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.     

Effects of screening of the interaction potential on the mobility characteristics of degenerate surface layers in compound semiconductors at low lattice temperatures

The rates of scattering of the conduction electrons in degenerate two-dimensional electron gas in the surface of compound semiconductors at low lattice temperatures have been obtained for interaction with the piezoelectric and deformation potential acoustic phonons, under different prevailing conditions. The calculations have been carried out taking due account of the screening of the interaction potential at low temperatures where again the phonon energy cannot be neglected in comparison to the average thermal energy of the electrons and, as a result, the equipartition approximation for the phonon distribution can hardly be valid. The scattering rates thus obtained for inversion layers in GaAs and ZnO are found to depend upon the carrier energy, the lattice temperature and the level of degeneracy in quite involved manners, which are very different from what follows if one makes the simplifying approximation of negligible phonon energy or disregards the effects of screening. The mobility characteristics are then obtained using these scattering rates. The results show how the screening of the interaction potential and the finite energy of the intravalley acoustic and piezoelectric phonons significantly change the mobility characteristics of the degenerate surface layers at low lattice temperatures. The inadequacies of the present theory are pointed out and recommendations for possible refinements are discussed.     

Charge carrier sorting over energy in semiconductors by means of phonon diffusion

A study is made of anomalous temperature fields which occur in finite semiconductor specimens. These fields are created by charge carrier sorting over energy due to mutual electron-phonon entrainment at arbitrary rates of electron and phonon energy relaxation at the boundaries. Expressions are found for entrainment levels which depend on specimen dimensions, cooling length, and electron and phonon energy relaxation rates at the boundaries, which when exceeded cause the electron temperature differential between the boundaries to exceed the temperature differential between the heater T₁ and cooler T₂, producing an initiating phonon flux, while for scattering on deformation acoustical phonons these differentials have opposite algebraic sign. In the case where the electrons are thermally insulated, while the phonons have ideal thermal contact with heater and cooler, for total entrainment the electron temperature differential produced by charge carrier sorting over energy due to phonon entrainment is an order of magnitude higher than T₁-T₂, and produces the major contribution to thermo-emf in sufficiently short specimens.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 36–41, February, 1988.In conclusion the authors express their deep gratitude to Yu. G. Gurevich for his interest in the study and fruitful discussions.     

Propagation of high power helicons in n-indium antimonide crystal

The propagation of high power helicon in n-InSb has been analysed taking into account the heating of the carriers by the electric field of the wave. The momentum and energy transfer of the electrons have been taken to be due to acoustic phonons and polar optical phonons scattering at 77°K respectively. The sample is assumed to be finite and the wave is incident on the semiconductor-free space interface. Calculations have been made for phase constant, attenuation constant, reflection coefficient and the electron temperature as function of the magnetic field and the wave amplitude. The theoretical results are found to be in qualitative agreement with the experimental observations of Laurinavichyus and Pozhela[14].     

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.     

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.     

Heating and cooling of a two-dimensional electron gas by terahertz radiation

The absorption of terahertz radiation by free charge carriers in n-type semiconductor quantum wells accompanied by the interaction of electrons with acoustic and optical phonons is studied. It is shown that intrasubband optical transitions can cause both heating and cooling of the electron gas. The cooling of charge carriers occurs in a certain temperature and radiation frequency region where light is most efficiently absorbed due to intrasubband transitions with emission of optical phonons. In GaAs quantum wells, the optical cooling of electrons occurs most efficiently at liquid nitrogen temperatures, while cooling is possible even at room temperature in GaN heterostructures.     

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.     

飞秒激光辐照下硅薄膜的非傅里叶能量输运研究

 在双曲双步输运模型基础上建立数值模型,针对超短脉冲激光作用下硅薄膜的微观能量输运过程展开理论研究。针对电子、晶格超快温升响应过程的数值模拟结果表明,电子作为主要能量载子在几皮秒内主导了能量输运过程。电声子之间的能量耦合系数主要依赖于电子温度,而不是晶格温度。能量耦合过程由于非平衡电子的弹道式输运而呈现非局域性。热波的传播速度与电子能量传播速度有相同量级,而大于硅材料中的声子平均速度。模型预测与相关实验结果吻合。     

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.     

Mobility as controlled by the transverse component of phonon wave vector in quantum layers at low temperatures

Without resorting to either the Kawaji’s simplified model of interaction with only two-dimensional phonons or to the equipartition approximation for the phonon distribution, the characteristics of the momentum relaxation time of the conduction electrons in a quantized surface layer for interaction with intravalley acoustic phonons have been analysed under the condition of low temperature. The scattering and the mobility characteristics thus obtained for an n-channel (1 0 0)-oriented Si inversion layer are apparently quite different from what follows in the traditional framework.     

Terahertz absorption by electrons and confined acoustic phonons in free-standing quantum wells

The acoustic phonon confinement in a free-standing quantum well (FSQW) results in an acoustic phonon energy quantization. Typical quantization energies are in the terahertz frequency range. Free electrons may absorb electromagnetic waves in this frequency range if they emit or absorb acoustic phonons. Therefore, the terahertz absorption reveals the characteristic features of the acoustic phonon spectrum in free-standing structures. We have calculated the absorption coefficient of an electromagnetic wave by free electrons in a FSQW in the terahertz frequency range. We took into account a time dependent electric field, an exact form of the acoustic phonon spectrum and eigenmodes, and electron interactions with confined acoustic phonons through the deformation potential. We demonstrate numerical results for GaAs FSQW of width 100 Å at low lattice temperatures in the frequency range 0.1-1 THz. The absorption coefficient exhibits several structures at frequencies corresponding to the lowest acoustic phonon modes. These features occur due to absorption of photons by electrons, which is accompanied by the emission of corresponding acoustic phonons.     

Features of electron-phonon interaction in nanotubes with chiral symmetry placed in a magnetic field

The interaction of electrons with acoustic phonons is considered in a nanotube with chiral symmetry placed in a magnetic field parallel to the nanotube axis. It is shown that in such a system, the electronic energy spectrum is not invariant under electron wavevector reversal and, therefore, the electron-phonon interaction is different for identical phonons with oppositely directed wavevectors. This phenomenon leads to the occurrence of an electromotive force during spatially homogeneous heating of an electron gas and to the presence of a term quadratic in current in the current-voltage characteristic of a nanotube.     

Energy loss to intravalley acoustic modes in nano-dimensional wire structures at low temperatures

The theory of rate of loss of energy of non-equilibrium electrons due to inelastic interaction with the intravalley acoustic phonons in a nano-dimensional semiconductor wire has been developed under the condition of low lattice temperature, when the approximations of the well known traditional theory are not valid. Numerical results are obtained for narrow-channel GaAs-GaAlAs wires structures. On comparison with other available results it is revealed that the finite energy of the intravalley acoustic phonons and, the use of the full form of the phonon distribution without truncation to the equipartition law, produce significant changes in the energy loss characteristics at low temperatures.     

Non-Maxwellian shape of electron distribution function in ionacoustic turbulence

In a DC discharge plasma system, in which two meshes are installed, the current-driven ion acoustic instability is excited when a de potential V_m is applied to one of them. When the instability fully grows, the system reaches a very turbulence state, the so-called ion acoustic turbulence. The experimental measurement of energy distribution function of electrons in ion acoustic turbulence measured by the Langmuir probe shows a non-Maxwellian nature along with electron heating     

Pseudogaps in incommensurate charge density waves and one-dimensional semiconductors

We consider pseudogap effects for electrons interacting with gapless modes. We study generic 1D semiconductors with acoustic phonons and incommensurate charge density waves. We calculate the subgap absorption as it can be observed by means of photoelectron or tunneling spectroscopy. Within the formalism of functional integration and adiabatic approximation, the probabilities are described by nonlinear configurations of an instanton type. Particularities of both cases are determined by the topological nature of stationary excited states (acoustic polarons or amplitude solitons) and by the presence of gapless phonons that change the usual dynamics to the quantum dissipation regime. Below the free-particle edge, the pseudogap starts with an exponential (stretched exponential for gapful phonons) decrease of the transition rates. Deeply within the pseudogap, they are dominated by a power law, in contrast to a nearly exponential law for gapful modes.     

The influence of abrupt electric field variations on the distribution function of hot electrons

Some analytical models of quiescent hot electron distributions are extended to the transient conditions, in order to describe the response of hot electrons to step changes in the magnitude of the electric field. These models apply to semiconductors having one or several equivalent energy minima in the conduction band, and isotropic lattice scattering due to low-energy acoustic phonons (elastic in-valley scattering) and to high energy single-level acoustic phonons (inelastic inter-valley scattering) or dispersionless optical phonons (inelastic in-valley scattering). Step changes in the field magnitude are considered with respect to the time and space (one-dimensional) variables, separately. In both cases, the spherically-symmetrical term ƒ_O of the electron distribution function may be expressed using a Laguerre polynomial expansion in the energy variable. For a positive step change in field magnitude, transient electron drift velocities in excess of the steady-state “scattering-limited” values are found in both silicon and germanium.     

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.     

Electron-phonon scattering in quantum point contacts

We study the negative correction to the quantized value 2e(2)/h of the conductance of a quantum point contact due to the backscattering of electrons by acoustic phonons. The correction shows activated temperature dependence and also gives rise to a zero-bias anomaly in conductance. Our results are in qualitative agreement with recent experiments studying the 0.7 feature in the conductance of quantum point contacts.     

通过形变势弱耦合表面极化子的性质

采用Huybrechts线性组合算符和幺正变换法,导出了晶体中电子与表面光学声子和表面声学声子均为弱耦合极化子的有效哈密顿量,并对两种极限情况进行了讨论。