Harmonic response of near-contact scanning force microscopy

One-dimensional harmonic oscillator theory was used to model tapping-mode atomic force microscope (TMAFM) operation in the near-contact region in the presence of gases and liquids. The force derivative of the tip-sample interaction changes the vibration amplitude and frequency at maximum amplitude of the cantilever. Additionally, the interaction is hydrodynamically damped by fluid motion around the tip and between the tip and the surface. Good agreement was found between theoretical and experimental amplitude as a function of height. For a sample-driven TMAFM operating in fluids, the cantilever can be very soft (spring constant ≪1 N/m) and operated at frequencies well above the fundamental. Under these conditions the cantilever and sample appear to act with a high spring constant, much like that used in a gaseous operation. The tip-sample interaction in the fluid is still mediated through the force derivative of the sample.