Design of parallel compensator and stabilizing controller to mitigate non-minimum phase behaviour of the Czochralski process

Abstract

This paper addresses the design of a parallel compensator and a stabilizing controller for the simplified crystal growth dynamics of the Czochralski (CZ) process, i.e., the process for the production of monocrystalline silicon ingots of uniform diameter. The diameter control of the produced ingots is achieved by a CCD camera measurement used to sense the radius of the boundary between the base of the growing crystal and the surrounding glowing meniscus — a raised melt surface connecting the crystal ingot with the flatter melt surface. Due to the intrinsic nature of the process, the bright ring radius measurement signal exhibits a non-minimum phase behaviour. A combination of the parallel compensator and a stabilizing controller is designed, such that the former provides for the mitigation of non-minimum phase behaviour, while the latter combined with the formal yields a suitable closed-loop performance.