A combined first principles and analytical treatment for determination of the surface elastic constants: application to Si(001) ideal and reconstructed surfaces

Abstract

Behavior of nanostructures, which are characterized by a large surface-to-volume ratio, is greatly influenced by their surface parameters, such as surface elastic moduli tensor. Accurate determination of the surface elastic constants by first principles is of particular interest. To this end, through consideration of the fundamental thermodynamic arguments for free solid surfaces, an analytical formulation for the change in specific Helmholtz surface free energy is developed. Relating this formulation to the corresponding energy calculated via first principles leads to the determination of the surface elastic moduli tensor. The surface mechanical properties, namely surface energy, surface stress, and surface elastic constants for Si(001) are all calculated for both cases of the reconstructed and ideal bulk terminated surface using ab initio method.

Keywords:

• surface elastic moduli tensor
• surface stress
• surface energy
• ab initio

Acknowledgements

A part of the calculations was carried out through the allocated nodes and computing time by the Computing Center of the School of Nano Science in the Institute for Research in Fundamental Sciences (IPM).