Redundancy-Aware Power Grid Electromigration Checking Under Workload Uncertainties
Bibliographic record
Abstract
Electromigration (EM) in on-die metal lines is becoming a significant problem in modern integrated circuits technology. Due to the high levels of current density on the die, the large number of metal lines, and the inherent conservatism in classical full-chip EM models, designers are finding it very hard to meet the area and design specs while guaranteeing EM reliability. The EM problem is most significant in power grid lines, because unlike signal and clock lines, they do not benefit from healing due to their mostly unidirectional currents. In this paper, we develop a new model, referred to as the mesh model, for power grid EM checking which takes into account the inherent redundancy of its mesh structure while determining the reliability. To implement the mesh model, we also develop a framework to estimate the change in statistics of an interconnect as its effective-EM current varies. In order to overcome the conservative assumptions that designers usually make about chip workloads, we also propose a novel vectorless mesh model technique to estimate the average minimum time-to-failure of a power grid under workload uncertainties. The results indicate that the series model, which is currently used in the industry, gives a pessimistic estimate of power grid MTF and reliability by a factor of 3-4. Finally, we exploit multithreading and grid locality to speedup our implementation by almost $6{\times }$ .
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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 | 0.005 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.000 |
| 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 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".