An analytical (mathematical) thermal stress model has been developed for an electronic assembly comprised of identical components bonded at their end portions and subjected to different temperatures. The model is used to assess the effect of the size (dimension in the x-direction) and compliance of the bonded regions (legs) on the maximum interfacial shearing stress that is supposedly responsible for the mechanical robustness of the assembly. The numerical example is carried out for a simplified two-legged Bismuth-Telluride-Alloy (BTA)-based thermoelectric module (TEM) design. It has been determined that thinner (dimension in the horizontal, x-direction) and longer (dimension in the vertical, y-direction) bonds (legs) could result in a considerable relief in the interfacial stress. In the numerical example carried out for a 10 mm long (dimension in the x-direction) TEM assembly with two peripheral 1 mm thick (dimension in the x-direction) legs, the predicted maximum interfacial shearing stress is only about 40% of the maximum stress in the corresponding homogeneously bonded assembly, when the bond occupies the entire interface between the assembly components. It has been determined also that if thick-and-short legs are employed, the maximum interfacial shearing stress might not be very much different from the stress in a homogeneously bonded assembly, so that there is no need, as far as physical design and robustness of the assembly is concerned, to use a homogeneous bond or a multileg system. The application of such a system might be needed, however, for the satisfactory functional (thermo-electrical) performance of the device. In any event, it is imperative that sufficient bonding strength is assured in the assembly. If very thin legs are considered for lower stresses, the minimum acceptable size (real estate) of the interfaces (in the horizontal plane) should be experimentally determined (say, by shear-off testing) so that this strength is not compromised. On the other hand, owing to a lower stress level in an assembly with thin-and-long legs, assurance of its interfacial strength is less of a challenge than for an assembly with a homogeneous bond or with stiff thick-and-short legs. The obtained results could be used particularly for considering, based on the suggested predictive model, an alternative to the existing TEM designs, which are characterized by multiple big (thick-and-long) legs. In our novel design, fewer small (thin-and-short) legs could be employed, so that the size and thickness of the TEM is reduced for the acceptable stress level.

References

References
1.
Lang
,
G. A.
,
Fehder
,
B. J.
, and
Williams
,
W. D.
, 1970, “
Thermal Fatigue in Silicon Power Transistors
,”
IEEE Trans. Electron Devices
,
17
, pp.
787
793
.
2.
Lau
,
J. H.
, ed., 1993,
Thermal Stress and Strain in Microelectronics Packaging
,
Van-Nostrand Reinhold
,
New York
.
3.
Bar-Cohen
,
A.
, and
Witzman
,
S.
, 1995, “
Thermally-Induced Failures in Electronic Equipment - Field Reliability Modeling
,”
Int. J. Microelectron. Packag.
,
1
, pp.
1
12
.
4.
Zeyfang
,
R.
, 1971, “
Stresses and Strains in a Plate Bonded to a Substrate: Semiconductor Devices
,”
Solid State Electron.
,
14
, pp.
1035
1039
.
5.
Hokanson
,
K. E.
, and
Bar-Cohen
,
A.
, 1995, “
Shear-Based Optimization of Adhesive Thickness for Die Bonding
,”
IEEE Trans. Compon., Hybrids, Manuf. Technol.
,
18
(
3
), pp.
578
584
.
6.
Driessen
,
A.
,
Baets
,
R. G.
,
McInerney
,
J. G.
, and
Suhir
,
E.
, eds., 2003,
Laser Diodes, Optoelectronic Devices, and Heterogeneous Integration
, Vol. 4947,
SPIE, Bellingham
,
WA.
7.
Suhir
,
E.
, 2009, “
Thermal Stress in a Bi-Material Assembly With a ‘Piecewise-Continuous’ Bonding Layer: Theorem of Three Axial Forces
,”
J. Appl. Phys., J. Phys. D
,
42
,
045507
.
8.
Suhir
,
E.
, 2001, “
Predicted Thermal Stresses in a Bi-Material Assembly Adhesively Bonded at the Ends
,”
J. Appl. Phys.
,
89
(
1
), pp.
120
129
.
9.
Suhir
,
E.
, 1995, “
‘Global’ and ‘Local’ Thermal Mismatch Stresses in an Elongated Bi-Material Assembly Bonded at the Ends
,”
Structural Analysis in Microelectronic and Fiber-Optic Systems
,
E.
Suhir
, ed.,
ASME Press
,
New York
.
10.
Schen
,
M.
,
Abe
,
H.
, and
Suhir
,
E.
, eds., 1994,
Thermal and Mechanical Behavior and Modeling
,
ASME
,
New York
.
11.
Suhir
,
E.
, 1986, “
Stresses in Bi-Metal Thermostats
,”
ASME J. Appl. Mech.
,
53
(
3
), pp.
657
660
.
12.
Suhir
,
E.
, 1989, “
Interfacial Stresses in Bi-Metal Thermostats
,”
ASME J. Appl. Mech.
,
56
(
3
), pp.
595
600
.
13.
Kuo
,
A.
, 1989, “
Thermal Stresses at the Edge of a Bimetallic Thermostat
,”
ASME J. Appl. Mech.
,
56
, pp.
585
589
.
14.
Eischen
,
J. W.
,
Chung
C.
, and
Kim
,
J. H.
, 1990, “
Realistic Modeling of the Edge Effect Stresses in Bimaterial Elements
,”
ASME J. Electron. Packag.
,
112
(
1
), pp.
16
23
.
15.
Min
G.
, and
Rowe
,
D. M.
, 1999, “
A Novel Thermoelectric Converter Employing Fermi Gas/Liquid Interfaces
,”
J. Appl. Phys., J. Phys. D
,
32
,
L26
L28
.
16.
Clin
,
T. H.
,
Turenne
,
S.
,
Vasilevskiy
,
D.
, and
Masut
,
R. A.
, 2009, “
Numerical Simulation of the Thermomechanical Behavior of Extruded Bismuth Telluride Alloy Module
,”
J. Electron. Mater.
,
38
(
7
), pp.
994
1001
.
17.
Yazawa
,
K.
, and
Shakouri
,
A.
, 2010, “
Cost-Efficiency Trade-Off and the Design of Thermoelectric Power Generators
,”
Environ. Sci. Technol.
,
45
(
17
), pp.
7548
7553
.
18.
Bell
,
L. E.
, 2008, “
Cooling, Heating, Generating Power, and Recovering Waste Heat With Thermoelectric Systems
,”
Science
,
321
, pp.
1457
1461
.
19.
Leonov
,
V.
, and
Vullers
,
R. J. M.
, 2009, “
Wearable Thermoelectric Generators for Body-Powered Devices
,”
J. Electron. Mater.
,
38
(
7
), pp.
1491
1498
.
20.
Yazawa
,
K.
,
Solbrekken
,
G.
, and
Bar-Cohen
,
A.
, 2005, “
Thermoelectric-Powered Convective Cooling of Microprocessors
,”
IEEE Trans. Adv. Packag.
,
28
(
2
), pp.
231
239
.
21.
Fukutani
,
K.
, and
Shakouri
,
A.
, 2006, “
Design of Bulk Thermoelectric Modules for Integrated Circuit Thermal Management
,”
IEEE Trans. Compon. Packag. Technol.
,
29
(
4
), pp.
750
757
.
22.
Mayer
,
P. M.
, and
Ram
,
R. J.
, 2006, “
Optimization of Heat Sink-Limited Thermoelectric Generators
,”
Nanoscale Microscale Thermophys. Eng.
,
10
, pp.
143
155
.
23.
Stevens
,
J. W.
, 2001, “
Optimum Design of Small Delta T Thermoelectric Generation Systems
,”
Energy Convers. Manage.
,
42
, pp.
709
720
.
24.
Kraemer
,
D.
,
Poudel
,
B.
,
Feng
,
H.-P.
,
Caylor
,
J. C.
,
Yu
,
B.
,
Yan
,
X.
,
Ma
,
Y.
,
Wang
,
X.
,
Wang
,
D.
,
Muto
,
A.
,
McEnaney
,
K.
,
Chiesa
,
M.
,
Ren
,
Z.
, and
Chen
,
G.
, 2011, “
High-Performance Flat-Panel Solar Thermoelectric Generators With High Thermal Concentration
,”
Nature Mater.
,
10
, pp.
532
538
.
25.
Gao
,
J.-L.
,
Du
,
Q.-G.
,
Zhang
,
X.-D.
, and
Jiang
,
X.-Q.
, 2011, “
Thermal Stress Analysis and Structure Parameter Selection for a Be2Te3-Based Thermoelectric Module
,”
J. Electron. Mater.
,
40
(
5
), pp.
884
888
.
26.
Antonova
,
E. E.
, and
Looman
,
D. C.
, 2005, “
Finite Elements for Thermoelectric Device Analysis
”,
Proceedings of the ICT 2005 24th International Conference on Thermoelectrics
.
27.
Luryi
,
S.
, and
Suhir
,
E.
, 1986, “
A New Approach to the High-Quality Epitaxial Growth of Lattice - Mismatched Materials
,”
Appl. Phys. Lett.
,
49
(
3
), pp.
140
142
.
You do not currently have access to this content.