A calibration method for lateral forces for use with colloidal probe force microscopy cantilevers

A calibration method is described for colloidal probe cantilevers that enables friction force measurements obtained using lateral force microscopy (LFM) to be quantified. The method is an adaptation of the lever method of Feiler et al. [A. Feiler, P. Attard, and I. Larson, Rev. Sci. Instum. 71, 2746 (2000)] and uses the advantageous positioning of probe particles that are usually offset from the central axis of the cantilever. The main sources of error in the calibration method are assessed, in particular, the potential misalignment of the long axis of the cantilever that ideally should be perpendicular to the photodiode detector. When this is not taken into account, the misalignment is shown to have a significant effect on the cantilever torsional stiffness but not on the lateral photodiode sensitivity. Also, because the friction signal is affected by the topography of the substrate, the method presented is valid only against flat substrates. Two types of particles, $20μm$ glass beads and $UO3$ agglomerates attached to silicon tapping mode cantilevers were used to test the method against substrates including glass, cleaved mica, and $UO2$ single crystals. Comparisons with the lateral compliance method of Cain et al. [R. G. Cain, S. Biggs, and N. W. Page, J. Colloid Interface Sci. 227, 55 (2000)] are also made.