Pulling rate, thermal and capillary conditions setting for rod growth

摘要

The purpose of this paper is to elaborate a procedure, based on a mathematical model, for the setting of the pulling rate, capillary and thermal conditions, in order to grow a cylindrical rod with prescribed radius and length, by edge-defined film-fed growth (EFG) method. First, in the case of an axisymmetric meniscus, we use simultaneously the catching and the angle fixation conditions in order to find a formula, which describes the fluctuation of the angle between the horizontal axis Or and the tangent line to the free surface of the meniscus at the three phase point. This angle appears in the system of differential equations which describes the evolution of the radius of the rod. During the growth this angle can fluctuate due to the fluctuations of the crystal radius, or crystallization front level, or pressure, respectively. In the second part of the paper it is shown in which kind this formula together with the energy balance equation at the crystallization front level can be used for setting the pulling rate, the thermal and capillary conditions to grow a cylindrical rod with prescribed radius and length. Numerical illustration and simulation are presented for rods having thermo-physical properties similar to NdYAG and InSb. This type of results can be useful for the experiment planning, since personal computer simulation is less expensive than experiment. With this aim the present study was undertaken.