Self-sensing graphene nanoelectromechanical systems

Nanoelectromechanical systems (NEMS) can measure very small forces and mass as has been showcased in the last decade by the demonstration of measurements ranging from single spin detection and mass spectroscopy to the read-out of the quantum ground state of a mesoscopic resonator. Mass spectroscopy with NEMS is particularly appealing because the vibrational frequency of NEMS is a sensitive function of its total mass; thus minute changes in mass due to added or removed adsorbate will change the resonance frequency of a nanomechanical resonator. Indeed, single molecule detection has recently been demonstrated using NEMS as a sensitive mass detector. To maximize mass as well as force sensitivity, resonators with low mass and high quality factors are required. Extreme stiffness, low mass, a high Young’s modulus and good conductivity makes one atom-thick graphene a most suitable candidate for NEMS. However, achieving quality factors higher than 103 at room temperature has been a bottleneck for graphene NEMS. Extensive studies have been carried out on graphene NEMS by employing both optical, and electrostatic transduction techniques. Optical transduction requires large and complicated experimental setups. This restricts the use of this technique to low temperatures and high magnetic fields. Electrostatic sensing, another commonly used technique requires more complex circuitry and can damp the motion due to electrostatic force. In this thesis the use of piezoresistive transduction to transduce motion of graphene resonator is explored. Major advantages of piezoresistive sensing over other sensing methods are its fairly linear response, robustness, simple measuring circuitry and implementation. It has been demonstrated in the present work that piezoresistive sensing is not only a simple but also an extremely effective electrical readout method for graphene based nanoelectromechanical systems. The first part of the thesis starts with an introduction to Nanoelectromechanical systems (NEMS), explaining how it originates from simple electromechanical systems and then later evolved from Microelectromechanical systems (MEMS). Finite element method (FEM) analysis confirms that the stresses are concentrated at the legs of H-shaped mechanical resonator which we have used to maximize the piezoresistive effect of graphene. Modal analysis is performed employing Comsol Multiphysics to carry out the simulations in order to predetermine the frequency range, which is as the same order of the experimentally measured resonance frequencies of the devices. Thermoelastic damping (TED) simulations are carried out to show comparison between different structures of the resonators. Detailed fabrication processes using standard e-beam lithography to fabricate fully suspended H shape graphene resonator have been developed. Graphene resonators are electronically characterized using piezoresistive sensing. Detailed measurements such as piezomechanical and thermomechanical, frequency and time domain measurements are carried out. One order higher Q-factors (103) than the previous reported values for double side clamped beams in ambient temperatures has been measured. The minimum detectable mass and force resolution of such resonators are estimated using the experimental results to be an astounding 0.95 – 1.54 zeptograms (10-21 g) and 11.7 – 21.6 aN/Hz1/2 at room temperature respectively. Various nonlinearities in graphene resonators such as nonlinearity in spring constant as well as higher order nonlinear damping are carefully considered. Simulations as well as experimental results showing various nonlinear effects such as saddle node bifurcation, super-harmonics, Pol-Duffing and unstable states are discussed. In the last part of the thesis, some additional data of the higher order resonance modes with symmetric and asymmetric shape of the devices have been demonstrated. Interesting behaviors such as peak splitting, resonance and anti-resonance peak, have been experimentally observed. This is further confirmed with the experimental results from the commercial cantilever using AFM.