The effects of non-uniform nanoscale deflections on capacitance in RF MEMS parallel-plate variable capacitors
Bibliographic record
Abstract
This paper analyzes in detail the effect of nanoscale non-uniform deflections, caused by the residual stress phenomenon and/or applied actuation dc voltages, on the capacitance in RF MEMS parallel-plate variable capacitors in an effort to determine the severity of this effect on the ideal parallel-plate capacitance expression normally used.Closed-form capacitance expressions and integrals are given for second order, fourth order, elliptic paraboloidal and hyperbolic paraboloidal models of the bending behavior of the top plate caused by the residual stress and/or actuation.The theoretical analysis is then verified using the finite-element modeling method and results from both analyses exhibit excellent agreement.The equations obtained are then applied to a fabricated chip and other fabricated capacitors in the literature.It was found that anticipating the capacitance using the ideal parallel-plate formula can deviate from the capacitance incorporating the deflections by as much as 80%.The presented equations better anticipate the real capacitance of actual fabricated chips and can take into account deflections in the top plate even if they were in the order of a few nanometers.
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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 | 0.000 |
| 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 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".