Abstract
We develop an empirical potential for silicon which represents a considerable improvement over existing models in describing local bonding for bulk defects and disordered phases. The model consists of two- and three-body interactions with theoretically motivated functional forms that capture chemical and physical trends as explained in a companion paper. The numerical parameters in the functional form are obtained by fitting to a set of ab initio results from quantum mechanical calculations based on density functional theory in the local density approximation, which include various bulk phases and defect structures. We test the potential by applying it to the relaxation of point defects, core properties of partial dislocations and the structure of disordered phases, none of which are included in the fitting procedure. For dislocations, our model makes predictions in excellent agreement with ab initio and tight-binding calculations. It is the only potential known to describe both the 30$^\circ$- and 90$^\circ$-partial dislocations in the glide set {111}. The structural and thermodynamic properties of the liquid and amorphous phases are also in good agreement with experimental and ab initio results. Our potential is the first capable of simulating a quench directly from the liquid to the amorphous phase, and the resulting amorphous structure is more realistic than with existing empirical preparation methods. These advances in transferability come with no extra computational cost, since force evaluation with our model is faster than with the popular potential of Stillinger-Weber, thus allowing reliable atomistic simulations of very large atomic systems.
Highlights
Silicon is one of the most intensely investigated materials
In order to determine the values of the adjustable parameters, we fit to a database that includes ab initio results[30], based on density functional theory in the local density approximation (DFT/LDA), for bulk properties, selected values along the unrelaxed concerted exchange (CE) path[31] for self-diffusion, some formation energies of unrelaxed point defects[32,33,34], a few key values in the generalized stacking fault (GSF) energy surface[35], and the experimental elastic constants[36]
This compilation of results includes the diamond cubic (DC) structure which is the ground state of Si, and several other high-coordination bulk structures. The latter structures were not included in the fitting database, our model provides a reasonable description of their energies and a good description of equilibrium lattice constants
Summary
Silicon is one of the most intensely investigated materials. Interest in silicon is mostly motivated by its great technological importance, but it is regarded as the prototypical covalent solid, on which theoretical concepts about covalent bonding can be tested, and new ideas can be explored. In this article we present a new empirical potential for silicon using a theoretically motivated functional form which emphasizes chemical and physical trends[21], and which is determined by fitting to a fairly small ab initio database with only 13 parameters. This potential represents a considerable improvement over existing models in describing local structures and extended defects. It provides a good description of point defects in the bulk, the concerted exchange path for self-diffusion, and elastic properties of bulk silicon.
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