Measuring true Young's modulus of a cantilevered nanowire: effect of clamping on resonance frequency

The effect of clamping on resonance frequency and thus measured Young's modulus of nanowires (NWs) is systematically investigated via a combined experimental and simulation approach. ZnO NWs are used in this work as an example. The resonance tests are performed in situ inside a scanning electron microscope and the NWs are cantilevered on a tungsten probe by electron-beam-induced deposition (EBID) of hydrocarbon. EBID is repeated several times to deposit more hydrocarbons at the same location. The resonance frequency increases with the increasing clamp size until approaching that under the "fixed" boundary condition. The critical clamp size is identified as a function of NW diameter and NW Young's modulus. This work: 1) exemplifies the importance of considering the effect of clamping in measurements of Young's modulus using the resonance method, and 2) demonstrates that the true Young's modulus can be measured if the critical clamp size is reached. Design guidelines on the critical clamp size are provided. Such design guidelines can be extended to other one-dimensional nanostructures such as carbon nanotubes.