An Analytical 3D-IC Thermal Simulation Framework Using Adaptive Rectangular Approximation and Conformal Mesh Method

This article proposes a novel analytical steady-state thermal simulation framework considering anisotropic thermal conductivity for 3-D integrated circuits (3D-ICs) that combine an adaptive rectangular discretization algorithm with a conformal meshing strategy to achieve enhanced computational efficiency and accuracy. To address the challenges of arbitrary power density distributions in modern 3D-ICs, we develop an adaptive rectangle approximation method that dynamically adjusts rectangular partition sizes based on local gradient analysis and error-controlled discretization criteria. The derived rectangular thermal sources are subsequently processed through a conformal meshing technique that preserves geometric fidelity while minimizing mesh complexity. For analytical solution derivation, we employ the domain decomposition method effectively to divide the multilayer 3-D structure into several individual layers with customized general solutions. Interlayer thermal coupling is resolved through interfacial boundary condition enforcement. Numerical simulations demonstrate that the proposed analytical thermal method achieves significant performance improvements, exhibiting $60\times $ acceleration over conventional finite element method (FEM) implementations while maintaining a maximum absolute error (MAX) below 0.5 K across multiple benchmark cases with 3D-ICs.