A global analysis of heat transfer in the CZ crystal growth of oxide: Recent developments in the model

In this paper, first, we reviewed our previous studies of the global analysis of heat transfer in an inductively heated Czochralski (CZ) furnace to grow oxide single crystals, in which it was assumed that the system is in a steady state and is axially symmetric. Particularly, it was emphasized that internal radiative heat transfer within oxide single crystals is important because oxide crystals are often semitransparent to infrared radiation. The results of the global analysis revealed that the melt/crystal interface shape is strongly affected by the absorption coefficient of such crystals as well as melt convection. Next, a new simple global model, in which unsteady, three-dimensional melt convection is taken into account in addition to radiative heat transfer in such crystals, is introduced. Here, it was shown numerically that when the crystal rotational Reynolds number is relatively large, melt convection becomes unsteady and three dimensional.