Determination of the natural frequency of a cantilevered ZnO nanowire resonantly excited by a sinusoidal electric field

The electric-field-induced mechanical resonance of an individual nanotube (NT) or nanowire (NW) has been utilized as a versatile technique for in situ measurement of the Young's modulus of the NT/NW in electron microscopes. The key step of this technique is to determine the fundamental natural frequency of the NT/NW. However, the emergence of super- and/or sub-harmonic resonances might make the determination uncertain. This paper investigates the resonance behaviour of ZnO NWs in a nanotip-nanowire system in order to clarify this obscurity. It is found that forced and parametric resonance are two basic modes of the observed multi-frequency resonances and that each mode exhibits a distinct characteristic. By controlling the driving force exerted on the NW to be either lateral or axial, the two otherwise entangled modes are clearly separated. Based on this resonance mode separation, a criterion for identifying the natural frequency of ZnO NWs is proposed.