Ab initioinvestigation of phosphorus diffusion paths in germanium

Ab initio calculations were performed to study phosphorus diffusion in germanium through vacancy and interstitial-mediated mechanisms as well as a correlated exchange mechanism without interaction with a mediating defect. It was found that the most favorable diffusion mechanism is sensitive to the position of the Fermi level within the band gap. For material with a midgap Fermi level, the neutral or singly positive phosphorus interstitial is the dominant diffusing species, while in n-type material, it is the doubly negative phosphorus-vacancy complex. For a Fermi level position of Eᵥ+0.5 eV, a barrier for phosphorus diffusion via the doubly negative phosphorus-vacancy defect of ~2.5 eV was calculated, which is roughly ~1 eV below the equivalent process in Si.