Deep Learning-Based Partial Inductance Extraction of 3-D Interconnects

A physics-informed deep learning-based scheme is introduced for computing partial inductances of interconnects. This scheme takes a physics-based skin depth map and a geometry identifier of the interconnects as inputs and provides the current density distribution on the interconnects as the output. The predicted currents are then used to compute the partial self-resistances, self-inductances, and mutual-inductances of the interconnects. The proposed method leverages an Attention U-net, a U-shaped convolutional neural network with attention modules. During the training of Attention U-net, a specifically designed loss function is used to ensure the accurate modeling of the currents on the structure as well as ports. The accuracy, efficiency, and generalization ability of this physics-informed deep learning method are demonstrated via inductance extraction of the interconnects with and without a ground plane, including straight single interconnects, interconnects with sharp bends, parallel interconnects, and multiple conductor crossover buses. Numerical results show that the proposed scheme can predict the current density distribution of one interconnect scenario in 15.63 ms on GPU, 1157x faster than the physics-based solver, while providing self-inductances, mutual-inductances, and self-resistances of interconnects with around 1%, 3%, and 4% <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${{\ell }_2}$</tex-math></inline-formula>-norm error, respectively.