Flow instability during crystal growth from the melt

Quality of semiconductor and oxide crystals grown from the melts in Czochralski crystal growth systems is significantly affected by the heat and mass transfer in the melts during growth. This paper reviews the present understanding of this heat and mass transfer, especially melt convection, from the results of flow visualization by using model and real semiconductor melts to the details of numerical calculation needed for quantitative modeling of melt convection. The characteristics of flow instabilities of melt convection with a low Prandtl number are also reviewed by focusing on the baroclinic, the Rayleigh-Benard, and thermoccapillary-Benard instabilities from the viewpoints of temperature and of the effect of rotation during crystal growth. The origin of the flow instabilities is also reviewed on the basis of geostrophic hydrodynamics, and the question whether silicon flow is completely turbulent or has an ordered structure is discussed. Magnetic suppression of melt flow is also reviewed, and some research on new approaches to growth from the melt including molecular dynamics and wavelet transformation will be introduced.