Active Cooling Design for Horizontal Ribbon Growth

Difficulty in producing thin ribbons at high production speeds has been a significant barrier in the adoption of the horizontal ribbon growth process for manufacturing low- cost silicon wafers. The use of active cooling devices, like helium jets, has allowed for intense heat removal from the ribbon tip leading to higher pull speeds. However, at the same time, this has also caused an increase in the thickness of the ribbon, making them unsuitable for commercial applications. In this paper, we analyze the results from a series of simulation studies and outline a general process to the effects of active cooling on the ribbons' growth rate and thickness. A linear scaling relationship between the limiting pull speed and the total heat removed is derived empirically for a family of Gaussian cooling profiles. These scaling relationships show that the intensity and spread of a cooling profile are directly tied to the growth rate limit and the ribbon's thickness, respectively.