Absolute Deflection Measurements in a Micro- and Nano-Electromechanical Fabry-Perot Interferometry System

Fabry-Perot laser interferometry is a common laboratory technique used to interrogate resonant micro- and nano-electromechanical systems (MEMS/NEMS). This method uses the substrate beneath a vibrating MEMS/NEMS device as a static reference mirror, encoding relative device motion in the reflected laser power. In this work, we present a general approach for calibrating these optical systems based on measurements of large-amplitude motion that exceeds one half of the laser wavelength. Utilizing the intrinsic nonlinearity of the optical transduction, our method enables the direct measurement of the system's transfer function (motion-to-detected-voltage). We experimentally demonstrate the use of this technique to measure vibration amplitudes and changes in the equilibrium position of a MEMS/NEMS device using monolithic silicon nitride and silicon cantilevers as sample systems. By scanning the laser along a cantilever surface, we spatially map static and dynamic deflection profiles simultaneously, and then compare the static profile against results from a commercial optical profilometer. We further demonstrate extension of our calibration technique to measurements taken at small amplitudes, where the optical transduction is linear, and to those taken in the frequency domain by a lock-in amplifier. Our aim is to present a robust calibration scheme that is independent of MEMS/NEMS materials and geometry, to completely negate the effects of nonlinear optical transduction, and to enable the assessment of excitation forces and MEMS/NEMS material properties through the accurate measurement of the MEMS/NEMS vibrational response.