Thermal interface materials (TIMs) are particulate composite materials widely used in the microelectronics industry to reduce the thermal resistance between the device and heat sink. Predictive modeling using fundamental physical principles is critical to developing new TIMs since it can be used to quantify the effect of particle volume fraction and arrangements on the effective thermal conductivity. The existing analytical descriptions of thermal transport in particulate systems do not accurately account for the effect of interparticle interactions, especially in the intermediate volume fractions of 30–80%. An efficient random network model (RNM) that captures the near-percolation transport in these particle-filled systems, taking into account the interparticle interactions and random size distributions, was previously developed by Kanuparthi et al. The RNM approach uses a cylindrical region to approximate the thermal transport within the filler particles and to capture the interparticle interactions. However, this approximation is less accurate when the polydispersivity of the particulate system increases. In addition, the accuracy of the RNM is dependent on the parameters inherent in an analytical description of thermal transport between two spherical particles and their numerical approximation into the network model. In the current paper, a novel semispherical approximation to the conductance of the fillers is presented as an alternative to the cylindrical region approximation used earlier. Compared with the cylindrical model, the thermal conductivities of the semispherical model are more closely to the finite element (FE) results. Based on the FE analysis, the network model is improved by developing an approximation of the critical cylindrical region between two spherical particles over which energy is transported. Comparing the RNM results with FE results and experimental data, a linear relationship of the critical parameter with the thermal conductivity ratio and the volume fraction was found that provides a more accurate prediction of the effective thermal conductivity of the particulate TIMs.

References

References
1.
Gowda
,
A.
,
Tonapi
,
S.
,
Reitz
,
B.
, and
Gensler
,
G.
,
2005
, “
Choosing the Right Thermal Interface Material
,”
Adv. Packag.
,
14
(
3
), pp.
14
18
.
2.
Yovanovich
,
M. M.
, and
Marotta
,
E. E.
,
2003
, “
Thermal Spreading and Contact Resistance
,”
Heat Transfer Handbook
,
A.
Bejan
, and
A. D.
Kraus
, eds.,
John Wiley and Sons
,
New York
, pp.
261
395
.
3.
Madhusudana
,
C. V.
,
1996
,
Thermal Contact Conductance
,
Springer-Veralag
,
New York
.
4.
Tummala
,
R. R.
,
Rymaszewski
,
E. J.
, and
Klopfenstein
,
A. G.
,
1996
,
Microelectronics Packaging Handbook—Part I
,
Chapman & Hall
,
New York
.
5.
Prasher
,
R.
,
2006
, “
Thermal Interface Materials: Historical Perspective, Status, and Future Directions
,”
Proc. IEEE
,
94
(
8
), pp.
1571
1586
.10.1109/JPROC.2006.879796
6.
Getty
,
R. C.
, and
Tatro
,
R. E.
,
1967
, “
Spacecraft Thermal Joint Conduction
,”
AIAA Thermophysics Specialist Conference
,
New Orleans, LA
, April 17-20,
AIAA
Paper No. 67-316.10.2514/6.1967-316
7.
Fletcher
,
L. S.
,
1990
, “
A Review of Thermal Enhancement Techniques for Electronics System
,”
IEEE Trans. Compon., Hybrids, Manuf. Technol.
,
13
(
4
), pp.
1012
1021
.10.1109/33.62543
8.
Marotta
,
E. E.
, and
Fletcher
,
L. S.
,
1996
, “
Thermal Contact Conductance of Selected Polymeric Materials
,”
J. Thermophys. Heat Transfer
,
10
(
2
), pp.
334
342
.10.2514/3.792
9.
Mirmira
,
S. R.
,
Marotta
,
E. E.
, and
Fletcher
,
L. S.
,
1997
, “
Thermal Contact Conductance of Adhesives for Microelectronic Systems
,”
J. Thermophys. Heat Transfer
,
11
(
2
), pp.
141
145
.10.2514/2.6232
10.
Xu
,
Y.
,
Luo
,
X.
, and
Chung
,
D. D. L.
,
2000
, “
Sodium Silicate Based Thermal Interface Material for High Thermal Contact Conductance
,”
ASME J. Electron. Packag.
,
122
, pp.
128
131
.10.1115/1.483144
11.
Mahajan
,
R.
,
Chiu
,
C.-P.
, and
Prashed
,
R.
,
2004
, “
Thermal Interface Materials: A Brief Review of Design Characteristics and Materials
,”
Electron. Cooling
,
10
(
1
), pp.
10
18
.
12.
Gwinn
,
J. P.
, and
Webb
,
R. L.
,
2003
, “
Performance and Testing of Thermal Interface Materials
,”
Microelectron. J.
,
34
(
1
), pp.
215
222
.10.1016/S0026-2692(02)00191-X
13.
Prismark Partners LLC
,
2001
, “
Thermal Interface Materials: Cool Materials for Hot Products
,” company report.
14.
Viswnaath
,
R.
,
Wakharkar
,
V.
,
Watwe
,
A.
, and
Lebonheur
,
V.
,
2000
, “
Thermal Performance Challenges From Silicon to Systems
,”
Intel Technol. J.
,
Q3
, pp.
1
15
15.
Maxwell
,
J. C.
,
1873
,
Electricity and Magnetism
,
1st ed.
,
Clarendon, Oxford
,
UK
.
16.
Rayleigh
,
L.
,
1892
, “
On the Influence of Obstacles Arranged in Rectangular Order Upon the Properties of a Medium
,”
Philos. Mag.
,
34
, pp.
481
502
.10.1080/14786449208620364
17.
Torquato
,
S.
,
2002
,
Random Heterogeneous Materials
,
Springer-Verlag
,
New York
.
18.
Hasselman
,
D. P. H.
, and
Johnson
,
L. F.
,
1987
, “
Effective Thermal Conductivity of Composites With Interfacial Thermal Barrier Resistance
,”
J. Compos. Mater.
,
21
, pp.
508
515
.10.1177/002199838702100602
19.
Nan
,
C. W.
,
Birringer
,
R.
,
Clarke
,
D. R.
, and
Gleiter
,
H.
,
1997
, “
Effective Thermal Conductivity of Particulate Composites With Interfacial Thermal Resistance
,”
J. Appl. Phys.
,
81
(
10
), pp.
6692
6699
.10.1063/1.365209
20.
Benvensite
,
Y.
,
1987
, “
Effective Thermal Conductivity of Composites With a Thermal Contact Resistance Between the Constituents: Non-Dilute Case
,”
J. Appl. Phys.
,
61
(
8
), pp.
2840
2843
.10.1063/1.337877
21.
McPhedran
,
R. C.
, and
McKenzie
,
D. R.
,
1978
, “
The Conductivity of Lattices of Spheres. I. The Simple Cubic Lattice
,”
Proc. R. Soc. London, Ser. A
,
359
, pp.
45
63
.10.1098/rspa.1978.0031
22.
McKenzie
,
D. R.
,
McPhedran
,
R. C.
, and
Derrick
,
G. H.
,
1978
, “
The Conductivity of Lattices of Spheres. II. The Body Centered and Face Centered Cubic Lattices
,”
Proc. R. Soc. London, Part A
,
362
, pp.
211
232
.10.1098/rspa.1978.0129
23.
Gu
,
G.
, and
Liu
,
Z.
,
1992
, “
Effects of Contact Resistance on the Thermal Conductivity of Composite Media With a Periodic Structure
,”
J. Phys. D: Appl. Phys.
,
25
, pp.
249
255
.10.1088/0022-3727/25/2/018
24.
Bruggeman
,
D.
,
1935
, “
Berechnung Verschiedener Physikalischer Konstanten Von Heterogenen Substanzen
,”
Ann. Phys. (Liepzig)
,
24
, pp.
636
679
.10.1002/andp.19354160705
25.
Landauer
,
R.
,
1952
, “
The Electrical Resistance of Binary Metallic Mixtures
,”
J. Appl. Phys.
,
23
, pp.
779
784
.10.1063/1.1702301
26.
Landauer
,
R.
,
1978
, “
Electrical Conductivity in Inhomogeneous Media
,”
Electrical, Transport and Optical Properties of Inhomogeneous Media
,
J. C.
Garland
and
D. B.
Tannera
, eds.,
AIP
,
New York
, pp.
2
43
.
27.
Every
,
A. G.
,
Tzou
,
Y.
,
Hasselman
,
D. P. H.
, and
Raj
,
R.
,
1992
, “
The Effect of Particle Size on the Thermal Conductivity of ZnS/Diamond Composites
,”
Acta Metall. Mater.
,
40
, pp.
123
129
.10.1016/0956-7151(92)90205-S
28.
Kanuparthi
,
S.
,
Zhang
,
X.
,
Subbarayan
,
G.
,
Sammakia
,
B. G.
,
Gowda
,
A.
, and
Tonapi
,
S.
,
2006
, “
Full-Field Simulations of Particulate Thermal Interface Materials: Separating the Effects of Random Distribution From Interfacial Resistance
,”
Proceedings of the 10th Intersociety Conference on Thermal and Thermomechanical Phenomena in Electronics Systems
(
ITHERM’06
),
San Diego, CA
, May 30–June 2, pp.
1276
1282
.10.1109/ITHERM.2006.1645492
29.
Kanuparthi
,
S.
,
Subbarayan
,
G.
,
Siegmund
,
T.
, and
Sammakia
,
B. G.
,
2008
, “
An Efficient Network Model for Determining the Effective Thermal Conductivity of Particulate Thermal Interface Materials
,”
IEEE Trans. Compon. Packag. Technol.
,
31
(
3
), pp.
1
11
.10.1109/TCAPT.2008.2001839
30.
Kanuparthi
,
S.
,
Zhang
,
X.
,
Subbarayan
,
G.
,
Siegmund
,
T.
,
Sammakia
,
B. G.
,
Gowda
,
A.
, and
Tonapi
,
S.
,
2006
, “
Random Network Percolation Model for Particulate Thermal Interface Materials
,”
Proceedings of the 10th Intersociety Conference on Thermal and Thermomechanical Phenomena in Electronics Systems
(
ITHERM'06
), San Diego, CA, May 30–June 2, pp.
1192
1198
.10.1109/ITHERM.2006.1645480
31.
Devpura
,
A.
,
Phelan
,
P. E.
, and
Prasher
,
R. S.
,
2000
, “
Percolation Theory Applied to the Analysis of Thermal Interface Materials in Flip-Chip Technology
,”
Proceedings of the 7th Intersociety Conference on Thermal and Thermomechanical Phenomena in Electronic Systems
(
ITHERM 2000
), Las Vegas, NV, May 23–26, Vol.
1
, pp.
21
28
.10.1109/ITHERM.2000.866803
32.
Devpura
,
A.
,
Phelan
,
P. E.
, and
Prasher
,
R. S.
,
2000
, “
Percolation Theory Applied to Study the Effect of Shape and Size of the Filler Particles in Thermal Interface Materials
,”
Proceedings of the ASME Heat Transfer Division
, Vol.
366
(
4
), pp.
365
371
.
33.
Devpura
,
A.
,
Phelan
,
P. E.
, and
Prasher
,
R. S.
,
2001
, “
Size Effects on the Thermal Conductivity of Polymers Laden With Highly Conductive Filler Particles
,”
Microscale Thermophys. Eng.
,
5
(
3
), pp.
177
189
.10.1080/108939501753222869
34.
Keblinski
,
P.
, and
Cleri
,
F.
,
2004
, “
Contact Resistance in Percolating Networks
,”
Phys. Rev. B
,
69
, pp.
184
201
.10.1103/PhysRevB.69.184201
35.
Ganapathy
,
D.
,
Singh
,
S.
,
Phelan
,
P.
, and
Prasher
,
R. S.
,
2005
, “
An Effective Unit Cell Approach to Compute Thermal Conductivity of Composites With Cylindrical Particles
,”
ASME J. Heat Transfer
,
127
, pp.
553
559
.10.1115/1.1915387
36.
Liang
,
X.-G.
,
Lukes
,
J. R.
, and
Tien
,
C.-L.
,
1998
, “
Anisotropic Thermal Conductance in Thin Layers of Disordered Packed Spheres
,”
Proceedings of the 11th International Heat Transfer Conference
, Kyongju, Korea, August 23–28, pp.
33
38
.
37.
Liang
,
X.-G.
, and
Ji
,
X.
,
2000
, “
Thermal Conductance of Randomly Oriented Composites of Thin Layers
,”
Int. J. Heat Mass Transfer
,
43
, pp.
3633
3640
.10.1016/S0017-9310(99)00387-7
38.
Matsukawa
,
M.
,
Tatezaki
,
F.
,
Ogasawara
,
H.
,
Noto
,
K.
, and
Yoshida
,
K.
,
1995
, “
Thermal Transport and Percolative Transition in the Ag-BPSCCO Composite System
,”
J. Phys. Soc. Jpn.
,
64
(
1
), pp.
164
169
.10.1143/JPSJ.64.164
39.
Kim
,
K. H.
,
Uehara
,
M.
,
Hess
,
C.
,
Sharma
,
P. A.
, and
Cheong
,
S.-W.
,
2000
, “
Thermal and Electronic Transport Properties and Two-Phase Mixtures in La5/8_xPrxCa3/8MnO3
,”
Phys. Rev. Lett.
,
84
(
13
), pp.
2961
2964
.10.1103/PhysRevLett.84.2961
40.
Batchelor
,
G. K.
, and
O'Brien
,
R. W.
,
1977
, “
Thermal or Electrical Conduction Through a Granular Material
,”
Proc. R. Soc. London, Ser. A,
355
(
1682
), pp.
313
333
.10.1098/rspa.1977.0100
41.
Dan
,
B.
,
Kanuparthi
,
S.
,
Subbarayan
,
G.
, and
Sammakia
,
B. G.
,
2009
, “
An Improved Network Model for Determining the Effective Thermal Conductivity of Particulate Thermal Interface Materials
,”
Proceeding of InterPACK Conference
,
San Francisco, CA
, July 19–23,
ASME
Paper No. InterPACK2009-89116, pp.
69
81
.10.1115/InterPACK2009-89116
42.
Dan
,
B.
,
Sammakia
,
B. G.
, and
Subbarayan
,
G.
,
2010
, “
On Refining the Parameters of a Random Network Model for Determining the Effective Thermal Conductivity of Particulate Thermal Interface Materials
,”
12th IEEE Intersociety Conference on Thermal and Thermomechanical Phenomena in Electronic Systems
(
ITHERM 2010
),
Las Vegas, NV
, June 2–510.1109/ITHERM.2010.5501349.
43.
Zhang
,
X.
, and
Subbarayan
,
G.
,
2006
, “
jNURBS: An Extensible Symbolic Object-Oriented Framework for Integrated Mesh-Less Analysis and Optimal Design
,”
Adv. Eng. Software
,
7
(
5
), pp.
287
311
.10.1016/j.advengsoft.2005.08.001
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