Radiative Heat Transfer in Freestanding Silicon Nitride Membranes
Why this work is in the frame
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Bibliographic record
Abstract
Freestanding silicon nitride ($\mathrm{Si}\mathrm{N}$) mechanical resonators are of central interest in applications such as temperature and mass sensing, and for fundamental optomechanical research. Understanding thermal coupling between a membrane resonator and its environment is required to predict thermal noise, frequency noise, and sensor responses to temperature changes. In this work, we provide closed-form derivations of intrinsic thermal-coupling quantities in freestanding thin films---namely, total thermal conductance with the surroundings, thermal response time, and the relative contribution of thermal radiation. Our model is valid for any freestanding thin film anchored on all sides when small temperature differences between the film and its environment are considered. We particularly emphasize the specific case of $\mathrm{Si}\mathrm{N}$, for which spectral emissivity is thoroughly investigated as a function of thickness and temperature. We find that radiative heat exchanges can play a non-negligible role, and can even dominate thermal coupling for membranes of sizes commonly used in optomechanics experiments. We find that our model is in agreement with preliminary experimental results on radiative heat transfer between a ceramic heater and a $3\ifmmode\times\else\texttimes\fi{}3\phantom{\rule{0.2em}{0ex}}{\mathrm{mm}}^{2}$ membrane in a high vacuum.
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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) | 0.001 | 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 | 0.000 |
| 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 it