On the dopant distribution along the crystal length in Czochralski growth

For the model problems approximately describing heat/mass transfer in Czochralski crystal growth effective evaporation and dissolving rates (oxygen from crucible to silicon) together with effective coefficient of equilibrium distribution of dopant are determined depending on parameters of the process. These effective quantities are used in calculation of dopant distribution along the crystals, that are grown both with the presence of the magnetic field and without it.