Effective Media Approximation in Investigating Heat Transfer through Multiple Sandwiched Layers of BEOL Materials

The semiconductor industry is set to transition from the current 3nm node to 5Å node by 2037. This advancement will lead to further shrinkage in the size of both the front end of line (FEOL) and back end of line (BEOL) of the semiconductor devices, as well as integration of 3D stacked chip architecture. All these anticipated changes pose considerable challenge for effective thermal management. The heat generated in these semiconductor devices must pass through the thin BEOL layers, prior to being dissipated through the attached heat sinks or heat pipes. Films with thicknesses in the nanometers range exhibit lower thermal conductivity than the same material in its bulk form. Moreover, depending on the method of deposition, thin films might manifest different in-plane and cross-plane thermal conductivities. Therefore, an accurate understanding of anisotropic heat transfer through multiple stacked layers of dielectrics is necessary before being used in BEOL. This work investigates the temperature signal response of sandwiched BEOL layers with varying arrangement of the layers, anisotropic thermal conductivities of the layers, dimensions of the heat source and the frequency of the applied current. The harmonic temperature rise profile of the top surface of a multilayered sample in the vicinity of a harmonically heated region is studied using two approaches:1) an analytical 2D heat conduction model with distinct multilayers layer and with and with an effective media layer, and 2) a 3D representative volume element (RVE) multiscale FEM scheme. The heated region investigated is either a long Joule heated wire of selected widths, or a Gaussian heat source of different radius. In the first analytical approach, thermal and geometric properties of all the individual BEOL layers, with and without the interfacial thermal resistances, are fed into the heat conduction model to obtain the in-plane temperature amplitude signal. In the second analytical approach, a single composite BEOL layer is assumed that has the effective thermal and geometric properties of all the individual layers and interfaces combined. Then, the composite properties are used to analytically obtain the in-plane temperature amplitude signal. In the simulation approach, we use a computational homogenization scheme to directly compute effective constitutive properties within the RVE. This approach is scalable to complex, heterogeneous BEOL geometries that are constructed directly from GDSII/OASIS design files. The temperature signals obtained from all three methods are then compared to investigate the limits of the effective media approximation and RVE in simulating anisotropic thermal transport in multilayered BEOL films.