Calibrating atomic force microscope detectors on soft surfaces

Quantitative force microscopy requires independant means of calibrating both cantilever stiffness and detector responsivity (i.e. the factor mapping cantilever deflection in nanometers to photo-detector signal in Volts). The conventional methods slowly approach the surface while observing either static bending or change in oscillation amplitude. Detector responsivity is then obtained under the assumption that the surface does not deform during the region of approach used for calibration. This assumption may be satisfied for large force and stiff sample, both of which risk damaging the tip. Here we present a new method for detector calibration based on Intermodulation AFM where the tip-surface force versus cantilever deflection is continuously monitored during the slow approach. This method allows us to calibrate the detector without the previously mentioned assumptions. We can therefore calibrate on any surface, hard or soft, or directly on the sample with the same magnitude of force used for quantitative imaging. We present the theory of this method and its experimental implementation on a variety of different surfaces.