基于对偶单元法的三维集成微系统电热耦合分析

Electrothermal coupling analysis of three-dimensional integrated microsystem based on dual cell method

随着三维集成微系统集成度和功率密度的提高,同时考察电设计与热管理的多场耦合分析势在必行.本文面向三维集成微处理器系统,通过改进的对偶单元法(dual cell method,DCM)实现了系统的快速电热分析.该方法通过引入泄漏功率、材料系数随温度的耦合,相比于传统有限元法在更新以及组装本构矩阵上有更大的优势.仿真验证表明,本文所采用的算法相比传统有限元法仿真速度提升了约30%.在考虑了材料系数以及泄露功率热耦合因素后,系统热点温度相对于考虑耦合前上升了20.8 K.最后采用本文所提出算法对三维集成微处理器系统进行布局研究,比较了硅通孔阵列常规布局和集中布局在处理器核心下方两种布局方式对上下层芯片热点温度的影响,研究了功率不均匀分配对两种布局的影响.

With the improvement of the integration and power density of three-dimensional integrated microsystem,it is imperative to simultaneously investigate the multi-field coupling analysis of electrical design and thermal management.This paper is to investigate a three-dimensional integrated microprocessor system and realize the rapid electrothermal analysis of the system through an improved dual cell method(DCM).This method decomposes the constitutive matrix into a constant matrix and a temperature-dependent matrix by introducing the coupling of leakage power and material coefficients with temperature.In the calculation,only the temperature-dependent matrix needs to be updated and assembled,which makes the calculation speed faster than the traditional finite element method.The simulation results show that the speed of the proposed algorithm is improved by about 30%compared with that of the traditional finite element method.After considering the thermal coupling factors of material coefficient and leakage power,the hot spot temperature of the system increases by 20.8 K compared with before coupling.Finally,the algorithm proposed in this paper is used to study the layout of three-dimensional integrated microprocessor system.The influence of TSV array conventional layout and centralized layout under the processor core(core-layout)on the hot spot temperature of upper and lower chips are compared,and the influences of uneven power distribution on the two layouts are studied.The results show that compared with the conventional layout of TSV array,the core-layout can reduce the hot spot temperature of processor,but it will aggravate the hot spot problem of DRAM at the same time.And when the power is not evenly distributed on the four cores,the hot spot of DRAM under the core-layout will be more seriously affected.In conclusion,the algorithm model proposed in this paper can quickly analyze the electrothermal coupling problem of 3D integrated microsystem,realize the hot spot prediction of the system,and provide theoretical guidance for designing the chip layout of 3D integrated microsystem.