We present an extensive study pertaining to the quantum-mechanical system of independent electrons in a magnetic field interacting with a finite or infinite number of point impurities (a concept that we develop below). The case where there is a single impurity is completely solved; namely, the corresponding scattering operators in two and three space dimensions are explicitly constructed and the electron spectrum is analyzed. Extension to the case where there is a finite number of impurities is straightforward. The situation is much more subtle when the set of impurities is infinite (albeit countable). We were able to derive the pertinent equations from which the spectrum and wave functions can be determined. Special effort is devoted to the study of a two-dimensional electron gas interacting with an infinite set of random point impurities located on the sites of a regular square lattice (with lattice constant d, say) subject to a perpendicular magnetic field B. It is shown that when the energy eigenvalue coincides with one of the Landau energies ${\mathit{E}}_{\mathit{n}}^{\mathit{B}}$ (n=0,1,...), there is a certain field ${\mathit{B}}_{\mathit{n}}$=(n+1)${\mathit{d}}^2$${\mathrm{\Phi }}_0$ (here ${\mathrm{\Phi }}_0$=hc/e), such that if B>${\mathit{B}}_{\mathit{n}}$, there exist disorder-independent extended eigenstates in the system. These wave functions are given analytically in closed form.

In the present paper, the pathway of ${\mathrm{H}}_2$ desorption from a dihydride species -${\mathrm{SiH}}_2$ on the Si(100) surface, -${\mathrm{SiH}}_2$→-Si+${\mathrm{H}}_2$ (-Si represents a surface Si atom site), is investigated. This pathway involves the recombination of two H atoms bonded to the same surface silicon atom. A three-layer cluster that consists of 12 silicon atoms and 20 hydrogen saturators is used to simulate the Si(100) surface and ab initio self-consistent-field and configuration-interaction theory is used to treat the cluster and desorption reactions. With the correction of zero-point vibrational energies, the ${\mathrm{H}}_2$ desorption energy and activation barrier are computed to be 48 and 53 kcal/mol, respectively. The corresponding adsorption barrier is 5 kcal/mol. Considering the experimental uncertainty and the uncertainty of our calculations, we conclude that the barrier of ${\mathrm{H}}_2$ desorption from the dihydride surface via -${\mathrm{SiH}}_2$ is consistent with the experimental result.

A multimode theory of coherent electron transport through nanostructures in resonance conditions is developed. It is shown that both peaks and inverted peaks of the transmission probabilities as functions of electron energy, such as have been found by computation in a variety of structures, are equally inherent to a local quasilevel, with Lorentzian forms at the quasilevel energy. Some model systems are also investigated. For both types of resonance, formulas in terms of the quasilevel properties are obtained for the multimode transmission and reflection probabilities, dwell times, and transmission and reflection delay times, versus electron energy. A consequence of the result for dwell times is that when all the itinerant states are filled through the resonance range (for one spin value) their density integrated over the site of the quasilevel is just that of one electron.

The problem of hydrogenic systems placed into strongly anisotropic media is solved exactly by using a metric space with a noninteger dimension α (1<α). This appraoch is an elegant and convenient way to treat the case of Wannier-Mott excitons confined in semiconductor superlattices, quantum wells, and quantum-well wires. Indeed, the relative motion of the electron-hole pair which constitutes such excitons can never be considered strictly one dimensional (1D), 2D, or 3D. In this paper, we propose a quantitative analysis of the shape of the optical-absorption edge near an excitonic energy gap, for any arbitrary value of α. We present an exact generalization of the calculations performed in the effective-mass approximation for allowed transitions by Elliot [Phys. Rev. 108, 1384 (1957)] in the three-dimensional case, and by Shinada and Sugano [J. Phys. Soc. Jpn. 21, 1936 (1966)] for two-dimensional media: this model includes contributions of bound states and of the so-called unbound states, which are responsible for an enhanced absorption continuum above the interband energy gap. At high energies, this continuum tends to behave like the α-dimensional valence-to-conduction joint density of states. The versatility of this approach should be particularly useful for modeling and improving the dynamic properties of optical modulators, for which not only the energy gap, but also the dimensionality of the excitonic absorption onset is modulated.

Exact analytic solutions of finite parabolic quantum wells are derived for both the unperturbed and the electric-field-applied cases. Several normalized parameters are defined so as to make our results universal within the scope of the envelope function approximation with a constant effective mass assumed. The Stark resonance position and the width in the electric-field-applied case can be obtained simultaneously from the complex eigenvalue ${\mathit{E}}_0$-iΓ/2 of the system. By comparing the results calculated, respectively, by employing the exact solutions and the infinite-parabolic-well approximation, the validity of the approximation is rigorously examined. It is shown that the infinite-parabolic-well approximation is valid only under certain conditions as discussed in the text.

We describe a general method of calculating exciton energies in shallow quantum wells. This technique is applicable to both single- and multiple-quantum-well systems, and is valid for both type-I and type-II systems, even under circumstances where the valence- and/or conduction-band offsets may be small compared to the exciton binding energy. Quantitative predictions of excitonic energies and relative intensities are made and compared with experimental data on a number of different shallow-well diluted magnetic semiconductor quantum well and superlattice systems. Based on these comparisons, it is shown that the model indeed provides a detailed description and analysis of the type-I–type-II transition and the behavior of excitons in a spin superlattice. In addition, the model also predicts and describes certain additional phenomena, such as metastable ‘‘above-gap’’ excitons which should exist in certain type-II systems. Also, reentrant type-I–type-II–type-I transitions are predicted under some circumstances.

A Si epitaxial layer was selectively grown on ${\mathrm{SiO}}_2$-patterned Si(100) with no miscut and on 1°, 3°, and 4° miscut vicinal surfaces by ultrahigh-vacuum chemical-vapor deposition using disilane. On the patterned Si(100) surfaces with and without miscuts, faceted (100) layers grew. Although {111} is energetically the most stable surface, the resulting facets had {311} orientation. This means that the {311} faceting is related to the growth kinetics rather than the energetics. Macroscopically, the {311} faceting is caused by the slower growth rate of the (311) surface than that of the (100) surface. On the vicinal surfaces, the top surface of the selectively grown layer was not vicinal but had exactly (100) orientation. This indicates the ready incorporation of adatoms into the step edges of (100) terraces and the subsequent step-flow growth mode. When the flowing step reaches the end of the top surface, it is swallowed into the facet and disappears. This decreases the step density and makes the vicinal surface flat. With respect to the swallowing of the growing steps at the facet corner, we propose a microscopic model for the {311} faceting.

We demonstrate the LO-phonon Raman intensity in GaAs/AlAs multiple quantum wells to be inversely proportional to the exciton homogeneous linewidth for photon energies resonant with the band-edge exciton. The strongest Raman scattering is seen at the low-energy side of the exciton peak, where the homogeneous linewidth is narrowest. The energy dependence of the linewidth deduced from the resonance Raman profile agrees well with that measured directly by degenerate-four-wave mixing.

The major obstacle for analytic calculations for electrons in the lowest Landau level arises from the degeneracy of the single-particle eigenstates. When the electron-electron interaction is included, the diagonal energy of different basis states is no longer the same and degenerate perturbation theory can be carried out. The near degeneracy of the single-particle states is manifested as an infrared-divergent perturbation series which is similar to that of a collection of one-dimensional interacting spinless chains. Thus a renormalization-group scheme can be developed. The range of the interparticle potential affects the change in diagonal energy for particle-hole fluctuations. For the Coulomb potential we find that the coupling constants remain unchanged over many length scales. The system remains gapless, consistent with recent transport and surface-acoustic-wave measurements.

First-principles calculations of the surface stress for the c(4×2) buckled-dimer reconstruction of the clean Si(100) surface reveal a significant relief of a compressive contribution to the stress in the direction parallel to the dimer rows, and thus a decrease of the stress anisotropy, when compared to similar calculations for 2×1 reconstructions. We show that the mechanism involved is not just the buckling but its alternation along a dimer row. Calculations using the c(4×2) model for the clean surface are also in close quantitative agreement with the experimentally measured excess tensile stress of the As-covered surface.

The chemical potential and the capacitance of a model quantum dot have been computed, including contributions of exchange and correlation in the limit of 0 K temperature. The Schro¨dinger equation has been solved self-consistently, taking into account the electron-electron Coulomb interaction and many-body effects within the framework of density-functional theory. We have also studied the effect of conducting backgates and of nearby electrodes using the method of images. Depending on the size of the dot, we derive a prevalance of either the quantization energy or the electrostatic energy: there is a smooth transition from predominant quantum effects for small dots to classical capacitance behavior for large dots. Our simulation reproduces characteristic effects that have been experimentally observed, such as the capacitance increase for increasing electron numbers and irregularities in the chemical potential values when randomly distributed charged impurities are present.

We report the occurrence of confined longitudinal-optical phonons in (CdTe${)}_{\mathit{n}}$(ZnTe${)}_{\mathit{n}}$ (n=2, 3, and 5) short-period superlattices as observed in their Raman spectra, complementing the infrared reflectivity studies in which confined transverse-optical phonons were reported [Phys. Rev. B 47, 1998 (1993)]. The dispersion of ZnTe-LO phonons in these highly strained superlattices, determined from the frequencies of the confined phonons is in agreement with inelastic neutron scattering data on bulk ZnTe. The present study also reveals in these superlattices confined CdTe-LO phonons as well as folded acoustic phonons for n=5.

A fractional quantized Hall state with filling fraction ν=p/(2mp+1) can be modeled as an integer quantized Hall state of transformed fermions, interacting with a Chern-Simons field. The electromagnetic response function for these states at arbitrary frequency and wave vector can be calculated using a semiclassical approximation or the random-phase approximation. However, such calculations do not properly take into account the large effective-mass renormalization which is present in the Chern-Simons theory. We show how the mass renormalization can be incorporated in a calculation of the response function within a Landau-Fermi-liquid theory approach such that Kohn’s theorem and the f-sum rules are properly satisfied. We present results of such calculations.

An analysis of the extended x-ray-absorption fine structure recorded at the Co ${\mathit{L}}_{2,3}$ edges of ${\mathrm{CoSi}}_2$ is presented. Absorption was monitored by partial fluorescence yield, allowing us to investigate samples buried in a silicon wafer by means of ion-beam synthesis. The absorption spectrum is not distorted by Bragg diffraction beams due to the low photon energies. The additional Co ${\mathit{L}}_1$ background is modeled by a splining procedure. The first-shell Co-Si distance in the annealed specimen was determined to be 2.32±0.05 Å.

We use ab initio local-density-approximation methods to develop an ab initio model of an a-Si and an a-Si:H surface. Starting with a supercell of bulk a-Si, we remove periodic boundary conditions in one direction and relax the sample using ab initio methods. H is added to remove bulk defects. The surface structure and coordination of atoms is discussed, and defect states are characterized. H is added to dangling bonds on the a-Si:H surface, creating a hydrogen-terminated a-Si:H surface. We explore the relationship between electronic and geometric surface defects.

Calculations on two forms of siloxenic clusters and periodic films have been performed to address the unusual luminescence in porous silicon and to further investigate how the optical gap varies as a function of hydroxyl- or hydrogen-passivator concentration. Within conventional approximations to the density functional theory, our optimized cluster calculations confirm that low-dimensional siloxenic complexes, of stoichiometry [Si]:[O]:[H] = 2:1:2, are most stable when the oxygen atoms form bridging bonds with pairs of silicon atoms. To aid in experimental characterization of siloxenic films, we present equilibrium geometries, electronic structures, chemically induced core-level shifts, and joint densities of states for two forms of siloxenic clusters.

The effect of spin-orbit interaction on persistent currents in mesoscopic Hubbard rings threaded by an Aharonov-Bohm flux is investigated, with attention focused on orbital magnetism. The nonperturbative treatment of the spin-orbit interaction developed by Meir et al. is combined with the Bethe ansatz solution in order to deal with this problem exactly. We find that the interplay of spin-orbit interaction and electron-electron interaction plays a crucial role, bringing about some remarkable effects on orbital magnetism.

The Rayleigh-Fano approach is used to study the scattering of p-polarized light from the deterministically shaped rough surface of a semiconductor in the vicinity of an isolated excitonic transition. Nonlocal effects are accounted by the Hopfield and Thomas dielectric function. A perturbative formalism is developed to calculate the amplitudes of the scattered fields up to second order on the roughness height. Numerical results are presented for the ${\mathit{A}}_{\mathit{n}=1\mathrm{}}$ excitonic transition of CdS using different choices of additional boundary conditions. Comparisons are made with the local model calculations and discussed in terms of resonant elastic scattering. The differential reflectance spectra peaks are also shown and interpreted as surface-exciton-polariton coupling.

The degenerate-four-wave-mixing response of excitons in GaAs quantum wells is modeled using the optical Bloch equations including exciton-exciton interactions. The results display a strong dependence on the polarization of the excitation pulses. The model predicts intensity and polarization dependences of the time-integrated signal and characteristic temporal features of the time-resolved and time-integrated response in excellent agreement with observations.

We observed by scanning tunneling microscopy (STM) a hexagonal superlattice on graphite with a period of 66 Å. Direct measurement of the angle between lattice vectors confirmed that the superlattice is a Moiré pattern caused by a 2.1° rotation of the topmost (0001) plane with respect to the bulk. The STM corrugation of 2.6 Å is not due to physical buckling, but to differences in electronic structure between AA-stacked, normal AB-stacked, and rhombohedral CAB-stacked graphite. The high tunneling current of AA-stacked regions is in agreement with the high density of states at the Fermi level calculated for AA graphite. The Moiré pattern changes, both the amplitude and the shape, with bias voltage. The observation provides a basis for a comparative study of surface electronic structures with different subsurface layer configuration, which is a vital test of our understanding of STM.