  With recent advances in scanning probe microscopy (SPM), it is now routine to
determine the atomic structure of surfaces and molecules while quantifying the
local tip-sample interaction potentials. Such quantitative experiments are
based on the accurate measurement of the resonance frequency shift due to the
tip-sample interaction. Here, we experimentally show that the resonance
frequency of oscillating probes used for SPM experiments change systematically
as a function of oscillation amplitude under typical operating conditions. This
change in resonance frequency is not due to tip-sample interactions, but rather
due to the cantilever strain or geometric effects and thus the resonance
frequency being a function of the oscillation amplitude. Our numerical
calculations demonstrate that the amplitude dependence of the resonance
frequency is an additional yet overlooked systematic error source that can
result nonnegligible errors in measured interaction potentials and forces. Our
experimental results and complementary numerical calculations reveal that the
frequency shift due to this amplitude dependence needs to be corrected even for
experiments with active oscillation amplitude control to be able to quantify
the tip-sample interaction potentials and forces with milli-electron volt and
pico-Newton resolutions.
