Modeling Method for the Equivalent Circuit of Hybrid Bonding Stacks

Finite element modeling (FEM) of hybrid bonding stacks for high-density 3D integration suffers from excessive computational load and prohibitive simulation time. To address this critical technical bottleneck, this paper proposes an analytical lumped-distributed equivalent circuit model based on multi-layer structures. The model incorporates both redistribution layer (RDL) parasitics and metal–insulator–semiconductor (MIS) depletion effects for comprehensive signal integrity analysis. Frequency-dependent RLGC electromagnetic parameters were extracted from through-silicon via (TSV) and RDL interconnects. These parameters were numerically calculated using MATLAB R2020a to construct the equivalent circuit model in ADS. The model was subsequently validated against COMSOL finite element simulations. The results demonstrated that the proposed methodology achieved maximum deviations below 5% for all S-parameters in double-layer structures. For 5-layer stacks, errors were controlled within 10% across the 0–40 GHz frequency range. Computation time was reduced from several minutes to seconds. The proposed equivalent circuit method significantly reduces computational time while maintaining accuracy, providing an efficient simulation methodology for signal integrity analysis and verification of hybrid bonding stack structures. Compared to existing single-layer models, this work extends the modeling approach to multi-layer hybrid bonding stacks while comprehensively accounting for both RDL parasitics and MIS depletion effects, addressing a critical gap in the current state of the art.