Thermoelastic contributions to picosecond-timescale reflectivity measurements in metals (abstract)

Abstract

The increase in temperature at the surface of a metal during absorption of optical energy is a dynamic, multistep process. This process has been studied in a variety of metallic systems because it provides direct insight into the fundamental interaction between conduction electrons and the rest of the material structure. In particular, high-time-resolution, ultrafast measurements of thermal and elastic transients have proven to be useful for investigating the structure, thermophysical properties, and elastic properties of thin films [C. A. Paddock and G. L. Eesley, J. Appl. Phys. 60, 285 (1986); C. Thomsen, H. T. Grahn, H. J. Maris, and J. Tauc, Phys. Rev. B 34, 4129 (1986); O. B. Wright, Phys. Rev. B 49, 9985 (1994)]. During ultrafast optical excitation of metals, the rapid deposition of energy causes the absorbing electrons to enter a superheated state, dispersing beyond the excitation volume before energy is deposited to the lattice. The rate of energy transfer between electrons and phonons is described using the electron–phonon coupling parameter; the same parameter that figures prominently in descriptions of classical superconductivity processes [P. B. Allen, Phys. Rev. Lett. 59, 1460 (1987)]. For experimental observations on long time scales (>1 ns), thermal transport measurements are assumed to be independent of elastic deformations in the material, and the analysis of the thermal and elastic responses can be separated. This can also be done for ultrafast signals, for which reflectivity measurements taken immediately after excitation can be modeled using a completely thermal analysis if reduced values for the electron–phonon coupling parameter are used. These reduced values are typically interpreted when strong electronic signals are not observed, and often vary substantially [G. Tas and H. J. Maris, Phys. Rev. B 49, 15046 (1994); V. E. Gusev and O. B. Wright, Phys. Rev. B 57, 2878 (1998); J. L. Hostetler, A. N. Smith, D. M. Czajkowsky, and P. M. Norris, Appl. Opt. 38, 3614 (1999)] from accepted values that are experimentally determined from measurements using the cooling rate of superheated electrons [S. D. Brorson, A. Kazeroonian, J. S. Moodera, D. W. Face, T. K. Cheng, E. P. Ippen, M. S. Dresselhaus, and G. Dresselhaus, Phys. Rev. Lett. 64, 2172 (1990)] or superconductivity. In this work, we show that these reduced values for the electron–phonon parameter tend to lower estimates of thermal diffusion at longer times producing significant deviations from measured results. By including elastic contributions to the modeled signal at all times, agreement with measured signals can be obtained for short and long times using values for materials parameters that are in agreement with those obtained from other techniques.