We present an exact solution for the hole subband dispersion of a [001] symmetric GaAs/${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As quantum well within the 6×6 Luttinger model, which extends previous work by Andreani, Pasquarello, and Bassani, Phys. Rev. B 36, 5887 (1987) for the 4×4 case. We employ symmetry arguments to decouple the Kramers doubly degenerate subband states and build well-defined parity states of the quantum-well reflection operator, which include the spin-split-off band. Numerical results are presented for the hole subband states and in-plane dispersion curves of a 66-Å AlAs-GaAs-AlAs quantum well, which show anticrossing behavior. The nature of anticrossings between the first and second and the eighth and ninth subbands is investigated by studying the bulk state decomposition of the envelope functions. In the vicinity of the first and second subband anticrossing, there is a negligible bulk GaAs spin-split-off band content. In contrast, in the region of the anticrossing for the higher eighth and ninth subband states, there is considerable GaAs spin-split-off band amplitude, as the GaAs spin-split-off band is nearby in energy.

The atomic and electronic structures of the {122} Σ=9 tilt and 〈111〉 Σ=7 and 〈011〉 Σ=3 twist boundaries in Si have been examined by using the transferable semiempirical tight-binding method. The effects of various kinds of structural disorder, except coordination defects, on the local electronic structure of Si at the interfaces have been analyzed, and the origins of band tails at grain boundaries in Si have been investigated. Odd-membered rings induce the changes in the shapes of the local densities of states (LDOS’s), where the densities of states are increased at the two minima among the three peaks of the bulk valence-band DOS and are decreased at the s-p mixing peak. Four-membered rings generate the LDOS’s of a particular shape, where the sharp s-like and p-like peaks are shifted toward the bottom and the top of the valence band, respectively, and the features between these two peaks are smoothed. Bond distortions, strictly bond stretchings and bond-angle distortions, generate states at the top of the valence band and at the bottom of the conduction band, inducing the peaks at the band edges in the LDOS’s. Greatly stretched bonds generate so-called weak-bond states, which consist of the bonding and antibonding states inside the minimum band gap. These states are deeper in the band gap and are more spatially localized at the bond and neighboring atoms than the shallow band-edge states caused by smaller bond distortions.

Dihedral-angle disorder does not induce such marked changes in the LDOS’s, although there exists a slight shift of the p-like peak toward lower energy, which seems to be related to the suppression of bulklike states at the top of the valence band. The present relations between the structural disorder and the local electronic structure of Si also apply to general disordered systems such as amorphous Si. It can be said that the effects of the respective kinds of structural disorder have been shown much more clearly than in the previous studies of amorphous Si because here the respective kinds of disorder can be arranged and buried properly between the bulk crystals in the configurations of grain boundaries. Regarding band tails, it has been shown that the band-edge states caused by bond distortions can penetrate into the minimum band gap according to the degree of bond distortions, and that those in the coincidence-site-lattice (CSL) tilt boundaries do not penetrate into the minimum band gap because of small bond distortions. The band-edge states coming from bond distortions are frequently localized in the interface layers, although these are not necessarily localized in the directions parallel to the interface. Greater bond distortions existing isolated or sparsely in the interface generate states deeper in the band gap with stronger localization behavior in the directions parallel to the interface as in the case of the present weak-bond states. The band tails at grain boundaries in Si observed experimentally can be explained by the distribution of such distorted or weak bonds in general grain boundaries or at defects in the CSL tilt boundaries. This is the first theoretical study that has successfully explained the origins of the band tails at grain boundaries in Si.

A quantum-mechanical study of the magneto-oscillations in asymmetric heterostructures is presented with the aim of clarifying the origin and the effects of the spin-orbit spin splitting in the conduction subband. The magnetization of the two-dimensional electron gas at the interface of modulation-doped III-V semiconductor heterojunctions is calculated as a function of applied magnetic field and carrier concentration, taking into account both spin-orbit (zero-field) spin-splitting contributions: one due to the ${\mathit{k}}^3$ bulk term and one due to the lack of specular symmetry ${\mathrm{\sigma }}_{\mathit{h}}$ along the growth direction. Regular beating patterns in the amplitude of the oscillations are shown to originate from the latter term. The ${\mathit{k}}^3$ term introduces a k-space anisotropy in the zero-field spin splitting. This leads to anomalous beating patterns, related to the occurrence of a magnetic breakdown at special points of the Fermi surface with a small spin splitting. Experimental evidence of regular beating patterns has been found in InAs-based heterostructures. The possibility of observing anomalous beating patterns in GaSb heterojunctions is discussed.

The 16×2 structure and the (17,15,1) 2×1 structure have been found on a Si(110) surface. Scanning-tunneling-microscope (STM) observations showed that the 16×2 structure was similar to the (17,15,1) 2×1 structure and both of them had a common structural unit. In the top view, the 16×2 structure is identical to the (17,15,1) 2×1 structure, but in the side view, the 16×2 structure is on the (110) plane and the (17,15,1) 2×1 structure on the (17,15,1) vicinal plane. A unit cell of the (17,15,1) 2×1 structure is identical to the common unit cell and that of the 16×2 structure is represented by a pair of the upper and lower terraces formed by the common unit cell. A rumpling model for the 16×2 structure and the (17,15,1) 2×1 structure is proposed on the basis of STM and ultraviolet-photoelectron-spectroscopy results, where Si atoms are displaced in the direction normal to the (110) surface and the displacement oscillates along the [110] direction. The corrugation in the rumpling is 0.5 nm.

We present measurements and calculations of femtosecond gain dynamics in ${\mathrm{In}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As/${\mathrm{Al}}_{\mathit{y}}$${\mathrm{Ga}}_{1\mathrm{-}\mathit{y}}$As strained-layer single-quantum-well diode lasers using a multiple-wavelength pump-probe technique. To aid in the interpretation of gain dynamics induced by both interband absorption and stimulated emission of photons, we develop a detailed theoretical model for gain dynamics in quantum-well laser diode structures and compare it with experimental measurements. In the model, transient gain and differential transmission are computed in a multiband effective-mass model including biaxial strain, valence subband mixing, and polar-optical-phonon scattering both within and between subbands. Transient photogeneration of electron-hole pairs by the pump pulse and subsequent relaxation of carriers by polar-optical-phonon scattering are calculated in a Boltzmann-equation framework.

Based upon Keldysh nonequilibrium Green functions, a theoretical formalism is developed to study the current-noise characteristics of one-dimensional double-barrier heterostructures. The effects of the Coulomb blockade on the I-V curve and on the current fluctuation is studied. For the static case a reduction of the full shot noise is observed. A connection between the noise frequency dependence and the transit time of the electron going through the structure is established.

We extend the work of Bottomley et al. [Appl. Phys. Lett. 63, 2324 (1993)] on second-harmonic generation from short-period (${\mathrm{Si}}_{\mathit{m}}$${\mathrm{Ge}}_{\mathit{n}}$${)}_{\mathit{p}}$ strained-layer superlattices (SLS) with n and m both odd integers. Such structures are theoretically predicted to be noncentrosymmetric and therefore should possess a large bulk, nonlinear susceptibility ${\mathrm{\chi }}^{\mathrm{}\left(2\right)\mathrm{}}$. However, the prior work showed that the inevitable presence of single atomic-height steps on the Si(001) substrate leads to the formation of antiphased domains within the SLS and hence a macroscopically centrosymmetric material. Here we report second-harmonic generation induced by a 775-nm beam on several samples of nominally (${\mathrm{Si}}_7$${\mathrm{Ge}}_3$${)}_{20}$ SLS’s grown on several substrates vicinal to Si(001), including those with biatomic-height steps; the latter substrates should allow in-phase domains to be grown. A nonzero, but weak bulk ${\mathrm{\chi }}^{\mathrm{}\left(2\right)\mathrm{}}$ is obtained. We propose that the weak nonlinear response is influenced by nonideal superlattice periodicity which results in the formation of antiphase domains along the growth direction. Suggestions are offered for how noncentrosymmetric SLS’s may eventually be realized.

Using a microscopic local-field formulation, the linear optical absorption of a multiple-quantum-well (MQW) structure associated with intersubband transitions is investigated. Taking as a starting point a fundamental self-consistent integral equation for the local field, the p-polarized electric-field distribution inside each quantum well in the MQW structure is studied. It is demonstrated that the local field is essentially determined from a set of linear algebraic equations. Within the infinite-barrier approximation with an effective well width, numerical calculations of the optical absorption spectra are presented for a GaAs/${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As multiple quantum well for different parameters such as the two-dimensional (sheet) electron concentration, the angle of incidence, and the number of wells. The numerical results show that the local-field effect leads to a notable blueshift of the peak-position energy in the absorption spectra as the sheet density of the electrons is increased, and that for larger angles of incidence the electromagnetic interaction among quantum wells gives rise to a significant broadening of the absorption peak when the number of wells is sufficiently large.

The influence of quantum interference (weak localization) on perpendicular transport of holes in superlattices is investigated. Due to heavy-hole effective mass, the miniband width is small and the collisional broadening Γ can be larger than the Fermi energy ${\mathrm{\varepsilon }}_{\mathit{F}}$. In such situations, the quasiparticle approximation breaks down and the particle-particle diffusion propagator (from coherent backscattering) contains the effective diffusion coefficient D${\mathrm{̃}}_{\mathit{Z}}$, which significantly differs from the classical one. In this case the Einstein relation between the effective diffusion constant and the conductivity is not valid. The correction to the conductivity caused by quantum interference is not small and leads to a large reduction in hole mobility. Numerical calculations of the hole mobility versus superlattice period and temperature are in good agreement with experimental results and show a significant deviation from previous theories.

We show that an asymmetric Fano profile in resonant Raman scattering results from the electron–LO-phonon interaction at a particular incident laser wavelength in a quantum well with appropriate structure parameters.

The effects of the spin-orbit interaction on the envelope-function equations for semiconductor heterostructures are investigated. The wave functions are expanded over a complete orthonormal set of spinors. The entire derivation is based solely on the Schrödinger equation as well as the completeness and orthonormality relations of the expansion bases. The envelope-function equations are found to be a set of integral equations, rather than a set of integrodifferential equations. It is verified that two aspects of the model including the spin-orbit interaction are the same as the spinless model. First, the exact envelope-function equations can be localized to be a set of differential equations if the envelope functions are slowly varying. Second, the localization effectively smooths the abruptness of the material transitions at semiconductor heterojunctions. However, in the vicinity of the heterojunction, the expressions for the coefficients of the localized envelope-function equations differ from the spinless model by a sinc [sinc(t)=sin(t)/t] term due to the spatial gradient in the spin-orbit-interaction operator. Finally, the exact envelope-function equations for the system, which is non-lattice-matched in the growth direction, are derived for the three-dimensional model with spin-orbit interaction.

The electronic structures of GaAs/${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$${\mathrm{Al}}_{\mathit{x}}$As quantum wires (corrugated superlattices) grown on (311)-oriented substrates are studied in the framework of the effective-mass envelope-function method. The electron and hole subband structure and optical transition matrix elements are calculated. When x=1, the results are compared with experiments, and it is found that the direct transition becomes an indirect transition as the widths of well and barrier become smaller.

The linear optical response of the GaAs(110) surface has been investigated by studying the adsorption of hydrogen on semi-insulating and variously doped GaAs(110) using both ellipsometry and reflectance difference spectroscopy. The surface optical properties were influenced by the hydrogen-induced change in surface geometry and, hence, the microscopic surface electronic structure, and by macroscopic band bending effects. We detected surface electronic transitions of the clean surface at 2.75 eV that disappear with hydrogen adsorption, as well as significant hydrogen-induced changes of the surface optical properties near the bulk critical points. Furthermore, it was observed that hydrogen adsorption leads to a significantly lower surface anisotropy, as compared to the clean surface, in the case of semi-insulating GaAs(110), where the band bending effects are negligible; the energy dependence of the surface anisotropy is similar to that reported in the literature for oxidized GaAs(110), but with a much smaller amplitude. The influence of doping is discussed in light of the band bending effects–the electric field effect and the unscreening of impurities in the depletion layer. We estimate the strength of these two contributions and conclude that the unscreening of impurities predominates over the electric field effect.

We studied the atomic and electronic properties of the polar GaAs/ZnSe(001) interface using first-principles total-energy calculations. Binding energy, atomic relaxations, local electric fields, and valence-band offsets are calculated for a variety of different interface structures. The abrupt interface is found to be energetically unstable for large supercells, whereas structures with an interface consisting of one or two mixed layers are energetically more stable. Among these structures an interface consisting of one mixed layer and a c(2×2) structure is found to be the most stable. The valence-band offset is not explained by a single structure but in terms of a degeneracy in the interface energy with respect to polarity which results in a vanishing interface dipole moment even for polar interfaces. Based on the first-principle results we derive a simple model that explains the arrangement of atoms within the mixed layer and gives insight into the mechanisms stabilizing certain interface structures.

The magnetic configuration of edge channels near the boundary of a quasi-two-dimensional electron gas in the integer quantum Hall regime is studied in the Hartree-Fock approximation. In earlier work [J. Dempsey, B. Y. Gelfand, and B. I. Halperin, Phys. Rev. Lett. 70, 3639 (1993)] electron-electron interactions were found to cause a spin-polarizing transition of the outermost edge states. These calculations are extended by including a nonequilibrium occupation of spin levels. A sudden reversal of edge-channel positions is predicted at values of the chemical-potential difference much smaller than the enhanced spin splitting at the edges. The crossings, which arise when edge channels switch position in open systems, are identified as solitonlike, one-dimensional magnetic domain walls. The interaction between these magnetic defects is investigated. Possible consequences and verification by experiment of the predictions are discussed.

In a two-dimensional electron system with a lateral superlattice potential in a perpendicular magnetic field, the Landau levels split into a complicated, self-similar, field-dependent spectrum, known as ‘‘Hofstadter’s butterfly.’’ We study transport along a strip of finite width, subject to a magnetic field over a long but finite interval, as a function of field and energy. The fractal structure shows up in the field and energy dependence of the magnetoconductance. The scale of this structure, given by one flux quantum per plaquette, ${\mathit{a}}^2$, is easily accessible with laboratory fields in the case of fabricated superlattices, where a is in the range of a≊1 μm. The three-dimensional butterfly resulting from plotting the conductance as a function of field and energy summarizes a number of well known facts about magnetotransport. Additional features are due to band gaps in the edge state spectrum. The lateral current distribution of the edge states, and downstream from the field region, is calculated. Reflections at the field–no-field boundaries cause Aharonov-Bohm ripples on the conductance plateaus. The amplitudes of these ripples depend in a nontrivial manner on how the magnetic field is switched on and off.

A discrete model is introduced to account for the time-periodic oscillations of the photocurrent in a superlattice observed by Kwok et al. in an undoped 40-period AlAs/GaAs superlattice. The basic ingredients are an effective negative-differential resistance due to the sequential resonant tunneling of the photoexcited carriers through the potential barriers, and a rate equation for the holes that incorporates photogeneration and recombination. The photoexciting laser acts as a damping factor ending the oscillations when its power is large enough. The model explains (i) the known oscillatory static I-V characteristic curve through the formation of a domain wall connecting high- and low-electric-field domains, and (ii) the photocurrent and photoluminescence time-dependent oscillations after the domain wall is formed. In our model, they arise from the combined motion of the wall and the shift of the values of the electric field at the domains. Up to a certain value of the photoexcitation, the nonuniform field profile with two domains turns out to be metastable: after the photocurrent oscillations have ceased, the field profile slowly relaxes toward the uniform stationary solution (which is reached on a much longer time scale). Multiple stability of stationary states and hysteresis are also found. An interpretation of the oscillations in the photoluminescence spectrum is also given.

The oscillatory part of the conductivity along the confining planes of a superlattice miniband under a perpendicular quantizing magnetic field was calculated, assuming a tight-binding approximation for the miniband dispersion. The manifestation of the belly and neck cross sections of the Fermi surface is studied as a function of the broadening of the electronic energy levels, miniband widths, and energy minigaps. The effects of the deviation from the nearest-neighbor tight-binding approximation upon the line shape of the magnetoresistance are studied. The model presented allows for a quantitative description of the magnetoresistance spectra and is in good agreement with recent experimental observations on ${\mathrm{InAs}}_{1\mathrm{-}\mathit{x}}$${\mathrm{Sb}}_{\mathit{x}}$/InSb doped superlattices and GaAs with a periodical planar doping of silicon.

A sum rule for electronic intersubband transitions has been derived following Kane’s model, beyond the quadratic dispersion relations. The sum rule takes into account the effects of nonparabolicity and the different effective masses in the well and barrier materials; it depends on the property of the ground state of the system and, as such, on the shape of the potential. The boundaries of the validity of matrix element computations are also discussed in the case where only the conduction band is included. Experimental results are presented for bound-to-bound and bound-to-continuum intersubband transitions in various types of ${\mathrm{Al}}_{\mathit{x}}$${\mathrm{In}}_{1\mathrm{-}\mathit{x}}$As/${\mathrm{Ga}}_{\mathit{y}}$${\mathrm{In}}_{1\mathrm{-}\mathit{y}}$As quantum well systems (single wells, coupled wells and quantum wells with Bragg confinement); the agreement with theory is excellent. In the last section of the paper, the effect of the electric field on the sum rule is investigated.

The electronic structures of the As/Si(001) 2×1 and Sb/Si(001) 2×1 surfaces with symmetric dimers are calculated self-consistently with the use of planar basis functions made of two-dimensional plane waves and one-dimensional Gaussian functions, based on local-density-approximation and norm-conserving pseudopotentials. The calculations show that both the As/Si(001) 2×1 and Sb/Si(001) 2×1 surfaces are semiconductors with energy gaps of about 1.0 eV. Both As and Sb surface bands have similar dispersion and are very different from that of the Si(001)2×1 surface. The calculated dispersion of surface states for As/Si(001) is in good agreement with the angle-resolved photoemission measurements. The calculated work functions are 5.56 and 4.03 eV for As/Si(001) and Sb/Si(001) surfaces, respectively. We find substantial charge transfer for the As/Si(001) surface, indicating a strong ionic character in the As-Si bonds and small charge transfer for the Sb/Si(001) surface, indicating covalent character in the Sb-Si bonds. The strong polar covalent bonding between surface As atoms and underlying Si atoms may be responsible for the stability of the As/Si(001) surface.