(A) numerical study of point defects in silicon single crystal in a Czochralski process

Abstract

Present study aims to investigate the effect of system variables on the behavior of point defects in a silicon crystal, which is grown by cusp-magnetic Czochralski method. The variables under the investigation consist of operating parameters and variables that describe the configuration of the counter-current loops: the operating parameters include the crucible rotational rate, the crystal rotational rate, and the strength of the magnetic field; and the variables of the configuration include the radii and the vertical distance of the loops from the melt-solid interface. Vacancy and self-interstitial point defects are adopted as point defects. At first, the melt-thermal effect on the crystal has been investigated by calculating temperature gradient at the melt-solid interface for fixed operating time. It is found that the crucible rotational rate, the strength of the magnetic field, and the radii of the loops significantly affect the centrifugal pumping flow due to the crucible rotation, resulting in large change in the melt-thermal effect on the crystal. The effect of the operating parameters on the density of the point defects is studied for fixed operating time when the radius of the crucible is equal to the depth of the molten melt. It is confirmed that the crucible rotational rate and the strength of the magnetic field significantly affect the density of the point defects in the silicon crystal. Also, the interaction between the variables of the configuration of the loops and the density of the point defects is investigated for operating time interval. The radii of the loops have a large effect in determining the density of the point defects in the crystal. However, the vertical distance of the loops and the change in the melt depth do not considerably change the density of the point defects within the studied ranges of the vertical distance and the operating time.