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-ts. Here, we present analytical results of Delta f(f(0),k,A) for several basic classes of F-ts. With these results, a method to calculate images is derived and demonstrated with an example.