**2.1. Why optical interferometer?**

the manufacturing stage. However, detection of poor adhesion is not easy. In particular, when the film material is poorly adhered but not causing a structural abnormality, detection is very difficult. Static methods such as acoustic imaging microscopy or X-ray diffractometry cannot beusedto identify theproblem.Dynamic analysis capable of characterizing the elastic behavior

Among dynamic techniques to evaluate the film adhesion strength, ultrasonic techniques [1–5] are the prevailing methods. In these methods, ultrasonic waves are excited in the substrate and film materials, and abnormality is detected from the propagation characteristics of the ultrasonic wave. The recent trend indicates that the film thickness is reduced for better performance of the thin-film system. This forces the ultrasonic wavelength to be shorter, hence the frequency to be higher. Reduction in the wavelength works well for the purpose of detecting defects or other nonuniform issues in the interface, as the spatial resolution is increased. However, for characterization of elasticity of the film-substrate interface, an increase in the frequency makes the analysis difficult. This is because normally, poor adhesion has lower elastic modulus than the healthy adhesion. Consequently, the frequency is too high to oscillate the poor adhesion effectively, and the signal representing the poor adhesion tends to be small. In other words, the detection system tries to probe the oscillatory behavior caused by the poor adhesion at a frequency on the blue side of the spectrum, as schematically illustrated in **Figure 1**. The transmissibility (the transfer function) of a me-

chanical oscillator decreases with a quadratic dependence on the frequency (*f*

Considering the above situation, we have devised an optical interferometric system to characterize the adhesion of thin films to their substrate [6]. A Michelson interferometer is used to analyze harmonic response of thin-film specimens when they are oscillated with an acoustic transducer. The film surface displacement resulting from the acoustic oscillation is detected as relative optical path changes behind the beam splitter. With the assumption that the filmsubstrate interface has a lower elastic modulus than the film or the substrate material and by choosing the acoustic frequency appropriately, it is possible to characterize the elastic behavior

−2) on the high

of the interface is essential.

62 Optical Interferometry

frequency side of the resonance.

**Figure 1.** Resonance curves with different resonant frequencies.

The substrate of typical thin film systems is of the order of 100 μm or less in thickness. In order to excite 10 waves in the substrate, the wavelength of the acoustic signal must be 10 μm or shorter. The acoustic velocity in silicon (a typical substrate) is 8 km/s. This results in the acoustic frequency higher than 800 MHz, leading to the situation where detection of elastic behavior associated with resonant frequency of the order of 100 MHz or less is difficult. Poor adhesion normally has a resonant frequency substantially lower than 100 MHz. In addition, most thinfilm systems are subject to environmental disturbance of much lower frequency. Therefore, the use of high acoustic frequency is unrealistic.
