Modeling and Experimental Vibration Analysis of Nanomechanical Cantilever Active Probes With Application to Ultra Small Mass Detection

This paper presents a precise modeling framework for modal characterization and dynamic response analysis of nanomechanical cantilever Active Probes with geometrical discontinuities. An experimental setup consisting of a commercial NMC Active Probe from Veeco and a state-of-the-art microsystem analyzer, the MSA-400 from Polytec, for non-contact vibration measurement is developed to verify the theoretical derivations. Mode shapes and modal frequency response of system for the first three modes obtained from the proposed model are compared with those obtained from the experiment and commonly used theory for uniform beams. Results indicate that the uniform beam model fails to accurately predict the actual system response in multiple-mode operation, while the proposed discontinuous beam model demonstrates good agreement with the experimental data. The Active Probe is then utilized in an ultra small mass detection application. For this, a sensitivity analysis is carried out to measure the added mass at the most sensitive mode of operation. Results indicate detection of tip masses as small as a few hundreds of picograms.