Effect of temperature on noncontact atomic force microscopy images

The purpose of this paper is to carry out a theoretical analysis of the effect of temperature on atomic force microscopy images using a model of a single-atom tip on the substrate. Assuming that the effect of temperature arises from the change in phonon distribution of the substrate, we first formulate the force acting on the tip in terms of the Debye–Waller factor (DWF) within a single phonon process. Next we calculate the force acting on the tip from substrate lattice with several current types of the potential for interaction between the tip and substrate. The types of potential are: (1) Gaussian; (2) exponential; (3) Morse; (4) Lennard–Jones. The general results are: (1) the effects of temperature increase with increasing temperature; (2) at low temperatures, the effects of zero-point motion play an important role.