Measuring the spring constant of atomic force microscope cantilevers: thermal fluctuations and other methods

Knowledge of the interaction forces between surfaces gained using an atomic force microscope (AFM) is crucial in a variety of industrial and scientific applications and necessitates a precise knowledge of the cantilever spring constant. Many methods have been devised to experimentally determine the spring constants of AFM cantilevers. The thermal fluctuation method is elegant but requires a theoretical model of the bending modes. For a rectangular cantilever, this model is available (Butt and Jaschke). Detailed thermal fluctuation measurements of a series of AFM cantilever beams have been performed in order to test the validity and accuracy of the recent theoretical models. The spring constant of rectangular cantilevers can also be determined easily with the method of Sader and White. We found very good agreement between the two methods. In the case of the V-shaped cantilever, we have shown that the thermal fluctuation method is a valid and accurate approach to the evaluation of the spring constant. A comparison between this method and those of Sader–Neumeister and of Ducker has been established. In some cases, we found disagreement between these two methods; the effect of non-conservation of material properties over all cantilevers from a single chip is qualitatively invoked. (Some figures in this article are in colour only in the electronic version)