Ultrasensitive mode-localized micromechanical electrometer

We report a highly sensitive prototype micromechanical electrometer that employs the phenomena of mode-localization and curve veering for monitoring minute charge fluctuations across an input capacitor. The device consists of a pair of weakly coupled, nearly identical single crystal silicon, double-ended tuning fork (DETF) resonators. An addition of charge across an input capacitor on one of the coupled resonators induces a differential axial strain on that resonator relative to the other consequently perturbing the structural symmetry of the nearly periodic system. The resulting shifts in the eigenstates for the same magnitudes of charge input are theoretically and experimentally demonstrated to be nearly three orders of magnitude greater than corresponding resonant frequency variations. The topology chosen may also be adapted for force or strain monitoring thereby widening the relevance of the results reported here to precision inertial sensing as well

A high-resolution micro-electro-mechanical resonant tilt sensor

This paper reports on the design and experimental evaluation of a high-resolution Micro-Electro-Mechanical (MEM) tilt sensor based on resonant sensing principles. The sensors incorporate a pair of double-ended tuning fork (DETF) resonant strain gauges, the mechanical resonant frequencies of which shift in proportion to an axial force induced by variations in the component of gravitational acceleration along a specified input axis. An analysis of the structural design of such sensors (using analytical and finite element modelling) is presented, followed by experimental test results from device prototypes fabricated using a silicon-on-insulator (SOI) MEMS technology. This paper reports measurement conducted to quantify sensor scale factor, temperature sensitivity, scale factor linearity and resolution. It is demonstrated that such sensors provide a ±90 degree dynamic range for tilt measurements with a temperature sensitivity of nearly 500 ppb/K (equating to systematic sensitivity error of approximately 0.007 degree/K). When configured as a tilt sensor, it is also shown that the scale factor linearity is better than 1.4% for a ±20° tilt angle range. The bias stability of a micro-fabricated prototype is below 500 ng for an averaging time of 0.8 seconds making these devices a potentially attractive option for numerous precision tilt sensing applications.This is the author's accepted manuscript. The final version is available from Elsevier at http://www.sciencedirect.com/science/article/pii/S0924424714004385

The effect of mass loading on spurious modes in micro-resonators

Dissipation mechanisms severely compromise the performance of micro-resonator based sensors. In this letter, we specifically examine the shift in resonant frequency of spurious modes towards the mode of interest during mass loading. This can result in modal interaction that degrades the response of the sensor. However, by understanding and controlling this effect we can overcome this key barrier to micro-resonator applications.This is the author accepted manuscript. The final version is available from AIP via http://dx.doi.org/10.1063/1.492759

Numerical Study of the Impact of Vibration Localization on the Motional Resistance of Weakly Coupled MEMS Resonators

This paper presents a numerical study of the impact of process-induced variations on the achievable motional resistance Rx of one-dimensional, two-dimensional, cyclic and cross-coupled architectures of weakly coupled, electrostatically transduced MEMS resonators operating in the 250 kHz range. We use modal analysis to find the Rx of such coupled arrays and express it as a function of the eigenvectors of the specific mode of vibration. Monte Carlo numerical simulations, which accounted for up to 0.75% variation in critical resonator feature sizes, were initiated for different array sizes and coupling strengths, for the four distinct coupling architectures. Improvements in the mean and standard deviation of the generated Rx distributions are reported when the resonators are implemented in a cross-coupled scheme, as opposed to the traditional one-dimensional chain. The two-dimensional coupling scheme proves to be a practical and scalable alternative to weakly coupled one-dimensional chains to improve the immunity to process variations. It is shown that a 75% reduction in both the mean and standard deviation of the Rx is achieved as compared to the traditional one-dimensional chain for a normalized internal coupling k > 10-2.The authors would like to gratefully acknowledge the Qualcomm European Research Studentships in Technology and the UK Engineering and Physical Sciences Research Council.This is the accepted manuscript. The final version is available from IEEE at http://dx.doi.org/10.1109/JMEMS.2014.2371072

Electrically coupled MEMS oscillators

In this paper, we demonstrate synchronization of two electrically coupled MEMS oscillators incorporating nearly identical silicon tuning fork microresonators. It is seen that as the output of the oscillators are coupled, they exhibit a synchronized response wherein the output amplitudes and signal-to-noise ratios of the two oscillators are improved relative to the case where the two oscillators are uncoupled. The observed output frequency of each oscillator before coupling is 219402.4 Hz and 219403.6 Hz respectively. In contrast, when the oscillators are driven simultaneously, they lock at a common output frequency of 219401.3 Hz and their outputs are found to be out-of-phase with respect to each other. A 6 dBm gain in output power and a reduction in the phase fluctuations of the output signal are observed for the coupled oscillators compared to the case when the oscillators are uncoupled

Common mode rejection in electrically coupled MEMS resonators utilizing mode localization for sensor applications

Measuring shifts in eigenstates due to vibration localization in an array of weakly coupled resonators offer two distinct advantages for sensor applications as opposed to the technique of simply measuring resonant frequency shifts: (1) orders of magnitude enhancement in parametric sensitivity and (2) intrinsic common mode rejection. In this paper, we experimentally demonstrate the common mode rejection capabilities of such sensors. The vibration behavior is studied in pairs of nearly identical MEMS resonators that are electrically coupled, and subjected to small perturbations in stiffness under different ambient pressure and temperature. The shifts in the eigenstates for the same parametric perturbation in stiffness are experimentally demonstrated to be over three orders of magnitude greater than corresponding resonant frequency variations. They are also shown to remain relatively constant to variations in ambient temperature and pressure. This increased relative robustness to environmental drift, along with the advantage of ultra-high parametric sensitivity, opens the door to an alternative approach to achieving higher sensitivity and stability in micromechanical sensors

Investigating vibration dynamics of cross-coupled MEMS resonators for reduced motional resistance

This paper investigates the vibration dynamics of a closed-chain, cross-coupled architecture of MEMS resonators. The system presented here is electrostatically transduced and operates at 1.04 MHz. Curve veering of the eigenvalue loci is used to experimentally quantify the coupling spring constants. Numerical simulations of the motional resistance variation against induced perturbation are used to assess the robustness of the cross-coupled system as opposed to equivalent traditional open-ended linear one-dimensional coupling scheme. Results show improvements of as much as 32% in the motional resistance between the cross-coupled system and its one-dimensional counterpart

Effects of mechanical and electrical coupling on the parametric sensitivity of mode localized sensors

We compare and contrast the effects of two distinctly different mechanisms of coupling (mechanical and electrical) on the parametric sensitivity of micromechanical sensors utilizing mode localization for sensor applications. For the first time, the strong correlation between mode localization and the phenomenon of 'eigenvalue loci-veering' is exploited for accurate quantification of the strength of internal coupling in mode localized sensors. The effects of capacitive coupling-spring tuning on the parametric sensitivity of electrically coupled resonators utilizing this sensing paradigm is also investigated and a mass sensor with sensitivity tunable by over 400% is realized

Limits to mode-localized sensing using micro- and nanomechanical resonator arrays

In recent years, the concept of utilizing the phenomenon of vibration mode-localization as a paradigm of mechanical sensing has made profound impact in the design and development of highly sensitive micro- and nanomechanical sensors. Unprecedented enhancements in sensor response exceeding three orders of magnitude relative to the more conventional resonant frequency shift based technique have been both theoretically and experimentally demonstrated using this new sensing approach. However, the ultimate limits of detection and in consequence, the minimum attainable resolution in such mode-localized sensors still remain uncertain. This paper aims to fill this gap by investigating the limits to sensitivity enhancement imposed on such sensors, by some of the fundamental physical noise processes, the bandwidth of operation and the noise from the electronic interfacial circuits. Our analyses indicate that such mode-localized sensors offer tremendous potential for highly sensitive mass and stiffness detection with ultimate resolutions that may be orders of magnitude better than most conventional micro- and nanomechanical resonant sensors