Nonlocality Effect in Atomic Force Microscopy Measurement and Its Reduction by an Approaching Method

In AFM measurements of surface morphology, the locality is a traditional assumption, i.e., the load recorded by AFM is simply the function of the distance between the tip of AFM and the point on a sample right opposite the tip [Giessibl, F. J., 2003, “Advances in Atomic Force Microscopy,” Rev. Mod. Phys., 75, pp. 949–983]. This paper presents that nonlocality effect may play an important role in atomic force microscopic (AFM) measurement. The nonlocality of AFM measurement results from two different finite scales: the finite scale of the characteristic intermolecular interaction distance and the geometric size of AFM tip. With a coupled molecular-continuum method, we analyzed this nonlocality effect in detail. It is found that the nonlocality effect can be formulated by a few dimensionless parameters characterizing the ratio of the following scales: the characteristic intermolecular interaction distance between the AFM tip and the sample, the characteristic size of the tip and the characteristic nano-structure and∕or the nanoscale roughness on the surface of a sample. The present work also suggests a data processing algorithm—the approaching method, which can reduce the nonlocality effect in AFM measurement of surface morphology effectively.