Stillinger-Weber potential, silicon

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. 

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. 

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... 

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)... 

Here V, V2, and represent the single-body interaction with external fields, two-body separation interactions, and three-body angular interactions respectively. Classical examples of such potentials include the simple two-body Lennard-Jones potential [7], three-body Stillinger-Weber potential for silicon [8], and multibody environment-dependent interatomic potential (EDIP) for silicon [9] and carbon [10], the forces being simply the negative gradient of the potential energy function with respect to position. 

The Stillinger-Weber potential has generally been used for modeling crystalline silicon however, more recently it has also been used for organic molecules as well. Another example of a three-body interatomic potential is the Tersoff potential (Tersoff 1988,1989), which also was created initially in an attempt to accurately model silicon solids. 

Interatomic potentials began with empirical formulations (empirical in the sense that analytical calculations based on them... no computers were being used yet... gave reasonable agreement with experiments). The most famous of these was the Lennard-Jones (1924) potential for noble gas atoms these were essentially van der Waals interactions. Another is the Weber potential for covalent interactions between silicon atoms (Stillinger and Weber 1985) to take into account the directed covalent bonds, interactions between three atoms have to be considered. This potential is well-tested and provides a good description of both the crystalline and... 

Different results were obtained in the case of the Stillinger-Weber (SW) potential for silicon (10). In this case, material deposited on the (ill) orientation was disordered, without distinct layers of atoms. Growth on the (100) face did produce about ten distinct layers at sufficiently high temperatures, although it is not clear whether thicker deposits would retain this order since some degeneration was observed as successive layers were deposited. 

The model surfaces chosen for this study are shown in Figs. 15 and 16. A bare silicon surface, a silicon surface with a single monolayer of Cl chemisorbed (Fig. 15), and a silicon surface with about 2.3 monolayers of Cl mixed into the top 20 A were chosen (Fig. 16). The potentials were Feil-Stillinger-Weber, and the simulations are described by Helmer and Graves (1998). For the results shown here, Ar+ and C1+ are used as the incident ions. 

Abstract Recrystallization of amorphous silicon is studied by classical molecular dynamics. First, a simulation scheme is developed to systematically determine the amorphous on crystal (a/c) silicon motion and compare it to established measurements by Olson and Roth [1], As a result, it is shown that MD simulations using Ter-soff [2] potential are adapted to simulate solid phase epitaxy, although a temperature shift to high values should be accounted for, while simulations using Stillinger-Weber [3] allows to study liquid phase epitaxy. In a second part, the simulation approach is applied to the case of a nanostructure [4] where classical recipes fail to achieve complete recrystallization. MD simulations are shown to be in agreement with experimental observations. The analysis of the structural evolution with time provide a support to understand the origin of the defects. 

Dereli G (1992) Stillinger-Weber type potentials in Monte-Carlo simulation of amorphous-silicon. Mol Simul 8(6) 351-360... 

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