A Quantitative Model for the Diffusion of Phosphorus in Silicon and the Emitter Dip Effect

TLDR

The study presents a quantitative model of phosphorus diffusion in silicon that explains electrically inactive P, the kink and tail regions, and the emitter dip effect. The model identifies three vacancy‑charge‑state diffusion coefficients, shows that in high‑concentration regions P+V= pairs dominate diffusion, and that at lower Fermi levels V= dissociates into P+V− pairs, generating excess V− vacancies that drive enhanced tail diffusion and, in npn structures, convert to V+ vacancies that increase base dopant diffusivity and produce the emitter dip. The model predicts that the enhanced tail diffusion and base dopant diffusivity can increase by up to a factor of 135 at 900 °C, driven by a steady‑state excess of V− vacancies generated through P+V− pair dissociation.

Abstract

A consistent model of P diffusion in Si is presented which accounts quantitatively for the existence of electrically inactive P, the "kink" and the tail regions of the P profile, and the emitter dip effect. In this model it is shown that three intrinsic P diffusion coefficients exist, each one associated with the diffusion of P with vacancies in three different charge states. In the so‐called "anomalous" high concentration region of the profile , it is shown that equilibrium concentration of P+ V= pairs dominates P diffusion and P electrical activity. At lower electron concentrations when the Fermi level is ∼0.11 eV below the conduction band, the V= vacancy gives up an electron, and the 0.3 eV lower binding energy of the resulting P+ V− pairs enhances the probability for pair dissociation by a factor of 10–35, depending on the temperature. This effect creates a steady‐state excess concentration of V−vacancies which flow away from the point of pair dissociation. The concentration of excess V− vacancies created is proportional to the number of P+ V=pairs created at the Si surface times the enhanced probability for pair dissociation. These vacancies in the V− charge state interact with P to create the enhanced tail diffusion. In a npn structure, the charge state of the excess vacancies becomes V+ in the base region, thus enhancing the diffusivity of the base dopant and causing the emitter dip effect. The magnitude by which the P tail diffusivity and the base dopant diffusivity are enhanced is the same and may reach a factor of 135 for a 900°C diffusion.