The influence of the solubility limit on acceptor diffusion in III-V compounds

Abstract

A simple model is proposed describing the diffusion of group II acceptors in III‐V semiconducting compounds in terms of reaction‐diffusion equations. This makes it possible to calculate the concentration profiles of both acceptors and other point defects at the same time. It turns out that it is the effect of the solubility limit of dopants that is responsible for the typical box‐like shape of the profiles showing a characteristic plateau. Furthermore, a physical interpretation is given of the markedly enhanced diffusion at high concentration. Finally, the limited application of the diffusion equation is discussed and a concentration dependent diffusion coefficient is calculated.

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] …”

Erratum: “Reply to “A Comment on ‘Atomistic models of vacancy-mediated diffusion in silicon’ ’’ ’’ [J. Appl. Phys. 79, 7409 (1996)]

“…[3][4][5][6] In Ref. 2, tracer diffusion was assumed, but an effective diffusivity of the form of Eq.…”