Defect Z-Depth Determination in 2.5D ICs Using Magnetic Field Imaging
Bibliographic record
Abstract
Defect localization and accurate depth determination in advanced heterogeneous integration (HI) packaging integrated circuits (ICs), particularly$2.5 \mathrm{D} / 3 \mathrm{D}$ICs, is critical for failure analysis and reliability assessment. Beyond lateral XY defect localization, vertical Z-depth estimation is essential for identifying the failure layer in stacked configurations, which is a challenge that conventional non-destructive testing (NDT) methods cannot effectively address. Due to restricted penetration depth and inadequate spatial resolution caused by the complex, multilayered material composition of HI packaging, conventional NDT techniques face intrinsic limitations in localizing defects along the z-axis. Magnetic field imaging (MFI) has emerged as a promising alternative, providing non-invasive and highresolution sensing of current-induced magnetic fields while being insensitive to variations in complex material structure in HI packaging. However, despite its advantages, MFI inherently produces intricate magnetic field data that require algorithms for depth extraction, an area that remains underexplored in both research and practical applications. In this paper, we propose an MFI-based variational method (VM) that employs fast Fourier transform (FFT)-based magnetic inverse optimization, grounded in the Biot-Savart law, to enable Z-depth determination of shortcircuit defects in 2.5D ICs. The effectiveness of the proposed VM approach is demonstrated on two representative defective 2.5D graphics processing units (GPUs): a signal-to-ground short at the C4 bump and a power-to-ground short at the μbump. These defect types are among the most commonly encountered failure modes in advanced 2.5D ICs. Validation against X-ray scans shows defect depth estimation errors of$\mathbf{5}-25 \mu ~\mathrm{m}$and 5$\mu \mathrm{m}$, respectively, thereby advancing the fault isolation capability for complex 2.5D/3D ICs.
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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 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.001 | 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".