It has long been recognized that the angular deflection of a typical atomic force microscope (AFM) cantilever under normal loading conditions can be profoundly influenced by the friction between the tip and the surface. It is shown here, that a remarkably quantifiable hysteresis occurs in the slope of normal force loading curves whenever the stiffness of the AFM cantilever is greater than that of the sample. This situation arises naturally in cantilever-on-cantilever calibration, but also when trying to measure the stiffness of nano-mechanical devices or test structures, or when probing any type of surface or structure that is much more compliant along the normal axis than along the lateral axes. Expressions and techniques for evaluating the coefficient of sliding friction between the cantilever tip and sample from normal force curves, as well as relations for determining the stiffness of a mechanically compliant sample are presented. The model is experimentally supported by the results of cantilever-on-cantilever spring constant calibrations. The cantilever stiffnesses determined agree with the values determined on the NIST electrostatic force balance (EFB) within the limits of the largest uncertainty component, which had a relative value less than 2.5 %. This points the way for quantitative testing of micro- and nanomechanical components, more accurate calibration of AFM force, and provides nanotribologists access to information about contact friction from normal force curves without having to sacrifice imaging capabilities.
Citation: Journal of Applied Physics
Pub Type: Journals
atomic force microscope, friction, calibration