A Simple Model for Obtaining the Power Distribution Yielding a Desired Temperature Distribution in Zone-Melting Recrystallization

Abstract

A simple one-dimensional method for obtaining the power distribution from a temperature distribution which is desirable for successful zone-melting recrystallization (ZMR) is proposed. The power distribution thus obtained can be realized by a tungsten-halogen lamp with a focusing mirror. The actual temperature distribution calculated by solving the heat flow equation two-dimensionally with the obtained power distribution as the input heat source shows very close agreement with the initially desired target, especially in the region where the temperature gradient must be controlled precisely. The enthalpy method has been used to incorporate the abrupt changes of the optical and thermal properties of silicon upon phase transition. It has been found that the temperature distribution is insensitive to some local changes in the input power distribution so that we can modify the input power distributions in such a way to make the mechanical processing of the focusing mirror easier. This method may be applied to systems other than the ZMR system which require the shaping of the temperature distribution.