Graphene trampoline resonators anchored by narrow tethers achieve high quality factors at room temperature, maintaining coherence and outperforming drumhead designs for potential nanomechanical sensing applications.
(Nanowerk Spotlight) Nanomechanical resonators operate by vibrating at well-defined frequencies, and tiny changes in their physical environment shift those vibrations in measurable ways. Their sensitivity depends on how slowly their motion decays. This property is captured by the quality factor, or Q, which describes how much vibrational energy remains after each cycle. A high Q produces a sharp resonance and allows detection of faint disturbances such as small forces, mass additions, or thermal signals.
Devices built from atomically thin membranes are attractive because their low mass favors high-frequency oscillation. The problem has been dissipation. When these ultrathin structures are clamped around their full perimeter, their vibrations leak into the larger substrate beneath them. That leakage (called clamping loss) dominates performance at room temperature and restricts the usefulness of two-dimensional resonators outside controlled laboratory environments.
A study published in Advanced Functional Materials (“Graphene Trampoline Nanomechanical Resonators with Very High Quality Factors and Broad Dynamic Ranges”) tackles this limitation not by changing the material but by changing how it is anchored. Instead of holding a suspended graphene membrane like a drumhead, the researchers cut it into a trampoline that attaches to the substrate through just a few narrow tethers. These tethers act as restricted bridges for vibrational energy. The membrane still oscillates freely, but the pathways through which energy can escape are far smaller.
The design keeps all of the advantages of an atomically thin material while reducing interaction with the surrounding structure.
The trampoline devices begin as circular graphene membranes stretched over micrometer-scale trenches etched into silicon oxide. The researchers then use a focused ion beam to carve away material until only a central pad connected by four or six thin arms remains. The milling continues only until the cut regions detach and drop away. The thickness of each membrane is measured near supported regions to avoid disturbing the suspended parts. This process preserves the mechanical integrity of the trampoline while maintaining the underlying crystalline sheet.
Design of 4- and 6-tether trampoline nanomechanical resonators. a) Illustration of circular drumhead resonator clamped fully at the edge of the micro-trench. Energy dissipates into the supporting structure through the clamped region (blue arrows). b) Measured nanomechanical resonance of a drumhead resonator, with a typical broadened linewidth at room temperature. Fitting to the finite-Q harmonic resonator model estimates f1 = 17.18 MHz with Q1 = 180. c) Trampoline geometry with 4 tethers, shaped by precise FIB milling, to reduce the clamping loss. Reduced clamping length results in lower dissipation of energy into the thermal bath. d) Response of an optically probed 4-tether graphene trampoline nanomechanical resonator. Due to lower dissipation, Q increases to Q1 = 670. e) Illustration of a 6-tether trampoline resonator with tether width w. f) Response of a 6-tether trampoline resonator demonstrating narrow linewidth. From fitting, estimated f1 = 18.55 MHz with Q1 = 2.5 × 103. Insets in (b), (d), and (f) show colored SEM images. The blue dots and red dashed lines indicate the experimental and fitted curves, respectively. The numbers in the top left corner of the SEM images indicate the device identification numbers. (Image: Reproduced with permission from Wiley-VCH Verlag) (click on image to enlarge)
To characterize how these structures behave, the authors use optical interferometry under moderate vacuum at room temperature. A modulated blue laser heats the membrane periodically, creating a thermal actuation signal, while a red probe laser tracks how the reflection changes as the membrane moves. Because this technique does not require physical contact with the device, it captures both thermomechanical motion and driven oscillations without altering the system being measured.
The performance difference between conventional drumheads and trampoline geometries is immediately evident. A fully clamped graphene membrane resonates at about 17.18 MHz and loses energy quickly, producing a quality factor near 180. When the same type of suspended membrane is reshaped into a four-tether trampoline, its fundamental driven mode appears near 12.96 MHz yet retains energy far more effectively, with a Q of about 670.
Even without external driving, three thermomechanical modes are visible at roughly 12.9, 20.6 and 34.9 MHz, and their quality factors reach as high as about 1.2 × 10³. These measurements demonstrate that reducing the number of anchor points lowers energy leakage while preserving frequency performance.
As the driving amplitude increases, the trampoline’s response reveals more complex behavior. At small oscillation amplitudes, the resonance peak remains stable. Once the displacement grows, the membrane stretches and its stiffness changes, pushing the resonance toward lower frequencies.
The study finds that this softening begins when the oscillation reaches a displacement on the order of 2.2 nm. By comparing that threshold to the noise detected in the thermomechanical signal, the authors calculate a usable operating range equivalent to about 72 dB. This is a large linear window for a membrane just a few nanometers thick, and it indicates resilience against distortion even when driven strongly.
The second vibrational mode of the same trampoline exhibits another nonlinear hallmark: hysteresis. When the excitation frequency is swept upward, the resonance peak traces one path through frequency space, but when swept downward, it traces a different path. This behavior is modeled using a nonlinear mechanical framework that includes a cubic term describing how stiffness changes with displacement. The fit yields a cubic coefficient of approximately −8 × 10¹³ N m⁻³, consistent with softening. The quintic term added to the model contributes minimally within the measured amplitude range. The paper attributes these nonlinear effects to the geometry of the membrane and to the heating introduced by the optical drive.
The most striking results come from trampolines supported by six tethers. One such device, roughly 7 μm across and several nanometers thick, shows its fundamental resonance at about 23.47 MHz. That mode maintains coherence with a quality factor close to 1.5 × 10⁴, more than an order of magnitude higher than the four-tether design and nearly two orders above the drumhead. Higher modes appear at approximately 43.5 and 67.2 MHz, and their quality factors reach around 9.5 × 10³ and 4.8 × 10³. The combination of frequency and coherence is captured by the f×Q product, which quantifies how many oscillation cycles remain coherent. For this six-tether device, the product reaches roughly 4.1 × 10¹¹ Hz, exceeding reported values for two-dimensional drumheads operating under similar conditions.
The authors also examine trampoline resonators at larger scales. A device with diameter around 10 μm shows undriven motion with a quality factor near 2.5 × 10⁴. When actuated, its first mode appears at about 24.50 MHz with a Q of roughly 9.1 × 10³, giving an f×Q product around 2.2 × 10¹¹ Hz. Even at 20 μm diameter, where a conventional drumhead would normally suffer substantial loss, a six-tether trampoline maintains a Q above 6.1 × 10³ at around 11 MHz. Throughout these tests, the suspended graphene remains visibly flat, without wrinkles or buckling, indicating that the tethered geometry preserves mechanical tension even as size increases.
The paper places these values in context with established nanomechanical platforms. Silicon nitride and silicon carbide resonators can achieve very high-quality factors, but they do so using structures that are many orders of magnitude larger in volume and operate at lower frequencies. The graphene trampolines remain compact, maintain frequencies in the tens of megahertz, and achieve coherence that surpasses fully clamped membranes without requiring extreme cooling.
The authors note that the narrow tether geometry increases thermal resistance, which may enable sensing applications where very small heat inputs or radiation levels cause measurable shifts in vibration. They also identify directions for further work, including adjustments to tether shapes, environmental conditions, and multimode interactions.
The study demonstrates that energy loss in ultrathin mechanical resonators can be addressed by rethinking how they are anchored. Rather than adding coatings, altering materials, or imposing complex boundary structures, the trampoline approach limits pathways for dissipation by reducing contact with the substrate. In doing so, it achieves high-coherence motion at room temperature using devices just a few micrometers wide. This geometry makes graphene more viable as a practical nanomechanical platform and shows that design at the scale of a single micron can change how energy flows through an atomically thin resonator.
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Philip X.-L. Feng (University of Florida, Gainesville)
, 0000-0002-1083-2391 corresponding author
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