Enhanced Diffusion of Dopants at Concentrations near the Solubility Limit

Abstract

When discussing diffusion processes of dopants at very high concentrations, i.e., close to their solubility limit, it is absolutely necessary to take into account the fact that the number of substitutional sites accessible to additional donors/acceptors is decreasing or equal to zero when their concentration approaches/exceeds the solubility limit. It turns out that this results in a largely enhanced diffusion at dopant concentrations comparable with their solubility limit. Furthermore, for simple diffusion mechanisms it is possible to derive an analytical expression for the effective diffusion coefficient, depending on the dopant concentration, which can be used in process modeling.) unless CC License in place (see abstract). ecsdl.org/site/terms_use address. Redistribution subject to ECS terms of use (see 128.6.218.72 Downloaded on 2015-04-04 to IP

Reply to ‘‘Comment on ‘Atomistic models of vacancy-mediated diffusion in silicon’ ’’ [J. Appl. Phys. 78, 2362 (1995)]

“…[12][13][14][15] In fact, despite extensive claims regarding the ability of the Antoncik model to match experiments, direct comparisons of that model to experimental results are notably lacking. 1,[3][4][5][6][7][8][9] Since it provides the basis for the arguments in Ref. 1, we return to the model proposed by Antoncik and show that it is based on a series of faulty assumptions.…”

“…We begin our response by directly rebutting these criticisms and continue by pointing out the fundamental errors underlying the alternative analysis proposed by Antoncik. 1,[3][4][5][6][7][8][9] Antoncik's 1 first point is that our ''conclusion that the very high increase of D eff at high concentrations is 'due to interactions of vacancies with more than one dopant atom''' 2 is ''questionable'' because it ''did not take into account the interaction of the dopant atom with its neighboring dopant atoms.'' To begin, it should be noted that the conclusion quoted above actually refers to the simulations, not the experiments.…”

“…In his criticism, Antoncik provides an alternative model to account for the experimental behavior observed by Larsen et al 10 to which we compare our simulation results. This model, which has been previously discussed at great length in a series of articles, [3][4][5][6][7][8][9] does not provide a plausible alternative explanation since, as is shown below, it is based on faulty assumptions regarding the basic processes which limit equilibrium solid solubility and control pair formation/dissolution. There certainly are direct dopant/ dopant interactions which lead to dopant aggregation and deactivation in silicon, but not of the type assumed in the Antoncik model.…”

“…3,[6][7][8][9] Given these equations and the assumptions that the pairing process is rapid relative to the evolution of the concentrations and that only paired donors diffuse, the effective diffusivity of the total donor concentration ͑paired and unpaired͒ can be written as 1,[7][8][9] …”

“…[18][19][20] The work of Bakeman and Borrego 21 is cited to support the approach used by Antoncik. 1,7 As in Refs. 1, 3-9, the analysis in Ref.…”