Comparison of finite element calculations and experimental measurements in edge-defined film-fed growth of silicon sheets

Abstract

Predictions of finite element analysis of heat and solute transfer in Edge-defined Film-fed Growth (EFG) of silicon sheets are compared to experimental measurements of crystal thickness, growth rate limits and solute segregation in 10 cm wide ribbon growth. The calculations are based on the two-dimensional thermal-capillary model of Ettouney et al. (J. Crystal Growth 62 (1983) 230) combined with an empirical model for the growth system temperature distribution and full solution of the convective transport equations for determining dopant segregation. The prediction of ribbon thickness as a function of growth rate is excellent for the entire speed range accessible with the system. The thermal-capillary limit for a growth rate of 4.3 cm/min obtained from the model also agrees with the observed maximum rate where the ribbon detached from the melt. Aluminum segregation across the ribbon thickness, as measured by spreading resistance, is accurately predicted as a function of growth rate when the possibility of surface-tension-driven convection is ignored.