Quasi-steady-state numerical simulation of Czochralski single crystal growth

We consider the steady-state growth of a single crystal by the liquid encapsulated Czochralski method. The mathematical model accounts for heat transfer in the crystal, melt and encapsulant, radiative heat exchange between the crucible and the surrounding furnace, formation of the growth interface and the melt/encapsulant interface meniscus, release of the latent heat during the phase transition. The time history of the growth is reconstructed from a sequence of steady state calculations with decreasing melt depth. The numerical method is based on explicit interface tracking. The employed computational procedure ensures global conservation of thermal energy. The response of prototype growth system for changes in pull rate or heater temperature is examined numerically.