Modeling of SiC growth from solution by top seeded solution growth (TSSG).


Growth of large SiC boules by TSSG is a long term process in which graphite crucible is not just a container for the melt but also serves as the carbon source and, since the crucible walls are chemically active, their shape changes significantly due to the dissolution of carbon on one hand and deposition of carbon or poly-SiC on the other hand. Such crucible evolution involving changes in the wall thickness and in the shape of the inside wall does not only determine carbon concentration, but also affects thermal profile and the flow pattern. The latter is particularly important in case of RF heating when changes in the wall thickness will affest the Lorentz force distribution in the solution (see Figure 2).

Capabilities of CGSim include modeling of RF heating, Lorentz forces, solution and gas flow including accelerated crucible rotation technique (ACRT), stresses and dislocations. Chemical model implemented in CGSim offers the user a choice of readily available metal solvents (Me):  Cr, Ti, Al, Fe.  User can choose one of the available solvent metals and specify initial solution composition. Chemical boundary conditions are calculated automatically. Composition of solution that takes into account crucible dissolution is also calculated automatically as well as respective physical properties of the melt. As a result, SiC growth rate, crucible dissolution and re-crystallisation rates are calculated.

flow vectors and temperature distribution in TSSG of SiC

Figure 1. Typical flow vectors and temperature distribution

Detailed 2D-3D numerical study of the effect of graphite crucible shape change on the heat transfer, flow pattern, mass transport and electromagnetic field during TSSG of SiC is given in [1]. The graphite crucible shape at each stage of the growth process was calculated using 2D axisymmetric steady global heat and mass transfer model. The crucible geometries obtained for each stage were used for 3D unsteady simulations. The investigation revealed a significant effect of the shape change of the crucible on the temperature, Lorentz force distribution induced by the RF heating system, flow pattern, carbon concentration in the solution, and the growth rate of SiC, see Figure 2.

 Instantaneous velocity magnitude (m/s) distribution in TSSG of SiC

Figure 2. Instantaneous velocity magnitude (m/s) distribution along the vertical cross section and flow stream-lines in the solution for the growth process times of 0 (left) and 6 h (right) in the 3D computation

Effect of turbulence. Optimization of ACRT

Accelerated crucible rotation technique (ACRT) can be applied to the solution growth of SiC. In this technique, stirring is achieved by alternating the direction of crucible rotation, Figure 3. Intensified turbulence in the melt enhances convection and facilitates carbon transport to the seed crystal. Also, turbulence increases thermal uniformity in the melt which, in turn, contributes to more uniform dissolution rate of the crucible. Accurate modeling analysis of this technique requires the use of advanced turbulence models. In CGSim, LES turbulence model is implemented and used for modeling of ACRT.

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[1] “Numerical investigation of the effect of shape change in graphite crucible during top-seeded solution growth of SiC” by
Yuji Mukaiyama, Masaya Iizuka, Andrey Vorob’ev, Vladimir Kalaev, Journal of Crystal Growth 475 (2017) 178–185

Alternating the direction of crucible rotation in ACRT

Figure 3. Alternating the direction of crucible rotation in ACRT