A liquid-bridge model for the float-zone processing of materials

Abstract

The floating-zone process for purifying semiconductor materials such as silicon is represented by a static liquid-bridge model. Meridians from more general liquid-bridge studies are selected to give the zone shapes. The growth angle ψ, which the melt/gas interface makes with the vertical at the three-phase confluence, is kept constant, using 11° for silicon. In dimensionless terms the analysis of this static model leads to approximate limits on the maximum possible rod radius R_max= 5 and zone length L_max= 2 for silicon. The capillary constant a is (2γ^lg/Δρg)^½ giving in actual dimensions the radius r_max=aR_max= 40 to 42 mm, depending on the value of a, and likewise the zone length l_max= 16 to 16.8 mm for silicon. The relevant data for germanium give R_max= 10 and L_max= 2 leading to r_max= 47.5 mm and l_max= 9.5 mm. The difference between the two R_max values is largely due to differences in the fractional volume decrease on melting. The mechanical and physicochemical stability of the growth is also discussed. It is suggested that interface curvatures and orientations are fundamental to steady and uniform crystal growth.