Mechanical Thermal Noise Research Articles

Design and Experimental Evaluation of a Low-Noise Backplate for a Grating-Based Optical Interferometric Sensor

Optical grating-based interferometric sensors have been the subject of prior investigations, with recent work focused on micromachined microphone applications. The silicon structure is similar in construction to capacitive microelectromechanical-system microphones, with the exception that the microphone backplate contains an optical-diffraction grating at the center. The grating serves as a beam splitter in this system, allowing only a portion of the incident light to pass to the diaphragm and back, enabling interferometric readout of diaphragm displacements. A cited advantage of this system is the ability to design highly perforated backplates with low mechanical damping and with the ability to realize low thermal-mechanical noise. Grating backplates, however, have their own unique optical design constraints different from capacitive sensors. This paper details a rigorous finite element computational fluid dynamics model for flow resistance of a grating backplate. The model is validated for a case study backplate fabricated in the epitaxial layer of a 2-μm silicon-on-insulator wafer. The dynamics of the backplate are studied in isolation from other microphone elements by mounting the backplate in close proximity to a rigid optical-reflector and using electrostatic actuation to vibrate the backplate for extraction of compliance, resonance frequency, and quality factor.

Performance of an optical stabilization system at NSLS beamline U12IR

A low-cost optical feedback system using dynamic mirrors has been developed at the NSLS for stabilizing the position and direction of an infrared synchrotron beam against thermal drift and mechanical noise. The system design has some unique features that potentially simplify installation into an existing infrared beamline. We describe the system and its features along with some performance results.

Passive ultrasonics using sub-Nyquist sampling of high-frequency thermal-mechanical noise.

Monolithic integration of capacitive micromachined ultrasonic transducer arrays with low noise complementary metal oxide semiconductor electronics minimizes interconnect parasitics thus allowing the measurement of thermal-mechanical (TM) noise. This enables passive ultrasonics based on cross-correlations of diffuse TM noise to extract coherent ultrasonic waves propagating between receivers. However, synchronous recording of high-frequency TM noise puts stringent requirements on the analog to digital converter's sampling rate. To alleviate this restriction, high-frequency TM noise cross-correlations (12-25 MHz) were estimated instead using compressed measurements of TM noise which could be digitized at a sampling frequency lower than the Nyquist frequency.

Deterministic quantum superpositions and Fock states of mechanical oscillators via quantum interference in single-photon cavity optomechanics

In this paper, we propose a scheme for deterministically preparing a quantum superposition $|{\ensuremath{\psi}}_{s}{\ensuremath{\rangle}}_{b}={C}_{0}{|0\ensuremath{\rangle}}_{b}+{C}_{\mathcal{N}}{|\mathcal{N}\ensuremath{\rangle}}_{b}$ between vacuum and an arbitrary Fock state ${|\mathcal{N}\ensuremath{\rangle}}_{b}$ of mechanical oscillators via strong single-photon optomechanical coupling. We consider an optomechanical cavity which contains a Kerr medium and is driven by two lasers, with one laser tuned to the cavity resonance and the other to the $\mathcal{N}$th lower sideband of the cavity. The amplitudes ${C}_{0}$ and ${C}_{\mathcal{N}}$ are determined only by the drive strengths in the absence of mechanical damping and the approximate Fock state $|{\ensuremath{\psi}}_{s}{\ensuremath{\rangle}}_{b}\ensuremath{\approx}{|\mathcal{N}\ensuremath{\rangle}}_{b}$ can be obtained with appropriate relative strengths of the lasers. It is revealed that the superposition results from destructive quantum interference. The analytical results are confirmed by exact numerical calculation, and it is also shown that the nonclassical state is robust against thermal mechanical noise.

Measurements of mechanical thermal noise and energy dissipation in optical dielectric coatings

In recent years, an increasing number of devices and experiments are shown to be limited by mechanical thermal noise. In particular, subhertz laser frequency stabilization and gravitational wave detectors that are able to measure fluctuations of ${10}^{\ensuremath{-}18}\text{ }\text{ }\mathrm{m}/\sqrt{\mathrm{Hz}}$ or less are being limited by thermal noise in the dielectric coatings deposited on mirrors. In this paper, we present a new measurement of thermal noise in low absorption dielectric coatings deposited on microcantilevers, and we compare it with the results obtained from the mechanical loss measurements. The coating thermal noise is measured on the widest range of frequencies with the highest signal-to-noise ratio ever achieved. In addition, we present a novel technique to deduce the coating mechanical losses from the measurement of the mechanical quality factor which does not rely on the knowledge of the coating and substrate Young's moduli. The dielectric coatings are deposited by ion beam sputtering. The results presented here give a frequency-independent loss angle of $(4.7\ifmmode\pm\else\textpm\fi{}0.2)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$ with a Young's modulus of 118 GPa for annealed tantala from 10 Hz to 20 kHz. For as-deposited silica, a weak frequency dependence ($\ensuremath{\propto}{f}^{\ensuremath{-}0.025}$) is observed in this frequency range, with a Young's modulus of 70 GPa and an internal damping of $(6.0\ifmmode\pm\else\textpm\fi{}0.3)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$ at 16 kHz, but this value decreases by one order of magnitude after annealing, and the frequency dependence disappears.

Towards a sub 15-dBA optical micromachined microphone.

Micromachined microphones with grating-based optical-interferometric readout have been demonstrated previously. These microphones are similar in construction to bottom-inlet capacitive microelectromechanical-system (MEMS) microphones, with the exception that optoelectronic emitters and detectors are placed inside the microphone's front or back cavity. A potential advantage of optical microphones in designing for low noise level is the use of highly-perforated microphone backplates to enable low-damping and low thermal-mechanical noise levels. This work presents an experimental study of a microphone diaphragm and backplate designed for optical readout and low thermal-mechanical noise. The backplate is 1 mm × 1 mm and is fabricated in a 2-μm-thick epitaxial silicon layer of a silicon-on-insulator wafer and contains a diffraction grating with 4-μm pitch etched at the center. The presented system has a measured thermal-mechanical noise level equal to 22.6 dBA. Through measurement of the electrostatic frequency response and measured noise spectra, a device model for the microphone system is verified. The model is in-turn used to identify design paths towards MEMS microphones with sub 15-dBA noise floors.

Generating robust optical entanglement in weak-coupling optomechanical systems

A pulsed scheme for generating robust optical entanglement via the coupling of two optical modes to a mechanical oscillator is proposed. This scheme is inspired by the S{\o}rensen-M{\o}lmer approach for entangling trapped ions in a thermal environment and is based on the use of optical driving pulses that are slightly detuned from the respective sideband resonance. We show that for certain pulse durations, the optomechanical interaction can return the mechanical oscillator to its initial state. The corresponding entanglement generation is robust against thermal mechanical noise in the weak as well as the strong coupling regimes. Significant optical entanglement can be generated in the weak coupling regime, even in the presence of a large thermal phonon occupation.

Viscous damping and spring force calculation of regularly perforated MEMS microstructures in the Stokes’ approximation

There are a number of applications for microstructure devices consisting of a regular pattern of perforations, and many of these utilize fluid damping. For the analysis of viscous damping and for calculating the spring force in some cases, it is possible to take advantage of the regular hole pattern by assuming periodicity. Here a model is developed to determine these quantities based on the solution of the Stokes’ equations for the air flow. Viscous damping is directly related to thermal–mechanical noise. As a result, the design of perforated microstructures with minimal viscous damping is of real practical importance. A method is developed to calculate the damping coefficient in microstructures with periodic perforations. The result can be used to minimize squeeze film damping. Since micromachined devices have finite dimensions, the periodic model for the perforated microstructure has to be associated with the calculation of some frame (edge) corrections. Analysis of the edge corrections has also been performed. Results from analytical formulas and numerical simulations match very well with published measured data.

Integrating magnetoresistive sensors with microelectromechanical systems for noise reduction

1/f noise is the dominant detection limit of magnetoresistive (MR) sensors at low frequency. The vertical motion flux modulation (VMFM) integrating with microelectromechanical systems (MEMS) can reduce 1/f noise by tens or hundreds of times, although thermal-mechanical noise possibly has strong impact on the detection ability of VMFM sensors like common MEMS sensors. Surprisingly, the voltage noise originated from thermal-mechanical noise is actually far less than the noise base of MR sensors, which indicates a great perspective for the integration of MEMS and MR sensors.

High resolution space quartz-flexure accelerometer based on capacitive sensing and electrostatic control technology

High precision accelerometer plays an important role in space scientific and technical applications. A quartz-flexure accelerometer operating in low frequency range, having a resolution of better than 1 ng/Hz(1/2), has been designed based on advanced capacitive sensing and electrostatic control technologies. A high precision capacitance displacement transducer with a resolution of better than 2 × 10(-6) pF/Hz(1/2) above 0.1 Hz, is used to measure the motion of the proof mass, and the mechanical stiffness of the spring oscillator is compensated by adjusting the voltage between the proof mass and the electrodes to induce a proper negative electrostatic stiffness, which increases the mechanical sensitivity and also suppresses the position measurement noise down to 3 × 10(-10) g/Hz(1/2) at 0.1 Hz. A high resolution analog-to-digital converter is used to directly readout the feedback voltage applied on the electrodes in order to suppress the action noise to 4 × 10(-10) g/Hz(1/2) at 0.1 Hz. A prototype of the quartz-flexure accelerometer has been developed and tested, and the preliminary experimental result shows that its resolution comes to about 8 ng/Hz(1/2) at 0.1 Hz, which is mainly limited by its mechanical thermal noise due to low quality factor.

Thermal-mechanical-noise-based CMUT characterization and sensing

When capacitive micromachined ultrasonic transducers (CMUTs) are monolithically integrated with custom-designed low-noise electronics, the output noise of the system can be dominated by the CMUT thermal-mechanical noise both in air and in immersion even for devices with low capacitance. Because the thermal-mechanical noise can be related to the electrical admittance of the CMUTs, this provides an effective means of device characterization. This approach yields a novel method to test the functionality and uniformity of CMUT arrays and the integrated electronics when a direct connection to CMUT array element terminals is not available. Because these measurements can be performed in air at the wafer level, the approach is suitable for batch manufacturing and testing. We demonstrate this method on the elements of an 800-μm-diameter CMUT-on-CMOS array designed for intravascular imaging in the 10 to 20 MHz range. Noise measurements in air show the expected resonance behavior and spring softening effects. Noise measurements in immersion for the same array provide useful information on both the acoustic cross talk and radiation properties of the CMUT array elements. The good agreement between a CMUT model based on finite difference and boundary element methods and the noise measurements validates the model and indicates that the output noise is indeed dominated by thermal-mechanical noise. The measurement method can be exploited to implement CMUT-based passive sensors to measure immersion medium properties, or other parameters affecting the electro-mechanics of the CMUT structure.

Emulated Analysis of the Preview-LQG Controller for Micromachined Tunneling Gyroscope

Only when the tunneling gap is maintained near 10Å can the micromachined tunneling gyroscope operate regularly to generate tunneling current which is so weak that it would be submerged by the thermal-mechanical noise, 1/f tunneling noise and so on. At the meantime, the dynamic range of the device will be reduced drastically by the nonlinearity of the tunneling effect. So a controller must be designed for the miniature tunneling gyroscope to realize a 10 Å tunneling gap to decrease the nonlinearity and so as to enlarge the band-width of the device. At the other hand, the signal-to-noise ratio can be raised by the controller. Because of the anti-interference and robusticity of the LQG control theory and the time-varying characteristic of Coriolis acceleration, the preview-LQG control strategy is selected to design the closed-loop system. The simulation results suggest that the tunneling gap can be controlled near its nominal value and the measured input angular rate can be estimated accurately by the preview-LQG controller even if the input angular rate is a slowly time-varying random signal.

Stable optical phase modulation with micromirrors

We measure the motional fluctuations of a micromechanical mirror using a Michelson interferometer, and demonstrate its interferometric stability. The position stability of the micromirror is dominated by the thermal mechanical noise of the structure. With this level of stability, we utilize the micromirror to realize an optical phase modulator by simply reflecting light off the mirror and modulating its position. The resonant frequency of the modulator can be tuned by applying a voltage between the mirror and an underlying electrode. Full modulation depth of ±π is achieved when the mirror resonantly excited with a sinusoidal voltage at an amplitude of 11 V.

Estimation of frequency noise in semiconductor lasers due to mechanical thermal noise

We evaluate mechanical thermal noise in semiconductor lasers, applying a methodology developed for fixed-spacer cavities for laser frequency stabilization. Our simple model determines an underlying fundamental limit for the frequency noise of free-running semiconductor laser, and provides a framework where the noise may be potentially reduced with improved design.

A vibration-free, thermally controlled setup for mechanical thermal noise measurements

We have developed a setup that offers a vacuum compatible, vibration-free experimental space with active thermal stabilization around room temperature, suitable for high sensitivity measurements. In this paper we describe the experimental setup from the thermal viewpoint and the design and implementation of the thermal control. Then we characterize the long-term performances of the control loop by using experimental data collected over 1 month: we show that our control is effective in reducing room temperature variations by a factor 100 over a few weeks, even in the presence of an internal dc heat source of 2 W.

High frequency ultrasonic imaging using thermal mechanical noise recorded on capacitive micromachined transducer arrays

The cross-correlation of diffuse thermal-mechanical noise recorded by two sensors yields an estimate of the ultrasonic waves propagating between them. We used this approach at high frequencies (1-30 MHz) on a capacitive micromachined ultrasonic transducer (CMUT) ring array (d = 725 μm), monolithically integrated with low noise complementary metal oxide semiconductor electronics. The thermal-mechanical noise cross-correlations between the CMUT array elements in immersion reveal both evanescent surface waves (below 10 MHz) and waves propagating primarily in the fluid (above 10 MHz). These propagating waves may allow passive imaging of scatterers closer to the array as compared to conventional pulse-echo systems, providing potentially higher resolution.

Ultrasonic sensing using thermal mechanical noise of capacitive micro-machined transducers

Monolithic integration of CMUTs and CMOS electronics minimizes interconnect parasitics which allows recording the actual thermal–mechanical component of the ultrasonic noise field. Consequently, an estimate of the pulse-echo response (or Greens function) between two CMUT sensors can be obtained from the cross-correlation of thermal–mechanical noise recorded by these two sensors, as shown by Weaver and Lobkiss [JASA, 113(5), 2611-21]. This provides a foundation for passive ultrasound imaging using only the thermal–mechanical noise field, without active transmitter elements. We designed and fabricated monolithic a 32 element CMUT-on-CMOS ring array (d = 725 μm) for intravascular imaging with low noise transimpedance amplifiers (TIAs) implemented in 0.35 μm CMOS technology. The bias voltage was set near the collapse value of the CMUT membrane to maximize receiver sensitivity. Demonstration experiments were conducted by immersing the CMUT array in a water bath to sense/image the water–air interface and compact targets from noise signals in the frequency band 14–25 MHz. These experimental results were consistent with the sensor and target locations and were validated using conventional pulse-echo measurements. This totally passive ultrasonic technique could improve ultrasound imaging of near-field targets in the deadzone created by active transmitters biasing the receivers and may lead to imaging using evanescent waves.

Front-end receiver electronics for high-frequency monolithic CMUT-on-CMOS imaging arrays

This paper describes the design of CMOS receiver electronics for monolithic integration with capacitive micromachined ultrasonic transducer (CMUT) arrays for highfrequency intravascular ultrasound imaging. A custom 8-inch (20-cm) wafer is fabricated in a 0.35-μm two-poly, four-metal CMOS process and then CMUT arrays are built on top of the application specific integrated circuits (ASICs) on the wafer. We discuss advantages of the single-chip CMUT-on-CMOS approach in terms of receive sensitivity and SNR. Low-noise and high-gain design of a transimpedance amplifier (TIA) optimized for a forward-looking volumetric-imaging CMUT array element is discussed as a challenging design example. Amplifier gain, bandwidth, dynamic range, and power consumption trade-offs are discussed in detail. With minimized parasitics provided by the CMUT-on-CMOS approach, the optimized TIA design achieves a 90 fA/√Hz input-referred current noise, which is less than the thermal-mechanical noise of the CMUT element. We show successful system operation with a pulseecho measurement. Transducer-noise-dominated detection in immersion is also demonstrated through output noise spectrum measurement of the integrated system at different CMUT bias voltages. A noise figure of 1.8 dB is obtained in the designed CMUT bandwidth of 10 to 20 MHz.

Electrostatic actuation of silicon optomechanical resonators

Cavity optomechanical systems offer one of the most sensitive methods for detecting mechanical motion using shifts in the optical resonance frequency of the optomechanical resonator. Presently, these systems are used for measuring mechanical thermal noise displacement or mechanical motion actuated by optical forces. Electrostatic capacitive actuation and detection have been shown previously for silicon micro electro mechanical resonators for application in filters and oscillators. Here, we demonstrate monolithic integration of electrostatic capacitive actuation with optical sensing using silicon optomechanical disk resonators and waveguides. The electrically excited mechanical motion is observed as an optical intensity modulation when the input electrical signal is at a frequency of 235 MHz corresponding to the radial vibrational mode of the silicon microdisk.

Pull-in-based μg-resolution accelerometer: Characterization and noise analysis

The pull-in time (tpi) of electrostatically actuated parallel-plate microstructures enables the realization of a high-sensitivity accelerometer that uses time measurement as the transduction mechanism. The key feature is the existence of a metastable region that dominates pull-in behavior, thus making pull-in time very sensitive to external accelerations. Parallel-plate MEMS structures have been designed and fabricated using a SOI micromachining process (SOIMUMPS) for the implementation of the accelerometer. This paper presents the experimental characterization of the microdevices, validating the concept and the analytical models used. The accelerometer has a measured sensitivity of 0.25μs/μg and a bandwidth that is directly related to the pull-in time, BW=1/2tpi≈50Hz. These specifications place this sensor between the state of the art accelerometers found both in the literature and commercially. More importantly, the resolution of the measurement method used is very high, making the mechanical–thermal noise the only factor limiting the resolution. The in-depth noise analysis to the system supports these conclusions. The total measured noise floor of 400μg (100μs) is mainly due to the contribution of the environmental noise, due to lack of isolation of the experimental setup from the building vibrations (estimated mechanical thermal noise of 2.8μg/√Hz). The low requirements of the electronic readout circuit makes this an interesting approach for high-resolution accelerometers.