Observation of resonance modes is the most straightforward way of studying mechanical oscillations because these modes have maximum response to stimuli. However, a deeper understanding of mechanical motion could be obtained by also looking at modal responses at frequencies in between resonances. A common way to do this is to force a mechanical object into oscillations and study its off-resonance behaviour. In this paper, we present visualisation of the modal response shapes for a mechanical drum driven off resonance. By using the frequency modal analysis, we describe these shapes as a superposition of resonance modes. We find that the spatial distribution of the oscillating component of the driving force affects the modal weight or participation. Moreover, we are able to infer the asymmetry of the drum by studying the dependence of the resonance modes shapes on the frequency of the driving force. Our results highlight that dynamic responses of any mechanical system are mixtures of their resonance modes with various modal weights, further giving credence to the universality of this phenomenon.
We investigate the tensile stress in freely suspended nanomechanical string resonators, and observe a material-independent dependence on the resonator length. We compare strongly stressed sting resonators fabricated from four different material systems based on amorphous silicon nitride, crystalline silicon carbide as well as crystalline indium gallium phosphide. The tensile stress is found to increase by approximately 50% for shorter resonators. We establish a simple elastic model to describe the observed length dependence of the tensile stress. The model accurately describes our experimental…
Studies involving nanomechanical motion have evolved from its detection and understanding of its fundamental aspects to its promising practical utility as an integral component of hybrid systems. Nanomechanical resonators' indispensable role as transducers between optical and microwave fields in hybrid systems, such as quantum communications interface, have elevated their importance in recent years. It is therefore crucial to determine which among the family of nanomechanical resonators is more suitable for this role. Most of the studies revolve around nanomechanical resonators of ultrathin st…
The motion of a vibrating object is determined by the way it is held. This simple observation has long inspired string instrument makers to create new sounds by devising elegant string clamping mechanisms, whereby the distance between the clamping points is modulated as the string vibrates. At the nanoscale, the simplest way to emulate this principle would be to controllably make nanoresonators slide across their clamping points, which would effectively modulate their vibrating length. Here, we report measurements of flexural vibrations in nanomechanical resonators that reveal such a sliding m…
Networks of coupled resonators are an ubiquitous concept in physics, forming the basis of synchronization phenomena, metamaterial formation, nonreciprocal behavior and topological effects. Such systems are typically explored using optical or microwave resonators. In recent years, mechanical resonators have entered the stage as universal building block for resonator networks, both for their well-controlled mechanical properties and for their eigenfrequencies conveniently located in the radio-frequency regime. Vertically oriented nanomechanical pillar resonators are ideally suited for the dense …
Dissipation dilution enables extremely low linear loss in stressed, high-aspect ratio nanomechanical resonators, such as strings or membranes. Here, we report on the observation and theoretical modelling of nonlinear dissipation in such structures. We introduce an analytical model based on von Kármán theory, which can be numerically evaluated using finite-element models for arbitrary geometries. We use this approach to predict nonlinear loss and (Duffing) frequency shift in ultracoherent phononic membrane resonators. A set of systematic measurements with silicon nitride membranes shows good ag…
The shape of a nanomechanical resonator profoundly affects its mechanical properties and determines its suitability for various applications, such as ultra-sensitive mass and force detection. Despite the promise of two-dimensional nanomechanical systems in such applications, full control over the shape of suspended two-dimensional materials, such as graphene, has not been achieved. We present an effective, single-step method to shape presuspended graphene into nanomechanical resonators with arbitrary geometries leading to enhanced properties in comparison to conventional drumheads. Our techniq…
We report on a nanomechanical engineering method to monitor matter growth in real time via e-beam electromechanical coupling. This method relies on the exceptional mass sensing capabilities of nanomechanical resonators. Focused electron beam induced deposition (FEBID) is employed to selectively grow platinum particles at the free end of singly clamped nanotube cantilevers. The electron beam has two functions: it allows both to grow material on the nanotube and to track in real time the deposited mass by probing the noise-driven mechanical resonance of the nanotube. On the one hand, this detect…
Nanomechanical resonators based on strained silicon nitride (Si$_3$N$_4$) have received a large amount of attention in fields such as sensing and quantum optomechanics due to their exceptionally high quality factors ($Q$s). Room-temperature $Q$s approaching 1 billion are now in reach by means of phononic crystals (soft-clamping) and strain engineering. Despite great progress in enhancing $Q$s, difficulties in fabrication of soft-clamped samples limits their implementation into actual devices. An alternative means of achieving ultra-high $Q$s was shown using trampoline resonators with engineere…
Nanomechanical silicon nitride (SiN) drum resonators are currently employed in various fields of applications that arise from their unprecedented frequency response to physical quantities. In the present study, we investigate the thermal transport in nanomechanical SiN drum resonators by analytical modelling, computational simulations, and experiments for a better understanding of the underlying heat transfer mechanism causing the thermal frequency response. Our analysis indicates that radiative heat loss is a non-negligible heat transfer mechanism in nanomechanical SiN resonators limiting the…
Engineered micro- and nanomechanical resonators with ultra-low dissipation constitute the ideal systems for applications ranging from high-precision sensing such as magnetic resonance force microscopy, to quantum transduction between disparate quantum systems. Traditionally, the improvement of the resonator's performance - often quantified by its Qf product (where Q is quality factor and f is frequency) - through nanomechanical engineering such as dissipation dilution and strain engineering, has been driven by human intuition and insight. Such an approach is inefficient and leaves aside a plet…
Atomic layer deposition (ALD), a layer-by-layer controlled method to synthesize ultrathin materials, provides various merits over other techniques such as precise thickness control, large area scalability and excellent conformality. Here we demonstrate the possibility of using ALD growth on top of suspended 2D materials to fabricate nanomechanical resonators. We fabricate ALD nanomechanical resonators consisting of a graphene/MoS$_2$ heterostructure. Using AFM indentation and optothermal drive, we measure their mechanical properties including Young's modulus, resonance frequency and quality fa…
We investigate mechanical mode coupling between the four fundamental flexural modes of two doubly-clamped, high-Q silicon-nitride nanomechanical string resonators. Strong mechanical coupling between the strings is induced by the strain mediated via a shared clamping point, engineered to increase the exchange of oscillatory energy. One of the resonators is controlled dielectrically, which results in strong coupling between its out-of-plane and in-plane flexural modes. We show both, inter-string out-of-plane-in-plane and 3-mode resonance of the four coupled fundamental vibrational modes of a res…
Quasicrystal Architected Nanomechanical Resonators via Data-Driven Design
Department of Precision and Microsystems Engineering, Delft University of Technology（代尔夫特理工大学精密与微系统工程系）；Department of Mechanical Engineering, Pohang University of Science and Technology（浦项科技大学机械工程系）
Nanomechanical resonators with ultra-high quality factors have become a central element in fundamental research, enabling measurements below the standard quantum limit and the preparation of long-lived quantum states. Here, I propose that such resonators will allow the detection of electron and nuclear spins with high spatial resolution, paving the way to future nanoscale magnetic resonance imaging instruments. The article lists the challenges that must be overcome before this vision can become reality, and indicates potential solutions.
Statistical Properties of a Fluctuation-Driven Nanomechanical Duffing Resonator
Boston University（波士顿大学）；Virginia Tech（弗吉尼亚理工大学）；James Madison University（詹姆斯麦迪逊大学）；Sabanci University（萨班哲大学）；Bilkent University（比尔肯特大学）；Gordon College（戈登学院）
Most technologies, including conventional mass spectrometry, struggle to measure the mass of particles in the MDa to GDa range. Although this mass range appears optimal for nanomechanical resonators, early nanomechanical-MS systems suffered from prohibitive sample loss, extended analysis time or inadequate resolution. Here, we report on a novel system architecture combining nebulization of the analytes from solution, their efficient transfer and focusing without relying on electromagnetic fields, and the mass measurements of individual particles using nanomechanical resonator arrays. This syst…
Nanoelectromechanical systems (NEMS) have proven outstanding performance in the detection of small masses down to single proton sensitivity. To obtain a high enough throughput for the application in practical mass spectrometry, NEMS resonators have to be arranged in two-dimensional (2D) arrays. However, all state-of-the-art electromechanical transduction methods rely on electrical lines placed close to the mechanical resonators, which drastically restricts the density of 2D resonator arrays. An exception is the transduction by surface acoustic waves (SAWs), which has so far only been shown for…
We present a method for the in-situ determination of Young's modulus of a nanomechanical string resonator subjected to tensile stress. It relies on measuring a large number of harmonic eigenmodes and allows to access Young's modulus even for the case of a stress-dominated frequency response. We use the proposed framework to obtain the Young's modulus of four different wafer materials, comprising the three different material platforms amorphous silicon nitride, crystalline silicon carbide and crystalline indium gallium phosphide. The resulting values are compared with theoretical and literature…
All-dry processing of 3C-SiC nanomechanical string resonators for extreme aspect ratios and high intrinsic quality factor
Technical University of Munich（慕尼黑工业大学）；Munich Center for Quantum Science and Technology (MCQST)（慕尼黑量子科学与技术中心）；TUM Center for Quantum Engineering (ZQE)（慕尼黑工业大学量子工程中心）
Nanomechanical systems have been proposed as an alternative computing platform for high radiation environments, where semiconductor electronics traditionally fail, as well as to allow improved gate densities and energy consumption. While there have been numerous demonstrations of individual nanomechanical logic gates leveraging the Duffing nonlinearity, the development of useful nanomechanical logic circuits depends strongly on the ability to cascade multiple logic gates. Here we show theoretically that cascading nanomechanical logic gates, where the output of one gate is fed into the input of…
Freestanding Silicon nitride (SiN) devices are central to the field of nanomechanical resonators and for other technology applications such as transmission electron imaging and nanopore bioassays. The nanofabrication techniques used for fabricating these devices often lack flexibility. While photolithography requires printing of an expensive photomask for each new design iteration, electron-beam lithography is extremely slow and commands high equipment cost. Here we demonstrate maskless rapid prototyping of freestanding SiN nanomechanical resonators fabricated by femtosecond laser ablation of …
Complex oxide thin films and heterostructures exhibit a profusion of exotic phenomena, often resulting from the intricate interplay between film and substrate. Recently it has become possible to isolate epitaxially grown single-crystalline layers of these materials, enabling the study of their properties in the absence of interface effects. In this work, we create ultrathin membranes of strongly correlated materials and demonstrate top-down fabrication of nanomechanical resonators made out of \ce{SrTiO3} and \ce{SrRuO3}. Using laser interferometry, we successfully actuate and measure the motio…
