Moisture Diffusion Inside the BEOL of an FC-PBGA Package
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Bibliographic record
Abstract
Moisture diffusion into the back-end-of-line (BEOL) can be critical for the reliability of electronic devices. With the objective of studying moisture diffusion into critical areas, such as the silicon–organic substrate interfaces of a flip chip plastic ball grid array (FC-PBGA), a multitude of impedance sensors sensitive to moisture are integrated inside the BEOL of a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$17\times17$ </tex-math></inline-formula> mm silicon die. The sensors are read by a dedicated custom circuit that allows accurate characterization of the moisture with in situ spatial measurements. This article presents the results obtained by the experimental acquisition system on the FC-PBGA module under a high-relative humidity (RH) level of up to 75%. This study shows the moisture behavior of the multiwalled carbon nanotube (MWCNT) sensors inside the BEOL during absorption and desorption. The behavior initially follows Fick’s law, with a constant increase in the RH. For long-term tests of more than 400 h, an asymptotic behavior is observed; when the concentration of a sensor reaches a value close to saturation, a two-dimensional finite-difference method (2D FDM) is used to estimate the saturation value. Thanks to the large number of sensors distributed on the BEOL, we first detect, during an absorption test, an increase in the RH. This increase is due, first of all, to a lateral moisture front with a constant velocity of about <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$90 ~\mu \text{m}$ </tex-math></inline-formula> /h moving through the underfill. Then, after 30 h of storage, a more complex diffusion through the organic substrate occurs, affecting the BEOL.
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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 | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| 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