Physical interpretation of frequency-modulation atomic force microscopy

Abstract

Frequency modulation atomic force microscopy is a method for imaging the surface of metals, semiconductors and insulators in ultrahigh vacuum with true atomic resolution. The imaging signal in this technique is the frequency shift $\ensuremath{\Delta}f$ of an oscillating cantilever with eigenfrequency ${f}_{0},$ spring constant k and amplitude A, which is subject to tip-sample forces ${F}_{\mathrm{ts}}.$ Here, we present analytical results of $\ensuremath{\Delta}{f(f}_{0},k,A)$ for several basic classes of ${F}_{\mathrm{ts}}.$ With these results, a method to calculate images is derived and demonstrated with an example.