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Theoretical study of photo-stimulated thermo-magnetoelectric effects in two-dimensional compositional superlattices using quantum kinetic equation
Abstract
Two scattering mechanisms, including the confined electron (CE)–confined acoustic phonon (CAP) scattering and the CE–confined optical phonon (COP) scattering, have been considered in the theoretical problem of photo-stimulated thermo-magnetoelectric effects (TME) occurring in two-dimensional compositional semiconductor superlattices (CSS). The quantum kinetic equation (QKE) method is applied to calculate the characteristic quantities of two typical photo-stimulated TME, namely, the Ettingshausen effect (EE) and the Peltier effect (PE). The obtained analytical results show that the external fields (the magnetic field B, the dc electric field E, the frequency and the amplitude of the laser radiation), the period of superlattice d as well as the temperature of the systems T are quantities that govern the quantum Ettingshausen coefficient (qEC) and the quantum Peltier coefficient (qPC).The presence of m-quantum number specifying phonon confinement in the analytical expression of the qEC and the qPC is as a demonstration for the influence of size effect on both the EE and the PE. The results are numerically estimated and graphed for the CSS to indicate the dependence of the qEC and the qPC on aforementioned quantities. Moreover, the confined phonons contribute to the magneto-phonon-photon resonance condition (MPPRC) in CSS. Therefore, the behaviors of the photo-stimulated TME within phonon confinement are different from the case of bulk phonons. Due to the confinement of an acoustic phonon, the Shubnikov–de Hass oscillations are observed with the changes in the amplitude and the posture when investigating the dependence of the qEC and the qPC on the magnetic field and the frequency of the laser radiation (LR). Meanwhile, resonance peaks of these coefficients are relocated under the influence of a COP. Besides, the confinement of phonons causes the changes in the magnitude of both the qEC and the qPC compared to the case of unconfined phonons. The obtained results hold true for all temperatures and contribute to perfecting the theory of the quantum TME in the low-dimensional semiconductor systems (LDSS).
The photostimulated Nernst effect in compositional semiconductor superlattices under the influence of a confined acoustic phonon is studied by using the quantum kinetic equation. The case of the confined electron-confined acoustic phonon scattering process is examined in detail. The obtained analytical results reveal that the Nernst coefficient (NC) depends on the external field such as magnetic field B, the frequency Ω, and the amplitude E 0 of the electromagnetic wave in a complicated way but also like a function of the temperature of the system and the period of the superlattice. It also depends on the quantum number m -describing the confined acoustic phonon. The theoretical results are depicted and discussed for GaAs/Al x Ga 1 − x As compositional semiconductors superlattices. The results indicate that the Shubnikov-De hass oscillations have appeared. The confined phonons make the magnitude of the Nernst coefficient higher and more obvious than the case of a bulk phonon. In addition, the magneto-photon resonance condition is also proved. Besides, the Nernst coefficient decreases significantly as the temperature increases. The oscillations Nernst coefficient in a magnetic field are consistent with the previous experimental.
The influence of confined optical phonons (confined OP) and electromagnetic waves on the Peltier effects in rectangular quantum wires (RQW) in a parallel magnetic field is investigated. Theoretical results for the parallel Peltier coefficient (PC) are determined using the quantum kinetic equation method. It is defined as a function of the external magnetic field, amplitude, and frequency of the electromagnetic wave, temperature, and size of the RQW, especially quantum numbers , and characterizing the confined OP. The theoretical results are numerically appraised and graphed for the GaAs RQW model. It shows that confined OP not only increases the parallel PC but also expands the resonance position compared to the unconfined OP case. Besides, the parallel PC increases significantly as the temperature rises and the confined OP is the main cause of the increase in the parallel PC at low temperatures. In addition, the resonance peaks of the parallel PC are shifted to the region of the larger magnetic field. When the width of the RQW is less than 20 nm, the parallel PC increases significantly. When the width of the RQW rises to infinity, the results of bulk semiconductors could be obtained.
By using a quantum kinetic equation for electrons, we studied magneto - thermoelectric effects in the doped semiconductor superlattice (DSSL) under the influence of electromagnetic waves (EMW). In case of the electron - acoustic phonon interaction, we have also figured out analytical expressions of the Ettingshausen coefficient (EC) in DSSL. These expressions are quite different from those which were obtained in the case of bulk semiconductors. The results are numerically calculated for the GaAs:Be/ GaAs:Si DSSL; we found that the EC depends on the characteristic parameters of EMW, temperature and the characteristic parameters of DSSL. The results are consistent with recently experimental observations but the EC is different from that in the bulk semiconductors or bismuth. In addition, the impact of the EMW on the Ettingshausen effect was also discovered. These are latest results which have been studied in terms of Ettingshausen effect in DSSL.
We investigate the influence of phonon confinement on the optically detected electrophonon resonance (ODEPR) effect and ODEPR line-width in quantum wells. The obtained numerical result for the GaAs/AlAs quantum well shows that the ODEPR line-widths depend on the well's width and temperature. Besides, in the two cases of confined and bulk phonons, the linewidth (LW) decreases with the increase of well's width and increases with the increase of temperature. Furthermore, in the small range of the well's width, the influence of phonon confinement plays an important role and cannot be neglected in considering the ODEPR line-width.
The magnetoresistivity (MR) is theoretically calculated in a compositional semiconductor superlattice (CSSL), subjected to a crossed DC electric field and magnetic field, in the presence of an intense electromagnetic wave (EMW). The magnetic field is oriented along the growth direction of the CSSL and the electron–acoustic phonon interaction is taken into account at low temperature. Numerical results for the GaN/AlGaN CSSL show the Shubnikov–de Haas (SdH) oscillations in the MR whose period does not depend on the temperature and amplitude decreases with increasing temperature. The temperature dependence of the relative amplitude of these oscillations is in good agreement with other theories and experiments in some two-dimensional (2D) electron systems. The influence of the EMW as well as superlattice structure on the MR is discussed and compared with available theoretical and experimental results.
The response of two-dimensional electron gas to temperature gradient in
perpendicular magnetic field under steady-state microwave irradiation is
studied theoretically. The electric currents induced by temperature gradient
and the thermopower coefficients are calculated taking into account both
diffusive and phonon-drag mechanisms. The modification of thermopower by
microwaves takes place because of Landau quantization of electron energy
spectrum and is governed by the microscopic mechanisms which are similar to
those responsible for microwave-induced oscillations of electrical resistivity.
The magnetic-field dependence of microwave-induced corrections to phonon-drag
thermopower is determined by mixing of phonon resonance frequencies with
radiation frequency, which leads to interference oscillations. The transverse
thermopower is modified by microwave irradiation much stronger than the
longitudinal one. Apart from showing prominent microwave-induced oscillations
as a function of magnetic field, the transverse thermopower appears to be
highly sensitive to the direction of linear polarization of microwave
radiation.
In recent years, devices based on the Peltier effect, which is the basis for solid-state thermoelectric cooling, have evolved rapidly to meet the fast-growing electronic industry. The Peltier effect corresponds to the heat extraction or absorption occurring at the contact between two different conducting media when a direct current (DC) electric current flows through this contact. A comprehensive study of the mechanisms of heating and cooling originated by an electrical current in semiconductor devices is reported. The thermoelectric cooling in n-n, p-p, and p-n junction contacts, as well as inhomogeneous bulk semiconductors, are analyzed. Both degenerate and nondegenerate electron and hole gases are considered. The role of recombination and nonequilibrium charge carriers in the contact cooling (heating) effect is discussed. Along with the above, special attention is paid to several aspects of nonequilibrium thermodynamics of thermoelectric phenomena involved in Peltier effect in semiconductors that demand a careful examination. The formulation of an adequate self-consistent theoretical model describing the Peltier effect is also presented.
The nonlinear absorption coefficient (NAC) of a strong electromagnetic wave (EMW) by confined electrons in quantum wells under the influences of confined phonons is theoretically studied by using the quantum transport equation for electrons. In comparison with the case of unconfined phonons, the dependence of the NAC on the energy (ħΩ), the amplitude (Eo) of external strong EMW, the width of quantum wells (L) and the temperature (T) of the system in both cases of confined and unconfined phonons is obtained. Two limited cases for the absorption: close to the absorption threshold (|kħΩ – ħω0| « ε) and far away from the absorption threshold (|kħΩ – ħωo| » ε) (k = 0,±1,±2,...,ωo and ε are the frequency of optical phonon and the average energy of electron, respectively) are considered. The formula of the NAC contains the quantum number m characterizing confined phonons and is easy to come back to the case of unconfined phonons and linear absorption. The analytic expressions are numerically evaluated, plotted and discussed for a specific case of the GaAs/GaAsAl quantum well. Results show that there are more resonant peaks of the NAC which appear in the case of confined phonons when Ω > ω0 than in that of unconfined phonons. The spectrums of the NAC are very different from the linear absorption and strongly depend on m.
We have studied transverse thermomagnetic effects in a quantum well (QW) with parabolic potential in the presence of a magnetic field parallel to the two-dimensional electron gas layer. The calculation was carried out for the case of elastic electron scattering on short-range potential for degenerate and non-degenerate electron gas. It is shown that the reviewed mechanism of charge carriers' relaxation is essential for the electroconductivity at low temperatures. In the quantum limit, the dependencies of the transverse Nernst–Ettingshausen coefficient and the thermopower on the magnetic field strength, the temperature and the carrier density are determined and analyzed. We have showed that the magnetothermopower is not determined by the entropy only, as is the case for bulk specimens.
Nonlinear Peltier coefficient of a doped InGaAs semiconductor is calculated numerically using the Monte Carlo technique. The Peltier coefficient is also obtained analytically for single parabolic band semiconductors assuming a shifted Fermi-Dirac electronic distribution under an applied bias. Analytical results are in agreement with numerical simulations. Key material parameters affecting the nonlinear behavior are doping concentration, effective mass, and electron-phonon coupling. Current density thresholds at which nonlinear behavior is observable are extracted from numerical data. It is shown that the nonlinear Peltier effect can be used to enhance cooling of thin film microrefrigerator devices especially at low temperatures.
In the present work, the case of a spherical quantum dot with parabolic confinement subjected to an external electric field with the presence of an impurity, the linear and third-order nonlinear optical absorption coefficients as well as refractive index changes have been calculated. The numerical method we are using for the calculation of the energy levels and the corresponding wave functions is the potential morphing method in the effective mass approximation. As our results indicate an increase of the electric field and/or the position of the impurity and/or the quantum dot radius redshifts the peak positions of the total absorption coefficient and total refractive index changes. Additionally, an increase of the position of the impurity and/or the quantum dot radius decreases the total absorption coefficient and increases the total refractive index changes. An increase also of the electric field decreases the total absorption coefficient but does not significantly affect the peak values of the total refractive index changes. Finally, an increase of the optical intensity considerably changes the total absorption coefficient as well as the total refractive index changes.
The one‐body linear response expressions (diagonal and nondiagonal) for the dc electrical conductivity, obtained in a previous paper, are applied to specific situations. In the case of ‘‘no collisional current’’ we evaluate the relaxation times which enter an expression (diagonal) for the longitudinal magnetoconductivity; in the case of ‘‘collisional current’’ another expression (diagonal) for the transverse magnetoconductivity is evaluated. The calculations are carried out in the framework of electron–phonon interaction in crystalline materials; various kinds of phonons are considered. The formula for ‘‘collisional current’’ is also used for an analytic evaluation of the phonon assisted hopping conductivity in crystalline and amorphous materials. The results are in harmony with those of the literature or are new. Further, the nondiagonal expression leads to a result for the oscillatory Hall effect, which, in contrast with previous results, is independent of the interaction (e.g., interaction with impurities).
We develop a theoretical model to the scattering time due to the electron-confined LO-phonon in GaAs-Al x Ga 1−x As superlattice taking into account the sub-band parabolicity. Using the new analytic wave function of electron miniband conduction of superlattice and a reformulation slab model for the confined LO-phonon modes, an ex-pression for the electron-confined LO-phonon scattering time is obtained. In solving nu-merically a partial differential equation for the phonon generation rate, our results show that for x = 0.45, the LO-phonon in superlattice changes from a bulk-like propagating mode to a confined mode. The dispersion of the relaxation time due to the emission of confined LO-phonons depends strongly on the total energy.
We consider a one-dimensional periodic potential, or “superlattice,” in monocrystalline semiconductors formed by a periodic variation of alloy composition or of impurity density introduced during epitaxial growth. If the period of a superlattice, of the order of 100 Å, is shorter than the electron mean free path, a series of narrow allowed and forbidden bands is expected due to the subdivision of the Brillouin zone into a series of minizones. If the scattering time of electrons meets a threshold condition, the combined effect of the narrow energy band and the narrow wave-vector zone makes it possible for electrons to be excited with moderate electric fields to an energy and momentum beyond an inflection point in the E-k relation; this results in a negative differential conductance in the direction of the superlattice. The study of superlattices and observations of quantum mechanical effects on a new physical scale may provide a valuable area of investigation in the field of semiconductors.
We study the extended acoustic-phonon modes in a cylindrical GaAs quantum wire embedded in bulk AlAs. There are two kinds of resonant acoustic-phonon modes related to the wire dimensions: one is entirely extended in the system and the other is almost confined in the wire. Displacement of extended phonon modes in the wire region is enhanced for the resonant modes. The dispersion relations of these resonant modes have subband structures similar to those of confined phonon modes in free-standing wires. Owing to the resonant modes, the extended phonon modes, in the wire region, have characters of confined phonon modes in a free-standing wire rather than the usual bulk phonon modes.
In elemental bismuth, 10(5) atoms share a single itinerant electron. Therefore, a moderate magnetic field can confine electrons to the lowest Landau level. We report on the first study of metallic thermoelectricity in this regime. The main thermoelectric response is off-diagonal with an oscillating component several times larger than the nonoscillating background. When the first Landau level attains the Fermi energy, both the Nernst and the Ettingshausen coefficients sharply peak, and the latter attains a temperature-independent maximum. These features are yet to be understood. We note a qualitative agreement with a theory invoking current-carrying edge excitations.
Photo-stimulated quantum thermo-magnetoelectric effects in doped two-dimensional semiconductor superlattices, including the photo-stimulated quantum Ettingshausen effect and the photo-stimulated quantum Peltier effect, have been theoretically studied by using the quantum kinetic equation method. In this work, we assume that the electron-confined acoustic phonon scattering is essential. Moreover, the presence of the laser radiation (LR) is also taken into account to determine the influence of confined phonons on the aforementioned effects. We have defined the analytical expressions for the kinetic tensors and the Ettingshausen and the Peltier coefficients, presented the numerically calculated the theoretical results for the GaAs:Si/GaAs:Be doped semiconductor superlattice and compared them with these for the case of an unconfined acoustic phonon. The results obtained indicated that the formulas for the kinetic tensors, the Ettingshausen coefficient (EC) and the Peltier coefficient (PC) contain the quantum number m specifying the confinement of a phonon and approach the results for an unconfined phonon as m goes to zero. We found that the kinetic tensors, the EC and the PC oscillate with changing magnetic field and that the confinement of a phonon causes a shift of the peaks in these oscillations to lower energy. The dependences of both EC and PC on the temperature were found to be nonlinear. Moreover, all the coefficients level off when the temperature was less than 4.5 K or greater than 5.5 K. The EC also depended on the doping concentration in a nonlinear way and reaches a positive constant value when the semiconductor superlattice was doped with a high concentration. Most of the numerical results showed that the magnitude of the tensors, the EC as well as the PC, within a confined acoustic phonon varie significantly in comparison with the unconfined phonon case. This means that the confinement of the phonon affects the thermo-magnetoelectric effect quantitatively and qualitatively. These results contribute to completing the theory of the thermo-magnetoelectric effects in the low-dimensional semiconductor systems.
The quantum magneto-thermoelectric effect in a two-dimensional compositional superlattice under the influence of an electromagnetic wave (EMW) in two cases is investigated. Two cases of the electron scattering mechanism are considered: the electron-acoustic phonon scattering and electron-optical phonon scattering. Analytical expressions for the quantum Ettingshausen coefficient (EC), the thermopower tensor, the thermoelectric tensor and the kinetic tensor are obtained by using a quantum kinetic equation. These expressions are numerically solved for the two-dimensional compositional superlattice GaAs/AlGaAs and the results are discussed. The results show that in the case of electron-acoustic phonon scattering, the Shubnikov-de Haas oscillations appear when we examine the dependences of the quantum EC, the thermopower tensor and the thermoelectric tensor on the magnetic field. In the case of electron-optical phonon scattering, resonance peaks that satisfy the condition of the inter-subband magneto-phonon resonance appear. In the two cases, the superlattice period (a parameter specific to the material) strongly affects the quantum magneto-thermoelectric effect. When the superlattice period is small, quantum EC oscillations (in the case of electron-acoustic phonon interaction) and quantum EC resonance peaks (in the case of electron-optical phonon interaction) appear. However, when the superlattice period is large, these oscillations and resonance peaks are not observed. Especially, the influence of electromagnetic waves on the quantum magneto-thermoelectric effect is also clarified. The quantum theory of the magneto-thermoelectric effect has been studied from low temperature to high temperature. This overcomes the limitations of the Boltzmann kinetic equation which was studied at high temperature. The results are new and can serve as a basis for further development of the theory of quantum magneto-thermoelectric effects in low-dimensional semiconductor systems.
We observe the phonon-drag voltage oscillations correlating with the
resistance oscillations under microwave irradiation in a two-dimensional
electron gas in perpendicular magnetic field. This phenomenon is explained by
the influence of dissipative resistivity modified by microwaves on the
phonon-drag voltage perpendicular to the phonon flux. When the lowest-order
resistance minima evolve into zero-resistance states, the phonon-drag voltage
demonstrates sharp features suggesting that current domains associated with
these states can exist in the absence of external dc driving.
We study a microscopic model of a thermocouple device with two connected
correlated quantum wires driven by a constant electric field. In such isolated
system we follow the time-- and position--dependence of the entropy density
using the concept of the reduced density matrix. At weak driving, the initial
changes of the entropy at the junctions can be described by the linear Peltier
response. At longer times the quasiequilibrium situation is reached with well
defined local temperatures which increase due to an overall Joule heating. On
the other hand, strong electric field induces nontrivial nonlinear
thermoelectric response, e.g. the Bloch oscillations of the energy current.
Moreover, we show for the doped Mott insulators that strong driving can reverse
the Peltier effect.
We suggest a theoretical method for the determination of valence-band offsets at alloy-type heterojunctions that is based on average-bond-energy theory in conjunction with a cluster expansion method. The application of this method to AlxGa1-xAs/GaAs produces results in very good agreement with relevant experimental data.
The properties of semiconductor superlattices---solid-state structures in which there exists, in addition to the periodic potential of the crystal lattice, a one-dimensional potential whose period is much longer than the lattice constant---are studied. The existence of the superlattice potential substantially alters the energy spectrum, as a result of which superlattices have a number of interesting properties which ordinary semiconductors do not have. Superlattices offer a unique possibility for altering their band structure practically arbitrarily. The characteristic features of the luminescence of superlattices (tunability of the emitted wavelengths, the excitonic nature of the radiation up to room temperature, strong suppression of impurity trapping, femtosecond kinetics, etc.) are being exploited to develop a new generation of light-emitting devices. The acoustic properties of superlattices are characterized by the existence of selective reflection of phonons. Semiconductor superlattices are characterized by substantially nonlinear transport properties, owing to the presence of very narrow minibands in their energy spectrum.
The Ettingshausen effect in semiconductors is mainly due to the generation of electron-hole pairs at one side of the sample and their recombination at the other side. The Ettingshausen coefficient is calculated, in agreement with Putley, as P=(Egkappaec)z(1+z)- 2(mue+muh) where z=(nhmuhnemue)-ratio of hole conductivity to electron conductivity. Eg is the gap energy, and kappa the thermal conductivity. We discuss this formula for intrinsic, p-type and n-type semiconductors. P goes through a maximum for p-type semiconductors near the temperature at which the Hall voltage goes through zero. Our results agree reasonably well with the measurements of Mette, Gärtner, and Loscoe of P as a function of temperature for different samples of germanium and silicon.
The electron self-energy and correction to the electron effective mass in a freestanding quantum wire with parabolic confining potential was investigated by the perturbation approach. Both the electron-confined longitudinal optical (LO) phonon and surface optical (SO) phonon interactions were considered. Results shows that, for small wire radius, the contributions of electron-LO phonon interaction to the electron self-energy and the correction to the electron effective mass are relatively small in compare with those of the electron-SO phonon interaction.
Instabilities in semiconductor heterostructure growth can be exploited for the self-organized formation of nanostructures, allowing for carrier confinement in all three spatial dimensions. Beside the description of various growth modes, the experimental characterization of structural properties, such as size and shape, chemical composition, and strain distribution is presented. The authors discuss the calculation of strain fields, which play an important role in the formation of such nanostructures and also influence their structural and optoelectronic properties. Several specific materials systems are surveyed together with important applications.
The unusual electrical and optical properties of three important types of semiconductor superlattices are reviewed. The artificial structures which were grown by molecular beam epitaxy (MBE) consist of a periodic sequence of ultrathin crystalline layers of alternating composition (AlxGa1-xAs/GaAs or GaxIn1-xAs/GaAsySb1-y) or of alternating doping (n-GaAs/p-GaAs). The electronic energy bands in these superlattives are split into quasi-two-dimensional subbands whose spacing and width can be tailored by appropriate choice of the design parameters of the structure. After a brief outline of the electronic properties of compositional superlattices, we discuss the unique properties of GaAs doping superlattices in detail. The space charge induced band edge modulation in doping superlattices leads to an indirect energy gap in real space. As a consequence, the electrons and holes are spatially separated and their recombination lifetimes are strongly enhanced, i.e. non-equilibrium free-carrier distributions can be metastable. This implies the unique possibility of tuning the carrier concentration in a given superlattice sample over a wide range. Tuning the carrier concentration, in turn, is associated with a strong variation of the effective energy gap, of the absorption coefficient, and of the two-dimensional subband structure. Experimental results on GaAs doping superlattices demonstrate the tunability of electron and hole conduction by selective electrodes and by photoexcitation, the optical tunability of the absorption coefficient, and the electrical and optical tunability of the luminescence. The two-dimensional subband structure and its tunability was observed by resonant Raman scattering and by Shubnikov-de-Haas measurements.
It is shown that the presence of intense laser radiation can result in the origination of “spreading” of kinetic effects even in a degenerate monopolar semiconductor with an isotropic energy spectrum, where the magnitude of such “photostimulated” effects can exceed the magnitude of corresponding effects in the absence of radiation, due to the thermal spread of current carriers in the energies or anisotropies of isoenergetic surfaces. Photostimulated Ettingshausen, Peltier, and transverse magnetoresistive effects are considered.
The third-order non-linear optical properties of CdSe and CdSe/ZnS core-shell quantum dots in solution with toluene were studied over a spectrum ranging from 450 to 680 nm using 225-fs pulses. The electronic and thermal contributions to the non-linearity, leading to positive or negative non-linear refractive indices, are investigated. Although the sign and magnitude of the non-linearity vary with wavelength, it was found to be of the same order of magnitude as that of bulk CdSe for the same photon energy-to-band gap ratio. However, because the absorption edge of CdSe quantum dots is blue-shifted relative to bulk, it permits fast optoelectronic applications in the visible spectrum by avoiding slow thermal effects normally associated with linear absorption.
We have studied the effect of an external magnetic field on electron-acoustic phonon scattering in rectangular quantum wires taking into account both electron and phonon confinement. A magnetic field has two major effects: (i) it dramatically quenches (by several orders of magnitude) intrasubband scattering due to acoustic phonons in hybrid “width” and “thickness” modes, and (ii) it increases electron interaction with evanescent hybrid surface modes that peak at the wire edges. A simple intuitive picture to elucidate the origin of these effects is presented.
Carrier capture times due to the emission of confined longitudinal optical phonons via electron–phonon (Fröhlich) interaction are calculated for GaAs‐Al x Ga 1-x As and In 0.47 Ga 0.53 As‐InP superlattices. A dielectric continuum model is used to describe the confined phonon modes and we use a Kronig–Penney type calculation for the electron envelope functions. We compare our results with capture times measured by several optical techniques and we discuss the importance of a knowledge of the carrier excitation details in order to obtain an appropriate interpretation of the experimental results. We show that electrons excited into confined states with a large kinetic energy strongly influence the overall capture times. © 1995 American Institute of Physics.
We observed simultaneously two types of Raman spectra in a GaAs/AlGaAs superlattice under high magnetic field: a folded longitudinal acoustic phonon, IFA, and a structureless background, IB. The temperature dependence of the intensities in both spectra was studied in the range 2–100K and it was established that the background spectrum is due to the first-order Raman scattering from acoustic phonons with a wide range of wave vectors.We obtained the expression for the intensities ratio IB/IFA. It depends on the relationship between the homogeneous and the inhomogeneous broadening of the intermediate state of the photoexcited e-h pair. A rapid decrease of IB observed at T 30K is thought to be due to the increase of the homogeneous width with temperature.
A review is given of theoretical concepts and experimental results on spontaneous formation of periodically ordered nanometer-scale structures on crystal surfaces. Thermodynamic theory is reviewed for various classes of spontaneously ordered nanostructures, namely, for periodically faceted surfaces, for periodic surface structures of planar domains, and for ordered arrays of three-dimensional coherently strained islands. All these structures are described as equilibrium structures of elastic domains. Despite the fact that driving forces of the instability of a homogeneous phase are different in each case, the common driving force for the long-range ordering of the inhomogeneous phase is the elastic interaction. The theory of the formation of multisheet structures of islands is reviewed, which is governed by both equilibrium ordering and kinetic-controlled ordering. For the islands of the first sheet, an equilibrium structure is formed, and for the next sheets, the structure of the surface islands meets the equilibrium under the constraint of the fixed structures of the buried islands. The experimental situation for the fabrication technology of ordered arrays of semiconductor quantum dots is analyzed, including a discussion of both single-sheet and multiple-sheet ordered arrays.
We calculate scattering rates for an electron interacting with polar optical phonons in a semiconductor quantum well based on a microscopic lattice-dynamics approach for the phonons. We employ an analytic approximation to lattice-dynamics results given by Huang and Zhu for quantum-well phonons. The resulting electron relaxation rates are compared with the rates obtained by employing ``slab'' and ``guided'' phonon modes which were used in previous studies. The intrasubband and intersubband electron relaxation rates are given as functions of quantum-well width, and the relative contributions of the confined and the interface modes are discussed for the three different phonon models.
We calculate, within the electron-temperature model, hot-electron intrasubband energy relaxation rates via LO-phonon emission in GaAs quantum wires, taking into account quantum degeneracy, dynamical screening, hot-phonon bottleneck, and, in particular, phonon confinement. Two prevailing macroscopic models of phonon confinement, namely, the slab or the electrostatic model and the guided or the mechanical model, are compared quantitatively. We find that the slab model, while giving relaxation rates comparable to the bulk-phonon emission rates, leads to an order of magnitude faster relaxation than the guided model. For reasonable parameter values, the hot-phonon-bottleneck effect is found to be the single most important physical mechanism determining energy relaxation. Numerical values for electronic-energy-loss rates in GaAs quantum wires are provided for both models of phonon confinement for a range of values of the relevant parameters, including confinement size, carrier density, hot-phonon lifetime, and electron temperature.
- P Vasilopoulos