Numerical modelling of the microscopic inhomogeneities during FZ silicon growth

Abstract

Transient axisymmetric numerical calculations of the hydrodynamic, temperature and solute concentration fields have been performed by means of FEM for the needle-eye FZ Silicon single-crystal growth process (diameter 4″) to analyse the microscopic inhomogeneities. The rotation of the single crystal and feed rod, the buoyancy, Marangoni and electromagnetic (EM) forces in the melt are taken into account. Axisymmetric velocity oscillations caused by hydrodynamic instabilities are considered and calculated numerically. Two mechanisms of the oscillating dopant incorporation in the crystal are investigated: (1) the direct influence of the transient velocity field on the concentration field due to convective solute transport and (2) the influence of the oscillating temperature field on the local growth rate and as a consequence on the oscillating dopant segregation process at the growth interface. It is shown that for the considered experimental set-up the first mechanism dominates for the microscopic inhomogeneities. The calculated oscillations of the dopant concentration in the grown crystal (striations) are compared to spreading resistance measurements.