晶体生长工艺之定向凝固.ppt

文档介绍：晶体生长工艺之定向凝固
FEMAGSoft © 2013
Very accurate and efficient 3D prediction of the melt flow and the global heat transfer
DS process simulation
FEMAGSoft © 2013
Direct solidification of multi-crystalline silicon with a square crucible
Method: 1. Mapping of the square cross-section onto a circle
2. Use of a particular expansion technique for all fields (velocity, pressure, temperature) in the transformed domain
Hypothesis: square symmetry of all averaged fields
Objective: global, quasi-steady or time-dependent
calculations at a reasonable cost
DS process simulation (cont’d)
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y
Y
x
X
z = x + iy
Z = X + iY
Real square cross-section
Transformed circular cross-section
DS process simulation (cont’d)
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Next steps
Write Z = X+iY = r eiq in the transformed domain
and expand all unknown fields as Fourier series
of cos q and sin q
Then put all equations in a weak form and make the problem discrete using a mixed spectral – finite element technique (using a 2D mesh)
This results in a system whose size is that of the 2D system multiplied by the number of Fourier modes considered and hence in a dramatic system size reduction.
DS process simulation (cont’d)
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Time-dependent simulation of DS process
Filling of a 20 cm side square crucible (“Minicaster” furnace)
Evolution of the temperature, velocity, oxygen and carbon concentration fields.
DS process simulation (cont’d)
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Evolution of temperature distribution
DS process simulation (cont’d)
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Evolution of oxygen distribution
Oxygen in the melt
Oxygen in the crystal
DS process simulation (cont’d)
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Evolution of carbon distribution
Carbon in the melt
Carbon in the crystal
DS process simulation (cont’d)
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Comparison of 3D FEM-spectral and 3D Cartesian simulations
DS process simulation (cont’d)
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Same isosurfaces :
- Colored : 3D FEM-Spectral
- Gray : 3D Cartesian
Isotherms