Abstract

This paper presents a model for the unsteady transport of a dopant during the vertical Bridgman crystal growth process with a planar crystal-melt interface and with an externally applied axial magnetic field. This dilute mass transport depends on the convective and diffusive mass transport of the dopant. The convective mass transport is driven by buoyant convection in the melt, which produces nonuniformities in the concentration in both the melt and the crystal. This convective transport is significant even for a strong magnetic field Bo=2 T. However, the electromagnetic damping of the melt motion produces a local region adjacent to the crystal-melt interface which is dominated by diffusion. Thus, this melt solidifies with a relatively radially uniform concentration, so that the radial distribution of dopants in the crystal is also relatively radially uniform. The transient model predicts the dopant distribution in the entire crystal. [S0022-1481(00)02301-X]

Issue Section:
Heat Transfer in Manufacturing
Keywords:
heat transfer, magnetohydrodynamics, mass transfer, crystal growth from melt, convection, magnetic field effects, Heat Transfer, Magnetohydrodynamics, Mass Transfer
Topics:
Convection, Crystal growth, Crystals, Magnetic fields, Diffusion (Physics), Heat transfer, Magnetohydrodynamics, Mass transfer, Flow (Dynamics)
1.
Chedzey
,
H. A.
, and
Hurle
,
D. T. J.
,
1966
, “
Avoidance of Growth-Striae in Semiconductor and Metal Crystals Grown by Zone-Melting Techniques
,”
Nature (London)
,
210
, pp.
933
–
934
.
2.
Utech
,
H. P.
, and
Flemings
,
M. C.
,
1966
, “
Elimination of Solute Banding in Indium Antimonide Crystals by Growth in a Magnetic Field
,”
J. Appl. Phys.
,
7
, pp.
2021
–
2024
.
3.
Kim
,
D. H.
,
Adornato
,
P. M.
, and
Brown
,
R. A.
,
1988
, “
Effect of Vertical Magnetic Field on Convection and Segregation in Vertical Bridgman Crystal Growth
,”
J. Cryst. Growth
,
89
, pp.
339
–
356
.
4.
Ma, N., and Walker, J. S., 1997, “Magnetic Damping of Melt Motions During Bridgman Crystal Growth in Microgravity,” SPIE International Symposium on Optical Science, Engineering and Instrumentation: Materials Research in Low Gravity, Vol. 3123, San Diego, CA, pp. 254–261.
5.
Ma, N., and Walker, J. S., 1999, “Segregation During Bridgman Crystal Growth in Space With an Axial Magnetic Field,” Proceedings of the International Colloquium: Modelling of Material Processing, Riga, Latvia, pp. 12–16.
6.
Ma
,
N.
, and
Walker
,
J. S.
,
1997
, “
Validation of Strong Magnetic Field Asymptotic Models for Dopant Transport During Semiconductor Crystal Growth
,”
J. Cryst. Growth
,
180
, pp.
401
–
409
.
7.
Kaiser
,
Th.
, and
Benz
,
K. W.
,
1998
, “
Floating-Zone Growth of Silicon in Magnetic Fields. Part III. Numerical Solution
,”
J. Cryst. Growth
,
183
, pp.
564
–
572
.
8.
Ma
,
N.
, and
Walker
,
J. S.
,
1997
, “
Dopant Transport During Semiconductor Crystal Growth With Magnetically Damped Buoyant Convection
,”
J. Cryst. Growth
,
172
, pp.
124
–
135
.
9.
Hurle, D. T. J., and Series, R. W., 1994, “Use of a Magnetic Field in Melt Growth,” Handbook of Crystal Growth, 2A, pp. 261–285.
10.
Walker, J. S., 1999, “Models of Melt Motion, Heat Transfer and Mass Transport During Crystal Growth With Strong Magnetic Fields,” The Role of Magnetic Fields in Crystal Growth: Progress in Crystal Growth and Characterization of Materials, Vol. 38, K. W. Benz ed., Elsevier, Amsterdam, pp. 185–213.
11.
Alboussie`re
,
T.
,
Neubrand
,
A. C.
,
Garandet
,
J. P.
, and
Moreau
,
R.
1997
, “
Segregation During Horizontal Bridgman Growth Under an Axial Magnetic Field
,”
J. Cryst. Growth
,
181
, pp.
133
–
144
.
12.
Watring, D. A., 1997, “Effects of Static Axial Magnetic Fields on Directional Solidification of HgCdTe (Mercury Cadmium Telluride, Mass Transfer, Microgravity),” Ph.D. dissertation, Massachusetts Institute of Technology, Cambridge, MA.
13.
Hjellming
,
L. N.
, and
Walker
,
J. S.
,
1987
, “
Melt Motion in a Czochralski Puller With an Axial Magnetic Field: Motion due to Buoyancy and Thermocapillarity
,”
J. Fluid Mech.
,
182
, pp.
335
–
368
.
14.
Ma
,
N.
, and
Walker
,
J. S.
,
1996
, “
Magnetic Damping of Buoyant Convection During Semiconductor Crystal Growth in Microgravity. Continuous Random g-Jitters
,”
Phys. Fluids
,
8
, pp.
944
–
953
.
15.
Adornato
,
P. M.
, and
Brown
,
R. A.
,
1987
, “
Convection and Segregation in Directional Solidification of Dilute and Non-Dilute Binary Alloys: Effects of Ampoule and Furnace Design
,”
J. Cryst. Growth
,
80
, pp.
155
–
190
.
16.
Ramachandran, N., and Watring, D. A., 1997, “Convection Damping by an Axial Magnetic Field During the Growth of HgCdTe by Vertical Bridgman Method—Thermal Effects,” 35th AIAA Aerospace Sciences Meeting and Exhibit, Paper No. 97-0450.
17.
Moreau, R., 1990, Magnetohydrodynamics, Kluwer, Boston.
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