Measurement and modelling of non-contact atomic force microscope cantilever properties from ultra-high vacuum to normal pressure conditions

The resonance frequency and Q-factor of cantilevers typically used for non-contact atomic force microscopy (NC-AFM) are measured as a function of the ambient pressure varied from 10−8 mbar to normal pressure. The Q-factor is found to be almost constant up to a pressure in the range of 10−2–10−1 mbar and then decreases by about three orders of magnitude when increasing the pressure further to normal pressure. The decrease in the resonance frequency measured over the same pressure range amounts to less than 1% where a significant change is observed in the range of 10–103 mbar. The pressure dependence of the effective Q-factor and resonance frequency is approximated by analytical models accounting for different processes in the molecular and viscous flow regimes. By introducing a heuristic approach for describing the pressure dependence in the transition regime, we are able to well approximate the cantilever properties over the entire pressure range.