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 Nanoscale imaging of elastic properties using scanning force microscopy has been studied intensively. Ultrasonic force microscopy (UFM) is a promising example of such imaging because it can be used to map nondestructively the elastic properties of relatively stiff materials such as metals and semiconductors with standard atomic force microscope (AFM) cantilevers.

 Elastic constants of Ge quantum dots on a Si substrate were investigated with waveguide ultrasonic force microscopy (WUFM). WUFM is a modified version of UFM, using ultrasonic excitation at the base of an AFM cantilever. The ultrasonic excitation travels down to the end of tip and modifies the distance between the tip and the sample surface at a much higher frequency than the fundamental resonance of the cantilever. Due to the nonlinear nature of the tip-sample interaction, the average position of the cantilever shifts away from the sample surface. This shift is related to the tip-sample interaction force dependent on elastic constants and adhesion.

 We operated WUFM at an excitation frequency of 60 MHz, a frequency significantly higher than in previous studies. The dots (about 15 nm in height and 20 nm in diameter) are clearly resolved both in topography and in WUFM. The ratio of the WUFM signal between the Si substrate and the dots is typically 1:4.

 The Johnson-Kendall-Roberts model of contact theory is combined with a simple mass-spring model for WUFM in order to study the WUFM contrast. Young's moduli and Poisson's ratios of the samples are fixed, whereas the work of adhesion is treated as a free parameter. We find that difference in the work of adhesion between the dots and the substrate is crucial to reproduce the experimental WUFM contrast.

K. Inagaki, O. B. Wright, O. V. Kolosov and G. A. D. Briggs,
Appl. Phys. Lett. 76, 1836 (2000).

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