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

Abstract

Abstract-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(N lg N ) 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 transmissionline 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 functionbased 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.

Layout-Driven Post-Placement Techniques for Temperature Reduction and Thermal Gradient Minimization

“…Equation (3) can be solved using numerical methods such as finite difference method (FDM) [27], [28], finite element method (FEM) [29], [30], or Green function based methods [31], [32]. Both the FDM and FEM methods discretize the entire chip and construct a system of linear equations.…”

Thermally-Aware Design

“…Green function-based methods have been used for thermal analysis in several works in the literature. [25][26][27][28][29] We focus here on the work presented by Zhan et al 25 This begins with the notion of Green functions, and introduces a number of efficiency enhancements that exploit the properties of the on-chip thermal analysis problem. One such property is that the primary on-chip heat sources are the devices, and the points at which the temperature is to be computed correspond to locations in the device layer or one of the interconnect layers.…”

An efficient thermal estimation scheme for microprocessors

“…Because advanced CMOS technologies are applied to IC production, a chip typically contains numerous gates, which increases the complexity of computation during thermal model analysis. Thus, several methods have been proposed to improve the efficiency of chip-level analysis, such as the alternating direction implicit (ADI) method [18], Green function method [20], and fast Poisson solver (FPS) method [21]. Another approach involves architecture-level analyses [1], where the circuits of a microprocessor are divided into microarchitecture blocks with related packaging layers, and each block is further transformed into a dynamic compact model for thermal analysis.…”