Improved methods and uncertainty analysis in the calibration of the spring constant of an atomic force microscope cantilever using static experimental methods

Abstract

There are many published methods to calibrate the spring constant of an atomic force microscope (AFM) cantilever needed for quantitative force measurement. Each method has its own merits and falls within three broad categories: dimensional, static experimental and dynamic experimental. We report, here, improved static experimental methods using a one- or a two-step calibration process using readily available equipment. The one-step method uses either a nanoindenter on cantilever method or dimensional means and the two-step method uses the first step to calibrate a reference cantilever which is then used for a cantilever on reference cantilever approach relevant to laboratories with many AFMs. For both static experimental methods, multi-positional methods using four or five positions along the cantilever are described and shown in practice to have lower uncertainty than a one-position method. Full uncertainties in all the methods are discussed and shown to be dominated by the uncertainty in the first step demonstrated here with a standard uncertainty of 8%, although this could be reduced to 5%. In the second, cantilever on reference cantilever step only a further 0.6% is added in quadrature.