A simple and approximate analytical model for the estimation of the thermal resistances in 3D stacks of integrated circuits

摘要

The purpose of this paper is to describe a simple analytical model, useful for system architects, which describes the thermal resistances between a hot spot and the cold heat sink in steady state conditions with constant material properties, while taking into account the impact of the lateral spreading. The total thermal resistance Rth_total is modeled as dependent on Rth_1D, the thermal resistance in the Z direction, perpendicular to the layers, and Rth_3D, the effects of the lateral spreading of the heat (the X and Y directions) from the hot spot. In a 1st step, the different layers are homogenized to obtain an equivalent anisotropic thermal conductivity per layer. It must be noticed that the presence of copper TSV increases the thermal conductivities in the Z direction but decreases this conductivity in XY directions, due to the very negative effect of the SiO2 layer surrounding the Cu. These conductivities are used in a 2nd step to compute Rth_1D, combining the individual thermal resistance of each layer. The 3rd step estimates Rth_3D by a simple analytical model. The few adjustable coefficients are fitted on several thousand FEM simulations.