Chemical Segregation of Titanium in Sapphire Single Crystals Grown by Micro-Pulling-Down Technique: Analytical Model and Experiments

The micro-pulling-down (mu-PD) process consists in pulling a crystal under a capillary channel placed at the bottom of a crucible. Despite it being limited to rather small liquid volumes, it is used to grow single crystal fibers and shaped crystals of various cross sections, mainly applied industrially for optical applications, such as lasers, optics, or scintillators. Consequently, those crystals should be doped with active elements to fit the target application. Unfortunately, whatever the growth parameters and the dopant type, quite often segregation problems are observed. It is generally believed that chemical partition in mu-PD technique is restricted to the first grown millimeters, but some experiments show that it is not always the case. An analytical one-dimensional model is presented, aiming to predict the longitudinal segregation along the growth direction. It is shown that it depends in practice on growth parameters such as capillary length, meniscus height, capillary section, and pulling rate. The characteristic numbers controlling the segregation profile are derived and a parametric study is performed in the case of Ti-doped sapphire single crystal fibers. Ti3+:Al2O3 single crystal fibers oriented along c-axis have been grown under stationary stable growth regime using different pulling rates and the longitudinal chemical segregation has been characterized by photoluminescence. Results are in agreement with the model predictions.