The dynamics, operability limits, and tuning of a proportional-integral feedback controller to stabilize detached vertical Bridgman crystal growth are analyzed using a capillary model of shape stability. 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. 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.
Bibliographical noteFunding Information:
This work was conducted at the University of Minnesota and was supported in part by the Minnesota Supercomputer Institute, the National Science Foundation , under Award DMR-1007885 , and the Department of Energy, National Nuclear Security Administration , under Award DE-FG52-08NA28768 . The content of the work does not necessarily reflect the position or policy of the United States Government, and no official endorsement should be inferred.
- A2. Bridgman technique
- A2. Detached growth
- A2. Dewetted growth
- A2. Process control
- A2. Proportional-integral control
- B1. Cadmium zinc telluride