Global Simulation of CZ and FZ Bulk Crystal Growth: from Quasi-Dynamic and Dynamic Modelling to Process Control and Crystal Quality Optimization

When Silicon ingots are grown for IC or PV applications, the crystal diameter has to conform to current market requirements while the crystal defects and composition have to be perfectly controlled. The present paper is devoted to illustrate CZ and FZ process optimization by use of the time-dependent FEMAG.2 software. First, the "off-line control" technique is devoted to determine the heater power and pull rate histories required to obtain a crystal of constant diameter and optimal quality by means of fully transient simulations. Other command parameters such as crystal and crucible rotation rates, magnetic field intensity, etc., can be optimized as well. Secondly, the use of quasi-dynamic numerical simulations shows very efficient to study the transient effects experienced by the system during bulk crystal growth, without necessitating a fully dynamic simulation. A main application of this technique is to improve the design of an automatic controller of the growth process.