Surface effect influence on the quality factor of microresonators

This paper presents a model to estimate the quality factor (Q) of a microresonator with surface roughness. The equation of motion of a thin resonator has been derived based on the Euler-Bernoulli beam theory and an extension of the “standard linear solid” model of interior friction to the material surface in the presence of an initial surface stress. The analysis demonstrates that the surface stress and roughness change the effective bending rigidity of the resonator as well as the Q factor. The Q factor has been studied as a function of the surface inclination angle and the Poisson ratio of the different surface films on a Silica substrate. The model can help to understand and quantify the size/material dependence of Q factor.