Surface–Volume–Surface Electric Field Integral Equation for Magneto-Quasi-Static Analysis of Complex 3-D Interconnects
Bibliographic record
Abstract
A novel single-source surface–volume–surface integral equation is proposed for accurate broadband resistance and inductance extraction in 3-D interconnects. The new equation originates in the volume integral equation (VIE) traditionally used for magneto-quasi-static modeling of current flow in 3-D wires. The latter is reduced to a surface integral equation by representing the electric field inside each conductor segment as a superposition of cylindrical waves emanating from the conductor's boundary. As no approximation is utilized and all underlying boundary conditions and pertinent equations are satisfied in the reduction, the new integral equation is rigorously equivalent to the solution of the traditional volume electric field integral equation. The rigorous nature of the proposed single-source surface integral equation is corroborated numerically. In this paper, a detailed description of the method of moments discretization for the proposed surface integral equation is also presented. Numerical solution of the proposed surface integral equation for a 12-conductor bond-wire package is used to demonstrate the accuracy of the method and its computational benefits compared to the traditional solution based on the VIE.
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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 | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 0.001 |
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".