Global Heat Transfer Model Research Articles

Computer Simulation of Point-Defect Fields and Microdefect Patterns in Czochralski-Grown Si Crystals

Computer simulation of the point-defect fields in Czochralski Si crystals is reported. Our model includes the following factors: for crystals, variable pull rate V(t), the lagging of crystallization rate \\widetildeV behind V, crystal length increasing with time l(t), temperature field T(r,z) dependent on l or \\widetildeV, and actual shape of the crystal–melt interface; for native point defects, transport with the moving crystal, Fickian diffusion and thermodiffusion, the vacancy–self-interstitial recombination, and annealing at the crystal surface. Temperature fields established during crystal growth are calculated using a global model of heat transfer in the system. Important cases of variable V and pulling halts are considered. Simulations successfully reproduce experimental data such as the shape and position of the interstitial and vacancy regions, including the R-OSF bands. The values of model constants, except for the critical point-defect concentrations, are the same as those obtained for pedestal Si crystals.

Global heat transfer model for Czochralski crystal growth based on diffuse-gray radiation

A new theoretical method for calculating view factors has been devised and a global heat transfer model for Czochralski (CZ) crystal growth developed. Good agreement was obtained between the model and experimental results for heater power when both radius and pull rate were constant. The model (1) includes global radiative heat exchange based on diffuse-gray radiation, (2) satisfactorily treats the moving curvature of the crystal-melt interface by applying the Stefan condition and the method of boundary-fitted coordinates, and (3) permits rapid calculation of the view factors.