A THERMAL-MODEL FOR CZOCHRALSKI SILICON CRYSTAL-GROWTH WITH AN AXIAL MAGNETIC-FIELD

This paper presents a thermal model for molten silicon in a Czochralski crystal puller system with an applied uniform axial magnetic field. The melt depth is treated as continually decreasing, which affects the thermal environment of the melt and crystal. The radiative heat loss and the input heat flux are treated as functions of time, with a constraint placed on the heat lost to the crystal from the melt. As the melt motion reaches a steady state rapidly, the temperature and flow fields are treated as instantaneously steady at each melt depth. The heat transport is a mixture of conduction and convection, and by considering the crystal and crucible to be rotating with the same angular velocity, the flows driven by buoyancy and thermocapillarity are isolated and provide the convective heat transport in the melt for the range of magnetic field strengths 0.2 ≤ B ≤ 1.0T. © 1990.