F. C. Wellstood

J. Senthilnath, Jayasanker Jayabalan, Zhuoyi Lin et al.

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.

J. Senthilnath, Chen Hao, F. C. Wellstood

In semiconductor packaging, accurately recovering 3D information is crucial for non-destructive testing (NDT) to localize circuit defects. This paper presents a novel approach called the 3D Magnetic Inverse Routine (3D MIR), which leverages Magnetic Field Images (MFI) to retrieve the parameters for the 3D current flow of a single-segment. The 3D MIR integrates a deep learning (DL)-based Convolutional Neural Network (CNN), spatial-physics-based constraints, and optimization techniques. The method operates in three stages: i) The CNN model processes the MFI data to predict ($\ell/z_o$), where $\ell$ is the wire length and $z_o$ is the wire's vertical depth beneath the magnetic sensors and classify segment type ($c$). ii) By leveraging spatial-physics-based constraints, the routine provides initial estimates for the position ($x_o$, $y_o$, $z_o$), length ($\ell$), current ($I$), and current flow direction (positive or negative) of the current segment. iii) An optimizer then adjusts these five parameters ($x_o$, $y_o$, $z_o$, $\ell$, $I$) to minimize the difference between the reconstructed MFI and the actual MFI. The results demonstrate that the 3D MIR method accurately recovers 3D information with high precision, setting a new benchmark for magnetic image reconstruction in semiconductor packaging. This method highlights the potential of combining DL and physics-driven optimization in practical applications.