Measurement uncertainties in resonant characteristics of MEMS resonators

This paper reports measurement of random uncertainties in resonant characteristics (resonance frequency and quality factor) of microelectromechanical system (MEMS) resonators. We employ different methods to extract resonant characteristics of 4 different MEMS resonators which are either clamped-free or clamped-clamped beams. Each beam type operates either in air or in a partial vacuum, and therefore, different vacuum levels can be examined. Three different methods, including frequency sweep, impulse response, and thermal noise, are applied to each resonator type excited with electrostatic or piezo-crystal actuation. We make a thorough analysis and comparison for three different methods. Depending on device type and operating condition, there exists a better and recommended way to extract resonant characteristics of MEMS resonators. For example, the impulse response is best-suited for the quality factor measurement of a clamped-clamped beam operating in a vacuum. Our results show that the quality factor of MEMS resonators may be noticeably different and exhibit appreciable systematic and random uncertainties, and suggests a better way to extract the quality factor for a given situation.