A Further Study on the Analytical Model for the Permeability in Flip-Chip Packaging
Bibliographic record
Abstract
The notion of permeability is very important in understanding and modeling the flow behavior of fluids in a special type of porous medium (i.e., the underfill flow in flip-chip packaging). This paper presents a new concept regarding permeability in a porous medium, namely two types of permeability: superficial permeability (with consideration of both the pore cross-sectional area and the solid matrix cross-sectional area) and pore permeability (with consideration of the pore cross-sectional area only). Subsequently, the paper proposes an analytical model (i.e., equation) for the pore permeability and superficial permeability of an underfill porous medium in a flip-chip packaging, respectively. The proposed model along with several similar models in literature is compared with a reliable numerical model developed with the computational fluid dynamics (CFD) technique, and the result of the comparison shows that the proposed model for permeability is the most accurate one among all the analytical models in literature. The main contributions of the paper are as follows: (1) the provision of a more accurate analytical model for the permeability of an underfill porous medium in flip-chip packaging, (2) the finding of two types of permeability depending on how the cross-sectional area is taken, and (3) the correction of an error in the others' model in literature.
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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 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.003 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.001 | 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 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".