Direct experimental measurement of femtonewton-scale momentum transfer force from electron beams
Electron beams (e-beams) are ubiquitous in imaging, patterning, and propulsion. This prevalence is rooted in the profound mastery of their wave-particle duality and energy-transfer pathways. Yet, a fundamental dimension remains largely unexplored: while the mechanical effect (i.e., the momentum transfer to a target) is theoretically known, quantification of its femtonewton-range force has remained elusive. This discrepancy represents a missing piece of the puzzle toward a comprehensive understanding of e-beam-matter interactions, and ultimately limits the multi-dimensional exploitation of e-beams. A force sensor combining femtonewton sensitivity, immunity to electromagnetic noise, compatibility with vacuum, and absolute calibration is critical to bridge the gap between theory and experiment. Here the FINEST (Femtonewton Interferometric Nanomechanical Electron-beam Sensing Technology) sensor is proposed and successfully tested to measure the force of an e-beam. FINEST is an optical-pressure-calibrated 3D spring-type optical sensor that operates reliably under e-beam conditions. Femtonewton-scale forces from 2-30 keV e-beams are directly measured, ranging from 505 fN to 13 pN. Both linear scaling with beam current and a non-monotonic energy dependence (peaking near 10 keV) are observed. Based on this calibrated force, the mechanical contribution to e-beam ice etching was quantitatively confirmed; its effect is orders of magnitude lower than the total etch depth and lacks noticeable energy dependence. By achieving the first direct experimental measurement of e-beam momentum transfer, this work adds a long-missing dimension to the physical landscape of e-beam processes. These findings provide a quantitative basis for furthering the multi-dimensional exploitation of e-beams, potentially transforming our approach to precision nanofabrication, sensing, and fundamental electron physics research.