Faster Monte Carlo simulations

Blue, James L.; Beichl, Isabel; Sullivan, Francis

doi:10.1103/physreve.51.r867

Cited by 128 publications

(101 citation statements)

References 5 publications

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“…The geometry of the step edges with some of the pertinent single jump processes is shown in Fig. 1 The KMC simulations were implemented using the algorithm by Bortz et al [14] with a binary tree structure [15]. This allowed us to grow up to five monolayers (ML) of Cu under realistic temperature and flux conditions to study the development of unstable ledge patterns.…”

Section: (Received 14 November 2000)mentioning

confidence: 99%

Instability and Wavelength Selection during Step Flow Growth of Metal Surfaces Vicinal to fcc(001)

et al. 2001

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We study the onset and development of ledge instabilities during growth of vicinal metal surfaces using kinetic Monte Carlo simulations. We observe the formation of periodic patterns at [110] close packed step edges on surfaces vicinal to fcc(001) under realistic molecular beam epitaxy conditions. The corresponding wavelength and its temperature dependence are studied by monitoring the autocorrelation function for step edge position. Simulations suggest that the ledge instability on fcc(1,1,m) vicinal surfaces is controlled by the strong kink Ehrlich-Schwoebel barrier, with the wavelength determined by dimer nucleation at the step edge. Our results are in agreement with recent continuum theoretical predictions, and experiments on Cu(1,1,17) vicinal surfaces.

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Section: (Received 14 November 2000)mentioning

confidence: 99%

Instability and Wavelength Selection during Step Flow Growth of Metal Surfaces Vicinal to fcc(001)

et al. 2001

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“…With a direct implementation, i.e., with the integration scheme [18], the order of the computation is O(N ), which is very time consuming. Other approaches are proposed like a three level search for spin systems [19]. The three-level search improves the efficiency of the search by determining coordinates of a spin to update one by one.…”

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confidence: 99%

Efficiency of rejection-free dynamic Monte Carlo methods for homogeneous spin models, hard disk systems, and hard sphere systems

2006

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We construct a rejection-free Monte Carlo method for the hard-disk system. Rejection-free Monte Carlo methods preserve the time-evolution behavior of the standard Monte Carlo method, and this relationship is confirmed for our method by observing nonequilibrium relaxation of a bondorientational order parameter. The rejection-free method gives a greater computational efficiency than the standard method at high densities. The rejection free method is implemented in a shrewd manner using optimization methods to calculate a rejection probability and to update the system. This method should allow an efficient study of the dynamics of two-dimensional solids at high density.

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“…For every deposition event, a random number between 0 and 1 was generated, and then the final deposited site was chosen by the BortzKalos-Lebowitz (BKL) method, which is considered to be effective algorithm for Monte Carlo simulations. 25 And the BKL method is as follows. The whole procedure is repeated in the next time step and so on, until the simulation is complete.…”

Section: -4mentioning

confidence: 99%

Analysis of polytype stability in PVT grown silicon carbide single crystal using competitive lattice model Monte Carlo simulations

et al. 2014

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Polytype stability is very important for high quality SiC single crystal growth. However, the growth conditions for the 4H, 6H and 15R polytypes are similar, and the mechanism of polytype stability is not clear. The kinetics aspects, such as surface-step nucleation, are important. The kinetic Monte Carlo method is a common tool to study surface kinetics in crystal growth. However, the present lattice models for kinetic Monte Carlo simulations cannot solve the problem of the competitive growth of two or more lattice structures. In this study, a competitive lattice model was developed for kinetic Monte Carlo simulation of the competition growth of the 4H and 6H polytypes of SiC. The site positions are fixed at the perfect crystal lattice positions without any adjustment of the site positions. Surface steps on seeds and large ratios of diffusion/deposition have positive effects on the 4H polytype stability. The 3D polytype distribution in a physical vapor transport method grown SiC ingot showed that the facet preserved the 4H polytype even if the 6H polytype dominated the growth surface. The theoretical and experimental results of polytype growth in SiC suggest that retaining the step growth mode is an important factor to maintain a stable single 4H polytype during SiC growth.

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Faster Monte Carlo simulations

Cited by 128 publications

References 5 publications

Instability and Wavelength Selection during Step Flow Growth of Metal Surfaces Vicinal to fcc(001)

Instability and Wavelength Selection during Step Flow Growth of Metal Surfaces Vicinal to fcc(001)

Efficiency of rejection-free dynamic Monte Carlo methods for homogeneous spin models, hard disk systems, and hard sphere systems

Analysis of polytype stability in PVT grown silicon carbide single crystal using competitive lattice model Monte Carlo simulations

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