Stabilizing detached Bridgman melt crystal growth: Proportional-integral feedback control

Stabilizing detached Bridgman melt crystal growth: Model-based nonlinear feedback control

“…The results presented below show that the nonlinear controller avoids the solution multiplicity encountered when using a conventional linear PI controller alone [30]. Operability limits of this nonlinear controller are also much less restrictive than the PI controller, making it easier to tune.…”

“…Our interest here is the possibility to actively manipulate this pressure difference to maintain a constant crystal radius (i.e. constant gap width), in a manner similar to our previous study of a proportional-integral (PI) controller [30]. In this work we extend the analysis to examine the behavior of a model-based, nonlinear controller, a block diagram of which is shown in Fig.…”

“…Our previous studies [15,30] demonstrated that a purely capillary model of shape stability is sufficient to capture the dynamics of the detached growth system. At this level of approximation, the effects of changes in hydrostatic pressure caused by gravity acting upon the height of melt above the meniscus are ignored, as is appropriate for examining shortertime dynamics, and the reduced order model is given by a single evolution equation for gap width, represented in dimensionless form by w ðR i ÀRÞ=R i , where R and R i are crystal radius at the triple phase line, and ampoule inner radius, respectively.…”

“…Conversely, shape unstable solutions will diverge from the equilibrium curve when perturbed from it. States for which aþyop are found to be shape unstable, independent of thermal effects [15,30,31], and will fail under open-loop operation.…”

Parametric sensitivity and temporal dynamics of sapphire crystal growth via the micro-pulling-down method

“…Perhaps more important is the demonstration of how these tools may be employed to obtain a more complete understanding of the physical underpinnings of a growth process, especially to promote the successful growth of a new material. Such models will play an increasingly important role in the future, providing important insight for the optimization of process design [43] and model-based control [44].…”