Highly optimized empirical potential model of silicon

Abstract

We fit an empirical potential for silicon using the modified embedded atom (MEAM) functional form, which contains a nonlinear function of a sum of pairwise and three-body terms. The three-body term is similar to the Stillinger-Weber form. We parametrized our model using five cubic splines, each with 10 fitting parameters, and fitted the parameters to a large database using the force-matching method. Our model provides a reasonable description of energetics for all atomic coordinations, Z, from the dimer (Z = 1) to fcc and hcp (Z = 12). It accurately reproduces phonons and elastic constants, as well as point defect energetics. It also provides a good description of reconstruction energetics for both the 30° and 90° partial dislocations. Unlike previous models, our model accurately predicts formation energies and geometries of interstitial complexes - small clusters, interstitial-chain and planar {311} defects.

Central-force decomposition of spline-based modified embedded atom method potential

“…The spline-based modified embedded atom method (s-MEAM) was proposed in 2000 by Lenosky et al [11] in order to describe the interactions in silicon. The starting point is the MEAM formalism [27], with the traditionally used functional forms subsequently replaced with cubic spline functions.…”

“…Furthermore, the description of the electronic density has been augmented with angular terms of very general nature, obviating the need to decide a priori on a particular character of angular dependence. Lenosky et al [11] demonstrate that their potential describes well the energetics of a wide range of configurations for Si (including the dimer, fcc and hcp) and is able to reproduce structural and elastic properties of a number of phases of bulk silicon.…”

“…Currently s-MEAM parameterisations are available only for Mo [22], Ti [31] and Si [11,32]. The parameterisation for Ti has been particularly successful, with the ability to describe complex martensitic phase transformations between the α, β and ω phases of titanium.…”

“…At the same time its predictions for elastic constants, phonon frequencies, surface energies and defect formation energies are in very good agreement with results obtained at the density functional theory (DFT) level of theory. With the successes of [11,22,31,32] in mind, we anticipate an increase in the number of available parameterisations of s-MEAM in the near future.…”

“…In [53] it was shown that for any multi-body potential with a continuously differentiable extension, the force that acts on a particle can always be expressed as a sum of central forces. In this work, building on the observations of Admal and Tadmor [53], we present expressions for the central force decomposition for potentials of the s-MEAM class [11], the popularity of which we expect to rise significantly in the near future.…”