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.     

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.     

Properties of nonadiabatic quantum fluctuations of the strongly coupled electron-phonon systems

A new variational-ansatz of states of electrons and phonons was proposed on the basis of the Holstein model in strongly coupled electron-phonon systems for studying the influence of nonadiabatic phonon fluctuation, arising from the motion and density fluctuation of electrons, on the properties of ground state, uncertainty relation, stability of polarons, charge density wave (CDW) and phonon staggered ordering. The new ansatz represents the correlation among the displacement and squeezing states of phonons and polaron’s state of electrons as well as the squeezing-antisqueezing effect. The correlation and squeezing-antisqueezing effect result in the decrease of ground state energy, enhancement of stability of the systems, increase of binding energy of the polarons, weakening of the growing speed of polaron narrowing of the electron band, increase of the charge density wave order and suppression of the increased tendency of anomalous quantum fluctuation of the phonons in such a case, when compared with the uncorrelated case in the systems. The results obtained show that the ground state determined by the new state ansatz is most stable, thus the new ansatz describing the properties of the coupled electron phonon systems is very relevant and available, especially in strongly coupled and largely squeezed cases. Supported by the National “973” Project of China (Grant No. 2007CB6103)     

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.     

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.     

Spatial dependence of the phonon energy spectrum in resistive film heaters

The steady state spatial dependence of the coupled electron-phonon distributions is studied in a heated metallic film generating high frequency phonons. The phonon energy density spectrum depends significantly on the direction of propagation. It is compared with the spectrum obtained in a substrate- phonon relaxation time model.     

Ultrafast response of surface electromagnetic waves in an aluminum film perforated with subwavelength hole arrays

The ultrafast dynamics of surface electromagnetic waves photogenerated on aluminum film perforated with subwavelength arrays of holes was studied in the visible spectral range by the technique of transient photomodulation with approximately 100 fs time resolution. We observed a pronounced blueshift of the resonant transmission band that reveals the important role of plasma attenuation in the optical response of nanohole arrays. The blueshift is inconsistent with plasmonic mechanism of extraordinary transmission and points to the crucial role of interference in the formation of transmission bands. The transient photomodulation spectra were successfully modeled within the Boltzmann equation approach for the electron-phonon relaxation dynamics, involving nonequilibrium hot electrons and quasiequilibrium phonons.     

Electron-phonon scattering in an asymmetric double barrier resonant tunneling structure

We calculate the electron-phonon scattering rate for an asymmetric double barrier resonant tunneling structure based on dielectric continuum theory, including all phonon modes, and show that interface phonons contribute much more to the scattering rate than do bulk-like LO phonons for incident energies which are approximately within an order of magnitude of the Fermi energy. The maximum scattering rate occurs for incident electron energies near the quantum well resonance. Subband nonparabolicity has a significant influence on electron-phonon scattering in these structures. We show that the relaxation time is comparable to the dwell time of electrons in the quantum well for a typical resonant tunneling structure. Received: 23 December 1997 / Revised: 24 March 1998 / Accepted: 9 March 1998     

Electron-lattice kinetics of metals heated by ultrashort laser pulses

We propose a kinetic model of transient nonequilibrium phenomena in metals exposed to ultrashort laser pulses when heated electrons affect the lattice through direct electron-phonon interaction. This model describes the destruction of a metal under intense laser pumping. We derive the system of equations for the metal, which consists of hot electrons and a cold lattice. Hot electrons are described with the help of the Boltzmann equation and equation of thermoconductivity. We use the equations of motion for lattice displacements with the electron force included. The lattice deformation is estimated immediately after the laser pulse up to the time of electron temperature relaxation. An estimate shows that the ablation regime can be achieved. Zh. éksp. Teor. Fiz. 115, 149–157 (January 1999) Published in English in the original Russian journal. Reproduced here with stylistic changes by the Translation Editor.     

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.     

Ultrafast electron relaxation in superconducting Bi(2)Sr(2)CaCu(2)O(8+delta) by time-resolved photoelectron spectroscopy

Time-resolved photoelectron spectroscopy is employed to study the dynamics of photoexcited electrons in optimally doped Bi{2}Sr{2}CaCu{2}O{8+delta} (Bi-2212). Hot electrons thermalize in less than 50 fs and dissipate their energy on two distinct time scales (110 fs and 2 ps). These are attributed to the generation and subsequent decay of nonequilibrium phonons, respectively. We conclude that 20% of the total lattice modes dominate the coupling strength and estimate the second momentum of the Eliashberg coupling function lambdaOmega{0}{2}=360+/-30 meV{2}. For the typical phonon energy of copper-oxygen bonds (Omega{0} approximately 40-70 meV), this results in an average electron-phonon coupling lambda<0.25.     

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.     

Ultrafast dynamics of surface electromagnetic waves in nanohole array on metallic film

We study the ultrafast dynamics of surface electromagnetic waves photogenerated on aluminum film perforated with subwavelength holes array by means of transient photomodulation with ∼100 fs time resolution. We observed a pronounced blueshift of the resonant transmission band that reveals the important role of plasma attenuation in the dynamics and that is inconsistent with plasmon–polariton mechanism of extraordinary transmission. The transient photomodulation spectra were successfully modeled within the Boltzmann equation approach for the electron–phonon relaxation dynamics, involving non-equilibrium hot electrons and quasi-equilibrium phonons.     

声子色散对量子点中弱耦合磁极化子声子平均数的影响

利用线性组合算符和幺正变换相结合的方法,研究了声子色散对抛物量子点中弱耦合磁极化子电子周围光学声子平均数的影响．计及纵光学(LO)声子色散,在抛物近似下导出了基态能量与量子点有效受限长度、声子色散系数、回旋共振频率以及电子-声子耦合常数之间的关系,电子周围光学声子平均数与声子色散系数以及电子-声子耦合常数的关系．数值计算结果表明在弱耦合情况下抛物量子点中磁极化子的基态能量随声子色散系数的增大而减小;电子周围光学声子平均数随声子色散系数增大而增大,随电子-声子耦合常数的增大而增大．     

Non-equilibrium electron and phonon dynamics in metals under femtosecond laser pulses

Different models for relaxation dynamics of electrons and phonons in a thin metal film heated by femto-pico second laser pulses have been discussed. The traditional two-temperature approach reveals to be inaccurate due to deviations of electrons and phonons from Fermi-Dirac and Bose-Einstein distributions, respectively. Coupled Boltzmann kinetic equations have been adapted for the quantum statistics to study the energy distribution of electrons and phonons in metals. Theoretical details have been discussed and a new solution method has been proposed overcoming numerical problems and improving stability, allowing the study of the dynamics until the complete relaxation. Numerical results have been compared with photoemission spectroscopy experimental data.     

声子色散对量子点中弱耦合磁极化子声子平均数的影响

利用线性组合算符和幺正变换相结合的方法,研究了声子色散对抛物量子点中弱耦合磁极化子电子周围光学声子平均数的影响。计及纵光学（ LO）声子色散,在抛物近似下导出了基态能量与量子点有效受限长度、声子色散系数、回旋共振频率以及电子－声子耦合常数之间的关系,电子周围光学声子平均数与声子色散系数以及电子－声子耦合常数的关系。数值计算结果表明在弱耦合情况下抛物量子点中磁极化子的基态能量随声子色散系数的增大而减小;电子周围光学声子平均数随声子色散系数增大而增大,随电子－声子耦合常数的增大而增大。     

Optical detection of the absorption of acoustical phonons by a two-dimensional electron gas in a magnetic field

The effect of absorption of nonequilibrium acoustical phonons on the intensity of recombination of a two-dimensional electron gas in a magnetic field is investigated. The nonequilibrium acoustical phonons are emitted in the relaxation of electrons in a tunnel junction deposited on the back side of a sample with a two-dimensional electronic channel. It is demonstrated that the optical signal showing the intensity of the recombination of nonequilibrium electrons from a photoexcited size-quantization subband can serve as a sensitive detector of acoustical phonons. Because the general heating of two-dimensional carriers and the intersubband transitions stimulated by the absorption of nonequilibrium acoustical phonons lead to effects of different sign, the useful signal can be discriminated unambiguously. Pis’ma Zh. éksp. Teor. Fiz. 69, No. 1, 30–35 (10 January 1999)     

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.     

Theoretical investigation of hot electron cooling process in GaAs/AlAs cylindrical quantum wire under the influence of an intense electromagnetic wave

Hot electrons cooling by phonons in GaAs/AlAs cylindrical quantum wire (CQW), under the influence of an intense electromagnetic wave (EMW), is studied theoretically. Analytic expression for the electron cooling power (CP) is derived from the quantum transport equation for phonons, using the Hamiltonian of interacting electron–optical phonon system. Both photon absorption and emission processes are considered. Numerical results show that the CP reaches maximum when the energy difference between electronic subbands equals the energy of an optical phonon plus the photon energy. Under the influence of the EMW, the negative CP is observed showing that electrons gain energy from phonon and photon instead of losing their energy. Also, the CP increases with increasing the EMW amplitude. Our results theoretically clarify the mechanism of the electron cooling process by phonons in the GaAs/AlAs CQW under the EMW, which is of significance for designing and fabricating high-speed nanoelectronic devices based on this material.     

The frequency dependence of phonon interactions at Terahertz-frequencies studied by time-resolved phonon spectroscopy

Phonon properties concerning propagation, frequency spectrum and lifetime in the Terahertz range have been investigated. The phonons have been produced by square wave Joule heating of thin constantan films evaporated onto a strongly doped ruby. Cross sections for phonon scattering at the Cr³⁺ impurity ions of the ruby were determined as a function of frequency. The theoretical estimate for mass defect scattering given by Klemens [9] is found to agree reasonably with the experimental results. Lifetime measurements indicate that phonons in ruby preferentially propagate in the transversal mode. Phonon frequency spectra in the constantan films were measured under experimental conditions, where the strength of electron phonon coupling is significant; thus electron-phonon relaxation times could be obtained as a function of frequency.