Calibration of the Tribolever. In order to convert the deflections of the pyramid of the Tribolever into forces, we need to calibrate the spring constants of the sensor in X-, Y- and Z-directions as accurately as possible. Such calibration is difficult in traditional AFM cantilevers, for which often an already calibrated cantilever is used or the thermal noise spectra is analyzed. The calibration of the Tribolever is rather straightforward. We record the thermal resonance vibration frequency of the cantilever using a Fast Fourier Transform (FFT) analyzer. We add spherical micro glass beads of different diameters (typically from 40 to 200 µm in diameter) on the rear side of the pyramid (before mounting the tip) and record the resonance frequency shift with the added mass. The mass of each micro glass bead can be estimated accurately using the Calibration of the Tribolever 25 density of the material and the diameter of the bead as observed in an SEM or a high-resolution optical microscope. With this method we can routinely obtain a calibration accuracy of 4% along X, Y and Z. k M + m For unclear reasons we have not been able to discriminate the resonance peaks of the Tribolever in the frequency spectrum of its displacement noise, even though the integrated noise level is only a factor 2 above the expected thermal noise level (see below). In order to still accurately measure the resonance frequencies of the Tribolever, we have used external excitation of the sensor with a loudspeaker connected to a sine wave generator, with which the sound frequency was ramped from 0 to 50 kHz. The lowest X, Y and Z resonance frequencies of the cantilever are below 50 kHz and these resonances are excited by the sound from the loudspeaker. If there are inhomogeneities in the dimensions of the X and Y arms because of the inhomogeneous etching, we sometimes observe split resonance peaks corresponding to the resulting, small differences between the spring constants in the two lateral directions. In practiced, we choose those cantilevers that have the equal X and Y spring constants, within 2%. Adding the mass of a glass bead shifts the resonance frequencies to lower values. If k is the Tribolever spring constant, M is the (effective) mass of the sensor and m is the added mass, the resonance frequency of the cantilever v is given by ν = 1 2π
