Floating-zone growth of silicon in magnetic fields - III. Numerical simulation

Numerical simulations to calculate temperature distributions, velocity fields, and dopant concentrations (Si:P) in silicon crystal growth by the floating-zone method have been performed. Critical Marangoni numbers Ma(cl) = 50, Ma(c2) = 80 for the onset of 3D stationary and time-dependent flow could be determined by stability analysis in good agreement with experimental values. Corresponding critical temperature differences (Delta T < 1 degrees C) make it impractical to avoid time-dependent flow and thus dopant striations in the grown crystal by altering temperature gradient or zone height. The calculation of axial segregation profiles for phosphorus doped silicon clearly indicates that even high axial magnetic fields B less than or equal to 5 T do not establish a diffusive regime due to residual Marangoni convection Magnetic damping of the convection leads to boundary-type flow close to the melt surface explaining experimental, radial segregation phenomena. (C) 1998 Elsevier Science B.V. All rights reserved.