Heat Transport in Silicon Nitride Drum Resonators and its Influence on Thermal Fluctuation-Induced Frequency Noise
Bibliographic record
Abstract
Silicon nitride ($\mathrm{Si}\mathrm{N}$) drumhead resonators offer a promising platform for thermal sensing owing to their high mechanical quality factor and the high temperature sensitivity of their resonance frequency. As such, gaining an understanding of heat transport in $\mathrm{Si}\mathrm{N}$ resonators as well as their noise limitations are of interest, both of which are goals of the present work. We first present measurements of radiative heat transport in $\mathrm{Si}\mathrm{N}$ membranes, which we use for benchmarking two recently proposed theoretical models. We measure the characteristic thermal response time of square $\mathrm{Si}\mathrm{N}$ membranes with a thickness of 90 \ifmmode\pm\else\textpm\fi{} 1.7 nm and side lengths from 1.5 to 12 mm. A clear transition between radiation- and conduction-dominated heat transport is measured, in close correspondence with theory. In the second portion of this work, we use our experimentally validated heat transport model to provide a closed-form expression for thermal fluctuation-induced frequency noise in $\mathrm{Si}\mathrm{N}$ membrane resonators. We find that, for large-area $\mathrm{Si}\mathrm{N}$ membranes, thermal fluctuations can be greater than thermomechanical contributions to frequency noise. For the specific case of thermal radiation sensing applications, we also derive the noise-equivalent power resulting from thermal fluctuation-induced frequency noise, and we show in which conditions it reduces to the classical detectivity limit of thermal radiation sensors. Our work therefore provides a path towards achieving thermal radiation sensors operating at the unattained fundamental detectivity limit of bolometric sensing. We also identify questions that remain when attempting to push the limits of radiation sensing; in particular, the effect of thermal fluctuation noise in closed-loop frequency tracking schemes remains to be clarified.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".