ETLA-3D: Equivalent Thin Layer Aggregation based Thermal FEM for Hybrid Bonding F2F 3D ICs

In 3D face-to-face (F2F) hybrid bonding ICs, sub-micrometer thin layers lead to an extreme aspect ratio between the lateral dimensions and the vertical thickness. This poses major challenges for finite element method (FEM) thermal simulation. To address this, we introduce ETLA-3D, a thermal FEM methodology based on equivalent thin-layer aggregation, designed specifically for hybrid bonding F2F 3D ICs. The method consolidates the physical properties of thin layers into their neighboring layers by introducing new integral terms into the FEM weak form, greatly reducing the complexity of meshing, the simulation degrees of freedom (DoFs) and the computational cost, while preserving accuracy. Experimental results show that ETLA-3D achieves up to 695.8 × faster runtime compared to the commercial FEM tool (COMSOL Multiphysics), with a maximum absolute error of less than 1.1°C. By combining high accuracy with exceptional efficiency, ETLA-3D establishes a reliable and efficient FEM framework to model the thermal behavior of F2F 3D ICs.