By means of force spectroscopy measurements performed with the cantilever first and second flexural modes under the frequency modulation detection method, the authors corroborate the validity of the relation between tip-surface interaction force and frequency shift for force spectroscopy acquisition using higher cantilever eigenmodes. They estimate a cantilever effective stiffness for the second eigenmode 73 times larger than the static stiffness. This large effective stiffness enables them to perform force spectroscopy with a cantilever oscillation amplitude (A0) as small as 3.6Å. The authors provide experimental evidence that, at such small A0 values, normalized frequency shift curves deviate from a A03∕2 scaling and the signal-to-noise ratio is considerably enhanced.
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Sugimoto et al. (2007) studied this question.