Understanding fundamental trade-offs in nanomechanical resonant sensors

Abstract

Nanomechanical resonators are used as high performance detectors in a variety of applications such as mass spectrometry and atomic force microscopy. Initial emphasis in nanomechanical resonant sensors based on tracking resonance frequency deviations was on increasing the sensitivity to the level of a single molecule, atom, and beyond. On the other hand, there are applications where the speed of detection is crucial, prompting recent works that emphasize sensing schemes with improved time resolution. Here, we first develop a general modeling framework and a comprehensive theory encompassing all resonance frequency tracking schemes currently in use. We then explore the fundamental trade-offs between accuracy and speed in three resonant sensor architectures, namely, the feedback-free open-loop approach, positive-feedback based self-sustaining oscillator, and negative-feedback based frequency-locked loop scheme. We comparatively analyze them in a unified manner, clarify some misconceptions and confusion that seem to exist in the literature, and unravel their speed vs accuracy characteristics.