Optically Read Coriolis Vibratory Gyroscope Based on a Silicon Tuning Fork N

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Lavrik and Datskos Microsystems & Nanoengineering (2019) 5:47 Microsystems & Nanoengineering https://doi.org/10.1038/s41378-019-0087-9 www.nature.com/micronano

ARTICLE Open Access Optically read Coriolis vibratory gyroscope based on a silicon tuning fork N. V. Lavrik 1 andP.G.Datskos 2

Abstract In this work, we describe the design, fabrication, and characterization of purely mechanical miniature resonating structures that exhibit gyroscopic performance comparable to that of more complex microelectromechanical systems. Compared to previous implementations of Coriolis vibratory gyroscopes, the present approach has the key advantage of using excitation and probing that do not require any on-chip electronics or electrical contacts near the resonating structure. More speciﬁcally, our design relies on differential optical readout, each channel of which is similar to the “optical lever” readout used in atomic force microscopy. The piezoelectrically actuated stage provides highly efﬁcient excitation of millimeter-scale tuning fork structures that were fabricated using widely available high-throughput wafer- level silicon processing. In our experiments, reproducible responses to rotational rates as low as 1.8 × 103°h−1 were demonstrated using a benchtop prototype without any additional processing of the raw signal. The noise-equivalent −1 3 rate, ΩNER, derived from the Allan deviation plot, was found to be <0.5° h for a time of 10 s. Despite the relatively low Q factors (<104) of the tuning fork structures operating under ambient pressure and temperature conditions, the measured performance was not limited by thermomechanical noise. In fact, the performance demonstrated in this proof-of-principle study is approximately four orders of magnitude away from the fundamental limit. 1234567890():,; 1234567890():,; 1234567890():,; 1234567890():,;

Introduction this area are beneficial for not only navigation applications Over the past two decades, micromechanical inertial but also fundamental geophysical studies and even tests of sensing devices, such as accelerometers and gyroscopes, general relativity theory and laws of gravity and inertia. – have been the subjects of extensive research1 3. Although Micromachined accelerometers and gyroscopes are accelerometers and gyroscopes based on microelec- some of the most important types of silicon-based devices tromechanical systems (MEMS) have already been successfully commercialized after the establishment of implemented in many commercial devices, there is still complementary metal oxide-semiconductor technology1. both fundamental and industrial interest in continued Since the first demonstration of a micromachined gyro- research efforts in this area. This interest is stimulated scope4, similar devices have been implemented using primarily by the need for miniature inertial sensing surface, bulk, and hybrid surface-bulk micromachining devices with figures of merit orders of magnitude better approaches. Although numerous gyroscope designs based than those of the existing state-of-the-art. Miniaturizing on a variety of physical principles have been described, the gyroscopes using innovative designs and microfabrication majority of MEMS gyroscopes are based on vibrating processes is an attractive solution to inertial sensing that mechanical elements that successfully utilize the effect of opens up new market opportunities2. Further advances in the Coriolis force. These devices, known as Coriolis vibratory gyroscopes (CVGs), are based on the transfer of energy between two vibration modes of a structure caused Correspondence: P G. Datskos ([email protected]) by Coriolis acceleration5. When rotated, a vibrating ele- 1 Center for Nanophase Materials Sciences, Oak Ridge National Laboratory, Oak ment is subjected to a sinusoidal Coriolis force that causes Ridge, TN 37931-6054, USA 2Mechanical and Thermal Engineering Sciences, National Renewable Energy secondary vibration orthogonal to the original vibrating Laboratory, Golden, CO 80401, USA

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direction. By sensing the secondary vibration, the rate of three dimensions using titanium-based alloys20. Further- rotation can be detected6. Interestingly, a similar principle more, recent advances in coherent light sources point to a is used by nature in certain insects that have vibrating promising path toward optical readout of CVGs with dumbbell-shaped organs, known as halteres, to aid their measurement of mechanical displacement that is below flight7,8. the shot-noise limit and that has a substantially improved A number of MEMS-based gyroscopic devices suitable signal-to-noise ratio21. for less demanding applications are now commercially available9. However, low-cost and high-performance Results devices are not yet available. Current state-of-the-art Analytical models of CVGs micromechanical CVGs require a few orders of magni- Typically, the operation of a CVG is described by a tude improvement in stability to be useful for navigation simplified model that involves a pair of coupled resonat- applications without assistance from the Global Posi- ing beams (tines) that can oscillate in two mutually tioning System. It is important to emphasize that the orthogonal planes (Fig. 1). The Coriolis force can be relatively poor performance of existing MEMS gyroscopes detected as the differential deflection of the tines in the is often limited by the multiple sources of readout noise direction perpendicular to the elliptical structures shown and drifts present in practical devices10. Although the in Fig. 1. The dynamics of oscillating structures in the more sophisticated MEMS gyroscope designs developed CVG studied in this work can be described by two cou- and implemented more recently have exhibited improved pled second-order differential equations22. The equations performance11, they are also associated with substantially of motion for the combined system shown in Fig. 1 under increased fabrication and operational complexity. the influence of a periodic external force, Fy, and an 22 The various sources of noise in micromechanical sys- angular frequency, Ωz, have been described previously . 12 13 tems and nanoscale resonators have been extensively An applied periodic force, Fy, causes the tines to oscil- studied with regard to their impact on the performance of late along the drive axis with a maximum amplitude, Δy, MEMS sensors. It is well-established that evaluation of and a maximum velocity, vy = ωyΔy. When a rotation rate, thermomechanical noise in CVGs can be useful in Ωz, is introduced along the z-axis, the Coriolis force, Fc = 14 assessing the ultimate limit of their performance and, in 2 mΩzvy, forces the tines to oscillate along the sense axis turn, making conclusions about potential improvements with an amplitude, Δx, related to the rotation rate, Ωz,by in practically achievable figures of merit15. However, the real-world performance of any MEMS gyroscope is typically affected more strongly by the multiple additional sources of noise and drifts associated with the readout and z overall mechanical stability of the device rather than by thermomechanical noise. As a result, various advanced designs and transduction methods that minimize drifts x and noise in MEMS have been explored to implement z CVGs with improved performance16,17. It should be noted that these strategies focus mostly on complex designs that y increase the Q factor, optimize the transduction efficiency, improve the sensitivity of the electronic readout method, and facilitate integration of CVGs onto MEMS chips. On the other hand, the important question of whether min- Vy iature CVGs with navigation-grade performance are fun- F damentally feasible has received relatively little attention c = 2 m in the recent literature. z V In our present proof-of-principle study, we use a dif- y ferential optical readout and focus on a micromechanical Sense axis CVG design that closely mimics the halteres, the gyro- y scopic sensory organs of insects7,18. This type of design, X with its inherent simplicity, can be straightforwardly implemented using well-established wafer-level proces- Drive axis sing while also addressing traditional challenges in sen- Fig. 1 Physical model of a double-tine CVG. The CVG is on a sing extremely small mechanical deformations. More platform that rotates horizontally, and the tines are actuated perpendicularly to the platform. Note that this model is applicable to a importantly, due to advances in additive manufacturing, wide variety of resonator shapes, such as a tuning fork or similar similar resonating structures can now be printed19 in Lavrik and Datskos Microsystems & Nanoengineering (2019) 5:47 Page 3 of 11

ref. 23 designs and their optimization from the standpoint of Δ ω fundamentally limited performance. This trade-off, along Δ ¼ rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2 y y Ω x z with the multidimensional nature of the parameter space ω2 2 ω2 ð1Þ ω2 À y þ 1 y 1 ω2 2 ω2 involved in Eq. (2), represents the main challenge in x x Qx x optimizing CVG designs. Furthermore, all the parameters where Ωz is the angular frequency along the z-axis, ωy = in Eq. (2), particularly the proof mass, resonance fre- 1/2 1/2 (ky/m) and ωx = (kx/m) are, respectively, the reso- quencies, and driving amplitude, are interrelated and nance frequencies of the tines along the y axis (drive axis) impose boundaries on the values for realistic designs. and x axis (sense axis), Qy and Qx are, respectively, the To address this challenge, we made two important quality factors of the oscillation along the drive axis and assumptions regarding the CVG resonance frequencies, ω ω Δω sense axis, and m is the effective mass of the oscillator. x and y. First, we assumed that the difference between ωx and ωy is relatively small. This assumption To determine the sensitivity of the CVG studied in this implies mode-matching resonance conditions for the work and its ultimate performance limit, we need to drive and sense modes, which is known to provide max- evaluate the noise-equivalent rotational rate, ΩNER, which imum gain and sensitivity due to a Q-amplified sense is defined as the rotational rate at which the signal-to- response27. However, in mode-matched operation, some noise ratio of the CVG equals unity24. Using Nyquist’s noise and drift sources tend to also be amplified. The relation14,23 for the spectral density of the fluctuating sense mode being shifted from the drive mode leads to force related to the CVG, we obtain for a bandwidth, B, improved thermal stability while also reducing gain and the thermal noise-equivalent rate, Ω 23. sensitivity. Therefore, a small difference between ω and sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi NER x ω can be considered optimal. Second, we assumed that k TBω y Ω ¼ B x ð2Þ there is a limited range of practically feasible resonance NER m Δy2 ω2Q y x frequencies for miniature CVGs. While this range is dif- ficult to rigorously determine, it can be estimated from In inertial navigation systems, the measured rotation previous experimental and theoretical studies on rate is integrated over time to determine the orientation, cantilever-like structures and MEMS devices. Most CVGs – and depending on the integration time, different noise operate in the kHz range28 30 due to the susceptibility of sources can introduce errors25,26. Thermomechanical lower-frequency mechanical resonators to external noise represents the lowest noise floor fundamentally vibrations. Microcantilevers used in scanning probe achievable in any MEMS CVG. Therefore, Eq. (2) can be microscopy have resonance frequencies in the range from used to analyze the fundamentally limited performance of ~2 to 200 kHz. The lower end of this range is of particular a CVG as a function of resonance parameters, mass, and interest to us because the lower the frequency is, the driving amplitude. greater the amplitude that can be achieved in a CVG for a The tuning fork used in the present work can be excited given Q factor, proof mass, and driving force. in such a way that two equal-proof masses are forced into To guide our designs, we calculated the noise- antiphase oscillations along the drive axis. The oscillation equivalent rotation (NER) limited by the thermo- due to the driving force is parallel to the support plane, mechanical noise as a function of proof mass for CVGs whereas the sensing direction (sense axis) is perpendicular with different Q factors while maintaining the resonance to the driving force. Under these conditions, the oscil- frequency and driving amplitude constant. In Fig. 2,we lating tines respond to angular rate inputs in directions show the calculated ΩNER for a CVG as a function of opposite to each other because of opposite Coriolis forces. effective mass, meff, and different quality factors. In these The differential response is expected to be nearly immune calculations, we used a realistic (for our design) actuation – to linear acceleration, which causes deflection of the tines amplitude, Δy = 10 3 m, drive and sense-mode fre- 4 −1 4 −1 in the same direction. quencies, ωy = 2.1 × 10 rad s and ωx = 1.7 × 10 rad s . From Eq. (2), the fundamentally limited performance of In Fig. 2, we also show the limits of performance required the CVG has a straightforward dependence on the values for gyroscopes for different applications (e.g., consumer, of the proof mass, driving amplitude and quality factor of automotive, tactical, and navigation)16,25,31. the sensing tines. From this perspective, it would be Figure 2 shows that navigation-grade CVGs are funda- − beneficial to have the largest possible tuning fork struc- mentally possible when the proof mass is >10 6 kg, even ture driven with the largest possible amplitude while also with Q factors in the range from 103 to 105. It should be minimizing any losses that negatively impact the quality noted that the dependence of ΩNER on the proof mass factor. However, these measures would counteract the shown in Fig. 2 is likely to overestimate the performance goal of miniaturization. Therefore, there is a nontrivial of smaller CVGs because their excitation with millimeter- trade-off between the concept of scaling down CVG scale amplitudes is not necessarily feasible. Lavrik and Datskos Microsystems & Nanoengineering (2019) 5:47 Page 4 of 11

A series of iterative parametric sweeps performed in –3 10 COMSOL allowed us to identify a CVG geometry with a Tactical − proof mass on the order of 10 6 kg and resonance fre- Q 10–4 = 10 quencies close to 3 kHz (Fig. 3). The total mass of a silicon 3 tuning fork with this geometry was calculated to be 2.45 × − 10 6 kg. It is important to note that effective proof masses ) –5

–1 10 and bending rigidities are somewhat different for each Navigation mode. As a reasonable approximation, we can calculate (° s

Q the effective mass for antiphase modes by assuming that NER –6 = 10

10 4 each tine is analogous to a cantilever with an effective Strategic mass equal to one-fourth of its total mass. For the silicon

–7 fork shown in Fig. 3, this approximation gives an effective 10 Q − = 10 proof mass of ~4.2 × 10 7 kg. The antiphase drive and 5 sense-mode spring constants are calculated to be 170 and −1 10–8 190 N m , respectively. –11 –9 –7 –5 –3 10 10 10 10 10 Our eigenfrequency analysis performed in COMSOL meff (kg) revealed the four lowest modes that are of the greatest Fig. 2 Calculated NEΩ as a function of CVG proof mass, m, for importance to the operation of the designed CVG. In different quality factors, Q. The driving amplitude is 10–3 m, and the accordance with the type of deformation involved in these ω = 4 −1 ω drive and sense-mode frequencies are y 2.1 × 10 rad s and x four modes (shown in Fig. 3a–d), we will refer to them as = 4 −1 Ω 1.7 × 10 rad s , respectively. The dashed lines show the NE for (a) in-phase drive, (b) in-phase sense, (c) antiphase drive, different grade gyroscopes and (d) antiphase sense modes. The values of the resonance frequencies corresponding to these modes are (a)

ab e In-phase mode

1 mm

cd f Antiphase mode

1 mm

Fig. 3 Eigenfrequency analysis for the CVG structures showing the four lowest modes. a in-phase (bending) drive mode of 2.01 kHz, b in-phase (bending) sense mode of 2.64 kHz, c antiphase (bending) drive mode of 3.2 kHz, and d antiphase (torsional) sense mode at 3.38 kHz. Also shown is the stroboscopic visualization of the driving modes: e in-phase motion of the tines (asymmetric mode) and f out-of-phase motion of the tines (symmetric mode). The double arrow indicates the direction of the applied excitation Lavrik and Datskos Microsystems & Nanoengineering (2019) 5:47 Page 5 of 11

2.01 × 103 Hz, (b) 2.64 × 103 Hz, (c) 3.2 × 103 Hz, and (d) somewhat smaller. However, the effect of a narrower neck 3.38 × 103 Hz. is not limited to a reduced frequency spread between It should be noted that the exact shape of the defor- these modes. It will also lower the frequencies of in-phase mations associated with each mode is very important for sense and drive modes and make the whole structure two main reasons. First, analysis of the deformations more susceptible to linear acceleration and mechanical allowed us to differentiate in-phase and antiphase modes shocks. Therefore, further improvements in the CVG and conclude that the Coriolis response should contribute design would involve a nontrivial optimization of the neck to the antiphase sense mode when the antiphase drive size and overall shape geometry of the structure. mode is excited. Second, we can identify the regions where the greatest deformations and, in turn, stresses Experimental characterization (color coded red corresponding to the maximum stress in We verified that the implemented CVG structures could − Fig. 3a–d) are localized. The latter is key to further opti- be resonantly driven with amplitudes approaching 10 3 m mization of the CVG designs in terms of mode coupling, near a frequency of 3 kHz. Depending on the way that the mechanical robustness, and ability to operate with very tuning fork was mounted in the piezo-driven stage, large vibration amplitudes. While such optimization is asymmetric (in-phase) or symmetric (antiphase) drive beyond the scope of the current study, our simulations modes could be excited. In Fig. 3e, f, we also show optical indicate that among the four modes, the in-phase drive images of the tuning fork oscillating in the asymmetric and sense modes are associated with the most significant mode (Fig. 3e) and symmetric mode (Fig. 3f) under stresses localized in the neck region of the tuning fork. stroboscopic lighting. Owing to stroboscopic lighting, the Because the in-phase drive and sense modes can be tines captured in each image in Fig. 3e, f correspond to readily excited by linear acceleration, an increase in the different phases of the oscillation. The approximate cross-section of this region and/or a decrease in its length amplitude of the drive-mode oscillation was estimated − can lead to CVG designs that are more immune to shock from these images to approach 10 3 m. An overview of and linear acceleration. At the same time, a narrower neck the frequency response of the actuated CVG is shown in region would lead to reduced clamping losses and, in turn, Fig. 4a. The frequency response was measured using a higher Q factors. Finally, frequency spreads between lock-in amplifier with a sweep generator connected to the various modes are strongly affected by the exact shape position-sensitive detector (PSD) and the piezo-actuator. and sizes of the neck region. In the tuning fork design The measured frequency spectrum shows a clear sign of selected for fabrication, the antiphase drive and sense resonance response at ~2.67 kHz. Taking into account modes are separated by only 180 Hz according to our our COMSOL simulations, we can conclude that this simulations. This frequency spread can be further resonance corresponds to the in-phase sense mode. From decreased by making the cross-section of the neck region the measured frequency response shown in Fig. 4a, we

10–8 Sense a Actuator –7 frequency 10 b 1 V excitation frequency No excitation

) –8 –9 10 10 –1/2 Drive Drive mode (m)

x frequency (m Hz x 10–9

Amplitude, Amplitude, 10–10 Amplitude, Amplitude, 10–10 Sense mode

–11 10 10–11 2400 2600 2800 3000 3200 3400 101 102 103 104 Frequency (Hz) Frequency (Hz) Fig. 4 CVG response as a function of frequency. a Frequency response of the actuated CVG. The sense-mode frequency was smaller than the

drive-mode frequency, which, in turn, was smaller than the piezo-actuator resonance: fsens < fdr < fpiezo. b Frequency response of the CVG with and without excitation demonstrating the readout noise, driving and sensing modes, and coupling between modes during excitation. The readout noise is <10−10 mHz−1/2. The actuation does not affect the baseline noise for f > 100 Hz. Mode coupling can cause the sensing tine to oscillate when CVG is actuated Lavrik and Datskos Microsystems & Nanoengineering (2019) 5:47 Page 6 of 11

ab1500 15 10° s–1

1000 10 5° s–1

500 2.5° s–1 5 (nm) (nm) x x 0 0

–500 –5 Amplitude, Amplitude, Amplitude, Amplitude,

–1000 –10 R = 0.999 z = –1.156 + 6.812 x –1500 –15 0204060 80 –80 –60 –40 –20 0 20 40 60 80 –1 Time (s) Rotation rate, z (° s )

Fig. 5 Temporal and rotational response of the CVG. a Responses of the CVG measured using nondifferential measurements. b A typical calibration curve obtained for a CVG structure in a nondifferential regime. The optical readout gain is 2.5 mV nm−1

3 determined the value of Qs = 6.8 × 10 . On the other advantage of generating the Coriolis forces exerted on hand, the antiphase sense mode corresponds to dynamic each tine in the opposite direction, while any spurious deformations under Coriolis force. linear acceleration generates forces in the same direction. The resonance feature shown in Fig. 4aat3.207×103 Hz Figure 5a shows the temporal responses obtained in the matches the frequency used to excite the antiphase drive nondifferential readout over a period of 80 s of continuous mode in our previous experiments (Fig. 3f) and is close to measurement by applying rotation rates Ωz of 2.5, 5, and − the prediction for the antiphase drive mode from our 10° s 1. eigenfrequency analysis. We want to point out that deflec- A typical calibration plot obtained using the non- tion of the tines in the drive mode does not directly con- differential readout is shown in Fig. 5b. The calibration tribute to deflection of the probing beam, which can explain plot can be approximated by a linear trend with a negli- the absence of the conventional Lorentzian shape in the gible offset and a correlation coefficient of 0.999. frequency response around the drive mode. Finally, the From the data obtained with the nondifferential mea- more distinct resonance at 3.238 × 103 Hz was due to the surement method, we estimated the lowest resolvable − resonance in the sample stage coupled to the piezo-stack. rotational rate to be <0.5° s 1. Next, we recorded the In Fig. 4b, we show a comparison of frequency responses of the CVG to rotation using the differential responses measured for the CVG with and without exci- measurement method (Fig. 6). Compared to the non- tation in a wider range. As shown in Fig. 4b, the optical differential measurements, the differential measurements − − readout has a noise floor below 10 10 mHz 1/2 in the resulted in a signal-to-noise ratio approximately three frequency range above 100 Hz. In this frequency range, times higher. The lowest rotational rate resolvable with − there was no measurable increase in the noise floor when differential readout was estimated to be <0.16° s 1. In this the drive mode was excited. Nonetheless, excitation of the work, the maximum rotational rate we measured was 9 × − drive mode caused a significant increase in the noise in 103°s 1, which gives a dynamic range32 of ~90 dB. For our the low-frequency part of the spectrum (below 100 Hz). experimental conditions, using Eq. (2), we estimated the −7 −1 This increase can be explained by substantial mode cou- thermal noise-equivalent rate, ΩNER, to be 4.4 × 10 °s − − − pling in the implemented device. and a scale factor [Eq. (1)] of ~8.1 × 10 9 m(°s 1) 1. In addition, we characterized the CVG by measuring the To quantify the performance of the CVG more rigor- temporal responses to rotation using both nondifferential ously and characterize its Allan variance, we measured the and differential optical readouts. The motion of each sensing baseline for a time period of 103 s. Figure 7 shows the tine was detected either separately using a nondifferential resulting Allan deviation (solid curve) as a function of readout or as the difference between Coriolis responses from time, τ. The Allan deviation fits on a straight line with a the two tines using a differential readout scheme. slope of −0.956 for times >4 s. For shorter times, the The CVG was driven at 3.207 × 103 Hz by applying an observed leveling off of the Allan deviation is due to the excitation voltage of 1 V to the piezo-stack and exciting lock-in amplifier integration time (0.3 s) used in our the symmetric (antiphase) mode. This mode has the measurements. The slope of approximately −1 in the Lavrik and Datskos Microsystems & Nanoengineering (2019) 5:47 Page 7 of 11

required in the actual implementation of a ﬁeldable gyro 100 based on the principles described in this work. We envi- –1 0.5° s sion that in an actual practical device, the amplitude of both the actuating and sensing tines will be read using 50 similar optical methods. We should point out that high precision motion control using optical PSD technology

(nm) has already been successfully implemented in various x 0 commercial devices, such as the latest generation of scanning galvanometers, which exhibit very high stability − with a reproducibility of 10 6 rad34.

Amplitude, Amplitude, An important question arises regarding the key factors –50 responsible for the experimentally measured noise present in our CVG prototype at levels 3–4 orders of magnitude above the thermomechanical noise limit. Depending on –100 the averaging time, a variety of stochastic processes can 0 200 400 600 800 affect the overall noise level and stability of a CVG. From Time (s) a purely phenomenological viewpoint, these stochastic Fig. 6 Temporal response of the CVG. Responses of the CVG processes can be classiﬁed as angle random walk, corre- measured using the differential optical readout method lated noise, bias instability, and rate random walk. For MEMS gyroscopes in general, the three most commonly discussed noise mechanisms are thermal noise, electro- ﬂ 22 103 nics icker noise, and accumulation of white noise .As CVG + readout applied to the optically read CVG studied in our present 2 10 Thermomechanical

) work, the flicker noise manifests itself in both laser noise –1 101 and PSD noise. Laser noise is known to be a dominant 0 10 Slope = –0.956 factor that limits the spatial accuracy and stability of optical readouts at the level of tens of picometers, which is 10–1 consistent with our experimentally measured frequency –2 10 Slope = –0.5 responses shown in Fig. 4a, b. To approach the theoretical Allan deviation (° h Allan deviation − − 10–3 limit of 1.6 × 10 4°h 1, surmounting the limitations 10–4 imposed by laser noise would be critical. 1 10 100 1000 In the present study, we used an “optical lever” readout Integration time (s) assembled in-house using readily available off-the-shell Fig. 7 Allan deviation plot of the CVG. The response of the CVG was components without any further optimization. It is well- measured using differential measurements. The dashed curve established that the dominant noise source in unopti- corresponds to the estimated thermomechanical noise of the CVG mized optical readouts, such as the one used in the present study, is laser noise12. The readout noise floor in this − − work was approximately < 10 10 Hz 1/2. In our previous Allan deviation plot is characteristic of quantization studies, we have shown that one way to overcome the noise33. Therefore, for the differential measurements, the laser noise threshold is to operate laser diodes slightly gyroscope with our optical readout exhibits a quantization below their lasing threshold35. In fact, optimized optical − noise of 0.11° and a bias instability of <0.5° h 1. The readouts can achieve very low noise floors and are com- dashed curve corresponds to the estimated thermo- parable to other types of MEMS readouts. For example, an mechanical noise of the CVG, with a theoretical angle optical readout of 35–125 μm long cantilevers provided a − − − random walk of 2.1 × 10 5°h 1/2. defection sensitivity better than 10 15 mHz1/236. Com- mercially implemented optical readouts in Doppler vib- − Discussion rometers can reach a resolution of 30 fm Hz 1/237. In the current proof-of-principle study, we used an open Commercially available atomic force microscopes with an − control loop system to drive a piezo-transducer. When optical readout routinely reach a noise level of ~10 12 operated in a controlled laboratory environment (T = m38. Perhaps a promising path toward optical readouts of 22 ± 1 °C), it provided stable amplitudes of the tuning fork CVGs with substantially improved signal-to-noise ratios21 tines to within 0.1%. Furthermore, using stroboscopic is adaptation of approaches developed recently in the visualization, we were able to visually monitor the tuning areas of gravitational wave detection and optical quantum fork motion. However, a closed control loop will be computing. Lavrik and Datskos Microsystems & Nanoengineering (2019) 5:47 Page 8 of 11

Table 1 Performance metrics of the optically read micromechanical CVG and state-of-the-art gyroscopes40,50–52

Parameter Optically read CVG FOGa MEMS MEMS DRGb Units

Dimensions Sensing element (8 × 5 × 2.5) × 10−11 (8 × 6 × 7) × 10−9 (4×4×3)×10−12 (0.03)2 ×5×10−4π m3 Gyroscope 0.2 × 0.4 × 1 (2 × 7 × 7) × 10−6 (1×1×4)×10−7 (1 × 1 × 4) × 10−7 Mass Sensing element 2.45 × 10−6 kg Gyroscope ~10 (lab system) <1.5 × 10−2 5×10−2 10−2 Drive mode 3.238 × 103 ~104 ~2 × 103 Hz Sense mode 2.670 × 103 ~104 ~2 × 103 Hz Minimum displacement 2.5 × 10−9 N/A <10−14 <10−14 m Quantization noise 1.1 × 10−1 <10−3 <10−2 <10−3 ° Bias instability <5 × 10−1 <5 × 10−3 <10−1 0.04 ° h−1 Angle random walk ~10 <10−2 <10−1 10−2 °h−1/2 Range ±9 × 103 ±103 ±103 ±102 °s−1 aFiber optic gyroscope bDisc resonator gyroscope

Our analysis indicates that navigation-grade perfor- state-of-the-art gyroscopes. For example, a MEMS disk − − mance (10 2°h 1) is fundamentally feasible for a CVG resonator gyroscope40 was recently shown to have a bias − − with a proof mass in the 10 6 kg range driven to instability of <0.04° h 1 with a long decay time of 74.9 s. millimeter-scale amplitudes at frequencies of a few kHz. This impressive performance for a MEMS gyroscope According to theoretical and computational guidance, we requires complex mechanical structures with a nontrivial implemented an entirely mechanical silicon CVG struc- fabrication process. The fabrication of the CVG structures ture with a thermomechanical noise floor well below we report in this work are relatively simple, and since the navigation-grade performance. However, the experimen- sensitivity of the optical readout can be substantially tally determined performance of the implemented CVG improved, we expect that in future studies, the perfor- was not limited by the fundamental noise source. In mance of the CVG described here will also be improved. particular, the smallest resolvable rotational rates mea- For example, in the present study, the position sensitivity − − − sured were ~0.16°s 1, whereas our analysis of the Allan was < 10 10 Hz 1/2, and achieving a 50× or better − deviation plot revealed a bias instability noise of ~0.5° h 1. improvement in the performance of the CVG gyro will − − It can be concluded that these experimentally determined require an optical readout sensitivity of ~10 12 mHz 1/2. figures of merit are limited by the noise and instabilities of This requirement seems realistic since optical readout − the optical readout, which are on the order of a few sensitivities of <10 14 m have already been demonstrated nanometers in terms of detectable deflections of the CVG in commercially available optical readouts37. tines. This conclusion points to two immediate strategies A potential path to miniaturization for the CVG based for developing a miniature CVG approaching navigation- on the principle described in this work is clearly indicated grade performance. First, larger responses can be achieved by recent advances in on-chip optical processing. Optical by increasing the Q factors of both drive and sense modes readouts have already been made smaller (digital versatile when the CVG is operated under vacuum conditions. disc and Blu-Ray players use miniaturized optical read- Second, the readout noise can be minimized by using the outs), and on-chip integration of optical sources is an same coherent source to generate two light beams for the active area of research. In a recent work, the combination two channels of the differential readout. Additional of integrated silicon photonics and MEMS was used to improvements can be achieved by combining signals from demonstrate position measurement on the picometer different coherent sources as well as by averaging signals scale under ambient conditions41. The path toward fur- from several tuning fork structures32,39. Optimization of ther miniaturization of a device based on the MEMS the CVG design can further reduce the noise and increase CVGs described in this work is directly linked to con- performance. In Table 1, we highlight specifications and tinued advances in on-chip optical processing. While fully performance metrics for the CVG studied in this work integrated photonic circuits are not a mature technology along with alternative existing state-of-the-art gyroscope yet, a number of complex on-chip optical systems have – technologies. already been demonstrated42 46. Ultimately, this work has In the present study, the CVG with an optical readout the potential to make feasible optical readouts that inte- − was found to exhibit a bias instability of <0.5° h 1, which is grate multiple lasers sources, optical elements and optical − a factor of ~50 lower than the performance of 0.01° h 1 for sensing and electronic processing on a chip with a Lavrik and Datskos Microsystems & Nanoengineering (2019) 5:47 Page 9 of 11

footprint similar to currently commercialized MEMS frequencies as a function of the tuning fork size and gyroscopes. shape, we compiled a series of three-dimensional models Finally, in the present proof-of-principle study, we used and carried out geometrical sweeps. a relatively simple design and fabrication process of purely mechanical resonating structures that can be used as Microfabrication gyroscopes with an optical readout. Although similar We used a straightforward microfabrication sequence designs have been studied before, the combination of a that relied on single-layer photolithography and deep MEMS CVG with an optical readout offers new oppor- reactive etching as the main steps. The CVG geometry tunities in both research and applications. As photonic was a V-shaped tuning fork type with two elliptical fea- circuits continue to improve and be integrated on-chip tures at the end of each tine. The process flow started with with mechanical devices, success on the path toward CVG photolithographic patterning of CVG shapes on a 100- miniaturization will strongly depend on the implementa- mm Si wafer that had 1 μm of thermally grown SiO2 on tion of suitable materials, photon sources, optical sensing both sides. After exposing and developing the photoresist systems, and processes compatible with foundry-level (SPR 220-3.0 MicroChem Inc.), the patterns were etched fabrication47. into the oxide on the front side of the wafer using fluorine-based (CHF3/O2 or C4/F8 processing gases) Materials and methods reactive ion etching. Once the oxide was etched through To overcome the limitations and drawbacks of previous the patterned areas, the wafers were processed using a CVG designs, we focused on an approach that takes deep reactive etch (Bosch process). The etch process advantage of silicon resonating structures that can be continued until the etching through the wafer stopped on batch-fabricated using relaxed design rules due to the the SiO2 layer present on the backside of the Si wafer. The absence of on-chip electronics. Using well-established final step included removal of any residual photoresist photolithographic patterning and wafer-scale proces- with oxygen plasma and removal of SiO2 with a solution sing48, we implemented resonator geometries compatible of hydrofluoric acid. Using the processing sequence out- with large oscillation amplitudes and, in turn, oscillation lined earlier, we fabricated a series of V-shaped CVG velocities. Furthermore, a modular optical readout based structures with varying sizes. A wafer with the fabricated on discrete components eliminates potential electronic CVG structures is shown in Fig. 8a, and Fig. 8b shows a interference without increased fabrication cost and close-up of one of the CVG structures used in the present − complexity. study. The CVG structures had a length l = 8×10 3 m, a − − width w = 5×10 4 m, and a thickness t = 2.50 × 10 4 m. CVG design and finite-element analysis To generate tuning fork geometries for fabrication, we CVG characterization used the following rationale. We focused on a symmetric We characterized individual CVG structures using the geometry with an anchoring region crossing the symmetry experimental setup shown in Fig. 8c, d. The overall size of plane to minimize clamping losses using an analogy to a the system we used in our studies was ~0.2 m3 and classic macroscopic tuning fork. A short neck region with includes all the measurement equipment, the electronics a curved geometry provided mechanical coupling between and the rotation table. The size of the gyroscope MEMS − the two tines. Smooth transitions between different device with the readout lasers and detectors was ~10 6 regions of the CVG structure were aimed at minimizing m3. The CVG structures used were measured as stand- localized stresses and reducing the likelihood of alone devices in an open-loop configuration using a net- mechanical failures of the CVG when driven to high work analyzer and a lock-in amplifier. The individual amplitudes or subjected to mechanical shocks. The nearly CVG structures were secured in an aluminum fixture square cross-section of the tines ensures that their flexural actuated using a miniature piezo-stack connected to a rigidities in two mutually orthogonal planes correspond- signal generator. The frequency generator provided either ing to the drive and sense modes are approximately the a constant drive frequency or a frequency sweep in the same. Because both the effective proof masses and range from ~100 Hz to 20 kHz. bending rigidities corresponding to the drive and modes Optical readout techniques for MEMS are typically are similar, these modes have similar frequencies and can based on reflecting a focused or collimated laser beam be made to match. from the free end of a cantilever and subsequently mea- The vibrational modes corresponding resonance fre- suring the position of the reflected light spot projected quencies inherent to a specific tuning fork geometry were onto a segmented photodiode or position-sensitive pho- quantified by performing eigenfrequency analysis in todetector. The use of a spatially sensitive photodiode COMSOL multiphysics software. Our models relied on allows the measurement of the position of the reflected linear elastic approximations. To calculate resonance laser spot, which, in turn, allows the determination of the Lavrik and Datskos Microsystems & Nanoengineering (2019) 5:47 Page 10 of 11

a c CCD camera

Laser 1 Laser 2

PSD 2 PSD 1

b d Laser 2 Laser 1

PSD 2 PSD 1

Fig. 8 Microfabricated CVG and experimetal setup. a Si wafer with the microfabricated CVG structures. For CVG fabrication, we used 100-mm- diameter Si wafers that were 250-μm thick. b A close-up of an individual CVG structure. c Schematic illustration of the experimental setup, and d a photograph of the implemented differential “optical lever” readout. The optical setup was mounted on a precision turntable for rotational rate measurements. The piezo-driven holder vibrates vertically at its point of attachment to the silicon tuning fork. All the optical readout components and the piezo-driven stage are mounted on the rotating platform and rotate together during characterization of rotational responses

− cantilever deformation. This particular implementation of 278° s 1. The temporal responses of the CVG to rotation the optical readout method was first proposed for use in were recorded without any additional signal processing or atomic force microscopy49. The dynamic deformations of filtering. the CVG tines were detected and quantified using this Spectral analysis of the motion of the CVG tines was contactless optical readout method. To measure the carried out to gain insights into the CVG operation, motion of both tines, two separate laser beams were performance, and noise. The resonance frequencies and focused on the elliptical features at the ends of each tine, quality factors of the CVG modes were evaluated by as shown in Fig. 8c. The laser photons reflected from each analyzing the output signal from each PSD using either a tine were captured by two position-sensitive detectors. spectrum analyzer or a lock-in amplifier and were con- This configuration allowed us to measure the motion of sistent with the eigenfrequency analysis of the CVG tun- each tine separately (nondifferential measurement) and ing fork geometry. determine the difference in displacement between the two tines (differential measurement). Acknowledgements Nondifferential and differential signals of the oscillating The work performed was supported by the Laboratory Directed Research and Development program at Oak Ridge National Laboratory. A portion of this tines were analyzed in the frequency range from 1 to research was conducted at the Center for Nanophase Materials Sciences, 20 kHz using a lock-in amplifier. Geometrical evaluations which is a DOE Office of Science User Facility. Oak Ridge National Laboratory is of our setup along with calibration allowed us to convert operated for the U.S. Department of Energy by UT-Battelle under Contract No. DE-AC05-00OR22725. This work was authored [in part] by the National the PSD output signal into a physically meaningful Renewable Energy Laboratory, operated by the Alliance for Sustainable Energy, mechanical deflection of each tine. The conversion coef- LLC, for the U.S. Department of Energy (DOE) under Contract No. DE-AC36- − ficient for our configuration was 2.5 mV nm 1. A digital 08GO28308. Funding is provided by the U.S. Department of Energy Office of Energy Efficiency and Renewable Energy Wind Energy Technologies Office. camera operating at 60 frames per second was used to The views expressed in the article do not necessarily represent the views of the visualize the motion of CVG tines under stroboscopic DOE or the U.S. Government. The U.S. Government retains and the publisher, illumination. The complete system was mounted on a by accepting the article for publication, acknowledges that the U.S. Government retains a nonexclusive, paid-up, irrevocable, worldwide license to stepper motor-driven rotational stage that provided con- publish or reproduce the published form of this work, or allow others to do so, −3 sistent rotational rates in the range from 2.78 × 10 to for U.S. Government purposes. Lavrik and Datskos Microsystems & Nanoengineering (2019) 5:47 Page 11 of 11

Authors’ contributions 23. Bao,M.H.Micro Mechanical Transducers: Pressure Sensors, Accelerometers and N.V.L. microfabricated the arrays, helped with the measurements, and helped Gyroscopes Vol. 8 (Elsevier, 2000). write the manuscript. P.G.D. designed the experiments and helped with the 24. Lavrik,N.V.,Sepaniak,M.J.&Datskos,P.G.Cantilevertransducersasaplatform preparation of the manuscript. for chemical and biological sensors. Rev. Sci. Instrum. 75,2229–2253 (2004). 25. Grewal, M. & Andrews, A. How good is your gyro [ask the experts]. IEEE Control Conflict of interest Syst. 30,12–86 (2010). The authors declare that they have no conflict of interest. 26. Kim, D. & M'Closkey, R. T. Spectral analysis of vibratory gyro noise. IEEE Sens. J. 13,4361–4374 (2013). Supplementary information accompanies this paper at https://doi.org/ 27. Jaber,N.,Ramini,A.&Younis,M.I.Multifrequencyexcitationofaclamped- 10.1038/s41378-019-0087-9. clamped microbeam: analytical and experimental investigation. Microsyst. Nanoeng. 2, 16002 (2016). 28. Guan,Y.,Gao,S.,Liu,H.&Niu,S.Accelerationsensitivityoftuningforkgyro- Received: 11 March 2019 Revised: 6 June 2019 Accepted: 7 July 2019 scopes: theoretical model, simulation and experimental verification. Microsyst. Technol. 21,1313–1323 (2015). 29. Leland, R. P. Mechanical-thermal noise in MEMS gyroscopes. IEEE Sens. J. 5, 493–500 (2005). References 30. Xie, L. et al. A z-axis quartz cross-fork micromachined gyroscope based on 1. Yazdi,N.,Ayazi,F.&Najafi, K. Micromachined inertial sensors. Proc. IEEE 86, shear stress detection. Sensors 10,1573–1588 (2010). 1640–1659 (1998). 31. Fitzgerald, A. M. Stanford Postion, Navigation and Time Symposium (Stanford 2.Acar,C.&Shkel,A.MEMS Vibratory Gyroscopes: Structural Approaches to University, Stanford, CA, 2013). Improve Robustness (Springer Science & Business Media, 2008). 32. Apostolyuk, V. Coriolis Vibratory Gyroscopes (Springer, 2016). 3. Yoon,S.,Park,U.,Rhim,J.&Yang,S.S.TacticalgradeMEMSvibratingring 33. El-Sheimy,N.,Hou,H.&Niu,X.Analysis and modeling of inertial sensors using gyroscope with high shock reliability. Microelectron. Eng. 142,22–29 (2015). Allan variance. IEEE Trans. Instrum. Meas. 57,140–149 (2007). 4. Greiff, P., Boxenhorn, B., King, T. & Niles, L. Silicon monolithic micromechanical 34. https://nutfieldtech.com/qs-7-opd-galvanometer-scanner/. gyroscope. In 1991 International Conference on Solid-State Sensors and Actua- 35. Grbovic, D. et al. Uncooled infrared imaging using bimaterial microcantilever tors, 1991. Digest of Technical Papers, TRANSDUCERS'91,966–968 (1991). arrays. Appl. Phys. Lett. 89, 073118 (2006). 5. Lutz, M. et al. A precision yaw rate sensor in silicon micromachining. Solid State 36. Fukuma, T. & Jarvis, S. P. Development of liquid-environment frequency Sens. Actuators 2,847–850 (1997). modulation atomic force microscope with low noise deflection sensor for 6. Norgia,M.&Donati,S.Hybridopto-mechanicalgyroscopewithinjection- cantilevers of various dimensions. Rev. Sci. Instrum. 77, 043701 (2006). interferometer readout. Electron. Lett. 37,756–758 (2001). 37. https://www.polytec.com/us/vibrometry/products/microscope-based-vibrom 7. Chan,W.P.,Prete,F.&Dickinson,M.H.VisualInputtotheefferentcontrol eters/uhf-120-ultra-high-frequency-vibrometer/. system of a Fly's "Gyroscope". Science 280, 289–292 (1998). 38. https://usa.jpk.com/products/atomic-force-microscopy/nanowizard-4- 8. Droogendijk,H.,Brookhuis,R.A.,deBoer,M.J.,Sanders,R.G.P.&Krijnen,G.J. nanoscience/specifications. M. Towards a biomimetic gyroscope inspired by the fly's haltere. J. R. Soc. 39. Waters,R.L.&Swanson,P.D.Waters,R.L.,&Swanson,P.D.U.S.PatentNo. Interface 11, 20140573 (2014). 8,991,250. U.S. Patent and Trademark Office, Washington, DC (2015). 9. Shaeffer, D. K. MEMS inertial sensors: a tutorial overview. IEEE Commun. Mag. 40. Li, Q. et al. 0.04 degree-per-hour MEMS disk resonator gyroscope with high- 51, 100–109 (2013). quality factor (510 k) and long decaying time constant (74.9 s). Microsyst. 10. Wen, H., Daruwalla, A. & Ayazi, F. Resonant pitch and roll silicon gyroscopes Nanoeng. 4,32(2018). with sub-micron-gap slanted electrodes: Breaking the barrier toward high- 41. Putrino, G., Martyniuk, M., Keating, A., Faraone, L. & Dell, J. On-chip read-out of performance monolithic inertial measurement units. Microsyst. Nanoeng. 3, picomechanical motion under ambient conditions. Nanoscale 7,1927–1933 16092 (2017). (2015). 11. Marek, J., Hoefflinger,B.&Gomez,U.M.CHIPS 2020 Vol. 2, 221–229 (Springer, 42. Guzman, F., Kumanchik, L. M., Spannagel, R. & Braxmaier, C. Compact fully 2016). monolithic optomechanical accelerometer. Preprint at http://arXiv.org/ 12. Datskos,P.G.,Lavrik,N.V.&Rajic,S.Performanceofuncooledmicrocantilever 1811.01049 (2018). thermal detectors. Rev. Sci. Instrum. 75,1134–1148 (2004). 43. Othman, A. M., Kotb, H. E., Sabry, Y. M., Terra, O. & Khalil, D. A. Toward on-chip 13. Cleland, A. N. & Roukes, M. L. Noise processes in nanomechanical resonators. J. MEMS-based optical autocorrelator. J. Light. Technol. 36,5003–5009 (2018). Appl. Phys. 92,2758–2769 (2002). 44. Rudé, M. et al. Interferometric photodetection in silicon photonics for phase 14. Gabrielson, T. B. Mechanical-thermal noise in micromachined acoustic and diffusion quantum entropy sources. Opt. Express 26, 31957–31964 (2018). vibration sensors. IEEE Trans. Electron Devices 40, 903–909 (1993). 45. Urino, Y. et al. High-density optical interconnects by using silicon photonics. 15. Annovazzi-Lodi, V. & Merlo, S. Mechanical–thermal noise in micromachined -Gener.Opt.Netw.DataCent.Short.ReachLinks9010, 901006 (2014). gyros. Microelectron. J. 30, 1227–1230 (1999). 46. Zhou, Z., Yin, B. & Michel, J. On-chip light sources for silicon photonics. Light. 16. Allen, J. Micro-system inertial sensing technology overview. Rapp. Tech., Sandia Sci. Appl. 4, e358 (2015). Natl Lab. 48,52(2009). 47. Midolo, L., Schliesser, A. & Fiore, A. Nano-opto-electro-mechanical systems. Nat. 17. Zhanshe, G. et al. Research development of silicon MEMS gyroscopes: a Nanotechnol. 13, 11 (2018). review. Microsyst. Technol. 21,2053–2066 (2015). 48. Datskos,P.G.,Lavrik,N.V.,Hunter,S.R.,Rajic,S.&Grbovic,D.Infraredimaging – 18. Hengstenberg, R. Biological sensors: Controlling the fly's gyroscopes. Nature using arrays of SiO2 micromechanical detectors. Opt. Lett. 37,39663968 392,757–758 (1998). (2012). 19. Credi,C.etal.Design,fabricationandtestingofthefirst 3D-printed and wet 49. Meyer,G.&Amer,N.M.Erratum:Novelopticalapproachtoatomicforce metallized z-axis accelerometer. Multidiscip. Digit. Publ. Inst. Proc. 1, 614 (2017). microscopy [Appl. Phys. Lett. 5 3, 1045 (1988)]. Appl. Phys. Lett. 53,2400–2402 20. Fiaz, H. S., Settle, C. R. & Hoshino, Ki Metal additive manufacturing for micro- (1988). electromechanical systems: Titanium alloy (Ti-6Al-4V)-based nanopositioning 50. https://www.draper.com/news-releases/draper-offers-high-performance- flexure fabricated by electron beam melting. Sens. Actuators A Phys. 249, mems-gyroscope-autonomous-vehicle-market. 284–293 (2016). 51. https://northropgrumman.litef.com/fileadmin/downloads/Datenblaetter/ 21. Pooser, R. C. & Lawrie, B. Ultrasensitive measurement of microcantilever dis- Datenblatt_uFors-3U_-3UC_-6U_-6UC.pdf. placement below the shot-noise limit. Optica 2,393–399 (2015). 52. El-Sheimy, N., Goodall, C., Abdelfatah, W., Atia, M. & Scannell, B. in Proc. of the 22. Trusov, A. A. Allan Variance Analysis of Random Noise Modes in Gyroscopes. 25th International Technical Meeting of the Satellite Division of the Institute of Ph. D. Thesis, University of California, Irvine, CA, USA (2011). Navigation 1634–1640 (Ion Gnss, 2012).