Energy transport in silicon–aluminum composite thin film during laser short-pulse irradiation

Energy transport in silicon–aluminum composite thin films due to short-pulse laser irradiation is examined. Frequency dependent phonon transport in the silicon film is considered to formulate equivalent equilibrium temperature while modified two-equation model is used in the aluminum film to obtain electron and phonon temperatures. Thermal boundary resistance across the films is incorporated in the analysis. Transmittance, reflectance, and absorption of the incident laser beam are determined using the transfer matrix method. Equivalent equilibrium temperatures resulted from frequency dependent and frequency independent solutions are compared. It is found that phonon temperature increase at the aluminum interface is suppressed by phonon transport to the silicon film, which is more pronounced at low laser pulse intensities. The influence of the ballistic phonons on equivalent equilibrium temperature in the silicon film is found to be significant.     

Effect of temperature oscillation on thermal characteristics of an aluminum thin film

Energy transport in aluminum thin film is examined due to temperature disturbance at the film edge. Thermal separation of electron and lattice systems is considered in the analysis, and temperature variation in each sub-system is formulated. The transient analysis of frequency-dependent and frequency-independent phonon radiative transport incorporating electron–phonon coupling is carried out in the thin film. The dispersion relations of aluminum are used in the frequency-dependent analysis. Temperature at one edge of the film is oscillated at various frequencies, and temporal response of phonon intensity distribution in the film is predicted numerically using the discrete ordinate method. To assess the phonon transport characteristics, equivalent equilibrium temperature is introduced. It is found that equivalent equilibrium temperature in the electron and lattice sub-systems oscillates due to temperature oscillation at the film edge. The amplitude of temperature oscillation reduces as the distance along the film thickness increases toward the low-temperature edge of the film. Equivalent equilibrium temperature attains lower values for the frequency-dependent solution of the phonon transport equation than that corresponding to frequency-independent solution.     

Size effect on phonon transport in two-dimensional silicon film

Phonon transport in two-dimensional silicon film is investigated and frequency dependent Boltzmann transport equation is solved numerically using discrete ordinate method. The transient effects of phonon transport in the film are incorporated in the analysis. The influence of film size on phonon transport is examined through equivalent equilibrium temperature in the film. It is found that increasing film thickness enhances phonon scattering and dispersion in the film while increasing equivalent equilibrium temperature. The rate of equivalent equilibrium temperature increase is high in the early heating period ( \(\hbox {t} \le 50\,\hbox {ps}\) ) and the rate of temperature increase becomes gradual in the film as the heating period progresses.     

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.     

Laser short-pulse heating of silicon-aluminum thin films

Energy transport in silicon-aluminum thin films is examined during the laser short-pulse irradiation subjected to the silicon film. The silicon film is considered to be at the top of the aluminum film. Thermal boundary resistance at the interface of the films is incorporated in the analysis. The absorption of laser radiation in the silicon and aluminum films is modeled using the transfer matrix method. Since the silicon film is dielectric, the phonon radiative transport basing the Boltzmann transport equation is incorporated to determine equivalent equilibrium temperature in the film while modified two-equation model is used to account for the non-equilibrium energy transport due to thermal separation of electron and phonon sub-systems in the aluminum film during the laser short-pulse heating process.     

Radiative phonon transport in silicon and collisional energy transfer in aluminum films due to laser short-pulse heating: Influence of laser pulse intensity on temperature distribution

Energy transfer across aluminum and silicon films through phonon transport is examined in line with the laser short-pulse interaction with the aluminum film. The modified two-equation model is incorporated to compute electron and lattice site temperatures in the aluminum film while phonon radiative transport is used to predict equilibrium temperature in the silicon film. The thermal boundary resistance is considered at the interface of the films in the analysis. The numerical scheme using the finite difference method is adopted to solve the governing equations of energy. It is found that lattice site temperature rise is gradual in the aluminum film in the late heating period. However, equilibrium temperature decay is sharp in the region of silicon interface during this period. The thermal boundary resistance lowers lattice site temperature considerably in the region of the aluminum interface.     

Electron and phonon relaxation in metal films perturbed by a femtosecond laser pulse

A theoretical investigation of the electron and phonon time-dependent distributions in an Ag film subjected to a femtosecond laser pulse has been carried out. A system of two coupled time-dependent Boltzmann equations, describing electron and phonon dynamics, has been numerically solved. In the electron Boltzmann equation, electron–electron and electron–phonon collision integrals are considered together with a source term for laser perturbation. In the phonon Boltzmann equation, only electron–phonon collisions are considered, neglecting laser perturbation and phonon–phonon collisions. Screening of the interactions has been accounted for in both the electron–electron and the electron–phonon collisions. The results show the simultaneous electron and phonon time-dependent distributions from the initial non-equilibrium behaviour up to the establishment of a new final equilibrium condition. PACS 72.10.-d; 71.10.Ca; 63.20.Kr     

A fluid model of the current-voltage characteristics of an electron emitting electrode immersed in a two electron temperature plasma

The current voltage characteristics of a negatively biased electron emitting electrode immersed in a two-electron temperature plasma are analyzed by a simple one dimensional fluid model. Based on the assumption that the electron density in the pre-sheath region obeys the Boltzmann law the Bohm criterion is derived in the form of a transcendental equation for the Mach number, which can have up to 3 solutions. According to these solutions the ion velocity at the sheath edge can be determined either by the hot or by the cool electron temperature. When it is determined by the cool electron temperature and the hot electron temperature is high enough the critical electron emission current from the collector can have a very pronounced local maximum and a minimum when regarded as a function of the electrode potential. Because of that the current voltage characteristics of the electrode may exhibit up to 3 different floating potentials. This result is in good agreement with the experimental observations reported in [J. Appl. Phys. 63, 5674 (1988)].     

Polar optic phonon scattering of two dimensional electron gas in a rectangular potential well

The mobility of a two-dimensional electron gas (2DEG) in a rectangular potential well formed in a AlGaAs/GaAs/AlGaAs structure scattered by polar-optic phonon is calculated by an iterative solution of Boltzmann equation. The values are significantly different from those calculated by using a relaxation time. The polar-optic mobility is found to dominate over acoustic mobility over a temperature range of 100–300 K when the well thickness is about 10 nm. The mobility values for 2DEG are, however, found to be lower than the bulk values.     

表面粗糙度对薄膜面向热导率的影响研究

通过求解声子辐射输运方程(EPRT)计算得到了薄膜的面向晶格热导率.在薄膜界面采用与声子波长相关的镜反射率模型,考虑了薄膜的厚度、温度和表面粗糙度等对其热导率的影响.结果表明,界面粗糙度对薄膜热导率的影响很大.减小界面粗糙度,会使得薄膜热导率大大增加.另外,薄膜厚度减小使得热导率峰值对应的温度增加.     

数值模拟飞秒激光加热金属的热电子发射

研究了超短超强激光脉冲与薄膜靶相互作用中产生的电子热发射.当超短激光脉冲与薄膜靶相互作用时,首先入射超短脉冲激光对吸收深度内的自由电子进行热激发,接下来热激发电子将能量传递到附近的晶格,再通过电子和晶格二体系的热传导,以及电子晶格间的热耦合,将能量传递到材料的内部.因此,电子在皮秒级甚至更短的时间内不能与晶格进行能量耦合,使电子温度超出晶格温度很多,电子热发射就变得非常明显了.用双温方程联合Richardson-Dushman方程的方法对飞秒脉冲激光照射金属靶的电子热发射进行了研究,结果发现电子热发射对飞     

Ballistic–diffusive phonon transport and size induced anisotropy of thermal conductivity of silicon nanofilms

The effective thermal conductivity of nanofilms is size dependent due to the diffusive–ballistic transport of phonons. In this paper, we investigate the cross-plane phonon transport from the viewpoint of the phonon Boltzmann equation. A predictive model for the size dependent thermal conductivity is proposed and agrees well with the results of molecular dynamics simulation for silicon nanofilms. The ballistic transport has different effects on the heat conduction in the in-plane or cross-plane directions, which causes the anisotropy of thermal conductivity of nanofilms. Such anisotropy is also size dependent and vanishes with the increase of film thickness.     

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)     

Nonlinear transport and heat dissipation in metallic carbon nanotubes

We show that the local temperature dependence of thermalized electron and phonon populations along metallic carbon nanotubes is the main reason behind the nonlinear transport characteristics in the high bias regime. Our model is based on the solution of the Boltzmann transport equation considering both optical and zone boundary phonon emission as well as absorption by charge carriers. It also assumes a local temperature along the nanotube, determined self-consistently with the heat transport equation. By using realistic transport parameters, our results not only reproduce experimental data for electronic transport but also provide a coherent interpretation of thermal breakdown under electric stress. In particular, electron and phonon thermalization prohibits ballistic transport in short nanotubes.     

Energy loss rate of two-dimensional electron gas in GaInAs/AlInAs, InSb/AlInSb and GaSb/AlGaAsSb heterostructures

Energy loss rates of two-dimensional electron gas in GaInAs/AlInAs, InSb/AlInSb and GaSb/AlGaAsSb heterostructures are theoretically investigated over a wide range of temperature based on the electron–one-phonon and electron–two-phonon interactions. Calculations are presented for electron acoustic one-phonon interaction via deformation potential and piezoelectric coupling and electron–LO phonon interaction with hot phonon effect. In addition, energy loss rate due to electron-two-zone edge transverse acoustic (TA) phonons is also presented. A very good agreement is obtained between the calculations and experimental data in GaInAs/AlInAs structure with the inclusion of electron–two-zone edge TA phonon interaction. In all these three structures energy loss is dominated by (i) acoustic one-phonon scattering at low temperatures, (ii) two-TA zone edge phonons at intermediate temperatures and (iii) LO phonons at high temperatures. It is observed that, hot phonon effect reduces the energy loss rate considerably in these structures.     

Dependence of electron and positron backscattering coefficients on Al film thickness

The backscattering coefficient of 1-4 keV electron and positron beams normally incident impinging on Al thin film targets is stochastically modeled within a Monte Carlo frame work. The aim of the present paper is to study the behavior of the backscattering coefficient as a function of the Al film thickness. To the authors’ knowledge, no theoretical or experimental work on the dependence of the positron backscattering coefficient on film thickness targets has been reported so far. It is found that the backscattering coefficient for both electron and positron beams presents different behaviors when the Al film thickness belongs to the nano-scale. Beyond this scale, the behavior becomes qualitatively similar.     

飞秒激光抽运探测热反射法对金属纳米薄膜超快非平衡传热的研究

随着微电子器件尺寸的减小、 工作频率的提高, 金属薄膜中电子与声子将处于非平衡状态, 这将导致微电子器件的热阻增大. 为准确地对这些微电子器件进行热管理, 电子-声子耦合系数的测量变得越来越重要. 本文采用飞秒激光抽运-探测热 反射法研究了不同厚度的金属纳米薄膜的非平衡传热过程. 通过抛物两步模型对实验数据进行拟合, 在拟合过程中引入电子温度与声子温度对反射率影响的比例关系, 从而优化了拟合结果. 通过对不同厚度的Ni膜与Al膜的电子-声子耦合系数的研究, 表明金属薄膜中的电子-声子耦合系数并不随薄膜厚度的改变发生变化. 实验结果还验证了探测光的反射率同时受到电子温度和声子温度的影响, 并通过数据分析量化了电子温度和声子温度对反射率的影响系数.     

Improved two-temperature model including electron density of states effects for Au during femtosecond laser pulses

The electron temperature dependences of the electron–phonon coupling factor and electron heat capacity based on the electron density of states are investigated for precious metal Au under femtosecond laser irradiation. The thermal excitation of d band electrons is found to result in large deviations from the commonly used approximations of linear temperature dependence of the electron heat capacity, and the constant electron–phonon coupling factor. Results of the simulations performed with the two-temperature model demonstrate that the electron–phonon relaxation time becomes short for high fluence laser for Au. The satisfactory agreement between our numerical results and experimental data of threshold fluence indicates that the electron temperature dependence of the thermophysical parameters accounting for the thermal excitation of d band electrons should not be neglected under the condition that electron temperature is higher than 10⁴ K.     

考虑界面散射的金属纳米线热导率修正

理论分析了声子和电子输运对Cu, Ag金属纳米线热导率的贡献. 采用镶嵌原子作用势模型描述纳米尺寸下金属原子间的相互作用, 应用平衡分子动力学方法和Green-Kubo函数模拟了金属纳米线的声子热导率; 采用玻尔兹曼输运理论和Wiedemann-Franz定律计算电子热导率; 并通过散射失配模型和Mayadas-Shatzkes模型引入晶界散射的影响. 在此基础上, 考察分析了纳米线尺度和温度的影响. 研究结果表明: Cu, Ag纳米线热导率的变化规律相似; 电子输运对金属纳米线的导热占主导地位, 而声子热导率的贡献也不容忽视; 晶界散射导致热导率减小, 尤其对电子热导率作用显著; 纳米线总热导率随着温度的升高而降低; 随着截面尺寸减小而减小, 但声子热导率所占份额有所增加. 关键词： 纳米线 热导率 表面散射 晶界散射     

Mobility of two-dimensional electron gas in JFETS limited by polar-optic and impurity scattering

The theory of mobility of a two-dimentional electron gas in JFET structures limited by polar-optic phonon and impurity scattering is developed in this work. The energy level and the wave function of the lowest subband are obtained by a variational procedure. The mobility limited by polar-optic phonon scattering is obtained by solving the Boltzmann equation iteratively. The expression for the impurity scattering limited mobility is obtained by using the variational wave function. For numerical calculation, however, the electron gas is assumed to be strictly two-dimensional. It is found that for experimental range of impurity concentration in GaAs JFETs, impurity scattering is the dominant process even at 300K.