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

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 Formula , 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.