The application of electric field to silicon semiconductors materials is used to modify the melt convection mode in Czochralski growth configuration and to control the structures at the surface of crystal. The nonlinear phenomena, the decrease of the stabilized applied voltage in closed circuit with the increase of the electric current, are observed experimentally. The mathematical model to predict the temperature of silicon crystal and the electric field in closed circuit is developed to study the electric current-induced Joule heating phenomena in silicon semiconductor materials. In this work, numerical simulations have been performed using Newton method and implicit Euler time integration. It has been demonstrated that numerical analyses are qualitative agreement with experimental results and it is possible to reproduce the nonlinear behavior in the application of electric current to silicon materials.
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