Topography Reconstruction From Nonlinear Distributed Interactions for Nanoscale Metrology Using an Iterative Approximation Method

Abstract This research presents a novel technique for precisely reconstructing measured topographies using a resonating nanofiber. The approach uses a model-based, iterative approximation method to analyze nonlinear, coupled interactions. Such modeling has the potential to enhance metrology methods, including Atomic Force Microscopy (AFM), which may experience inaccuracies when functioning under distributed interactions. An iterative decoupling method is proposed to effectively disaggregate these interactions and accurately reconstruct the topography. This methodology involves the systematic movement of a vibrating fiber over a measured surface while continuously monitoring variations in its natural frequency. Subsequently, the interactions are decoupled, employing a series of successive approximations. The effectiveness of this approach has been substantiated through numerical simulations of the Van der Waals (VdW) interaction forces between a nanowire and nanoscale topography, as well as through experimental validation utilizing magnetic interactions between a magnetic topography and a beam. The results conclusively demonstrate the capacity to accurately reconstruct the measured topography, affirming its applicability for enhancing AFM metrology and addressing other nonlinear inverse problems.