Influence of electron-boundary scattering on thermoreflectance calculations after intra- and interband transitions induced by short-pulsed laser absorption

Patrick E. Hopkins

Phys. Rev. B 81, 035413 – Published 12 January 2010

Abstract

Ultrashort pulsed lasers are effective tools for use in a wide array of nanoscale applications, ranging from precise machining of nanomaterials, to deposition of nanocomposites, to diagnostics for observations of transport properties on atomistic time and length scales. One critical caveat of these applications is predicting and controlling the temperature of the materials after the absorbed laser pulse. At relatively low absorbed laser powers, the temperature can be determined from the reflected energy from the laser pulse off the sample surface as the reflectivity and the temperature change are linearly related. However, as laser pulses become more powerful, thereby inducing large temperature changes, and as materials continue to decrease in characteristic lengths, thereby causing substrate interference affecting the absorbed energy, the determination of the temperature from reflectance becomes more complicated than the traditionally assumed linear relation. In this work, a reflectance model is developed that accounts for large temperature fluctuations in thin-film metals by utilizing the temperature dependencies of the intraband (“free” electron) and interband (“bound” electron) dielectric functions and multiple reflection theory. Electron-electron, electron-phonon, and electron-substrate scattering are exploited and the change in reflectance as a function of these various scattering events is studied in the case of both intra- and interband excitations. This thermoreflectance model is compared to thermoreflectance data on thin Au films.

Received 4 September 2009

DOI:https://doi.org/10.1103/PhysRevB.81.035413

Authors & Affiliations

Patrick E. Hopkins^*

Engineering Sciences Center, Sandia National Laboratories, Albuquerque, New Mexico 87185-0346, USA

^*pehopki@sandia.gov

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Vol. 81, Iss. 3 — 15 January 2010

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Images

Figure 1
(Color online) Reflectivity data as a function of wavelength of bulk Au (red squares) and bulk Si (blue circles) along with calculations for the reflectivity as a function of wavelength for bulk Au (solid line) using the reflectivity model discussed in Sec. 2. The dotted and dashed lines show reflectivity calculations of Au films of various thicknesses on a bulk Si substrate using the reflectivity model taking into account reflections from the Au/Si interface via Eq. (2).Reuse & Permissions
Figure 2
(Color online) (a) Thermoreflectance signal on a 20 nm Au film on a bulk Si substrate for three different changes in electron temperatures. The inset shows the thermoreflectance signal for bulk Au for the same three changes in electron temperature. (b) Thermoreflectance signal of Au film of various thicknesses on a Si substrate.Reuse & Permissions
Figure 3
(Color online) (a) 800 nm thermoreflectance signal for Au films of varying thickness on a Si substrate assuming an insulated $(τ_{b} = 0)$ Au/Si interface along with experimental thermoreflectance data taking at 800 nm for thin Au films (film thicknesses are 20, 30, 40, and 50 nm) on Si substrates (Ref. 8). The predicted thermoreflectance signal of Au/Si at 800 nm assuming no electron-boundary scattering is much greater (absolute value) than the measured data, to the point where the measured data appear approximately zero compared to the predictions. (b) Calculations for $Δ R / R$ with varying values for $τ_{b}^{- 1}$ . As $τ_{b}^{- 1}$ increases, the magnitude of the 800 nm thermoreflectance signal for 20 nm Au/Si decreases. (c) $Δ R / R$ for different Au film thicknesses for Au/Si compared to the data from Hopkins et al. (Ref. 8) assuming $τ_{b}^{- 1} = 2.0 \times 10^{16} s^{- 1}$ . Taking into account electron-boundary scattering drastically improves the predictions of $Δ R / R$ .Reuse & Permissions
Figure 4
(Color online) Change in the thermoreflectance signal as a function of temperature for different electron-boundary scattering rates at three different wavelengths—(a) 800 nm; (b) 506 nm; and (c) 400 nm—for a 20 nm Au film on a Si substrate. The values shown are the changes in the thermoreflectance signal due to electron-boundary scattering for a 20 nm Au film—the absolute values of the difference between $Δ R / R$ using $τ_{b}^{- 1}$ listed in the figure and $Δ R / R$ when $τ_{b}^{- 1} = 0$ —this is effectively showing the sensitivity of the thermoreflectance signal to $τ_{b}^{- 1}$ . Comparing the thermoreflectance signal at the varying wavelengths shows that at high temperatures, $Δ R / R$ is nearly 3–4 times greater when probing at 800 nm than when probing interband transitions for $τ_{b}^{- 1}$ expected in thin Au films [i.e., on the order of $10^{16} s^{- 1}$ (Ref. 27)]. The insets show the thermoreflectance signals as a function of temperature for a 20 nm Au film assuming $τ_{b}^{- 1} = 0$ for the different wavelengths.Reuse & Permissions
Figure 5
(Color online) Sensitivity of the 20 nm Au/Si thermoreflectance signal to electron-boundary scattering as a function of wavelength for two different electron temperatures, 1000 and 3000 K. The thermoreflectance signal of Au is much more sensitive to electron-boundary scattering in the free-electron regime.Reuse & Permissions

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