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

The dynamics and operability limits of a nonlinear-proportional-integral controller designed to stabilize detached vertical Bridgman crystal growth are studied. The manipulated variable is the pressure difference between upper and lower vapor spaces, and the controlled variable is the gap width at the triple-phase line. The controller consists of a model-based nonlinear component coupled with a standard proportional-integral controller. The nonlinear component is based on a capillary model of shape stability. Perturbations to gap width, pressure difference, wetting angle, and growth angle are studied under both shape stable and shape unstable conditions. The nonlinear-PI controller allows a wider operating range of gain than a standard PI controller used alone, is easier to tune, and eliminates solution multiplicity from closed-loop operation.

► Detached Bridgman growth can be stabilized by nonlinear model-based control.
► Nonlinear controller has broader operability limits than linear PI controller.
► PI control added in series with nonlinear control reduces bias from model error.