Effective Medium Approximation in Investigating Heat Transfer Through Multiple Sandwiched Layers of BEOL Materials

Abstract Thermal management of semiconductor devices is becoming more challenging with the progressing technology nodes. Implementation of advanced device platforms such as CFET and advanced chip architecture such as 3DVLSI, would result in thermal transport through the thin back-end-of-line (BEOL) layers. An accurate understanding of anisotropic heat transfer through multiple stacked layers of dielectrics and metal interconnects is therefore necessary, and is garnering some research interests. The thermal analysis can be conducted either through a heterogenized approach, using the individual properties of all the BEOL layers, or a homogenized approach, by assuming a single medium with effective thermal and geometric properties. This work investigates the temperature response of sandwiched BEOL layers with and without the effective medium approximation, using both a time dependent 2D analytical model and a steady state 2D multiscale FEM scheme. It is observed through the analytical study that the effective medium approximation is accurate at low frequency and at larger dimension of the heat source. Moreover, at larger heater widths and larger laser it is independent of the anisotropic thermal conductivities of the layer(s) at larger heater widths. Results from the multiscale FEM model are consistent showing an increase in homogenization error as heater size decreases.