Atomistic modeling of high-concentration effects of impurity diffusion in silicon

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Abstract
The vacancy mechanism of dopant diffusion in silicon is investigated on a microscopic model level. The concentration dependence of the dopant diffusion constant in the high-concentration regime is simulated using the Monte-Carlo method and an atomistic model of clustering and precipitation. The simulation takes into account the microscopic forces between particles (dopant atoms and vacancies) in a quantitative manner. Since sufficiently accurate data for the binding strength and shape of the interaction potentials are not available, we analyze a variety of model approaches for these interactions to come to general conclusions for the macroscopic consequences of microscopic models. First, pure attractive forces between dopants and vacancies as usually assumed in the literature [S. M. Hu, Phys. Status Solidi B 60, 595 (1973)] are discussed. In contradiction to previous results from the literature [S. T. Dunham and C. D. Wu, J. Appl. Phys. 78, 2362 (1995)] we find that with this approach it is not possible to fit the experimental results. Also, models with repulsive dopant–dopant potentials of Coulomb shape together with attractive dopant–vacancy forces are found to give unrealistic results. On the other hand, a good fit to the experimental data is obtained with the assumption of a nonbinding dopant–vacancy interaction that only increases the mobility of the vacancy in the neighborhood of a dopant. The parameters of the atomistic potential are derived from a fit of the simulations to the experimental values. The simulation results for the different microscopic approaches are also used to give an assessment of the validity of models for high-concentration diffusion that are based on percolation theory [D. Mathiot and J. C. Pfister, J. Phys. (France) Lett. 43, L-453 (1982); D. Mathiot and J. C. Pfister, J. Appl. Phys. 66, 970 (1989)].