Heat and mass transfer during crystal growth

Quality of semiconductor and oxide crystals which are grown from the melts plays an important role for electronic and/or optical devices. The crystal quality is significantly affected by the heat and mass transfer in the melts during crystal growth in a growth furnace such as Czochralski or horizontal Bridgman methods. This paper reviews the present understanding of phenomena of the heat and mass transfer of the melts, especially instability of melt convection from the detailed numerical calculation, which helps to understand the melt convection visualized using X-ray radiography. Large scale simulation of melt convection during crystal growth is also reviewed. Characteristics of flow instabilities of melt convection with a low Prandtl number (ratio between momentum and thermal diffusivities) are also reviewed by focusing on the instabilities of baroclinic, the Rayleigh-Benard and the Marangoni-Benard, from the points of view of temperature, rotating and/or magnetic field effects during crystal growth. Oxygen concentration in grown crystals is also discussed how melt convection affects.