Simulation of intrinsic point defect properties and vacancy clustering during Czochralski germanium crystal growth

Results are presented of the simulation of vacancy agglomeration in Czochralski-grown germanium crystals. Molecular dynamics (MD) calculations using a Stillinger and Weber potential are used to determine the thermodynamic properties of intrinsic point defects in germanium. It is shown that the vacancy diffusivity derived from Stillinger and Weber MD calculations does not lead to realistic vacancy cluster distributions. Using a corrected value of the vacancy diffusivity, taking into account experimental data for the self-diffusion coefficient, leads to the correct vacancy cluster size distributions. The good agreement with respect to size between calculated vacancy cluster distributions and observed pits on germanium wafer surfaces strongly suggests that these pits originate from voids formed by vacancy clustering and vacancy diffusion controlled cluster growth during the cooling of the crystal.