This paper presents a model for the unsteady species transport for the growth of alloyed semiconductor crystals during the vertical Bridgman-Stockbarger process with a steady axial magnetic field. During growth of alloyed semiconductors such as germanium-silicon (GeSi) and mercury-cadmium-telluride (HgCdTe), the solute’s concentration is not small, so that density differences in the melt are very large. These compositional variations drive compositionally driven buoyant convection, or solutal convection, in addition to thermally driven buoyant convection. These buoyant convections drive convective transport, which produces nonuniformities in the concentration in both the melt and the crystal. This transient model predicts the distribution of species in the entire crystal grown in a steady axial magnetic field. The present study presents results of concentration in the crystal and in the melt at several different stages during crystal growth.

1.
Walker
,
J. S.
,
Henry
,
D.
, and
BenHadid
H.
, 2002, “
Magnetic Stabilization of the Buoyant Convection in the Liquid-Encapsulated Czochralski Process
,”
J. Cryst. Growth
0022-0248,
243
(
1
), pp.
108
116
.
2.
Flemings
,
M. C.
, 1974,
Solidification Processing
,
McGraw-Hill
, New York.
3.
Khine
,
Y. Y.
,
Banish
,
R. M.
, and
Alexander
,
J. I. D.
, 2002, “
Convective Effects during Diffusivity Measurements in Liquids with an Applied Magnetic Field
,”
Int. J. Thermophys.
0195-928X,
23
(
3
), pp.
649
666
.
4.
Watring
,
D. A.
, and
Lehoczky
,
S. L.
, 1996, “
Magneto-hydrodynamic Damping of Convection during Vertical Bridgman-Stockbarger Growth of HgCdTe
,”
J. Cryst. Growth
0022-0248,
167
(
3∕4
), pp.
478
487
.
5.
Ramachandran
,
N.
, and
Watring
,
D. A.
, 1997, “
Convection Damping by an Axial Magnetic Field during Growth of HgCdTe by Vertical Bridgman Method — Thermal Effects
,”
35th AIAA Aerospace Sciences Meeting and Exhibit
, Paper No. 97-0450,
Reno, NV
.
6.
Alboussière
,
T.
,
Moreau
,
R.
, and
Camel
,
D.
, 1991, “
Influence of a Magnetic Field on the Solidification of Metallic Alloys
,”
Comptes Rendus de l'Academie des Sciences
,
313
(
7
), pp.
749
755
.
7.
Ma
,
N.
, and
Walker
,
J. S.
, 2000, “
A Model of Dopant Transport during Bridgman Crystal Growth with Magnetically damped Buoyant Convection
,”
ASME J. Heat Transfer
0022-1481,
122
(
1
), pp.
159
164
.
8.
Hart
,
J. E.
, 1971, “
On Sideways Diffusive Instability
,”
J. Fluid Mech.
0022-1120,
49
, pp.
279
288
.
9.
Ma
,
N.
, 2003, “
Solutal Convection during Growth of Alloyed Semiconductor Crystals in a Magnetic Field
,”
J. Thermophys. Heat Transfer
0887-8722,
17
(
1
), pp.
77
81
.
10.
Wang
,
X.
, and
Ma
,
N.
, 2004, “
Strong Magnetic Field Asymptotic Model for Binary Alloyed Semiconductor Crystal Growth
,”
J. Thermophys. Heat Transfer
0887-8722,
18
(
4
), pp.
476
480
.
11.
Liu
,
Y.
,
Dost
,
S.
,
Lent
,
B.
, and
Redden
,
R. F.
, 2003, “
A Three Dimensional Numerical Simulation Model for the Growth of CdTe Single Crystals by the Traveling Heater Method under Magnetic Field
,”
J. Cryst. Growth
0022-0248,
254
(
3∕4
), pp.
285
297
.
12.
Timchenko
,
V.
,
Chen
,
P. Y. P.
,
Leonardi
,
E.
,
Davis
,
G. D.
, and
Abbaschian
,
R.
, 2002, “
A Computational Study of Binary Alloy Solidification in the MEPHISTO Experiment
,”
Int. J. Heat Fluid Flow
0142-727X,
23
(
3
), pp.
258
268
.
13.
Brailovskaya
,
V. A.
,
Zilberberg
,
V. V.
, and
Feoktistova
,
L. V.
, 2000, “
Numerical Investigation of Natural and Forced Solutal Convection above the Surface of a Growing Crystal
,”
J. Cryst. Growth
0022-0248,
210
(4)
, pp.
767
771
.
14.
LeMarec
,
C.
,
Guerin
,
R.
, and
Haldenwang
,
P.
, 1997, “
Pattern Study in the 2-D Solutal Convection above a Bridgman-type Solidification Front
,”
Phys. Fluids
1070-6631,
9
(11)
, pp.
3149
3161
.
15.
LeMarec
,
C.
,
Guerin
R.
, and
Handenwang
,
P.
, 1996, “
Radial Macrosegregation Induced by 3D Patterns of Solutal Convection in Upward Bridgman Solidification
,”
J. Cryst. Growth
0022-0248,
169
(1)
, pp.
147
160
.
16.
Garandet
,
J. P.
, and
Alboussière
,
T.
, 1999, “
Bridgman Growth: Modelling and Experiments
,”
The Role of Magnetic Fields in Crystal Growth, Progress in Crystal Growth and Characterization of Materials
Vol.
38
,
K. W.
Benz
, ed.,
Elsevier Science Publishers
, New York, pp.
73
132
.
17.
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 Science Publishers
, New York, pp.
195
213
.
18.
Ma
,
N.
, and
Walker
,
J. S.
, 1997, “
Dopant Transport during Semiconductor Crystal Growth with Magnetically Damped Buoyant Convection
,”
J. Cryst. Growth
0022-0248,
172
(1∕2)
, pp.
124
135
.
19.
Ma
,
N.
, and
Walker
,
J. S.
, 2001, “
Inertia and Thermal Convection during Crystal Growth with a Steady Magnetic Field
,”
J. Thermophys. Heat Transfer
0887-8722,
15
(1)
, pp.
50
54
.
20.
Hirtz
,
J. M.
, and
Ma
,
N.
, 2000, “
Dopant Transport during Semiconductor Crystal Growth. Axial Versus Transverse Magnetic Fields
,”
J. Cryst. Growth
0022-0248,
210
(4)
, pp.
554
572
.
21.
Ma
,
N.
, and
Walker
,
J. S.
, 2000, “
A Parametric Study of Segregation Effects during Vertical Bridgman Crystal Growth with an Axial Magnetic Field
,”
J. Cryst. Growth
0022-0248,
208
(1∕4)
, pp.
757
771
.
You do not currently have access to this content.