Three-dimensional calculations of facets during Czochralski crystal growth

Abstract

Facets occur in bulk crystal growth of oxides and also in those of semiconductors. They are the origin of many problems during growth, like e.g. twinning, oscillating menisci, constitutional undercooling, spiral growth. It is still a challenge to understand the mechanisms in the non-linear coupling of faceted growth, melt flow, and radiation. In Czochralski growth computations have to be fully 3D because the shape of the crystal is no longer axi-symmetric when side facets appear. In this paper we introduce a numerical approach for a 3D computing of fluid flow, thermal transport and faceted growth in a Czochralski environment. The numerical algorithm is based on lattice Boltzmann methods for thermal and velocity fields calculations while interface motion is calculated by directly applying an interface motion operator at each interface node-point. The results show that the macroscopic shape of the interface and the crystal shape are significantly affected by facets.