An experimental and three-dimensional numerical investigation of the Czochralski solidification of single silicon crystals
Abstract
The Czochralski (CZ) process is an art, and as such it requires the experience and luck of the operator to produce a high-quality crystal. Fundamental understanding of the process is needed in order to reduce the level of empiricism used. This research was directed towards investigating the melt flow and temperature field in a Czochralski grower through experimental and numerical analysis. The experimental analysis was performed at NEC Fundamental Research Laboratory in Japan under a joint research project funded by the National Science Foundation. Temperature was measured in a rotating silicon melt using two stationary thermocouples at fixed radii but different angular and vertical positions. The crucible radius was 35 mm and the crystal radius was 17.5 mm. Crystal and crucible co-rotation rates of 1, 2, 4, 6, and 8 rpm were studied using a Grashof number between 2.60E + 7 and 4.40E + 7. The length scale used to define the Grashof number was the melt height. Flow visualization data was also collected. Thermal oscillations were detected at each rotation rate. At 6 and 8 rpm, the flow was non-axisymmetric. Also, at these rates, a two-lobed thermal wave pattern was detected in a horizontal plane, and a tilt of this pattern with height was detected. These results were found to be similar to the behavior of rotating annular duct experiments used to simulate atmospheric motions. At 1 and 4 rpm, the frequency of oscillation was found to be a function of the Grashof number. However, at 6 and 8 rpm, the frequency was nearly independent of the Grashof number.^ In the numerical analysis, the three-dimensional, unsteady equations of conservation for mass, energy, and momentum were discretized using the finite-element code FI-DAPT$\sp{\rm TM}$. A Prandtl number of 0.0189 and a series of Grashof numbers between 9.3E + 4 and 5.8E + 6 was used. With no rotation of the crystal and crucible, the temperature changed with time at Grashof numbers of 1.4E + 6 or larger. Due to the small time steps needed to obtain stable solutions, it was concluded that the computational scheme was too expensive for modeling thermal oscillations. ^
Subject Area
Engineering, Chemical|Engineering, Materials Science
Recommended Citation
Vicki Blondine Booker,
"An experimental and three-dimensional numerical investigation of the Czochralski solidification of single silicon crystals"
(January 1, 1997).
Dissertations available from ProQuest.
Paper AAI9727195.
http://repository.upenn.edu/dissertations/AAI9727195
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