THEORETICAL-ANALYSIS AND DESIGN CONSIDERATIONS FOR FLOAT-ZONE REFINEMENT OF ELECTRONIC GRADE SILICON SHEETS

The finite element method is used to solve a detailed model of heat an d momentum transport in the vertical float-zone refinement of thin sil icon sheets. The model formulation is much like that used to study flo at-zone refinement Of cylindrical ingots, but the dominant physical me chanisms differ because of the much smaller length scale. The curvatur e of the meniscus remains nearly constant under all conditions due to the dominance of surface tension. The solid-liquid interface deviates considerably from a planar shape, contrary to the assumption of previo us studies. The release and uptake of latent heat appear to play only minor roles in determining this shape, which results primarily from th e sharp decrease of silicon emissivity upon melting. Strong flow in th e melt due to the Marangoni effect is driven by large temperature grad ients (O(100 K/cm)) at the melt surface, whereas buoyancy effects are negligible. Effective Reynolds numbers exceeding 10(3) are calculated. Multiple solutions are found under some circumstances. The different solution branches show little difference in the temperature field or f ree surface shape, but show a large difference in the flow held, which is likely to affect the redistribution of impurities. Transient calcu lations are used to determine the thickness variation of the sheet dur ing the approach to steady state.