A control procedure for the shape of a Nd:YAG and Nd:YVO4 cylindrical bar grown by edge-defined film-fed growth method under oscillated furnace pressure

Abstract

Abstract The main purpose of this paper is to give a model based proof of the fact that the effect of the variations of the pressure p in the furnace can be compensated by an adequate variation of the pulling rate v in order to assure a constant diameter of a Nd:YAG and Nd:YVO4 cylindrical bar grown from the melt by EFG method. Using a nonlinear model, those (p, v) couples are found for which the system of differential equations, which governs the evolution of the crystal radius r = r(t) and the meniscus height h = h(t), has asymptotically stable steady-state solution (r∗, h∗). By interpolation the dependencies of r∗ = r∗(p, v), h∗ = h∗(p, v) and the growth path S i.e. those (p, v) couples for which r∗(p, v) = rf (where rf represents the desired radius) are determined. Using the growth path S, for a given variation of the pressure (during the growth) an adequate variation of the pulling rate is found, which assures that the crystal radius constantly equal to rf. Numerical results are given for a Nd:YAG and Nd:YVO4 cylindrical bar of rf = 2.0 (mm), grown in a furnace in which the vertical temperature gradient is k = 33 (K/mm).