Mode Coupling and Nonlinearities in Micro/Nano Electromechanical Systems

Abstract

Micro and nanoelectromechanical systems have shown tremendous potential in applications ranging from sensing to obtaining ultrastable oscillators for timing. They have also opened avenues for fundamental quantum studies and exploring nonlinear dynamics. The advent of CNTs and two-dimensional materials has enabled extreme miniaturization of resonators, allowing mass sensitivities down to a proton limit. This is possible since the mass resolution is proportional to the mass of the resonator itself. The limit of detection is also proportional to the frequency stability of the resonator. This is a measure of the uncertainty associated with the frequency measurement. Frequency stability can be effected either by the measurement noise or noise intrinsic to the device's mechanical response. In this thesis, we have explored the room temperature frequency stability of MoS2 resonators in the linear regime. The work involves the fabrication of local gated MoS2 resonators. The devices are characterized using capacitive actuation and homodyne detection techniques. Allan deviation is used as a tool to measure the frequency stability of MoS2 resonators. We study the effect of actuation drive (both AC and DC) on the resonator's frequency stability and correlate it with the signal to noise ratio of the device. The frequency stability measured in MoS2 resonators corresponds to a mass resolution of few attograms. We further identify the various noise sources present in the system through the slope of Allan deviation plots. Recently, Antonio et al. have demonstrated improved frequency stability due to nonlinear intermodal coupling. Coupled resonators have also been shown to enhance the sensitivity of mass sensors and hold promise for future nanomechanical technologies. The linear and nonlinear coupling between modes and/or resonators has enabled the observation of dynamics similar to optomechanics, such as phonon lasing and state squeezing. Nonlinear coupling enables the transfer of energy between vibrational modes having resonant frequencies far apart. Internal resonance is the most common form of nonlinear coupling mechanism. The necessary condition for mechanical modes to be coupled through internal resonance is that the ratio of resonant frequencies of coupled modes should be close to an integer (n=1,2,3). Previous studies on internal resonance have been restricted to clamped-clamped beams. However, our expriemental understanding of modal coupling through internal resonance is limited as it requires the meticulous design of device parameters to obtain resonant modes that are commensurate. Two-dimensional materials such as graphene and metal dichalcogenides have highly tunable resonant frequencies, enabling internal resonance conditions to be easily satisfied. Moreover, vibrational modes of a two-dimensional resonator are coupled through the intrinsic strain in the membrane. Thus, two-dimensional materials serve as a great platform to understand the dynamics of coupled systems. In this work, we demonstrate strong tunable intermodal coupling due to 2:1 internal resonance in MoS2 drum resonators. The modal peak splitting, a signature of coupling, is observed in the linear regime itself in addition to the nonlinear regime. We show the tunability of this coupling with applied gate bias. The simulations enabled us to qualitatively understand the effect of excitation force, frequency detuning and modal coupling strength on the resonator dynamics. Understanding internal resonance in two-dimensional membranes would enable new possibilities in signal transduction and frequency conversion. It could also help in improving the frequency stability of MoS2 resonators through the intermodal coupling. Coupling between different modes of a resonator is not just limited to two-dimensional materials but has also been reported in MEMS structures like clamped-clamped beams and curved arches. Advanced fabrication techniques have paved the way for a new class of MEMS structures, the piezo-micromachined ultrasonic transducer (pMUT). The majority of pMUTs/diaphragms are designed to operate in a linear dynamic range. But, at larger vibrational amplitudes, the nonlinear effect strongly affects the device dynamics. Careful control of these nonlinearities could pave the way to improved stability in microsensors, such as phase fluctuation reduction, frequency control and in-situ amplification schemes. Thus, it is imperative to understand and tune device nonlinearities. Previously tuning of nonlinearities has been achieved in mechanical resonators using capacitive techniques. But the same has not been demonstrated for piezoelectrically actuated ZnO diaphragms. In this thesis, we present the tuning of nonlinearity through diaphragm curvature in these devices. We calculate the effective nonlinearity through the device's backbone curve response and relate it with the diaphragm curvature. Nonlinearity in these resonators also leads to intermodal coupling and energy exchange between the commensurate vibrational modes. We further demonstrate the transfer of energy from the coupled higher vibrational mode to the fundamental mode of the pMUT. This coupling in the future would enable ultrastable piezo-based oscillators.