A simple non-equilibrium theory of non-contact dissipation force microscopy

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Abstract
The tip-surface interaction in the non-contact atomic force microscopy (NC-AFM) leads to energy dissipation. Recently, this effect has been harnessed to obtain images with atomic resolution. In an important paper Gauthier and Tsukada (GT) (1999 Phys. Rev. B 60 11716) suggested a theory of this, so-called non-contact dissipation force microscopy (NC-DFM) using a stochastic approach within a simple one-atomic representation of the surface. In this paper we elaborate on this model further, stressing the importance of a consistent non-equilibrium consideration. Then, using a more general model, we offer an alternative derivation based on a rather simple approach to non-equilibrium phenomenon used by Kirkwood for the Brownian motion. We show that our method leads to the final result similar to that obtained in the GT paper. We also discuss some other models for the energy dissipation in NC-AFM. In particular, we emphasise that the `stick and slip' (or adhesion hysteresis) model of energy dissipation, although containing a specific element which requires additional features to be incorporated in our model, is to be considered using non-equilibrium methods.