The quantitative determination of friction forces by atomic force microscopy (AFM) in nanotribology requires the conversion of the output voltage signal of the sector area-sensitive photodiode to force using (a) the torsional spring constant of the cantilever and (b) the lateral sensitivity of the photodiode. Many existing methods provide calibration factors with large errors and suffer from poor reproducibility. We report on the fabrication, validation, and application of a new, universally applicable standard specimen that enables one to accurately calibrate all types of AFM cantilevers and tips for quantitative friction force measurements. The Si(100) calibration standard, which exhibits 30 and 50 mum wide notches with tilt angles theta between 20 degrees and 35 degrees with respect to the wafer surface, was fabricated by focused ion beam (FIB) milling. The quantification of friction forces obtained on this universal standard specimen using a direct method (the improved wedge calibration method, as introduced by Ogletree, Carpick, and Salmeron Rev. Sci. Instrum. 1996, 67, 3298-3306), which yields (a) and (b) simultaneously, was critically tested for various types of Si3N4 integrated cantilever-tip assemblies. The error in the calibration factors obtained was found to be ca. 5%, which is a significant improvement compared to errors of 30-50% observed for the often applied two-step calibration procedures of cantilever lateral force constant and photodiode sensitivity. As demonstrated for oxidized Si(100), thin films of poly(methyl methacrylate) (PMMA), and micropatterned self-assembled monolayers (SAMs) on gold, the calibration of various V-shaped and single beam cantilevers based on the application of the new universal standard in conjunction with the direct wedge method proposed allows one to conveniently perform quantitative nanotribological measurements for a wide range of materials and applications.

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The calibration factors for atomic force microscopy (AFM) friction force measurements in liquid media are shown to be different by 25-74% compared to measurements in air. Even though it is significantly more precise, the improved wedge calibration method using a universal calibration specimen suffers, as all other widely applied methods, from the drawback that friction force calibration factors acquired in air cannot be used for measurements in liquids for the most common liquid cell designs. The effect of laser light refraction and the dependence of the calibration factors on the refractive index of the imaging medium is captured quantitatively in a simple model that allows one to conveniently rescale the values of lateral photodiode sensitivity obtained in air. Hence a simple, yet precise calibration of lateral forces is now also feasible for AFM in liquids.

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