Chao Han

Due to the excellent material properties of crystal quartz and its simple and effective structure, the quartz double ended tuning fork (DETF) is widely used as a resonance sensing element in resonator sensors, where its quality factor has an important effect on the overall accuracy and stability of such sensors. To optimise the quality factor of quartz DETF, the influence of structural dimensions on structural and air damping is analysed, and the theoretical model used to calculate the quality factor is summarised. Further, under the premise of fabricating resonators with sufficient force–frequency sensitivity, the quality factors of quartz DETFs of different structural dimensions are simulated through finite element simulation. The theoretical model and simulation calculation of the quality factor of quartz DETFs mutually verify its effectiveness. Moreover, an experimental platform was built, and three quartz DETFs with different dimensions were fabricated to test their quality factor. The quality factors of the three DETFs in air and vacuum are 3467.3, 1925.8, 4442.4 and 32 997.6, 11 559.1, 24 795.7, respectively, which means that the environmental factors and their structural dimensions have a great influence on quality factor. With the simulation method and summarised theoretical model in this paper, the quality factor was studied with comprehensive structural damping (thermal damping loss and support loss) and air damping (resistance damping, slide film damping, and squeeze film damping). The influence of the structure size on the quality factor was analysed in detail, including the length of the decoupling region, the distance between the tines, and the length and width of the tines, and the main influencing factors were obtained, providing a basic and comprehensive reference for designing quartz DETF.

In this study, the application of micro-leverage in the monolithically all-quartz resonant accelerometer is proposed. The magnification of the micro-leverage structure used for a large size double-ended tuning fork (DETF) was analyzed. The effect of DETF’s dimension both on its own force–frequency sensitivity and micro-leverage’s magnification was investigated. Through the study of the relationship between DETF’s force–frequency sensitivity and micro-leverage’s magnification, the effect of micro-leverage and the DETF system on the sensitivity of the accelerometer was obtained. The problem of big error in theoretical calculation of micro-leverage magnification was solved because the structural arrangement of the output beam was ignored in the derivation process. The correctness of the analysis was verified by theoretical calculation, simulation, and the experiment. The equivalent structures of tension (compression) stiffness and flexural stiffness of the micro-leverage output beam were obtained by analyzing and simplifying the composite structure of the link beam and DETF. By simplifying the mechanical model of micro-leverage, the amplification factor K of micro-leverage is deduced to be 23. Therefore, the theoretical sensitivity of the sensor is 15.6 Hz/g. The experimental results show that the sensitivity of the accelerometer with the micro-leverage is 16.1 Hz/g, which is close to the theoretical analysis results.

This study proposes a highly stable differential resonant accelerometer that is monolithically micro-machined from a piece of ultrapure, single z-cut crystal quartz. The overall structure of quartz accelerometer is centrally symmetrical, which comprises two double-ended tuning forks (DETFs), two link beams, two micro-leverages, a proof mass, and a quartz frame. Micro-leverages and DETFs are perpendicular to each other and are located around the chip, which maximizes the utilization of the sensor area and is conducive to the miniaturization of the sensor. The effectiveness of the structure was verified by theoretical analysis, simulation, and experiment. The structure with differential arrangement can eliminate common mode disturbances, such as temperature, to improve sensitivity to acceleration. Within the measurement range of ±100 g, the sensor's sensitivity, which is measured by experiments, is 17.72 Hz/g, with a velocity random walk of 0.84 μg/√ Hz and bias instability of 3.05 μg, which is consistent with the theoretical analysis results. [2020-0309]

This paper describes the design, fabrication, and testing of an integrated packaged sensor that is composed of a micro resonant accelerometer and a temperature sensor. The resonant accelerometer with differential configuration consists of double quartz resonators and a silicon substrate. When acceleration is applied along the sensing axis, the inertial force induced by the proof mass will transfer force to the resonators, which causes an opposite frequency shift of the dual quartz resonators. The loaded acceleration can be measured through detecting the differential frequency shift. The symmetric differential configuration response to spurious effects of thermal loading and inelastic effect causing prestress in the resonators is similar, which can be reduced by detecting the differential frequency, effectively. However, during the manufacture and packaging process, the otherness of residual stress in two quartz resonators results in that the response of resonators to temperature variation is not strictly the same. In other words, this temperature drift cannot be eliminated by the structure design. Thus, a temperature sensor and an accelerometer were packaged in a shell together. These novel integrated sensors can measure acceleration and temperature simultaneously. With the testing temperature data, a novel temperature compensation that is a combination of the variable coefficient regression and least squares support vector machine is used for improving the performance of the accelerometer. By means of this compensation and field programmable gate array, a real-time and online compensation is achieved. The tumble testing results indicate that the sensitivity of the accelerometer is ∼16.97 Hz/g. With the temperature compensation, the output drift of the scale factor is improved by 0.605 Hz/g in the full temperature range, which is from 0.072 Hz/g to 0.015 Hz/g. The drift of zero bias is improved from 345 mg to 1.9 mg.

Quartz is widely used in microelectromechanical systems (MEMS). Especially, MEMS quartz resonators are applied to sensors and serve as sensitive elements. The capability of deep etching is a limitation for the application. Presented in this paper is a deep and high accuracy reactive ion etching method applied to a quartz resonator etching process with a Cr mask. In order to enhance the capability of deep etching and machining accuracy, three kinds of etching gas (C₄F₈/Ar, SF₆/Ar and SF₆/C4F₈/Ar), bias power, inductively coupled plasma (ICP) power and chamber pressure were studied in an industrial reactive ion etching machine (GDE C200). Results indicated that the SF₆/C₄F₈/Ar chemistry gas is the suitable and optimal choice. Experiment results indicate that Cr (chromium) mask can obtain a higher selectivity than aluminum and titanium mask. A “sandwich” structure composed of Al layer-Cr layer-Al layer-Cr layer was proposed. The Al (aluminum) film can play the role of releasing stress and protecting gold electrodes, which can enhance the thickness of metal mask. An optimized process using SF₆/C₄F₈/Ar plasmas showed the quartz etching rate of 450 nm/min. Meanwhile, a microchannel with a depth of 75.4 µm is fabricated, and a nearly vertical sidewall profile, smooth surface is achieved.

Single-crystal quartz material is widely applied in the manufacture of resonators and sensors, but it is difficult to process because of its high hardness. A novel way to fabricate single-crystal quartz structures is proposed in this paper; the method includes quartz-on-silicon (QoS) technology and inductively coupled plasma (ICP) etching, which makes it feasible to fabricate complex structures with crystal quartz. The QoS method encompasses the bonding of silicon and quartz, followed by the thinning and polishing of quartz, which can enable the fabrication of an ultra-thin quartz wafer on silicon. In this way, instead of the conventional wet etching with hydrofluoric acid, the quartz layer can be easily etched using the ICP dry-etching method. Then, the structure of the pure quartz material is obtained by removing the silicon wafer. In addition, the silicon layer can be processed into the appropriate structure. This aspect overcomes the difficulty of processing a complex structure of single-crystal quartz with different crystal orientations. Thin single-crystal quartz wafers of Z-cut with a thickness of less than 40 μm were obtained by using this method, and a complex three-dimensional structure with an 80 μm width was also acquired by the ICP etching of the quartz wafer. The method can be applied to make both crystal-oriented quartz-based sensors and actuators, such as quartz resonant accelerometers.