Modeling of phosphorus diffusion in Ge accounting for a cubic dependence of the diffusivity with the electron concentration

Up to now, P diffusion in Ge is modeled with an effective diffusivity involving at most a quadratic dependence with the free electron concentration (n). However, recent theoretical studies suggest the existence of a triply negatively charged state for the free vacancy in germanium and experimental data indicate that the E center (PV pair) in Ge has a double acceptor state. These two facts would be consistent with a diffusivity model involving a cubic dependence with n. In this paper the validity of this approach is checked for both pure thermal diffusion (intrinsic and extrinsic) and implanted phosphorus, using either our own experiments or other data available from the literature. Although some discrepancies still exist in some cases for the redistribution of implanted P, it is shown that the introduction of this cubic dependence significantly improves the overall agreement as compared with the usual model.