Transient Thermal Analysis of 3-D Integrated Circuits Packages by the DGTD Method
KAUST DepartmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Electrical Engineering Program
Department of Electronic Engineering, King Abdullah University of Science and Technology, Thuwal 23955, Saudi Arabia.
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AbstractSince accurate thermal analysis plays a critical role in the thermal design and management of the 3-D system-level integration, in this paper, a discontinuous Galerkin time-domain (DGTD) algorithm is proposed to achieve this purpose. Such as the parabolic partial differential equation (PDE), the transient thermal equation cannot be directly solved by the DGTD method. To address this issue, the heat flux, as an auxiliary variable, is introduced to reduce the Laplace operator to a divergence operator. The resulting PDE is hyperbolic, which can be further written into a conservative form. By properly choosing the definition of the numerical flux used for the information exchange between neighboring elements, the hyperbolic thermal PDE can be solved by the DGTD together with the auxiliary differential equation. The proposed algorithm is a kind of element-level domain decomposition method, which is suitable to deal with multiscale geometries in 3-D integrated systems. To verify the accuracy and robustness of the developed DGTD algorithm, several representative examples are benchmarked.
CitationLi P, Dong Y, Tang M, Mao J, Jiang LJ, et al. (2017) Transient Thermal Analysis of 3-D Integrated Circuits Packages by the DGTD Method. IEEE Transactions on Components, Packaging and Manufacturing Technology: 1–10. Available: http://dx.doi.org/10.1109/TCPMT.2017.2666259.
SponsorsThis work was supported in part by the National Science Foundation of China under Grant 61234001 and Grant 61674105 and in part by the University Grants Council of Hong Kong under Contract AoE/P-04/08. Recommended for publication by Associate Editor