Crystal radius and temperature regulation in Czochralski crystallization process
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Bibliographic record
Abstract
In this paper we explore modelling and regulation techniques for temperature and crystal growth control in an industrially important process of Czochralski crystal growth. First, a geometrical model for both crystal growth and radius evolution dynamics is developed and a controller is designed based on an input-output linearization to regulate and track a desired reference crystal radius. The pulling based regulated crystal radius control provides a time-varying shape (geometry) evolution of the underlying time-varying partial differential equation describing the crystal temperature dynamics. A low dimensional time-varying parabolic PDE model obtained by Galerkin method is used for regulation of the triple point temperature (melt-solid-encapsulant intersection). The coupling among finite-dimensional crystal radius and triple point temperature regulation is given by the perturbation in the crystal growth parameters and it is induced by possible solid-melt interface temperature fluctuations. We provide a unified regulation framework for such a complex coupled system of crystal growth and temperature regulation in order to improve operational and economic features associated with the Czochralski crystal growth process.
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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 | 0.000 | 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 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.003 | 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