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Colloidal probes are often used in force microscopy when the geometry of thetip-sample interaction should be well controlled. Their calibration requiresthe understanding of their mechanical response, which is very sensitive to thedetails of the force sensor consisting of a cantilever and the attachedcolloid. We present analytical models to describe the dynamics of thecantilever and its load positioned anywhere along its length. The thermal noisecalibration of such probes is then studied from a practical point of view,leading to correction coefficients that can be applied in standard forcemicroscope calibration routines. Experimental measurements of resonancefrequencies and thermal noise profiles of raw and loaded cantileversdemonstrate the validity of the approach.

Thermal noise calibration of functionalized cantilevers for force microscopy: effects of the colloidal probe position