The influence of roughness on the mechanical spectroscopy of SiO2 nanorods grown by e-beam irradiation

An extension of Euler-Bernoulli theory based on variational methods for solving flexural vibrations of nanorods has been developed which takes into account geometrical surface roughness effects, as well as internal and external friction. We apply this method to study the vibrations of e-beam induced SiO2 nanorods in the range of 10 nm in diameter and 450 nm in length. Image detection of surface roughness was carried out with the Canny edge detection algorithm. The measured surface height-height correlation function is used to characterize the surface roughness and to test for self-affine behavior. A scheme for generating random rough surfaces representative of the measured SiO2 is described along with a statistical analysis of their effect on resonant frequencies and quality factors.