The dependence of the dopant distribution on the pulling rate and on the capillary channel radius in the case of a Nd:YVO 4 cylindrical bar grown from the melt by EFG method

Abstract

The dependence of the Nd 3+ ion distribution on the pulling rate v and on the capillary channel radius R cap, in an YVO 4 cylindrical bar grown from the melt by EFG method with melt replenishment is determined. Using COMSOL Multiphysics 3.3, the coupled incompressible Navier–Stokes and conservative convection–diffusion equations were solved in the stationary and time dependent cases for different pulling rates v in the range [1 × 10 −10, 1 × 10 −6] m/s and for different capillary channel radii. The computations reveal that in the stationary case, for a given R cap, there exist critical pulling rate values v ′ depending on R cap, at which the Nd 3+ ion concentration has a maximum. If v increases in the range [1 × 10 −10, v ′ ] then the impurity concentration increases, and after that the concentration decreases slowly remaining in average equal to the initial impurity concentration in the melt. In the time dependent case, after a transition period which depends on v and R cap, the impurity concentrations tend to those obtained in the stationary case. In the transition period there exists a slight non-homogeneity of the dopant distribution, and after that the concentration of Nd 3+ ions in the crystal is almost equal to C 0, as it was reported by practical crystal growers.