Thermal Modeling and Analysis of Equivalent Thermal Properties for Advanced BEOL Stacks

Abstract

In this article, we introduce a modular thermal modeling methodology, BTE-FEM, that combines the Boltzmann transport equation (BTE) with finite element modeling (FEM) for simulations of advanced back-end-of-line (BEOL) stacks with high accuracy and efficiency. BTE-FEM is validated against direct BTE-based simulations using simplified BEOL stack test cases across various technology nodes and via connectivity configurations. It is demonstrated that conventional FEM, using bulk material properties, increasingly underestimates the BEOL thermal resistance as the technology node scales. In contrast, the BTE-FEM developed in this study demonstrates good agreement with direct BTE simulations for all test cases, but at much shorter runtimes. The impact of material properties, metal densities, and boundary conditions on the derived BEOL thermal properties are benchmarked and the developed models are experimentally validated at two distinct technology nodes. Finally, the developed methodology is applied to a 12-layer, 18 nm metal pitch BEOL stack from an A10 high density core design, demonstrating its ability to simulate complex and realistic BEOL routings with the precision of direct BTE simulations while substantially reduced simulation time. This approach enables extensive design of experiments (DOEs) for fast turnaround design iterations.