Robust atomic force microscopy using multiple sensors

Atomic force microscopy typically relies on high-resolution high-bandwidth cantilever deflection measurements based control for imaging and estimating sample topography and properties. More precisely, in amplitude-modulation atomic force microscopy (AM-AFM), the control effort that regulates deflection amplitude is used as an estimate of sample topography; similarly, contact-mode AFM uses regulation of deflection signal to generate sample topography. In this article, a control design scheme based on an additional feedback mechanism that uses vertical z-piezo motion sensor, which augments the deflection based control scheme, is proposed and evaluated. The proposed scheme exploits the fact that the piezo motion sensor, though inferior to the cantilever deflection signal in terms of resolution and bandwidth, provides information on piezo actuator dynamics that is not easily retrievable from the deflection signal. The augmented design results in significant improvements in imaging bandwidth and robustness, especially in AM-AFM, where the complicated underlying nonlinear dynamics inhibits estimating piezo motions from deflection signals. In AM-AFM experiments, the two-sensor based design demonstrates a substantial improvement in robustness to modeling uncertainties by practically eliminating the peak in the sensitivity plot without affecting the closed-loop bandwidth when compared to a design that does not use the piezo-position sensor based feedback. The contact-mode imaging results, which use proportional-integral controllers for cantilever-deflection regulation, demonstrate improvements in bandwidth and robustness to modeling uncertainties, respectively, by over 30% and 20%. The piezo-sensor based feedback is developed using H∞ control framework.