Image Calculations with a Numerical Frequency-Modulation Atomic Force Microscope

We investigated the implementation of a numerical tool able to mimic an experimental noncontact atomic force microscope (nc-AFM). Main parts of an experimental setup are modeled and are implemented inside a computer code. The goal was to build a numerical AFM (n-AFM) as versatile, efficient, and powerful as possible. In particular, the n-AFM can be used in the two working regimes, that is, in attractive and repulsive regimes, with settings for a standard AFM cantilever oscillating with a large amplitude (typically, 10 nm) or for a tuning-fork probe with ultrasmall amplitudes (∼0.01 nm). We present various tests to show the reliability of the n-AFM used as a frequency-modulation AFM (FM-AFM). As an example, we calculated FM-AFM images of adsorbed molecular systems, which range from two-dimensional planar molecules to corrugated systems with a three-dimensional molecule. The submolecular resolution of the FM-AFM is confirmed to originate from repulsive Pauli-like interactions between the tip and the sample. The versatility of the n-AFM is finally discussed in the perspective of new functionalities that will be included in the future.