The aim of this project was the numerical computation of the defect concentrations in the growing crystal. The temperature distribution of the crystal is computed by a macroscopic heat transfer model in the entire growth system. This model takes into account heat conduction, radiation and convection of all components and thus is related to the design of the furnace. The defect transportation can be described by a system of reaction-diffusion equations which incorporates highly temperature-dependent parameters including the diffusion coefficients of the point defects. However, these diffusion coefficients cannot be measured experimentally due to the high temperatures in the furnace. Therefore, we approximated them on a microscopic scale by atomic simulations. The macroscopic parameters can then be computed by means of statistical mechanics which requires large length and time scales.
The combination of the macroscopic equations for the point defect concentrations and temperature distribution together with the results of the microscopic simulations thus can in general describe the whole growth process, thereby relating growth conditions to crystal properties.
[1] | M. Griebel, L. Jager, and A. Voigt, Predicting Material Parameters for Intrinsic Point Defect Diffusion in Silicon Crystal Growth, Solid State Phenomena, 95-96:35-40, 2004. |
[2] | M. Griebel, L. Jager and A. Voigt, Computing Diffusion Coefficients of Intrinsic Point Defects by Atomistic Simulations, in preparation. |