A quantitative model for the coupled diffusion of phosphorus and point defects in silicon

In this paper, we develop and analyze models for the coupled diffusion of dopants and point defects, since such models have been observed to display the qualitative aspects of high concentration phosphorus diffusion profiles such as the characteristic 'kink and tail.' We begin by describing a general model for phosphorus diffusion via dopant/defect pairs assuming local equilibrium for electronic processes, but not for chemical processes. Using this system, along with parameters based on experimental data previously reported in the literature, we test common model assumptions. Our analysis concludes that dopant/defect pairing reactions are near local equilibrium, but that defect recombination reactions are not. When then use a simplified model, based on the assumption that the pairing reactions are near equilibrium to simulate phosphorus profiles. By including diffusion of phosphorus via negatively-charged phosphorus/vacancy pairs, in addition to diffusion via phosphorus/interstitial pairs which dominates in intrinsic materials, we are able to match experimental phosphorus diffusion profiles with surface concentrations ranging from intrinsic to solid-solubility at 900 and 1000 degree C, while remaining consistent with the broad range of previously observed behavior of phosphorus and point defects in silicon.