Mode-shape perturbation induced by analyte adsorption in nanomechanical sensors

Abstract

Nanomechanical resonators offer important benefits for the sensing of physical stimuli such as the mass of an added molecule. To map out the local shape properties of the physical stimuli, such as the distribution of the mass density of a molecule, sensory information should be collected through multiple modes of a mechanical sensor. By utilizing the specific mode shapes, the spatial distribution of a physical stimulus can be reverse calculated. However, the mode shapes of a sensor may deviate from their ideal forms once analytes start to accumulate on the sensor. As a result, algorithms based on the ideal form of the mode shapes no longer work accurately. Here, we developed a theoretical framework to calculate the change in the mode shapes of a nanomechanical beam after analyte adsorption. We verified the theoretical model by performing finite element simulations and comparing the change in the mode shapes obtained from each approach. Monte Carlo simulations were performed to relate the maximum deviation in the mode shapes to the surface roughness of the sensor after analyte accumulation. By predicting the change in the mode shapes and using the corrected forms, the accuracy of the nanomechanical sensing can be improved significantly.