INTERFACE FLUCTUATIONS IN CZOCHRALSKI CRYSTAL-GROWTH

We construct a mathematical model of interface fluctuations in Czochra lski crystal growth based on the thermal balance across the growing in terface. The model describes time-dependent growth rate in relation to fluctuations in crystal pull rate and melt flow viewed as external pe rturbations. Complexities in the flow of a silicon melt are characteri zed in terms of time series forecast about melt thermal fluctuations a ctually observed beneath a growing crystal. The melt exhibits self-aff ine random motion with spatial and temporal structure specific to cruc ible rotation rate. The influence of the complex flow to crystal growt h is discussed on the basis of the model proposed. (C) 1995 American I nstitute of Physics.