Analytical Heat Transfer Model for Thermal Through-Silicon Vias

Thermal issues are one of the primary challenges in 3-D integrated circuits. Thermal through-silicon vias (TTSVs) are considered an effective means to reduce the temperature of 3-D ICs. The effect of the physical and technological parameters of TTSVs on the heat transfer process within 3-D ICs is investigated. Two resistive networks are utilized to model the physical behavior of TTSVs. Based on these models, closed-form expressions are provided describing the flow of heat through TTSVs within a 3-D IC. The accuracy of these models is compared with results from a commercial FEM tool. For an investigatedthree-plane circuit, the average error of the first and second models is 2% and 4%, respectively. The effect of the physical parameters of TTSVs on the resulting temperature is described through the proposed models. For example, the temperature changes non-monotonically with the thickness of the silicon substrate. This behavior is not described by the traditional single thermal resistance model. The proposed models are used for the thermal analysis of a 3-D DRAM-uP system where the conventional model is shown to considerably overestimate the temperature of the system.