The semiconductor industry, following Moore's law, has consistently followed a trajectory of miniaturization that enables design engineers to achieve greater levels of innovation in the same or smaller die footprints. According to Samsung technologists, the next generation of semiconductor technology will cost about $10 billion to create. Alternatively, improved performance through lowering of signal delays can also be achieved using stacked or 3D packaging. With this architectural achievement come cooling challenges as it is difficult to utilize conventional cooling technology and especially when stacking logic and memory processors for high end applications. The accumulation of excessive heat within the stack is a challenge that has caused thermal engineers to focus on the issue of extracting this heat from the system. Thus, one important aspect of design is the ability to obtain an accurate analytical temperature solution of the multilayer stack packages beforehand in order to sustain the reliability of the 3D stack packages albeit for a more simplified configuration. This study addresses the analytical solution of temperature distribution in multilayer bodies by using the Mathematica code developed in this study. The numerical approach using ansys Workbench is discussed, and the results are compared with the one obtained analytically.

References

References
1.
Tittle
,
C. W.
,
1965
, “
Boundary Value Problems in Composite Media
,”
J. Appl. Phys.
,
36
, pp.
1486
1488
.10.1063/1.1714335
2.
Padovan
,
J.
,
1974
,“
Generalized Sturm-Liouville Procedure for Composite Domain Anisotropic Transient Heat Conduction Problems
,”
AIAA J.
,
12
, pp.
1158
1160
.10.2514/3.49440
3.
Salt
,
H.
,
1983
, “
Transient Conduction in a Two-Dimensional Composite Slab-I. Theoretical Development of Temperature Modes
,”
Int. J. Heat Mass Transfer
,
26
, pp.
1611
1616
.10.1016/S0017-9310(83)80080-5
4.
Salt
,
H.
,
1983
, “
Transient Conduction in Two-Dimensional Composite Slab-II. Physical Interpretation of Temperature Modes
,”
Int. J. Heat Mass Transfer
,
26
, pp.
1617
1623
.10.1016/S0017-9310(83)80081-7
5.
Mikhailov
,
M. D.
, and
Ozisik
,
M. N.
,
1986
, “
Transient Conduction in a Three-Dimensional Composite Slab
,”
Int. J. Heat Mass Transfer
,
29
, pp.
340
342
.10.1016/0017-9310(86)90242-5
6.
de Monte
,
F.
,
2000
, “
Transient Heat Conduction in One-Dimensional Composite Slab.A ‘Natural’ Analytical Approach
,”
Int. J. Heat Mass Transfer
,
43
, pp.
3607
3616
.10.1016/S0017-9310(00)00008-9
7.
Aviles-Ramos
,
C.
,
Haji-Sheikh
,
A.
, and
Beck
,
J. V.
,
1998
, “
Exact Solution of Heat Conduction in Composites and Application to Inverse Problems
,”
ASME J. Heat Transfer
,
120
, pp.
592
599
.10.1115/1.2824316
8.
Haji-Sheikh
,
A.
, and
Beck
,
J. V.
,
2002
, “
Temperature Solution in Multi-Dimensional Multi-Layer Bodies
,”
Int. J. Heat Mass Transfer
,
45
, pp.
1865
1877
.10.1016/S0017-9310(01)00279-4
9.
Haji-Sheikh
,
A.
,
Beck
,
J. V.
, and
Agonafer
,
D.
,
2003
, “
Steady State Heat Conduction in Multi-Layer Bodies
,”
Int. J. Heat Mass Transfer
,
46
, pp.
2363
2379
.10.1016/S0017-9310(02)00542-2
10.
Ghalambor
,
S.
,
Agonafer
,
D.
, and
Haji-Sheikh
,
A.
,
2012
, “
Determination of Steady State Temperature in a Two-Layer Body With Different Form Factors
,”
Int. J. Heat Mass Transfer
,
55
, pp.
7434
7443
.10.1016/j.ijheatmasstransfer.2012.07.030
11.
Kaisare
,
A.
,
Agonafer
,
D.
,
Haji-Sheikh
,
A.
,
Chrysler
,
G.
,
Mahajan
,
R.
,
2009
, “
Development of an Analytical Model to a Temperature Distribution of First Level Package With a Non-Uniformly Powered Die
,”
ASME J. Electron. Packag.
,
31
, p.
011005
.10.1115/1.3068303
12.
de Monte
,
F.
,
2004
, “
Traverse Eigenproblem of Steady-State Heat Conduction for Multi-Dimensional Two-Layer Slabs With Automatic Computation of Eigenvalues
,”
Int. J. Heat Mass Transfer
,
47
, pp.
191
201
.10.1016/j.ijheatmasstransfer.2003.07.002
13.
Haji-Sheikh
,
A.
, and
Beck
,
J. V.
,
2000
, “
An Efficient Method of Computing Eigenvalues in Heat Conduction
,”
Numer. Heat Transfer, Part B
,
38
, pp.
133
156
.10.1080/104077900750034643
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