Atomic-scale topographic and friction force imaging and cantilever dynamics in friction force microscopy

Friction force microscopy (FFM) is commonly used for micro-, nano-, and atomic-scale topographic and friction (lateral) force imaging of surfaces. The experimental-obtained topographic and friction force images are closely correlated to the cantilever dynamics since in FFM, the normal and lateral forces between the cantilever tip and sample surface are measured from the cantilever flexural and twist angles. To understand the cantilever dynamics under tip-surface interaction and its effects on the measured topographic and friction force maps, efficacious models that can accurately simulate the cantilever behavior in operating conditions of FFM are essential. In this paper, a three-dimensional (3D) finite element (FE) beam model is employed to simulate the atomic-scale topographic and friction force profiling process in FFM. The tip-sample interaction forces are modeled as the interatomic forces between the tip and sample surface. It is identified that the topographic and lateral force maps obtained in FFM experiments are the combined results of the real spatial distributions of 3D tip-sample interatomic forces and cantilever dynamics. The experimental-obtained hexagonal (full atomic structure) and trigonal (atomic resolution of every other atom) topographic images of graphite surfaces are reproduced in simulations with different combinations of cantilever geometries, applied normal loads, and scan directions. Based on the simulated results, the methods to realize the observation of the full atomic structure of graphite are discussed.