In a crystal growth process the physical phenomena occur on different length scales, starting form the unit cell of most inorganic crystals with dimensions in the order of a few nanometers and going to the bulk crystals with dimensions in the order of several tens of centimeters. Therefore it’s impossible to build a mathematical model that describes the crystal growth process completely.
A challenge for the numerical modeling is to identify the most appropriate numerical methods to describe the phenomena that occur on different levels. At mesoscopic level (~10-6 m), where the focus in on studying the growth behavior of grains, mainly Lattice-Boltzmann methods and phase-field models are used, whereas, for the description of the phenomena at macroscopic level (>10-3 m), like conduction, convection and diffusion, usually the finite volume and finite element methods are used.
In this talk we will report on the results obtained on two levels of length. At macroscopic level, the physical phenomena that influence the crystal growth process (conduction, convection, diffusion) have been studied using the STHAMAS3D software. On mesoscopic level, in collaboration with researchers from the Leibniz Institute for Crystal Growth (IKZ) in Berlin, a modeling software, based on a phase-field model, has been developed in order to study the formation of the multicrystalline structure of a silicon ingot grown by directional solidification process.
In order to accurately describe the main features of the fluid flow a large scale numerical grid is required. Also, in order to obtain realistic solutions, the computation time must account for at least 800 s in real time. At the mesoscopic level, while the computational domain is much smaller, the numerical model requires the use of a small time step (in the order of 5∙10-10 s) and of a small lattice step (in the order of 3.86∙10-7 m) for describing the underlying physical phenomena. These characteristics at both levels lead to high computation time. Therefore, in order to obtain meaningful physical solutions in a reasonable amount of time high performance computing is strongly recommended.