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

Abstract

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.