With the increasing interest in nanostructures and thin films, the need for a quantitative measuring method for elastic constants on the nanometer scale has become more evident. The fundamental physical quantity characterizing the elastic constants is the acoustic phase velocity. Due to the strong localization of surface acoustic waves (SAWs) in the near-surface region, SAWs are particularly favored for such investigations. The velocity measurement is commonly performed by time delay and acoustic far-field methods. Therefore the lateral resolution of the velocity measurement is restricted by the wavelength involved to some tens of microns. Recently, we introduced the scanning acoustic force microscope (SAFM) for the measurement of SAW amplitude distributions with nanometer lateral resolution. The key to detecting high-frequency surface oscillations by the slowly responding force microscope cantilever is the nonlinear force curve. This nonlinearity can be exploited in a heterodynetype setup for high-frequency wave mixing of a probe and a reference wave, revealing the phase of the probe wave. The difference frequency can be chosen to be as low as 1 kHz. We present measurements of the phase velocity over a lateral distance of 19:9 nm. The phase velocity dispersion due to Au layers on a quartz substrate was measured over distances as small as 200 nm and compared with calculations. © 1998 Springer-Verlag.
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