An Axis Symmetric 2D Description of the Growth Process of a Single Crystal Hollow Tube Grown from the Melt by Pulling Down Method

This paper is an axis symmetric 2D description of a single crystal tube growth process by micro-pulling–down (PD) method. The description concerns the following aspects: the inner and outer free surfaces equations and the pressure differences across this free surfaces (section 2.); limits of the pressure differences across the free surfaces (section 3.); static stability of the capillary free surfaces (section 4). In section 5 the above aspects are numerically investigated in the case of the growth of a silicon micro tube of inner radius equal to 4.28x10-3[m] and outer radius equal to 4.72x10-3 [m]. The advantage of this description is that it helps to better understand the dependence of the inner and outer radius size of the tube on the pressure difference across the inner and outer free surface respectively, and may help the automation of manufacturing.