Recent experimental and theoretical studies revealed that dopants in germanium ͑Ge͒ cluster with lattice vacancies ͑V͒. The existence of these larger clusters has been recently predicted and is important as they can contribute to the low activation of dopants in Ge. With the use of electronic structure calculations we study the binding energies of clusters formed with the association of dopant atoms and vacancies. As an example of the kinetics of such clusters the diffusion of two phosporous-vacancy ͑P 2 V͒ clusters via the ring mechanism of diffusion in predicted. These P 2 V clusters are important as they can act as precursors for the formation of the larger P 3 V and P 4 V clusters. The present study provides information on the structure of clusters and is consistent with recent experimental results, which indicate that the formation of clusters in heavily doped Ge is possible. In agreement with experiment, we predict that the diffusion of P V pairs is retarded by the addition of a further P atom. © 2010 American Institute of Physics. ͓doi:10.1063/1.3361115͔Ge has the potential to replace silicon ͑Si͒ in advanced nanoelectronic devices because of its higher mobility of holes and electrons, compatibility with Si manufacturing processes, increased dopant solubility, and smaller band gap.1 For the fabrication of Ge-based devices, it is important to form shallow junctions with high electrically active dopant concentrations. The absolute control required for these processes necessitates the determination of the migration properties of dopants in Ge. 2 This is particularly important for dopants such as P or arsenic ͑As͒ that present problematic diffusion and activation control. 3,4 In recent studies, it has been concluded that self and dopant atom diffusion in Ge is mainly described on the basis of the V-mechanism. 2,5-8 The formation of clusters containing two dopant atoms surrounding a V has been recently observed. 7 These are important as they can act as precursors for the formation of larger D n V m clusters. The formation of D n V m clusters can lead to the trapping of charge in the cluster, therefore the donor atoms do not donate their electron nor do the acceptor atoms accept their electron from the Ge lattice. This may lead to the deactivation of a significant part of the total dopant dose. The formation and relative concentrations of the larger D n V clusters have been recently predicted with the use of density functional theory ͑DFT͒ and mass action analysis. 9-11 For heavily phosphorous-doped Ge secondary ion mass spectroscopy ͑SIMS͒ measurements reveal that a significant amount of the dose is trapped in characteristic humps, which have been attributed to clustering. 4,12 For other technologically important such as boron ͑B͒, aluminum ͑Al͒, gallium ͑Ga͒, indium ͑In͒ carbon ͑C͒, Si, nitrogen ͑N͒, and antimony ͑Sb͒, there are only a few studies investigating their clustering and diffusion ͑for example Refs. 2, 6, and 7 and references therein͒. The aim of this study is to compare the migration energy barrie...