Accurate measurement of Atomic Force Microscope cantilever deflection excluding tip-surface contact with application to force calibration.

Considerable attention has been given to the calibration of AFM cantilever spring constants in the last 20 years. Techniques that do not require tip-sample contact are considered advantageous since the imaging tip is not at risk of being damaged. Far less attention has been directed toward measuring the cantilever deflection or sensitivity, despite the fact that the primary means of determining this factor relies on the AFM tip being pressed against a hard surface, such as silicon or sapphire; which has the potential to significantly damage the tip. A recent method developed by Tourek et al. in 2010 involves deflecting the AFM cantilever a known distance from the imaging tip by pressing the cantilever against a sharpened tungsten wire. In this work a similar yet more precise method is described, whereby the deflection of the cantilever is achieved using an AFM probe with a spring constant much larger than the test cantilever, essentially a rigid cantilever. The exact position of loading on the test cantilever was determined by reverse AFM imaging small spatial markers that are milled into the test cantilever using a focussed ion beam. For V shaped cantilevers it is possible to reverse image the arm intersection in order to determine the exact loading point without necessarily requiring FIB milled spatial markers, albeit at the potential cost of additional uncertainty. The technique is applied to tip-less, beam shaped and V shaped cantilevers and compared to the hard surface contact technique with very good agreement (on average less than 5% difference). While the agreement with the hard surface contact technique was very good the error on the technique is dependent upon the assumptions inherent in the method, such as cantilever shape, loading point distance and ratio of test to rigid cantilever spring constants. The average error ranged between 2 to 5% for the majority of test cantilevers studied. The sensitivity derived with this technique can then be used to calibrate the cantilever spring constant using the thermal noise method, allowing complete force calibration to be accurately performed without tip-sample contact.