Internal resonances and nonlinearities in atomically thin resonators

Abstract

The advent of carbon nanotubes (CNTs) and atomically thin membranes such as Graphene and layered transition metal chalcogenides (TMDs) have spurred research in the area of Nanoelectromechanical Systems (NEMS) due to their extraordinary mechanical properties and ultralow mass density. These properties make the resonators extremely responsive to external stimuli. This is particularly important for research from both application and fundamental points of view. Nonlinearities in these devices play a vital role in the dynamics as dimensions are reduced to atomic scale. The primary emphasis of this thesis work is to understand various aspects of nonlinearities and manipulate them to enhance the performance of atomically thin NEMS. We demonstrate all electrical actuation and detection of atomically thin MoS2-NEMS in three distinct actuation-detection schemes. We observe multiple vibrational modes of the device and unlike previously reported work on 2D materials, we are able to drive these devices in the strongly nonlinear regime to observe nonlinear coupling. We observe multiple internal resonances for the first time in atomically thin resonators. The internal resonances are likely to occur in systems with large nonlinear mode couplings leading to the spillover of the energy pumped into one mode to other vibrational modes. We also explicitly demonstrate the existence of multiple frequency-plateaus and tunability of internal resonance frequency from one plateau to another plateau with back gate voltage. We provide a qualitative picture for the presence of narrowly spaced multiple internal resonance frequencies. This ability to strongly couple different modes has implications in applications such as high stability oscillator and sensors over a wide range of drive levels. We demonstrate that 2D material based NEMS devices can exhibit strong nonlinear effects that can significantly affect the performance of the device. A clear understanding of nonlinearities and ability to control and manipulate them to enhance the performance are pivotal for applications of these devices. We report an electrostatic mechanism to control the nonlinearities of an atomically thin NEMS. The exquisite control enables us to demonstrate hardening, softening and mixed nonlinear behaviours in the device. The electrostatic control over nonlinearities is utilized to effectively nullify Duffing nonlinearity in a specific regime to improve the dynamic range by ~20dB at room temperature. A simple 1D stretched-string model predicts that mechanical contribution to the nonlinearities is dominated over capacitive contribution and determines the dynamics of the device. The observed mixed behaviour is a result of cross-coupling between strong quadratic and quartic nonlinearities, an aspect explained by the method of multiple scale analysis. We also implement all electrical actuation and detection techniques to characterize monolayer CVD-MoS2 resonator, which is imperative to study from the perspective of large-scale fabrication of 2D-NEMS. The excellent electrical and mechanical properties observed in exfoliated MoS2 based devices are also observed in devices fabricated using CVD grown MoS2. We perform simulations to capture cancellation voltage of the Duffing nonlinearity for a wide range of in-built strain and length of the resonator for different thickness of the membrane. We further experimentally demonstrate and validate our simulated result on the effect of in-built strain in the resonator on the cancellation voltage of Duffing nonlinearity. The simulation and observed result can serve as a simple guide to design and control nonlinearities and effectively improve the linear dynamic range in these devices for next generation of sensors fabricated using these materials. Linear dissipation in NEMS has been studied extensively both theoretically and experimentally. Nonlinear dissipation in NEMS has been studied rarely through experimentation. Exclusive characterization of nonlinear damping has been proven difficult as it is masked by the stronger quadratic and cubic nonlinearities. However, our ability to cancel out the effective Duffing nonlinearity constant, allow us to study nonlinear damping in these devices efficiently. We strictly maintain the amplitude responses well below the critical amplitude throughout the measurements. The van der Poll Duffing equation is used to model the devices. The nonlinear dissipation is characterized by “dissipation backbone curve” analysis and broadening of resonance width with increasing drive voltage. The results clearly indicate that along with nonlinear dissipation, nonlinear spring constant also contributes to the broadening of resonance width. We observe that “dissipation backbone curve” analysis is a much accurate technique to estimate nonlinear dissipation coefficient (η). Analysis of a high strain device indicates that η might depend on the strain, and its value decreases with in-built strain. We demonstrate that the FM technique is highly nonlinear detection scheme even if we strictly maintain the driving force and frequency response in the linear regime. This also contributes to the broadening of the resonance width and as a result, η can be overestimated