## 3 Experimental Section  
### Preliminary Experiment with Doppler Vibrometry  
We first studied the harmonic response of a thin-film specimen using a laser Doppler vibrometer (LDV, Model: OFV 5000, Polytec, Irvine, CA, USA [19] with Displacement Decoder Model: DD300, Polytec, Irvine, CA, USA [20]) [21]. Figure 4 illustrates the experimental arrangement. The operation principle of LDV can be found elsewhere [22]. In short, it works in the following fashion. A laser beam is applied normal to an oscillating surface. The sensor of the LDV compares the optical frequency of the reflected laser beam with the incident beam. Due to the Doppler effect, the frequency of the reflected beam is shifted depending on the velocity of the oscillation. From the detected frequency shift, the oscillation amplitude is estimated. A pair of polystyrene thin-films were used in this experiment. In the first specimen, 100 nm-thick polystyrene was coated on a 750 \(\upmu\)m-thick silicon substrate without pre-coating surface treatment (untreated polystyrene-coated specimen). The silicon substrate was cut along the [1, 0, 0] plane. In the second specimen, polystyrene of the same thickness was coated on the same silicon substrate after the surface was treated with the oxygen-plasma bombardment technique. An acoustic transducer was attached to the rear surface of the specimen to oscillate it at 50 kHz. The transducer was driven with a function generator (Model 395, Wavetek, San Diego, CA, USA) with a pure sinusoidal output. Figure 5 compares the resultant displacement of the film surface for the untreated and treated specimens along with the oscillation of the transducer surface. (The signals for the untreated and treated specimens are shifted vertically for better visibility. The amplitude of the signals in nm exceeds the maximum value specified by the manufacturer for an unknown reason. However, since the signals do not exhibit any saturation-like behavior, the argument made here is considered legitimate. The absolute amplitude of the oscillation does not affect the gist of the argument.) Here, the middle graph is for the case when the transducer was oscillated without a specimen; the top and bottom graphs are the cases where the treated and untreated specimens were attached, respectively. The top and bottom graphs are shifted vertically for better visibility. As expected, the untreated specimen shows greater oscillation amplitude, indicating that the adhesion is weaker. (Figure 5 indicates that the signal from the treated specimen and the transducer only is much noisier than the signal from the untreated specimen. The reason for this observation is not totally clear. A possible explanation is that: (a) the untreated one is least noisy because the amplitude of the signal is the greatest (among the three signals); (b) the amplitude of the transducer-only signal is not much smaller than the untreated, but the signal is much noisier than the untreated case because the surface of the transducer was not as smooth as the specimen; (c) the treated signal is noisy because the signal was low.) There is a phase difference between the untreated and treated specimens, as will be discussed shortly. Consider the film surface motion based on the theory of harmonic oscillation. The harmonic response of an oscillatory system of spring constant \(k\), damping coefficient \(b\) and mass \(m\) driven at angular frequency \(\omega\) is given as a solution to the following equation of motion. \[m\ddot{x}+b\dot{x}+kx=fe^{i\omega t} \tag{6}\]  
Here, \(x(t)\) is the displacement from the equilibrium position of \(m\), and \(f\) is the amplitude of the driving force. In the present context, \(k\) and \(b\) represent the elasticity and viscosity of the adhesion; \(m\) is the mass of the thin-film; and \(\omega\) is the angular frequency of the acoustic transducer. The particular solution to Equation (6) can be put in the following form in general. \[x(t)=Ae^{i(\omega t-\delta)} \tag{7}\]  
Figure 4: Doppler vibrometry setup.