Modeling, Design and Experimental Characterization of Bending Resonant Circular Nano Cantilevers

This work reports on a new type of nano cantilever, the symmetric circular one, and provides results of its outof- plane bending natural frequency by means of analytical modeling and experimental testing. The cantilever, with a 225 nm thickness and planar dimensions smaller than 10 μm, can be implemented in dynamic nano electromechanical applications such as atomic force microscopy, surface topology characterization or resonance-shift mass detection. An analytic model is proposed that considers the distributed stiffness and inertia properties through an accurate distribution function. The model also captures the short-beam character of this structure and the related shear effects. Several silicon nitride nano cantilevers have been surface-micromachined and tested by using in-vacuum laser excitation and interferometric measurement of the bending resonant response. The model predictions and the experimental results indicated minimal errors. Based on this agreement, the analytical model was utilized to further analyze the influence of the basic geometric parameters on the cantilever's natural frequency.