A fresh insight into the microcantilever-sample interaction problem in non-contact atomic force microscopy

The atomic force microscope (AFM) system has evolved into a useful tool for direct measurements of intermolecular forces with atomic-resolution characterization that can be employed in a broad spectrum of applications. The non-contact AFM offers unique advantages over other contemporary scanning probe techniques such as contact AFM and scanning tunneling microscopy, especially when utilized for reliable measurements of soft samples (e.g., biological species). Current AFM imaging techniques are often based on a lumped-parameters model and ordinary differential equation (ODE) representation of the micro-cantilevers coupled with an adhoc method for atomic interaction force estimation (especially in non-contact mode). Since the magnitude of the interaction force lies within the range of nano-Newtons to pica-Newtons, precise estimation of the atomic force is crucial for accurate topographical imaging. In contrast to the previously utilized lumped modeling methods, this paper aims at improving current AFM measurement technique through developing a general distributed-parameters base modeling approach that reveals greater insight into the fundamental characteristics of the microcantilever-sample interaction. For this, the governing equations of motion are derived in the global coordinates via the Hamilton's Extended Principle. An interaction force identification scheme is then designed based on the original infinite dimensional distributed-parameters system which, in turn, reveals the unmeasurable distance between AFM tip and sample surface. Numerical simulations are provided to support these claims.