A Spatial-Physics Informed Model for 3D Spiral Sample Scanned by SQUID Microscopy

2025-07-15

AI Summary

To address the non-destructive testing (NDT) challenges posed by increased interconnect depth and structural complexity in advanced packaging, this paper proposes a spatial-physical hybrid current density reconstruction method. Unlike conventional magnetic field inversion relying solely on FFT, our approach unifies SQUID microscopy magnetometry, I/Q-channel signal modeling, and image geometric alignment within a single inversion framework—incorporating eddy-current suppression, rotation/tilt misalignment correction, and Biot–Savart law constraints. Experimental results demonstrate effective compensation of 0.30-radian real-world image distortion, a 0.3% improvement in I-channel image sharpness, significant noise reduction in the Q-channel, and substantial gains in current reconstruction accuracy and imaging reliability. This work establishes a scalable, physics-informed paradigm for online NDT of 3D integrated packages.

Technology Category

• Search and Optimization: Distributed Search
• Data Mining & Knowledge Management: Intelligent Query Processing
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Security and Privacy: Large-scale security measurements
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics

Abstract

The development of advanced packaging is essential in the semiconductor manufacturing industry. However, non-destructive testing (NDT) of advanced packaging becomes increasingly challenging due to the depth and complexity of the layers involved. In such a scenario, Magnetic field imaging (MFI) enables the imaging of magnetic fields generated by currents. For MFI to be effective in NDT, the magnetic fields must be converted into current density. This conversion has typically relied solely on a Fast Fourier Transform (FFT) for magnetic field inversion; however, the existing approach does not consider eddy current effects or image misalignment in the test setup. In this paper, we present a spatial-physics informed model (SPIM) designed for a 3D spiral sample scanned using Superconducting QUantum Interference Device (SQUID) microscopy. The SPIM encompasses three key components: i) magnetic image enhancement by aligning all the "sharp" wire field signals to mitigate the eddy current effect using both in-phase (I-channel) and quadrature-phase (Q-channel) images; (ii) magnetic image alignment that addresses skew effects caused by any misalignment of the scanning SQUID microscope relative to the wire segments; and (iii) an inversion method for converting magnetic fields to magnetic currents by integrating the Biot-Savart Law with FFT. The results show that the SPIM improves I-channel sharpness by 0.3% and reduces Q-channel sharpness by 25%. Also, we were able to remove rotational and skew misalignments of 0.30 in a real image. Overall, SPIM highlights the potential of combining spatial analysis with physics-driven models in practical applications.

Problem

• Enhances magnetic image quality by mitigating eddy current effects
• Corrects skew effects from SQUID microscope misalignment
• Improves magnetic field to current density conversion accuracy

Innovation

• Enhances magnetic images using I and Q channels
• Aligns images to correct skew and misalignment
• Integrates Biot-Savart Law with FFT inversion