Demonstration of Frequency Stability limited by Thermal Fluctuation Noise in Silicon Nitride Nanomechanical Resonators

Abstract: The frequency stability of nanomechanical resonators (NMR) dictates the performance level of many state-of-the-art sensors (e.g., mass, force, temperature, radiation) that relate an external physical perturbation to a resonance frequency shift. While this is obviously of fundamental importance, accurate models and understandings of sources of frequency instability are not always available. The contribution of thermomechanical noise to frequency stability has been well studied in recent years and is often the fundamental performance limitation. Frequency stability limited by thermal fluctuation noise has attracted less interest but is nevertheless of fundamental importance notably in temperature sensing applications. In particular, temperature-sensitive NMR have become promising candidates for replacing traditional bolometers in infrared radiation sensing. However, reaching the ultimate detectivity limit of thermal radiation sensors requires their noise to be dominated by fundamental thermal fluctuation, which has not been demonstrated to date. In this work, we first develop a theoretical model for computing the frequency stability of NMR by considering the effect of both additive phase noise (i.e., thermomechanical, and experimental detection noise) and thermal fluctuation noise in a close-loop frequency tracking scheme. We thereafter validate this model experimentally and observe thermal fluctuation noise in SiN drum resonators of various sizes. Our work shows that by using resonators of specific characteristics--such as high temperature sensitivity, high mechanical quality factors, and high mass-to-thermal-conductance ratio--one can minimize additive phase noise below thermal fluctuation noise. This paves the way for NMR-based radiation sensors that can reach the fundamental detectivity limit of thermal radiation sensing and outperform existing technologies.