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

A series of unsteady three-dimensional (3-D) numerical simulations were carried out to examine the flow field and the radial segregation of silicon (Si) in a GexSi1−x melt during Czochralski (Cz) process. In addition to the gravity driven natural convection (buoyant convection), the effect of convection driven by surface tension on the free surface of the melt was included in the model, by considering thermal, as well as solutal Marangoni convection. The concentration and flow fields during crystal growth are presented for several temperature differences (ΔT), driving buoyant and Marangoni convection. It was found that the maximum silicon concentration difference at the growth interface decreases as temperature difference increases due to higher flow velocities in the vicinity of the interface. However, temporal fluctuations of Si concentration at the interface increase at higher temperature differences. The effects of aspect ratio (Ar) were also considered in the model. It was found that the radial segregation of Si at the crystal-melt interface improves as the aspect ratio of the melt in the crucible decreases.