电子学报 ›› 2012, Vol. 40 ›› Issue (5): 865-870.DOI: 10.3969/j.issn.0372-2112.2012.05.001

• 学术论文 •    下一篇

一种堆叠式3D IC的最小边界热分析方法

余慧, 吴昊, 陈更生, 童家榕   

  1. 复旦大学专用集成电路与系统国家重点实验室, 上海 200433
  • 收稿日期:2011-03-18 修回日期:2011-12-21 出版日期:2012-05-25
    • 通讯作者:
    • 陈更生

A Minimal Boundary Thermal Analysis Method for Stacked 3D IC

YU Hui, WU Hao, CHEN Geng-sheng, TONG Jia-rong   

  1. ASIC and System State Key laboratory, Fudan University, Shanghai 200433, China
  • Received:2011-03-18 Revised:2011-12-21 Online:2012-05-25 Published:2012-05-25

摘要: 目前的热分析工具仅仅支持单芯片的热分析,而堆叠式的三维芯片(3D IC)在同一封装中包含多个堆叠的芯片,对芯片的散热和温度管理提出了更高的要求,并且在热分析过程中需要处理复杂的边界条件.本文提出的最小边界法可以准确且有效地处理堆叠式3D IC的边界条件,简化了三维芯片封装的热模型;同时,本文提出在堆叠式3D IC的稳态热量分析中通过将连接点分类、采用预处理矩阵的方法加速整个全局热传导矩阵的求解过程,从而简化热分析流程.实验结果表明:将有限元方法作为基本的热分析方法,用最小边界法处理堆叠式3D IC,可以准确分析芯片的热分布;同时通过高效的预处理矩阵可以减少共轭梯度法求解中90%的迭代次数.

关键词: 热分析, 有限元方法, 3D IC, 最小边界

Abstract: Current thermal analysis tools can only efficiently handle 3D integrated circuits with simple structure.To deal with more complicated stacked 3D integrated circuits,more complex,and error-prone boundary conditions need to be set up.In this paper,we propose simple,yet efficient method,called minimal boundary method, to handle the complicated boundary conditions by transforming the 3D stacked structure to a structure with simple boundary (thus for easy boundary condition set up).To boost the thermal analysis via iterative conjugate gradient method,we construct a novel preconditioner,which consists of the thermal conductor matrices of the building blocks of the stacked 3D structure as its diagonal blocks.Experimental results show that by using finite element method along with the proposed minimal boundary pre-processing,we can obtain accurate thermal analysis results.The proposed preconditioner can reduce the 90% iterations in the conjugate gradient method.

Key words: thermal analysis, the finite element method, 3D IC, the minimal boundary

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