ABSTRACT
BFPR harnesses thermal vibrations of the cantilever to probe the interaction potential. As the cantilever vibrates in the proximity of the sample, it encounters different regions of the interaction potential. Ordinarily, this information is lost in the DC averaging, yet it can be recovered by oversampling the deflection signal at a frequency higher than thermal resonance frequency. A histogram of the probe positions taken from a region of such 'noisy' force curve contains information about the sum of the interaction potential and the harmonic cantilever potential well. Specifically, the histogram of the cantilever positions is populated according to the Boltzmann-weighted distribution:
p(x) = po-z k»T , (34)
where Uts refers to the potential of the tip-sample interactions and J / c a n t refers to the cantilever spring potential. Inverting the position histogram according to equation (34) produces the sum of two potentials (Fig. 15A-C). The cantilever potential can then be recovered from a section of the force curve recorded far away from the surface. Subtraction of the cantilever potential then recovered a small section of the interaction potential near the average tip-sample separation at this point (Fig. 15D, E). Researchers have also developed an algorithm which 'stitched' these pieces to recover the full potential energy profile (Fig. 15F, G).
