An efficient multiscale numerical modelling method for thermal analysis of integrated circuits

As integrated circuits become more densely integrated with multiscale geometries and numerous microstructural features, thermally induced failure becomes a major concern, while direct finite element (FE) thermal analysis remains computationally expensive because it requires a very large number of elements. To improve computational efficiency, this study proposes a multiple-representative-volume-element (multiple-RVE) macroscopic equivalent modelling method for FE thermal analysis of IC structures. The method converts the original fine structured mesh into coarse rectangular elements, calculates local material volume fractions within each coarse element, and assigns direction-dependent equivalent thermal conductivities to construct a structured macroscopic mesh with spatially varying anisotropic thermal properties. Case studies on periodic-symmetric and non-periodic-asymmetric IC structures show that the proposed method predicts the macroscopic temperature field with accuracy close to that of a refined FE reference model, with maximum-temperature errors of 0.28% and 0.17%, respectively. For the non-periodic-asymmetric structure, the plane-wise comparison at the selected plane gives a maximum relative temperature-field error of 7.93% between the proposed method and the refined reference model. Relative to a conventional FE baseline with a practical coarse mesh, the computational efficiency improves by factors of 2.12 and 8.63, respectively. Parametric studies further show that the number of macroscopic elements controls the balance between accuracy and efficiency, and that the series/parallel conductivity model agrees better with the refined FE reference model than the other tested effective thermal conductivity models.