3D-Simulation of Czochralski Crystal Growth

In cooperation with the FH Nürnberg, the LSTM Erlangen conducts research in the field of crystal growth for several years now, focusing on the Czochralski process. With this method, more than 90% of the silicon single crystals for the electronics industry are produced. The process principle is simple: Starting with a seed, the crystal is directly pulled from the melt (Fig. 1 and 2). However, the physics involved is difficult since many different forces are acting on the melt, leading to a complex flow structure which is fully turbulent, three-dimensional and highly instationary. This strongly influences the shape of the phase interface between melt and crystal, which is crucial for the quality of the resulting crystal, especially in terms of homogeneity of properties and crystal lattice defects.


Fig. 1: Silicon single crystal after pulling (c Siltronic AG)



Fig. 2: Schematic view of the Czochralski process

In a research project at LSTM Erlangen, the turbulent structures in a Czochralski crucible were analyzed using a Direct Numerical Simulation (DNS), resolving all scales and considering all occurring effects such as buoyancy, Coriolis and centrifugal forces, Marangoni convection, and thermal radiation (Fig. 3) [1]. The DNS data were also taken as a reference to validate the Large-Eddy Simulation technique (LES), which is used for modeling the turbulence. It could be shown that using LES, the computational effort could be reduced significantly maintaining sufficient accuracy [2].
With the application of the LES method, several studies were conducted aiming at controlling the melt flow and thus the shape of the phase interface, which was explicitly computed using moving grids (Fig. 4). Different configurations with rotation and counterrotation of the crystal and crucible were investigated as well as magnetic fields. In this context, also the mechanism of oxygen dissolution, transport and evaporation was simulated [3].



Fig. 3: Iso-surface of dimensionless temperature difference 0.1 between instantaneous and average temperature showing turbulent thermal plumes



Fig. 4: Dynamic simulation of crystal-melt interface, with (a) crucible rotation and (b) crystal cooling from the top



(Priv.-Doz. Dr.-Ing. M. Breuer, Prof. Dr.-Ing. A. Delgado, Institute of Fluid Mechanics (LSTM) FAU Erlangen-Nürnberg and Dipl.-Ing. A. Raufeisen, Prof. Dr.-Ing. T. Botsch, Department of Process Engineering (VT) GSO-H Nürnberg)