Chaotic feature of silicon melt turbulence and its influence on crystal growth

Abstract

We investigate the relationship between temperature fluctuations of a silicon melt and silicon crystal growth striations in a Czochralski crystal growth system by means of time series analysis estimating the degrees of visible determinism in observed data. A diagnostic test for smoothness in time evolution of observed fluctuations [Phys. Rev. Lett. 70, 580 (1993)] is applied to time series analysis. The method seems immune to noise contamination of observational data. Temperature fluctuations of the melt are observed at three radial positions along the crystal diameter under the crystal-melt interface. Crystal growth striations of as-grown silicon crystals along the growth axis are observed at the corresponding radial positions. At a low crucible rotational rate, determinism in the flow of the melt becomes less visible toward the center of the crucible. The opposite trends are observed at a high crucible rotational rate. Such dynamical properties of the melt are found to be embedded in the growth striations. The influence of the melt turbulence on crystal growth is discussed in the framework of the previous model for growth interface fluctuations.