Compact lateral thermal resistance modeling and characterization for TSV and TSV array

Thermal issues are among the major concerns for 3D stacked ICs, and Through silicon vias (TSVs) are used to effectively reduce the temperature of 3D ICs. Normally, TSV is considered as a good thermal conductor in its vertical direction, and its vertical thermal resistance has been studied extensively. However, lateral heat transfer of TSVs, which is also important, was largely ignored in the past. In this paper, we propose an accurate physics-based model for lateral resistance of TSVs in terms of physical and material parameters, and discuss the conditions valid for model accuracy. In addition to modeling the lateral thermal resistance of a single TSV, the proposed thermal model is also applicable to TSV arrays or TSV farms. We show that the TSV insulation linear and space between TSVs could impose a significant impact on TSV thermal behavior. The new TSV thermal model can be easily integrated into a finite difference based thermal analysis framework to improve analysis efficiency. The accuracy of the model is validated against a commercial finite element tool - COMSOL. Experimental results show that the proposed TSV lateral thermal resistance model is very accurate for both a single TSV and TSV arrays.