Measurement of Submilligram Masses Using Electrostatic Force

The redefinition of the kilogram within the International system of units provides a direct link between mass and Planck's constant. With this in place, it becomes possible to realize the kilogram using electrical metrology. We describe a method that scales this mass measurement approach to the submilligram level using an electrostatic force balance (EFB). Through traceable determination of capacitance, voltage, and position within the balance, the mass values of submilligram artifacts are determined. An uncertainty analysis is carried out on these measurements. Results show a substantial reduction in uncertainty relative to those currently available through conventional approaches based on kilogram subdivision for true mass. Since the EFB measurements are carried out in a vacuum, conversion to conventional mass requires an air buoyancy correction at the location of use. Despite additional uncertainty added by buoyancy correction, the use of the EFB method decreases uncertainty in submilligram mass measurement by an order of magnitude.