Semi–Direct Numerical Simulation of a Czochralski Melt Flow on High–Performance Computers

Abstract

The three-dimensional and time-dependent turbulent flow field and heat transfer of the melt in a Czochralski crystal growth process were predicted using an efficient block-structured finite-volume Navier-Stokes solver. From semi-direct numerical simulations, detailed information of instantaneous and time-averaged quantities were obtained. Two different crucible rotation rates were considered,,f2c = ---2 rpm and ---5 rpm, whereas the crystal rotation was kept constant at,f29 = 20 rpm. Exact boundary conditions for the temperature were obtained from experiments. The time-averaged results are discussed and it is shown that, due to velocity and temperature fluctuations underneath the crystal, the growth conditions are superior at higher crucible rotation rates. The main reason for this is the stabilizing effect of the centrifugal forces. Furthermore, it is shown that the boundary layer below the crystal is very thin, so that the influence on the bulk flow is negligible. Rotation will mainly maintain the circular shape of the crystal and ensure the homogeneous distribution of dopants.