Modelling the dynamics and control design for Czochralski, Liquid Encapsulated Czochralski and Floating Zone processes

The need for high quality crystals constantly rise. It is especially obvious in connection with the evolution of electronics and optoelectronics At the present time all the basic methods for crystal growing are known. So the question arises-what further developments are needed to create further advances? Without doubt first of all it is necessary to speak about perfecting crystal growing equipment. Perfecting modern equipment will enhance and accommodate the results of our understanding of the crystallization physics and provide solutions to the various physical tasks at the atomic and macroscopic levels. Each new step in the process of perfecting the technology and production processes demands large intellectual and material inputs. The continual updating of pullers requires constructive solutions and control systems Mathematical modelling of the methods of crystallization enables one to more rapidly create the software for the digital systems which are a feature of the latest achievements of physics, that is IT engineering and the modern theory of automatic control Here we consider the problem of mathematical modelling of crystallization processes from the melt by Czochralski, Liquid Encapsulated Czochralski and Floating Zone methods based on linearization of three conservation laws. the heat, mass and the growth angle constancy is reviewed in depth. Special attention is given to the problem of the dynamical analysis of these processes in open and closed states and to the synthesis of the digital control of crystal diameter for the weight technique The main problems discussed involve the determination of the parameters required for calculating such control systems together with the use of the multichannel parametric PID regulator involving the state variable observer concept. In addition briefly considered are the problems of digital filtering of the measurement noise based on multidimentional Kalman filters and the determination of mechanical stability limits for static menisci (C) 2010 Elsevier Ltd All rights reserved.