Vacancy Characteristics During Silicon Crystal Cooling via Kinetic Lattice Monte Carlo Simulations

Vacancy characteristics during silicon crystal growth were investigated via kinetic lattice Monte Carlo simulations. We obtained the diffusivity of vacancy clusters independently of the diffusivity of free vacancies, and diffusivities of both free and clustered vacancies were divided into two regimes at temperatures of 1,405 +/- 45 K. At temperatures below 1,360 K, the diffusivity of free vacancies was determined from the expression: 1.0 x 10(-4) exp(-0.46/k(B)T) cm(2)/s. The diffusivity of free vacancies at temperatures above 1,450 K was determined within a large margin of error from the expression: 1.0 x 10(-5) exp(-0.1/k(B)T)similar to 6.0 x 10(1) exp(-2.1/k(B)T) cm(2)/s. The effective migration energies of vacancy clusters were estimated to be 2.1-3.5 eV below the melting temperature. These results explained the difference between vacancy diffusivities reported in previous papers, including theoretical and experimental works.