Two dimensional analysis of axial segregation by convection-diffusion model in batchwise and continuous Czochralski process

It is shown theoretically that uniform axial dopant concentration distribution can be made throughout the crystal by continuous Czochralski process. Numerical simulation are performed for the transient two-dimensional convection-diffusion model. A typical value of the growth and system parameters for Czochralski growth of p-type, 4 inches silicon crystal was used in the numerical calculations. Using this model with proper model parameter, the axial segregation in batchwise Czochralski growth can be described. It is studied by comparing with the experimental data. With this model parameter, the uniform axial concentration distribution of dopant is predicted in continuous Czochralski process.