Three-dimensional simulation and analysis of heat transfer and flow field in micro-floating zone of LHPG with asymmetrical perturbation

Abstract

Under symmetrical conditions, the micro-floating zone of a laser-heated pedestal growth (LHPG) system displays a symmetrical double eddy flow field distribution. However, as the perturbation increases, the double eddy flow field distribution changes from symmetry to tilt, resulting in unstable flow field vibration. This study investigated the influence of the molten zone on the shape (at vapor–liquid and solid–liquid interfaces) and flow field distribution resulting from tilting the CO2 laser heating ring and the gravity field. This tilt is caused by spatial perturbations resulting from mounting the source rod and seed on pedestals with an alignment that slightly deviates from the growth axis of the LHPG system. The feasibility of growing crystal fibers using the micro-floating zone of the LHPG in the horizontal plane was further investigated. After selecting YAG as the growth material, we evaluated various reduction ratios, source rod scales, surface tensions, and thermocapillary coefficients for the two types of perturbation. Deviation in the laser heating ring significantly influenced the solid–liquid interface and the symmetry of the flow field in the molten zone. However, as long as the laser heating ring remained close to symmetrical, the influence on the molten zone of the larger deviation in the gravity field was limited. Therefore, growing crystal fibers using the micro-floating zone of the LHPG system in the horizontal plane is possible for materials that possess the correct physical properties at appropriate source rod scales. The three-dimensional simulation of this asymmetry includes the effects of the diameter reduction ratio and laser heating, and also modifies Lan's thermocapillary floating numerical model. The modified model calculates the physical grid through a non-orthogonal body-fitting grid transformation using the control-volume finite-difference method. To enhance the simulation and represent the physical system more accurately, we compared the shape of the molten zone of the simulation and the experiment. In practice, spatial perturbations can be controlled to within a range of approximately 3°. Using a 500-μm-diameter source rod and a 0.5 diameter reduction ratio as the baseline, we compared the flow field distribution in the molten zone with a 300-μm-diameter source rod and a 0.5 diameter reduction ratio as well as with a 500-μm-diameter source rod and a 0.25 diameter reduction ratio. Finally, a LHPG system undergoing horizontal growth was also simulated for a 1000-μm-diameter source rod and a gravity field perpendicular to the direction of crystal growth for further analysis.