Functional Kernel-Based Modeling of Wavelet Compressed Optical Emission Spectral Data: Prediction of Plasma Etch Process
Bibliographic record
Abstract
This study reports the use of a kernel-based process model, consisting of kernel partial least squares regression and kernel ridge regression, to model etch rate and uniformity in a plasma etch process. In order to characterize the plasma etch process, a 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4 - 1</sup> fractional factorial design was implemented on the process parameters: CHF <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> flow rate, CF <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sub> flow rate, RF power, and pressure. In this modeling, both functional data and <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">in situ</i> optical emission spectroscopy (OES) data associated with the etch response were used to formulate the model. In an effort to effectively deal with the complexity of the data, wavelet transformation with vertical-energy-thresholding (VET) shrinkage procedures were used to reduce the dimensions of the functional data. In addition, a Bayesian information criterion (BIC) was used to select the best subset to improve the model predictions. The proposed kernel-based approaches were evaluated by comparing them to conventional neural networks (NNs)-based modeling and linear-based regression techniques. Comparisons revealed that the proposed approach exhibits an improved prediction over NNs and linear-based models. Implicated in the study is a detection of process fault patterns by combining the kernel-based modeling, wavelet transformation with VET, and BIC.
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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 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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".