In the microelectronics industry, the multilayered structures are found extensively where the microelectronic device/system is manufactured as a compound system of different materials. Recently, a variety of new materials have emerged in the microelectronics industry with properties superior to Silicon, enabling new devices with extreme performance. Such materials include β-Gallium-oxide (β-Ga2O3), and black phosphorus (BP), which are acknowledged to have anisotropic thermal conductivity tensors. In many of these devices, thermal issues due to self-heating are a problem that affects the performance, efficiency, and reliability of the devices. Analytical solutions to the heat conduction equation in such devices with anisotropic thermal conductivity tensor offer significant computational savings over numerical methods. In this paper, general analytical solutions for the temperature distribution and the thermal resistance of a multilayered orthotropic system are obtained. The system is considered as a multilayered three-dimensional (3D) flux channel consisting of N-layers with different thermal conductivities in the three spatial directions in each layer. A single eccentric heat source is considered in the source plane while a uniform heat transfer coefficient is considered along the sink plane. The solutions account for the effect of interfacial conductance between the layers and for considering multiple eccentric heat sources in the source plane. For validation purposes, the analytical results are compared with numerical solution results obtained by solving the problem with the finite element method (FEM) using the ANSYS commercial software package.

References

References
1.
Higashiwaki
,
M.
,
Sasaki
,
K.
,
Kuramata
,
A.
,
Masui
,
T.
, and
Yamakoshi
,
S.
,
2014
, “
Development of Gallium Oxide Power Devices
,”
Phys. Status Solidi A
,
211
(
1
), pp.
21
26
.
2.
Jain
,
A.
, and
McGaughey
,
A. J. H.
,
2015
, “
Strongly Anisotropic in-Plane Thermal Transport in Single-Layer Black Phosphorene
,”
Sci. Rep.
,
5
, p.
8501
.
3.
Zhu
,
J.
,
Chen
,
J. Y.
,
Park
,
H.
,
Gu
,
X.
,
Zhang
,
H.
,
Karthikeyan
,
S.
,
Wendel
,
N.
,
Campbell
,
S. A.
,
Dawber
,
M.
,
Du
,
X.
,
Li
,
M.
,
Wang
,
J. P.
,
Yang
,
R.
, and
Wang
,
X.
,
2016
, “
Revealing the Origins of 3D Anisotropic Thermal Conductivities of Black Phosphorus
,”
Adv. Electron. Mater.
,
2
(
5
), p.
1600040
.
4.
Kim
,
J. S.
,
Jeon
,
P. J.
,
Lee
,
J.
,
Choi
,
K.
,
Lee
,
H. S.
,
Cho
,
Y.
,
Lee
,
Y. T.
,
Hwang
,
D. K.
, and
Im
,
S.
,
2015
, “
Dual Gate Black Phosphorus Field Effect Transistors on Glass for NOR Logic and Organic Light Emitting Diode Switching
,”
Nano Lett.
,
15
(
9
), pp.
5778
5783
.
5.
Liu
,
G.
,
Sun
,
H. Y.
,
Zhou
,
J.
,
Li
,
Q. F.
, and
Wan
,
X. G.
,
2016
, “
First-Principles Study of Lattice Thermal Conductivity of Td-WTe2
,”
New J. Phys.
,
18
, p.
033017
.
6.
Wong
,
M. H.
,
Morikawa
,
Y.
,
Sasaki
,
K.
,
Kuramata
,
A.
,
Yamakoshi
,
S.
, and
Higashiwaki
,
M.
,
2016
, “
Characterization of Channel Temperature in Ga2O3 Metal-Oxide-Semiconductor Field-Effect Transistors by Electrical Measurements and Thermal Modeling
,”
Appl. Phys. Lett.
,
109
(
19
), p.
193503
.
7.
Guo
,
Z.
,
Verma
,
A.
,
Wu
,
X.
,
Sun
,
F.
,
Hickman
,
A.
,
Masui
,
T.
,
Kuramata
,
A.
,
Higashiwaki
,
M.
,
Jena
,
D.
, and
Luo
,
T.
,
2015
, “
Anisotropic Thermal Conductivity in Single Crystal β-Gallium Oxide
,”
Appl. Phys. Lett.
,
106
(
11
), p.
111909
.
8.
Darwish
,
A. M.
,
Bayba
,
A. J.
, and
Hung
,
H. A.
,
2004
, “
Thermal Resistance Calculation of Algangan Devices
,”
IEEE Trans. Microwave Theory Tech.
,
52
(
11
), pp.
2611
2620
.
9.
Kennedy
,
D. P.
,
1960
, “
Spreading Resistance in Cylindrical Semiconductor Devices
,”
J. Appl. Phys.
,
31
(
8
), pp.
1490
1497
.
10.
Kokkas
,
A. G.
,
1974
, “
Thermal Analysis of Multiple-Layer Structures
,”
IEEE Trans. Electron. Devices
,
Ed-21
(
11
), pp.
674
681
.
11.
Yovanovich
,
M. M.
,
1975
, “General Expressions for Constriction Resistances Due to Arbitrary Flux Distributions at Non-Symmetric, Coaxial Contacts,”
AIAA
Paper No. 75-188.
12.
Yovanovich
,
M. M.
,
Muzychka
,
Y. S.
, and
Culham
,
J. R.
,
1999
, “
Spreading Resistance in Isoflux Rectangles and Strips on Compound Flux Channels
,”
J. Thermophys. Heat Transfer
,
13
(
4
), pp.
495
500
.
13.
Yovanovich
,
M. M.
,
2003
, “
Thermal Resistances of Circular Source on Finite Circular Cylinder With Side and End Cooling
,”
ASME J. Electron. Packag.
,
125
(
2
), pp.
169
177
.
14.
Yovanovich
,
M. M.
,
2005
, “
Four Decades of Research on Thermal Contact, Gap and Joint Resistance in Microelectronics
,”
IEEE Trans. Compon. Packag. Technol.
,
28
(
2
), pp.
182
206
.
15.
Muzychka
,
Y. S.
,
Culham
,
J. R.
, and
Yovanovich
,
M. M.
,
2003
, “
Thermal Spreading Resistance of Eccentric Heat Sources on Rectangular Flux Channels
,”
ASME J. Electron. Packag.
,
125
(
2
), pp.
178
185
.
16.
Muzychka
,
Y. S.
,
Yovanovich
,
M. M.
, and
Culham
,
J. R.
,
2006
, “
Influence of Geometry and Edge Cooling on Thermal Spreading Resistance
,”
AIAA J. Thermophys. Heat Transfer
,
20
(
2
), pp.
247
255
.
17.
Muzychka
,
Y. S.
,
2006
, “
Influence Coefficient Method for Calculating Discrete Heat Source Temperature on Finite Convectively Cooled Substrates
,”
IEEE Trans. Compon. Packag. Technol.
,
29
(
3
), pp.
636
643
.
18.
Muzychka
,
Y. S.
,
Bagnall
,
K. R.
, and
Wang
,
E. N.
,
2013
, “
Thermal Spreading Resistance and Heat Source Temperature in Compound Orthotropic Systems With Interfacial Resistance
,”
IEEE Trans. Compon., Packag., Manuf. Technol.
,
3
(
11
), pp.
1826
1841
.
19.
Muzychka
,
Y. S.
,
2014
, “
Spreading Resistance in Compound Orthotropic Flux Tubes and Channels With Interfacial Resistance
,”
J. Thermophys. Heat Transfer
,
28
(
2
), pp.
313
319
.
20.
Muzychka
,
Y. S.
,
2015
, “Thermal Spreading Resistance in a Multilayered Orthotropic Circular Disk With Interfacial Resistance and Variable Heat Flux,”
ASME
Paper No. IPACK2015-48243.
21.
Gholami
,
A.
, and
Bahrami
,
M.
,
2014
, “
Thermal Spreading Resistance Inside Anisotropic Plates With Arbitrarily Located Hotspots
,”
J. Thermophys. Heat Transfer
,
28
(
4
), pp.
679
686
.
22.
Bagnall
,
K. R.
,
Muzychka
,
Y. S.
, and
Wang
,
E. N.
,
2014
, “
Analytical Solution for Temperature Rise in Complex, Multi-Layer Structures With Discrete Heat Sources
,”
IEEE Trans. Compon., Packag., Manuf. Technol.
,
4
(
5
), pp.
817
830
.
23.
Hahn
,
D. W.
, and
Ozisik
,
M. N.
,
2012
,
Heat Conduction
,
Wiley
,
Hoboken, NJ
.
24.
Muzychka
,
Y. S.
,
Yovanovich
,
M. M.
, and
Culham
,
J. R.
,
2004
, “
Thermal Spreading Resistance in Compound and Orthotropic Systems
,”
J. Thermophys. Heat Transfer
,
18
(
1
), pp.
45
51
.
25.
Kakac
,
S.
, and
Yener
,
Y.
,
1993
,
Heat Conduction
,
3rd ed.
,
Taylor and Francis
,
Malabar, FL
.
26.
Ozisik
,
M. N.
,
1968
,
Boundary Value Problems of Heat Conduction
,
International Textbook
,
Scranton, PA
.
27.
Arpaci
,
V.
,
1966
,
Conduction Heat Transfer
,
Addison-Wesley
,
New York
.
28.
MATLAB, 2016, “MATLAB Release
2016b
,” The MathWorks Inc., Natick, MA.
29.
ANSYS, 2015, “ANSYS® Release 16.2,” ANSYS Inc., Canonsburg PA.
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