A curvilinear finite volume-based numerical methodology has been developed that can be effectively used for simulation of the Bridgman and Czochralski (Cz) crystal growth processes. New features of grid generation have been devised and added to the original formulation (Zhang et al., 1995, 1996) to make it suitable for global modeling. The numerical model can account for convection in both the melt and the gas phases, convection/radiation in the furnace, and conduction in all solid components. Results for Bridgman growth show that the flow pattern and interface shape strongly depend on thermal conductivities of the crystal, melt, and ampoule materials. Transient simulations have been performed for the growth of Bismuth crystal in a Bridgman-Stockbarger system and the growth of GaAs crystal using liquid-encapsulated Czochralski (LEC) technique. This is the first time that a global high-pressure LEC model is able to account for convective flows and heat transfer and predict the interface shape and its dynamics.
Issue Section:
Featured Section—Heat Transfer in Manufacturing
Topics:
Crystal growth,
Simulation,
Crystals,
Convection,
Flow (Dynamics),
Shapes,
Computer simulation,
Dynamics (Mechanics),
Furnaces,
Gallium arsenide,
Heat conduction,
Heat transfer,
High pressure (Physics),
Manufacturing,
Materials processing,
Mesh generation,
Modeling,
Radiation (Physics),
Transients (Dynamics)
1.
Adornato
P. M.
Brown
R. A.
1987
, “Convection and Segregation in Directional Solidification of Dilute and Non-dilute Binary Alloys: Effects of Ampoule and Furnace Design
,” J. Crystal Growth
, Vol. 80
, pp. 155
–190
.2.
Baumgartl
J.
Bune
A.
Koai
K.
Mu¨ller
G.
1993
, “Global Simulation of Heat Transport, Including Melt Convection in a Czochralski Crystal Growth Process—Combined Finite Element/Finite Volume Approach
,” Materials Science and Engineering
, Vol. A173
, pp. 9
–13
.3.
Brown
R. A.
1988
, “Theory of Transport Processes in Single Crystal Growth from the Melt
,” AIChE J.
, Vol. 34
, No. 6
, pp. 881
–911
.4.
Carslaw, H. S., and Jaeger, J. C., 1959, Conduction of Heat in Solids, Oxford University Press, London.
5.
Dupret, F., and van den Bogaert, N., 1994, “Modelling Bridgman and Czochralski Growth,” Handbook of Crystal Growth, Vol. 2b, D. T. J. Hurle, ed., North-Holland, New York.
6.
Dupret
F.
Necodeme
P.
Ryckmans
Y.
Wouters
P.
Crochet
M. J.
1990
, “Global Modeling of Heat and Mass Transfer in Crystal Growth Furnaces
,” Int. J. Heat Mass Transfer
, Vol. 33
, pp. 1849
–1871
.7.
Fainberg
J.
Leister
H.-J.
Mu¨ller
G.
1997
, “Numerical Simulation of the LEC-growth of GaAs Crystals with Account of High Pressure Gas Convection
,” J. Crystal Growth
, Vol. 180
, pp. 517
–523
.8.
Glicksman
M. E.
Coriell
S. R.
McFadden
G. B.
1986
, “Interaction of Flows with the Crystal-Melt Interface
,” Ann. Rev. Fluid Mech.
, Vol. 18
, pp. 307
–335
.9.
Liang
M. C.
Lan
C. W.
1996
, “Three-dimenstional Convection and Solute Segregation in Vertical Bridgman Crystal Growth
,” J. Crystal Growth
, Vol. 167
, pp. 320
–332
.10.
Lide, D. R., 1995, Handbook of Chemistry and Physics, 76th Ed., CRC Press, New York.
11.
Kim
D. H.
Brown
R. A.
1991
, “Modelling of the Dynamics of HgCdTe Growth by the Vertical Bridgman Method
,” J. Crystal Growth
, Vol. 114
, pp. 441
–434
.12.
Kinney
T. A.
Brown
R. A.
1993
, “Application of Turbulence Modeling to the Integrated Hydrodynamic Thermal-Capillary Model of Czochralski Crystal Growth of Silicon
,” J. Crystal Growth
, Vol. 132
, 551
–574
.13.
Koai
K.
Sonnenberg
K.
Wenzl
H.
1994
, “Influence of Crucible Support and Radial Heating on the Interface Shape during Vertical Bridgman GaAs Growth
,” J. Crystal Growth
, Vol. 137
, pp. 59
–63
.14.
Maruyama
S.
Aihara
T.
1994
, “Radiation Heat Transfer of a Czochralski Growth Furnace with Arbitrary Specular and Diffuse Surfaces
,” Int. J. Heat Mass Transfer
, Vol. 37
, pp. 1723
–1731
.15.
Ouyang
H.
Shyy
W.
1996
, “Multizone Simulation of the Bridgman Growth Process of β-NiAl Crystal
,” Int. J. Heat Mass Transfer
, Vol. 39
, No. 10
, pp. 2039
–2051
.16.
Ramachandran
P. A.
Dudukovic
M. P.
1985
, “Simulation of Temperature Distribution in Crystals Grown by Czochralski Method
,” J. Crystal Growth
, Vol. 71
, pp. 399
–408
.17.
Santailler, J. L., Duffar, T., Theodore, F., Boiton, P., Barat, C., Angelier, B., Giacommentti, N., Dusserre, P., and Nabot, J. P., 1996, “Some Features of Two Commercial Softwares for the Modeling of Bulk Crystal Growth Processes,” 2nd Int. Conf. on Modeling in Crystal Growth, Durbuy, Belguim.
18.
Tsukada
T.
Kakinoki
K.
Hozawa
M.
Imaishi
N.
1995
, “Effect of Internal Radiation within Crystal and Melt on Czochralski Crystal Growth of Oxide
,” Int. J. Heat Mass Transfer
, Vol. 38
, No. 15
, pp. 2707
–2714
.19.
Zhang
H.
Moallemi
M. K.
1995
, “A Multizone Adaptive Grid Generation Technique for Simulation of Moving and Free Boundary Problems
,” Num. Heat Transfer
, Vol. B27
, pp. 255
–276
.20.
Zhang
H.
Prasad
V.
1995
, “A Multizone Adaptive Process Model for Crystal Growth at Low and High Pressures
,” J. Crystal Growth
, Vol. 155
, pp. 47
–65
.21.
Zhang
H.
Prasad
V.
Moallemi
M. K.
1996
, “A Numerical Algorithm Using Multizone Adaptive Grid Generation for Multiphase Transport Processes with Moving and free Boundaries
,” Num. Heat Transfer
, Vol. B29
, pp. 399
–421
.22.
Zheng
L.
Larson
D. J.
1997
, “Thermoelectric Effects on Interface Demarcation and Directional Solidification in Bismuth
,” J. Crystal Growth
, Vol. 180
, pp. 293
–304
.23.
Zou
Y. F.
Zhang
H.
Prasad
V.
1996
, “Dynamics of melt-crystal interface and thermal stresses in Czochralski crystal growth processes
,” J. Crystal Growth
, Vol. 166
, pp. 476
–482
.
This content is only available via PDF.
Copyright © 1998
by The American Society of Mechanical Engineers
You do not currently have access to this content.
