Publisher's Note: Rate-equation approach to irreversible island growth with cluster diffusion [Phys. Rev. E<b>84</b>, 021604 (2011)]

Hubartt, Bradley; Kryukov, Y. A.; Amar, Jacques G.

doi:10.1103/physreve.84.059901

Cited by 3 publications

(4 citation statements)

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“…Model (I) is based on Smoluchowski aggregation kinetics − and allows for: cyclic generation of single atoms on both the substrate surface and the NPs (deposition); surface diffusion and irreversible aggregation of single atoms; atom attachment to NP (adatom capture); and NP diffusion and coalescence. The NP mobility was assumed to follow a power law of the kind D k = D 1 ( t ) k – s , ,,,− where k is the number of atoms comprising the NP, D 1 ( t ) is the diffusion rate of adatoms, and s > 0. The value of the exponent s typically ranges between 0 and 2 depending on the diffusion mechanism and is, in general, a poorly understood function of NP morphology, NP–substrate interaction, reacting atmosphere, and temperature. ,, As such, here it is regarded as a fitting parameter.…”

mentioning

confidence: 99%

Understanding and Controlling the Aggregative Growth of Platinum Nanoparticles in Atomic Layer Deposition: An Avenue to Size Selection

Grillo

Bui

Moulijn

et al. 2017

J. Phys. Chem. Lett.

111

182

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We present an atomistic understanding of the evolution of the size distribution with temperature and number of cycles in atomic layer deposition (ALD) of Pt nanoparticles (NPs). Atomistic modeling of our experiments teaches us that the NPs grow mostly via NP diffusion and coalescence rather than through single-atom processes such as precursor chemisorption, atom attachment, and Ostwald ripening. In particular, our analysis shows that the NP aggregation takes place during the oxygen half-reaction and that the NP mobility exhibits a size- and temperature-dependent scaling. Finally, we show that contrary to what has been widely reported, in general, one cannot simply control the NP size by the number of cycles alone. Instead, while the amount of Pt deposited can be precisely controlled over a wide range of temperatures, ALD-like precision over the NP size requires low deposition temperatures (e.g., T < 100 °C) when growth is dominated by atom attachment.

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confidence: 99%

Understanding and Controlling the Aggregative Growth of Platinum Nanoparticles in Atomic Layer Deposition: An Avenue to Size Selection

Grillo

Bui

Moulijn

et al. 2017

J. Phys. Chem. Lett.

111

182

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“…The conceptual simplicity of the KRE theory also allows easy adjustment of the various growth processes and their rates. Most recently, an improved self-consistent KRE approach to irreversible island growth has been developed by Hubartt et al [11], which accurately reproduces results obtained from KMC simulations.…”

Section: Introductionmentioning

confidence: 78%

“…In the present model, we neglect adatom detachment from the islands, and explicit island capture rates [11]. In a previous study of submonolayer growth in the Cu/Cu(100) and Cu/Cu(111) systems [51], the island diffusion coefficients were calculated using KMC simulations and then used to calculate the corresponding island size distributions using the KRE approach in the case of hyperthermal deposition.…”

Section: Kinetic Rate Equation Model Of Growthmentioning

confidence: 99%

Multiscale modeling of submonolayer growth for Fe/Mo (110)

Mašín

Kotrla

et al. 2013

Eur. Phys. J. B

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Abstract. We use a multiscale approach to study a lattice-gas model of submonolayer growth of Fe/Mo(110) by Molecular Beam Epitaxy. To begin with, we construct a two-dimensional lattice-gas model of the Fe/Mo(110) system based on first-principles calculations of the monomer diffusion barrier and adatom-adatom interactions. The model is investigated by equilibrium Monte Carlo (MC) simulations to compute the diffusion coefficients of Fe islands of different sizes. These quantities are then used as input to the coarse-grained Kinetic Rate Equation (KRE) approach, which provides time evolution of the island size distributions for a system undergoing diffusion driven aggregation within the 2D submonolayer regime. We calculate these distributions at temperatures T = 500 K and 1000 K using the KRE method. We also employ direct kinetic MC simulations of our model to study island growth at T = 500 K, and find good agreement with the KRE results, which validates our multi-scale approach.

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“…Originally, this selfconsistent theory was formulated for diffusion-limited irreversible growth. 22 Later it has been extended to include detachment kinetics, 23,24 and to examine capture numbers in the presence of cluster diffusion 25 and adsorbate interactions. 26,27 Our goal here is to generalize the self-consistent theory of diffusion-limited growth to multi-component systems.…”

Section: Introductionmentioning

confidence: 99%

Self-consistent rate theory for submonolayer surface growth of multicomponent systems

2014

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The self-consistent rate theory for surface growth in the submonolayer regime is generalized from mono-to multi-component systems, which are formed by codeposition of different types of atoms or molecules. As a new feature, the theory requires the introduction of pair density distributions to enable a symmetric treatment of reactions among different species. The approach is explicitly developed for binary systems and tested against kinetic Monte Carlo simulations. Using a reduced set of rate equations, only a few differential equations need to be solved to obtain good quantitative predictions for island and adatom densities, as well as densities of unstable clusters.

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Publisher's Note: Rate-equation approach to irreversible island growth with cluster diffusion [Phys. Rev. E84, 021604 (2011)]

Cited by 3 publications

References 0 publications

Understanding and Controlling the Aggregative Growth of Platinum Nanoparticles in Atomic Layer Deposition: An Avenue to Size Selection

Understanding and Controlling the Aggregative Growth of Platinum Nanoparticles in Atomic Layer Deposition: An Avenue to Size Selection

Multiscale modeling of submonolayer growth for Fe/Mo (110)

Self-consistent rate theory for submonolayer surface growth of multicomponent systems

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