Ultrasensitive Resonant Electrometry Utilizing Micromechanical Oscillators

Real-time monitoring of minute quantities of charge plays an important role in quantum-physics research and electrical measurements within modern high-end scientific instruments. High-precision charge detection approaching the single-electron level at room temperature in analog or digital electronics is limited due to the considerable thermal noise. Herein, we propose a method of charge measurement with a resolution of 0.17 e/\ensuremath{\surd}Hz at room temperature by resonant electrometry based on tracking the quasidigital frequency output of a highly force-sensitive oscillator. Real-time charge monitoring by 67 electrons per step is performed. We demonstrate a charge prebiased scheme for physically manipulating the quadratic nature of charge sensing of the oscillator into parabolic and linear forms with dramatic improvements in metrics such as sensitivity and resolution. Theoretical models for describing the underlying physics of both the charge measurement and resolution amplification schemes are established and validated. Due to the high quality factor of the resonator, the theoretical limit for the charge-input referred noise of the electrometer induced by thermomechanical noise is estimated in the order of ${10}^{\ensuremath{-}4}\phantom{\rule{0.25em}{0ex}}\mathrm{e}$/\ensuremath{\surd}Hz. This study also provides insights of resonant sensing applied to the next generation of electrometers and associated instrumentation systems.