Research Papers

Reduced Order Modeling of Transient Heat Transfer in Microchip Interconnects

[+] Author and Article Information
Arman Nokhosteen

Department of Mechanical Engineering,
K.N. Toosi University of Technology,
Tehran 19919-43344, Iran
e-mail: armannokhosteen@gmail.com

M. Soltani

Department of Mechanical Engineering,
K.N. Toosi University of Technology,
Tehran 19919-43344, Iran;
Department of Earth & Environmental Sciences;
Waterloo Institute for Sustainable Energy (WISE),
University of Waterloo,
Waterloo, ON N2L 3G1, Canada;
HVAC&R Management Research Center,
Niroo Research Institute,
Tehran 1468617151, Iran
e-mail: msoltani@uwaterloo.ca

Banafsheh Barabadi

Mechanical Engineering Department,
Massachusetts Institute of Technology,
Cambridge, MA 02139
e-mail: bana@mit.edu

1Corresponding author.

Contributed by the Electronic and Photonic Packaging Division of ASME for publication in the JOURNAL OF ELECTRONIC PACKAGING. Manuscript received April 14, 2018; final manuscript received October 2, 2018; published online February 25, 2019. Assoc. Editor: Amy Marconnet.

J. Electron. Packag 141(1), 011002 (Feb 25, 2019) (9 pages) Paper No: EP-18-1029; doi: 10.1115/1.4041666 History: Received April 14, 2018; Revised October 02, 2018

The high current densities in today's microelectronic devices and microchips lead to hotspot formations and other adverse effects on their performance. Therefore, a computational tool is needed to not only analyze but also accurately predict spatial and temporal temperature distribution while minimizing the computational effort within the chip architecture. In this study, a proper orthogonal decomposition (POD)-Galerkin projection-based reduced order model (ROM) was developed for modeling transient heat transfer in three-dimensional (3D) microchip interconnects. comsol software was used for producing the required data for ROM and for verifying the results. The developed technique has the ability to provide accurate results for various boundary conditions on the chip and interconnects domain and is capable of providing accurate results for nonlinear conditions, where thermal conductivity is temperature dependent. It is demonstrated in this work that a limited number of observations are sufficient for mapping out the entire evolution of temperature field within the domain for transient boundary. Furthermore, the accuracy of the results obtained from the developed ROM and the stability of accuracy over time is investigated. Finally, it is shown that the developed technique provides a 60-fold reduction in simulation time compared to finite element techniques.

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Fig. 1

Three-dimensional domain used in this study

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Fig. 2

Eigenvalues and energy captured (in percent) by different modes. (a)–(d) correspond to case studies A–D, respectively.

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Fig. 3

Flowchart of POD method procedure

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Fig. 4

(a) is the temperature profile at 100 μs for case A based on COMSOL results and (b) is the temperature profile at 100 μs based on POD results

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Fig. 5

(a) is the temperature profile at 100 μs for case B based on COMSOL results and (b) is the temperature profile at 100 μs based on POD results

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Fig. 6

Error versus time for case A and case B

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Fig. 7

COMSOL temperature profiles at t = 30 μs when thermal conductivity is temperature dependent in case C. (a) is the temperature profile based on COMSOL results and (b) is the temperature based on POD results.

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Fig. 8

Error versus time for case C

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Fig. 9

(a) and (b) show results obtained via COMSOL and POD method, respectively, at 20 μs for case D

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Fig. 10

Locations marked on the domain investigated in caseD

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Fig. 11

Temperature versus time for four nodes in case D. (a)–(d) correspond to temperature at locations (a)–(d), respectively, shown in Fig. 10.



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