Kinetic Monte Carlo simulations of heteroepitaxial growth

Biehl, Michael; Ahr, M.; Kinzel, Wolfgang; Much, Florian

doi:10.1016/s0040-6090(02)01267-1

Cited by 23 publications

(21 citation statements)

References 8 publications

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“…We have used these local updates in our earlier work, developing an efficient numerical procedure, the Expanding Box Method, to perform these calculations [15,22]. Similar ideas have been used in offlattice simulations [35,36], where this is typically referred to as a "frozen crystal" approximation. The local calculations leave small residual forces at the boundaries, which accumulate over the course of the calculation, and must occasionally be relaxed by performing a full, global solution of the system.…”

Section: Local Energy Methodsmentioning

confidence: 99%

Kinetic Monte Carlo simulation of heteroepitaxial growth: Wetting layers, quantum dots, capping, and nanorings

Schulze

Smereka

2012

Phys. Rev. B

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A new kinetic Monte Carlo algorithm that efficiently accounts for elastic strain is presented and applied to study various phenomena that take place during heteroepitaxial growth. For example, it is demonstrated that faceted quantum dots occur via the layer-by-layer nucleation of pre-pyramids on top of a critical layer with faceting occurring by anisotropic surface diffusion. It is also shown that the dot growth is enhanced by the depletion of the critical layer which leaves behind a wetting layer. Capping simulations provide insight into the mechanisms behind dot erosion and ring formation. The algorithm used for the simulations presented here is based on the observation that adatom and dimer motion is essentially decoupled from the elastic field. This is exploited by decomposing the film into two parts: the weakly bonded portion and the strongly bonded portion. The weakly bonded portion is taken to evolve independent of the elastic field. In this way the elastic field need only be updated infrequently. Extensive validation reveals that there is little loss of fidelity but the algorithm is fifteen to twenty times faster.

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Section: Local Energy Methodsmentioning

confidence: 99%

Kinetic Monte Carlo simulation of heteroepitaxial growth: Wetting layers, quantum dots, capping, and nanorings

Schulze

Smereka

2012

Phys. Rev. B

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“…Reactions are nodes of the graph representing the biochemical network and a directed edge from node i to j exists if a product of reaction i is a reactant of reaction j. Storing such a dependency graph enables a straightforward implementation of an O(1) version of steps (5) and (6).…”

Section: Linear Time Algorithmmentioning

confidence: 99%

“…Once a reaction has been performed in steps (4) and (5), the update portion of the SSA-CR algorithm is performed in step (6). The new propensity of each dependent reaction is compared to its old value.…”

Section: Figure 16: Composition and Rejection Algorithm For Random Vamentioning

confidence: 99%

“…For the general amorphous case, it may be possible to use bond length and angle expectations to significantly reduce the volume of space that need be probed for potential vacant sites near an occupied site. Not surprisingly, most off lattice models of surface deposition and diffusion in the literature are 2D [6,57,58,85] and existing 3D models are for a simple cubic lattice [69,81].…”

Section: Off Lattice Surface Deposition Modelingmentioning

confidence: 99%

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Crossing the mesoscale no-man<U+2019>s land via parallel kinetic Monte Carlo.

Garcia-Cardona

Webb²,

Wagner³

et al. 2009

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The kinetic Monte Carlo method and its variants are powerful tools for modeling materials at the mesoscale, meaning at length and time scales in between the atomic and continuum. We have completed a 3 year LDRD project with the goal of developing a parallel kinetic Monte Carlo capability and applying it to materials modeling problems of interest to Sandia. In this report we give an overview of the methods and algorithms developed, and describe our new open-source code called SPPARKS, for Stochastic Parallel PARticle Kinetic Simulator. We also highlight the development of several Monte Carlo models in SPPARKS for specific materials modeling applications, including grain growth, bubble formation, diffusion in nanoporous materials, defect formation in erbium hydrides, and surface growth and evolution.3

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“…Off lattice KMC simulations of heteroepitaxial growth in 1 + 1 dimensions were presented in a series of papers [3,10,12]. Prior to this, off lattice KMC had been used to investigate diffusion on strained surfaces [23].…”

Section: Modeling Elastic Effectsmentioning

confidence: 99%

Computation of strained epitaxial growth in three dimensions by kinetic Monte Carlo

Russo

Smereka

2006

Journal of Computational Physics

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A numerical method for computation of heteroepitaxial growth in the presence of strain is presented. The model used is based on a solid-on-solid model with a cubic lattice. Elastic effects are incorporated using a ball and spring type model. The growing film is evolved using kinetic Monte Carlo (KMC) and it is assumed that the film is in mechanical equilibrium. The force field in the substrate is computed by an exact solution which is efficiently evaluated using the fast Fourier transform, whereas in the growing film it is computed directly. The system of equations for the displacement field is then solved iteratively using the conjugate gradient method. Finally, we introduce various approximations in the implementation of KMC to improve the computation speed. Numerical results show that layer-by-layer growth is unstable if the misfit is large enough resulting in the formation of three dimensional islands.

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Kinetic Monte Carlo simulations of heteroepitaxial growth

Cited by 23 publications

References 8 publications

Kinetic Monte Carlo simulation of heteroepitaxial growth: Wetting layers, quantum dots, capping, and nanorings

Kinetic Monte Carlo simulation of heteroepitaxial growth: Wetting layers, quantum dots, capping, and nanorings

Crossing the mesoscale no-man<U+2019>s land via parallel kinetic Monte Carlo.

Computation of strained epitaxial growth in three dimensions by kinetic Monte Carlo

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