Resonant elastic scattering of light from single quantum wells in semiconductor multilayers

A theory is developed for steady-state elastic scattering of light via quasi-2D excitons from a quantum well (QW) whose interfaces are randomly rough. The study is mainly focused on the angle dependences of radiation giving direct information about static disorder responsible for the elastic scattering. A nonlocal excitonic susceptibility is expressed in terms of random profile functions of QW interfaces. Treated is elastic scattering of light from a disordered QW in the following actual dielectric environments: (i) a uniform background, (ii) a Fabry–Perot film with rough boundaries, and (iii) a semiconductor microcavity. The cross-sections are derived analytically for scattering of linearly polarized light to the lowest (Born's) approximation with arbitrary roughness statistics. The spectral and angle dependencies of scattering intensity are analyzed numerically in the absolute-value scale with Gaussian correlation of interface roughness. The probability 10⁻² was found for the exciton-mediated scattering of a photon from a QW interface roughness whose root-mean-square height is on the level of 2×10⁻¹ nm. This probability is shown to exceed by two orders of magnitude that is typical of resonant scattering from either a single semiconductor surface or rough boundaries of a semiconductor Fabry–Perot film containing the QW. The scattering spectrum of a QW placed in a microcavity is predicted to have a doublet structure whose components are associated with the cavity exciton–polaritons.     

Resonance elastic scattering of light by a quantum well with statistically uneven boundaries

A theory is formulated for the elastic scattering of light through quasi-two-dimensional exciton states in a quantum well with randomly uneven walls. The nonlocal exciton susceptibility is expressed in terms of random functions describing the shape of the quantum well boundaries up to and including linear terms in the unevenness height. The resonance elastic scattering cross sections in the presence of arbitrary statistical unevenness are calculated in the Born approximation for all channels in which the initial and final states are represented by an electromagnetic TM or TE mode. The spectral and angular dependences of the scattering probability are calculated with the unevenness characterized by Gaussian correlation functions. It follows from numerical estimates that elastic scattering in quantum wells should be observed for unevenness having an rms height of the order of the thickness of an atomic monolayer. Fiz. Tverd. Tela (St. Petersburg) 41, 330–336 (February 1999)     

Effect of dimension and type of model on statistical characteristics of scattered light

The effect of the type of the model describing a non-Gaussian relief, as well as of the problem dimension, on the statistical characteristics of scattered monochromatic light is considered. A difference in the shape of diffuse scattering indicatrices was observed for different types of surface models (with identical height distributions and autocorrelation functions). The effects revealed because more pronounced with an increase in the deviation of surface height distribution from normal and with an increase in the roughness height.     

ELECTRON-INTERFACE PHONON SCATTERING IN ASYMMETRIC SEMICONDUCTOR QUANTUM WELL STRUCTURES

Electron-interface phonon scattering rates in asymmetric single quantum well and step quantum well structures are calculated by means of the interaction Fr?hlich-like Hamiltonian between an electron and interface optical phonons in a four-layer heterostructure given re-cently. The intrasubband and intersubband electron scattering rates are given as functions of quantum well width, step width and step height. We have found that the electron scattering depends strongly on the potential parameters and the usual selection rules for these tran-sitions are broken down in asymmetric heterostructures; the interface LO modes are more important than the interface TO modes for the electron-interface phonons scattering in het-erostructures; the intrasubband scattering rates are insensitive functions of step width and step height, and the intersubband scattering rates are complicated functions of step height and step width in step quantum wells. Moreover, we have also observed that the scattering rates for intrasubband and intersubband transitions have no obvious changes in the case that the first or second subband energy level crosses the step height in a step quantum well.     

Spontaneous emission and elastic scattering of light from quantum-well excitons in a Fabry-Perot microcavity

A theory of spontaneous emission and elastic light scattering by quasi-two-dimensional excitons in a quantum well placed in a Fabry-Perot microcavity is developed. The problem is solved by means of electrodynamic Green’s functions with inclusion of fluctuations of the quantum-well width and cavity wall shape treated as a perturbation. General expressions are found in a zero approximation of perturbation theory (plane interfaces) for the radiative decay rates of quasi-two-dimensional excitons and for their energy shifts in the cavity. The boundary conditions for the electromagnetic field are taken into account through the coefficients of inward light reflection from the cavity walls. Resonance contributions to the scattering cross sections, which differ in the polarizations (p or s) of the incident and scattered waves, are derived in the lowest (Born) approximation in quantum-well width fluctuations. The spectral and angular dependences of elastic light scattering are studied numerically for Gaussian and exponential correlation functions. It is shown that the contribution from quantum-well width fluctuations to light scattering exceeds that due to single interfaces (surfaces) of a heterostructure by two orders of magnitude.     

Anisotropic Interface Roughness Scattering in a Lateral Superlattice

A novel interface roughness due to the perturbation of the periodic interface structure is studied theoretically for a lateral superlattice realized by an interface corrugated quantum well. It is found by numerical simulation that the correlation function for interface roughness can be well modeled by a sinusoidal function with an exponential decay in the direction of corrugation. Such a feature makes the correlation function far from a Gaussian function which is extensively used as a theoretical approximation of the correlation function for interface roughness. With such a correlation function, the influence of interface roughness scattering on electronic transport in the lateral superlattice is investigated. Consequently, it gives rise to a high anisotropy of electronic transport both in the absence and presence of a magnetic field, by which the relevant experiments can be well explained.     

Anisotropic Interface Roughness Scattering in a Lateral Superlattice

A novel interface roughness due to the perturbation of the periodic interface structure is studied theoretically for a lateral superlattice realized by an interface corrugated quantum well. It is found by numerical simulation that the correlation function for interface roughness can be well modeled by a sinusoidal function with an exponential decay in the direction of corrugation. Such a feature makes the correlation function far from a Gaussian function which is extensively used as a theoretical approximation of the correlation function for interface roughness. With such a correlation function, the influence of interface roughness scattering on electronic transport in the lateral superlattice is investigated.Consequently, it gives rise to a high anisotropy of electronic transport both in the absence and presence of a magnetic field, by which the relevant experiments can be well explained.     

Exciton energy relaxation on acoustic phonons in double-quantum-well structures

The paper analyzes the rate of energy relaxation involving acoustic phonon emission between exciton states in a double quantum well. A theoretical study is made of the part played by two mechanisms, one of which is a one-step transition with emission of an acoustic phonon and the other is a two-step transition, which includes elastic exciton scattering from interface nonuniformities followed by energy relaxation within an exciton subband. The rate of the two-step transition in real double quantum wells is shown to be higher than that of the one-step transition. As follows from calculations, the fast energy relaxation between exciton states is determined by the elastic scattering of phonons from the interface.     

Transport theory for quantum wells with an electric field across the well: a new concept for a transistor

The transport properties of a two-dimensional electron gas in a quantum well with infinite barriers and with an electric field across the well as perturbation is calculated for zero temperature. Background impurity doping, remote impurity doping and interface roughness scattering are considered. The effects which are linear in the electric field are calculated. We suggest an experiment to measure the differences in the interface roughness scattering at the two interfaces of the quantum well by the electric field effect. We also discuss a possible device application of the field effect and describe a transistor working at the metal-insulator transition.     

Untersuchung der Lichtstreuung von transparenten Einfachschichten auf Glassubstraten

Investigations of Light Scattering from Transparent Single Layers on Glass Substrates In the present paper the influence of stochastic interface roughness as well as film thickness on light scattering from dielectric single layers is investigated. By calculations carried out on base of Elson's vector scattering theory especially the importance of correlation functions of microroughness is analyzed. Measurements made from sputtered TiO₂-films show dominating interface scattering and an interference phenomenon, depending on film thickness.     

Electron mobility in a modulation doped AlGaN/GaN quantum well

We consider a two dimensional electron gas confined to a modulation doped AlGaN/GaN quantum well and study the dependence of low field mobility on various parameters such as composition, well width, remote impurity and interface roughness as a function of temperature. GaN is assumed to be in the zincblende structure. Acoustic and optical phonon, ionized remote impurity and interface roughness scatterings are taken into account in mobility calculations. The scattering rates are calculated using the self-consistently calculated wave functions obtained from the numerical solution of Poisson and Schr?dinger equations. Also found from the self-consistent solutions are the potential profile at the junction, the energy levels in the well and electron concentrations in each level. Ensemble Monte Carlo method is used to find the drift velocities of the two dimensional electrons along the interface under an applied field. The mobility of two dimensional electrons is obtained from the drift velocity of electrons. It is found that while remote impurity scattering is very effective for small values of spacer layer and doping concentrations, increasing Al concentration reduces the mobility of electrons. The effect of surface roughness, on the other hand, on mobility is almost independent of well width. The results of our simulations are compatible with the existing experimental data.     

Well-width dependence of interface roughness scattering in GaAs/Ga1 − xAlxAs quantum wells

Well-width dependence of quantum and transport mobilities of electrons in GaAs/GaAlAs multiple quantum wells is studied for wells with widths ranging between 50 Å and 145 Å Experimental results are obtained from the amplitude analysis of the Shubnikov–de Haas (SdH) oscillations and from conventional Hall measurements at temperatures betweenT = 15 K and 4.2 K. A novel technique is employed to estimate, theoretically, the interface roughness parameters from electron quantum and transport lifetimes. The modelling is carried out for a range of layer fluctuations, width (Δ) and lateral size (Λ), as to obtain the best fit to the experimental results for individual samples. Our results indicate that the interface roughness scattering limits equal both quantum and transport mobilities at low temperatures, and that the nature of scattering by interface roughness (small or large angle) depends not only on the size and the width of the fluctuations but also on the distribution of these fluctuations within the samples. Therefore, unlike the predictions of the existing theoretical models, which assume constant values of Δ and Λ for all well widths, the well-width dependence of interface roughness scattering cannot be verified experimentally.     

Low temperature electron mobility in Ga0.5In0.5P/GaAs quantum well structures

We analyse the low temperature subband electron mobility in a Ga_0.5In_0.5P/GaAs quantum well structure where the side barriers are delta-doped with layers of Si. The electrons are transferred from both the sides into the well forming two dimensional electron gas (2DEG). We consider the interface roughness scattering in addition to ionised impurity scattering. The effect of screening of the scattering potentials by 2DEG on the electron mobility is analysed by changing well width. Although the ionized impurity scattering is a dominant mechanism, for small well width the interface roughness scattering happens to be appreciable. Our analysis can be utilized for low temperature device applications.      

Measurement of roughness of two interfaces of a dielectric film by scattering ellipsometry

The polarization of light scattered by oxide films thermally grown on photolithographically generated microrough silicon surfaces was measured as functions of scattering angle. Using the predictions of first-order vector perturbation theory for scattering from interfacial roughness to interpret the results, the roughness of each interface and the correlation function between the two interfaces can be determined. The results show the spatial frequency dependence of the SiO (2)/Si interface smoothening.     

Investigation of interface roughness cross-correlation properties of optical thin films from total scattering losses

The interface roughness and interface roughness cross-correlation properties affect the scattering losses of high-quality optical thin films. In this paper, the theoretical models of light scattering induced by surface and interface roughness of optical thin films are concisely presented. Furthermore, influence of interface roughness cross-correlation properties to light scattering is analyzed by total scattering losses. Moreover, single-layer TiO₂ thin film thickness, substrate roughness of K9 glass and ion beam assisted deposition (IBAD) technique effect on interface roughness cross-correlation properties are studied by experiments, respectively. A 17-layer dielectric quarter-wave high reflection multilayer is analyzed by total scattering losses. The results show that the interface roughness cross-correlation properties depend on TiO₂ thin film thickness, substrate roughness and deposition technique. The interface roughness cross-correlation properties decrease with the increase of film thickness or the decrease of substrates roughness. Furthermore, ion beam assisted deposition technique can increase the interface roughness cross-correlation properties of optical thin films. The measured total scattering losses of 17-layer dielectric quarter-wave high reflection multilayer deposited with IBAD indicate that completely correlated interface model can be observed, when substrate roughness is about 2.84 nm.     

Determining angles of incidence and heights of quantum dot faces by analyzing X-ray diffuse and specular scattering

Scattering of X rays by structures with multilayer ensembles of quantum dots MBE-grown in the In(Ga)As-GaAs system is studied by high-resolution grazing X-ray reflectometry. The peaks of the diffuse scattering intensity are discovered for the first time in structures with both vertically uncorrelated and vertically correlated quantum dots. It is shown that the position of the peak is totally determined by angle of inclination of the quantum dot pyramidal faces (the so-called blaze condition for diffraction gratings), which was theoretically predicted earlier. Comparison with the results of scattering simulation carried out by the technique of boundary integral equations indicates that a simple geometrical condition allows one to exactly determine the value of from the position of the intensity peak, the shape of which depends on many parameters. As follows from the theory and experiment, the width and height of the peaks for samples with vertically correlated quantum dots are larger than for those with uncorrelated dots. The roughness and interdiffusion of interfaces and the height of quantum dots are found from the position and amplitude of Bragg peaks. Thus, the conventional application of high-resolution grazing X-ray reflectometry is extended in this work to determination of the quantum dot geometry.     

Electron mobility limited by surface and interface roughness scattering in AlxGa1-xN/GaN quantum wells

The electron mobility limited by the interface and surface roughness scatterings of the two-dimensional electron gas in AlxGa1-xN/GaN quantum wells is studied. The newly proposed surface roughness scattering in the AlGaN/GaN quantum wells becomes effective when an electric field exists in the AlxGa1-xN barrier. For the AlGaN/GaN potential well, the ground subband energy is governed by the spontaneous and the piezoelectric polarization fields which are determined by the barrier and the well thicknesses. The thickness fluctuation of the AlGaN barrier and the GaN well due to the roughnesses cause the local fluctuation of the ground subband energy, which will reduce the 2DEG mobility.     

Diffuse X-ray scattering from crystalline structures with quantum dots of pyramidal shape

Diffuse scattering from crystalline structures with quantum dots (QDs) in the shape of a regular truncated pyramid with a square base is investigated. The elastic strains around QDs are calculated using the Green function method. The fields of the QD atomic displacements and the angular distribution of scattering intensity in the reciprocal space as functions of the QD concentration are simulated numerically. The influence of a pyramidal QD cross section by the diffraction plane on the diffuse X-ray scattering is demonstrated.     

Interference in light scattering from slightly rough dielectric layers

The scattering of light from a slightly rough surface overlying a reflecting surface is investigated. It is shown that the long-scale component of the roughness spectrum plays a critical role in the scattering patterns obtained. The scattered interference patterns are critically dependent on small variation of the rms height of the long-scale component of the roughness. Conventional perturbation theory is found to be invalid in cases in which interference phenomena in the scattering are of importance. A model is proposed that quantitatively describes the measured angular intensity distributions.