Czochralski silicon crystal growth: Modeling and simulation study

Czochralski (CZ) crystal growth process is a widely used technique in the manufacturing of silicon crystals and other semiconductor materials such as germanium (Ge) and gallium arsenide (GaAs). The ultimate goal for the Integrated Circuit (IC) industry is to have the highest quality substrate. There is a huge interest to manipulate the thermal field in both the melt and crystal and control the melt convection and crystal-annealing rate in order to reduce growth striations, impurity and dopant inhomogeneity concentrations, excess point defects generation at interface, and micro defects nucleation and growth within the growing crystal. The objective of this investigation has been to facilitate and spearhead the development of a simple/efficient simulation tool for the accurate prediction of global thermal and flow fields and the melt-crystal interface position in the CZ process. The numerical algorithm employs a rectangular (fixed or non-uniform) mesh for enhanced computational efficiency and an enthalpy-based technique for interface tracking. Turbulent flow in the melt is accounted for by utilizing a K-&egr; model. Radiative heat transfer is modeled in a lumped parameter sense without appreciably compromising on solution accuracy to further allow for CPU times savings. The simulation tool is validated in a number of benchmark flows such as Wheeler's problem. For the CZ crystal growth process, an entire growth cycle has been computed and reliable predictions for the evolution of interface position, and flow/thermal field characteristics have been obtained. The enhanced CPU efficiency of the approach developed here could help integrate it into on-line control strategies.