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

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 (n[formula omitted] 1020 cm-3), 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. © 1977, The Electrochemical Society, Inc. All rights reserved.

Duke Scholars

Author Richard B. Fair Electrical and Computer Engineering