Scanning Probe Microscope Force Reconstruction Algorithm via Time-Domain Analysis of Cantilever Bending Motion

摘要

We present a new solution to the Euler-Bernoulli equation that describes the bending motion of the Scanning Probe Microscopy (SPM) cantilever in the time domain that is, without resorting to frequency methods. The approach presented here is original in two ways. First, a new boundary condition is presented that explicitly takes into consideration useable experimental voltage versus time signals. This scheme introduces conceptual clarity into force reconstruction methods--the final objective of SPM spectroscopy. To be precise, the paper treats the cantilever sensor as an input-output system with an explicitly supplied filter, thus allowing users to unequivocally convert measured voltage traces to desired force versus separation curves. Second, based on the algorithm a plain operational rule is proposed to establish whether common simplified approaches (specifically the one-degree of freedom harmonic oscillator) may be used for processing the data in hand, or if the full algorithm is necessary.