Mathematical Model for the Simulation of Crystallization of CdTe in a Vertical Bridgman Furnace.
- PDF / 1,081,715 Bytes
- 6 Pages / 414.72 x 648 pts Page_size
- 44 Downloads / 240 Views
Mathematical Model for the Simulation of Crystallization of CdTe in a vertical Bridgman Furnace. Ch.Steer, M.Hage-Ali, P.Siffert CNRS, Lab. Phase, F-67037 Strasbourg CEDEX, Tlhance
ABSTRACT Temperature measurements in a crystal growth ampoule of CdTe (Cadmium Telluride) are very difficult. Mathematical simulation is a very powerful tool to predict the behavior and temperature distribution during crystal growth. We applied this technique to the bulk growth of large single crystals of CdTe. The simulation revealed that for CdTe, it is possible to create a convex interface shape during growth, necessary for single crystal growth. The controlling parameter is the temperature profile along the ampoule. The temperature gradient is rather meaningless, as we can show with our simulations. We will present some crystals grown under good and bad thermal conditions.
Introduction Mathematical models present great advantages over try and error experiments:
"*identical starting and boundary conditions for every experiment "* no interference of the system while probing or measuring "* every point can be probed easily "* simulation is much quicker than real crystal growth runs (some seconds
compared to
4 weeks for THM experiments)
"* less expensive than real growth runs These features make computer simulations to a appropriate tool to optimize the crystal growth conditions. We used the simulation tool to optimize the growth of CdTe singlecrystals, but it may be used for the optimization of every other material. CdTe is known to be a very difficult material for crystallization. It is very aggressive in the molten state, even platinum thermocouple are easily dissolved. Protection by quartz capillaries is possible, but the ampoule will be very fragile and the perturbation of the temperature distribution is considerable. The Mathematical Model of Heat Transfer The purpose of the finite elements model is to study the influence of the external temperature profile along the ampoule on the interface shape. The interface shape should be convex to favor single crystalline growth. Some remarkable analytical approaches were made by Naumann [2]. Analytical approaches are very difficult due to the nonlinearities during the phase transition at solidification and radiation heat transfer. Models using finite elements approach don't have this drawback [3]. We used a finite elements approach [4] to have full flexibility in choosing a temperature profile. Our model is based on basic heat conduction, considering the Mat. Res. Soc. Symp. Proc. Vol. 302. ©1993 Materials Research Society
238
80
75
1100
7065-
1098
6055 -
1096
50-50-
0
75-
75-
70-
7 70
10 1100
65-
65-
1098
60"
6055 t
55-
1092
35"N30-
,~
1096
_•50-0
1094- -
545S40
54545 -
25-6
35-
N30-•
25-
25
1086
2015"
200 15---
10
10
..
1084
-
5-
o oo
35-
S30-
_1088
2015--
194
540
V)40-
-
M0-
80'
5-
1090 -1088-
10661084
5Tmelt
0
-18-12 -6
0
6
R [mrn]
12 18
0-,
1040 1060 10o0 1100 1120 T [grad C]
0
-18-12 -6 0
6
R [mrm]
12 18
Fi
Data Loading...
