Research On The Marangoni-thermocapillary Convection In A Czochralski Pool With Bidirectional Temperature Gradients

The Czochralski(Cz) crystal growth technique is one of the most important methods of producing single crystals, which is the widely used method in industrial silicon single crystal growth. The melt flow plays a significant importance on the heat and mass transfer during the process of crystal growth. Furthermore, a more complicated melt flow is formed as a result of the combined actions of the thermal convection, forced convection as well as the surface tension driven flows. However, due to the effective acceleration of gravity, the acceleration of a few orders of magnitude decreases and the buoyancy convection is hard to occur. Here, the Marangoni or thermocapillary convection plays an important role on the crystal quality. The Marangoni convection is caused by the temperature gradient perpendicular to the free surface, and the thermocapillary convection is driven by the temperature parallel to the free surface.Over the past few decades, numerous works were devoted to investigate the characteristics of Marangnoni convection or thermocapillary convection. However, the vertical and horizontal temperature gradients usually coexist in many actual engineering applications. Thus, in this paper, we present a series of three dimensional numerical simulations in a shallow Czochralski configuration subject to a horizontal temperature gradient and a vertical temperature gradient with vertical heat flux. A fundamental understanding of the characteristics of the Marangoni-thermocapillary flow is gained. Besides, the respective roles of horizontal temperature gradient and vertical bottom heat flux in these convections are also discussed. The numerical results are as follows:The respective roles of the horizontal temperature difference and vertical bottom heat flux in convection are given: horizontal temperature difference(Ma) makes free surface temperature increase from the area near the crystal to the crucible side wall, which arises the surface fluid flows from the crucible side wall to the crystal, while the bottom heat flux makes free surface temperature decrease from the middle region of the pool to the crystal and crucible side wall. The relative strength of the two kinds of force determines the melt flow pattern.When a small heat flux is applied to the bottom of the crucible, the different melt flow patterns change with an increasing Ma. When Ma is small, namely Ma<Macr1, the flow is a two-dimensional axisymmetric steady flow. When Q plays a leading role in convection, the highest free surface temperature appears in the middle region of the pool, and the melt flow is characterized by two counter-rotating roll cells. On the other hand, the flow is characterized by two co-rotating roll cells when Ma dominates the convection. With a larger Macr1<Ma<Macr2 imposed at the bottom, the flow translate to three-dimensional steady state, the free surface temperature decline along the side wall of the crucible to the crystal side, and the surface temperature fluctuation emerge on the free surface with the spoken patterns. In addition, the number of the spokes remained about the same while the shape of the spokes changes with the increasing Ma or Q. A further increasing Ma>Macr2, the flow becomes unsteady. The instability of hydrothermal wave, double spokes pattern and petal type are obtained.