Noise in microelectromechanical system resonators

Microelectromechanical system (MEMS) and nanoelectromechanical system (NEMS) based resonators and filters, ranging in frequencies from kHz to GHz, have been proposed. The question of how the stabilities of such resonators scale with dimensions is examined in this paper, with emphasis on the noise characteristics. When the dimensions of a resonator become small, instabilities that are negligible in macro-scale devices become prominent. The effects of fluctuations in temperature, adsorbing/desorbing molecules, outgassing, Brownian motion, Johnson noise, drive power and self-heating, and random vibration are explored. When the device is small, the effects of fluctuations in the numbers of photons, phonons, electrons and adsorbed molecules can all affect the noise characteristics. For all but the random vibration-induced noise, reducing the dimensions increases the noise. At submicron dimensions, especially, the frequency noise due to temperature fluctuations, Johnson noise, and adsorption/desorption are likely to limit the applications of ultra-small resonators.     

Zeptogram-scale nanomechanical mass sensing

Very high frequency (VHF) nanoelectromechanical systems (NEMS) provide unprecedented sensitivity for inertial mass sensing. We demonstrate in situ measurements in real time with mass noise floor approximately 20 zg. Our best mass resolution corresponds to approximately 7 zg, equivalent to approximately 30 xenon atoms or the mass of an individual 4 kDa molecule. Detailed analysis of the ultimate sensitivity of such devices based on these experimental results indicates that NEMS can ultimately provide inertial mass sensing of individual intact, electrically neutral macromolecules with single-Dalton (1 amu) resolution.     

Modeling and in-situ observation of mechanical resonances in single, vertically-oriented carbon nanofibers

In this paper, we have analyzed mechanical resonances in carbon nanotubes (CNTs) based on single, vertically-oriented tubes for their potential application in high-frequency, high-Q, miniaturized resonators. The nano-electro-mechanical (NEM) resonators were modeled using a commercially available finite-element-simulator, where the electro-mechanical coupling of the CNT to an incoming AC signal on a probe in close proximity was examined. The modeling results confirmed that the mechanical resonance was maximized when the frequency of the input signal was equal to the first order harmonic of the CNT. An investigation of the resonance frequency was also performed for various geometrical parameters of our unique three-dimensional (3D) NEMS architecture. Finally, in-situ observations of mechanical resonance in single, vertically oriented tubes is also reported, where such measurements were conducted inside a scanning-electron-microscope. This work suggests that our vertically oriented tubes are potentially well-suited for resonator applications, such as filter banks in communication systems or for mass sensing applications.     

Nanotribology and nanomechanics in nano/biotechnology

Owing to larger surface area in micro/nanoelectromechanical systems (MEMS/NEMS), surface forces such as adhesion, friction, and meniscus and viscous drag forces become large when compared with inertial and electromagnetic forces. There is a need to develop lubricants and identify lubrication methods that are suitable for MEMS/NEMS. For BioMEMS/BioNEMS, adhesion between biological molecular layers and the substrate, and friction and wear of biological layers may be important, and methods to enhance adhesion between biomolecules and the device surface need to be developed. There is a need for development of a fundamental understanding of adhesion, friction/stiction, wear, the role of surface contamination and environment, and lubrication. MEMS/NEMS materials need to exhibit good mechanical and tribological properties on the micro/nanoscale. Most mechanical properties are known to be scale dependent. Therefore, the properties of nanoscale structures need to be measured. Component-level studies are required to provide a better understanding of the tribological phenomena occurring in MEMS/NEMS. The emergence of micro/nanotribology and atomic force microscopy-based techniques has provided researchers with a viable approach to address these problems. This paper presents an overview of micro/nanoscale adhesion, friction, and wear studies of materials and lubrication studies for MEMS/NEMS and BioMEMS/BioNEMS. It also presents a review of scale-dependent mechanical properties, and stress and deformation analysis of nanostructures.     

Amplitude response of Fabry-Perot frequency discriminators

The amplitude noise responses of optical-frequency-discriminating systems, based on Fabry-Perot cavities with intensity noise compensation, are analyzed considering also the effect of the resonator transient. From the point of view of amplitude noise immunity, systems based on transmission or reflection alone behave in a quite similar way within the discriminator bandwidth, whereas a proper combination of both these signals not only increases the sensitivity to frequency noise but also allows for higher rejection to amplitude noise.     

Influence of surface effects on the pull-in instability of NEMS electrostatic switches

The influence of surface effects, including residual surface stress and surface elasticity, on the pull-in instability of electrostatic switches in nanoelectromechanical systems (NEMS) is studied using an Euler-Bernoulli beam model. This model is inherently nonlinear due to the driving electrostatic force and Casimir force which become dominant at the nanoscale. Since no exact solutions are available for the resulting nonlinear differential equation, He's homotopy perturbation method (HPM) is used to get the approximate analytical solutions to the static bending of NEMS switches, which are validated by numerical solutions of the finite difference method (FDM). The results demonstrate that surface effects play a significant role in the selection of basic design parameters of NEMS switches, such as static deflection, pull-in voltage and detachment length. Surface effects on low-voltage actuation windows are also characterized for these switches. The present study is envisaged to provide useful insights for the design of NEMS switches.     

Fabry-Perot resonator with interferometric read-out for low noise applications

New readout configurations for a Fabry-Perot (FP) resonator (or frequency discriminator) that combine the reflected and transmitted waves are analyzed in detail. The waves may be combined in a Sagnac (S) or Mach-Zehnder (MZ) configuration and tuned to a dark port (DP) to suppress the carrier frequency. To achieve this in a standard FP resonator, the mirror reflectance must be extremely well matched, which is a difficult and expensive task. Suppressing the carrier minimizes the Shot noise floor of a Pound-Drever-Hall (PDH) frequency-stabilized laser. Moreover, depending on the amount of carrier suppression, a high amount of power may be injected into the resonator without saturating or destroying the photodetector at the discriminator output. Because the sensitivity of the frequency discriminator is also proportional to the injected power, a large improvement in frequency noise can be achieved for high power PDH-stabilized lasers utilizing only a small phase modulation index.     

Compact CMOS current conveyor for integrated NEMS resonators

A fully integrated nanoelectromechanical system (NEMS) resonator together with a compact built-in complementary metal-oxide-semiconductor (CMOS) interfacing circuitry is presented. The proposed low-power second generation current conveyor circuit allows measuring the mechanical frequency response of the nanocantilever structure in the megahertz range. Detailed experimental results at different DC biasing conditions and pressure levels are presented for a real mixed electromechanical system integrated through a combination of in-house standard CMOS technology and nanodevice post-processing based on nanostencil lithography. The proposed readout circuit can be adapted to operate the nanocantilever in closed loop as a stand-alone oscillator.     

矩形共振腔截面纵横比对其共振频率影响研究

亥姆赫兹共振腔具有良好的低频消声性能,被广泛地应用于低频消声方面.在实际应用中,共振腔的使用往往受到安装空间的限制,有时候只能安装矩形腔.利用定体积定长度时的矩形共振腔模型,从理论上探讨了腔体纵横比对共振腔共振频率的影响.同时设计了发动机进气消声器性能测试专用实验台,从实验角度研究了腔体截面纵横比与共振频率之间的关系.理论与实验初步结果表明,在算例条件下截面纵横比对共振频率影响不大,在应用时可以不考虑纵横比问题.所讨论内容对其它条件下的研究有借鉴作用.     

基于碳纳米管的纳机电系统的可控稳定振动

采用数值方法研究了基于双壁碳纳米管的纳机电系统在周期性简谐驱动力作用下实现稳定振动的条件.确定了获得持久稳定的振动的系统和控制力参数.计算和分析了双壁碳纳米管的操作特性.结果表明,通过选择合适的驱动振幅和频率,能够实现双壁碳纳米管的持久稳定振动.该方法对于进一步研究基于碳纳米管的纳机电系统的设计有重要的参考价值.     

High-Q whispering gallery traveling wave resonators for oscillator frequency stabilization

Usually a frequency-stabilized standing wave resonator-oscillator incorporating a resonator as a frequency discriminator requires a circulator to separate the injected and reflected wave, A ferrite circulator is a noisy device and can limit the phase noise or frequency stability. Moreover, we show that the noise in a circulator varies, and detailed low noise measurements are necessary to choose an appropriate quiet circulator. Thus, by realizing a configuration that does not require a circulator, an improvement in performance and reliability can be obtained. A solution to this problem is to design a high-Q whispering gallery traveling wave (WGTW) resonator. This device naturally separates the injected and reflected wave in the same way as a ring cavity at optical frequencies, without degrading the frequency discrimination. Q-factor measurements of a WGTW sapphire resonator are presented, along with a derivation of critical parameters to maximize the frequency discrimination. New measurements of noise in ferrite circulators and isolators have also been made, which is followed with a discussion on oscillator design.     

Modified continuum model for stability analysis of asymmetric FGM double-sided NEMS: Corrections due to finite conductivity,surface energy and nonlocal effect

Finite conductivity, surface energy and nonlocal effect can influence the electromechanical performance of micro/nano-electromechanical systems (MEMS/NEMS). However, these factors are yet ignored on stability analysis of MEMS/NEMS fabricated from functionally graded materials (FGM). In this paper, dynamic stability of double-sided NEMS fabricated from non-symmetric FGM is investigated incorporating finite conductivity, surface energy and nonlocal effect. The Gurtin–Murdoch model and Eringen's elasticity are employed to consider the surface energy and nonlocal effect, respectively. Effect of finite conductivity of FGM on electrostatic and Casimir attractions is incorporated via relative permittivity and plasma frequency of the material. The stability analysis of the nanostructure is conducted by plotting time history and phase portraits. Moreover, bifurcation analysis is conducted to investigate the stability of the fixed points of the nano-structure. The validity of the proposed model is examined by comparing the results of the present study with those reported in the literature. The impact of various parameters i.e. finite conductivity, nonlocal parameter, surface stresses and material characteristics on the dynamic instability of the NEMS are addressed.     

On the 1/f frequency noise in ultra-stable quartz oscillators

The frequency flicker of an oscillator, which appears as a 1/f3 line in the phase noise spectral density, and as a floor on the Allan deviation plot, originates from two basic phenomena, namely, (1) the 1/f phase noise turned into 1/f frequency noise via the Leeson effect, and (2) the 1/f fluctuation of the resonator natural frequency. The discussion on which is the dominant effect, thus on how to improve the stability of the oscillator, has been going on for years without giving a clear answer. This article tackles the question by analyzing the phase noise spectrum of several commercial oscillators and laboratory prototypes, and demonstrates that the fluctuation of the resonator natural frequency is the dominant effect. The investigation method starts from reverse engineering the oscillator phase noise in order to show that if the Leeson effect was dominant, the resonator merit factor Q would be too low as compared to the available technology.     

Stressed carbon nanotube devices for high tunability,high quality factor,single mode GHz resonators

The emerging applications of nanoelectromechanical systems (NEMS) in ground-state cooling, quantum manipulation, communication devices, etc., call for a nanoresonator with high frequency, quality factor, and tunability, as well as easy integration. Here we show that such a nanoresonator can be achieved by using a unique assembly technique that transfers the stressed inner shell of carbon nanotubes (CNTs) to a self-aligned device geometry. The as-fabricated nanoresonator shows excellent comprehensive performance, i.e., high frequency (2–3 GHz), high tunability (80–110 MHz/V), high quality factor (3 × 10⁴), and single mode operation. The defect-free nature of the inner shell of the CNT gives rise to a high quality factor, and the preloaded tension improves the resonant frequency and tunability. This resonator with excellent performance also enables the integration of homogeneous devices and will play a key role in the emerging applications of NEMS.

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Self-transducing silicon nanowire electromechanical systems at room temperature

Electronic readout of the motions of genuinely nanoscale mechanical devices at room temperature imposes an important challenge for the integration and application of nanoelectromechanical systems (NEMS). Here, we report the first experiments on piezoresistively transduced very high frequency Si nanowire (SiNW) resonators with on-chip electronic actuation at room temperature. We have demonstrated that, for very thin (~90 nm down to ~30 nm) SiNWs, their time-varying strain can be exploited for self-transducing the devices' resonant motions at frequencies as high as approximately 100 MHz. The strain of wire elongation, which is only second-order in doubly clamped structures, enables efficient displacement transducer because of the enhanced piezoresistance effect in these SiNWs. This intrinsically integrated transducer is uniquely suited for a class of very thin wires and beams where metallization and multilayer complex patterning on devices become impractical. The 30 nm thin SiNW NEMS offer exceptional mass sensitivities in the subzeptogram range. This demonstration makes it promising to advance toward NEMS sensors based on ultrathin and even molecular-scale SiNWs, and their monolithic integration with microelectronics on the same chip.     

纳机电系统

纳机电系统(NEMS)是基于微机电系统发展起来的新兴技术领域，同时也是纳米技术的重要组成部分．文中介绍了NEMS器件的微小尺寸、超高频率和超低能耗等重要特性，并列举了NEMS在生物、信息和纳米流体学等领域的应用．最后讨论了NEMS在发展中遇到的问题和涉及到的关键技术，如微观效应的影响，NEMS加工技术，NEMS的设计、仿真和优化，NEMS器件的驱动与检测，NEMS器件与宏观世界的通讯等．     

Tailoring the microstructure and surface morphology of metal thin films for nano-electro-mechanical systems applications

Metallic structural components for micro-electro-mechanical/nano-electro-mechanical systems (MEMS/NEMS) are promising alternatives to silicon-based materials since they are electrically conductive, optically reflective and ductile. Polycrystalline mono-metallic films typically exhibit low strength and hardness, high surface roughness, and significant residual stress, making them unusable for NEMS. In this study we demonstrate how to overcome these limitations by co-sputtering Ni-Mo. Detailed investigation of the Ni-Mo system using transmission electron microscopy and high-resolution transmission electron microscopy (TEM/HRTEM), x-ray diffraction (XRD), nanoindentation, and atomic force microscopy (AFM) reveals the presence of an amorphous-nanocrystalline microstructure which exhibits enhanced hardness, metallic conductivity, and sub-nanometer root mean square (RMS) roughness. Uncurled NEMS cantilevers with MHz resonant frequencies and quality factors ranging from 200-900 are fabricated from amorphous Ni-Mo. Using a sub-regular solution model it is shown that the electrical conductivity of Ni-Mo is in excellent agreement with Bhatia's structural model of electrical resistivity in binary alloys. Using a Langevin-type stochastic rate equation the structural evolution of amorphous Ni-Mo is modeled; it is shown that the growth instability due to the competing processes of surface diffusion and self-shadowing is heavily damped out due to the high thermal energies of sputtering, resulting in extremely smooth films.     

共振型进气消声器腔体尺寸对其共振频率影响研究

亥姆赫兹共振腔结构简单,且有良好的低频消声性能,近几年来广泛地应用于发动机进排气消声上.由于其消声有效带宽很窄,共振频率的精确确定直接关系到消声器能否有效消声,但是通常所采用的集中参数模型有时候会失效.建立了共振腔型消声器一维轴向声传播模型,揭示了圆形旁支型共振进气消声器的消声机理.同时对连接管长度的修正问题做了阐述,得出了共振腔一维轴向传播模型共振频率的计算公式.此外,设计了发动机进气消声器性能测试专用实验台,从实验角度研究了共振频率与腔体尺寸之间的关系.撰写为正确设计亥姆赫兹共振腔型进气消声器提供一个重要方法.     

Phonons in slow motion: dispersion relations in ultrathin Si membranes

We report the changes in dispersion relations of hypersonic acoustic phonons in free-standing silicon membranes as thin as ～8 nm. We observe a reduction of the phase and group velocities of the fundamental flexural mode by more than 1 order of magnitude compared to bulk values. The modification of the dispersion relation in nanostructures has important consequences for noise control in nano- and microelectromechanical systems (MEMS/NEMS) as well as opto-mechanical devices.     

Expected quality factor of a simple tuned oscillator

A positive feedback system oscillating under self-sustained mode is shown to have an extremely high gain. Modeled as one port, the expected Q is much higher than the loaded Q-factor of the resonator. With just thermal noise present, random phase/frequency deviation is linear. Centered about the oscillator frequency omega/(0), noise frequency on both sides is more amplified with decreasing separation distance. Ultimately, frequency pulling may result in synchronous locking with hysteresis, which occurs because a real oscillator displays a truncated limiting curve. Once locked onto a signal, smaller levels are ignored. A new approach to the design and characterization of a simple tuned oscillator is offered: According to the phenomenon of injection locking, there exists an expected quality factor relating the shape of the truncated limiting curve to an ideal curve. In this paper, synthesis and innovative analytical methods of academic interest are revealed: 1) application of the transducer loss method is revised to establish a new method for oscillator characterization; 2) a transparent method of normalizing a two-port network in the presence of white noise is developed; and 3) in quartz crystal controlled oscillators, characterization of the noise originating from an equivalent noise-resistance determined from parameter of the quartz crystal is proposed. It is shown that the two-port model can also be approximated on a one-port basis. In conclusion, a sample of closed-form estimation of expected Q-factor order of magnitude of piezoelectric resonator oscillators is calculated.