Experimentally Validated Thermal Modeling Prediction for BEOL and BSPDN Stacks

In this study, we present a novel thermal modeling prediction methodology for advanced back-end-of-line (BEOL) and backside power delivery network (BSPDN) stacks. In the first step, a modular thermal modeling approach, combining the Boltzmann transport equation (BTE) with Finite element modeling (FEM) is proposed and benchmarked to be valid on BEOL stacks to capture the material thermal properties across nano to micro scales. Subsequently, an analytical model has been developed to accurately estimate the out-of-plane thermal resistance in BEOL stacks as a function of metal line and via density, dielectric thermal conductivity, and size-dependent metal thermal properties for the stacked via configuration. The predictive model is then extended to randomized BEOL test cases and realistic design-layout-based 12-layer BEOL stacks with 18 nm metal pitch. The interlayer dielectric (ILD) thermal properties and the impact of via connectivity configurations were experimentally validated using a foundry test vehicle. Finally, the developed thermal model is applied to two test cases, where the thermal conductivity mapping for the BEOL design layout presents a unique capability to include the discretized thermal information of BEOL and BSPDN stacks, and the analytical model applied to BSPDN configurations enables a fast and accurate estimation of the effective out-of-plane thermal properties of BSPDN stacks.