In a microelectronic device, thermal transport needs to be simulated on scales ranging from tens of nanometers to hundreds of millimeters. High accuracy multiscale models are required to develop engineering tools for predicting temperature distributions with sufficient accuracy in such devices. A computationally efficient and accurate multiscale reduced order transient thermal modeling methodology was developed using a combination of two different approaches: “progressive zoom-in” method and “proper orthogonal decomposition (POD)” technique. The capability of this approach in handling several decades of length scales from “package” to “chip components” at a considerably lower computational cost, while maintaining satisfactory accuracy was demonstrated. A flip chip ball grid array (FCBGA) package was considered for demonstration. The transient temperature and heat fluxes calculated on the top and bottom walls of the embedded chip at the package level simulations are employed as dynamic boundary conditions for the chip level simulation. The chip is divided into ten function blocks. Randomly generated dynamic power sources are applied in each of these blocks. The temperature rise in the different layers of the chip calculated from the multiscale model is compared with a finite element (FE) model. The close agreement between two models confirms that the multiscale approach can predict temperature rise accurately for scenarios corresponding to different power sources in functional blocks, without performing detailed FE simulations, which significantly reduces computational effort.

References

References
1.
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
.10.1115/1.2957318
2.
Joshi
,
Y.
,
2012
, “
Reduced Order Thermal Models of Multiscale Microsystems
,”
ASME J. Heat Transfer
,
134
(
3
), p.
031008
.10.1115/1.4005150
3.
Christiaens
,
F.
,
Vandevelde
,
B.
,
Beyne
,
E.
,
Mertens
,
R.
, and
Berghmans
,
J.
,
1998
, “
A Generic Methodology for Deriving Compact Dynamic Thermal Models, Applied to the PSGA Package
,”
IEEE Trans. Compon., Packag., Manuf. Technol., Part A
,
21
(
4
), pp.
565
576
.10.1109/95.740047
4.
Lasance
,
C.
,
Vinke
,
H.
,
Rosten
,
H.
, and
Weiner
,
K. L.
,
1995
, “
A Novel Approach for the Thermal Characterization of Electronic Parts
,”
Eleventh Annual IEEE Semiconductor Thermal Measurement and Management Symposium
(
SEMI-THERM XI
), San Jose, CA, Feb. 7–9.10.1109/STHERM.1995.512044
5.
Gerstenmaier
,
Y.
, and
Wachutka
,
G.
,
2002
, “
Rigorous Model and Network for Transient Thermal Problems
,”
Microelectron. J.
,
33
(
9
), pp.
719
725
.10.1016/S0026-2692(02)00055-1
6.
Krueger
,
W.
, and
Bar-Cohen
,
A.
,
1992
, “
Thermal Characterization of a PLCC-Expanded Rjc Methodology
,”
IEEE Trans. Compon., Hybrids, Manuf. Technol.
,
15
(
5
), pp.
691
698
.10.1109/33.180032
7.
Celo
,
D.
,
Xiao Ming
,
G.
,
Gunupudi
,
P. K.
,
Khazaka
,
R.
,
Walkey
,
D. J.
,
Smy
,
T.
, and
Nakhla
,
M. S.
,
2005
, “
Hierarchical Thermal Analysis of Large IC Modules
,”
IEEE Trans. Compon. Packag. Technol.
,
28
(
2
), pp.
207
217
.10.1109/TCAPT.2005.848530
8.
Hua
,
Y.
, and
Yu
,
Z.
,
1989
, “
Generalized Pencil-of-Function Method for Extracting Poles of an EM System From Its Transient Response
,”
IEEE Trans. Antennas Propag.
,
37
(
2
), pp.
229
234
.10.1109/8.18710
9.
Hua
,
Y.
, and
Yu
,
Z.
,
1991
, “
On SVD for Estimating Generalized Eigenvalues of Singular Matrix Pencil in Noise
,”
IEEE Trans. Signal Process.
,
39
(
4
), pp.
892
900
.10.1109/78.80911
10.
Zao
,
L.
,
Tan
,
S. X. D.
,
Hai
,
W.
,
Quintanilla
,
R.
, and
Gupta
,
A.
,
2011
, “
Compact Thermal Modeling for Package Design With Practical Power Maps
,”
International Green Computing Conference and Workshops
(
IGCC
), Orlando, FL, July 25–28.10.1109/IGCC.2011.6008577
11.
Duo
,
L.
,
Tan
,
S. X. D.
,
Pacheco
,
E. H.
, and
Tirumala
,
M.
,
2009
, “
Architecture-Level Thermal Characterization for Multicore Microprocessors
,”
IEEE Trans. VLSI Syst.
,
17
(
10
), pp.
1495
1507
.10.1109/TVLSI.2008.2005193
12.
Lumley
,
J. L.
,
1967
, “
The Structure of Inhomogeneous Turbulent Flows
,”
Atmospheric Turbulence and Radio Wave Propagation
,
Nauka
,
Moscow
, pp.
166
178
.
13.
Holmes
,
P.
,
Lumley
,
J. L.
, and
Berkooz
,
G.
,
1998
,
Turbulence, Coherent Structures, Dynamical Systems and Symmetry
,
Cambridge University Press
, Cambridge, UK.
14.
Barabadi
,
B.
,
Joshi
,
Y.
, and
Kumar
,
S.
,
2011
, “
Prediction of Transient Thermal Behavior of Planar Interconnect Architecture Using Proper Orthogonal Decomposition Method
,”
ASME
Paper No. IPACK2011-52133. 10.1115/IPACK2011-52133
15.
Comsol
,
2011
, “
comsol Version 4.2
,” Comsol Multiphysics, Inc., Burlington, MA, http://www.comsol.com
16.
Chatterjee
,
A.
,
2000
, “
An Introduction to the Proper Orthogonal Decomposition
,”
Curr. Sci.
,
78
(
7
), pp.
808
817
.http://www.currentscience.ac.in/Downloads/article_id_078_07_0808_0817_0.pdf
17.
Berkooz
,
G.
,
Holmes
,
P.
, and
Lumley
,
J.
,
1996
,
Turbulence, Coherent Structures, Dynamical Systems and Symmetry
(Cambridge Monographs on Mechanics),
Cambridge University Press
, Cambridge, UK, pp.
1200
1208
.
18.
Graham
,
M. D.
, and
Kevrekidis
,
I. G.
,
1996
, “
Alternative Approaches to the Karhunen–Loeve Decomposition for Model Reduction and Data Analysis
,”
Comput. Chem. Eng.
,
20
(
5
), pp.
495
506
.10.1016/0098-1354(95)00040-2
19.
Rowley
,
C. W.
,
Colonius
,
T.
, and
Murray
,
R. M.
,
2001
, “
Dynamical Models for Control of Cavity Oscillations
,”
AIAA
Paper No. 2001-2126. 10.2514/6.2001-2126
20.
Samadiani
,
E.
,
Joshi
,
Y.
,
Hamann
,
H.
,
Iyengar
,
M. K.
,
Kamalsy
,
S.
, and
Lacey
,
J.
,
2012
, “
Reduced Order Thermal Modeling of Data Centers Via Distributed Sensor Data
,”
ASME J. Heat Transfer
,
134
(
4
), p.
041401
.10.1115/1.4004011
21.
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
.10.1016/j.compchemeng.2007.06.004
22.
Incropera
,
F. P.
,
Bergman
,
T. L.
,
Lavine
,
A. S.
, and
Dewitt
,
D. P.
,
2011
,
Fundamentals of Heat and Mass Transfer
,
Wiley
, Hoboken, NJ.
23.
Chang
,
K. C.
,
Li
,
Y.
,
Lin
,
C. Y.
, and
Lii
,
M. J.
,
2004
, “
Design Guidance for the Mechanical Reliability of Low-K Flip Chip BGA Package 1
,”
37th International Microelectronics and Packaging Society (IMAPS) Topical Workshop and Exhibition on Flip Chip Technology
, Long Beach, CA, Nov. 14–18, pp. 21–24.
24.
Tang
,
L.
, and
Joshi
,
Y. K.
,
2005
, “
A Multi-Grid Based Multi-Scale Thermal Analysis Approach for Combined Mixed Convection, Conduction, and Radiation Due to Discrete Heating
,”
ASME J. Heat Transfer
,
127
(
1
), pp.
18
26
.10.1115/1.1852495
25.
Barabadi
,
B.
,
Kumar
,
S.
,
Sukharev
,
V.
, and
Joshi
,
Y. K.
,
2012
, “
Multi-Scale Transient Thermal Analysis of Microelectronics
,”
ASME
Paper No. IMECE2012-89864. 10.1115/IMECE2012-89864
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