Size and surface orientation effects on thermal expansion coefficient of one-dimensional silicon nanostructures

We perform classical molecular dynamics simulations based on the Tersoff interatomic potential to investigate the size and surface orientation dependence of lattice constant and thermal expansion coefficient of one-dimensional silicon nanostructures. Three different surface orientations of silicon are considered, i.e., Si(110), Si(111), and Si(100) with 2x1 reconstruction. For each surface orientation, we investigate nanostructures with thicknesses ranging from 0.3 to 5.0 nm. We compute the vibrational amplitude of surface atoms, lattice constant, and thermal expansion coefficient as a function of size and temperature, and compare them for different surface orientations. An analytical expression is developed to compute the variation of the thermal expansion coefficient with size of the nanostructure.