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Dubrovskii VG, Berdnikov YS. Natural scaling of size distributions in homogeneous and heterogeneous rate equations with size-linear capture rates. J Chem Phys. 2015;142(12):124110doi: 10.1063/1.4916323.
Dubrovskii, V. G., & Berdnikov, Y. S. (2015). Natural scaling of size distributions in homogeneous and heterogeneous rate equations with size-linear capture rates. The Journal of chemical physics, 142(12), 124110. https://doi.org/10.1063/1.4916323
Dubrovskii, V G, and Berdnikov, Yu S. "Natural scaling of size distributions in homogeneous and heterogeneous rate equations with size-linear capture rates." The Journal of chemical physics vol. 142,12 (2015): 124110. doi: https://doi.org/10.1063/1.4916323
Dubrovskii VG, Berdnikov YS. Natural scaling of size distributions in homogeneous and heterogeneous rate equations with size-linear capture rates. J Chem Phys. 2015 Mar 28;142(12):124110. doi: 10.1063/1.4916323. PMID: 25833568.
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J Chem Phys. 2015 Mar 28;142(12):124110. doi: 10.1063/1.4916323.

Natural scaling of size distributions in homogeneous and heterogeneous rate equations with size-linear capture rates.

The Journal of chemical physics

V G Dubrovskii, Yu S Berdnikov

Affiliations

  1. St. Petersburg Academic University, Khlopina 8/3, 194021 St. Petersburg, Russia.

PMID: 25833568 DOI: 10.1063/1.4916323

Abstract

We obtain exact solutions of the rate equations for homogeneous and heterogeneous irreversible growth models with linear size dependences of the capture rates. In the limit of high ratios of diffusion constant over deposition rate, both solutions yield simple analytical scaling functions with the correct normalizations. These are given by the cumulative distribution function and the probability density function of the gamma-distribution in homogeneous and heterogeneous cases, respectively. Our size distributions depend on the value of the capture rate a in the reaction of joining two mobile monomers A1 (A1 + A1 → A2) or the monomer attachment to the reactive defect B (A1 + B → AB). In homogeneous cases, the size distribution is monotonically decreasing regardless of a. In heterogeneous growth, the distribution is monotonically decreasing when a ≤ 1 and monomodal when a > 1. The obtained solutions describe fairly well the experimental data on the length distributions of Al, Ga, In, and Mn adatom chains on Si(100)-2 × 1 surfaces.

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