Thermomechanical-Noise-Limited Capacitive Transduction of Encapsulated MEM Resonators

The thermomechanical motion imposes the fundamental noise limit in room-temperature resonant sensors and oscillators. Due to the inherently low sensitivity of capacitive transduction in microelectromechanical (MEM) resonators, its effects are often masked by noise in the subsequent amplifier and measurement stages. In this work, we demonstrate a capacitive transduction scheme for measuring kHz-MHz frequency MEM resonators across 1 μm capacitive gaps with 99.8% thermomechanical-noise-limited resolution. We delineate the transimpedance gain and noise of our custom off-chip differential transimpedance amplifier setup. The thermomechanical noise spectrum can provide estimates of the resonant frequency, quality factor, and electromechanical transduction factor comparable to the commonly used driven response, without the downsides of capacitive feedthrough or nonlinearity.