Experimental/Analytical Evaluation of the Effect of Tip Mass on Atomic Force Microscope Calibration

Quantitative studies of material properties and interfaces using the atomic force microscope (AFM) have important applications in engineering, biotechnology and chemistry. Emerging studies require an estimate of the stiffness of the probe so that the forces exerted on a sample can be determined from the measured displacements. Numerous methods for determining the spring constant of AFM cantilevers have been proposed, yet none accounts for the effect of the mass of the probe tip on the calibration procedure. This work demonstrates that the probe tip does have a significant effect on the dynamic response of an AFM cantilever by experimentally measuring the first few modes of a commercial AFM probe and comparing them with those of a theoretical model for a cantilever probe that does not have a tip. The mass and inertia of an AFM probe tip are estimated from scanning electron microscope images and a simple model for the probe is derived and tuned to match the first few modes of the actual probe. Analysis suggests that both the method of Sader and the thermal tune method of Hutter and Bechhoefer give erroneous predictions of the area density or the effective mass of the probe. However, both methods do accurately predict the static stiffness of the AFM probe due to the fact that the mass terms cancel so long as the mode shape of the AFM probe does not deviate from the theoretical model. The calibration errors that would be induced due to differences between mode shapes measured in this study and the theoretical ones are estimated. 1