Performance Enhancement in High-Speed Contact-Mode Atomic Force Microscopy

Abstract

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> Atomic force microscopy is having a substantial impact on nanosciences and technologies. However, the low atomic- force-microscope (AFM) scanning speed continues to be a major obstacle that impedes the widespread adoption of AFM-based systems. This paper presents a controller design approach for constant-force contact-mode AFM operation to enhance the AFM system performance with respect to the scanning speed and the image accuracy. The purpose of the controller is to maintain a constant force between the cantilever tip and the sample surface through suitable displacement of the base end of the cantilever. Given that the sample surface profile is unknown, the difficulty in the controller design lies in attempting to regulate the contact force against an unknown and time-varying signal. To overcome this problem, it is proposed in this paper to use a two-step adaptive regulator design approach. The first step involves the use of the <formula formulatype="inline"><tex Notation="TeX">$Q$</tex></formula> parameterization of stabilizing controllers to construct a set of parameterized stabilizing controllers. The second step involves tuning the <formula formulatype="inline"><tex Notation="TeX">$Q$</tex> </formula> parameter in the expression of stabilizing controllers so that the tuned controller converges to the desired controller needed to achieve regulation. The proposed strategy makes it possible to use small contact forces and high scanning speeds, hence improving the performance of contact-mode AFM systems. </para>