Stillinger-Weber potential

The function/c is a smoothing function with the value 1 up to some distance Yy (typically chosen to include just the first neighbour shell) and then smoothly tapers to zero at the cutoff distance, by is the bond-order term, which incorporates an angular term dependent upon the bond angle 6yk- The Tersoff pofenfial is more broadly applicable than the Stillinger-Weber potential, but does contain more parameters. 

Thermodynamic properties. A molecular-dynamics simulation method (using a steepest decent method) with Stillinger-Weber potential is employed to optimize structures and to obtain the cohesive en-... 

A full-scale treatment of crystal growth, however, requires methods adapted for larger scales on top of these quantum-mechanical methods, such as effective potential methods like the embedded atom method (EAM) [11] or Stillinger-Weber potentials [10] with three-body forces necessary. The potentials are obtained from quantum mechanical calculations and then used in Monte Carlo or molecular dynamics methods, to be discussed below. 

In a similar study, Khor and Das Sarma studied the diffusion of Si, Si2 and Si3 on the (001), (011), and (111) surfaces of silicon. In their study, the forces on all of the atoms were determined by the Stillinger-Weber potential. For single atoms on all surfaces, they report an upper bound for diffusion of 4.8 X 10 cm /sec at 1600K. This value is significantly less than both the range determined by NoorBatcha of 2.031 x 10" to 15.8 x 10" cm /sec ", and the experimental estimate of 10 cm /sec. They also report that diatomic Si2 molecules diffuse more readily than single atoms on the Si(l 11) surface. 

For atoms with sp3 hybridization (e.g., Si in Si02), the parameter cosdg = —1/3 corresponds to the angle in the tetrahedron. The three-body term with an angular dependence is also used in the Stillinger-Weber potential [63] for systems with the diamond lattice... 

As can be seen, there are eight parameters in the Stillinger-Weber potential A,B,p, q, /r, Tc, Z, and a. These parameters are fitted to experimental data, such as lattice constants and cohesive energy, for the diamond stmcture. The angle is the angle centered on atom i. If djik is 1010.47°, cos 6jii = the angular function has a minimum of zero, which... 

After ealeulating discrete values of frequency and relaxation time for the polarization mode and different wave veetors, a continuous function for the relaxation time and dispersion relations can be established for eaeh mode. The results shown in Fig. 3 are obtained with the Lennard-Jones potential for Argon. An approach similar to that described above can be applied with the Stillinger-Weber potential for silieon. 

Silicon thin film thermal conductivities are predicted using equilibrium molecular dynamics and the Grccn-Kubo relation. Periodic boundary conditions are applied in the direetions parallel to the thin film surfaees (Fig. 5). Atoms near the surfaces of the thin film are subjeeted to the above-described repulsive potential in addition to the Stillinger-Weber potential [75]. Simulations were also performed adding to each surface four layers of atoms kept frozen at their crystallographic positions, in order to eompare the dependence of the predieted thermal eonduetivities on the surface boundary eonditions. We found that the thermal eonduetivities obtained using frozen atoms or the repulsive potential are identical within the statistical deviations, exeept for the in-plane thermal eonduetivity of films with thickness less than 10 nm [79]. Therefore, in the present study, we present only the predietions obtained with the repulsive potential. 

Ion-enhanced etching mechanisms using MD were addressed by Barone and Graves (1995a,b, 1996) in several papers. In the first paper, the Stillinger-Weber potentials were used for Si-Si, Si-F, and F-F interactions. Si-Ar... 

The novel feature associated with the Stillinger-Weber potentials is this angular term. To be more specific, the three-body terms have an angular dependence of the form... 

Forces Associated with Stillinger-Weber Potentials Obtain an expression for the forces between atoms in a system characterized by the Stillinger-Weber potential. An explicit expression may be found in Wilson etal. (1990). 

Use the Stillinger-Weber potential to determine the energy vs volume curves for Si in the diamond cubic, simple cubic, fee, bee and yS-Sn structures. 

Use the Stillinger-Weber potential to compute the unrelaxed vacancy formation energy in Si. 

Energetics of Surfaces Using Stillinger-Weber Potentials Compute the energy of the unrelaxed and unreconstructed (100) surface in Si. Next, use either static energy minimization or molecular dynamics to relax this surface and examine the resulting reconstruction. 

There is another family of models that also favors local tetrahedral arrangements in the liquid phase and shows LLPTs. This family of models is based on the Stillinger Weber potential [86], originally proposed as a model for Si. It has also been reparameterized in order to model germanium [15] and water [87]. In this model, atoms interact via a basic two-body interaction term, Vzir), plus a three-body interaction term, W3 (r, 6), that favors the local tetrahedral arrangement v = V2 (r) + Xv3 (r, 9), where X controls the tetrahedrality of the model. For small values of X, the LLPT is not observed and for very large values, crystallization occurs only for intermediate values of X, the LLPT is observed in simulations [40,88]. 

The Stillinger-Weber potential, so far the most widely used interaction potential for silicon, comprises a two- and a three-body interaction potential. The crystalline phase of silicon at low pressures is in the diamond cubic structure, and it melts into a high-density liquid phase. Stillinger and Weber, after a search through a class of interaction potentials with two- and three-body interactions, defined their empirical potential as follows ... 

The Stillinger-Weber potential is one of the best model potentials for studying the liquid and supercooled liquid phases of silicon, since the parameters of the model potential are chosen explicitly to predict the structural properties of real liquid silicon. However, whether the model faithfully captures temperature variations of thermophysical, structural, and dynamic properties are unclear, and we should expect that the results obtained from the simulation will be sensitive to the model parameters. The finding of a liquid liquid transition in supercooled silicon using the SW potential has been interrogated by Beaucage and Mousseau... 

Mainly in the field of materials science various types of potentials have been developed based on the concept of the bond order. " Like for reactive force fields also for the application of these potentials a specification of the atomic positions is sufficient. Although many of these potentials like the Tersoff potential, the Stillinger-Weber potential, the Breimer potential and many others have been introduced already one or two decades ago, they are still frequently used in materials simulations, in particular for semiconductors. For metallic systems the embedded atom method (EAM) and the modified embedded atom method (MEAM) introduced by Baskes and coworkers are widely distributed. 

Application The authors applied this methodology to the investigation of Si. In particular, they studied brittle fracture mechanisms (crack propagation, determination of the stress-strain curve, and so on), vacancy diffusion, and gliding of a pair of partial dislocations at finite temperature. In all of these applications, the authors used a tight-binding (TB) scheme to perform the quantum calculations, and the Stillinger-Weber potential (SW) for the classical ones. 

Y. Lee, G.S. Hwang, Force-matching-based parametrization of the Stillinger-Weber potential for thermal conduction in silicon. Phys. Rev. B 85, 125204-1-5 (2012)... 

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