Impact of surface and residual stresses and electro-/magnetostatic axial loading on the suspended nanomechanical based mass sensors: A theoretical study

Abstract

Suspended nanomechanical mass sensors are capable to detect the attached molecules or particles through the shifts in the resonant frequencies. However, surface and residual stresses can as well cause a shift of the sensor resonances. As result, understanding the impact of stresses in an accuracy and sensitivity of the mass sensors is a fundamental requirement for a rigorous analysis of experimental data. Here, we present a detailed theoretical study of the suspended nanomechanical resonators and mass sensors under axial load created by surface (residual) stresses or electrostatic (magnetostatic) forces. Easily accessible formulas allowing one either to accurately predict the resonant frequencies of the beam under tension/compression or to disentangle the effects of stresses (axial forces) and the molecule mass on the frequency shift of the suspended mass sensors have been derived. A dimensionless parameter enabling us a simple characterization of the device vibrational regime (i.e., beam, string, or beam-to-string transition) has been identified. Based on the results, the applicability limits of the classical beam theory with and without axial loading have been found. We also show that tuning the beam resonant frequencies enhances the mass sensitivity.