A thermal-capillary mechanism for a growth rate limit in edge-defined film-fed growth of silicon sheets

Capillarity, acting to set the shape of the melt/gas interfaces, and heat transfer can interact to cause limits to steady-state growth of thin silicon sheets by the Edge-Defined Film-Fed Growth (EFG) method. A finite-element/Newton solution method for a two-dimensional thermal-capillary model of EFG is used to show that limiting values of pull rate exist beyond which steady-state growth is impossible. The pull rate limit is also predicted by a one-dimensional heat transfer model valid when the die sides and menisci are almost parallel and when the thermal conductivities of melt, crystal, and die are all equal. Both the one- and two-dimensional heat transfer models show that heat loss from the melt is dominated by conduction into the crystal and slow heat release to the ambient along the length of the ribbon. The limiting pull rate results from the reduced efficiency of conduction through the melt caused by the curvature of the meniscus which increases height of the die top above the level of the melt. Thermal-capillary limits are predicted for both positive and negative pressure differences across the meniscus.