The mechanism of dopant transport and segregation in high-pressure liquid-encapsulated Czochralski (HPLEC) grown III-V compound crystals (e.g., GaAs, InP) has been numerically studied using an integrated model, MASTRAPP. The model approximates the melt flow in the crucible as a quasi-steady-state, laminar, and axisymmetric flow, but the gas flow is considered as turbulent. Based on the physics of the growth process, a two-time-level scheme has been implemented where the dopant transport and growth are simulated at a smaller time scale while flow and temperature solutions are obtained from quasi-static calculations. Detailed numerical analyses are performed for the conditions of pure crystal rotation, pure thermally driven natural convection, and pure crucible rotation as well as for mixed flow with all of these forces present simultaneously. The dopant transport and segregation in these cases are well correlated to the corresponding melt flow pattern. Very weak radial segregation is predicted for pure crystal rotation because the resulting melt flow leads to a fairly flat solute boundary layer. The natural convection, on the other hand, produces a nonuniform boundary layer along the melt/crystal interface. This leads to a strong radial segregation with a high concentration along the central axis of the crystal. The crucible rotation has a similar effect. The combined effect of all of these flow mechanisms produces a strong radial segregation, whose extent depends on the relative strength of the driving forces. In all of these cases, strong melt flows lead to thin boundary layers that result in decreased longitudinal segregation. The predictions agree well with the experimental observations reported in the literature.
Interfacial flow dynamic micro-response and spatiotemporal evolution of flow pattern for thermocapillary–buoyancy convection in a liquid bridge