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

Abstract

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.