Excess vacancy generation by E-center dissociation in the case of phosphorus diffusion in silicon

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Abstract
Phosphorus diffusion equations in silicon are proposed taking into account the following: Phosphorus diffuses as E centers; an E center is formed by pairing a negatively ionized vacancy with a positively ionized phosphorus atom; with increasing phosphorus concentration, the equilibrium concentration of negatively ionized vacancies increases and the ionization rate of phosphorus decreases. The equations are solved numerically under the boundary conditions of constant surface concentrations of total phosphorus atoms and negatively ionized vacancies. The phosphorus diffusion coefficient depends not only on the vacancy concentration but also on its gradient. The excess vacancies are generated by the E-center dissociation. The concentration and the distribution of the excess vacancies are good enough to explain qualitatively the anomalous diffusion of phosphorus, except the kink in the phosphorus concentration profile.