MEMS-based oscillators are an emerging class of highly miniaturized, batch manufacturable timing devices that can rival the electrical performance of well-established quartz-based oscillators. In this review, a description is given of the key properties of a MEMS resonator that determine the overall performance of a MEMS oscillator. Piezoelectric, capacitive and active resonator transduction methods are compared and their impact on oscillator noise and power dissipation is explained. An overview is given of the performance of MEMS resonators and MEMS-based oscillators that have been demonstrated to date. Mechanisms that affect the frequency stability of the resonator, such as temperature-induced frequency drift, are explained and an overview is given of methods that have been demonstrated to improve the frequency stability. The aforementioned performance indicators of MEMS-based oscillators are benchmarked against established quartz and CMOS technologies.

https://iopscience.iop.org/article/10.1088/0960-1317/22/1/013001/pdf

A review of MEMS oscillators for frequency reference and timing applications

Summary It is shown how the well-known photoeffects observed at semiconductor electrodes can be used to construct an electrochemical photocell. The photovoltaic effects in such cells are based on the formation of a Schottky barrier at the interface between a semiconductor and a suitable redox electrolyte. A cell design is developed and some results with CdS, CdSe or GaP electrodes are presented. The characteristics of such photocells and the problems involved in their application as solar cells are discussed.

Electrochemical Solar Cells are Schottky Barrier Devices. A Citation-Classic Commentary on Electrochemical photo and solar cells: Principles and some experiments

Dissipation in nanoelectromechanical systems

This paper is a review of the remarkable progress that has been made during the past few decades in design, modeling, and fabrication of micromachined resonators. Although micro-resonators have come a long way since their early days of development, they are yet to fulfill the rightful vision of their pervasive use across a wide variety of applications. This is partially due to the complexities associated with the physics that limit their performance, the intricacies involved in the processes that are used in their manufacturing, and the trade-offs in using different transduction mechanisms for their implementation. This work is intended to offer a brief introduction to all such details with references to the most influential contributions in the field for those interested in a deeper understanding of the material.

Micromachined Resonators: A Review

http://smc.neuralcorrelate.com/files/publications/distasi_etal_nbr13.pdf

Saccadic velocity as an arousal index in naturalistic tasks

This paper presents fabrication, characterization, and modeling of micro/nanoelectromechanical high-frequency resonators actuated using thermal forces with piezoresistive readout. Thermally actuated single-crystalline silicon resonators with frequencies (up to 61 MHz) have been successfully demonstrated. It is shown both theoretically and experimentally that, as opposed to the general perception, thermal actuation can be a viable actuation mechanism for high-frequency resonators, and using appropriate design guidelines, this actuation mechanism could even be more suitable for higher frequency rather than lower frequency applications. It has been shown through comprehensive thermoelectro-mechanical modeling that thermal-piezoresistive nanomechanical resonators with frequencies in the gigahertz range can exhibit motional conductance values as high as 1 mA/V while consuming static power as low as a few microwatts.

/pdf/high-frequency-thermally-actuated-electromechanical-4lkz8scc5g.pdf

High-Frequency Thermally Actuated Electromechanical Resonators With Piezoresistive Readout

This paper reports on a new type of high-frequency mode-matched gyroscope with significantly reduced dependencies on environmental stimuli such as temperature, vibration, and shock. A novel stress-isolation system is used to effectively decouple an axis-symmetric bulk-acoustic wave (BAW) vibratory gyro from its substrate, minimizing the effect that external sources of error have on the offset and scale factor of the device. Substrate-decoupled (SD) BAW gyros with a resonance frequency of 4.3 MHz and Q values near 60 000 were implemented using the high aspect ratio poly and single-crystal silicon (HARPSS) process to achieve ultra-narrow capacitive gaps. Wafer-level packaged sensors were interfaced with a customized application-specific integrated circuit (ASIC) to achieve low variations in the offset across temperature (±26° s−1 from −40 to 85 °C), supreme random-vibration immunity (0.012° s−1 gRMS−1) and excellent shock rejection. With a scale factor of 800 μV (°s−1)−1, the SD-BAW gyro system attains a large full-scale range (±1250° s−1) with a non-linearity of less than 0.07%. A measured angle-random walk (ARW) of 0.39°/√h and a bias instability of 10.5°h−1 are dominated by the thermal and flicker noise of the integrated circuit (IC), respectively. Additional measurements using external electronics show bias-instability values as low as 3.5°h−1, which are limited by feed-through signals coupled from the drive loop to the sense channel, which can be further reduced through proper re-routing of the gyroscope pin-out configuration. Scientists in the USA have developed a device for measuring rotation that is resilient against shock and vibration. A team led by Diego Serrano at Qualtre Inc. fabricated a micrometer-scale gyroscope that is decoupled from motion in the substrate on which it is built. Micromachined gyroscopes usually comprise a low-frequency resonant cantilever or membrane, and rotation is detected through a corresponding change in the resonance pattern of the resonator. However, such devices are susceptible to external sources of vibrations. Serrano’s team created a device known as a bulk acoustic wave gyroscope that is made of a disk of silicon and supports high frequency resonance inherently resistant to random external vibrations. The disk is surrounded by a series of electrodes that can fine tune the properties of the disk to further improve performance.

/pdf/substrate-decoupled-bulk-acoustic-wave-gyroscopes-design-and-3k3suqplt7.pdf

Substrate-decoupled, bulk-acoustic wave gyroscopes: Design and evaluation of next-generation environmentally robust devices.

This paper, the second of two parts, presents extensive measurement and characterization results on fabricated thermally actuated single-crystal silicon MEMS resonators analyzed in part I. The resonators have been fabricated using a single mask process on SOI substrates. Resonant frequencies in a few hundreds of kHz to a few MHz and equivalent motional conductances as high as 102 mA V−1 have been measured for the fabricated resonators. The measurement results have been compared to the resonator characteristics predicted by the model developed in part I showing a good agreement between the two. Despite the relatively low frequencies, high quality factors (Q) of the order of a few thousand have been measured for the resonators under atmospheric pressure. The mass sensitivities of some of the resonators were characterized by embedding them in a custom-made test setup and deposition of artificially generated aerosol particles with known size and composition. The resulting measured mass sensitivities are of the order of tens to hundreds of Hz ng−1 and are in agreement with the expected values based on the resonator's physical dimensions. Finally, measurement of mass density of arbitrary airborne particles in the surrounding lab environment has been demonstrated.

Fabrication and characterization of thermally actuated micromechanical resonators for airborne particle mass sensing: II. Device fabrication and characterization

In this work, we study temperature drift behavior of thermally actuated high frequency single crystalline silicon resonators and demonstrate temperature compensation of such via a combination of N-type degenerate doping and adjustment of the operating bias current. Significant suppression of the large negative temperature coefficient of frequency (TCF) for the resonators (−40ppm/°C) has been demonstrated using phosphorous degenerate doping resulting in even slightly positive TCF for some of the devices. Furthermore, it is shown that the TCF for such resonators can be fine tuned by changing the operating bias current enabling very close to zero TCF to be realized. Temperature compensation results for several resonators with different frequencies ranging from 3MHz to 60MHz are presented. TCF as low as −0.05ppm/°C (−50ppb/°C) has been demonstrated for an 8.2MHz resonator, which to the best of our knowledge is the lowest reported value for silicon-based micromechanical resonators.

Sub-100ppb/°C temperature stability in thermally actuated high frequency silicon resonators via degenerate phosphorous doping and bias current optimization

The internal thermoelectromechanical transduction loop in micromechanical resonant structures has been studied in this work and utilized to electronically enhance their quality factor or generate spontaneous mechanical vibrations. Electrothermal force generation in a micromechanical structure can be coupled to the structural stress through piezoresistive effect. Under certain conditions (specially having a negative piezoresistive coefficient in n-type crystalline silicon), this could allow mechanical vibrations of the structure to feed from a dc bias current applied to the structure, forming an electromechanical energy pump. At lower dc bias currents, the mechanical energy generated by the pump can only compensate a portion of the mechanical losses of the resonant structure, leading to self-Q-enhancement, whereas at higher currents, it can fully compensate all the mechanical losses, leading to self-sustained oscillation. Extensional-mode dual-plate resonators with frequencies as high as 18.1 MHz were fabricated, and quality factor amplification was successfully demonstrated for such. The ability of such resonators to initiate and maintain self-sustained oscillations under both vacuum and atmospheric pressures has also been demonstrated. Frequencies as high as 19.4 MHz, output voltage peak-to-peak amplitudes as high as 825 mV, and power consumptions as low as a few milliwatts have been demonstrated for such self-sustained oscillators.

Amir Rahafrooz

Papers

High-Frequency Thermally Actuated Electromechanical Resonators With Piezoresistive Readout

Substrate-decoupled, bulk-acoustic wave gyroscopes: Design and evaluation of next-generation environmentally robust devices.

Fabrication and characterization of thermally actuated micromechanical resonators for airborne particle mass sensing: II. Device fabrication and characterization

Sub-100ppb/°C temperature stability in thermally actuated high frequency silicon resonators via degenerate phosphorous doping and bias current optimization

Thermal-Piezoresistive Energy Pumps in Micromechanical Resonant Structures