Frequency Domain Modeling of Interconnects Based on Assemble Neural Network for 3D Integration

This paper proposes a novel neural network architecture combining convolutional and transposed convolutional neural networks to accurately and efficiently model <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">S</i>-parameter of interconnects for 3D integration. The network incorporates physical consistency constraints, specifically causality and passivity, into its design to ensure the physical effectiveness of the output. The transposed convolutional network serves as a sub-network to map the relationship between the geometrical parameters and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">S</i>-parameter for sub-structures. Then, the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">S</i>-parameters of individual sub-structures are cascaded for dealing with a complex structure composed of sub-structures. A coupling neural network, with causality and passivity constraints, is developed to map the coarse cascaded <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">S</i>-parameters to the fine accurate <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">S</i>-parameters. With the help of this high-dimensional space mapping, a small amount of electromagnetic simulation data of complex interconnect structures is sufficient to learn the relationship between cascaded and real <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">S</i>-parameters. To ensure the completeness of the training set distribution when training CONN on small datasets, a sensitivity analysis-based training set screening method is proposed to enhance the training performance of CONN. The proposed algorithm is demonstrated in two different assemble structure applications. The results highlight the effectiveness, flexibility and versatility of the proposed architecture in modeling complex structures with small costly simulation data while maintaining accuracy and physical consistency.