2D modeling of Czochralski crystal growth

Limitations of the 2D approach
Phase boundary crystal-melt
Boundary conditions for velocity components
Checklist for model preparation
Execution

The 2D Cz modeling can be broken into particular tasks of:

The first two tasks are usually strongly connected with each other and should be considered in the coupled mode. Additionally the global heat transport in the whole furnace should be computed together with the melt flow. The temperature distribution at the boundary of the melt volume is first resulted from the thermal computation with conduction and radiation in the environment of the crystal and the melt but without the detailed effect of the convective heat transfer in the melt. The account of the convective effect changes the boundary temperature, that in turn changes the characteristic Grashof number of the melt flow and possibly the direction of the heat flux in the adjacent regions.

Once the melt flow and the phase boundary are computed, the defects in the crystal and the species transport in the melt can be executed in the postprocessor mode, because they have no back influence on the melt flow. This assumption is true in most of cases for the species transport, obvious the thermosolutal effect and effect on the transport properties of the melt or on the thermal expansion coefficient is theoretically possible.

The computation of the species transport or of more general computation with chemical reactions underlie to the common rules described in the other sections. The only speciality of the species transport in the melt is, the segregation boundary condition should be applied to the boundary crystal - melt. The numerical parameter of the segregation boundary condition is the segregation coefficient which is entered into the model as a melt material property.

Related Procedures

Czochralski setup parameters