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.
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