V(Z) curves technique for elastic characterization of thin films


The development of the first high-frequency scanning acoustic microscope was motivated by the idea of using an acoustic field to study the spatial variations of elastic properties of materials with nearly optical resolution. However, it was soon found that the acoustic microscope could be used for measuring the velocity of SAWs. To analyze the image formation in the reflection acoustic microscope, Atalar, Quate, and Wickramasinghe (Appl. Phys. Lett., 31, 791, 1977, ) monitored the amplitude of the transducer voltage V as a function of lens-to-sample spacing z, or the V(z) curve. They found that the V(z) curve ''has a characteristic response that is dependent upon the elastic properties of the reflecting surface''. Later Weglein and Wilson (Weglein, Wilson, Electronics Lett., 14, 352, 1978) reported the periodicity of dips appearing in the V(z) curves. They called the central portion of the V(z) curve, which has a periodic character, the acoustic material signature (AMS). It was soon established that the periodicity of the V(z) curve was linked to surface wave propagation. The application of a ray model for wave propagation in the acoustic microscope by Parmon and Bertoni (Electron. Lett., 15,  684, 1979) yielded a clear physical picture of signal formation in the reflection acoustic microscope and provided a simple formula for determining the SAW velocity from acoustic microscopy measurements. The next step toward quantitative measurements of anisotropic materials was taken by Kushibiki and coworkers (Kushibiki, Ohkubo,  Chubachi, Electron. Lett., 17,  520, 1981) who invented the line-focus-beam (LFB) technique or the line focus acoustic microscope (LFAM). This made it possible to measure the anisotropy of surface acoustic waves on a crystal surface. Considerable progress in quantitative acoustic microscopy of anisotropic multilayered structures has been made since the time of the invention of the acoustic microscope (see Zinin, P. V. Quantitative Acoustic Microscopy of Solids, in Handbook of Elastic Properties of Solids, Liquids, and Gases. Volume I: Dynamic Methods for Measuring the Elastic Properties of Solids, Levy, M., Bass, H., Stern, R., and Keppens, V. Academic Press, New York, 2001, pp. 187-226.).



V(Z) curve of the PAA layer on aluminum.

   Several methods have been developed [8] for extracting the SAW velocity VSAW from the recorded V(z) curve. For practical reasons, only the amplitude of the signal is generally measured, from which velocity and attenuation can be calculated. The standard method of analyzing V(z) curves was developed by Kushibiki and Chubachi ( IEEE Trans. Sonics Ultrason. 32, 189, 1985) in 1985 for the LFAM and is also commonly applied to a point focus lens. The method is based on the ray model proposed by Parmon and Bertoni. They postulated that the periodical character of the V(z) curve is determined by interference of two rays: central ray and the SAW ray. Specular ray is incident normally onto the specimen and is reflected back along the same path. Rayleigh wave ray is incident at a critical angle and excites a leaky SAW along the surface. Simple ray approach gives following expression for velocity of the surface wave VSAW.


VSAW = VW [1-(1- VW/(f Δ z ))2]-1/2


where Δ z distance between minima in the V(z) curve, VW is sound velocity in water, f is the sound frequency.