Friction in nanoelectromechanical systems: Clamping loss in the GHz regime

The performance of a wide variety of ultra-sensitive devices employing nanoelectromechanical resonators is determined by their mechanical quality factor, yet energy dissipation in these systems remains poorly understood. Here we develop a comprehensive theory of friction in high frequency resonators caused by the radiation of elastic energy into the support substrate, referred to as clamping loss. The elastic radiation rate is found to be a strong increasing function of resonator frequency, and we argue that this mechanism will play an important role in future microwave-frequency devices.