Temperature dependences of the electron-phonon coupling, electron heat capacity and thermal conductivity in Ni under femtosecond laser irradiation

The electron temperature dependences of the electron-phonon coupling factor, electron heat capacity and thermal conductivity are investigated for Ni in a range of temperatures typically realized in femtosecond laser material processing applications, from room temperature up to temperatures of the order of 10⁴ K. The analysis is based on the electronic density of states obtained through the electronic structure calculations. Thermal excitation of d band electrons is found to result in a significant decrease in the strength of the electron-phonon coupling, as well as large deviations of the electron heat capacity and the electron thermal conductivity from the commonly used linear temperature dependences on the electron temperature. Results of the simulations performed with the two-temperature model demonstrate that the temperature dependence of the thermophysical parameters accounting for the thermal excitation of d band electrons leads to higher maximum lattice and electron temperatures achieved at the surface of an irradiated Ni target and brings the threshold fluences for surface melting closer to the experimentally measured values as compared to the predictions obtained with commonly used approximations of the thermophysical parameters.     

Raman scattering by electron and phonon excitations in FeSi

The temperature evolution of Raman scattering by electron and phonon excitations in FeSi is studied within the range of 10–500 K. At low temperatures, the frequency dependence for the spectra of light scattered by electrons exhibits vanishing intensity in the range up to 500–600 cm^–1, which suggests the existence of an energy gap of about 70 meV. The calculations of the electronic excitation spectra based on the band structure determined using the LDA+DMFT technique (local electron density + dynamic mean field approximation) are in good agreement with the low-temperature experimental data and confirm that FeSi is a material with intermediate electron correlations. The changes in the shape of the electronic excitation spectrum and in the self-energy of optical phonons indicate a transition to the metallic state above 100 K. The analysis of experimental data demonstrates an appreciable decrease in the electron lifetime with the growth of temperature determining the (insulator–poor metal) transition.     

Influence of the Diagonal and Off-Diagonal Electron–Phonon Interactions on the Formation of Local Polarons and Their Band Structure in Materials with Strong Electron Correlations

For systems with strong electron correlations and strong electron–phonon interaction, we analyze the electron–phonon interaction in local variables. The effects of the mutual influence of electron–electron and electron–phonon interactions that determine the structure of local Hubbard polarons are described. Using a system containing copper–oxygen layers as an example, we consider the competition between the diagonal and off-diagonal interactions of electrons with the breathing mode as the polaron band structure is formed within a corrected formulation of the polaron version of the generalized tight-binding method. The band structure of Hubbard polarons is shown to depend strongly on the temperature due to the excitation of Franck–Condon resonances. For an undoped La₂CuO₄ compound we have described the evolution of the band structure and the spectral function from the hole dispersion in an antiferromagnetic insulator at low temperatures with the valence band maximum at point (π/2, π/2) to the spectrum with the maximum at point (π, π) typical for the paramagnetic phase. The polaron line width at the valence band top and its temperature dependence agree qualitatively with angle-resolved photoemission spectroscopy for undoped cuprates.     

物理参数变化对短脉冲激光激励温度场的影响

 为研究多物理参数（耦合系数、电子热导率、电子热容、晶格热容）同时随温度变化对短脉冲激光辐照金属材料产生温度场分布的影响,基于双温耦合理论,建立了短脉冲激光辐照金属材料金的加热过程的有限元求解模型。在同时考虑脉冲激光的空间、时间分布和多参数同时随温度变化的情况下,得到短脉冲激光辐照金属材料金激励产生的温度场二维瞬态分布,并进一步比较了多物理参数同时随温度变化和采用室温物理参数两种情况下温度场分布的区别。数值结果表明：多物理参数同时随温度变化使电子温度和晶格温度的上升变快,最大值变大,而且使得材料中激光穿透直接辐照到的区域温度变高。     

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     

Thermal analysis of intense femtosecond laser ablation of aluminum

This paper numerically simulates the process of ablation of an aluminum target by an intense femtosecond laser with a fluence of 40 J/cm 2 based on the two-temperature equation,and obtains the evolution of the free electron temperature and lattice temperature over a large temporal and depth range,for the first time. By investigating the temporal evolution curves of the free electron temperature and lattice temperature at three representative depths of 0,100 nm and 500 nm,it reveals different characteristics and mechanisms of the free electron temperature evolution at different depths. The results show that,in the intense femtosecond laser ablation of aluminum,the material ablation is mainly induced by the thermal conduction of free electrons,instead of the direct absorption of the laser energy; in addition,the thermal conduction of free electrons and the coupling effect between electrons and lattice will induce the temperature of free electrons deep inside the target to experience a process from increase to decrease and finally to increase again.     

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.     

Hot electron effects in optically-pumped mid-infrared intersubband semiconductor laser

A theoretical investigation of an optically-pumped mid-infrared intersubband semiconductor laser is presented. The influence of electrons and dopant ions on the conduction band structure is simulated with a self-consistent Poisson–Schrödinger solver. Electron-polar optical phonon interactions are calculated by using a macroscopic phonon model with electromagnetic boundary conditions. In order to assess the influence of the electronic temperature on the device optical performances, electron dynamics under optical pumping are investigated within a rate equation model where particle and energy flow equations are derived from Boltzmann's equation with Fermi statistics. Our calculations show that population inversion between the first and second excited states can occur at 77 K under intersubband optical excitation.     

The thermodynamic properties and special features of spectra of elementary excitations of unstable valence Sm-and Ce-based compounds

The experimental data on the spectra of elementary excitations measured by inelastic neutron scattering and on the heat capacity and the coefficient of thermal expansion are used to analyze the correlation between the spectral characteristics of the electron and phonon subsystems and the special features of the temperature dependence of the thermodynamic properties of a number of unstable valence Sm-and Ce-based compounds. The anomalous behavior of the thermodynamic properties of these compounds is defined by the special features of their phonon and electron (4f and conduction electrons) spectra. The rearrangement of the 4f-electron spectrum as a result of temperature variation plays a decisive part in the formation of temperature dependences of the heat capacity and the coefficient of thermal expansion of unstable valence systems.     

Thermalization time of thin metal film heated by short pulse laser

Based on the hyperbolic two-step heat conduction model, using the Laplace transform and numerical inverse transform method (Riemann-sum approximation method), the thermal behaviour of thin metal films has been studied during femtosecond pulse laser heating. Also the thermalization time, which is the time for the electron gas and solid lattice to reach thermal balance, has been studied in detail. The values of thermalization time for silver (Ag), gold (Au), copper (Cu) and lead (Pb) are obtained. The effects of material parameters of the thin metal film on the thermalization time are considered for the four kinds of metals by changing one of the parameters and regarding the other parameters as constant. For a typical metal material, the order of the thermalization time is of the order of hundreds of picoseconds. The thermalization time decays exponentially with the increase of phonon－electron coupling factor or electron gas thermal conductivity, and it increases linearly with the increase of the ratio of lattice heat capacity to electron gas heat capacity. However, the relaxation time of the electron gas has very little effect on the thermalization time.     

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.     

Thermodynamics of phonon-stabilized Fermi distributions with application to uranium

Since phonons are built on the free energy of electrons, their frequencies can be altered by thermal electronic excitations, implying that thermal electronic excitations can alter the phonon entropy. The effect of this extra phonon entropy on electronic distribution functions and thermodynamic properties is calculated in the limit of classical vibrations. The phonon entropy stabilizes electrons above the Fermi level by more than the usual k _B T. The thermodynamic coupling of electron and phonon degrees of freedom allows far more heat capacity than in equivalent independent systems. The method developed is used to explain uranium data from the literature.     

Substrate influence in electron-phonon coupling measurements in thin Au films

Accurate understanding and measurement of the energy transfer mechanisms during thermal nonequilibrium between electrons and the surrounding material systems is critical for a wide array of applications. With device dimensions decreasing to sizes on the order of the thermal penetration depth, the equilibration of the electrons could be effected by boundary effects in addition to electron-phonon coupling. In this study, the rate of electron equilibration in 20 nm thick Au films is measured with the Transient ThermoReflectance (TTR) technique. At very large incident laser fluences which result in very high electron temperatures, the electron-phonon coupling factors determined from TTR measurements deduced using traditional models are almost an order of magnitude greater than predicted from theory. By taking excess electron energy loss via electron-substrate transport into account with a proposed three temperature model, TTR electron-phonon coupling factor measurements are more in line with theory, indicating that in highly nonequilibrium situations, the high temperature electron system looses substantial energy to the substrate in addition to that transferred to the film lattice through coupling.     

Analysis of heat capacity of platinum: Electron-phonon effects and anharmonic contribution

The heat capacity results for platinum from 80 to 1000 K, reported in our previous paper, have been analyzed. The contributions of bare electrons and harmonic phonons to the heat capacity have been evaluated from the available data on the band structure and the phonon spectrum of platinum. At low temperatures, the present estimates for the temperature dependence of the electron-phonon enhancement agree qualitatively with those derived from theoretical calculations found in the literature. The anharmonic heat capacity obtained is negative and linear with temperature in the vicinity of the Debye temperature (237 K), and becomes constant above 450 K. The enhancement in the heat capacity above 1000 K has been analyzed and found to be due mainly to the enlargement of the dilation term corresponding to the similar enhancement in the thermal expansion.     

Observation of low‐wavenumber out‐of‐plane optical phonon in few‐layer graphene

Few‐layer graphene grown by chemical vapor deposition has been studied by Raman and ultrafast laser spectroscopy. A low‐wavenumber Raman peak of ~120 cm⁻¹ and a phonon‐induced oscillation in the kinetic curve of electron–phonon relaxation process have been observed, respectively. The Raman peak is assigned to the low‐wavenumber out‐of‐plane optical mode in the few‐layer graphene. The phonon band shows an asymmetric shape, a consequence of so‐called Breit‐Wigner‐Fano resonance, resulting from the coupling between the low‐wavenumber phonon and electron transitions. The obtained oscillation wavenumber from the kinetic curve is consistent with the detected low‐wavenumber phonon by Raman scattering. The origin of this oscillation is attributed to the generation of coherent phonons and their interactions with photoinduced electrons. Copyright © 2012 John Wiley & Sons, Ltd.     

Femtosecond laser interactions with dielectric materials: insights of a detailed modeling of electronic excitation and relaxation processes

Electronic excitation–relaxation processes induced by ultra-short laser pulses are studied numerically for dielectric targets. A detailed kinetic approach is used in the calculations accounting for the absence of equilibrium in the electronic subsystem. Such processes as electron–photon–phonon, electron–phonon and electron–electron scatterings are considered in the model. In addition, both laser field ionization ranging from multi-photon to tunneling one, and electron impact (avalanche) ionization processes are included in the model. The calculation results provide electron energy distribution. Based on the time-evolution of the energy distribution function, we estimate the electron thermalization time as a function of laser parameters. The effect of the density of conduction band electrons on this time is examined. By using the average electron energy, a new criterion is proposed based on determined damage threshold in agreement with recent experiments (Sanner et al. in Appl. Phys. Lett. 96:071111, 2010).     

Wave-vector dependence of electron-optical phonon coupling in GaAs

Induced non equilibrium distribution of optical phonons allows direct measurement of electron-phonon coupling as a function of phonon wave-vector K. Results indicate that near K=0(K<20, 000 cm^?1 coupling between TO phonons and electrons is independent of K whereas LO phonons show a K^-2 dependence. Results also suggest that electron relaxation in the conduction band by multiple phonon production is quite significant.     

Reconstruction of bands in metallic hydrogen

The generalized theory of normal properties of a metal for the case of the properties of the electronic band of electron–phonon systems with a variable electron density of states is used to study the normal phase of metallic hydrogen at a pressure of 500 GPa and a temperature of 200 K. We calculated the frequency dependence of the real ReΣ(ω) and imaginary ImΣ(ω) parts of the self-energy part of the electron Green’s function Σ(ω), as well as the electron density of states N(ε) of the stable phase of metallic hydrogen with the I41/amd symmetry at a pressure of 500 GPa, renormalized by the strong electron–phonon coupling. It is found that the electron conduction band of the I41/amd phase of metallic hydrogen undergoes insignificant reconstruction near the Fermi level because of the renormalization by the electron–phonon coupling.     

Impurity band in SnBi<Subscript>4</Subscript>Se<Subscript>7</Subscript>: thermoelectric power and electrical resistivity measurements

Thermoelectric power and electrical resistivity measurements on polycrystalline samples of Bi₂Se₃ and stoichiometric ternary compound in the quasi-binary system SnSe–Bi₂Se₃ in the temperature range of 90–420 K are presented and explained assuming the existence of an impurity band. The variation of the electron concentration with temperature above 300 K is explained in terms of the thermal activation of a shallow donor, by using a single conduction band model. The density of states effective mass m ^*=0.15m ₀ of the electrons, the activation energy of the donors, their concentration, and the compensation ratio are estimated. The temperature dependence of the electron mobility in conduction band is analyzed by taking into account the scattering of the charge carriers by acoustic phonon, optical phonon, and polar optical phonon as well as by alloy and ionized impurity modes. On the other hand, by considering the two-band model with electrons in both the conduction and impurity bands, the change in the electrical resistivity with temperature between 420 and 90 K is explained.