To reduce the product development time and achieve first-pass silicon success, fast and accurate estimation of very-large-scale integration (VLSI) interconnect, packaging and 3DI (3D integrated circuits) thermal profiles has become important. Present commercial thermal analysis tools are incapable of handling very complex structures and have integration difficulties with existing design flows. Many analytical thermal models, which could provide fast estimates, are either too specific or oversimplified. This paper highlights a methodology, which exploits electrical resistance solvers for thermal simulation, to allow acquisition of thermal profiles of complex structures with good accuracy and reasonable computation cost. Moreover, a novel accurate closed-form thermal model is developed. The model allows an isotropic or anisotropic equivalent medium to replace the noncritical back-end-of-line (BEOL) regions so that the simulation complexity is dramatically reduced. Using these techniques, this paper introduces the thermal modeling of practical complex VLSI structures to facilitate thermal guideline generation. It also demonstrates the benefits of the proposed anisotropic equivalent medium approximation for real VLSI structures in terms of the accuracy and computational cost. © 2006 IEEE.


Electrical and Computer Engineering


International Business Machines Corporation, Grant None

Keywords and Phrases

Equivalent thermal conductivity; finite difference method; interconnects; Joule heating; packaging; resistance solver; thermal analysis; three-dimensional integration (3DI); very-large-scale integration (VLSI)

International Standard Serial Number (ISSN)


Document Type

Article - Journal

Document Version


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Publication Date

01 Nov 2010