High-pressure liquid-encapsulated Czochralski growth (HPLEC) of InP
Unlike the conventional Czochralski process, modeling of high-pressure liquid-encapsulated Czochralski (HPLEC) method is particularly complicated, because account must be taken of turbulent gas and melt convection as well as of the encapsulant preventing phosphorus evaporation from the melt. The heat transfer interactions between the recirculating gas, the B2O3 layer and the crystal is very complex and requires especially accurate simulation.
To study the influence of the gas flow on the thermal field in the crystal, we used a 3D unsteady model that can directly resolve turbulent eddies and their contribution to the heat exchange. We considered gas convection together with heat transfer in the crystal and encapsulant flow in an industrial HPLEC InP set-up, paying special attention to the temperature gradients in the crystal as they determine the thermal stresses.
The computational procedure included preliminary simulation of global heat transfer in the whole set-up (Figure 1) with the account of all the heat exchange modes — convective, radiative and conductive — performed using a 2D axisymmetric steady-state model. The resulting thermal field was used to set boundary conditions for the 3D computational domain, see Figure 2.
The results demonstrate an essentially non-axisymmetrical flow structure with multi-scale vortices in different areas of the computational domain. The solution is generally characterized by an upward flow along the pulling rod, a downward flow along the cool external wall and two re-circulating zones in the area between the crystal and the crucible, with the most intensive unsteady convection observed at the center of the growth set-up, around the crystal and the pulling rod, see Figures 3 (a, b).
 “Prediction of the melt/crystal interface geometry in liquid encapsulated Czochralski growth of InP bulk crystals”, E.N. Bystrova, V.V. Kalaev, O.V. Smirnova, E.V. Yakovlev, Yu.N. Makarov, J. Crystal Growth, 250 (2003) pp. 189–194.
 “3D unsteady analysis of gas turbulent convection during HPLEC InP growth”, E.N. Bystrova, V.V. Kalaev, J. Crystal Growth, 287 (2006) pp. 275–280.