Inverting amplitude and phase to reconstruct tip–sample interaction forces in tapping modeatomic force microscopy

Abstract

Quantifying the tip–sample interaction forces in amplitude-modulated atomic forcemicroscopy (AM-AFM) has been an elusive yet important goal in nanoscale imaging,manipulation and spectroscopy using the AFM. In this paper we present a general theoryfor the reconstruction of tip–sample interaction forces using integral equations forAM-AFM and Chebyshev polynomial expansions. This allows us to reconstruct thetip–sample interactions using standard amplitude and phase versus distance curvesacquired in AM-AFM regardless of tip oscillation amplitude and in both the net attractiveand repulsive regimes of oscillation. Systematic experiments are performed to reconstructinteraction forces on polymer samples to demonstrate the power of the theoreticalapproach.