An axis symmetric 2D description of the dynamics of a single crystal micro fiber growth from the melt by micro- pulling- down method. Part.1

In this paper the first part of an axis symmetric description of a single crystal micro fiber growth process by micro-pulling-down method is presented.the description concerns the following aspects:the free surface equation and the pressure difference across the free surface (section 2);limits of the pressure difference p across the free surface (section3;the fiber radius change due to the change of the pressure difference p,and the fiber radius size control(section 4);the static stability of the free surface (section 5). The above aspects are numerically illustrated in case of the growth of a silicon fiber of radius equal to 0.0001 m by using the Maple 17 software. This description can be helpful in the better understanding of the growth process and in the automation of manufacturing