Uehlein Markus, Weber Sebastian T, Rethfeld Baerbel
Department of Physics and Research Center OPTIMAS, Technische Universität Kaiserslautern, Erwin-Schrödinger-Straße 46, 67663 Kaiserslautern, Germany.
Nanomaterials (Basel). 2022 May 12;12(10):1655. doi: 10.3390/nano12101655.
When an ultrashort laser pulse excites a metal surface, only a few of all the free electrons absorb a photon. The resulting non-equilibrium electron energy distribution thermalizes quickly to a hot Fermi distribution. The further energy dissipation is usually described in the framework of a two-temperature model, considering the phonons of the crystal lattice as a second subsystem. Here, we present an extension of the two-temperature model including the non-equilibrium electrons as a third subsystem. The model was proposed initially by E. Carpene and later improved by G.D. Tsibidis. We introduce further refinements, in particular, a temperature-dependent electron-electron thermalization time and an extended energy interval for the excitation function. We show results comparing the transient energy densities as well as the energy-transfer rates of the original equilibrium two-temperature description and the improved extended two-temperature model, respectively. Looking at the energy distribution of all electrons, we find good agreement in the non-equilibrium distribution of the extended two-temperature model with results from a kinetic description solving full Boltzmann collision integrals. The model provides a convenient tool to trace non-equilibrium electrons at small computational effort. As an example, we determine the dynamics of high-energy electrons observable in photo-electron spectroscopy. The comparison of the calculated spectral densities with experimental results demonstrates the necessity of considering electronic non-equilibrium distributions and electron-electron thermalization processes in time- and energy-resolved analyses.
当一个超短激光脉冲激发金属表面时，在所有自由电子中只有少数会吸收一个光子。由此产生的非平衡电子能量分布会迅速热化至热费米分布。进一步的能量耗散通常在双温度模型的框架内进行描述，该模型将晶格声子视为第二个子系统。在此，我们提出了双温度模型的一个扩展，将非平衡电子作为第三个子系统纳入其中。该模型最初由E. 卡尔佩内提出，后来由G.D. 齐比迪斯改进。我们进一步进行了细化，特别是引入了与温度相关的电子 - 电子热化时间以及激发函数的扩展能量区间。我们分别展示了原始平衡双温度描述和改进后的扩展双温度模型的瞬态能量密度以及能量转移率的比较结果。查看所有电子的能量分布，我们发现扩展双温度模型的非平衡分布与求解完整玻尔兹曼碰撞积分的动力学描述结果吻合良好。该模型提供了一个便捷工具，能够以较小的计算量追踪非平衡电子。例如，我们确定了光电子能谱中可观测到的高能电子的动力学。计算得到的光谱密度与实验结果的比较表明，在时间和能量分辨分析中考虑电子非平衡分布和电子 - 电子热化过程是必要的。
