114 Crystal Growth and Evaluation of Silicon for VLSI and ULSI
within the melt are signicantly reduced, and the radial temperature gradient is increased
(whereas the temperature gradient decreases with respect to depth). These results regard-
ing temperature and oxygen concentration are all in good agreement with experimental
observations.
Hjellming and Walker [233] studied the mass transport of dopants and impurities in
the silicon melt of a CZ crystal puller with a uniform axial magnetic eld. For magnetic
eld strengths 1 = B
o
= 5T, the dominant ow elds are those driven by buoyancy and the
growth of the crystal (the pulling of the crystal and the raising of the crucible bottom).
According to them, the mass transport is intrinsically u