Geostrophic turbulence in CZ silicon crucible

Abstract

In the CZ silicon process, silicon melt convection is affected by the Coriolis force as a rotating fluid system. As a result, a special fluid motion called baroclinic instability appears and disturbs the single crystal growth. Since the Coriolis force will increase the curvature of the fluid particle paths, when the curvature exceeds the crucible size, another unstable fluid motion, the so-called geostrophic turbulence, is expected to occur at higher Taylor numbers. This study investigates the geostrophic turbulence by numerical flow simulation and experimental observations in an actual CZ crucible. In the numerical flow simulation, we solved 3D differential equations on a cylindrical lattice of 80×60×65 points, where the Rayleigh number of the system was fixed to be 2.7×10 7. With the Taylor number higher than 1×10 11, the calculated fluid motion and temperature structure produce a polka-dot pattern, which continues from the melt surface to the bottom. When the Taylor number is increased, the vertical vorticity component increases extremely. In the actual CZ crucible, temperature profiles on the melt surface were recorded by video camera thermometer in the same conditions as in the numerical simulation. The thermal images of the melt surface also show a fluctuating polka-dot pattern consisting of high temperature areas as seen in the numerical simulation results. The size and amplitude of the high temperature areas decrease with increase of the Taylor number, thus thermal clusters will relax the radial gradient and fluctuations. The Fourier power spectrum of the time dependent fluctuations has an f −4 behavior, which statistically indicates 2D turbulence. These facts observed both in numerical simulations and the actual experiment are completely consistent with the characteristics of geostrophic turbulence.