Growth Dynamics of Single Void during Czochralski Silicon Crystal Growth Using Phase-Field Modeling

Abstract

To investigate the growth dynamics of the single void during Czochralski silicon growth as well as capture the basic features of the diffusion-controlled dynamic mechanisms, a phase field method has been developed. The free energy of the system involving the chemical free energy and the gradient energy is presented. Numerical tests were performed to examine the capability of this model, and the results show that: the void grows due to the absorption of vacancies in the matrix, which essentially reduces the free energy of the system; with the growth of the void, there forms vacancy concentration gradient towards the void in the matrix; the increase of initial vacancy concentration contributes to a larger void size and growth rate.