Drumhead Resonators Research Articles

Buckling-induced transmission switching in phononic waveguidesa).

On-chip phononic circuits tailor the transmission of elastic waves and couple to electronics and photonics to enable new signal manipulation capabilities. Phononic circuits rely on waveguides that transmit elastic waves within desired frequency passbands, which are typically designed based on the Bloch modes of the constitutive unit cell of the waveguide, assuming periodicity. Acoustic microelectromechanical system waveguides composed of coupled drumhead resonators offer megahertz operation frequencies for applications in acoustic switching. Here, we construct a reduced-order model (ROM) to demonstrate the mechanism of transmission switching in coupled drumhead-resonator waveguides. The ROM considers the mechanics of buckling under the effect of temperature variation. Each unit cell has two degrees of freedom: translation to capture the symmetric bending modes and angular motion to capture the asymmetric bending modes of the membranes. We show that thermoelastic buckling induces a phase transition triggered by temperature variation, causing the localization of the first-passband modes, similar to Anderson localization caused by disorders. The proposed ROM is essential to understanding these phenomena since Bloch mode analysis fails for weakly disordered (<5%) finite waveguides due to the disorder amplification caused by the thermoelastic buckling. The illustrated transmission control can be extended to two-dimensional circuits in the future.

Ultra-Tuning of nonlinear drumhead MEMS resonators by Electro-Thermoelastic buckling

Nonlinear micro-electro-mechanical systems (MEMS) resonators open new opportunities in sensing and signal manipulation compared to their linear counterparts by enabling frequency tuning and increased bandwidth. Here, we design, fabricate and study drumhead resonators exhibiting strongly nonlinear dynamics and develop a reduced order model (ROM) to capture their response accurately. The resonators undergo electrostatically-mediated thermoelastic buckling, which tunes their natural frequency from 4.7 to 11.3 MHz, a factor of 2.4× tunability. Moreover, the imposed buckling switches the nonlinearity of the resonators between purely stiffening, purely softening, and even softening-to-stiffening. Accessing these exotic dynamics requires precise control of the temperature and the DC electrostatic forces near the resonator’s critical-buckling point. To explain the observed tunability, we develop a one-dimensional physics-based ROM that predicts the linear and nonlinear response of the fundamental bending mode of these drumhead resonators. The ROM captures the dynamic effects of the internal stresses resulting from three sources: The residual stresses from the fabrication process, the mismatch in thermal expansion between the constituent layers, and lastly, the applied electrostatic forces. The novel ROM developed in this article not only replicates the observed tunability of linear (within 5.5 % error) and nonlinear responses even near the states of critical buckling but also provides insightful intuition on the interplay among the softening and stiffening, which is invaluable for the precise design of similar devices. This remarkable nonlinear and large tunability of the natural frequency are valuable features for on-chip acoustic devices in broad applications such as signal manipulation, filtering, and MEMS waveguides.

Strain-Modulated Dissipation in Two-Dimensional Molybdenum Disulfide Nanoelectromechanical Resonators.

Resonant nanoelectromechanical systems (NEMS) based on two-dimensional (2D) materials such as molybdenum disulfide (MoS2) are interesting for highly sensitive mass, force, photon, or inertial transducers, as well as for fundamental research approaching the quantum limit, by leveraging the mechanical degree of freedom in these atomically thin materials. For these mechanical resonators, the quality factor (Q) is essential, yet the mechanism and tuning methods for energy dissipation in 2D NEMS resonators have not been fully explored. Here, we demonstrate that by tuning static strain and vibration-induced strain in suspended MoS2 using gate voltages, we can effectively tune the Q in 2D MoS2 NEMS resonators. We further show that for doubly clamped resonators, the Q increases with larger DC gate voltage, while fully clamped drumhead resonators show the opposite trend. Using DC gate voltages, we can tune the Q by ΔQ/Q = 448% for fully clamped resonators, and by ΔQ/Q = 369% for doubly clamped resonators. We develop the strain-modulated dissipation model for these 2D NEMS resonators, which is verified against our measurement data for 8 fully clamped resonators and 7 doubly clamped resonators. We find that static tensile strain decreases dissipation while vibration-induced strain increases dissipation, and the actual dependence of Q on DC gate voltage depends on the competition between these two effects, which is related to the device boundary condition. Such strain dependence of Q is useful for optimizing the resonance linewidth in 2D NEMS resonators toward low-power, ultrasensitive, and frequency-selective devices for sensing and signal processing.

Buckling-mediated phase transitions in nano-electromechanical phononic waveguides

Acoustic signals in the megahertz to gigahertz regimes enable applications in phononic, electric and photonic circuitry. Hence, advancement in these multi-physics circuitries requires studying the transmission of elastic waves in micro/nano-electromechanical systems. Therefore, our work investigated the transmission of flexural waves in unidirectional phononic waveguides of coupled nano-electromechanical drumhead resonators. In particular, we studied the manipulation and tailoring of the transmission by thermal control of buckling within the waveguide. We showed—via experimental and computational evidence—that buckling tunes the frequency of transmission within the waveguide as determined by previous studies in literature. However, in our work, we demonstrated that excessive buckling stops the transmission in the fundamental (lowest frequency) passband of the waveguide, thus, inducing a phase transition in the waveguide leading to the absence of transmission in the respective frequency range. We computationally proved that this buckling-mediated phase transition necessitates the presence of weak inhomogeneities (∼5% variations) within the waveguide, which are inevitable in any fabrication process. In fact, these inhomogeneities are amplified due to buckling-residual stresses leading to structural aperiodicity that only affects the fundamental passband by converting the extended shapes of the transmission modes into localized shapes that prevent signal propagating throughout the waveguide.

Dissipation from Interlayer Friction in Graphene Nanoelectromechanical Resonators.

A unique feature of two-dimensional (2D) materials is the ultralow friction at their van der Waals interfaces. A key question in a new generation of 2D heterostructure-based nanoelectromechanical systems (NEMS) is how the low friction interfaces will affect the dynamic performance. Here, we apply the exquisite sensitivity of graphene nanoelectromechanical drumhead resonators to compare the dissipation from monolayer, Bernal-stacked bilayer, and twisted bilayer graphene membranes. We find a significant difference in the average quality factors of three resonator types: 53 for monolayer, 40 for twisted and 31 for Bernal-stacked membranes. We model this difference as a combination of change in stiffness and additional dissipation from interlayer friction during motion. We find even the lowest frictions measured on sliding 2D interfaces are sufficient to alter dissipation in 2D NEMS. This model provides a generalized approach to quantify dissipation in NEMS based on 2D heterostructures which incorporate interlayer slip and friction.

Buckling-Mediated Phase Transitions in Nano-Electromechanical Phononic Waveguides

Waveguides for mechanical signal transmission in the megahertz to gigahertz regimes enable on-chip phononic circuitry, which brings new capabilities complementing photonics and electronics. Lattices of coupled nano-electromechanical drumhead resonators are suitable for these waveguides due to their high Q-factor and precisely engineered band structure. Here, we show that thermally induced elastic buckling of such resonators causes a phase transition in the waveguide leading to reversible control of signal transmission. Specifically, when cooled, the lowest-frequency transmission band associated with the primary acoustic mode vanishes. Experiments show the merging of the lower and upper band gaps, such that signals remain localized at the excitation boundary. Numerical simulations show that the temperature-induced destruction of the pass band is a result of inhomogeneous elastic buckling, which disturbs the waveguide's periodicity and suppresses the wave propagation. Mechanical phase transitions in waveguides open opportunities for drastic phononic band reconfiguration in on-chip circuitry and computing.

Stochastic Stress Jumps Due to Soliton Dynamics in Two-Dimensional van der Waals Interfaces.

The creation and movement of dislocations determine the nonlinear mechanics of materials. At the nanoscale, the number of dislocations in structures become countable, and even single defects impact material properties. While the impact of solitons on electronic properties is well studied, the impact of solitons on mechanics is less understood. In this study, we construct nanoelectromechanical drumhead resonators from Bernal stacked bilayer graphene and observe stochastic jumps in frequency. Similar frequency jumps occur in few-layer but not twisted bilayer or monolayer graphene. Using atomistic simulations, we show that the measured shifts are a result of changes in stress due to the creation and annihilation of individual solitons. We develop a simple model relating the magnitude of the stress induced by soliton dynamics across length scales, ranging from <0.01 N/m for the measured 5 μm diameter to ∼1.2 N/m for the 38.7 nm simulations. These results demonstrate the sensitivity of 2D resonators are sufficient to probe the nonlinear mechanics of single dislocations in an atomic membrane and provide a model to understand the interfacial mechanics of different kinds of van der Waals structures under stress, which is important to many emerging applications such as engineering quantum states through electromechanical manipulation and mechanical devices like highly tunable nanoelectromechanical systems, stretchable electronics, and origami nanomachines.

Nano-electromechanical Drumhead Resonators from Two-Dimensional Material Bimorphs.

Atomic membranes of monolayer 2D materials represent the ultimate limit in the size of nano-electromechanical systems. However, new properties and new functionalities emerge by looking at the interface between layers in heterostructures of 2D materials. Here, we demonstrate the integration of 2D heterostructures as tunable nano-electromechanical systems, exploring the competition between the mechanics of the ultrathin membrane and the incommensurate van der Waals interface. We fabricate electrically contacted 5 or 6 μm circular drumheads of suspended heterostructure membranes of monolayer graphene on monolayer molybdenum disulfide (MoS2), which we call a 2D bimorph. We characterize the mechanical resonance through electrostatic actuation and laser interferometry detection. The 2D bimorphs have resonance frequencies of 5-20 MHz and quality factors of 50-700, comparable to resonators from monolayer or few-layer 2D materials. The frequencies and eigenmode shapes of the higher harmonics display split degenerate modes, showing that the 2D bimorphs behave as membranes with asymmetric tension. The devices display dynamic ranges of 44 dB, with an additional nonlinearity in the dissipation at small drive. Under electrostatic frequency tuning, devices display a small tuning of ∼20% compared with graphene resonators, which have >100%. In addition, the tuning shows a kink that deviates from the tensioned membrane model for atomic membranes and corresponds with a changing in stress of 14 mN/m. A model that accounts for this tuning behavior is the onset of interlayer slip in the heterostructure, allowing the tension in the membrane to relax. Using density functional theory simulations, we find that the change in stress at the kink is much larger than the predicted energy barrier for interlayer slip of 0.102 mN/m in an incommensurate 2D heterostructure but smaller than the energy barrier for an aligned graphene bilayer of 35 mN/m, suggesting a local pinning effect at ripples or folds in the heterostructure. Finally, we observe an asymmetry in tuning of the full width at half-maximum that does not exist in monolayer resonators. These findings demonstrate a new class of nano-electromechanical systems from 2D heterostructures and unravel the complex interaction of membrane morphology versus interlayer adhesion and slip on the mechanics of incommensurate van der Waals interfaces.

Cross-Linked Gold-Nanoparticle Membrane Resonators as Microelectromechanical Vapor Sensors.

We report a novel approach for the detection of volatile compounds employing electrostatically driven drumhead resonators as sensing elements. The resonators are based on freestanding membranes of alkanedithiol cross-linked gold nanoparticles (GNPs), which are able to sorb analytes from the gas phase. Under reduced pressure, the fundamental resonance frequency of a resonator is continuously monitored while the device is exposed to varying partial pressures of toluene, 4-methylpentan-2-one, 1-propanol, and water. The measurements reveal a strong, reversible frequency shift of up to ∼10 kHz, i.e., ∼5% of the fundamental resonance frequency, when exposing the sensor to toluene vapor with a partial pressure of ∼20 Pa. As this strong shift cannot be explained exclusively by the mass uptake in the membrane, our results suggest a significant impact of analyte sorption on the pre-stress of the freestanding GNP membrane. Thus, our findings point to the possibility of designing highly sensitive resonators, which utilize sorption induced changes in the membrane's pre-stress as primary transduction mechanism.

Energy Dissipation in Graphene Mechanical Resonators with and without Free Edges.

Graphene-based nanoelectromechanical systems (NEMS) have high future potential to realize sensitive mass and force sensors owing to graphene’s low mass density and exceptional mechanical properties. One of the important remaining issues in this field is how to achieve mechanical resonators with a high quality factor (Q). Energy dissipation in resonators decreases Q, and suppressing it is the key to realizing sensitive sensors. In this article, we review our recent work on energy dissipation in doubly-clamped and circular drumhead graphene resonators. We examined the temperature (T) dependence of the inverse of a quality factor () to reveal what the dominant dissipation mechanism is. Our doubly-clamped trilayer resonators show a characteristic -T curve similar to that observed in monolayer resonators: ∝ above ∼100 K and ∝ below ∼100 K. By comparing our results with previous experimental and theoretical results, we determine that the and dependences can be attributed to tensile strain induced by clamping metals and vibrations at the free edges in doubly-clamped resonators, respectively. The -T curve in our circular drumhead resonators indicates that removing free edges and clamping metal suppresses energy dissipation in the resonators, resulting in a linear T dependence of in a wide temperature range.

Electrostatically driven drumhead resonators based on freestanding membranes of cross-linked gold nanoparticles.

Freestanding, nanometer-thin membranes of alkanedithiol cross-linked gold nanoparticles represent elastic, mechanically robust and electrically conductive materials, which are interesting for the fabrication of novel nano- and microelectromechanical devices. In this work we present the first electrostatically driven drumhead resonators based on such nanoparticle membranes. These circular membranes have a thickness of 33 to 52 nm, a diameter of either 50 μm or 100 μm, and are equally spaced from their back electrode by ∼10 μm. Using an interferometric nanovibration analyzer various vibrational modes with resonance amplitudes of up to several 100 nm could be detected when the membranes are excited by applying AC voltages (<30 V) with drive frequencies of up to 2 MHz. Further, spatial amplitude distributions of different vibrational modes could be imaged. The devices showed fundamental resonance frequencies in the high kHz range and quality factors Q up to ∼2000. Finally, vibrational spectra and observed mode patterns could be well interpreted using the theory for a clamped circular membrane with negligible bending stiffness. Our findings mark an important step towards the integration of freestanding gold nanoparticle composite membranes into electromechanical devices with various applications, such as novel types of pressure or mass sensors.

Black phosphorus nanoelectromechanical resonators vibrating at very high frequencies.

We report on the experimental demonstration of a new type of nanoelectromechanical resonator based on black phosphorus crystals. Facilitated by a highly efficient dry transfer technique, crystalline black phosphorus flakes are harnessed to enable drumhead resonators vibrating at high and very high frequencies (HF and VHF bands, up to ∼100 MHz). We investigate the resonant vibrational responses from the black phosphorus crystals by devising both electrical and optical excitation schemes, in addition to measuring the undriven thermomechanical motions in these suspended nanostructures. Flakes with thicknesses from ∼200 nm down to ∼20 nm clearly exhibit elastic characteristics transitioning from the plate to the membrane regime. Both frequency- and time-domain measurements of the nanomechanical resonances show that very thin black phosphorus crystals hold interesting potential for moveable and vibratory devices and for semiconductor transducers where high-speed mechanical motions could be coupled to the attractive electronic and optoelectronic properties of black phosphorus.

Energy dissipation in edged and edgeless graphene mechanical resonators

We examined the temperature (T) dependence of the inverse of quality factors (Q−1) of edged and edgeless graphene resonators to evaluate energy dissipation in these resonators. We found that Q−1 in an edgeless drumhead resonator shows a linear T dependence in a wide range of 20–300 K, while that in an edged doubly clamped resonator shows T2 and T0.3 dependence above and below ∼100 K, respectively. On the basis of these experimental results, and by comparing them with the previous experimental and numerical studies, we discuss the energy dissipation mechanisms in these resonators. The dissipation at free edges causes the T0.3 dependence in the lower temperature regime, and tensile strain due to the thermal contraction of the clamped-end metal will lead to the T2 behavior in the higher temperature regime. We demonstrate that elimination of these dissipation sources provides wide-ranging linear-T dependence of Q−1 in our drumhead resonators.

Graphene nanoelectromechanical systems as stochastic-frequency oscillators.

We measure the quality factor Q of electrically driven few-layer graphene drumhead resonators, providing an experimental demonstration that Q ∼ 1/T, where T is the temperature. We develop a model that includes intermodal coupling and tensioned graphene resonators. Because the resonators are atomically thin, out-of-plane fluctuations are large. As a result, Q is mainly determined by stochastic frequency broadening rather than frictional damping, in analogy to nuclear magnetic resonance. This model is in good agreement with experiment. Additionally, at larger drives the resonance line width is enhanced by nonlinear damping, in qualitative agreement with recent theory of damping by radiation of in-plane phonons. Parametric amplification produced by periodic thermal expansion from the ac drive voltage yields an anomalously large line width at the largest drives. Our results contribute toward a general framework for understanding the mechanisms of dissipation and spectral line broadening in atomically thin membrane resonators.

Invited Presentation: Graphene Nanoelectromechanical Systems As Stochastic-Frequency Oscillators

We measure the quality factor Q of electrically-driven few-layer graphene drumhead resonators, providing an experimental demonstration that Q ~ 1/T , where T is the temperature. We develop a model that includes intermodal coupling and tensioned graphene resonators, yielding good quantitative agreement to experiment. Because the resonators are atomically thin, out-of-plane fluctuations are large. As a result Q is mainly determined by stochastic frequency broadening rather than frictional damping, in analogy to nuclear magnetic resonance. Additionally, at larger drives the resonator linewidth is enhanced by nonlinear damping, in qualitative agreement with a recent theory of damping by radiation of in-plane phonons[1]. Parametric amplification produced by periodic thermal expansion from the ac drive voltage yields an anomalously large linewidth at the largest drives. Our results contribute towards a general framework for understanding the mechanisms of dissipation and spectral line broadening in atomically thin membrane resonators.1. Croy, A.; Midtvedt, D.; Isacsson, A.; Kinaret, J. M. Phys. Rev. B 2012, 86, 235435.

Self-Assembled Nanoparticle Drumhead Resonators

The self-assembly of nanoscale structures from functional nanoparticles has provided a powerful path to developing devices with emergent properties from the bottom-up. Here we demonstrate that freestanding sheets self-assembled from various nanoparticles form versatile nanomechanical resonators in the megahertz frequency range. Using spatially resolved laser-interferometry to measure thermal vibrational spectra and image vibration modes, we show that their dynamic behavior is in excellent agreement with linear elastic response for prestressed drumheads of negligible bending stiffness. Fabricated in a simple one-step drying-mediated process, these resonators are highly robust and their inorganic-organic hybrid nature offers an extremely low mass, low stiffness, and the potential to couple the intrinsic functionality of the nanoparticle building blocks to nanomechanical motion.

Pressure dependent resonant frequency of micromechanical drumhead resonators

We examine the relationship between squeeze film effects and resonance frequency in drum-type resonators. We find that the resonance frequency increases linearly with pressure as a result of the additional restoring force contribution from compression of gas within the drum cavity. We demonstrate trapping of the gas by squeeze film effects and geometry. The pressure sensitivity is shown to scale inversely with cavity height and sound radiation is found to be the predominant loss mechanism near and above atmospheric pressure. Drum resonators exhibit linearity and sensitivity suitable to barometry from below 10 Torr up to several atmospheres.

Coupled micromechanical drumhead resonators with practical application as electromechanical bandpass filters

This paper treats the theoretical and experimental behavior of coupled mechanical resonators viewed as potential elements of high-Q electromechanical bandpass filters. The benefits of the novel placement of the resonators in a closed ring are discussed, as are the consequences of variations in resonator mass and coupling strength. The modeling is tested using drumhead resonators that are coupled by the sharing of a portion of their perimeters. The test structures, nominally 100 µm in diameter, were made using silicon nitride films and wet etching techniques. The precise size of the resonators, set by the etching time, determined the amount of drumhead overlap and hence the strength of the coupling. Damping of the MHz resonators was controlled by adjusting the ambient gas pressure. Optical interference techniques were used to measure the response of the resonator furthest from the electrostatically-driven member of the ring. The highest-order device studied had 20 resonators and functioned close to prediction with no frequency trimming.