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The case of a rough potential energy surface: Discrepancies between results of NEB and MD calculations

Posselt, M.


Vacancy migration is studied in a silicon crystal with atomic interactions described by the Kumagai potential [1]. The basic functional form of this potential is very similar to the Tersoff potential. The main improvements concern the values of the elastic constants and the melting temperature. However, the potential energy surface is as rough as in the case of the Tersoff potential. In the ground state the vacancy has the “normal” tetrahedral configuration. The migration in the rugged potential energy landscape leads to peculiarities. Extensive Molecular Dynamics (MD) calculations show that the atomic mechanism of the migration process depends on temperature. The vacancy migration energy changes at about 1000 K: At lower and higher temperatures it is about 0.71 and 0.41 eV, respectively. Investigations on the dominating defect structure show that below about 1000 K the tetrahedral vacancy prevails whereas at higher temperature a modified version of the tetrahedral vacancy, the split vacancy and other configurations become dominant.
Applying the Nudged Elastic Band (NEB) method to the potential energy surface in the ground state, the transition between neighboring tetrahedral vacancy structures was studied. A number of intermediate metastable states were found, amongst them the modified version of the tetrahedral vacancy and the split vacancy. The maximum barrier for the migration between one ground state configuration to another is about 0.9 eV, whereas a barrier of about 0.3 eV is found for the transition from the split to the modified tetrahedral structure. Comparing with the results of MD simulations one may assume that in the high temperature range the vacancy moves mainly between high-energy configurations such as the split and the modified tetrahedral structure. The reason why the vacancy is not very often found in the ground state is not completely clear. Obviously, the free energy landscape at elevated temperature differs strongly from the ground-state energy landscape. Vibrational degrees of freedom may lead to the narrowing of the path to the tetrahedral state while the path between the high energy states may become much broader.
[1] T. Kumagai et al., Comput. Mater. Sci. 39, 457 (2007)

Keywords: molecular dynamics; nudged elastic band method; potential energy surface

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