Thermal Response of Metals to Ultrashort-Pulse Laser Excitation

Abstract

Both electron thermal conductivity and thermal exchange with the lattice can cool an electron distribution initially heated on a metallic surface with an ultrashort laser pulse. The interplay between the two processes allows the electron-lattice coupling parameter to be determined. We report measurements of optical damage to molybdenum and copper. Damage caused by pulses have a duration TL ^ 1 nsec can be understood only with a two-temperature model of metals.PACS numbers: 72.15.Eb, 78.47.+p A reliable value of the electron-phonon coupling constant g in metals ^ has wide implications, perhaps even in the field of superconductivity.^ Recent investigations^'^ have deduced or inferred experimental values of g. However, a large uncertainty remains because of the difficulty in firmly relating observations to theory. The experimental approach has been to diagnose the electron temperature either by photon-assisted electron emission^ or by the change in reflection^'^ (or transmission^) of visible light near the rf-state resonance. These processes are all limited to relatively weak excitation, the former because of space-charge effects and the latter because of nonlinear saturation processes. ^ Moreover, in the case of thick samples, the initial reduction of the electron temperature that is measured at the surface is mainly due to the fast electron diff*usion process,^ and unless correctly treated leads to an incorrect value of g. Thin samples, on the other hand, can have anomalously fast electron cooling due to electron-impurity and electron-surface scattering.This paper reports a new method of determining g. It relies on competition between two fast processes: electron-lattice energy exchange and electron thermal conduction. The former cools electrons heated with an ultrashort 10-/im pulse (penetration depth -200 A) by transferring their heat to the lattice. The latter removes energy from the surface.The paper has a second purpose. A theory is developed to describe the pulse-duration dependence of optical damage to metals, and experimental results are presented in support of the theory.The heat transport inside the metal can be described with the following one-dimensional, two-temperature model ^:Ce-l-Te-^^K^Te-g(Te-Ti) +A(x,t) (l) at ox ox andQ^Ti=g(Te-Ti),(2) ot where x is the direction perpendicular to the surface.The electron heat capacity Ce is given by Ce =CeTe, Ce being a constant,^ and K is the heat conductivity. According to Sommerfeld's model,^ KozTe/v, where v = Vee + Vei and Vee and Vei are the electron-electron and electron-phonon collision frequencies, respectively. Te and Ti are, respectively, the electron and lattice temperatures and d is the lattice heat capacity. A{xj) is a source term and g is the electron-phonon coupling constant.As a guide, we will derive some approximate scaling laws for the response of a metal to an ultrashort pulse. These scaling laws have two essential roles. First, they allow quantities that are necessary to understand the following measurements to be introduced. Second, they...

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“…The linear variation of coupling term with (T e − T i ) is classic in TTM : we have taken γ = γ 0 as 3 × 10 16 WK −1 m −3 for copper 22 , and 3 × 10 17 WK −1 m −3 for aluminum 20 . It must be noticed that the values of K e and γ are subject to considerable uncertainty in literature 3 .…”

“…Obviously, numerical calculations are always requiring additional information such as electron-phonon or electron-electron relaxation times, which may be extracted, from experimental data 22,23 . Reciprocally, comparison between simulations and experiments allows to validate physical data introduced into the theoretical models.…”

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