Percolation and cluster distribution. III. Algorithms for the site-bond problem

Hoshen, Joseph; Klymko, P. W.; Kopelman, Raoul

doi:10.1007/bf01011170

Cited by 55 publications

(28 citation statements)

References 41 publications

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“…On the other hand, Si atoms are newly allocated to the cells neighboring the outermost surface cells, together with the neutrals accompanied, when the redeposition and/or deposition of etch/sputter products occur. In addition, Sicontaining cells floating in vacuum often occur during simulation, which are removed by percolation according to the Hoshen-Kopelman algorithm; [63][64][65] this is a second one of the key procedures in the cell-based simulations such as ASCeM, because unphysically roughened surface features tend to occur without percolation.…”

Section: Surface Advancementmentioning

confidence: 99%

Surface roughening and rippling during plasma etching of silicon: Numerical investigations and a comparison with experiments

Tsuda¹,

Nakazaki²,

Takao³

et al. 2014

Journal of Vacuum Science &Amp; Technology B, Nanotechnology and Microelectronics: Materials, Processing, Measurement, and Phen

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Surface loss rates of H and Cl radicals in an inductively coupled plasma etcher derived from time-resolved electron density and optical emission measurementsModeling of fluorine-based high-density plasma etching of anisotropic silicon trenches with oxygen sidewall passivation Atomic-or nanometer-scale surface roughening and rippling during Si etching in high-density Cl 2 and Cl 2 /O 2 plasmas have been investigated by developing a three-dimensional atomic-scale cellular model (ASCeM-3D), which is a 3D Monte Carlo-based simulation model for plasma-surface interactions and the feature profile evolution during plasma etching. The model took into account the behavior of Cl þ ions, Cl and O neutrals, and etch products and byproducts of SiCl x and SiCl x O y in microstructures and on feature surfaces therein. The surface chemistry and kinetics included surface chlorination, chemical etching, ion-enhanced etching, sputtering, surface oxidation, redeposition of etch products desorbed from feature surfaces being etched, and deposition of etch byproducts coming from the plasma. The model also took into account the ion reflection or scattering from feature surfaces on incidence and/or the ion penetration into substrates, along with geometrical shadowing of the feature and surface reemission of neutrals. The simulation domain was taken to consist of small cubic cells of atomic size, and the evolving interfaces were represented by removing Si atoms from and/or allocating them to the cells concerned. Calculations were performed for square substrates 50 nm on a side by varying the ion incidence angle onto substrate surfaces, typically with an incoming ion energy, ion flux, and neutral reactant-to-ion flux ratio of E i ¼ 100 eV, C i 0 ¼ 1.0 Â 10 16 cm À2 s À1 , and C n 0 /C i 0 ¼ 100. Numerical results showed that nanoscale roughened surface features evolve with time during etching, depending markedly on ion incidence angle; in effect, at h i ¼ 0 or normal incidence, concavo-convex features are formed randomly on surfaces. On the other hand, at increased h i ¼ 45 or oblique incidence, ripple structures with a wavelength of the order of 15 nm are formed on surfaces perpendicularly to the direction of ion incidence; in contrast, at further increased h i ! 75 or grazing incidence, small ripples or slitlike grooves with a wavelength of <5 nm are formed on surfaces parallel to the direction of ion incidence. Such surface roughening and rippling in response to ion incidence angle were also found to depend significantly on ion energy and incoming fluxes of neutral reactants, oxygen, and etch byproducts. Two-dimensional power spectral density analysis of the roughened feature surfaces simulated was employed in some cases to further characterize the lateral as well as vertical extent of the roughness. The authors discuss possible mechanisms responsible for the formation and evolution of the surface roughness and ripples during plasma etching, including stochastic roughening, local micromasking, and effects of ion reflection, surface temp...

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Section: Surface Advancementmentioning

confidence: 99%

Surface roughening and rippling during plasma etching of silicon: Numerical investigations and a comparison with experiments

Tsuda¹,

Nakazaki²,

Takao³

et al. 2014

Journal of Vacuum Science &Amp; Technology B, Nanotechnology and Microelectronics: Materials, Processing, Measurement, and Phen

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show abstract

“…A serial Monte Carlo program for a general crystal structure was developed using the Metropolis et al (1953), Swendsen and Wang (1987) and Wolff (1989) methods for the spin models of Ising (1925) and Heisenberg (1928). In contrast to the Metropolis method the latter algorithms do not flip single spins but a cluster of spins, which were calculated with the Hoshen-Kopelman algorithm (Hoshen et al 1979). The Curie temperature was determined as the intersection of the fourth-order cumulant of magnetization-temperature curves for different sized systems (Shan-Ho and Salinas 1998).…”

Section: Estimate Of the Curie Temperature (T C )mentioning

confidence: 99%

Ab initioscreening methodology applied to the search for new permanent magnetic materials

et al. 2013

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Machine learning (ML) is increasingly becoming a helpful tool in the search for novel functional compounds. Here we use classification via random forests to predict the stability of half-Heusler (HH) compounds, using only experimentally reported compounds as a training set. Cross-validation yields an excellent agreement between the fraction of compounds classified as stable and the actual fraction of truly stable compounds in the ICSD. The ML model is then employed to screen 71,178 different 1:1:1 compositions, yielding 481 likely stable candidates. The predicted stability of HH compounds from three previous high throughput ab initio studies is critically analyzed from the perspective of the alternative ML approach. The incomplete consistency among the three separate ab initio studies and between them and the ML predictions suggests that additional factors beyond those considered by ab initio phase stability calculations might be determinant to the stability of the compounds. Such factors can include configurational entropies and quasihar-monic contributions.

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“…Although the algorithm was initially applied in statistical physics, nowadays it is used in many diverse fields [ Zhang and Seaton , 1996; Moreira and Barrufetb , 1996; Eddi et al , 1996; Kinney et al , 1994; Hamimov et al , 1989]. The algorithm has been used in ordered lattices with only links, only nodes, or both links and nodes [ Hoshen et al , 1979; Campos et al , 1997; Hoshen , 1980]. The HK algorithm is well‐developed for lattice environments, and less developed for nonlattice environments, such as the disordered networks considered here.…”

Section: Napl Clustersmentioning

confidence: 99%

Impact of wettability alteration on two‐phase flow characteristics of sandstones: A quasi‐static description

Al-Futaisi

Patzek

2003

Water Resources Research

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[1] We describe a two-phase pore network simulator of drainage and imbibition which integrates a realistic representation of pore connectivity and morphology, a quasi-static description of fluid displacement mechanisms, and a sound representation of the wetting properties of a sedimentary rock and of their alteration. The simulator works with 3-D disordered networks of cylindrical ducts with triangular, square, and circular cross sections obtained directly from the analysis of microfocused computed tomography (CT) images of rock samples. All pore-level displacement mechanisms (piston type, snap off, and cooperative pore body filling) are considered with arbitrary receding and advancing contact angles. Bond invasion percolation description is used in primary drainage, while bond site invasion percolation with ordinary percolation on a dual network and compact cluster growth is used in secondary imbibition. In this paper, we resolve how to calculate the relative permeability of nonaqueous phase liquid (NAPL) in the quasi-static approximation of imbibition and illustrate spatial distribution of the clusters of trapped NAPL using our generalization to disordered networks of the Hoshen-Kopelman clusterlabeling algorithm. To understand the impact of wettability alteration on the capillary pressure and relative permeability functions, we perform a series of drainage and imbibition simulations by changing the range of advancing contact angles. Our study indicates that in imbibition, transport properties of a permeable solid are quite sensitive to the hysteresis between the receding and advancing contact angle. This sensitivity reflects competition among the different displacement mechanisms, which shapes the relative permeabilities, capillary pressures, and the distribution of the trapped NAPL.

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Percolation and cluster distribution. III. Algorithms for the site-bond problem

Cited by 55 publications

References 41 publications

Surface roughening and rippling during plasma etching of silicon: Numerical investigations and a comparison with experiments

Surface roughening and rippling during plasma etching of silicon: Numerical investigations and a comparison with experiments

Ab initioscreening methodology applied to the search for new permanent magnetic materials

Impact of wettability alteration on two‐phase flow characteristics of sandstones: A quasi‐static description

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