Imaging material properties by resonant tapping-force microscopy: A model investigation

Abstract

The interaction of a cantilever performing a forced oscillation with a sample in a tapping-mode scanning force microscope is investigated within a simple model. The tip together with the cantilever is modeled as a periodically driven, damped harmonic oscillator. The viscoelastic sample is described by a friction force acting on the tip while it is in contact and a harmonic potential. The penetration of the probe and the phase shift of the oscillator due to contact with the sample are calculated for various sample parameters. In particular, an approximate solution of the model equations for the phase shift is presented. Moreover, a relation between the elastic constant of the model and the elastic modulus of a material is presented. © 1996 The American Physical Society.