Ab initioinvestigation of phosphorus diffusion paths in germanium

Abstract

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 ${E}_{v}+0.5\text{ }\text{eV}$, a barrier for phosphorus diffusion via the doubly negative phosphorus-vacancy defect of $\ensuremath{\sim}2.5\text{ }\text{eV}$ was calculated, which is roughly $\ensuremath{\sim}1\text{ }\text{eV}$ below the equivalent process in Si.