Lateral force calibration in atomic force microscopy: A new lateral force calibration method and general guidelines for optimization

Proper force calibration is a critical step in atomic and lateral force microscopies (AFM/LFM). The recently published torsional Sader method [C. P. Green et al., Rev. Sci. Instrum. 75, 1988 (2004)] facilitates the calculation of torsional spring constants of rectangular AFM cantilevers by eliminating the need to obtain information or make assumptions regarding the cantilever's material properties and thickness, both of which are difficult to measure. Complete force calibration of the lateral signal in LFM requires measurement of the lateral signal deflection sensitivity as well. In this article, we introduce a complete lateral force calibration procedure that employs the torsional Sader method and does not require making contact between the tip and any sample. In this method, a colloidal sphere is attached to a "test" cantilever of the same width, but different length and material as the "target" cantilever of interest. The lateral signal sensitivity is calibrated by loading the colloidal sphere laterally against a vertical sidewall. The signal sensitivity for the target cantilever is then corrected for the tip length, total signal strength, and in-plane bending of the cantilevers. We discuss the advantages and disadvantages of this approach in comparison with the other established lateral force calibration techniques, and make a direct comparison with the "wedge" calibration method. The methods agree to within 5%. The propagation of errors is explicitly considered for both methods and the sources of disagreement discussed. Finally, we show that the lateral signal sensitivity is substantially reduced when the laser spot is not centered on the detector.