Toshiyuki Fujiwara

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 soli 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 SiO and CO 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.

Turbulent heat transfer through the melt in silicon Czochralski growth

Abstract The effects of crucible rotation rate on the melt temperature are measured in a production scale Si Czochralski puller in order to examine a k -ϵ model of turbulence as a heat transfer model. The experimental results show that (1) the time-averaged temperature of melt surface decreases by the order of 10 K with increasing crucible rotation rate from 2 to 10 rpm and (2) the melt temperature fluctuates with the magnitude of 10–20 K peak-to-peak. The analytical results based on the k -ϵ model reproduce the nature of experimental results. The use of the turbulence model is reasonable for thermal modeling of Si Czochralski growth.

Global heat transfer model for Czochralski crystal growth based on diffuse-gray radiation

A new theoretical method for calculating view factors has been devised and a global heat transfer model for Czochralski (CZ) crystal growth developed. Good agreement was obtained between the model and experimental results for heater power when both radius and pull rate were constant. The model (1) includes global radiative heat exchange based on diffuse-gray radiation, (2) satisfactorily treats the moving curvature of the crystal-melt interface by applying the Stefan condition and the method of boundary-fitted coordinates, and (3) permits rapid calculation of the view factors.

Study of characteristics of the crystal temperature in a Czochralski puller through experiment and simulation

Abstract The characteristics of the temperature of the 2 inch Si crystal in a CZ puller are studied through experiments and simulations. The mechanism determining the temperature is briefly described. The principal results are: (1) the temperature was fundamentally determined by the distance from the surface of the melt, (2) at the same distance, the temperature at the top portion of the crystal was higher than that at other portions, and (3) for a pull-rate of less than 1 mm/min, the temperature was almost the same as that with zero pull-rate.