Computational analysis of heat transfer, thermal stress and dislocation density during resistively Czochralski growth of germanium single crystal

In this paper, a set of numerical simulations of fluid flow, temperature gradient, thermal stress and dislocation density for a Czochralski setup used to grow IR optical-grade Ge single crystal have been done for different stages of the growth process. A two-dimensional steady state finite element method has been applied for all calculations. The obtained numerical results reveal that the thermal field, thermal stress and dislocation structure are mainly dependent on the crystal height, heat radiation and gas flow in the growth system.