The Effects of Peltier Marking on Semiconductor Growth in a Magnetic Field
This research represents a model for three dimensional semiconductor growth in a vertical Bridgman process within an externally applied magnetic field with the additional effects of Peltier marking. The magnetic field is strong enough that inertial effects can be neglected and that viscous effects are confined to boundary layers. The objective of this research is a first step in the development of a method to accurately predict the distribution of dopants and species in the melt after a current pulse with a given duration and strength, with a given magnetic field and with a given crystal-melt interface shape. The first model involves an asymptotic solution to provide physical clarification of the flow. In both models the crystal/melt interface is modeled as fr=3r2 where 3<1 . The first model incorporates a variable, a which ranges from 0.25 to 1.0. The second model involves an analytical solution with an arbitrary Ha and a<1 . These models show the how the azimuthal velocity varies with increasing Ha and how the stream function varies in the meridional problem. This gives insight into how the dopant is mixed during the crystal growth process. The results demonstrate that current pulses with relatively weak magnetic fields and modest interface curvature can lead to very strong mixing in the melt.
University of Illinois - Urbana-Champaign
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University of Illinois at Urbana-Champaign