Comparison of different methods to calibrate torsional spring constant and photodetector for atomic force microscopy friction measurements in air and liquid.

A number of atomic force microscopy cantilevers have been exhaustively calibrated by a number of techniques to obtain both normal and frictional force constants to evaluate the relative accuracy of the different methods. These were of either direct or indirect character-the latter relies on cantilever resonant frequencies. The so-called Sader [Rev. Sci. Instrum. 70, 3967 (1999)] and Cleveland [Rev. Sci. Instrum. 64, 403 (1993)] techniques are compared for the normal force constant calibration and while agreement was good, a systematic difference was observed. For the torsional force constants, all the techniques displayed a certain scatter but the agreement was highly encouraging. By far the simplest technique is that of Sader, and it is suggested in view of this validation that this method should be generally adopted. The issue of the photodetector calibration is also addressed since this is necessary to obtain the cantilever twist from which the torsional force is calculated. Here a technique of obtaining the torsional photodetector sensitivity by combining the direct and indirect methods is proposed. Direct calibration measurements were conducted in liquid as well as air, and a conversion factor was obtained showing that quantitative friction measurements in liquid are equally feasible provided the correct calibration is performed.