Research Group of Prof. Dr. M. Griebel
Institute for Numerical Simulation

Point defects in silicon crystals


Prof. Dr. Michael Griebel
Dr. Axel Voigt
Dipl.-Phys. Lukas Jager
Dr. Christian Weichmann
Dipl.-Math. Ralf Wildenhues


Modern fabrication of semiconductor devices requires a high quality of the base material. Therefore the growth process of crystalline silicon has to be improved continuously. The formation of the crystal is influenced by the appearance of point defects in the lattice. These point defects grow during the annealing process to microdefects which directly affect the quality of the semiconductor devices. Thus the aim of industrial research is to avoid the formation of these defects during the crystal growth process. This can be done by optimizing the temperature distribution in the furnace and the pull velocity of the growing crystal. Both parameters affect the defect distribution. The phenomenological $v/G$ law relates the quotient of the growing velocity $v$ and the temperature gradient $G$ at the interface between the melt and the crystal to the surviving point defect species. A critical value of this quotient means that the growing crystal is perfect. The control of the growth process with respect to this optimal quotient is a very difficult task.

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.


Research Center Caesar


[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.