Ab initio investigation of phosphorus and boron diffusion in germanium

P and B diffusion has been modeled in Ge using ab initio   methods along with the formation energies and electrical levels of various PxVyPxVy defects expected to be important in the deactivation of P in heavily n-doped Ge. The calculated activation barrier for B diffusion is found to be substantially lower than the measured barrier. However, the exceptionally large pre-exponential factor in the measured diffusivity points to a Meyer–Neldel rule operating and accounting for the discrepancy. The magnitude of the theoretical diffusivity is about a factor 10 lower than observed. For P diffusion, the experimental and theoretical results are in much closer agreement. The formation energy calculations show that all PxVyPxVy clusters are stable with respect to their component defects, and all but P4VP4V are predicted to introduce acceptor levels into the band gap. A simple analysis of possible formation mechanisms and Coulombic contributions suggests that as in Si, P3VP3V is the most important compensating center in heavily n-doped Ge.