the dependence of nanosecond photoluminescence decay upon temperature, excitation energy, and emission energy. Our results suggest that the photoluminescence in stain-etched porous silicon might be due to the presence of siloxene-type bonding configuration in an amorphous alloy of silicon, oxygen, and hydrogen.

We have calculated the contribution of the lowest-order vertex-correction diagram to the direct gap of silicon at the Γ point, taking into account the dynamic screening of the electron-electron interaction. Our best calculation yields a contribution of 0.12 eV. This result supports the assumption of the GW approximation that vertex corrections can be neglected. We do not find a significant shift of the absolute energies.

Local-density-functional theory is used to determine the structure of minimum energy of a substitutional boron atom in diamond and a hydrogen atom bonded to that point defect. It is found that the substitutional boron is an on-site impurity with a vibrational frequency of 1228 ${\mathrm{cm}}^{\mathrm{-}1}$. It is also found that the hydrogen atom takes up a position in a 〈100〉 direction relative to the boron atom. This is in contrast to the structure of similar acceptor-hydrogen complexes in silicon and other tetrahedrally bonded semiconductors. The vibrational frequency associated with the stretching mode of the boron-hydrogen bond is calculated to be between 2540 ${\mathrm{cm}}^{\mathrm{-}1}$ and 2655 ${\mathrm{cm}}^{\mathrm{-}1}$.

The fine structure of the P excitons in β-${\mathrm{ZnP}}_2$ is studied by two-photon absorption. Due to the anisotropy of the crystal a giant energy splitting of the 2P exciton states of up to 7 meV is observed. This splitting allows the determination of the reduced masses without an external field. The following values are obtained: ${\mathrm{\mu }}_{\mathit{a}}$=0.47${\mathit{m}}_0$, ${\mathrm{\mu }}_{\mathit{b}}$=0.53${\mathit{m}}_0$, and ${\mathrm{\mu }}_{\mathit{c}}$=0.088${\mathit{m}}_0$.

A numerical simulation of the antiferromagnetic spin pairing of neighboring magnetic ions within a diluted magnetic semiconductor is presented. Utilizing a random distribution of the magnetic ions requires the inclusion of nearest-neighbor interactions only in order to give agreement with the low-field bulk-magnetization properties observed experimentally. However, the latter are shown to be a relatively insensitive measure of the degree of ordering in the alloy system, and the experimental results could equally well be accounted for by assuming appreciable alloy clustering. The simulations also show that there is an enhancement in the paramagnetism associated with the interface layers in a quantum-well structure.