Diffusion and defect reactions between donors, C, and vacancies in Ge. II. Atomistic calculations of related complexes

Electronic structure calculations are used to study the stability, concentration, and migration of vacancy-donor (phosphorus, arsenic, and antimony) complexes in germanium, in the presence of carbon. The association of carbon with mobile vacancy-donor pairs can lead to energetically favorable and relatively immobile complexes. It is predicted that the complexes formed between lattice vacancies, carbon, and antimony substitutional atoms are more stable and less mobile compared to complexes composed of vacancies, carbon, and phosphorus or arsenic atoms. Then, with the use of mass action analysis, the relative concentrations of the most important complexes are calculated, which depend also on their relative stability not just their absolute stability. Overall, the theoretical predictions are consistent with experimental results, which determined that the diffusion of vacancy-donor defects is retarded in the presence of carbon, especially in samples with a high concentration of carbon. In addition, the calculations provide information on the structure and the equilibrium concentration of the most important complexes and details of their association energies.