Calibration of Atomic Force Microscope soft cantilevers based on μ-LDV: metrological insight on the constitutive experimental parameters of Sader’s formulas for flexural and torsional effective spring constant

This study investigates the experimental parameters relevant to the application of Sader's formulations for determining the effective flexural and torsional spring constants of compliant soft cantilevers used in Atomic Force Microscopy (AFM), including detailed uncertainty budgets. At INRiM, a significant upgrade of the metrological AFM system is currently underway, with the goal of enabling traceable and accurate characterization of material properties at the nanoscale. While procedures ensuring metrological traceability to the International System of Units (SI) for nanoscale displacements along the lateral (x-y) and vertical (z) axes have already been established, an equivalent traceability chain for force measurements at the nanoscale has yet to be realized. Due to the intrinsic difficulties of achieving direct force traceability at micro-and nano-scales, an indirect approach is adopted: nanoscale forces are inferred from the calibrated spring constants of AFM cantilevers. In this context, the elastic properties of the cantilevers are evaluated using micro-Laser Doppler Velocimetry, by analysing their fundamental flexural and torsional resonance frequencies along with the corresponding damping characteristics of free oscillations. These measurements are interpreted within the framework of Sader's theoretical model.