Simulation of the thermal fluctuation according to the melt height in a CZ growth system

Abstract

Single crystal growth by the Czochralski method is widely used for semiconductor materials. Solar cells, notable for their potential in next generation energy applications, make extensive use of silicon, while accounting for over 90% of the solar energy market. The crucible size increases have resulted in unstable and complex flow patterns within the melt, which were not previously found for smaller melt sizes. Therefore, we employ experimentation on a model system and numerical simulation to observe flow within the melt, the control of which may be expected to be of great assistance in analyzing and preventing the formation of defects within the grown single crystal wafers. The present study makes use of both numerical simulations and model system experiments to observe temperature and flow patterns within a large-scale melt, in order to better analyze and prevent instabilities within the melt. Temperature and flow patterns were observed depending on parameters such as crystal rotation, crucible rotation and melt depth in a large cylindrical crucible. The numerical model is based on a time-dependent and three-dimensional standard k– ε turbulent model using the analytical software package CFD-ACE+, version 2006. When both the crystal and crucible are rotated simultaneously, an asymmetrical temperature profile results, creating thermal fluctuations within the melt. In addition, a decreased melt depth results in a lower degree of thermal fluctuation, with the maximum thermal fluctuation being pushed outwards towards the crucible side wall.