Silicon Resonator With ppb-Level Linear Temperature Coefficient of Frequency
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Bibliographic record
Abstract
This paper presents a geometrically modified silicon resonator made from degenerately doped silicon (DD-Si) that exhibits a linear temperature coefficient of frequency (<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">TCF<sub>1</sub> </i>) of + 23 ppb/°C. A combination of additive and subtractive geometrical modifications is applied to bulk-mode resonators fabricated on n-type silicon wafer with phosphorus doping concentration of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$9.34\times 10^{19}$</tex-math> </inline-formula> cm<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−3</sup>. The approach is broadly applicable to silicon resonators for passive compensation of their temperature coefficients of frequency (<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">TCFs</i>) and is demonstrated to achieve first order of temperature insensitivity without adding fabrication complexity. The temperature-dependent response of DD-Si is analyzed for these modified designs. This resonator’s extracted quadratic temperature coefficient of frequency (<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">TCF<sub>2</sub> </i>) is around -10 ppb/°C<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup>. Combined, the device demonstrates a turnover temperature around 26°C, with a total frequency variation of approximately 38 ppm across the temperature range of -<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$35~^{\circ }$</tex-math> </inline-formula>C to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$+ 85~^{\circ }$</tex-math> </inline-formula>C.[2025-0120]
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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 | 0.002 | 0.000 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
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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