All-optical measurement of in-plane and out-of-plane Young's modulus and Poisson's ratio in silicon wafers by means of vibration modes
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Bibliographic record
Abstract
An all-optical technique was developed to determine the in-plane and out-of-plane Young's modulus, E, and Poisson's ratio, σ, in silicon wafers through excitation and detection of vibration modes. The technique is remote, non-destructive and works on-line, making it an attractive inspection tool for use in semiconductor foundries. Vibration modes were generated by a pulse from a frequency-doubled Q-switched Nd:YAG laser and detected by a commercial heterodyne Michelson interferometer. Because of their importance as component substrates in the electronic and MEMS industries, both the 100 and 111 silicon wafers were investigated. It was found that the resonance frequencies of the first pure torsional and of the first hybrid (torsional and flexural) modes varied continuously and symmetrically with respect to a 90° rotation of the wafer around the centre, while the resonance frequencies of the first and second pure flexural modes remained constant. On the basis of this experimental observation, we could correlate the resonance frequencies of the two former and two latter modes with the in-plane and out-of-plane mechanical parameters E and σ, respectively. A novel inverse method for circular anisotropic plates was then derived to extract the in-plane and out-of-plane parameters from the resonance frequency measurements. The results obtained by this approach were in good agreement with the standard values calculated by the theory of elasticity.
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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 | 0.001 | 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 | 0.001 |
| 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 it