Nonequilibrium band occupation and optical response of gold after ultrafast XUV excitation

Ndione, Pascal D.; Weber, Sebastian T.; Gericke, D. O.; Rethfeld, Baerbel

doi:10.1038/s41598-022-08338-2

“…Comparison of the simulated electron distribution function with the experimental emission spectra enabled estimating the thermalization time in aluminum as 10 fs. However, longer-lasting non-equilibrium may be expected in some cases [71], or, perhaps, under long-pulse irradiation continuously driving the electronic system out of equilibrium.…”

Section: Discussionmentioning

confidence: 99%

Electronic nonequilibrium effect in ultrafast-laser-irradiated solids

Medvedev

2023

Phys. Scr.

1

0

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This paper describes the effects of electronic nonequilibrium in a simulation of ultrafast laser irradiation of materials. The simulation scheme based on tight-binding molecular dynamics, in which the electronic populations are traced with a combined Monte Carlo and Boltzmann equation, enables the modeling of nonequilibrium, nonthermal, and nonadiabatic (electron-phonon coupling) effects simultaneously. The electron-electron thermalization is described within the relaxation-time approximation, which automatically restores various known limits such as instantaneous thermalization (the thermalization time τ e − e → 0 ) and Born-Oppenheimer (BO) approximation ( τ e − e → ∞ ). The results of the simulation suggest that the non-equilibrium state of the electronic system slows down electron-phonon coupling with respect to the electronic equilibrium case in all studied materials: metals, semiconductors, and insulators. In semiconductors and insulators, it also alters the damage threshold of ultrafast nonthermal phase transitions induced by modification of the interatomic potential due to electronic excitation. It is demonstrated that the models that exclude electron-electron thermalization (using the assumption of τ e − e → ∞ , such as BO or Ehrenfest approximations) may produce qualitatively different results, and a reliable model should include all three effects: electronic nonequilibrium, nonadiabatic electron-ion coupling, and nonthermal evolution of interatomic potential.

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“…Note that the optical parameters are actually time-dependent, since they depend on the state of electrons and phonons. For example, they vary with temperature [ 68 , 69 , 70 ] or band occupation [ 41 , 42 ]. This was, however, not considered in our simulation.…”

Section: Appendix A1 Heat Capacitiesmentioning

confidence: 99%

“…The non-equilibrium between electrons and phonons is approximately captured by the two-temperature model (TTM) first established by Anisimov et al [ 37 ]. It is well-known, well-validated on time scales of thermalized electrons [ 2 , 38 ], and easily extendable [ 39 , 40 , 41 , 42 ]. Several modifications of the TTM have been proposed to capture the main features of the electronic or phononic non-equilibrium [ 17 , 43 , 44 , 45 , 46 ].…”

Section: Introductionmentioning

confidence: 99%

Influence of Electronic Non-Equilibrium on Energy Distribution and Dissipation in Aluminum Studied with an Extended Two-Temperature Model

Markus

¹

,

Weber

²

,

Rethfeld

³

2022

Self Cite

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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.

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“…5 Gold, with its unique electronic structure, serves in many cases as a prototype for studying ultrafast dynamics. 1,[6][7][8] Here, we present a comprehensive model describing the transient density response in gold excited by extreme ultraviolet 9 (XUV) and visible light. 10 The model includes a detailed description of the excitation, and relaxation pathways involving one core state (4f ) and the two upper electron bands (5d and 6sp).…”

Section: Introductionmentioning

confidence: 99%

“…As demonstrated by our previous findings, visible light excitation leads to an overpopulation of the sp-band, 10 driven primarily by photo-excitation, while XUV irradiation results in an underpopulation of the sp-band, dominated by subsequent impact ionization. 9 Here, we additionally assume that the excess energy from the Auger recombination of the 4f -holes is transferred to several d-band electrons. In such a case, we demonstrate the ability of our model of XUV-excited gold to capture a density overshoot.…”

Section: Introductionmentioning

confidence: 99%

Modeling the density response in gold after XUV and optical excitation

Ndione,

Weber,

Gericke

et al. 2024

High-Power Laser Ablation VIII

0

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We study the electron density response in gold after excitation with XUV and visible light. We have introduced the concept of occupational nonequilibrium and developed multiband rate equations that track the occupation in each active electron band. The rate equations also track the energy content of the sp-and d-electrons and can be coupled to the phonons. Our results show that visible light excitation leads to an overpopulation of the sp-band, driven primarily by photo-excitation, while XUV irradiation results in an underpopulation of the sp-band, dominated by subsequent impact ionization. However, assuming that the excess energy from the Auger recombination process is transferred to multiple d-electrons, we showcase that XUV-exited gold can lead to an overpopulation of the sp-band. In addition, using a detailed balance of Auger and impact ionization coefficients, we show that a single-rate relaxation time approach is sufficient to describe the imbalance between the impact ionization rate and the Auger recombination rate.

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Nonequilibrium band occupation and optical response of gold after ultrafast XUV excitation

Cited by 6 publications

References 53 publications

Electronic nonequilibrium effect in ultrafast-laser-irradiated solids

Electronic nonequilibrium effect in ultrafast-laser-irradiated solids

Influence of Electronic Non-Equilibrium on Energy Distribution and Dissipation in Aluminum Studied with an Extended Two-Temperature Model

Modeling the density response in gold after XUV and optical excitation

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