3D Magnetic Inverse Routine for Single-Segment Magnetic Field Images

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.