(646b) Control of the Detached Bridgman Crystal Growth Process

Detached Bridgman growth represents a radical change over existing industrial crystallization technology.  In this process, first observed in space-based growth, the melt dewets the wall, allowing the crystal to pull away from the ampoule. Detached growth eliminates deleterious interactions between the growing crystal and the ampoule, dramatically improving crystal quality.   However, the promising early results of microgravity experiments have been difficult to advance in terrestrial growth systems due to a number of instabilities that can be manifest during growth.  In particular, the growth of most semiconductor crystals is inherently unstable due to shape instabilities associated with thermal-capillary interactions set by growth and ampoule wetting angles. 

In this presentation, we discuss the dynamics, operability limits, and tuning of several feedback controllers to stabilize detached vertical Bridgman crystal growth. The controlled variable is the pressure difference between upper and lower vapor spaces, and the output variable is gap width at the triple-phase line. Open and closed loop dynamics of step changes in these state variables are analyzed under both shape stable and shape-unstable growth conditions. Effects of step changes in static contact angle and growth angle are also studied. Proportional and proportional-integral control can stabilize unstable growth, but only within tight operability limits imposed by the narrow range of allowed meniscus shapes. These limits are used to establish safe operating ranges of controller gain. Strong nonlinearity of the capillary model restricts the range of perturbations that can be stabilized, and under some circumstances stabilizes a spurious operating state far from the set point. Stabilizing detachment at low growth angle proves difficult and becomes impossible at zero growth angle.  Substantially better performance is shown to arise from a model-based control scheme implemented with a simple analytical expression derived from capillary statics.