High performance feedback for fast scanning atomic force microscopes

Abstract

We identify the dynamics of an atomic force microscope (AFM) in order to design a feedback controller that enables faster image acquisition at reduced imaging error compared to the now generally employed proportional integral differential (PID) controllers. First, a force model for the tip–sample interaction in an AFM is used to show that the dynamic behavior of the cantilever working in contact mode can be neglected for control purposes due to the relatively small oscillation amplitude of the cantilever in response to a defined topography step. Consequently, the dynamic behavior of the AFM system can be reduced to the behavior of the piezoelectric scanner making the design of a model based controller for the AFM possible. Second, a black box identification of the scanner of a commercial AFM (Nanoscope IIIa, Digital Instruments) is performed using subspace methods. Identification yields a mathematical model of the scanner which allows us to design a new controller utilizing H∞ theory. Finally, this controller is implemented on an existing AFM and operated in contact mode. We demonstrate that such an H∞-controlled AFM system, while scanning at rates five times faster than conventional PID-controlled systems, operates with reduced measurement error and allows scanning at lower forces.

Imaging stability in force-feedback high-speed atomic force microscopy

“…The striation pattern has been observed previously and found to be due to the resonant vibration of the piezo tube scanner (e.g. [20][21][22][23][24]). Therefore, the dominant factor that limits the response speed of the system at 0.1 s per frame was the resonance of the piezo tube [14].…”

Nonlinear behaviour of self-excited microcantilevers in viscous fluids

“…Potential sources of nonlinearities include: nonlinear electronic components required for signal conditioning [11,12], nonlinear stress-strain relation of the cantilever material subject to large deformations [15,16] and nonlinear forces between the probe and the sample or surrounding viscous fluids [17]. As a result, the dynamics of these systems are often very complex and several cases of chaos [18] and bifurcations [19,20] on the response of the resonators have been reported.…”

A Tutorial on the Mechanisms, Dynamics, and Control of Atomic Force Microscopes

“…More details about these models can be found in [10], [11], [58], [59], but the tip sample interaction has a general shape as shown in Figure 7, generated by (1). The nonlinearity of the interaction force clearly shows why feedback operation for tracking the sample topography is crucial for obtaining reliable data about the sample surface.…”

“…The solution involves either an improved model and/or a higher-order robust controller. Because tube scanners often lack X-Y sensors, much of the original advanced feedback control work was done in the Z direction [59], [86], while feedforward controllers were developed for the X-Y motions [74], [81], [82]. The advent of sensored X-Y stages has led to feedback control methods being developed for X-Y motions as well [87], [88].…”

“…The nonlinear tip-sample interaction force can be represented by various models. Two popular models are the DMT (Derjagin, Muller, Toropov) model (e.g., [58]) and the Lennard-Jones potential combined with a modified Hertz model (e.g., [59]). The Lennard-Jones potential [10], [11] results in the interaction force,…”