Dynamical behaviour of Czochralski melts and its influence on crystal growth

Abstract

Complexities in the flow of the silicon melt in a Czochralski and a double-layered Czochralski crystal growth system are characterized in terms 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 forecasting technique. Information entropy of the thermal sequences is estimated 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 rotation rate. The spatial and temporal structures of the flows are, however, totally different between the growth systems. The influence of the flows on the crystal-growth process is discussed in relation to randomness in the thermal sequences.