Multiscale diffusion Monte Carlo simulation of epitaxial growth

Chou, Chuan-Chih; Falk, Michael L.

doi:10.1016/j.jcp.2006.01.012

Cited by 19 publications

(14 citation statements)

References 23 publications

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“…Typical examples include the tau-leap method of Gillespie,75 methods that include coarse-grained species, 76 spatially adaptive coarse grained KMC methods, 77,78 continuum mesoscopic models, 79 and multiscale KMC algorithms for epitaxial film growth. [80][81][82][83][84] We have validated our methodology for decoupling diffusive processes from the rest of the kinetic events by confirming that the underlying Markovian random walk process results: (a) in the same diffusivity for the diffusive species and (b) in the same film growth rate and film structural properties as the original brute force KMC algorithm for the same set of physicochemical input data (e.g., silicon hydride composition), for some initial but long enough time.…”

Section: Diffusion Modellingsupporting

confidence: 52%

A hybrid kinetic Monte Carlo method for simulating silicon films grown by plasma-enhanced chemical vapor deposition

Tsalikis

Baig

Mavrantzas

et al. 2013

The Journal of Chemical Physics

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We present a powerful kinetic Monte Carlo (KMC) algorithm that allows one to simulate the growth of nanocrystalline silicon by plasma enhanced chemical vapor deposition (PECVD) for film thicknesses as large as several hundreds of monolayers. Our method combines a standard n-fold KMC algorithm with an efficient Markovian random walk scheme accounting for the surface diffusive processes of the species involved in PECVD. These processes are extremely fast compared to chemical reactions, thus in a brute application of the KMC method more than 99% of the computational time is spent in monitoring them. Our method decouples the treatment of these events from the rest of the reactions in a systematic way, thereby dramatically increasing the efficiency of the corresponding KMC algorithm. It is also making use of a very rich kinetic model which includes 5 species (H, SiH 3 , SiH 2 , SiH, and Si 2 H 5 ) that participate in 29 reactions. We have applied the new method in simulations of silicon growth under several conditions (in particular, silane fraction in the gas mixture), including those usually realized in actual PECVD technologies. This has allowed us to directly compare against available experimental data for the growth rate, the mesoscale morphology, and the chemical composition of the deposited film as a function of dilution ratio. © 2013 AIP Publishing LLC. [http://dx

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Section: Diffusion Modellingsupporting

confidence: 52%

A hybrid kinetic Monte Carlo method for simulating silicon films grown by plasma-enhanced chemical vapor deposition

Tsalikis

Baig

Mavrantzas

et al. 2013

The Journal of Chemical Physics

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“…We used the multi-scale method to simulate the diffusion of ions and additives in the diffusion layer (5). Figure 3 illustrates the relation between the simulation system and the corresponding real system.…”

Section: Multi-scale Methodsmentioning

confidence: 99%

Simulation of Three-Dimensional Solid-by-Solid Model and Application to Electrochemical Engineering

Kaneko¹,

Hiwatari²,

Ohara³

et al. 2010

ECS Trans.

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A multi-scale kinetic Monte Carlo method has been developed for the molecular simulation of electrodeposition. The basic system is the solid-by-solid model which is a new model for crystal growth with vacancy formation. This model is extended to include the solution and the diffusion layer to take into account the concentration overpotential. The migration of ions in solution is simulated by the coarse-grained random walk. Since the time and length scales in the diffusion layer are largely different from those of the atomic events on the electrode surface, a multi-scale simulation method has been used for the diffusion layer. We have performed the simulation of copper electrodeposition and confirmed that the shape evolution of the surface can be simulated with the formation of the concentration gradient in the diffusion layer.

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“…(An overview of KMC and CGKMC methods is available in [4] and the references therein.) Hybrid methods are available [6,29,12] in which continuum regions far from growth sites are coupled with a KMC method close to the growth sites.…”

Section: Introductionmentioning

confidence: 99%

“…Although approximate methods such as CGKMC and ID have had success in achieving improved computational speed, these too can fail when accuracy is critically important for events occurring at scales below that of the applied coarse grid [6]. In this work we address an application for which KMC is too time-consuming and approximate methods are unable to capture all of the relevant details of the phenomenon of interest: the atomic-scale nucleation and growth of thin metal deposits by electrodeposition at the very low rates associated with epitaxial and/or single crystal growth.…”

Section: Introductionmentioning

confidence: 99%

An exact and efficient first passage time algorithm for reaction–diffusion processes on a 2D-lattice

Bezzola¹,

Bales²,

Alkire³

et al. 2014

Journal of Computational Physics

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We present an exact and efficient algorithm for reaction-diffusion-nucleation processes on a 2D-lattice. The algorithm makes use of first passage time (FPT) to replace the computationally intensive simulation of diffusion hops in KMC by larger jumps when particles are far away from step-edges or other particles. Our approach computes exact probability distributions of jump times and target locations in a closed-form formula, based on the eigenvectors and eigenvalues of the corresponding 1D transition matrix, maintaining atomic-scale resolution of resulting shapes of deposit islands. We have applied our method to three different test cases of electrodeposition: pure diffusional aggregation for large ranges of diffusivity rates and for simulation domain sizes of up to 4096 × 4096 sites, the effect of diffusivity on island shapes and sizes in combination with a KMC edge diffusion, and the calculation of an exclusion zone in front of a step-edge, confirming statistical equivalence to standard KMC simulations. The algorithm achieves significant speedup compared to standard KMC for cases where particles diffuse over long distances before nucleating with other particles or being captured by larger islands.

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Multiscale diffusion Monte Carlo simulation of epitaxial growth

Cited by 19 publications

References 23 publications

A hybrid kinetic Monte Carlo method for simulating silicon films grown by plasma-enhanced chemical vapor deposition

A hybrid kinetic Monte Carlo method for simulating silicon films grown by plasma-enhanced chemical vapor deposition

Simulation of Three-Dimensional Solid-by-Solid Model and Application to Electrochemical Engineering

An exact and efficient first passage time algorithm for reaction–diffusion processes on a 2D-lattice

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