Phase field modelling on the growth dynamics of double voids of different sizes during czochralski silicon crystal growth

To investigate their dynamics and interaction mechanisms, the growth process of the two voids with different sizes during Czochralski silicon crystal growth were simulated by use of an established phase field model and its corresponding program code. On the basis of the several phase field numerical simulation cases, the evolution laws of the double voids were acquired as follows: the phase field model is capable to simulate the growth process of double voids with different sizes; there are two modes of their growth, that is, either mutual integration or competitive growth; the exact moment of their fusion can be also captured, and it is τ of 7.078 (simulation time step of 14156) for the initial vacancy concentration of 0.02 and the initial space between two void centers of 44Δx.