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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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References

Bilotti, A. A. , 1974, “ Static Temperature Distribution in IC Chips With Isothermal Heat Sources,” IEEE Trans. Electron Devices, 21(3), pp. 217–226. [CrossRef]
Andrews, R. V. , 1955, “ Solving Conductive Heat Transfer Problems With Electrical-Analogue Shape Factor,” Chem. Eng. Prog., 51, pp. 67–71. https://www.osti.gov/biblio/4382113
Gray, P. R. , and Hamilton, D. J. , 1971, “ Analysis of Electro Thermal Integrated Circuits,” IEEE J. Solid-State Circuits, 6(1), pp. 8–14. [CrossRef]
Cook, J. T. , Joshi, Y. K. , and Doraiswami, R. , 2004, “ Interconnect Thermal Management of High Power Packaged Electronic Architectures,” IEEE Semiconductor Thermal Measurement and Management Symposium (SEMI-THERM), San Jose, CA, Mar. 9–11, pp. 30–37.
Subrina, S. , 2012, “ Heat Transfer in Graphene Interconnect Networks With Graphene Lateral Heat Spreaders,” IEEE Trans. Nanotechnol., 11(4), pp. 777–781. [CrossRef]
Bosch, E. G. T. , and Sabry, M. N. , 2002, “ Thermal Compact Models for Electronic Systems,” IEEE Semiconductor Thermal Measurement and Management Symposium (SEMI-THERM), San Jose, CA, Mar. 12–14, pp. 21–29.
Huang, W. , Stan, M. R. , and Skadron, K. , 2005, “ Parameterized Physical Compact Thermal Modeling,” IEEE Trans. Compon. Packag. Manuf. Technol., 28, pp. 615–622. [CrossRef]
Bansal, A. , Meterelliyoz, M. , Singh, S. , Choi, J. H. , Murthy, J. , and Roy, K. , 2006, “ Compact Thermal Models for Estimation of Temperature-Dependent Power/Performance in FinFET Technology,” IEEE Asia and South Pacific Conference on Design Automation (ASP-DAC 2006), Yokohama, Japan, Jan. 24–27, pp. 237–242.
Gurrum, S. P. , Joshi, Y. K. , King, W. P. , Ramakrishna, K. , and Gall, M. , 2008, “ A Compact Approach to On-Chip Interconnect Heat Conduction Modeling Using the Finite Element Method,” ASME J. Electron. Packag., 130(3), p. 031001. [CrossRef]
Berkooz, G. , Holmes, P. , and Lumley, J. , Turbulence, Coherent Structures, Dynamical Systems and Symmetry, Cambridge University Press, New York.
Kirby, M. , and Sirovich, L. , 1990, “ Application of the Karhunen-Loeve Procedure for the Characterization of Human Faces,” IEEE Trans. Pattern Anal. Mach. Intell., 12(1), pp. 103–108. [CrossRef]
Pearson, K. , 1901, “ LIII. On Lines and Planes of Closest Fit to Systems of Points in Space,” London, Edinburgh, Dublin Philos. Mag. J. Sci., 2(11), pp. 559–572. [CrossRef]
Corigliano, A. , Dossi, M. , and Mariani, S. , 2013, “ Domain Decomposition and Model Order Reduction Methods Applied to the Simulation of Multi-Physics Problems in MEMS,” Comput. Struct., 122, pp. 113–127. [CrossRef]
Rama, R. R. , Skatulla, S. , and Sansour, C. , 2016, “ Real-Time Modelling of Diastolic Filling of the Heart Using the Proper Orthogonal Decomposition With Interpolation,” Int. J. Solids Struct., 96, pp. 409–422. [CrossRef]
Antoranz, A. , Ianiro, A. , Flores, O. , and Garcia-Villalba, M. , 2018, “ Extended Proper Orthogonal Decomposition of Non-Homogeneous Thermal Fields in a Turbulent Pipe Flow,” Int. J. Heat Mass Transfer, 118, pp. 1264–1275. [CrossRef]
Mahapatra, P. S. , Chatterjee, S. , Mukhopadhyay, A. , and Manna, N. K. , 2016, “ Proper Orthogonal Decomposition of Thermally-Induced Flow Structure in an Enclosure With Alternately Active Localized Heat Sources,” Int. J. Heat Mass Transfer, 94, pp. 373–379. [CrossRef]
Gao, X. , Hu, J. , and Huang, S. , 2016, “ A Proper Orthogonal Decomposition Analysis Method for Multimedia Heat Conduction Problems,” ASME J. Heat Transfer, 138(7), p. 071301. [CrossRef]
Blanc, T. J. , Jones, M. R. , and Gorrell, S. E. , 2016, “ Reduced-Order Modeling of Conjugate Heat Transfer Processes,” ASME J. Heat Transfer, 138(5), p. 051703. [CrossRef]
Hamim, S. U. , and Singh, R. P. , 2017, “ Proper Orthogonal Decomposition-Radial Basis Function Surrogate Model-Based Inverse Analysis for Identifying Nonlinear Burgers Model Parameters From Nanoindentation Data,” ASME J. Eng. Mater. Technol., 139(4), p. 041010. [CrossRef]
Al-Shudeifat, M. A. , Al Mehairi, A. , Saeed, A. S. , and Balawi, S. , 2018, “ Application of Proper Orthogonal Decomposition Method to Cracked Rotors,” ASME J. Comput. Nonlinear Dyn., 13(11), p. 111006. [CrossRef]
Sinha, A. , Chauhan, R. O. , and Balasubramanian, S. , 2018, “ Characterization of a Superheated Water Jet Released Into Water Using Proper Orthogonal Decomposition Method,” ASME J. Fluids Eng., 140(8), p. 081107. [CrossRef]
Wangkun, J. , Helenbrook, B. T. , and Cheng, M. C. , 2014, “ Thermal Modeling of Multi-Fin Field Effect Transistor Structure Using Proper Orthogonal Decomposition,” IEEE Trans. Electron Devices, 61, pp. 2752–2759. [CrossRef]
Wangkun, J. , Helenbrook, B. T. , and Cheng, M. C. , 2016, “ Fast Thermal Modeling of FinFET Circuits Based on Multiblock Reduced-Order Model,” IEEE Trans. Comput.-Aided Des. Integr. Circuits Syst., 35(7), pp. 1114–1124. [CrossRef]
Barabadi, B. , Kumar, S. , and Joshi, Y. K. , 2017, “ Transient Heat Conduction in On-Chip Interconnects Using Proper Orthogonal Decomposition Method,” ASME J. Heat Transfer, 139(7), p. 072101. [CrossRef]
Barabadi, B. , Kumar, S. , Sukharev, V. , and Joshi, Y. K. , 2015, “ Multiscale Transient Thermal Analysis of Microelectronics,” ASME J. Heat Transfer, 137(3), p. 031002.
Bizon, K. , Continillo, G. , Russo, L. , and Smula, J. , 2008, “ On POD Reduced Models of Tubular Reactor With Periodic Regimes,” Comput. Chem. Eng., 32(6), pp. 1305–1315. [CrossRef]
Bagnall, K. R. , Yuri, S. , and Wang, E. N. , 2014, “ Application of the Kirchhoff Transform to Thermal Spreading Problems With Convection Boundary Conditions,” IEEE Trans. Compon. Packag. Manuf. Technol., 4(3), pp. 408–420. [CrossRef]
Lide, R. D. , 2004, CRC Handbook of Chemistry and Physics, 84th ed., CRC Press, Boca Raton, FL.
Morzynski, M. , Stankiewics, W. , Noack, B. R. , Thiele, F. , King, R. , and Tadmor, G. , 2006, “ Generalized Mean-Field Model for Flow Control Using a Continuous Mode Interpolation,” AIAA Paper No. 2006-3488.
Shinde, V. , Longatte, E. , Baj, F. , and Hoarau, Y. , 2015, “ A Galerkin-Free Model Reduction Approach for the Navier-Stokes Equations,” J. Comput. Phys., 309, pp. 148–163. [CrossRef]
Lieu, T. , Farhat, C. , and Lesoinne, M. , 2006, “ Reduced-Order Fluid/Structure Modeling of Complete Aircraft Configuration,” Comput. Methods Appl. Mech. Eng., 195(41–43), pp. 5730–5742. [CrossRef]
Amsallem, D. , and Farhat, C. , 2008, “ Interpolation Method for Adapting Reduced-Order Models and Application to Aeroelasticity,” AIAA J., 46(7), pp. 1803–1813. [CrossRef]
Raghupathy, A. P. , Ghia, U. , and Ghia, K. , 2009, “ Boundary-Condition-Independent Reduced-Order Modeling of Complex 2D Objects by POD-Galerkin Methodology,” IEEE Semiconductor Thermal Measurement and Management Symposium (SEMI-THERM), San Jose, CA, Mar. 15–19, pp. 208–215.

Figures

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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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