Fabry-Perot interferometric calibration of van der Waals material-based nanomechanical resonators

One of the challenges in integrating nanomechanical resonators made from van der Waals materials in optoelectromechanical technologies is characterizing their dynamic properties from vibrational displacement. Multiple calibration schemes using optical interferometry have tackled this challenge. However, these techniques are limited only to optically thin resonators with an optimal vacuum gap height and substrate for interferometric detection. Here, we address this limitation by implementing a modeling-based approach via multilayer thin-film interference for in situ, non-invasive determination of the resonator thickness, gap height, and motional amplitude. This method is demonstrated on niobium diselenide drumheads that are electromotively driven in their linear regime of motion. The laser scanning confocal configuration enables a resolution of hundreds of picometers in motional amplitude for circular and elliptical devices. The measured thickness and spacer height, determined to be in the order of tens and hundreds of nanometers, respectively, are in excellent agreement with profilometric measurements. Moreover, the transduction factor estimated from our method agrees with the result of other studies that resolved Brownian motion. This characterization method, which applies to both flexural and acoustic wave nanomechanical resonators, is robust because of its scalability to thickness and gap height, and any form of reflecting substrate.