Control of multi-zone resistive heater in low temperature gradient BGO Czochralski growth with a weighing feedback, based on the global dynamic heat transfer model

Dynamic global model of oxide Czochralski process with weighing control

“…For example, in Ref. [15] the two-level cascade control was simulated to analyze the BGO Czochralski process in a set-up with a three-zone heater. In the present paper we restricted our consideration to a commonly used PID controller…”

“…In Ref. [15] this approach was successfully used for improving the control of multi-zone heater in low temperature gradient BGO Czochralski growth with a weighing feedback. In the present paper a global dynamic model of the oxide Czochralski process is developed.…”

Growing high-quality Bi12SiO20 crystals of large diameter (85 mm)

“…Recently, we have proposed [13,14] a physically justified approach to constructing these relations that is based upon optimization of the global heat exchange in the crystallization zone. According to this, a preset shape of the solid-liquid interface (crystallization front) is used to determine the laws of heat evolution in all heated zones, for which violation of the thermal balance (Stefan condition) at the interface would be minimized for each particular length of the growing crystal.…”

“…According to this, a preset shape of the solid-liquid interface (crystallization front) is used to determine the laws of heat evolution in all heated zones, for which violation of the thermal balance (Stefan condition) at the interface would be minimized for each particular length of the growing crystal. Use of this approach in developing the strategy of control over the growth of BGO crystals with a eulitine structure gave excellent results [14]. There fore, it was of interest to apply this method to growing sillenite crystals (BSO) with different physical proper ties, and this all the more so because there were serious grounds to believe that BSO crystal ingots of large diameter could not be obtained by other methods.…”

“…The BSO crystals were grown in a crystallization setup with a multizone heater analogous to that used to develop the method of control over the BGO crystal growth [14]. However, in order to obtain BSO crystals of desired transverse size, all geometric dimensions of the setup (including crucible) were increased by a fac tor of 1.7.…”