Physical interpretation of frequency-modulation atomic force microscopy

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 $\Delta f$ 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 $\Delta {f(f}_0,k,A)$ for several basic classes of $F_{\mathrm{ts}}.$ With these results, a method to calculate images is derived and demonstrated with an example.