Abstract
Analytical expressions for the noise affecting the different signals of interest in frequency-modulation dynamic force microscopy are derived. Two noise sources are considered, the thermomechanical noise of the cantilever and the noise of the deflection sensor. It is shown that distinguishing between amplitude and phase noise is crucial for a good understanding of the instrument. When the tip is far from the sample surface, in the absence of any tip-substrate interaction, the system reduces to two independent feedback loops, the first one maintaining the amplitude at a set point value and the other one keeping a constant phase lag between the tip oscillation and the cantilever excitation force. Closer to the surface, in the presence of tip-substrate interaction, these two loops become coupled to an extent that is determined by the nonlinear character of the cantilever oscillation induced by this interaction. The approximations introduced in deriving these analytical expressions are validated by numerical simulations and a comparison with experimental measurements is proposed. This modeling of the noise in frequency-modulation dynamic force microscopy allows us to derive most of the previously published results in a clear and unified framework. In addition, it demonstrates that the oscillator nonlinearities play an essential role in determining the noise level of the instrument, an effect that was not considered before.
23 More- Received 8 January 2009
DOI:https://doi.org/10.1103/PhysRevB.79.235401
©2009 American Physical Society