Modeling and signal integrity analysis of silicon interposer channels based on MTL and KBNN

In this paper, the equivalent circuit model of interconnect channels in silicon interposer is developed for three-dimensional integrated circuit (3-D IC) based on the theory of multi-conductor transmission line (MTL). The deep neural network (DNN) is employed to learn the nonlinear mapping relationship between the geometric parameters and the distributed parameters, and it is demonstrated that the DNN has a high prediction accuracy. In the implementation, a coarse model is firstly developed by solving the scattering parameters of the model using the chain parameter matrix. The model is optimized using a knowledge-based neural network (KBNN), and a fine model is then established. The numerical examples demonstrate that the optimized model can achieve high accuracy. Finally, the inner contour of the worst-case eye diagrams of the channel is generated using the peak distortion algorithm (PDA), with the worst eye width and height obtained.