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51 Mat. Res. Soc. Symp. Proc. Vol. 543 ©1999 Materials Research Society

Mechanicalproperties of the cantilever The measurement of the kinetic friction force can be made more reproducible and precise when we have selected and calibrated the appropriate cantilever. The selection of the appropriate cantilever depends on the magnitude of the forces to be measured and the sensitivity of the force measurement system. The critical elements of the force measurement system are: * the cantilever, * the piezoceramic transducer, * the laser and deflection optics, * the Position Sensitive Detector (PSD) system. To make quantitative friction force measurements requires that the PSD photocurrent be converted to force. This can be done if the torsional and normal spring constants are determined for the cantilever and the changes in PSD photocurrent can be related to the magnitude of the

deflection of the cantilever in each of the essential directions.

Determining the cantilever spring constant can be done either by calculation or in situ measurement. The calculation of the spring constants requires an accurate measure of the physical dimensions of the cantilever and length of the tip. The physical dimensions combined with the Young's modulus for the cantilever material are enough information to calculate each of the three spring constants 1 . The in-situ measurement methods are quite varied. One approach is to measure the change of the cantilever deflection2 or resonance frequency 3 with increasing applied mass. Another approach is to extract the spring constant from the power spectrum of the cantilever thermal fluctuations 4. In each case, only the normal force spring constant is measured. Buenviaje et al. 5 proposed an indirect calibration method that uses a reference surface with a well defined friction coefficient (g) in combination with a dimensionally calibrated cantilever to establish the lateral spring constant of the unknown cantilever. Comparing the lateral force measured with calibrated cantilever on the reference surface with the lateral force response of the unknown cantilever, also on a reference surface, provides an indirect but effective method to determine the lateral spring constant. Ogletree et al.6 have demonstrated a direct method to calibrate the lateral response of cantilever. Their technique uses a crystal of SrTiO 3 with a wedge plane of known angle of inclination. The lateral force can be measured as a function of applied load while sliding along the slope of the wedge plane. To successfully use these techniques requires that each of the experimental planes of the instrument is perfectly parallel or the possible induced cross-talk between the normal and lateral forces is compensated electronically. No one method has yet emerged as preferred and adopted as a standard. We have chosen to use the calculation approach to establish the cantilever force constants. Our cantilevers are bar shaped pure silicon prepared by Nanosensors. They are not coated to enhance reflectivity.