predictions from the thickness dependent intraband reflectance model derived by Smith and Norris (Ref. 26). The nonlinearity and substrate dependency are apparent showing that at high temperatures and thin films, this model must be used as opposed to Eq. (6) when only intraband transitions are induced. The inset shows the equilibrium reflectance off the surface of an Au film on both Si and substrates as a function of film thickness at a wavelength of 800 nm (1.55 eV). For films thinner than 50 nm, the reflectance deviates by more than 10% from the bulk reflectance, indicating that for films in this range the absorbed laser energy in TTR experiments could be affected by the underlying substrate.
Phase corrected TTR data on 30 and 50 nm Au/glass samples taking with incident laser fluence. The data are normalized at the peak reflectance to show the difference in cooling profiles of the electron systems after laser heating. The initial time is defined at the time of peak reflectance. The inset shows the calculations of the TTM, assuming homogeneous heating [Eqs. (9)–(11)] fit to the first 2.0 ps of the data after laser heating. The best fit resulted in different for the two laser fluences.
Best fit measured on eight different Au samples using 10 and incident laser fluence. Associated with each data point is the corresponding maximum electron temperature determined from the TTM fit. As temperature decreases, the measured also decreases, yet the trends of with temperature show different dependencies depending on the substrate, showing evidence of substrate interference in electron-phonon equilibration. The 20 nm data are from Hopkins and Norris (Ref. 27). The inset recasts the measured on the different samples as a function of predicted maximum electron temperature achieved after pump absorption predicted by the TTM. The different trends between the measured data and predicted with the model of Chen et al. (Ref. 60) suggest that scattering at the film/substrate boundary is affecting measurements. The difference between the Au/Si and Au/glass measurements suggests that the properties of the substrate also affect measurements.
determined from the TTR data analyzed with the three temperature model. The continued increase in measured on the Au/glass samples demonstrates the temperature dependence of electron-interface scattering and how if affects . The difference in the Au/Si and Au/glass trends shows the effect that the conductive Si substrate has on . In the thinner samples, in which high electron temperatures are achieved during laser heating, scattering events around the film/substrate interface cause an increase in electron-phonon scattering. The effects of these scattering events are more pronounced on Si than glass due to the thermally conductive nature of Si, and therefore heat is more readily removed from the Au electron system.
Properties used in TTM calculations for Au films.
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