  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.
