Stability of dynamic force microscopy with the self-oscillator method

Dynamic force microscopy (DFM) with the self-oscillator (SO) method is not generally subjected to the instability effects typical of tapping-mode DFM, as confirmed experimentally. The inherent stability of SO-DFM is related to phase locking of the cantilever oscillation to the excitation signal. Such phase locking determines univocally the oscillation state (i.e. amplitude and frequency) on the resonance curve, even when multiple amplitude values are compatible with a given frequency. By modelling the behaviour of an air-operated DFM system, it is found that, while stabilizing tip/surface distance for DFM imaging at constant frequency shift, and beyond a certain critical phase value, instabilities are possible in the SO constant-excitation amplitude mode. However, such instabilities cannot affect dynamic force spectroscopy approach curves, because of phase locking. By extension to vacuum operation, this result can confirm the origin of jumps in frequency shift found on some experimental DFM approach curves, for instance between non-passivated silicon tips to specific surface atomic sites of reconstructed silicon, since instrumental effects of the SO method can be ruled out.