Silicon Nanomechanical Resonators Research Articles

Design and Fabrication of Capacitive Silicon Nanomechanical Resonators with Selective Vibration of a High-Order Mode.

This paper reports the design and fabrication of capacitive silicon nanomechanical resonators with the selective vibration of a high-order mode. Fixed-fixed beam capacitive silicon resonators have been successfully produced by the use of electron beam lithography, photolithography, deep reactive ion etching, and anodic bonding methods. All resonators with different vibration modes are designed to have the same resonant frequency for performance comparison. Measurement results show that higher-order mode capacitive silicon resonators can achieve lower insertion loss compared to that of lower-order mode capacitive silicon resonators. The motional resistance of the fourth mode vibration resonator is improved by 83%, 90%, and 93% over the third, second, and first mode vibration resonators, respectively.

Single and mechanically coupled capacitive silicon nanomechanical resonators

The design, fabrication and evaluation of single and mechanically coupled capacitive silicon nanomechanical resonators is reported. The structure of resonators is fabricated on a silicon on insulator wafer and transferred to a Tempax glass substrate by anodic bonding. A finite element method simulation has been conducted to investigate the vibration modes of the resonators. Single beam resonator with a length of 21.3 μm, a width of 500 nm, a thickness of 5 μm and the capacitive gap size of about 300 nm shows a nonlinear response. The amplitude of frequency response increases as the frequency is swept upward, and then suddenly jumps to a lower value. The mechanically coupled capacitive silicon nanomechanical resonator with a number of 100 individual beams above is successfully fabricated. Some resonant peaks can be observed, which shows that most nanomechanical resonators are mechanically coupled and synchronised. A mechanical resonance at a high frequency of ∼7.2 MHz in flexural mode has been detected. A small motional resistance of 1.2 kΩ has been achieved by the mechanical coupling.

Phonon counting and intensity interferometry of a nanomechanical resonator

In optics, the ability to measure individual quanta of light (photons) enables a great many applications, ranging from dynamic imaging within living organisms to secure quantum communication. Pioneering photon counting experiments, such as the intensity interferometry performed by Hanbury Brown and Twiss to measure the angular width of visible stars, have played a critical role in our understanding of the full quantum nature of light. As with matter at the atomic scale, the laws of quantum mechanics also govern the properties of macroscopic mechanical objects, providing fundamental quantum limits to the sensitivity of mechanical sensors and transducers. Current research in cavity optomechanics seeks to use light to explore the quantum properties of mechanical systems ranging in size from kilogram-mass mirrors to nanoscale membranes, as well as to develop technologies for precision sensing and quantum information processing. Here we use an optical probe and single-photon detection to study the acoustic emission and absorption processes in a silicon nanomechanical resonator, and perform a measurement similar to that used by Hanbury Brown and Twiss to measure correlations in the emitted phonons as the resonator undergoes a parametric instability formally equivalent to that of a laser. Owing to the cavity-enhanced coupling of light with mechanical motion, this effective phonon counting technique has a noise equivalent phonon sensitivity of 0.89±0.05. With straightforward improvements to this method, a variety of quantum state engineering tasks using mesoscopic mechanical resonators would be enabled, including the generation and heralding of single-phonon Fock states and the quantum entanglement of remote mechanical elements.

Silicon nano-mechanical resonators fabricated by using tip-based nanofabrication

We report fabrication of silicon nano-mechanical resonators where the key nanolithography step is performed by using tip-based nanofabrication (TBN). Specifically, a heated atomic force microscope tip deposited polystyrene nanowires that were used together with a lithographically patterned aluminum to serve as an etch mask for silicon resonators their anchors. Using this nanofabrication technique, we demonstrate the fabrication of different types of silicon nano-mechanical resonator devices, including those that are either singly or doubly clamped and having either straight or curvilinear features. Typical dimensions for the width and thickness of these devices is in the range of several hundred nanometers. We characterized the mechanical resonance properties of these devices by using laser Doppler vibrometry and compared the measured response with finite element simulations. Typical resonance frequency values ranged from 1 to 3 MHz and typical quality factor values ranged from 100 to 150. The combination of TBN along with conventional microfabrication processes could help to realize new types of nano-devices.

Correction: Corrigendum: Quantum Limit of Quality Factor in Silicon Micro and Nano Mechanical Resonators

Micromechanical resonators are promising replacements for quartz crystals for timing and frequency references owing to potential for compactness, integrability with CMOS fabrication processes, low cost, and low power consumption. To be used in high performance reference application, resonators should obtain a high quality factor. The limit of the quality factor achieved by a resonator is set by the material properties, geometry and operating condition. Some recent resonators properly designed for exploiting bulk-acoustic resonance have been demonstrated to operate close to the quantum mechanical limit for the quality factor and frequency product (Q-f). Here, we describe the physics that gives rise to the quantum limit to the Q-f product, explain design strategies for minimizing other dissipation sources, and present new results from several different resonators that approach the limit.

Quantum Limit of Quality Factor in Silicon Micro and Nano Mechanical Resonators

Micromechanical resonators are promising replacements for quartz crystals for timing and frequency references owing to potential for compactness, integrability with CMOS fabrication processes, low cost, and low power consumption. To be used in high performance reference application, resonators should obtain a high quality factor. The limit of the quality factor achieved by a resonator is set by the material properties, geometry and operating condition. Some recent resonators properly designed for exploiting bulk-acoustic resonance have been demonstrated to operate close to the quantum mechanical limit for the quality factor and frequency product (Q-f). Here, we describe the physics that gives rise to the quantum limit to the Q-f product, explain design strategies for minimizing other dissipation sources, and present new results from several different resonators that approach the limit.

Nanoelectromechanical system-integrated detector with silicon nanomechanical resonator and silicon nanochannel field effect transistor

We demonstrate the fabrication and operation of an integrated device containing a nanoelectromechanical system and an integrated detector. This on-chip silicon nanochannel field effect transistor is used to measure the motion of a silicon nanomechanical resonator at room temperature. Furthermore, we describe the operation of the device as a silicon-based room-temperature on-chip amplifier for improved displacement detection of nanomechanical resonators.

Noise color and asymmetry in stochastic resonance with silicon nanomechanical resonators

Stochastic resonance with white noise has been well established as a potential signal amplification mechanism in nanomechanical two-state systems. While white noise represents the archetypal stimulus for stochastic resonance, typical operating environments for nanomechanical devices often contain different classes of noise, particularly colored noise with a 1/f spectrum. As a result, improved understanding of the effects of noise color will be helpful in maximizing device performance. Here we report measurements of stochastic resonance in a silicon nanomechanical resonator using 1/f noise and Ornstein-Uhlenbeck noise types. Power spectral densities and residence time distributions provide insight into asymmetry of the bistable amplitude states, and the data sets suggest that 1/fα noise spectra with increasing noise color (i.e. α) may lead to increasing asymmetry in the system, reducing the achievable amplification. Furthermore, we explore the effects of correlation time τ on stochastic resonance with the use of exponentially correlated noise. We find monotonic suppression of the spectral amplification as the correlation time increases.

Silicon nanomechanical resonators with a double-triangle cross section leading to an enhanced mass sensitivity

We report on a silicon nanomechanical resonator fabricated with a double-triangle cross section, leading to an enhanced mass sensing capabilities. We analytically derive the dependence of the mass detection limit on, respectively, the moment of inertia and the cross section of a beam resonator. We conclude that our scaling compatible fabrication scheme can yield an enhancement of as much as 2.3 with regard to regular, rectangular resonators of the same size. We experimentally confirm the shape dependence of the resonant frequency and maximum drive energy, supporting our model for the mass detection limit.

Study of laser-induced self-oscillations in silicon nanomechanical resonators

We report a study of laser-induced oscillation of nanomechanical resonators. The modes of motion of single-stage and double-stage paddle resonators are first assessed using finite element analysis and experimentally observed using piezoelectric actuation of the devices. The flexural modes of the same devices are then excited at resonance using laser-induced thermal effects. As the actuating power is gradually increased, the resonators experience three phases of resonance characterized by distinct changes of amplitude and number of peaks observed. In addition, the resonant frequencies initially show a steady decrease with actuating power followed by a distinct increase. Finally, a sharpening of the resonant response is also observed as actuating power is increased. However, such peak sharpening is also accompanied by instabilities of the center frequency. These instabilities could be induced by a frequency mismatch between the parametric actuation mechanism and the natural resonance of the device, or by optically induced temperature fluctuations along the length of the resonator supports.

Gorsky damping in nanomechanical structures

The critical frequency of Gorsky damping coincides with the structural resonant frequencies of nanomechanical structures over a wide range of solute diffusivities. A lower bound of 1 at.% hydrogen in silicon is estimated for Gorsky damping to attain values comparable to previously measured loss coefficients of single-crystal silicon nanomechanical cantilever-beam resonators.