Compact Lateral Thermal Resistance Model of TSVs for Fast Finite-Difference Based Thermal Analysis of 3-D Stacked ICs

• Published in: IEEE transactions on computer-aided design of integrated circuits and systems Vol. 33; no. 10; pp. 1490 - 1502
• Main Authors: Liu, Zao, Swarup, Sahana, Tan, Sheldon X.-D, Chen, Hai-Bao, Wang, Hai
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.10.2014; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Accuracy; Finite element analysis; Heat transfer; Insulation; Integrated circuit modeling; Integrated circuits; Mathematical analysis; Mathematical models; Silicon; Thermal analysis; Thermal resistance; Three dimensional; Through-silicon vias; 3-D stacked ICs; TSVs; finite difference method; lateral resistance model; thermal analysis
• ISSN: 0278-0070; 1937-4151
• DOI: 10.1109/TCAD.2014.2334321

Thermal issue is the leading design constraint for 3-D stacked integrated circuits (ICs) and through silicon vias (TSVs) are used to effectively reduce the temperature of 3-D ICs. Normally, TSV is considered as a good thermal conductor in its vertical direction, and its vertical thermal resistance has been well modeled. 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 thermal resistance of TSVs in terms of physical and material parameters, and study the conditions for model accuracy. For TSV arrays or farm, we show that the space or pitch between TSVs has a significant impact on TSV thermal behavior and should be properly considered in the TSV models. The proposed lateral thermal resistance model is fully compatible with the existing modeling approaches, and thus we could build a more accurate complete TSV thermal model. The new TSV thermal model can be easily integrated into a finite difference (FD) 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 improved TSV thermal model (with proposed lateral thermal model) could greatly improve the accuracy of FD method in thermal simulation comparing with the existing method.