NUMERICAL-SIMULATION OF MAGNETIC LIQUID-ENCAPSULATED CZOCHRALSKI GROWTH OF GALLIUM-ARSENIDE

The present study involves the development and application of numerical techniques to simulate a liquid-encapsulated Czochralski growth chamber. The equations solved are the conservation equations for the mass, momentum, and energy for the melt and encapsulant. For the crystal, crucible liner, and support, the energy conservation equation is solved. The shapes of the melt-crystal interface, meniscus and crystal diameter are determined through solutions to the differential equations which are derived from the kinematic conditions at the specific interface, and are not assumed a priori. Calculations have shown that the influence of fluid motion of the encapsulant upon the temperature gradient along the crystal surface cannot be ignored even if the system is operating with a dc magnetic field. This is because the encapsulant, boric oxide, is not electrically conductive, so that the magnetic field does not inhibit convection. Depending on the depth of the melt, a 0.2-T magnetic field may or may not be strong enough to completely suppress the bulk melt motion. The locations of the flow vortices have direct influence on the shape of the melt-crystal interface. In the present studies, simulations have been performed for a process time of about 2 h. In these calculations, the crucible translating rate at each time step is calculated based on the global mass balance condition while the heater power is maintained constant. Calculations were also performed to investigate a technique to control the crystal diameter by adjusting the crucible translating rate. It was found that the crucible translating rate is a slow response parameter but if used in an increase/decrease sequence, it can be an efficient way to control the size of the crystal.