The Effects of Gas‐Phase Convection on Carbon Contamination of Czochralski‐Grown Silicon

Measurements of carbon incorporated into a 2 in. diam Czochralski silicon crystal are compared with predictions computed using a three‐step simulation: ( i ) the temperature field is computed throughout the melt and all solid regions of the furnace without heat transfer by gas convection; ( ii ) the temperature and flow fields for the argon purge gas are computed with the temperatures at all solid surfaces set from the first step in the simulation; ( iii ) the concentrations of dilute and in the purge gas, as well as the concentration of carbon in the melt, are computed using the temperature and flow fields computed in step ( ii ). The concentration of carbon in the crystal is readily computed from the concentration of carbon in the melt. The predicted carbon concentrations are approximately a factor of 2 lower than the measured concentrations, with the discrepancy likely due to inaccurate thermodynamic and kinetic data. Additional simulations show that the concentration of carbon in the crystal increases with increasing gas pressure and decreases with increasing mass flux of gas through the furnace at constant pressure. Finally, convective cooling by the flowing gas is shown to be unimportant relative to radiation thereby justifying the decoupling used in the first step of the simulation.