We report on the fabrication of nanometer-scale mass sensors with subattogram sensitivity. Surface micromachined polycrystalline silicon and silicon nitride nanomechanical oscillators were used to detect the presence of well-defined mass loading. Controlled deposition of thiolate self-assembled monolayers on lithographically defined gold dots were used for calibrated mass loading. We used a dinitrophenyl poly(ethylene glycol) undecanthiol-based molecule (DNP-PEG4-C11thiol) as a model ligand for this study. Due to the fact that the gold mass is attached at the distance $l_0$ from the end $\mathrm{x=l}$ of the cantilever beam, an additional moment evolves in the boundary condition of the oscillator, which was taken into consideration through the rotational inertia of the attached mass. We showed that the corresponding correction of the frequency is on the order of ${\mathrm{\gamma (l}}_0\mathrm{/l),}$ where γ is the attached mass normalized to the mass of the beam. The rotational inertia correction to the frequency is on the order of ${\mathrm{\gamma (l}}_0{\mathrm{/l)}}^2.$ The adopted approach permits accurate determination of the eigenfrequency in the framework of the Euler–Bernoulli beam when rotational inertia of the attached mass is included. From the resonant frequency shift, the mass of the adsorbed species was determined and compared to results obtained by other techniques. Utilizing vacuum encapsulation, we demonstrate sensing capability in the attogram regime of the adsorbed self-assembled monolayer.

A detailed study of the transient nonlinear dynamics of an electrically actuated micron scale beam is presented. A model developed using the Galerkin procedure with normal modes as a basis accounts for the distributed nonlinear electrostatic forces, nonlinear squeezed film damping, and rotational inertia of a mass carried by the beam. Special attention is paid to the dynamics of the beam near instability points. Results generated by the model and confirmed experimentally show that nonlinear damping leads to shrinkage of the spatial region where stable motion is realizable. The voltage that causes dynamic instability, in turn, approaches the static pull-in value.