The extended wedge method: Atomic force microscope friction calibration for improved tolerance to instrument misalignments, tip offset, and blunt probes

One of the major challenges in understanding and controlling friction is the difficulty in bridging the length and time scales of macroscale contacts and those of the single asperity interactions they comprise. While the atomic force microscope (AFM) offers a unique ability to probe tribological surfaces in a wear-free single-asperity contact, instrument calibration challenges have limited the usefulness of this technique for quantitative nanotribological studies. A number of lateral force calibration techniques have been proposed and used, but none has gained universal acceptance due to practical considerations, configuration limitations, or sensitivities to unknowable error sources. This paper describes a simple extension of the classic wedge method of AFM lateral force calibration which: (1) allows simultaneous calibration and measurement on any substrate, thus eliminating prior tip damage and confounding effects of instrument setup adjustments; (2) is insensitive to adhesion, PSD cross-talk, transducer/piezo-tube axis misalignment, and shear-center offset; (3) is applicable to integrated tips and colloidal probes; and (4) is generally applicable to any reciprocating friction coefficient measurement. The method was applied to AFM measurements of polished carbon (99.999% graphite) and single crystal MoS₂ to demonstrate the technique. Carbon and single crystal MoS₂ had friction coefficients of μ = 0.20 ± 0.04 and μ = 0.006 ± 0.001, respectively, against an integrated Si probe. Against a glass colloidal sphere, MoS₂ had a friction coefficient of μ = 0.005 ± 0.001. Generally, the measurement uncertainties ranged from 10%-20% and were driven by the effect of actual frictional variation on the calibration rather than calibration error itself (i.e., due to misalignment, tip-offset, or probe radius).