Nonlinear, coupled, and parametric nanoelectromechanical systems

Abstract

Advances in nanoscience and nanotechnology hold enormous promises to benefit humankind in basic research, industry, and everyday life. One particular class of the vast field of nanodevices is resonant nanoelectromechanical systems (NEMS), which have recently attracted considerable research interest. While many of obstacles have been overcome in fundamental physics and engineering research of NEMS, intriguing questions and technological challenges remain unmet. This thesis is primarily focused on the studies of parametric, nonlinear, and coupled NEMS resonators. In this work the first very high-frequency (VHF) nanomechanical degenerate parametric amplifiers have been demonstrated by employing both magnetomotive and piezoelectric parametric pumping. A mechanical gain of 1000 and quality factor enhancement of 75 have been achieved. Such parametric resonators and nanomechanical amplification make it possible to evade the often-dominant transducer and amplifier noise, thus offering possibilities for improving the sensitivity of NEMS sensors, for exploring mechanical-domain signal processing, and for noise squeezing in precision physics measurements. The thesis also focuses on the rich dynamics and physics of coupled NEMS resonators. First, the major mechanisms of coupling are investigated both experimentally and analytically. The formalism for characterizing a new basis of vibration modes for strongly coupled nanoresonators is developed and experimentally demonstrated for systems with two, three and ten NEMS devices. By employing a pair of coupled resonators for long-term drift compensation, considerable improvement in resonator frequency stability is demonstrated. Simple linear interaction in nonlinear nanomechanical resonators is shown to generate remarkably complex and rich behavior including spontaneous state transition and chaos. Finally, the complexity of the system is further increased when coupled and parametric effects are combined. A novel nanomechanical amplification mechanism has been discovered, based on the dynamical changes that an input signal induces in the topology of a bifurcation diagram of a system of two weakly coupled parametric resonators. Another interesting phenomenon—nondegenerate parametric NEMS amplification is demonstrated in the case of strong coupling. This is a promising route to low noise mechanical displacement sensing because it not only provides a fundamentally noiseless amplification mechanism, but also it decouples pump and signal frequency.