Influence of diffusion and nonequilibrium populations on noble-gas plasmas in electric arcs

Measurements and calculations of temperatures, densities, and field-strength-current characteristics of cascade arcs burning in noble gases under atmospheric pressure are reported. The evaluation of measured arc data assuming Saha equilibrium [complete local thermal equilibrium (LTE)] is not in agreement with the detailed solution of the balance equations. The temperatures of electrons and heavy particles and the density of electrons and neutrals have to be determined from the set of rate equations, from the equation of state, connection with the electron energy balance and the equation of state, the energy balance of the electron gas, and of the total plasma. Solutions of these equations are compared with results following from measured line intensities only solving the rate equations in connection with the electron energy balance and the equation of state. For helium, both methods give results which agree within a few percent. The deviations from Saha equilibrium are caused by diffusion and the overpopulation of ground state atoms. The excited atoms, however, are nearly in equilibrium with free electrons in the range of electron densities reached in our experiment (partial LTE). Measurements of E-I characteristics agree with calculated data, if diffusion is taken into account. A simple criterion for the limit between diffusion-dominated plasma and a plasma in thermal equilibrium is derived.     

Thermodynamic theory of transport processes in semiconductors

Important energetic processes in semiconductors are analyzed from the point of view of equilibrium and irreversible thermodynamics. After carefully defining the necessary local variables and current densities, the continuity equations for particles, energy, and entropy are derived, leading to an expression for entropy generation. From this, the conjugate fluxes and affinities are directly obtained and the transport equations written using these quantities. The Onsager relations are applied to the kinetic coefficients defined in the transport equations and, after further manipulations, the experimental transport parameters may be found in terms of these quantities. Particular care is taken to ensure that the thermal conductivity is correctly defined. A new thermoinjection coefficient is found which describes the transport of heat by electrons and holes under conditions of zero total electric current and zero temperature gradient. The heat dissipation is derived in a number of different ways and compared with formula proposed by other authors. Expressions for the generation of useful external work using both photovoltaic and thermoelectric conversion are also found and related to the difference between free energy input and entropy generation. The equations presented form a suitable basis for the improved design of energy conversion devices. In two Appendixes, the thermodynamic methods used in the main text are compared with those based on the Boltzmann transport equations for electrons, holes, and phonons. Theoretical expressions are derived in these Appendixes for the kinetic coefficients. Issues relating to the definition of internal energy and chemical potential are analyzed in a third Appendix     

Formulation of a tail electron hydrodynamic model based on MonteCarlo results

In this paper, the Monte Carlo method is applied to uniform and n ⁺-n^--n⁺ structures of silicon to study the behavior of tail electrons and to develop a new set of hydrodynamic equations based on tail electron statistics. Each term in these equations is calibrated under both nonhomogeneous and homogeneous electric fields. Terms associated with surface integral of the carriers and carrier momentum over an iso energy surface: (ℰ=ℰ_th ) are introduced. The new tail electron hydrodynamic model yields the density (n₂) and the average energy (w₂) of tail electrons and is shown to predict hot electron effects accurately     

A simplified impact ionization model based on the average energy ofhot-electron subpopulation

A previously developed nonlocal impact ionization model based on the average energy of hot-electron subpopulation has been further simplified. The system of hydrodynamic transport equations consisting of three equations for these high-energy electrons has been reduced to a single equation. The simulation results for n⁺-n-n⁺ structures are in good agreement with Monte Carlo (MC) calculations. The model is easily applicable to two-dimensional (2-D) problems by exploiting the current flow line approach     

Efficient and accurate use of the energy transport method in devicesimulation

Important questions in the application of the highly efficient energy transport method for electron device simulation are addressed by comparing an energy transport calculation with a Monte Carlo calculation used as a control. It is shown that, to calculate average electron energy, it is necessary to incorporate velocity overshoot at certain points in device simulations. Further, energy relaxation times must be taken as functions of energy and may be used as a vehicle for compensation for the neglect of backscattering of cold electrons in regions where energy is rapidly changing. Finally, incorporation of the heat flow vector appears to be unnecessary in the cases studied     

Specific features of optical orientation and relaxation of electron spins in quantum wells with a large spin splitting

The processes of optical spin orientation and spin relaxation of electrons are treated theoretically for semiconductor quantum wells, in which the spin splitting of the energy spectrum is comparable with the characteristic energy of charge carriers. The density matrix of photoexcited electrons at the instant of optical excitation is obtained in explicit form. A system of kinetic equations describing the behavior of the spin density matrix at an arbitrary relation between the average energy of charge carriers and the spin splitting is derived. It is demonstrated that, upon photoexcitation, a noticeable degree of orientation can be attained only in the pulse mode of operation, when the photoexcitation pulse duration is comparable with the period of spin precession in the field of spin splitting. It is shown that the total spin of the ensemble of electrons exhibits oscillations damping with time; the shape and damping time of the oscillations are sensitive to the parameters of photoexcitation and the spin splitting.     

自由电子激光器的位相条件

基于相对论电子在光场和静态磁场作用下的能量方程和洛仑兹方程,分析了自由电子激光器运转的位相条件。结果表明,入射光波相对于相对论电子束的初位相ψ在第1和第4象限,相对论电子的能量将主要表现为能量减低,初位相ψ在第2和第3象限主要表现为使相对论电子进一步被加速。     

周期磁场中的相对论电子与光辐射的能量交换

基于相对论电子在周期磁场和光辐射场作用下的运动方程,讨论了相对论电子与光辐射之间的有效的能量交换。结果表明,相对论电子与光辐射只有在满足共振条件的频率上发生能量交换。光辐射是被相对论电子放大还是成为加速电子运动的动力,取决于两者的位相关系。     

The effect of reflecting contacts on high-field transport

The effect of reflecting contacts on high-field transport is investigated by detailed Monte Carlo simulations of electron transport in an n^-GaAs region that terminates in an n⁺GaAs/metal contact. We determine that the average electron velocity in the n^-region of the device decreases rapidly (because of reflections at the contact) as the doping concentration in the n⁺contact region decreases. We study the n⁺concentration range of 2 × 10¹⁸cm^-3to 1 × 10¹⁹cm^-3The probability of reflection at the contact is found to depend sensitively on the energy and momentum of the electrons impinging on the contact region as long as transport at the contact is dominantly by tunneling. The dependence is weaker for transport through the contact by thermionic emission. The velocity degradation due to electrons reflected at the contact is less severe for high electric fields with the electrons transferred to the upper valleys.     

超强激光等离子体中的相对论性朗缪尔孤子

为了研究相对论性朗缪尔孤子的特性,对从动力论出发所获得的超强等离子体中相对论性强朗缪尔湍动控制方程组进行了理论分析。结果表明,随着电子的平均洛伦兹因子以及场的湍动参量增加,朗缪尔孤子的波包半宽变窄,孤子总能量和总动量相应地增大,且电子的相对论效应对孤子总能量和动量的非线性部分的影响远大于线性部分。该研究可为超强激光等离子体中相关的非线性现象提供新的理论参考。     

AlInGaN量子阱垒层材料的优化

采用k·p方法理论,考虑了极化电场和自由载流子重新分布等因素,通过薛定谔方程和泊松方程自洽求解得到InGaN/AlInGaN,InGaN/GaN,InGaN/InGaN,InGaN/AlGaN量子阱导带和价带的能带结构,并由此计算了不同量子阱结构的自发发射谱.分析对比发现AlInGaN材料特有的自发极化和压电极化效应在阱垒界面处形成的极化电荷对量子阱发光特性有重要的影响.以AlInGaN为垒,优化其中各元素的组分可以减小极化电场的影响,提高量子阱自发发射谱强度.同时,综合考虑了极化电荷和势垒高度的影响,提出了具体的优化方法,并给予了物理解释.     

Gyrotron Electron Beams: Velocity and Energy Spread and Beam Instabilities

The stability of the electron beams and maximum share of the electrons oscillatory energy, i.e. finally efficiency, power, and pulse duration of the gyrotron to a considerable extent depend on the velocity and the energy spread (VESP) of the HEB. The basic factors determining VESP in the helical beams are discussed. Among these factors static (initial velocities, cathode heterogeneities, space charge fields) and dynamic (negative mass and diochotron instabilities and a global instability connected with the capture of the electrons in the gyrotron adiabatic trap) factors are considered. Qualitative models of the excitation of the space charge oscillation as well the parasite electromagnetic radiation of the HEB are developed. Some experimental data of the investigation of the parasitic electromagnetic radiation spectrum in one gyrotron are discussed. The methods of the experimental investigation of the VESP are described.     

Numerical modeling of hot electrons in n-GaAs Schottky-barrierdiodes

The drift-diffusion model, with the inclusion of the energy balance equations, is used to model DC properties of n-GaAs Schottky diodes at high forward bias voltages. The boundary condition for the energy balance equation at the Schottky contact is based on the assumption that the energy flow across the interface is equal to the energy carried by the electrons. The effects of thermionic-field emission and image force lowering are modeled with a field-dependent barrier height. The incorporation of these two effects resulted in very good agreement between simulated and measured I-V characteristics for diodes with different doping concentrations of the epitaxial layer     

Investigation of Properties of Motion of Superconductive Electrons in Superconductors by Nonlinear Quantum Mechanical Theory

The properties and rules of motion of superconductive electrons in steady and time-dependent non-equilibrium states of superconductors are studied by using the Ginzberg-Landau （GL） equations and nonlinear quantum theory. In the absence of external fields, the superconductive electrons move in the solitons with certain energy and velocity in a uniform system, The superconductive electron is still a soliton under action of an electromagnetic field, but its amplitude, phase and shape are changed. Thus we conclude that superconductivity is a result of motion of soliton of superconductive electrons. Since soliton has the feature of motion for retaining its energy and form, thus a permanent current occurs in superconductor. From these solutions of GL equations under action of an electromagnetic field, we gain the structure of vortex lines-magnetic flux lines observed experimentally in type-Ⅱ superconductors. In the time-dependent nonequilibrium states of superconductor, the motions of superconductive electrons exhibit still the soliton features, but the shape and amplitude have changed. In an invariant electric-field, it moves in a constant acceleration. In the medium with dissipation, the superconductive electron behaves still like a soliton, although its form, amplitude, and velocity are altered. Thus we have to convince that the superconductive electron is essentially a soliton in both non-equilibrium and equilibrium superconductors.     

A simple model for computer simulation of Schottky-barrier diodes

To simulate the electrical characteristics of metal-semiconductor Schottky barrier diodes, a numerical analysis program based on the Shockley's semiconductor equations has been established. The thermionic emissions of electrons and holes from semiconductor to metal as well as the electric field in the interfacial layer are taken as the derivative boundary conditions of the nonlinear equations. The forward and reverse current-voltage characteristics of various metal-silicon and metal-silicide-silicon Schottky barrier diodes can be simulated by properly choosing the zero-field barrier height and the interfacial-layer capacitance. The barrier height variation as a function of applied voltage is related to the space-charge density and the interfacial-layer capacitance. The nonideality of forward characteristics is attributed to the bending of majority carrier imref and the raising of barrier height. The soft behavior of reverse characteristics can be modeled in terms of the interfacial-layer capacitance.     

基于COMSOL的感应耦合等离子体刻蚀机流体模型

流体动力学模型被广泛地用于感应耦合等离子体（ICP）的仿真,即使连续性方程在这样低的压力下通常会被认为是不适用的。本课题模拟了一个真实的充满氩等离子体的ICP刻蚀机。本模拟基于一个多物理场仿真软件——COMSOL,一种偏微分方程求解器。正如其他的等离子体流体模型所示,在本模型中用漂移扩散近似描述离子,对电子运动用准中性假设,用简化的Maxwell方程计算电磁场,用电子能量方程求解电子温度,用Navier-Stokes方程来描述中性背景气体。本文展示了在功率200W和气压1.33Pa（10 mTorr）条件下的2维等离子体参数分布情况。进而对比了电子数密度和电子温度随功率的变化。我们确信在预测值与真实值之间存在不一致情况,造成这种差异的原因主要是电子能量分布函数（eedf）的麦克斯韦假设以及对碰撞截面和反应速率的缺失。     

A critical examination of the assumptions underlying macroscopictransport equations for silicon devices

Assumptions used to derive macroscopic transport equations for silicon devices are critically examined. The position- and momentum-dependent distribution function for a silicon n-i-n diode is obtained from a rigorous solution to the Boltzmann equation, and various macroscopic quantities, such as the electron temperature tensor, energy and heat fluxes, and mobility, are rigorously evaluated and compared with widely used approximations. The common approximation of the heat flux by Fourier's law is shown to differ substantially from the actual heat flux. The results also show that at a given energy, the mobility within a submicrometer device can be much different than that for electrons at the same energy in bulk silicon     

An investigation into density-wave propagation within high-temperature superconducting plasmas for use in creating traveling-wave devices

This paper theoretically investigates a novel application of high-temperature superconductors where the superconductor serves as the active component in a microwave or millimeter traveling-wave amplifier. A guided electromagnetic wave interacts with a dc superconducting electron current to set up charge-density gradients within the superconducting electron "plasma." The electromagnetic wave gradually extracts energy from the superconducting electrons by traveling in phase synchronism with these charge gradients. The interaction mechanism is similar to that of a conventional traveling-wave tube amplifier or oscillator. We have modeled the wave behavior of superconducting electrons using the London equations and a two-fluid approach. Our model includes dissipation within the superconductor, and it shows that traveling-wave devices may be possible using high-quality thin-film superconductors in which dissipation is kept low.     

Particle conservation in the hot‐carrier solar cell

In conventional p–n junction solar cells, carrier multiplication by impact ionisation, is negligible, owing to the low temperature of the electron–hole pairs. This leads to particle conservation between the net number of absorbed photons and the number of electron–hole pairs withdrawn from the cell. In hot‐carrier solar cells, in which electrons are at a high temperature by assuming suppression of electron–phonon scattering, such particle conservation leads to peculiar results. Numerical calculations show that entire current–voltage characteristics with meaningful values of temperature and chemical potential do not exist. If the energy at which electron–hole pairs are extracted is smaller than the average energy of absorbed photons, the temperature of the electrons and holes becomes much larger than the tem perature of the sun. When the extraction energy is larger than the average energy of the absorbed photons, an entire current–voltage curve cannot always be obtained. It follows that impact ionisation and Auger recombination cannot be neglected when the thermal energy of the electron–hole pairs is comparable to the bandgap of the absorber. Accounting for these processes results in current–voltage characteristics that are well behaved. Copyright © 2005 John Wiley & Sons, Ltd.     

The Linear and Self-Consistent Nonlinear Theory of the Electron Cyclotron Maser Instability

In this paper the linear and nonlinear theory of the electron cyclotron maser instability is considered. The configuration used to study the maser instability consists of relativistic electrons gyrating about and drifting along a uniform magnetic field within a parallel plate waveguide. Relativistic effects associated with the gyrating electrons are responsible for excitation of the transverse electric mode in the waveguide. Linear theory shows that the growth rate maximizes when the axial beam velocity coincides with the axial wave group velocity of the excited electromagnetic wave. This allows us to perform the nonlinear analysis in a frame where both the axial wave number and axial beam velocity vanish. We have found that the maser instability exists only if the perpendicular beam energy exceeds a threshold value. Our analysis also describes the temporal nonlinear evolution of the field amplitude and frequency of a single excited wave. The nonlinear wave dynamics are self-consistently determined from the nonlinear particle orbits through the force and wave equations. The nonlinear analysis shows that there are two possible mechanisms for the saturation of the unstable wave: 1) depletion of the available free energy associated with the rotating particles and 2) phase trapping of the gyrating electrons in the wave. The initial beam parameters determine which of the two mechanisms is responsible for saturation. Competition between the two saturation mechanisms leads to a peaking in the energy conversion efficiency as a function of beam energy. Numerical results of the nonlinear formalism show that energy conversion efficiencies from the particles to the wave can be as high as 60 percent in the beam frame. Furthermore, by appropriately contouring the external magnetic field, among other things, efficiencies as high as 70 percent can be realized.