Neural Network for Surface-Profile Estimation of Atomic Force Microscope

Abstract

This paper describes a methodology for implementing an identification algorithm for an atomic force microscope to estimate a surface profile of a sample. A microbeam of the atomic force microscope is modeled as an Euler-Bernoulli beam. A tip-sample interaction force used here is a piecewise function described by the attractive van der Waals force and the repulsive Derjaguin-Muller-Toporov force which can represent the indentation made by a tip of the microbeam into the sample surface. The identification of the instantaneous gap between the tip of the undeformed microbeam and the sample surface is implemented on line based on a trained input-output recurrent network. With the measured cantilevered-beam-tip motion supplied to the recurrent network, the recurrent network is going to compute the estimated gap. The approach being used in this study is in contrast to the conventional approach in that it is based on the signal in the time domain instead of in the frequency domain; therefore, the number of steps involved is fewer. When comparing the proposed approach with the adaptive-tracking controllers based on adaptive control Lyapunov functions, the proposed approach outperforms the adaptive-tracking controllers significantly. Whereas the adaptive-tracking controllers require much more measured signals to supply to the controllers and the parameter estimator. Instead, the proposed approach has to store two units in the tapped-delay-line memory while the identification algorithm is running.