Squeeze-Film Effect on Atomically Thin Resonators in the High-Pressure Limit.

The resonance frequency of membranes depends on the gas pressure due to the squeeze-film effect, induced by the compression of a thin gas film that is trapped underneath the resonator by the high-frequency motion. This effect is particularly large in low-mass graphene membranes, which makes them promising candidates for pressure-sensing applications. Here, we study the squeeze-film effect in single-layer graphene resonators and find that their resonance frequency is lower than expected from models assuming ideal compression. To understand this deviation, we perform Boltzmann and continuum finite-element simulations and propose an improved model that includes the effects of gas leakage and can account for the observed pressure dependence of the resonance frequency. Thus, this work provides further understanding of the squeeze-film effect and provides further directions into optimizing the design of squeeze-film pressure sensors from 2D materials.

Multi-layer graphene pirani pressure sensors.

The operating principle of Pirani pressure sensors is based on the pressure dependence of a suspended strip's electrical conductivity, caused by the thermal conductance of the surrounding gas which changes the Joule heating of the strip. To realize such sensors, not only materials with high temperature dependent electrical conductivity are required, but also minimization of the suspended strip dimensions is essential to maximize the responsivity and minimize the power consumption. Due to this, nanomaterials are especially attractive for this application. Here, we demonstrate the use of a multi-layer suspended graphene strip as a Pirani pressure sensor and compare its behavior with existing models. A clear pressure dependence of the strip's electrical resistance is observed, with a maximum relative change of 2.75% between 1 and 1000 mbar and a power consumption of 8.5 mW. The use of graphene enables miniaturization of the device footprint by 100 times compared to state-of-the-art. Moreover, miniaturization allows for lower power consumption and/or higher responsivity and the sensor's nanogap enables operation near atmospheric pressure that can be used in applications such as barometers for altitude measurement. Furthermore, we demonstrate that the sensor response depends on the type of gas molecules, which opens up the way to selective gas sensing applications. Finally, the graphene synthesis technology is compatible with wafer-scale fabrication, potentially enabling future chip-level integration with readout electronics.

High-Frequency Stochastic Switching of Graphene Resonators Near Room Temperature.

Stochastic switching between the two bistable states of a strongly driven mechanical resonator enables detection of weak signals based on probability distributions, in a manner that mimics biological systems. However, conventional silicon resonators at the microscale require a large amount of fluctuation power to achieve a switching rate in the order of a few hertz. Here, we employ graphene membrane resonators of atomic thickness to achieve a stochastic switching rate of 4.1 kHz, which is 100 times faster than current state-of-the-art. The (effective) temperature of the fluctuations is approximately 400 K, which is 3000 times lower than the state-of-the-art. This shows that these membranes are potentially useful to transduce weak signals in the audible frequency domain. Furthermore, we perform numerical simulations to understand the transition dynamics of the resonator and use analytical expressions to investigate the relevant scaling parameters that allow high-frequency, low-temperature stochastic switching to be achieved in mechanical resonators.

Inkjet-Printed High-Q Nanocrystalline Diamond Resonators.

Diamond is a highly desirable material for state-of-the-art micro-electromechanical (MEMS) devices, radio-frequency filters and mass sensors, due to its extreme properties and robustness. However, the fabrication/integration of diamond structures into Si-based components remain costly and complex. In this work, a lithography-free, low-cost method is introduced to fabricate diamond-based micro-resonators: a modified home/office desktop inkjet printer is used to locally deposit nanodiamond ink as ∅50-60 µm spots, which are grown into ≈1 µm thick nanocrystalline diamond film disks by chemical vapor deposition, and suspended by reactive ion etching. The frequency response of the fabricated structures is analyzed by laser interferometry, showing resonance frequencies in the range of ≈9-30 MHz, with Q-factors exceeding 104 , and (f0 × Q) figure of merit up to ≈2.5 × 1011 Hz in vacuum. Analysis in controlled atmospheres shows a clear dependence of the Q-factors on gas pressure up until 1 atm, with Q ∝ 1/P. When applied as mass sensors, the inkjet-printed diamond resonators yield mass responsivities up to 981 Hz fg-1 after Au deposition, and ultrahigh mass resolution up to 278 ± 48 zg, thus outperforming many similar devices produced by traditional top-down, lithography-based techniques. In summary, this work demonstrates the fabrication of functional high-performance diamond-based micro-sensors by direct inkjet printing.

Graphene Squeeze-Film Pressure Sensors.

The operating principle of squeeze-film pressure sensors is based on the pressure dependence of a membrane's resonance frequency, caused by the compression of the surrounding gas which changes the resonator stiffness. To realize such sensors, not only strong and flexible membranes are required, but also minimization of the membrane's mass is essential to maximize responsivity. Here, we demonstrate the use of a few-layer graphene membrane as a squeeze-film pressure sensor. A clear pressure dependence of the membrane's resonant frequency is observed, with a frequency shift of 4 MHz between 8 and 1000 mbar. The sensor shows a reproducible response and no hysteresis. The measured responsivity of the device is 9000 Hz/mbar, which is a factor 45 higher than state-of-the-art MEMS-based squeeze-film pressure sensors while using a 25 times smaller membrane area.

Nanoelectromechanical Sensors Based on Suspended 2D Materials.

The unique properties and atomic thickness of two-dimensional (2D) materials enable smaller and better nanoelectromechanical sensors with novel functionalities. During the last decade, many studies have successfully shown the feasibility of using suspended membranes of 2D materials in pressure sensors, microphones, accelerometers, and mass and gas sensors. In this review, we explain the different sensing concepts and give an overview of the relevant material properties, fabrication routes, and device operation principles. Finally, we discuss sensor readout and integration methods and provide comparisons against the state of the art to show both the challenges and promises of 2D material-based nanoelectromechanical sensing.

Opto-thermally excited multimode parametric resonance in graphene membranes.

In the field of nanomechanics, parametric excitations are of interest since they can greatly enhance sensing capabilities and eliminate cross-talk. Above a certain threshold of the parametric pump, the mechanical resonator can be brought into parametric resonance. Here we demonstrate parametric resonance of suspended single-layer graphene membranes by an efficient opto-thermal drive that modulates the intrinsic spring constant. With a large amplitude of the optical drive, a record number of 14 mechanical modes can be brought into parametric resonance by modulating a single parameter: the pre-tension. A detailed analysis of the parametric resonance allows us to study nonlinear dynamics and the loss tangent of graphene resonators. It is found that nonlinear damping, of the van der Pol type, is essential to describe the high amplitude parametric resonance response in atomically thin membranes.