DYNAMICAL BEHAVIOR OF CZOCHRALSKI MELTS AND ITS INFLUENCE ON CRYSTAL-GROWTH

Complexities in the flow of the silicon melt in a Czochralski and a do uble-layered Czochralski crystal growth system are characterized in te rms of nonlinear predictions of the melt temperature fluctuations that are observed at a sampling time of 1 s using thermocouples at various locations in the melt. The Sugihara-May method is employed as the for ecasting technique. Information entropy of the thermal sequences is es timated from the dependence of the normalized root-mean-squared error of prediction on the prediction-time interval. The dynamical behaviour of the flows is related to temporally correlated random motion added to regular motion with scaling exponents specific to the crucible rota tion rate. The spatial and temporal structures of the flows are, howev er, totally different between the growth systems. The influence of the flows on the crystal-growth process is discussed in relation to rando mness in the thermal sequences.