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

We present a long-term bias drift compensation algorithm for high quality factor ( Q -factor) MEMS rate gyroscopes using real-time temperature self-sensing. This approach takes advantage of linear temperature dependence of the drive-mode resonant frequency for self-compensation of temperature-induced output drifts. The approach was validated using a vacuum packaged silicon Quadruple Mass Gyroscope (QMG), with signal-to-noise ratio (SNR) enhanced by isotopic Q -factors of 1.2 million. Owing to the high Q -factors, measured frequency resolution of 0.01 ppm provided a temperature self-sensing precision of 0.0004 °C, on par with the state-of-the-art MEMS resonant thermometers. The real-time self-compensation yielded a total bias error of 2°/h and a scale-factor error of 700 ppm over temperature range of 25–55 °C. The presented approach enabled repeatable long-term rate measurements required for MEMS gyrocompassing applications with a milliradian azimuth precision.

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Compensation of drifts in high-Q MEMS gyroscopes using temperature self-sensing

Resonators fabricated in heavily doped silicon have been noted to have a reduced frequency-temperature dependence compared with lightly doped silicon. The resonant frequency of silicon microelectromechanical systems (MEMS) resonators is largely governed by the material’s elastic properties, which are known to depend on doping. In this paper, a suite of different types and orientations of resonators were used to extract the first- and second-order temperature dependences of the elastic constants of p-doped silicon up to 1.7e20 $\mathrm{cm}^{\mathrm {\mathbf {-3}}}$ , and n-doped up to 6.6e19 $\mathrm{cm}^{\mathrm {\mathbf {-3}}}$ . It is shown that these temperature-dependent elastic constants may be used in finite element analysis to predict the frequency-temperature dependence of similarly doped silicon resonators. [2013-0331]

Temperature Dependence of the Elastic Constants of Doped Silicon

This paper will provide an update of SiTime's TCXO technology and benchmark 4G & GPS specifications to show that SiTime's MEMS oscillators are capable of meeting these challenging specifications. This MEMS-based TCXO is able to achieve the following which was considered possible only with quartz oscillators: phase noise of −145dBc/Hz @ 10kHz offset and 19.2MHz carrier, frequency stability of 0.2 ppm over industrial temperature range (−40 to 85°C), Allan deviation of 3e-10 using 1 sec averaging time, and random phase jitter of 0.5ps RMS integrated from 12kHz to 20MHz.

Low jitter and temperature stable MEMS oscillators

An overview of microelectromechanical systems (MEMS) resonators for frequency reference and timing applications is presented. The progress made in the past few decades in design, modeling, fabrication and packaging of MEMS resonators is summarized. In particular, the state-of-the-art technologies for improving the overall performance of MEMS resonators, such as quality factor ( $Q$ ), motional impedance, temperature sensitivity, and initial frequency uniformity, are reviewed in detail. The challenges and opportunities during the commercialization of MEMS resonators are also stated, and future development trends driven either by technology or market are outlined. This paper intends to provide an outlook for possible research directions of MEMS resonators in frequency reference and timing applications. With outstanding reliability, unique multi-frequency functionality on a single chip, and high accuracy, MEMS resonators show great potential for replacing the quartz crystal resonators which have been dominating the timing market since 1920s. [2020-0106]

MEMS Resonators for Frequency Reference and Timing Applications

This paper describes the first 32 kHz low-power MEMS-based oscillator in production. The primary goal is to provide a small form-factor oscillator (1.5 × 0.8 mm 2 ) for use as a crystal replacement in space-constrained mobile devices. The oscillator generates an output frequency of 32.768 kHz and its binary divisors down to 1 Hz. The frequency stability over the industrial temperature range (–40 °C to 85 °C) is ±100 ppm as an oscillator (XO) or ±3 ppm with optional calibration as a temperature compensated oscillator (TCXO). Supply currents are 0.9 µA for the XO and 1.0 µA for the TCXO at supply voltages from 1.4 V to 4.5 V. The MEMS resonator is a capacitively-transduced tuning fork at 524 kHz. The circuitry is fabricated in 180 nm CMOS and includes low power sustaining circuit, fractional-N PLL, temperature sensor, digital control, and low swing driver.

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A 3 ppm 1.5 × 0.8 mm 2 1.0 µA 32.768 kHz MEMS-Based Oscillator

/pdf/mems-enables-oscillators-with-sub-ppm-frequency-stability-1m3bx5jwu3.pdf

Mems enables oscillators with sub-ppm frequency stability and sub-ps jitter

Real-time clocking for space-constrained mobile and wearable applications require low-power 32.768 kHz references with small form-factor and tight frequency stability, at a competitive price built in an ultra-high volume capable manufacturing process. Legacy 32 kHz quartz-based technology has reached the limits of miniaturization, performance and cost. In this work, a temperature compensated 32 kHz MEMS-based oscillator (TCXO), in a 1.55 mm × 0.85 mm × 0.55 mm form factor, with ±5 ppm frequency stability over −40°C to 85°C, will be presented. The combination of wafer-level chip scale packaging (WL-CSP) and silicon MEMS technology has enabled the smallest and best-in-class 32 kHz clocking solution for very high volume applications. The underlying MEMS system packaging and test technologies will be presented along with the electrical and reliability results.

2-die wafer-level chip scale packaging enables the smallest TCXO for mobile and wearable applications

Degenerately doped semiconductor materials are deployed within resonant structures to control the first and higher order temperature coefficients of frequency, thereby enabling temperature dependence to be engineered without need for cumulative material layers which tend to drive up cost and compromise resonator performance.

Temperature-engineered MEMS resonator

A method of manufacturing a micromachined resonator having a moveable member comprising forming the moveable member from a material having a first concentration of dopants of a first impurity type, depositing a dopant carrier layer on or over at least a portion of the moveable member, wherein the dopant carrier layer includes one or more dopants of the first impurity type, transferring at least a portion of the one or more dopants from the dopant carrier layer to the moveable member, wherein, in response, the concentration of dopants of the first impurity type in the moveable member increases (for example, to greater than 10 19 cm −3 , and preferably between 10 19 cm −3 and 10 21 cm −3 ). The method further includes removing the dopant carrier layer and may include providing an encapsulation structure over the moveable member of the micromachined resonator.

Ginel C. Hill

Papers

A 3 ppm 1.5 × 0.8 mm 2 1.0 µA 32.768 kHz MEMS-Based Oscillator

Mems enables oscillators with sub-ppm frequency stability and sub-ps jitter

2-die wafer-level chip scale packaging enables the smallest TCXO for mobile and wearable applications

Temperature-engineered MEMS resonator

MEMS device and method of manufacturing same