Dynamic analysis of torsional resonance mode of atomic force microscopy and its application to in-plane surface property extraction

In the torsional resonance (TR) mode of atomic force microscopy (AFM), the changes in the torsion-related dynamic characteristics of a tip-cantilever system due to in-plane (lateral) tip-sample interaction are used for surface property imaging. This paper investigates the fundamental dynamics of a tip-cantilever system when it is operated in TR mode, with or without tip-sample interaction. With the actual location of the tip on the cantilever taken into consideration, modal analysis is carried out to obtain the cantilever TR frequencies/mode shapes under linear elastic tip-sample interaction. The relations of lateral contact stiffness and viscosity to torsional amplitude/phase shift are established. A comprehensive understanding on the effects of lateral contact stiffness and viscosity, driving frequency, and tip location on the cantilever torsional amplitude/phase shift is achieved by parametric analysis. The basic methodology to extract in-plane surface properties in TR mode is described. This work will help in advancing the development and applications of the techniques and instruments using TR mode of AFM.