Accelerated Chip-Level Thermal Analysis Using Multilayer Green's Function

Continual scaling of transistors and interconnects has exacerbated the power and thermal management problems in the design of ultralarge-scale integrated (ULSI) circuits. This paper presents an efficient thermal-analysis method of O(NlgN) complexity, where N is the number of blocks that discretize the heat-source or temperature-observation regions. The method is named LOTAGre and formulated using the Green's function for heat conduction through multiple-layer materials, which account for the structure of ULSI chips and the accompanying heat sinks and mounting accessories. In addition to analyzing the thermal effects of the distributive heat sources, LOTAGre also considers the ambient temperature effects that are generally excluded in conventional Green's function-based thermal-analysis tools in order to avoid the concomitant analytical complexity. By employing the well-known eigen-expansion technique and classical transmission-line theory, fully analytical and explicit formulas are derived in this paper for the multilayer Green's function with the inclusion of the s-domain version, the homogeneous and inhomogeneous solutions to the heat-conduction equation. Then, the discrete cosine transform and its inversion are employed to accelerate the numerical computation of the homogeneous and inhomogeneous solutions. This paper includes extensive experimental results to demonstrate that LOTAGre can be as accurate as FLUENT, a sophisticated computational fluid dynamics tool, while speeding up the simulation run time by two to three orders of magnitude in comparison to FLUENT as well as conventional Green's function-based thermal-analysis methods. This paper also discusses the limitations of using the traditional single-layer thermal model in thermal analysis for approximating a multilayer chip structure