Research On Fundamental Characteristics Of Themocapillary-Marangoni-rotation Convection In A Czochralski Pool With Bidirectional Temperature Gradients Under Microgravity

The Czochralski process is one of the most important methods of crystal growth. It is widely used to obtain silicon single crystals, which the crucible is rotated to smooth the temperature field. The crucible is also heated from the side wall and the bottom. Thus, the melt flow is driven by the thermocapillary, centrifugal, buoyancy and Coriolis forces. These forces interact with each other in the melt and make the melt flow difficult to be controlled. In the microgravity and space environment, the buoyancy convection is gone. The other three forces drive the flow and have a huge effect on the quality of the crystal. Until now, most of the researches are focused on the melt flow which under the unidirectional temperature gradient. Yet, the horizontal and vertical temperature gradients always exist in the Cz crystal growth process at the same time. These two temperature gradients drive the melt flow from two different directions which make the flow much more complex than the unidirectional situation. In this paper, the themocapillary-Marangoni-rotation and the themocapillary-Marangoni convections of silicon melt in the Cz configuration were investigated by a series of three dimensional numerical simulations. The studies are focused on the respective roles of different driven forces. The basic flow pattern and instability characteristics are obtained. The critical Marangoni numbers(Mac) are gained. The transform disciplines of the different instability flow patterns are discussed. The reasons for flow instability are analyzed. The obtained results not just expand the theory of themocapillary-Marangoni and themocapillary-Marangoni-rotation convections but lay a solid theoretical foundation for the crystal growth process with or without gravity. The main results are as follows:Firstly, the basic flow of themocapillary-Marangoni convection is studied by the numerical simulations, the respective roles of horizontal temperature gradient(Ma) and the vertical bottom heat flux(Q) are discussed: with the increase of Ma and decrease of Q, the number of flow cells in the melt changes from two to three. The anticlockwise flow cell near the crystal is driven by the Ma and Q. The anticlockwise flow cell near the crucible wall and the clockwise flow cell are driven by Ma and Q respectively; these two flow cells inhibit each other. The flow strength of different flow cells decides the flow patterns of the basic flow. The basic flow changes into three-dimensional oscillatory flow when Ma increases to Mac. The Mac decreases significantly with the increase of Q.Secondly, the characteristics of three-dimensional oscillatory flow are studied. With the increase of Ma, the flow instability is increased. The surface temperature fluctuation patterns are changed with the increase of Ma. At the beginning, the surface temperature fluctuation is a double-petal shaped wave which does not rotate. Then it changes into a curved spokes wave. After that, it changes into a double oscillatory structure: the outside is a three-dimensional steady state and the inside is a three-dimensional oscillatory flow. At last it changes into an oscillatory wave which amplitude various with the time. The transform disciplines are the result of the role transition of Ma and Q. With the increase of Q, the surface temperature fluctuation patterns are barely changed and the flow instability is increased. When the flow is unsteady, the melt starts to rotate. The surface azimuthal velocity fluctuation is increased with the increase of flow instability. The radial velocity is much larger than the azimuthal velocity. So the azimuthal velocity fluctuation could be used to reflect the flow instability while the radial velocity fluctuation could be used to reflect the flow strength.Finally, the effects of Ma and the rotate speed of the crucible(Rec) on themocapillary-Marangoni-rotation convection are studied. With the increase of Ma, the flow pattern changes as the same as the themocapillary-Marangoni convection when the flow is steady. But the change is small. With the increase of Rec, the strength of the flow outward from the centre is decreased. The strength of surface rotation is increased. The strength of the radial flow near the crucible wall is increased. When the flow is unsteady, with the increase of Ma; the surface temperature fluctuation is increased at first, and then decreasing, finally increased again. Because the Ma disturbs the flow at beginning, then it balances with the other forces, finally it dominates the flow. With the increase of Rec, the surface temperature fluctuation is increased at first, then decreasing, next increased again, and finally decreasing. Since the melt flow driven by the Rec is more complicated. The flow cells occupy each other's flow zone with the increase of Rec that makes the flow instability increased when the Rec balanced with the other forces. After the Rec dominates the flow, the surface temperature fluctuation decreased. It means that increasing the Rec could make the flow more stable after the Rec dominates the flow.