Temperature frequency stability study of extensional mode N-doped silicon MEMS resonator
Bibliographic record
Abstract
Analytical and numerical modeling techniques are presented to predict n-type-doped silicon resonators’ temperature coefficient frequencies for the extensional mode of vibration by modeling of single-crystal silicon ([100] and [110]) directions. We utilized a previously reported empirical exponential expression for the uniaxial deformation potential that allows us to determine the deformation potential constant. It was observed that by using the empirical model of exponential expression for the uniaxial deformation potential, our result shows that the frequency variation with temperature is closely dependent on the direction and the variation of the different doping levels. We apply our analytical model to the [100] and [110] length extensional modes of a Microelectromechanical Systems (MEMS) resonator. We calculated the resonance frequency with temperature dependence and found that the first-order temperature coefficient frequency shows zero values at doping concentration levels of 0.5 and 1 × 1019 cm−3, which indicates the existence of frequency turnover at room temperature. We also extended our study by finite element analysis of MEMS resonators to investigate the mode shapes and resonant frequency for different aspect ratios in the extensional mode of vibration. It is observed that the mode shapes are more stressed with higher aspect ratios, and the frequency variation (ppm) of the resonance frequency between the [100] and [110] crystal directions of the MEMS resonator increases with increasing aspect ratios.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| 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 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 source (direct Gemma or distilled Codex), 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".