Abstract
We propose a force-spectroscopy technique where a higher order mode of a cantilever is excited simultaneously with the first. Resonance tracking of both vibration modes through a frequency modulation scheme provides a way to extract topographical information and the gradient of the tip-sample interaction within a single surface scan. We provide an analytic treatment of the scheme, derive expressions relating frequency shifts of the higher mode and the tip-sample forces, and offer two methods of improving the accuracy of reconstruction of the force gradient. Finally, we confirm our predictions by numerical simulations.
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