Nonlinearities in nanoelectromechanical systems (NEMS) play a vital role in dynamics of the device. Clear understanding of nonlinearities and ability to tune and manipulate them to enhance the performance are crucial for applications with these devices. Here, we utilize an electrostatic mechanism to tune the geometric nonlinearity of an atomically thin NEMS. The exquisite tuning enables us to demonstrate hardening, softening, and mixed nonlinear responses in the device. The electrostatic tuning over the nonlinearity is utilized to effectively nullify Duffing nonlinearity in a specific regime. The observed mixed nonlinear response is the result of cross coupling between strong quadratic and quartic nonlinearities, an aspect explained by method of multiple scale analysis.

Parametric amplification is widely used in diverse areas from optics to electronic circuits to enhance low level signals by varying relevant system parameters. Parametric amplification has also been performed in several micro-nano resonators including nano-electromechanical system (NEMS) resonators based on a two-dimensional (2D) material. Here, we report the enhancement of mechanical response in a MoS drum resonator using degenerate parametric amplification. We use parametric pumping to modulate the spring constant of the MoS resonator and achieve a 10 dB amplitude gain. We also demonstrate quality factor enhancement in the resonator with parametric amplification. We investigate the effect of cubic nonlinearity on parametric amplification and show that it limits the gain of the mechanical resonator. Amplifying ultra-small displacements at room temperature and understanding the limitations of the amplification in these devices is key for using these devices for practical applications.

We use sapphire substrate for fabrication of the device to reduce parasitic capacitance. Low parasitic capacitance allows us to use homodyne electrical measurement technique. Homodyne electrical measurement scheme offers a simpler set-up and is faster technique compared to the other techniques such as heterodyne frequency mixdown and frequency modulation technique. 1 To fabricate the device, a metal gate Ti/Pt (15/10 nm) is deposited on the substrate using thermal deposition. Next, 300 nm thick is deposited using plasma enhanced chemical vapor deposition SiO 2 (PECVD). A circular window is exposed, covering the remaining with Cr mask. The circular SiO 2 trench is obtained by etching the exposed using reactive ion etching (RIE). For the source-SiO 2 drain metal contact pads, Cr/Au (5/50 nm) is deposited a few away from the trench. To suspend μm membrane, a PDMS sheet with exfoliated flake is placed on top of the circular trench MoS 2 MoS 2 and the flake is transferred over it such that the membrane also makes contacts with source-drain pads. 2

We use frequency response of CVD-MoS2 resonator as a probe to estimate the linear thermal expansion coefficient of the material and evaluate the effect of strain on the effective Duffing nonlinearity.

Bifurcation amplifiers are known for their extremely high sensitivity to weak input signals. We implement a bifurcation amplifier by harnessing the Duffing nonlinearity in a parametrically excited MoS 2 nano-electromechanical system. We utilize the ultra-sensitive switching response between the two states of the bifurcation amplifier to detect as well as register charge-fluctuation events. We demonstrate openloop real-time detection of ultra-low electrical charge perturbations of magnitude <10 e at room temperature. Furthermore, we show latching of the resonator onto one of the two states in response to short-lived charge fluctuations. These charge detectors offer advantages of roomtemperature operation and tunable operation in the radio frequency regime, which could open several possibilities in quantum sensing.