Nanomechanical String Resonators Research Articles

Strain engineering of nonlinear nanoresonators from hardening to softening

Although strain engineering and soft-clamping techniques for attaining high Q-factors in nanoresonators have received much attention, their impact on nonlinear dynamics is not fully understood. In this study, we show that nonlinearity of high-Q Si3N4 nanomechanical string resonators can be substantially tuned by support design. Through careful engineering of support geometries, we control both stress and mechanical nonlinearities, effectively tuning nonlinear stiffness of two orders of magnitude. Our approach also allows control over the sign of the Duffing constant resulting in nonlinear softening of the mechanical mode that conventionally exhibits hardening behavior. We elucidate the influence of support design on the magnitude and trend of the nonlinearity using both analytical and finite element-based reduced-order models that validate our experimental findings. Our work provides evidence of the role of soft-clamping on the nonlinear dynamic response of nanoresonators, offering an alternative pathway for nullifying or enhancing nonlinearity in a reproducible and passive manner.

Tuning the Q-factor of nanomechanical string resonators by torsion support design

In recent years, the Q-factor of Si3N4 nanomechanical resonators has significantly been increased by soft-clamping techniques using large and complex support structures. To date, however, obtaining similar performance with smaller supports has remained a challenge. Here, we make use of torsion beam supports to tune the Q-factor of Si3N4 string resonators. By design optimization of the supports, we obtain a 50% Q-factor enhancement compared to the standard clamped–clamped string resonators. By performing experimental and numerical studies, we show that further improvement of the Q-factor is limited by a trade-off between maximizing stress and minimizing torsional support stiffness. Thus, our study also provides insight into dissipation limits of high-stress string resonators and outlines how advanced designs can be realized for reaching ultimate f0×Q product while maintaining a small footprint.

Universal Length Dependence of Tensile Stress in Nanomechanical String Resonators

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 data. This opens a perspective for stress-engineering the mechanical quality factor of nanomechanical string resonators.

Tuning the nonlinear dispersive coupling of nanomechanical string resonators

We investigate nonlinear dispersive mode coupling between the flexural in- and out-of-plane modes of two doubly clamped, nanomechanical silicon nitride string resonators. As the amplitude of one mode transitions from the linear response regime into the nonlinear regime, we find a frequency shift of two other modes. The resonators are strongly elastically coupled via a shared clamping point and can be tuned in and out of resonance dielectrically, giving rise to multimode avoided crossings. When the modes start hybridizing, their polarization changes. This affects the nonlinear dispersive coupling in a nontrivial way. We propose a theoretical model to describe the dependence of the dispersive coupling on the mode hybridization.

Influence of clamp-widening on the quality factor of nanomechanical silicon nitride resonators

Nanomechanical resonators based on strained silicon nitride (Si3N4) have received a lot of attention in fields such as sensing and quantum optomechanics due to their exceptionally high quality factors (Qs). Room-temperature Qs approaching 1×109 are now in reach by means of phononic crystals (soft-clamping) and strain engineering. Despite great progress in enhancing Qs, difficulties in the fabrication of soft-clamped samples limit their implementation into actual devices. An alternative means of achieving ultrahigh Qs was shown using trampoline resonators with engineered clamps, which serves to localize the stress to the center of the resonator while minimizing stress at the clamping. The effectiveness of this approach has since come into question from recent studies employing string resonators with clamp-tapering. Here, we investigate this idea using nanomechanical string resonators with engineered clampings similar to those presented for trampolines. Importantly, the effect of orienting the strings diagonally or perpendicularly with respect to the silicon frame is investigated. It is found that increasing the clamp width for diagonal strings slightly increases Qs of the fundamental out-of-plane mode at small radii, while perpendicular strings only deteriorate with increasing clamp width. Measured Qs agree well with finite element method simulations even for higher-order resonances. The small increase cannot account for previously reported Qs of trampoline resonators. Instead, we propose the effect to be intrinsic and related to surface and radiation losses.

Stress control of tensile-strained In1−xGaxP nanomechanical string resonators

We investigate the mechanical properties of freely suspended nanostrings fabricated from tensile-stressed, crystalline In1−xGaxP. The intrinsic strain arises during epitaxial growth as a consequence of the lattice mismatch between the thin film and the substrate, and is confirmed by x-ray diffraction measurements. The flexural eigenfrequencies of the nanomechanical string resonators reveal an orientation dependent stress with a maximum value of 650 MPa. The angular dependence is explained by a combination of anisotropic Young's modulus and a change of elastic properties caused by defects. As a function of the crystal orientation, a stress variation of up to 50% is observed. This enables fine tuning of the tensile stress for any given Ga content x, which implies interesting prospects for the study of high Q nanomechanical systems.

Tailoring stress in pyrolytic carbon for fabrication of nanomechanical string resonators

In order to achieve high resonance frequencies and quality factors of pyrolytic carbon MEMS string resonators the resonator material needs to have a large tensile stress. In this study, the influence of pyrolysis temperature, dwell time and ramping rate on the residual stress in thin pyrolytic carbon films is investigated with the bending plate method. The results show that the pyrolysis temperature is the most important parameter for tailoring the residual stress, with a transition from tensile stress at temperature below 800ºC to compressive stress at temperatures above 800ºC. Two kinds of photoresist: positive (AZ5214E) and negative (SU-8) and different pyrolysis conditions are used to fabricate pyrolytic carbon string resonators at variable pyrolysis conditions. The best performance is obtained for devices with a length of 400 μm fabricated at a pyrolysis temperature of 700ºC, ramping rate of 30ºC/min and 10 min dwell time corresponding to the conditions for maximum tensile stress in pyrolytic carbon thin films. The optimized pyrolytic carbon string resonators have resonant frequencies above 300 kHz and quality factors (Q) in the order of 104, which is suitable for their application as nanomechanical sensors.

Strong 4-mode coupling of nanomechanical string resonators

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 resonances of the four coupled fundamental vibrational modes of a resonator pair, giving rise to a simple and a multimode avoided crossing, respectively.

Nanomechanical Pyrolytic Carbon Resonators: Novel Fabrication Method and Characterization of Mechanical Properties

Micro- and nanomechanical string resonators, which essentially are highly stressed bridges, are of particular interest for micro- and nanomechanical sensing because they exhibit resonant behavior with exceptionally high quality factors. Here, we fabricated and characterized nanomechanical pyrolytic carbon resonators (strings and cantilevers) obtained through pyrolysis of photoresist precursors. The developed fabrication process consists of only three processing steps: photolithography, dry etching and pyrolysis. Two different fabrication strategies with two different photoresists, namely SU-8 2005 (negative) and AZ 5214e (positive), were compared. The resonant behavior of the pyrolytic resonators was characterized at room temperature and in high vacuum using a laser Doppler vibrometer. The experimental data was used to estimate the Young’s modulus of pyrolytic carbon and the tensile stress in the string resonators. The Young’s moduli were calculated to be 74 ± 8 GPa with SU-8 and 115 ± 8 GPa with AZ 5214e as the precursor. The tensile stress in the string resonators was 33 ± 7 MPa with AZ 5214e as the precursor. The string resonators displayed maximal quality factor values of up to 3000 for 525-µm-long structures.

Nanomechanical IR spectroscopy for fast analysis of liquid-dispersed engineered nanomaterials

The proliferated use of engineered nanomaterials (ENMs), e.g. in nanomedicine, calls for novel techniques allowing for fast and sensitive analysis of minute samples. Here we present nanomechanical IR spectroscopy (NAM-IR) for chemical analysis of picograms of ENMs. ENMs are nebulized directly from dispersion and efficiently collected on nanomechanical string resonators through a non-diffusion limited sampling method. Even very small amounts of sample can convert absorbed IR light into a measurable frequency detuning of the string through photothermal heating. An IR absorption spectrum is thus readily obtained by recording this detuning of the resonator over a range of IR wavelengths. Results recorded using NAM-IR agree well with corresponding results obtained through ATR-FTIR, and remarkably, measurement including sample preparation takes only a few minutes, compared to ∼2 days sample preparation for ATR-FTIR. Resonator dimensions play an important role in NAM-IR, a relationship which will be elaborated here.

Low-Power Photothermal Probing of Single Plasmonic Nanostructures with Nanomechanical String Resonators

We demonstrate the direct photothermal probing and mapping of single plasmonic nanostructures via the temperature-induced detuning of nanomechanical string resonators. Single Au nanoslits and nanorods are illuminated with a partially polarized focused laser beam (λ = 633 nm) with irradiances in the range of 0.26-38 μW/μm(2). Photothermal heating maps with a resolution of ∼375 nm are obtained by scanning the laser over the nanostructures. Based on the string sensitivities, absorption efficiencies of 2.3 ± 0.3 and 1.1 ± 0.7 are extracted for a single nanoslit (53 nm × 1 μm) and nanorod (75 nm × 185 nm). Our results show that nanomechanical resonators are a unique and robust analysis tool for the low-power investigation of thermoplasmonic effects in plasmonic hot spots.