Nonlinear nanoelectromechanical systems

Nano-electro-mechanical systems (NEMS), used as sensors for small masses and forces, have traditionally been operated in the linear regime. While convenient for engineering applications, the linear regime is getting harder to maintain as the devices grow smaller. The first part of this thesis develops a theoretical framework for analysis of nonlinear nanomechanical devices and establishes that nonlinear effects become more significant in smaller resonators. As a result, nonlinear nanomechanical resonators offer a convenient playground for studies of nonlinear dynamics as well as open up new possibilities for enhancing performance of NEMS devices. To illustrate both of these trends, the thesis presents experimental investigations of nonlinear dynamics using nanoresonators and demonstrates several effects in nonlinear NEMS in an effort to build the foundation necessary for engineering highly sensitive, versatile, and controllable NEMS devices. As an example of exploring nonlinear dynamics with NEMS, we present the experimental mapping of basins of attraction of a nonlinear platinum nanowire resonator. We also measure the rate of the observed noise-induced transitions between two stable states in the nonlinear regime as the artificial noise is added to the system. An additional set of experiments demonstrates increased versatility of NEMS devices made possible by their intrinsic nonlinearity. Devices with tunable frequency, nonlinearity, and dynamic range are explored experimentally and theoretically. We show how to induce the coupling of orthogonal modes in nanomechanical resonators. We also detect multiple higher-order modes in doubly-clamped beams and observe increased dynamic range of operation in these modes. Several ideas for further experiments with nonlinear nanomechanical resonators are proposed.