Modeling Shape Evolution During the Growth of Oxide Single Crystals from the Melt via the Czochralski Technique

Simon Brandon, Chemical Engineering, Technion, Haifa, Israel
Oleg Weinstein, Chemical Engineering, Technion, Haifa, Israel
Wolfram Miller, Simulation And Characterization, Leibniz Institute For Crystal Growth, Berlin, Germany

The Czochralski (CZ) process is one of the most important methods for growing large single crystals from the melt. It is widely applied in the growth of several classes of materials, including pure and compound semiconductors as well as fluorides and oxides.

Large scale modeling of CZ crystal growth dates back to the 1980s and has since been successful in providing an (often quantitative) understanding of a number of key features and phenomena observed during growth. However, even though close to three decades have past since the first large scale CZ modeling studies, several challenges still exist. Of relevance to this contribution are those related to interface attachment kinetics and capillarity.  Of general interest is the understanding of anisotropic shape evolution due to a combination of these two phenomena, which are of particular importance in oxide material systems (that tend to exhibit faceted or partially faceted shaped crysyals).

In this contribution we will discuss our work aimed at elucidating the combined impact of interface attachment kinetics and capillarity on CZ growth. In particular we will focus on the relation between crystallographic orientation, kinetic parameters, interfacial undercooling, growth angle and how these may combine to influence crystal shape and quality. The model involves a three dimensional and dynamic analysis of heat transport and melt flow using Lattice Boltzmann models (LBMs), where a two dimensional unstructured mesh (embedded within the 3D LBM grid) is utilized to represent the melt/crystal and melt/gas interfaces. At the melt/crystal interface this 2D mesh is advanced in accordance with classical interface attachment mechanisms; the melt/gas interface is deformed to conform to the Young-Laplace equation and pre-defined contact and growth angles are enforced at the melt/crucible/gas and melt/crystal/gas triple phase lines respectively