Anisotropic effects on the radial breathing mode of silicon nanowires: An ab initio study

The effect of orientation on the frequency of the radial breathing mode (RBM) of silicon nanowires (SiNWs) is investigated by means of the first principles Density Functional Theory approach through the generalized gradient approximation. We compare the RBM frequency of SiNWs orientated in three different directions, [0 0 1], [1 1 1], and [1 1 0]. The RBM is observed by the calculation of the phonon band structure and density of states of the SiNWs through the supercell finite displacement method. Results show that the SiNWs are stable in the three chosen directions since there are no negative frequencies in their phonon band structure and density of states. A clear dependence of the RBM frequency with respect to the growth direction of the nanowires and the phonon confinement was observed as the RBM frequency decreased with an inverse power law in each nanowire direction, with the fitting parameters dependent on the growth direction. These results are important since they could be used as a fingerprint to identify them within different spectroscopy techniques such as Raman.