Three-dimensional unsteady convection in LiCaAlF6-Czochralski growth

Three-dimensional modelling of melt flow and segregation during Czochralski growth of GexSi1−x single crystals

“…As a result the average Si concentration at the growth interface decreases with time except during the initial stages where the average concentration increases for a short time interval after the initial sharp drop. The decrease in the average Si concentration at the growth interface will result in a gradual decrease in the Si content of the grown crystal along the growth direction as observed from the GeSi crystals grown on earth [7,8]. The variation of the average Si concentration at the growth interface involves small amplitude periodic oscillations at rather low values, T values of 6.0 K. At higher temperature differences the amplitude of the average Si concentration at the interface is higher which will result in higher Si inhomogeneities in the grown crystal.…”

“…These variations incorporate micro-segregations, the growth striations, into the grown crystal. Therefore, a large number of studies were conducted in order to understand the effect of Marangoni convection in Cz growth method [1][2][3][4][5][6][7]. The results show that even in low-Pr melts, the presence of Marangoni convection strongly affects the flow pattern and so ignoring Marangoni convection causes a large deviation of flow fields.…”

Global analysis of heat transfer in CZ crystal growth of oxide taking into account three-dimensional unsteady melt convection: Investigation of the coupling method between 2D and 3D models

“…In the x-y plane, also, the rotation of the flow and temperature fields can be observed, and the vortex center deviates from the central axis. The direction of such rotation is opposite to that of crystal rotation, and the period is approximately 30 s. Such a rotating nature of the flow and thermal fields in the melt was observed in the previous numerical studies [17,19], and the origin of the nature was considered to be a baroclinic instability. cross-correlation of instantaneous fluctuations of velocity and temperature as well as the averaged velocity field in the 3D model are transferred to the 2D model.…”

“…It is well known that oxide melt convection in a CZ crucible is generally unsteady and three-dimensional. In the last decade, extensive studies [13][14][15][16][17][18][19] on the unsteady three-dimensional convection in the oxide or fluoride melt have been carried out. For instance, it was demonstrated numerically that the axisymmetric flow and thermal fields in the CZ melt change to the non-axisymmetric and oscillatory ones as the crystal rotation rate increases, and that the fields in the melt iso-rotate or counter-rotate to the direction of crystal rotation depending on the crystal rotation rate.…”

Simulation of the thermal fluctuation according to the melt height in a CZ growth system

“…Evstratov et al [9] revealed the baroclinic instability on the melt periphery by varying the crucible rotation rate. Zhong Zeng et al [10] suggested that no surface wave structure is observed in CZIM (CZ model including Marangoni) model, however, surface wave structure appears in CZEM (CZ model excluding Marangoni convection) model for crystal rotation o s 4 32 rpm. Son and coauthors [11,12] and Nam et al [13] used Wood's metal (Pr =0.019) and numerical simulation.…”