Learning Localized Spatial Material Properties of Substrates in Ultra-Thin Packages Using Markov Chain Monte Carlo and Finite Element Analysis
Bibliographic record
Abstract
Thinned silicon dies and thin substrates using thin core and coreless structures have enabled thin packages. For robust manufacturing and reliability of these parts, solving the warpage problem is key. While current finite element methodologies can provide some insights at the design stage, these simulations are only as accurate as the inputs such as the material properties and the stress-free temperatures. Electronic substrates are especially challenging to characterize and model as they are laminates consisting of a core with layers of resin and metal lines on either side. In this work, a hybrid approach using Markov Chain Monte Carlo (MCMC) and Finite Element Analysis (FEA) is used to learn the spatially varying properties of the substrate from Digital Image Correlation (DIC) measurements of the warpage. The analysis is carried out at room temperature and at an elevated temperature point. Image analysis on electrical artwork is also carried out to correlate the material properties to the substrate metal density. These results will be useful to package and substrate designers to understand how material properties vary over the substrate and how temperature and metal density affect material properties so that robust design for future packages to minimize warpage can be initiated by careful routing of metal lines depending on the locally desired properties of the stack.
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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 | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.001 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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".