| Summary: | 碩士 === 國立臺灣大學 === 化學工程學研究所 === 90 === Three-dimensional (3D) simulation is carried out for the vertical Bridgman growth of gallium-doped germanium in a graphite ampoule under arbitrary gravitational and magnetic orientations. Both pseudo-steady state and fully time dependent calculations are carried out. For both fields in the axial direction, calculated results are in good agreement with those obtained by using a 2D model based on the stream function/vorticity formation. The scaling law for velocity damping by the magnetic field agrees well with the boundary layer approximation being |max|Ha-2, where max is the maximum melt velocity and Ha the Hartmann number. The flow damping by the horizontal magnetic field shows the same trend, but much more efficient. However, for 3D calculations at a large magnetic field strength, due to the poorer numerical resolution of the grid in the thin Hartmann layer near the wall, the flow damping fails to follow the scaling law. For stronger flows at normal gravity or tilted gravity, using the axial magnetic field is hard to damp the flow sufficiently unless having very large field strength.
Once the flow is suppressed, the radial segregation tends to increase first due to poorer dopant mixing. With a high enough strength, the radial segregation could be then reduced until the diffusion limit is reached, where the segregation is controlled by the interface concavity. Similarly, the effective segregation coefficient Keff is approaching to the diffusion limit with the increasing magnetic fields. Again, for both the horizontal magnetic field is far more efficient than the axial one. Interestingly, there is one exception. When the gravity is aligned with the growth axis, i.e., the perfect vertical growth configuration, the flow cell is stretched along the axial direction by the axial magnetic field. As a result, the back mixing increases and thus Keff decreases with the magnetic field strength at the beginning. Once the magnetic field is increased further, back mixing is then reduced until the diffusion limit is reached. Axial dopant segregation is also investigated through the fully transient calculations. Beside the more detailed information at different stages of the growth can be obtained, the trend in the flow damping and segregation is similar to that using the pseudo steady state calculations.
|
|---|
