**3.4. Driving frequency sweep**

**Figure 12.** Spectrum peak value as a function of input voltage to transducer.

76 Optical Interferometry

**Figure 13.** Oscillation amplitude estimated for each voltage input.

By repeating the same measurement as the lower row of **Figure 8**, it is possible to find out the frequency dependence of the film surface. As is the case of **Figure 8**, the input voltage to the acoustic transducer is adjusted so that the oscillation amplitude of the transducer surface is the same for all the driving frequencies tested. **Figure 14** shows the result of such a series of measurement for a driving frequency range of 8–14.5 KHz. Here, the vertical axis is the value of the Fourier spectrum peak obtained from the intensity profile across the fringe pattern averaged over five rows near the vertical center of the fringe images. In accordance with the argument made above, the higher the peak, the smaller the film surface oscillation. Since the transducer surface has the same oscillation amplitude for all the driving frequencies, the frequency dependence of the film surface oscillation observed in this figure represents the transducer surface to the film surface transfer function. Since the transfer function of the substrate and film materials themselves are considered to be unity

**Figure 14.** Driving frequency sweep of Fourier spectrum peak value.

in this frequency range, the transfer function represents the elastic property of the film-substrate interface. The lower the spectrum peak the greater the oscillation on the film surface, which can be interpreted as the greater oscillation of the interface.

The transfer function shown in **Figure 14** is obtained for five rows near the vertical center of the fringe image. By repeating the same procedure for other rows, it is possible to draw a map of the transfer function. **Figure 15** shows a three-dimensional map obtained in this fashion for four specimens; the untreated, treated, and bare silicon specimens. Here one horizontal axis is the row number and the other horizontal axis is the driving frequency. The top two plots are the cases when silicon substrates only are used (called the bare silicon specimens), and the bottom two plots are cases when the treated and untreated specimens are used. The treated and untreated specimens are attached to two different acoustic transducers. To eliminate the effect associated with the use of the different transducer, one bare silicon specimen is attached to the same transducer as the treated specimen and the other bare silicon specimen is attached to the other transducer used for the untreated specimen.

**Figure 15.** Fourier spectrum peak for several rows as a function of driving frequency.

The two plots for the bare silicon specimens appear to be flat, indicating that the bare silicon specimens do not have clear frequency dependence in the oscillation. On the other hand, the treated and untreated specimens show frequency dependences. As mentioned above, the frequency dependence represents the elastic characteristics of the substrate-film interface.

It is interesting to note that the untreated specimen shows a crater-like pattern around row 250 through 280 near driving frequency of 10 KHz. It is possible to interpret this pattern as representing the so-called blister effect [9–11]; the interface has a weakly adhered spot where the film experiences membrane-like oscillation when the specimen is driven. The treated specimen does not show a crater-like pattern. Instead, there is a valley running through all rows around the driving frequency of 8 KHz. We observed similar patterns in the treated and untreated specimens for a number of times. It is possible that the precoating surface treatment makes the adhesion more uniform so that the chances of the specimen having blisters is lower. These observations particularly interest us because there is no established technique to evaluate the blister effect non-destructively.
