The physical vapor transport (PVT) method is widely adopted to produce semiconductor materials including silicon carbide (SiC). This work focuses on the role of thermal radiation for the heat transfer inside the PVT reactor. The radiation is characterized by two dimensionless parameters relating to the SiC charge and to the growth chamber. A simulation program is set up with the finite-volume method (FVM), considering heat generation, conduction, and radiation under the steady-state condition. Comprehensive results are obtained by tuning values of dimensionless parameters and the associated controlling variables, such as the cooling temperature and the coil current density, and illustrated in the phase diagrams. From the study, we find that the charge size has negligible influence on the temperature field, the crucible conduction determines the temperature level, and the relative strength of the chamber radiation against the crucible conduction modifies the temperature field on the SiC ingot. Finally, design guidelines are proposed with the instructive phase diagram to achieve the optimized thermal performance of the PVT reactor.

References

References
1.
Chaussende
,
D.
,
Wellmann
,
P. J.
, and
Pons
,
M.
,
2007
, “
Status of SiC Bulk Growth Processes
,”
J. Phys. D: Appl. Phys.
,
40
(
20
), pp.
6150
6158
.
2.
Glass
,
R. C.
,
Henshall
,
D.
,
Tsvetkov
,
V. F.
, and
Carter
,
C. H.
,
1997
, “
SiC Seeded Crystal Growth
,”
Phys. Status Solidi B
,
202
(
1
), pp.
149
162
.
3.
Matsunami
,
H.
, and
Kimoto
,
T.
,
1997
, “
Step-Controlled Epitaxial Growth of SiC: High Quality Homoepitaxy
,”
Mater. Sci. Eng.: B
,
20
(
3
), pp.
125
166
.
4.
Ivanov
,
P. A.
, and
Chelnokov
,
V. E.
,
1992
, “
Recent Developments in SiC Single-Crystal Electronics
,”
Semicond. Sci. Technol.
,
7
(
7
), pp.
863
880
.
5.
Furusho
,
T.
,
Sasaki
,
M.
,
Ohshima
,
S.
, and
Nishino
,
S.
,
2003
, “
Bulk Crystal Growth of Cubic Silicon Carbide by Sublimation Epitaxy
,”
J. Cryst. Growth
,
249
(
1–2
), pp.
216
221
.
6.
Chen
,
Q. S.
,
Zhang
,
H.
,
Prasad
,
V.
,
Balkas
,
C. M.
, and
Yushin
,
N. K.
,
2001
, “
Modeling of Heat Transfer and Kinetics of Physical Vapor Transport Growth of Silicon Carbide Crystals
,”
ASME J. Heat Transfer
,
123
(
6
), pp.
1098
1109
.
7.
Sudarshan
,
T. S.
, and
Maximenko
,
S. I.
,
2006
, “
Bulk Growth of Single Crystal Silicon Carbide
,”
Microelectron. Eng.
,
83
(
1
), pp.
155
159
.
8.
Sugiyama
,
N.
,
Okamoto
,
A.
,
Okumura
,
K.
,
Tani
,
T.
, and
Kamiya
,
N.
,
1998
, “
Step Structures and Dislocations of SiC Single Crystals Grown by Modified Lely Method
,”
J. Cryst. Growth
,
191
(
1–2
), pp.
84
91
.
9.
Wellmann
,
P.
,
Herro
,
Z.
,
Winnacker
,
A.
,
Pusche
,
R.
,
Hundhausen
,
M.
,
Masri
,
P.
,
Kulik
,
A.
,
Bogdanov
,
M.
,
Karpov
,
S.
,
Ramm
,
M.
, and
Makarov
,
Y.
,
2005
, “
In Situ Visualization of SiC Physical Vapor Transport Crystal Growth
,”
J. Cryst. Growth
,
275
(
1–2
), pp.
E1807
E1812
.
10.
Dhanaraj
,
G.
,
Dudley
,
M.
,
Ma
,
R. H.
,
Zhang
,
H.
, and
Prasad
,
V.
,
2004
, “
Design and Fabrication of Physical Vapor Transport System for the Growth of SiC Crystals
,”
Rev. Sci. Instrum.
,
75
(
9
), pp.
2843
2847
.
11.
Hofmann
,
D.
,
Eckstein
,
R.
,
Kolbl
,
M.
,
Makarov
,
Y.
,
Muller
,
S. G.
,
Schmitt
,
E.
,
Winnacker
,
A.
,
Rupp
,
R.
,
Stein
,
R.
, and
Volkl
,
J.
,
1997
, “
SiC-Bulk Growth by Physical-Vapor Transport and Its Global Modelling
,”
J. Cryst. Growth
,
174
(
1–4
), pp.
669
674
.
12.
Selder
,
M.
,
Kadinski
,
L.
,
Durst
,
F.
,
Straubinger
,
T.
, and
Hofmann
,
D.
,
1999
, “
Numerical Simulation of Global Heat Transfer in Reactors for SiC Bulk Crystal Growth by Physical Vapor Transport
,”
Mater. Sci. Eng.: B
,
61
(2), pp.
93
97
.
13.
Chen
,
X. J.
,
Liu
,
L. J.
,
Tezuka
,
H.
,
Usuki
,
Y.
, and
Kakimoto
,
K.
,
2008
, “
Optimization of the Design of a Crucible for a SiC Sublimation Growth System Using a Global Model
,”
J. Cryst. Growth
,
310
(
7–9
), pp.
1810
1814
.
14.
Wang
,
X. L.
,
Cai
,
D.
, and
Zhang
,
H.
,
2007
, “
Increase of SiC Sublimation Growth Rate by Optimizing of Powder Packaging
,”
J. Cryst. Growth
,
305
(
1
), pp.
122
132
.
15.
Liu
,
X.
,
Chen
,
B. Y.
,
Song
,
L. X.
,
Shi
,
E. W.
, and
Chen
,
Z. Z.
,
2010
, “
The Behavior of Powder Sublimation in the Long-Term PVT Growth of SiC Crystals
,”
J. Cryst. Growth
,
312
(
9
), pp.
1486
1490
.
16.
Chen
,
X. J.
,
Nishizawa
,
S.
, and
Kakimoto
,
K.
,
2010
, “
Numerical Simulation of a New SiC Growth System by the Dual-Directional Sublimation Method
,”
J. Cryst. Growth
,
312
(
10
), pp.
1697
1702
.
17.
Gao
,
B.
,
Chen
,
X. J.
,
Nakano
,
S.
,
Nishizawa
,
S.
, and
Kakimoto
,
K.
,
2010
, “
Analysis of SiC Crystal Sublimation Growth by Fully Coupled Compressible Multi-Phase Flow Simulation
,”
J. Cryst. Growth
,
312
(
22
), pp.
3349
3355
.
18.
Meyer
,
C.
, and
Philip
,
P.
,
2005
, “
Optimizing the Temperature Profile During Sublimation Growth of SiC Single Crystals: Control of Heating Power, Frequency, and Coil Position
,”
Cryst. Growth Des.
,
5
(
3
), pp.
1145
1156
.
19.
Knippenberg
,
W. F.
,
1963
,
Growth Phenomena in Silicon Carbide
,
Echt, Valkenburg
, The Netherlands.
20.
Raback
,
P.
,
Yakimova
,
R.
,
Syvajarvi
,
M.
,
Nieminen
,
R.
, and
Janzen
,
E.
,
1999
, “
A Practical Model for Estimating the Growth Rate in Sublimation Growth of SiC
,”
Mater. Sci. Eng.: B
,
61
(2), pp.
89
92
.
21.
Ma
,
R. H.
,
Zhang
,
H.
,
Prasad
,
V.
, and
Dudley
,
M.
,
2002
, “
Growth Kinetics and Thermal Stress in the Sublimation Growth of Silicon Carbide
,”
Cryst. Growth Des.
,
2
(
3
), pp.
213
220
.
22.
Muller
,
S. G.
,
Glass
,
R. C.
,
Hobgood
,
H. M.
,
Tsvetkov
,
V. F.
,
Brady
,
M.
,
Henshall
,
D.
,
Malta
,
D.
,
Singh
,
R.
,
Palmour
,
J.
, and
Carter
,
C. H.
,
2001
, “
Progress in the Industrial Production of SiC Substrates for Semiconductor Devices
,”
Mater. Sci. Eng.: B
,
80
(
1–3
), pp.
327
331
.
23.
Ma
,
R. H.
,
Zhang
,
H.
,
Dudley
,
M.
, and
Prasad
,
V.
,
2003
, “
Thermal System Design and Dislocation Reduction for Growth of Wide Band Gap Crystals: Application to SiC Growth
,”
J. Cryst. Growth
,
258
(
3–4
), pp.
318
330
.
24.
Ma
,
R. H.
,
Zhang
,
H.
,
Ha
,
S.
, and
Skowronski
,
M.
,
2003
, “
Integrated Process Modeling and Experimental Validation of Silicon Carbide Sublimation Growth
,”
J. Cryst. Growth
,
252
(
4
), pp.
523
537
.
25.
Pons
,
M.
,
Anikin
,
M.
,
Chourou
,
K.
,
Dedulle
,
J. M.
,
Madar
,
R.
,
Blanquet
,
E.
,
Pisch
,
A.
,
Bernard
,
C.
,
Grosse
,
P.
,
Faure
,
C.
,
Basset
,
G.
, and
Grange
,
Y.
,
1999
, “
State of the Art in the Modelling of SiC Sublimation Growth
,”
Mater. Sci. Eng.: B
,
61
(2), pp.
18
28
.
26.
Mercier
,
F.
,
Dedulle
,
J. M.
,
Chaussende
,
D.
, and
Pons
,
M.
,
2010
, “
Coupled Heat Transfer and Fluid Dynamics Modeling of High-Temperature SiC Solution Growth
,”
J. Cryst. Growth
,
312
(
2
), pp.
155
163
.
27.
Chen
,
Q. S.
,
Zhang
,
H.
,
Prasad
,
V.
,
Balkas
,
C. M.
,
Yushin
,
N. K.
, and
Wang
,
S.
,
2001
, “
Kinetics and Modeling of Sublimation Growth of Silicon Carbide Bulk Crystal
,”
J. Cryst. Growth
,
224
(
1–2
), pp.
101
110
.
28.
Geiser
,
J.
,
Klein
,
O.
, and
Philip
,
P.
,
2006
, “
Transient Numerical Study of Temperature Gradients During Sublimation Growth of SiC: Dependence on Apparatus Design
,”
J. Cryst. Growth
,
297
(
1
), pp.
20
32
.
29.
Klein
,
O.
, and
Philip
,
P.
,
2003
, “
Transient Numerical Investigation of Induction Heating During Sublimation Growth of Silicon Carbide Single Crystals
,”
J. Cryst. Growth
,
247
(
1–2
), pp.
219
235
.
30.
Biro
,
O.
, and
Preis
,
K.
,
1989
, “
On the Use of the Magnetic Vector Potential in the Finite-Element Analysis of Three-Dimensional Eddy Currents
,”
IEEE Trans. Magn.
,
25
(
4
), pp.
3145
3159
.
31.
Kitanin
,
E. L.
,
Ramm
,
M. S.
,
Ris
,
V. V.
, and
Schmidt
,
A. A.
,
1998
, “
Heat Transfer Through Source Powder in Sublimation Growth of SiC Crystal
,”
Mater. Sci. Eng.: B
,
55
(
3
), pp.
174
183
.
32.
Modest
,
M. F.
,
2003
,
Radiative Heat Transfer
,
Academic Press
, New York.
33.
Ma
,
R. H.
,
Chen
,
Q. S.
,
Zhang
,
H.
,
Prasad
,
V.
,
Balkas
,
C. M.
, and
Yushin
,
N. K.
,
2000
, “
Modeling of Silicon Carbide Crystal Growth by Physical Vapor Transport Method
,”
J. Cryst. Growth
,
211
(
1–4
), pp.
352
359
.
34.
Patankar
,
S. V.
,
1980
,
Numerical Heat Transfer and Fluid Flow
,
CRC Press
, Boca Raton, FL.
35.
Roy
,
A.
,
Mackintosh
,
B.
,
Kalejs
,
J. P.
,
Chen
,
Q. S.
,
Zhang
,
H.
, and
Prasad
,
V.
,
2000
, “
A Numerical Model for Inductively Heated Cylindrical Silicon Tube Growth System
,”
J. Cryst. Growth
,
211
(
1–4
), pp.
365
371
.
36.
Sparrow
,
E. M.
,
Eckert
,
E. R. G.
, and
Irvine
,
T. F.
,
1961
, “
The Effectiveness of Radiating Fins With Mutual Irradiation
,”
J. Aerosp. Sci.
,
28
(
10
), pp.
763
772
.
37.
Klein
,
O.
,
Philip
,
P.
,
Sprekels
,
J.
, and
Wilmanski
,
K.
,
2001
, “
Radiation- and Convection-Driven Transient Heat Transfer During Sublimation Growth of Silicon Carbide Single Crystals
,”
J. Cryst. Growth
,
222
(
4
), pp.
832
851
.
38.
Su
,
J.
,
Chen
,
X. J.
, and
Li
,
Y.
,
2014
, “
Numerical Design of Induction Heating in the PVT Growth of SiC Crystal
,”
J. Cryst. Growth
,
401
, pp.
128
132
.
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