Progress toward Système International d'Unités traceable force metrology for nanomechanics

Recent experiments with the National Institute of Standards and Technology (NIST) Electrostatic Force Balance (EFB) have achieved agreement between an electrostatic force and a gravitational force of 10⁻⁵N to within a few hundred pN/μN. This result suggests that a force derived from measurements of length, capacitance, and voltage provides a viable small force standard consistent with the Système International d’Unités. In this paper, we have measured the force sensitivity of a piezoresistive microcantilever by directly probing the NIST EFB. These measurements were linear and repeatable at a relative standard uncertainty of 0.8%. We then used the calibrated cantilever as a secondary force standard to transfer the unit of force to an optical lever–based sensor mounted in an atomic force microscope. This experiment was perhaps the first ever force calibration of an atomic force microscope to preserve an unbroken traceability chain to appropriate national standards. We estimate the relative standard uncertainty of the force sensitivity at 5%, but caution that a simple model of the contact mechanics suggests errors may arise due to friction.