Mutual entrainment of hot electrons and optical phonons in polar semiconductors

Kinetic equations for nonequilibrium electrons and optical phonons are constructed and solved for the case in which the interaction between these particles is the primary mechanism for the relaxation of the electron energy and quasimomentum. The calculations reflect the circumstance that for the optical phonons the equivalent primary relaxation mechanism is the interaction with acoustic phonons (which are at equilibrium in this case). Constitutive equations are derived for polar semiconductors which reflect the mutual entrainment of electrons and optical phonons. Energy balance equations, which determine the temperatures of these particles, are also derived. These temperatures are generally different from each other and from the reservoir temperature.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 32–36, February, 1984.We wish to thank É. A. Kaner and I. B. Levinson for useful discussions.     

Theory of nonlinear effects in semiconductors with a nondiffusion approximation for acoustic phonons

Momentum and energy balance equations in impurity semi-metals and degenerate semiconductors are derived and investigated in a nondiffusion approximation for the acoustic phonons with arbitrary heating and entrainment of electrons and phonons taken into account. It was shown that the diffusion approximation is not satisfied even for relatively weak electrical fields. In cases of thermal entrainment and no heating of the phonons, cases are possible when the electron temperature becomes equal to and less than the lattice temperature, which is associated with radiation obtained from the energy field by electrons in the form of acoustic phonons at a point of acoustic instability. If mutual entrainment and heating of electrons and phonons occurs then the crystal boundaries are the main channel of energy and momentum relaxation. Necessary conditions delimiting the strong changes of all the galvano- and thermomagnetic effects at a point of acoustic instability are found in every specific case.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 11–16, November, 1990.     

A criticism of the standard treatment of phonon drag

By the study of a simple example, namely the evolution in timet of an electron-phonon system with fixed, total momentum, it is shown that the “standard” treatment of “phonon drag”, which involves solving the (linearized and spatially homogeneous) coupled electron and phonon Boltzmann equations by an iteration procedure, is not always correct. In the asymptotic limit (t→∞), the iteration or “standard” procedure does not give the “correct” (i.e. the equilibrium statistical mechanical) result for the distribution of momentum between electrons and phonons. However, a proper treatment of the Boltzmann equations does lead to the “correct” sharing of momentum between electrons and phonons fort→∞. All the calculations in this paper are performed for metals at high temperatures (i.e.,T>Θ_D, the Debye temperature).     

Relaxation between electrons and surface phonons of a homogeneously photoexcited metal film

The energy relaxation between the hot degenerate electrons of a homogeneously photoexcited metal film and the surface phonons (phonon wave vectors in two dimensions) is considered under Debye approximation. The state of electrons and phonons is described by equilibrium Fermi and Bose functions with different temperatures. Two cases for electron scattering by the metal surface, namely specular and diffuse scattering, are considered.     

An electrohydrodynamics model for non-equilibrium electron and phonon transport in metal films after ultra-short pulse laser heating

The electrons and phonons in metal films after ultra-short pulse laser heating are in highly non-equilibrium states not only between the electrons and the phonons but also within the electrons. An electrohydrodynamics model consisting of the balance equations of electron density, energy density of electrons, and energy density of phonons is derived from the coupled non-equilibrium electron and phonon Boltzmann transport equations to study the nonlinear thermal transport by considering the electron density fluctuation and the transient electric current in metal films, after ultra-short pulse laser heating. The temperature evolution is calculated by the coupled electron and phonon Boltzmann transport equations, the electrohydrodynamics model derived in this work, and the two-temperature model. Different laser pulse durations, film thicknesses, and laser fluences are considered. We find that the two-temperature model overestimates the electron temperature at the front surface of the film and underestimates the damage threshold when the nonlinear thermal transport of electrons is important. The electrohydrodynamics model proposed in this work could be a more accurate prediction tool to study the non-equilibrium electron and phonon transport process than the two-temperature model and it is much easier to be solved than the Boltzmann transport equations.     

Scattering of electrons in the GaAs/AlAs transistor structure

This paper reports on the results of a self-consistent calculation of the rates of electron scattering from surface roughnesses, acoustic phonons, and polar optical phonons in a transistor structure based on a GaAs quantum wire in an AlAs matrix at temperatures T = 77 and 300 K. The rates of electron scattering are calculated in the electric-quantum limit approximation with due regard for both the collisional broadening of the electron energy spectrum and the Pauli principle. The influence of the gate voltage on these rates is investigated. The wave function of electrons and the energy level of their quantum ground state are determined by the self-consistent solution of the Poisson and Schrödinger equations.     

Electron capture by charged impurities in semiconductors under conditions of spatial diffusion

The capture of electrons by charged impurities in semiconductors due to spatial diffusion is investigated theoretically. In a semiconductor, an electron either can be captured by the field of a charged impurity if this electron loses energy by emitting phonons or can be ionized from the trapping state if it acquires energy by absorbing phonons. The electron trapping is governed by a change in the distribution function of electrons in both coordinate and momentum space. The trapping coefficient is calculated under the condition where it is determined by the diffusion redistribution of the electron density in the field of a charged impurity.     

Effects of Screening and Finite Phonon Energy on the Transport in Quantized Layers in Compound Semiconductors

Analytical expressions for the momentum relaxation times of the conduction electrons in a non-degenerate two dimensional electron gas in the surface of a compound semiconductor have been obtained for interactions with the piezoelectric and deformation potential acoustic phonons taking due account of the screening of the perturbing potential under the the condition of low lattice temperature when the phonon energy cannot be neglected in comparison to the average thermal energy of the electrons and for that matter the equipartition approximation for the phonon distribution is hardly valid. The relaxation times calculated for inversion layers in GaAs and ZnO are found to depend upon the carrier energy, the lattice temperature and the impurity concentration in rather complex manners which are significantly different from what follows from the traditional approach of either neglecting the phonon energy or disregarding the process of screening. It is seen how the finite value of the phonon energy and the screening of the perturbing potential change the mobility characteristics significantly at the low lattice temperatures. The temperature dependence of the zero field mobility that one obtains using the relaxation times calculated here is quite different from the traditional laws.     

电子初始能量对双向流二极管空间电荷限制流密度的影响

 从理论上研究了阴极发射电子初始能量对一维平面非相对论性双向流二极管内空间电荷限制电子、离子流密度的影响,并与阴极发射电子初始能量为0情况下的空间电荷限制电子、离子流密度进行了比较。     

电子初始能量对双向流二极管空间电荷限制流密度的影响

从理论上研究了阴极发射电子初始能量对一维平面非相对论性双向流二极管内空间电荷限制电子、离子流密度的影响,并与阴极发射电子初始能量为0情况下的空间电荷限制电子、离子流密度进行了比较。     

Influence of Nonequilibrium LO Phonons on High-frequency Performance of One-dimensional Hot Electrons in Quantum Wires of Polar Semiconductors

Small-signal ac transport of degenerate one-dimensional hot electrons in quantum wires of GaAs and In_0.53Ga_0.47As is studied for lattice temperatures of 77 K and 300 K. The carrier energy loss via polar optic phonons and momentum losses via polar optic phonons, acoustic phonons and ionized impurities are included in the calculations. Alloy disorder scattering in momentum loss is additionally incorporated for (In,Ga)As. The consideration of nonequilibrium optical phonons or hot phonons is found to enhance the 3dB cut-off frequency (f_3dB) considerably, where the ac mobility falls to 0.707 of its low frequency value. f_3dB is generally higher for (In,Ga)As quantum wire than for GaAs.     

Monte-carlo calculation of electron transport in polar semiconductors

The momentum distribution of electrons in a polar semiconductor under the influence of an electric field is calculated using a Monte-Carlo method. The scattering is assumed to be exclusively by polar optical phonons. From the distribution function, average momentum and electron temperature are calculated, and compared with similar calculations based on a displaced Maxwellian distribution. Some characteristic features are common for the two models, in particular the phenomenon of electron cooling at low lattice temperatures. However, in contrast to the displaced Maxwellian distribution computations, the Monte-Carlo calculations show that a rapid increase of electron temperature takes place at very low fields, before the onset of cooling. Also the anisotropy of the distribution is entirely different in the two models.A detailed discussion of runaway in connection with Monte-Carlo calculations is given.     

Electron momentum density and Compton profile by a semi-empirical approach

Here we propose a semi-empirical approach to describe with good accuracy the electron momentum densities and Compton profiles for a wide range of pure crystalline metals. In the present approach, we use an experimental Compton profile to fit an analytical expression for the momentum densities of the valence electrons. This expression is similar to a Fermi–Dirac distribution function with two parameters, one of which coincides with the ground state kinetic energy of the free-electron gas and the other resembles the electron–electron interaction energy. In the proposed scheme conduction electrons are neither completely free nor completely bound to the atomic nucleus. This procedure allows us to include correlation effects.We tested the approach for all metals with Z=3–50 and showed the results for three representative elements: Li, Be and Al from high-resolution experiments.     

The kinetics of low-temperature electron-phonon relaxation in a metallic film following instantaneous heating of the electrons

The theoretical analysis of experiments on pulsed laser irradiation of metallic films sputtered on insulating supports is usually based on semiphenomenological dynamical equations for the electron and phonon temperatures, an approach that ignores the nonuniformity and the nonthermal nature of the phonon distribution function. In this paper we discuss a microscopic model that describes the dynamics of the electron-phonon system in terms of kinetic equations for the electron and phonon distribution functions. Such a model provides a microscopic picture of the nonlinear energy relaxation of the electron-phonon system of a rapidly heated film. We find that in a relatively thick film the energy relaxation of electrons consists of three stages: the emission of nonequilibrium phonons by “hot” electrons, the thermalization of electrons and phonons due to phonon reabsorption, and finally the cooling of the thermalized electron-phonon system as a result of phonon exchange between film and substrate. In thin films, where there is no reabsorption of nonequilibrium phonons, the energy relaxation consists of only one stage, the first. The relaxation dynamics of an experimentally observable quantity, the phonon contribution to the electrical conductivity of the cooling film, is directly related to the dynamics of the electron temperature, which makes it possible to use the data of experiments on the relaxation of voltage across films to establish the electron-phonon and phonon-electron collision times and the average time of phonon escape from film to substrate. Zh. éksp. Teor. Fiz. 111, 2106–2133 (June 1997)     

Theorie des stimulierten Raman-Effekts

We consider stimulated Raman emission in solids, placed in a plane laser beam external to the cavity. The Hamiltonian of the system of phonons, electrons and electromagnetic fields is derived within the framework of a generalized adiabatic approximation for electrons and nuclei. It contains terms due to nonlinear interactions between electrons and phonons. Because the usual time-dependent perturbation theory cannot describe coherence effects properly we turn toHeisenberg's equations of motion for the operators of photons, phonons and electron excitations. In order to solve these equations in the steady state we apply an iteration procedure. We start with the light waves which give rise to electron transitions. The electrons such excited create phonons which then react on the electrons. Finally the electrons are coupled again to the lightfield. This procedure yields besides the usual wellknown Raman process two main processes occurring in stimulated Raman emission: a coupled two step Raman process and a parametric process. In the first one two phonons are involved. If the linewidth of phonons is comparable to the phonon frequencies the non-resonant parts of the above processes also become important. In solving the set of coupled equations for the light amplitudes, obtained from the iteration procedure, we only consider terms due to the first Stokes, the first anti-Stokes and the laser line. We then find frequency shifts of these lines due to the stimulated emission which are of the order of the linewidth of photons if this linewidth is very much smaller than that of phonons as it is the case in solids. This means that the coupled two step Raman process is dominant, in good agreement with measurements ofChiao andStoicheff in calcite.     

Electron-phonon drag in degenerate conductors in a magnetic field

Mutual drag of electrons and phonons in degenerate conductors in classical magnetic fields is considered. It is shown that the coupled kinetic equations for nonequilibrium electron and phonon distribution functions can be transformed into a system of Volterra’s inhomogeneous integral equations. A solution is found to the system of integral equations with inclusion of all terms yielding contributions linear in the degeneracy parameter. An analysis is made of the effect of a magnetic field on momentum relaxation in an electron-phonon system.     

High field transport properties in a GaN/AlGaN heterostructure

The drift velocity, electron temperature, electron energy and momentum loss rates of a two-dimensional electron gas are calculated in a GaN/AlGaN heterojunction (HJ) at high electric fields employing the energy and momentum balance technique, assuming the drifted Fermi–Dirac (F–D) distribution function for electrons. Besides the conventional scattering mechanisms, roughness induced new scattering mechanisms such as misfit piezoelectric and misfit deformation potential scatterings are considered in momentum relaxation. Energy loss rates due to acoustic phonons and polar optical phonon scattering with hot phonon effect are considered. The calculated drift velocity, electron temperature and energy loss rate are compared with the experimental data and a good agreement is obtained. The hot phonon effect is found to reduce the drift velocity, energy and momentum loss rates, whereas it enhances the electron temperature. Also the effect of using drifted F–D distribution, due to high carrier density in GaN/AlGaN HJs, contrary to the drifted Maxwellian distribution function used in the earlier calculations, is brought out.     

Transient magnetoresponse of photoexcited electrons: Negative cyclotron absorption and evolution of Faraday angle

The transient magnetooptical response of electrons with partly inverted initial distribution produced by an ultrashort optical pulse near the optical phonon energy is studied theoretically. Transient cyclotron absorption and Faraday rotation of polarization plane are considered for bulk semiconductors (GaAs, InAs, and InSb) as well as for a GaAs-based quantum well. Damping of the response due to electron momentum relaxation associated with elastic scattering from acoustic phonons is taken into account in calculations, as well as the evolution of the electron distribution due to quasi-elastic energy relaxation at acoustic phonons and effective inelastic transitions accompanied by spontaneous emission of optical phonons. Nonstationary negative absorption in the cyclotron resonance conditions and peculiarities of Faraday rotation of the polarization plane associated with partial inversion of the initial distribution are considered. The possibility of transient enhancement of the probe field under cyclotron resonance conditions is indicated.     

Nonlinear Theory of Coupled Electron-Hole Transport

A theoretical investigation is carried out to examine the Coulomb interaction effects in linear and nonlinear transport of a coupled electron-hole system which consists of an electron layer and a hole layer separated by a potential barrier. In this we apply the balance equation method to examine the induced current in one charged layer when the other layer is subject to a constant electric field. Nonlinear balance equations are developed for both the electrons and the holes, with Coulomb interactions among them, as well as interactions of the charge carriers with phonons and impurities. Numerically obtained linear results exhibit qualitative agreement with experimental data in regard to dependencies on temperature and carrier densities. Nonlinear effects are shown to be important at low temperatures, in agreement with experimental results.