Influence of surface modification on the quality factor of microresonators

Noise measurements were performed to determine the quality factor ($Q$) as a function of gas pressure $P$ for microresonators in cantilever form with systematically modified surfaces. In the free-molecular regime, which is dominated by internal energy losses, $Q$ was substantially decreased by more than an order of magnitude with increasing surface roughness. At higher pressures, within the molecular regime, $Q$ showed the typical inverse linear dependence on pressure $Q\ensuremath{\sim}{P}^{\ensuremath{-}1}$. However, in the molecular regime the $Q$ factor also showed a strong dependence on surface morphology as indicated by surface area calculations using measured roughness data and compared to those obtained from $Q\ensuremath{\sim}{P}^{\ensuremath{-}1}$ plots.