Selecting the optimum engineering model for the frequency response of fcc nanowire resonators

The full potential of the nanoelectromechanical systems, NEMS, as one of the leading examples among the new-generation sensing technologies, is yet to be realized. One of the main challenges on the road is the mechanical modeling of their core elements, the tiny mechanical building blocks such as the nanowire resonators. The success of the engineering design of such miniaturized systems will depend heavily on the availability of accurate mechanistic models with the least possible computational cost. Although a variety of models are available for this purpose, the boundaries between their admissible domains remain rather vague. For example, analytical approaches including Euler–Bernoulli and Timoshenko beam theories provide closed-form solutions and work reasonably well for moderate nanowire geometries, and hence, they are frequently utilized in the literature. However, their validity in the case of extreme surface-to-volume ratios remains questionable. Classical finite element method can partially be used to address these deficiencies. On the other hand, molecular dynamics provide accurate results, while nanowire geometries studied with this computationally demanding technique usually remain confined to dimensions below those of practical interest. To address these issues, a benchmarking study among analytical and numerical techniques is carried out, where Surface Cauchy–Born theory serves as the reference. Using gold nanowires with different dimensions and boundary conditions, it is observed that analytical models are applicable within a length-to-thickness ratio range of 7–11 in the fixed–fixed configuration, whereas they can be used safely within a length-to-thickness ratio range of less than 25 in the fixed–free configuration. Deviations as high as 50% are encountered for length-to-thickness ratios exceeding 11 for both the analytical approach and the classical finite element method in the fixed–fixed structure. The deviations are quantitatively linked to the dominance of the surface effect through the use of the Surface Cauchy–Born model. For length-to-thickness ratios less than 7, the lack of cross-sectional deformations in analytical treatment is also observed to lead to high deviations for the fixed–fixed configuration through the comparison with higher-order beam theories. Results are verified with silver nanowires as well. The work provides a guideline for selecting the optimum mechanical model given the nanowire resonator dimensions and boundary conditions.