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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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