Finite size effect on nanomechanical mass detection: the role of surface elasticity

Nanomechanical resonators have recently been highlighted because of their remarkable ability to perform both sensing and detection. Since the nanomechanical resonators are characterized by a large surface-to-volume ratio, it is implied that the surface effect plays a substantial role on not only the resonance but also the sensing performance of nanomechanical resonators. In this work, we have studied the role of surface effect on the detection sensitivity of a nanoresonator that undergoes either harmonic vibration or nonlinear oscillation based on the continuum elastic model such as an elastic beam model. It is shown that the surface effect makes an impact on both harmonic resonance and nonlinear oscillations, and that the sensing performance is dependent on the surface effect. Moreover, we have also investigated the surface effect on the mechanical tuning of resonance and sensing performance. It is interestingly found that the mechanical tuning of resonance is independent of the surface effect, while the mechanical tuning of sensing performance is determined by the surface effect. Our study sheds light on the importance of the surface effect on the sensing performance of nanoresonators.