Quantitative Determination of the Mechanical Properties of Nanomembrane Resonators by Vibrometry In Continuous Light

Abstract

We present an experimental study of the bending waves of freestanding \ce{Si3N4} nanomembranes using optical profilometry in varying environments such as pressure and temperature. We introduce a method, named Vibrometry in Continuous Light (VICL) that enables us to disentangle the response of the membrane from the one of the excitation system, thereby giving access to the eigenfrequency and the quality ($Q$) factor of the membrane by fitting a model of a damped driven harmonic oscillator to the experimental data. The validity of particular assumptions or aspects of the model such as damping mechanisms, can be tested by imposing additional constraints on the fitting procedure. We verify the performance of the method by studying two modes of a $478~\textrm{nm}$ thick \ce{Si3N4} freestanding membrane and find $Q$ factors of $2 \times 10^4$ for both modes at room temperature. Finally, we observe a linear increase of the resonance frequency of the ground mode with temperature which amounts to $550~\textrm{Hz}/^{\circ}\mathrm{C}$ for a ground mode frequency of $0.447~\textrm{MHz}$. This makes the nanomembrane resonators suitable as high-sensitive temperature sensors