Faceting at the silicon (100) crystal-melt interface: Theory and experiment

Landman, Uzi; Luedtke, W. D.; Barnett, R. N.; Cleveland, C. L.; Ribarsky, M. W.; Arnold, E.; Ramesh, S.; Baumgart, Helmut; Martínez, Alberto Pastor; Khan, Babar Shahzad

doi:10.1103/physrevlett.56.155

Cited by 147 publications

(38 citation statements)

References 7 publications

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“…The surface tension of the interface gives rise to a free energy barrier that the system has to overcome to transform from one phase to the other [1]. A conceptual appealing and widely used strategy to overcome the hysteresis problem is to preform simulations starting from an initial configuration with two phases in a periodic box [2][3][4][5][6][7][8][9][10][11][12][13][14]. When a steady state situation is reached the stable phase will grow at the expense of the other phase.…”

Section: Introductionmentioning

confidence: 99%

Determining the phase diagram of water from direct coexistence simulations: The phase diagram of the TIP4P/2005 model revisited

Conde

Gonzalez

Abascal

et al. 2013

The Journal of Chemical Physics

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Computing phase diagrams of model systems is an essential part of computational condensed matter physics. In this paper we discuss in detail the interface pinning (IP) method for calculation of the Gibbs free energy difference between a solid and a liquid. This is done in a single equilibrium simulation by applying a harmonic field that biases the system towards two-phase configurations. The Gibbs free energy difference between the phases is determined from the average force that the applied field exerts on the system. As a test system we study the Lennard-Jones model. It is shown that the coexistence line can be computed efficiently to a high precision when the IP method is combined with the Newton-Raphson method for finding roots. Statistical and systematic errors are investigated. Advantages and drawbacks of the IP method are discussed. The high pressure part of the temperature-density coexistence region is outlined by isomorphs. I. INTRODUCTIONAn important aspect of computational condensed matter physics is to compute phase diagrams of model systems. The naive approach is to preform a long-time simulation at a selected state point and hope that the system by itself finds its preferred phase, i.e. the phase with the lowest Gibbs free energy. In most cases this strategy is not viable since first-order transitions are associated with hysteresis. Thus the system is likely to be stuck in a metastable phase. The origin of this hysteresis effect is the formation of an interface between two phases. The surface tension of the interface gives rise to a free energy barrier that the system has to overcome to transform from one phase to the other [1]. A conceptual appealing and widely used strategy to overcome the hysteresis problem is to preform simulations starting from an initial configuration with two phases in a periodic box [2][3][4][5][6][7][8][9][10][11][12][13][14]. When a steady state situation is reached the stable phase will grow at the expense of the other phase. The disadvantages of this approach are that: i) it relates to a non-equilibrium computation that cannot be done ad infinitum; ii) a sufficiently large system is needed to reach the steady state growth; iii) thermal fluctuation will result in some probability that the system will move towards the disfavored phase. In a recent paper [15] these problems were resolved by introducing the so-called "interface pinning" (IP) method. In short, the idea of this method is to compute the average force needed to keep the system in the two-phases state. This is done by connecting the system to a harmonic field which couples to an order-parameter that distinguished between the two phases of interest. The Gibbs free energy difference between the phases is determined by the average force that the applied field exerts on the system. Thus, a standard * ulf.pedersen@tuwien.ac.at ad infinitum equilibrium simulation gives the information needed to computed the Gibbs free energy difference between the two phases of interest.The purpose of this paper is to give a detailed ...

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Section: Introductionmentioning

confidence: 99%

Determining the phase diagram of water from direct coexistence simulations: The phase diagram of the TIP4P/2005 model revisited

Conde

Gonzalez

Abascal

et al. 2013

The Journal of Chemical Physics

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“…Early work from Landman et al 20 revealed the formation of ͕111͖ oriented facets in MD simulations of a SW Si crystalmelt interface with an average orientation normal to ͑100͒; the study also showed crystalline ordering in the melt region close to the interface. Subsequent work by Luedtke et al 21 to investigate crystal growth from the melt at the ͑111͒ interface of SW Si showed clearly the qualitative nature of the "layerby-layer" growth mode for this faceted interface.…”

Section: Introductionmentioning

confidence: 99%

Kinetic coefficient of steps at the Si(111) crystal-melt interface from molecular dynamics simulations

Buta

Asta

Hoyt

2007

The Journal of Chemical Physics

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Nonequilibrium molecular dynamics simulations are applied to the investigation of step-flow kinetics at crystal-melt interfaces of silicon, modeled with the Stillinger-Weber potential ͓Phys. Rev. B 31, 5262 ͑1985͔͒.Step kinetic coefficients are calculated from crystallization rates of interfaces that are vicinals of the faceted ͑111͒ orientation. These vicinal interfaces contain periodic arrays of bilayer steps, and they are observed to crystallize in a step-flow growth mode at undercoolings lower than 40 K. Kinetic coefficients for both ͓110͔ and ͓121͔ oriented steps are determined for several values of the average step separation, in the range of 7.7-62.4 Å. The values of the step kinetic coefficients are shown to be highly isotropic, and are found to increase with increasing step separation until they saturate at step separations larger than ϳ50 Å. The largest step kinetic coefficients are found to be in the range of 0.7-0.8 m / ͑sK͒, values that are more than five times larger than the kinetic coefficient for the rough ͑100͒ crystal-melt interface in the same system. The dependence of step mobility on step separation and the relatively large value of the step kinetic coefficient are discussed in terms of available theoretical models for crystal growth kinetics from the melt.

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“…Note also that SW potential has been used in a number of studies related to crystal-melt interface. 2,5,28 Nonetheless, it will be necessary to study the dependence of ␥ on the model potential 29 by employing several different potentials of silicon ͓e.g., Tersoff-89 ͑Ref. 30͔͒ and this task will be undertaken as a future work.…”

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Anisotropy of crystal-melt interfacial free energy of silicon by simulation

Apte

Zeng

2008

Applied Physics Letters

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We extend the cleaving wall method to a nonpairwise additive potential. Using this method, we compute the anisotropy of crystal-melt interfacial free energy γ for Stillinger–Weber potential of silicon [F. H. Stillinger and T. A. Weber, Phys. Rev. B 31, 5262 (1985)]. The calculated γ for (100), (111), and (110) orientations are 0.42±0.02, 0.34±0.02, and 0.35±0.03J∕m2, respectively. The anisotropy in γ we found is consistent with the experimental observation that Si(100)-melt interface develops (111) facets and also helps in explaining a higher undercooling observed for Si(111)-melt interface in Czochralski method.

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Faceting at the silicon (100) crystal-melt interface: Theory and experiment

Cited by 147 publications

References 7 publications

Determining the phase diagram of water from direct coexistence simulations: The phase diagram of the TIP4P/2005 model revisited

Determining the phase diagram of water from direct coexistence simulations: The phase diagram of the TIP4P/2005 model revisited

Kinetic coefficient of steps at the Si(111) crystal-melt interface from molecular dynamics simulations

Anisotropy of crystal-melt interfacial free energy of silicon by simulation

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