Modeling of mechanical effects related to operation of atomic force microscopes

Abstract

One of the key directions of the modern development of nanotechnologies is related to the “bottom-up” technology involving the construction of multiscale structures composed of basic nano-and subnatoelements like atoms, molecules, and biocells. Such technology can be implemented and developed due to the appearance and perfection of scanning probe microscopy and, primarily, its particular type, viz. atomic force microscopy. We propose an analytic review of various working modes of atomic force microscopes (AFMs). For the dynamic mode, the relation between the description of flexural and torsional vibrations of the AFM cantilever in a simplified oscillator model and the description based on the beam model in the continuum mechanics is discussed in detail. For the static working mode of the AFM, a detailed analysis of features associated with clamping of the cantilever and its nonuniformity is carried out and inaccuracies introduced by the disregard of the resilience of clamping and poor control of the variation of thickness along the cantilever during its operation and preparation are estimated. A preliminary version of the algorithm that can be applied for numerical modelling of the contact interaction between the AFM working element and the surface being investigated in constructing a virtual AFM is described in the concluding part of the article.