Differentiating contributions of electrons and phonons to the thermoreflectance spectra of gold

To better understand the many effects of temperature on the optical properties of metals, we experimentally and theoretically quantify the electron vs phonon contributions to the thermoreflectance spectra of gold. We perform a series of pump/probe measurements on nanoscale Pt/Au bilayers at wavelengths between 400 and 1000 nm. At all wavelengths, we find that changes in phonon temperature, not electron temperature, are the primary contributor to the thermoreflectance of Au. The thermoreflectance is most sensitive to the electron temperature at a wavelength of ∼480 nm due to interband transitions between $d$ states and the Fermi level. At 480 nm, the electron temperature is responsible for ∼20% of the total thermoreflectance. In the near infrared, the electron temperature is responsible for $<2\%$ of the total thermoreflectance. We also compute the thermoreflectance spectra of Au from first principles. Our calculations further confirm that phonon temperature dominates thermoreflectance of Au. Most of the thermoreflectance of Au is due to the effect of the phonon population on electron lifetime.

Figure 1

Two temperature model calculations for the Au/Pt bilayer for a pump wavelength of 783 nm. (a) Absorption of the pump beam vs depth. (b)–(d) Electron temperature (solid lines) and phonon temperature (dashed lines) vs depth at delay times of 0, 10, and 100 ps. Nonequilibrium between electrons and phonons in the Au layer persists for ∼100 ps. (e) Electron and phonon temperature of the Au surface as a function of delay time. The shaded region represents the uncertainty in the electron and phonon temperature profiles due to uncertainties in thermal model parameters.

Figure 2

Pump/probe data for the Au reflectance at 480, 695, and 960 nm. The transient reflectance of the Au layer depends on wavelength due to changes in electron vs phonon temperature sensitivity. Lines are thermal model predictions for the change in reflectance with different values for the electron temperature sensitivity parameter $a$. The shaded region represents our estimates for uncertainty in the electron and phonon temperature profiles due to uncertainties in thermal model parameters.

Figure 3

Band structure of gold, including electron-phonon interaction contribution, along high-symmetry path in the Brillouin zone for temperature of 300 K (top) and 600 K (bottom). Calculations are done in a 4 × 4 × 4 supercell with thermal displacements of atoms (blue and red circles in the right panels). The band structure is unfolded into a primitive unit cell, as indicated with color on the plot. Darker colors correspond to larger intensity.

Figure 4

(a) Sensitivity of the thermoreflectance to the electron temperature as a function of photon energy, $a\left(\omega \right)$. (b) and (c) Electron (blue) and total (red) thermoreflectance as a function of photon energy. Measured data are shown with symbols, while first-principles calculated results are shown with lines.

Figure 5

Decomposition of the calculated thermoreflectance as a function of photon energy. Three panels show (a) contributions from the electron occupation, (b) volume expansion, and (c) thermally displaced atoms. The primary effect of thermally displaced atoms is on the electron-phonon lifetime.