A control procedure for the shape of a Nd:YAG and Nd:YVO_4 cylindrical bar grown by edge-defined film-fed growth method under oscillated furnace pressure

摘要

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:YVO_4 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) = r_f (where r_f 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 r_f. Numerical results are given for a Nd:YAG and Nd:YVO_4 cylindrical bar of r_f = 2.0 (mm), grown in a furnace in which the vertical temperature gradient is k = 33 (K/mm).