Effect of the crucible/crystal rotation on thermocapillary instability in a shallow Czochralski configuration

Abstract

To understand the effects of crucible/crystal rotation on the instability of thermocapillary flow in a shallow Czochralski configuration, a series of linear stability analysis were performed by using Legendre spectral element method, and the energy analysis was applied to explore the instability mechanism. The results indicate that there are two types of instabilities with the increase of dimensionless crucible rotation rate ωc. Thermocapillary force and crucible rotation are the main causes of flow instability for low and high crucible rotation rate, respectively. In the interval 1627<ωc < 1822, with the increase of Marangoni number, three turning points were observed, indicating three transitions between two-dimensional axisymmetric steady flow and three-dimensional oscillatory flow due to the interaction between thermocapillary force and crucible rotation. For crystal rotation, two oscillatory modes for flow instability were observed. When the dimensionless crystal rotation rate is small (ωs < 3600), the oscillatory flow rotates in the opposite direction of the crystal rotation, but in the same direction in the case of large crystal rotation rate (ωs > 3600), and the thermocapillary force is the primary inducement of flow instability.