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 (ℓ/z<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">o</inf>), where ℓ is the wire length and z<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">o</inf> 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<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">o</inf>, y<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">o</inf>, z<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">o</inf>), length (ℓ), current (I), and current flow direction (positive or negative) of the current segment. iii) An optimizer then adjusts these five parameters (x<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">o</inf>, y<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">o</inf>, z<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">o</inf>, ℓ, 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.