## 3 Experimental Section
### Analysis on Ti-Si Thin-Film Specimens with the Acousto-Optical Method
#### 3.2.2 Observation of Resonance-Like Behavior  
With the use of the interferometer setting shown in Figure 2, experiments were conducted numerous times with the treated and untreated thin-film specimens listed in Table 2. Figure 7 plots the peak value of the Fourier spectrum observed for each specimen as a function of the driving frequency (called the driving frequency sweep). For each specimen, the peak value is normalized to that of the bare silicon evaluated at the same driving frequency (called the peak ratio). The driving frequency sweep of the peak ratio shows some features. In the Ti-only specimen case, the untreated specimen shows valleys around 14.5 kHz and 27 kHz (called the valley frequency). Similarly, the treated specimen shows valleys at 7 kHz, 13 kHz and 22.5 kHz. The higher valley frequencies observed in the respective specimens are approximately integer multiples of the lowest value. This indicates the possibility that the observed series of valley frequencies represents harmonics of the resonance for the respective specimen, being consistent with the above argument that the film-substrate interfaces have resonance in the swept frequency range. A previous study on Au-coated \begin{table}
\begin{tabular}{c c c c} \hline
**Film material** & **Ti** & **Ti-Au** & **Ti-Pt** \\ \hline T (nm) & 75 & 10/100 & 10/100 \\ \(\rho\) (kg/m\({}^{3}\)) & 4510 & 4510/19,030 & 4510/21,450 \\ M (kg) & \(8.4\times 10^{-9}\) & \(5.0\times 10^{-8}\) & \(5.5\times 10^{-8}\) \\ mass ratio & 1 & 2.4 & 2.5 \\ \hline \end{tabular}
\end{table} 
Table 2: Specimens. T: film thickness; \(\rho\): density of the film material; M: total film mass; mass ratio: the ratio of the square root of the mass of the Ti-Au and T-Pt films to that of the Ti film. Figure 7: Peak ratio as a function of driving frequency. The valley frequencies indicated in (**a**) the Ti-only specimen are measured values. The valley frequencies pointed to by arrows in (**b**) Ti-Pt and (**c**) Ti-Au indicate valley frequencies estimated from those in (**a**) and the mass ratio defined in Table 2.  
thin-film specimens clearly shows that the valley observed in the driving frequency sweep around the higher central frequency is the second harmonic of the valley observed around the lower central frequency [17]. Based on the assumption that the elastic property of the Ti-substrate interface is independent of the additional metal layers on top of the Ti layer and on the mass ratio shown in Table 2, the valley frequencies observed in the Ti-only case can be converted to the Ti-Pt and Ti-Au cases. Table 3 lists the valley frequencies estimated in this fashion for the Ti-Pt and Ti-Au specimens. In the driving frequency sweeps shown in Figure 7, the valley frequencies estimated for the Ti-Pt (b) and Ti-Au (c) specimens are indicated with arrows. Valleys are seen approximately at these estimated frequencies. In Table 3, the valley frequencies are grouped as Valley 1 and Valley 2. Valley 1 refers to the lower frequency pair of valley frequencies observed in the untreated and treated specimens of the same kind. Similarly, Valley 2 refers to the higher frequency pairs. Notice that in each pair, the valley frequency of the untreated specimen is 15% to 20% higher than the treated specimen. This is consistent with the results from the Doppler vibrometry shown in Table 1. These observations support the interpretation that the valleys in the driving frequency sweeps represent the resonance behaviors of the film-substrate interface. The reduction in the fringe contrast, _i.e.,_ the peak ratio, is very sensitive to the optical alignment and other factors. The longer in the optical path that the interfering laser beams overlap each other, the greater the modulation depth (\(J_{0}(\delta)\) in Equation (4)). The air flow near the interferometer and floor vibration also affect the fringe contrast. The driving frequency sweeps, the Ti-Pt case in particular, indicate that the data fluctuate vigorously near valleys.