Fig. 1. The computational grid and the temperature distribution in the VCz system for 4" GaAs crystal growth

VCz growth of 100 mm GaAs

Numerical analysis of VCz and LEC growth is usually more complicated than the analysis of conventional CZ growth because of turbulent gas convection and the presence of encapsulant layer. The experimental regimes with high crucible rotation rates pose additional difficulties for numerical treatment because of strong velocity gradients.

Using CGSim software we performed 3D unsteady analysis of experimental regimes with high crucible rotation rates for 100 mm GaAs VCz crystal growth and studied the effect of the optical characteristics of the encapsulant on the melt flow and the crystallization front geometry.

Global heat exchange in the growth system has been simulated using 2D steady state approach. The computational grid and obtained temperature distribution in the CI 358 puller modified for 100 mm GaAs VCz growth are shown in Figure 1.

Fig. 2. The temperature distributions and the flow patterns obtained in the 2D computations. The encapsulant is considered an opaque (a) or transparent (b) medium.

Here we present computational results for two cases opposite with respect to the radiative properties of the encapsulant layer: opaque and completely transparent. Detailed temperature and velocity distributions for these two cases are presented in Figure 2, where one can see the effect of the encapsulant optical properties on both the temperature distribution and the melt flow.

Detailed analysis of heat transfer and melt/encapsulant flows in the crystallization zone was performed within a 3D unsteady approach. Computations were coupled with 2D steady computations of the global heat transfer trough iterational exchange of thermal boundary conditions.

Fig. 3. An example of the 3D block-structured computational grid for crystallization zone.

Fig. 4. The instantaneous flow patterns obtained in the 3D computations. The encapsulant is considered an opaque (a) or transparent medium (b).

Fig. 5. Comparison of the computed and experimental crystallization front shape. The encapsulant is considered an opaque (a) or transparent medium (b).

The results obtained using CGSim with the account of the turbulent melt convection and the encapsulant flow are generally in reasonable agreement with the experiment. However, if the encapsulant is assumed to be opaque, the interface deflection tends to be slightly overestimated, and vice versa: when encapsulant is simulated as competely transparent medium the interface deflection is slightly underestimated, see Figure 5.

References

1. "3D computations of melt convection andcrystallization front geometry during VCz GaAs growth", O.V. Smirnova, V.V. Kalaev, Yu.N. Makarov, Ch. Frank-Rotsch, M. Neubert, P. Rudolph, J. Crystal Growth, 266 (2004) pp. 67–73.