A Mode-Matched Silicon-Yaw Tuning-Fork Gyroscope With ...
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A Mode-Matched Silicon-Yaw Tuning-Fork Gyroscope With Subdegree-Per-Hour Allan Deviation Bias Instability Mohammad Faisal Zaman, Member, IEEE, Ajit Sharma, Member, IEEE, Zhili Hao, Member, IEEE, Member, ASME, and Farrokh Ayazi, Senior Member, IEEE
Abstract—In this paper, we report on the design, fabrication, and characterization of an in-plane mode-matched tuning-fork gyroscope (M2 -TFG). The M2 -TFG uses two high-quality-factor (Q) resonant flexural modes of a single crystalline silicon microstructure to detect angular rate about the normal axis. Operating the device under mode-matched condition, i.e., zero-hertz frequency split between drive and sense modes, enables a Q-factor mechanical amplification in the rate sensitivity and also improves the overall noise floor and bias stability of the device. The M2 -TFG is fabricated on a silicon-on-insulator substrate using a combination of device and handle-layer silicon etching that precludes the need for any release openings on the proof-mass, thereby maximizing the mass per unit area. Experimental data indicate subdegree-per-hour Brownian noise floor with a measured Allan deviation bias instability of 0.15◦ /hr for a 60-μm-thick 1.5 mm × 1.7 mm footprint M2 -TFG prototype. The gyroscope exhibits an open-loop rate sensitivity of approximately 83 mV/◦ /s in vacuum. [2007-0100] Index Terms—Mode-matching, silicon-on-insulator (SOI), tuning fork, vibratory microgyroscope.
I. I NTRODUCTION
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ICROMACHINED gyroscopes constitute one of the fastest growing segments of the microsensor market. The application domain of these devices is rapidly expanding from automotive to consumer electronics and personal navigation systems. Small form factor, light weight, and low power consumption make micromachined gyroscopes ideal for use in handheld applications, many of which require multiaxis sensitivity. Gaming consoles, image stabilization in digital cameras, and traction control systems in automobiles represent applications in which angular-rate resolution on the order of Manuscript received May 11, 2007; revised November 16, 2007, April 28, 2008, and July 21, 2008. First published September 30, 2008; current version published December 4, 2008. This work was supported by the DARPA HERMIT Program under Contract W31P4Q-04-1-R001. Subject Editor G. K. Fedder. M. F. Zaman was with the School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0250 USA. He is now with Qualtré, Inc., Atlanta, GA 30308 USA (e-mail: [email protected]). A. Sharma is with Texas Instruments Incorporated, Dallas, TX 75243 USA (e-mail: [email protected]). Z. Hao is with the Department of Mechanical Engineering, Old Dominion University, Norfolk, VA 23529-0246 USA (e-mail: [email protected]). F. Ayazi is with the School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0250 USA, and also with Qualtré, Inc., Atlanta, GA 30308 USA (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/JMEMS.2008.2004794
0.1◦ /s is sufficient. Microelectromechanical-system (MEMS) gyroscopes, however, have yet to break into the high-precision market that requires sub-0.1◦ /hr resolution and bias stability. Applications in this area include gyrocompassing, the process of utilizing the Earth’s rotation to determine the direction of true north. Other applications include short-range navigation (in the absence of the GPS signal) and guidance deployed in autonomous vehicles [1]. Micromachined vibratory gyroscopes are based on the Coriolis induced transfer of energy between two vibration modes of a microstructure. They can operate in either mode-matched or split-mode condition. Under mode-matched condition, the sense mode is designed to have the same (or nearly the same) resonant frequency as the drive mode. Hence, the rotationinduced Coriolis signal is amplified by the mechanical quality factor of the sense mode. In split-mode condition, the drive and sense modes are separated in resonant frequency. The sense mode is then a controlled mode that operates similar to an accelerometer and measures the Coriolis acceleration [2]–[4]. Due to Q-factor amplification, gyroscopes operated under mode-matched configuration offer higher sensitivity and better resolution. Resonant-matched devices are themselves further classified into two types, depending upon the nature of their operating modes [5]. Class-I devices rely on nondegenerate vibration modes for driving and sensing. Tuning-fork and frame gyroscopes are examples of class-I gyroscopes [6]–[8]. Class-II devices, such as shell-type gyroscopes, on the other hand, function with degenerate vibration modes [9], [10]. Gyroscope resolution, along with bias stability, sensitivity, and bandwidth, play an important role in defining its application area. A review of the noise expressions in [9] highlights the key parameters that affect performance. In order to attain the subdegree-per-hour noise performance, a vibratory gyroscope must attain high-Q mode-matched operation, large resonant proof-mass, and large drive amplitude. In this paper, the authors introduce the mode-matched tuning-fork gyroscope (M2 -TFG): an in-plane single crystalline silicon yaw-rate tuning-fork device that incorporates all the earlier specifications within a single framework. The concept and operation of the M2 -TFG is discussed in Section II. Section III describes the micromachining processes involved in the fabrication of prototype devices. Characterization results of the operating resonant modes of the M2 -TFG are the subject of Section IV, while Section V deals with the examination of microsystem performance. This paper
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Fig. 1. SEM overview of an M2 -TFG implemented on 40-μm-thick SOI substrate.
concludes with the performance summary of an optimized M2 TFG design in Section VI. II. D ESIGN The M2 -TFG, as shown in the SEM image in Fig. 1, is comprised of two proof-masses, supported by a network of flexural springs, and anchored at a central post. A collection of capacitive control electrodes is symmetrically distributed around the proof-masses. The operating principle is based upon a standard tuning fork’s response to rotation. The two proof-masses are analogous to tines and driven in-plane into resonance along the x-axis using electrostatic comb-drive electrodes. An input rotation signal normal to the device plane (along z-axis) causes a Coriolis induced transfer of energy to the sense vibration mode. The resulting in-plane displacement is sensed capacitively at sense electrodes located along the y-axis. The operating mode shapes of the M2 -TFG may be viewed as shown in Fig. 2. An advantage in utilizing a symmetric tuning-fork architecture is the inherent differential nature of the sense mode. As a result, linear acceleration is rejected as common mode signal without the need for complex electronics. The anchor design of the M2 -TFG satisfies two critical properties: mechanical coupling and resonant-mode isolation. The mechanical coupling, promoted by the central ladder-shaped anchor structure, allows synchronization of the phases of the proof-masses even in the presence of minor fabrication imperfections. The second important function enabled by the anchor is the isolation of the in-plane operating modes from the two other existing inplane resonant modes. These are the pseudodrive mode (both proof-masses vibrate along the drive axis in the same direction) and the pseudosense mode (both proof-masses vibrate along the sense axis in the same direction). These two modes correspond to the symmetric and antisymmetric modes of a tuning-fork structure and are also influenced by Coriolis acceleration. In the current M2 -TFG design, these modes occur at least 200 Hz away from the operating modes of interest.
Fig. 2. Resonant in-plane operating modes of the M2 -TFG (motion exaggerated for clarity).
The flexural-spring design must satisfy a host of critical properties. The ideal spring design must ensure large mobility along both axes. To this effect, a fishhook architecture was adopted which ensures that the mode shapes have two directional flexibility [11]. The current spring structure enables 4–6-μm drive-mode displacements. The second important criterion is to ensure that the two operating-mode frequencies lie in close proximity to one another while remaining isolated from the out-of-plane resonant modes. Detailed finite-element analysis simulations of the flexural springs and anchor were performed in ANSYS to optimize the dimensions to allow the sense mode to occur 50–150 Hz higher than the drive mode. Upon fabrication, the sense-mode frequency is electrostatically tuned to match the drive-mode frequency. A key performance parameter of vibratory gyroscopes is the mechanical quality factor (Q) of its operating modes. In order to achieve higher sensitivity and better rate resolution and drift, the design of gyroscopes with large sense-mode Q is pursued. A large drive-mode Q is also necessary for improved bias stability as well as ensuring large drive amplitudes using small drive voltages—a desirable feature required in low-power CMOS interfacing [12], [13]. The energy-dissipation mechanisms associated with the M2 -TFG design are air damping, support loss, thermoelastic damping (TED), surface loss, and the intrinsic loss of silicon. Hence, the overall mechanical Q for an operating mode is expressed as the sum of all these contributions. 1 1 1 1 = + + Q QAir Damping QSupport QTED 1 1 + + . (1) QSurface QIntrinsic Among them, the effect of air damping may be eliminated by operating the gyroscope in vacuum, while the contribution of
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Fig. 3. Outline of the fabrication process flow for SOI M2 -TFG.
Fig. 4. (a) Close-up of the drive and sense gaps and (b) view of the anchor support posts (as seen from handle layer) for a 40-μm-thick SOI prototype.
surface loss can be made negligible through optimized processing. With QIntrinsic being very high in silicon, this leaves TED and support loss as the primary loss mechanisms in the M2 -TFG design. By simplifying the structure, one may identify basic trends required to operate in a region of high QTED . As shown in Fig. 2, during the flexural vibrations in the operating resonant modes, the proof-masses only undergo translational motion. The spring structures, unlike the proof-masses, experience structural deformation. Half the tuning-fork structure in each operating mode may be viewed as a beamlike resonator with an added proof-mass symmetric with respect to the centerline. This simplified model was utilized to estimate the TED of the structure [14]. The mechanism responsible for TED in solids is the lack of thermal equilibrium between various parts of the vibrating solid. Based on the theory of linear thermoelasticity, the governing equations for thermoelastic uncoupled flexuralmode vibrations in a beamlike resonator with added proofmass are the same as that of a simple flexural beam. The addition of the proof-mass modifies the resonant frequency (ω0 ). The QTED in the M2 -TFG structure may be estimated from the equation of a simple flexural beam expressed in [14]. The QTED is a function of the flexural-spring width (b) and the operating frequency (ω0 ). In the current M2 -TFG design, the flexural-spring dimensions and operating-frequency regime were tactically selected to operate in a region away from the Debye peak of the QTED curve. During resonant flexural vibrations, the proof-masses exert a time-harmonic load on the support structure. Acting as an excitation source, this time-harmonic load excites elastic waves propagating through the support. The vibration energy dissipated through elastic-wave propagation in the support media represents the support loss. The complexity of the anchor geometry and composition prevented an accurate analysis of the
support loss. However, the flexural beams were designed with high-aspect ratio to minimize support loss [15]. III. F ABRICATION The prototype M2 -TFGs are implemented on an silicon-oninsulator (SOI) substrate. The fabrication-process flow is shown in Fig. 3. The moving sections of the structure and the area under the comb drives are first released from the rear by etching the handle silicon layer through to the buried-oxide layer using the Bosch process. The buried oxide is then removed in a reactive-ion-etching system. Finally, the device layer is patterned all the way through; leaving behind a suspended structure whose anchor is supported to the substrate via support posts. SEM images of fabricated M2 -TFG are shown in Figs. 1 and 4. The device-layer silicon etching was performed using the advanced-silicon-etch process developed by surface technology systems. At high plasma densities, the silicon-etch profile tends to have a high lateral etch rate at the Si−SiO2 interface, an effect commonly referred to as notching. Eliminating the buriedoxide layer underneath the M2 -TFG area prevents structural damage via notching (as shown in Fig. 5). However, it does not prevent notching from occurring at the oxide interface in the electrode boundaries. The resultant accumulation of silicon debris compromises electrical isolation. Notching arises as a result of deflection of incoming ions onto the sidewalls due to charge build-up at the surface of the buried oxide. By reducing the operating RF frequency from 13.56 MHz to 380 kHz, it is possible to generate a surplus of low-energy ions. These low-energy ions are able to neutralize the excess charge build-up resulting in debris-free electrode trenches [16]. By ramping RF platen power and adjusting etchant flow rates, it was possible to attain a trench aspect ratio as high as 18 : 1
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Fig. 5.
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View of the flexural springs observed from the handle-layer openings.
with the low-frequency RF module. A short HF etch was performed to release areas under the anchor support posts shown in Fig. 4(b). The fabrication process, an improvization of the SOI– MUMPS process [17], is simple and precludes the requirement of any perforations in the proof-mass, resulting in a larger mass per unit area. The simultaneous elimination of the ground plane under the comb drives prevents the excitation of the out-of-plane modes and detrimental effects associated with comb levitation. The fact that all the electrodes and the structure are defined using a single mask ensures that there are no horizontal misalignment errors of actuation/ sense gaps. IV. D EVICE C HARACTERIZATION Preliminary open-loop characterization of the M2 -TFG is performed using dedicated analog front-end electronics (AFE) implemented by means of discrete amplifiers. The M2 -TFG die is mounted on the AFE board and wire bonded to pads that interface with transimpedance amplifiers. This AFE board is then placed in the vacuum chamber, and device characterization is performed. The devices were characterized in 1-mtorr vacuum, and an Agilent 4395A network analyzer was used to measure the frequency response. The measured drive and sense resonant modes for a prototype 40-μm-thick M2 -TFG are shown in Fig. 6. In this particular device, the driveand sense-mode Q’s were measured as 78 000 and 45 000, respectively. As shown in Fig. 2, the vibrations in the drive resonant mode effectively ensure force cancellation at the anchor. However, the vibrations in the sense resonant mode introduce forces to the anchor regions. These forces are offcenter and lead to a net torque along the support structure. As a result, the drivemode Q is expected to be higher than the sense-mode Q due to effective torque cancellation. This fact has been verified in Table I which tabulates the average Q values recorded over five samples in two batches of 40-μm-thick M2 -TFGs. In addition, as predicted from [14], a device with larger beamwidth displays lower Q-factor operating modes. A. Mode Matching and Quadrature Nulling Mode matching is performed by increasing the dc polarization voltage (VP ) on the MEMS structure until electrostatic
Fig. 6. Measured (top) drive and (bottom) sense resonant-mode Q. TABLE I MEASURED FREQUENCY AND Q FOR TWO BATCHES OF M2 -TFGs
spring softening decreases the sense-mode frequency to become equal to the drive-mode frequency. The capacitive clearance between the drive-mode flexures and the sense electrodes are large enough to ensure that the drive mode remains relatively constant as shown in Fig. 7. Despite an optimized flexural design, in practice, fabrication imperfections can lead to nonzero offdiagonal elements in the spring stiffness and damping-coefficient matrices. This results in an undesirable zero-rate output (ZRO) signal commonly referred to as quadrature. Quadrature error prevents perfect overlap of the drive and sense resonant modes. Only through the minimization of this error component will near-perfect mode matching be possible [18]. Unlike Coriolis acceleration, which is proportional to the proof-mass velocity, quadrature errors are
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B. Temperature Characterization
Fig. 7. Calculated tuning characteristics of M2 -TFG sense and drive modes.
In order to ensure high performance, it is essential that mode matching is maintained over temperature. The M2 -TFG was tested under both matched- and split-mode conditions to accurately determine the effects of temperature on the operating modes. Fig. 10 shows the measured frequency variation of the individual unmatched resonant modes of a M2 -TFG prototype (beamwidth ∼ 21 μm, f0 ∼ 18.4 kHz) as a function of temperature. Such frequency variation is attributed to the temperature dependence of Young’s modulus of single crystalline silicon substrate. The drive-mode temperature coefficient of frequency (TCF) is measured to be—21.75 ppm/◦ C. The TCF of the drive and sense resonant modes vary by less than 1 ppm/◦ C. Table II highlights Q-factor degradation in individual operating resonant modes at increased temperatures. This observation is attributed to elevated TED [19]. A separate M2 -TFG device under mode-matched condition (operating at 15 kHz) was also subjected to the TCF measurement test (see Fig. 11). Mode matching is maintained over the temperature range of 25–100 ◦ C (without requiring any closed-loop quadrature compensation or frequency tuning). Hence, a single temperature-compensation circuit will suffice to maintain mode matching over temperature. A mode-matched Q-factor degradation was observed at elevated temperature similar to the split-mode characterization.
V. P ERFORMANCE A NALYSIS
Fig. 8. View of the quadrature minimization electrodes of the 40-μm-thick SOI M2 -TFG prototype.
accelerations attributed to the proof-mass position. Quadratureminimization electrodes are situated at corners of each proofmass. Reducing quadrature error requires electrostatic forces which are in phase with the motion of the proof-mass while in drive-mode resonance. The forcing function can be accomplished by slightly unbalancing the bias voltages applied to the structure for mode matching (as shown in Fig. 8). This force is directly proportional to the proof-mass displacement (i.e., a time-varying force). By adjusting VQ at one of the two electrodes, it is possible to align the proof-masses by reducing the offdiagonal components of the stiffness matrix of the system [13]. In the current mode-matching implementation, typical values of VQ and |VP ± VQ | are approximately ±20 and 10–20 V, respectively. From an initial separation of approximately 60 Hz, the drive and sense frequencies were matched electronically by varying the polarization voltage and adjusting the appropriate quadrature voltages as shown in Fig. 9. Mode matching is achieved to within the precision of the measurement setup and equipment (better than 0.1 Hz). The M2 -TFG is the first reported high-Q mode-matched implementation (i.e., zero-hertz frequency split) of a class-I vibratory microgyroscope [6].
In order to extract the rotation-rate information from the sense electrodes, a considerable amount of signal processing is required. The signal-processing circuitry shown in Fig. 12 has been implemented using discrete electronic components and consists of two main blocks: 1) drive loop to maintain resonance in the drive mode and 2) sense channel that extracts the rotation rate from the output at the sense electrodes. The drive loop uses a digital phase-locked loop (PLL) to lock to the drive resonant frequency and supplies the actuation voltage to the drive-comb electrodes. The variable gain amplifier maintains constant drive amplitude and prevents overdriving the sensor. The front-end of the M2 -TFG sense channel is comprised of two discrete transimpedance amplifier chains that process signals from a pair of mechanically differential-sense electrodes, as shown in Fig. 12. There is an additional adjustable gain stage immediately beyond the transimpedance front-end (not shown). Any offset that manifests itself on each signal chain is cancelled before being fed into the differential amplifier. The sense channel further consists of a synchronous demodulator to extract the rate signal from the sensor output. The PLL generates a signal that is in phase with the drive velocity. This square wave is used in a synchronous demodulator and mixed with the incoming signal from the sensor and, subsequently, low passed filtered to obtain the rate signal. A synchronous demodulator maintains inherent phase information while demodulating the AM signal. This phase relationship is used to distinguish between the rotation rate and quadrature signal. A customized
ZAMAN et al.: SILICON-YAW M2 -TFG WITH SUBDEGREE-PER-HOUR ALLAN DEVIATION BIAS INSTABILITY
Fig. 9.
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Collection of plots showing mode matching of the 40-μm-thick SOI M2 -TFG prototype.
Fig. 10. Temperature variation of the individual operating resonant modes. TABLE II MEASURED OPERATING-MODE Q-FACTOR WITH TEMPERATURE Fig. 11. Temperature variation of the mode-matched resonant peak.
CMOS–IC implementing the drive and sense loop of the M2 -TFG has been demonstrated in [12]. A. Scale-Factor Measurements The setup used to measure the rotation rate sensitivity of the M2 -TFG device is shown in Fig. 13. An ideal Aerosmith singleaxis rate table (Model 1291 BR) was used to generate rotation signals at various rates. The rotation rate sensitivity response of a 40-μm-thick M2 -TFG under mode-matched operation and a fully differential configuration (using four sense electrodes) are shown in Fig. 14. The inset shows the signal observed at one sense electrode. The perfectly mode-matched device with QEFF of 42 000 exhibits a rate sensitivity of 20 mV/◦ /s (with post-TIA gain stage of ten). Fig. 15 shows the response of the M2 -TFG to a 6◦ /s 100-mHz sinusoidal input rotation signal. B. Allan Variance Analysis The scale factor of the M2 -TFG is a direct function of the mode-matched Q and its stability over time. It was experi-
mentally verified that the measured QEFF remained constant at the initial value of 42 000 over an extended period of time (under constant temperature and vacuum). The ZRO of a modematched M2 -TFG was sampled every 100 ms for a period of 12 h. The normalized bias value of the gyroscope is shown in Fig. 16. The initial 1 h of data were rejected to allow the system to stabilize at the set temperature. The remaining data were used for Allan variance analysis to characterize the long-term stability of the mode-matched device (interfaced with discrete electronics). The root Allan variance plot of the M2 -TFG is shown in Fig. 17. From this graph, the estimated angle random walk is determined to be 0.045◦ /hr while the measured bias instability of the system, without applying any prewhitening or filtering, is 0.96◦ /hr [20]. C. Dynamic Range and Bandwidth Control At perfect mode-matched operation, the linear dynamic range of the 40-μm device is ±20◦ /s for the drive-mode amplitude (xdrive ) of 3 μm, and the effective sensor bandwidth is 0.5 Hz. Such specifications are compatible with high-precision measurement and calibration functions such as gyrocompassing and platform stabilization [20]. While perfect mode matching provides exceptional enhancements in bias stability, it places certain limitations on the dynamic range
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Fig. 12. Schematic of the interface signal-processing circuitry for the M2 -TFG.
Fig. 14. Rate sensitivity plot for the M2 -TFG under mode-matched operation. (Inset) Signal at one sense electrode. Fig. 13. Experimental setup of the M2 -TFG.
and sensor bandwidth—critical parameters to other gyroscope applications such as commercial/automotive electronics and navigation/guidance systems. The advantage of the M2 -TFG mode-matching scheme is that the high gain that is achieved by leveraging the QEFF can be traded off for increased linear dynamic range and sensor bandwidth. Equation (2) gives the expression for the current measured at the sense channel in response to a rotation signal ISENSE =
2VP Cs0 QEFF Xdrive Ωz ds0
(2)
with other parameters such as polarization voltage (VP ), initial rest gap (ds0 ), and operating frequency kept relatively constant; the scale factor can be controlled by varying the QEFF . As
Fig. 15.
Device response to sinusoidal input rotation signal.
described in [13], this may be accomplished by introducing a controlled mismatch between the drive and sense resonantmode frequencies by slightly varying the VP . Fig. 18 shows
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Fig. 19. Scale-factor comparison under two different matched conditions. Fig. 16. Time-domain plot of the ZRO (recorded at 25
◦ C).
TABLE III PERFORMANCE COMPARISON OF 40-μm M2 -TFG UNDER TWO DIFFERENT MATCHING CONDITIONS
TABLE IV PARAMETER COMPARISON OF M2 -TFG IMPROVEMENTS
Fig. 17. Root Allan variance plot of the 40-μm M2 -TFG prototype.
Fig. 18. Near mode-matched operation. (Inset) Two-hertz frequency split.
the frequency response of a second 40-μm M2 -TFG device with similar resonant-mode Q’s but operated with a 2-Hz mode mismatch (i.e., Δf ∼ 2 Hz). As shown, the QEFF is
now ∼10 000, which is still significantly higher than other micromachined gyroscopes conventionally operated with a few percent of mode mismatch. Fig. 19 shows a comparison of the scale-factor plots for the sensor with a frequency split of 2 Hz and the mode-matched case. While the linear operating range for the mode-matched case is limited to under ±50◦ /s, it is increased to ±150◦ /s when the bandwidth is increased to 2 Hz (both measurements done at reduced drive amplitude of approximately 1 μm). The scale factor has decreased to 7.2 mV/◦ /s. It must be noted that the scale factors observed in this graph have been electronically compensated (post-TIA gain of 36) to account for reduction in drive amplitude. The bias drift for the M2 -TFG under both the conditions were compared using the Allan variance technique. Due to the reduction in QEFF , the bias drift for the 2-Hz bandwidth case was 4.1◦ /hr as compared to approximately 1◦ /hr recorded for the perfectly mode-matched case (when operated using drive amplitude approaching 3 μm). The topic of bandwidth control
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Fig. 20. (Left) SEM overview of the 60-μm-thick M2 -TFGs. (Right) Sense capacitance area enhancement in detail.
Fig. 22.
Fig. 21. Measured mode-matched Q for the 60-μm SOI M2 -TFG.
of the M2 -TFG is currently under investigation. In [21], the authors attempt to enhance device bandwidth by introducing a controlled mode splitting. Table III compares performance metrics of two M2 -TFGs operating under varying mode-matched conditions. VI. D EVICE -P ERFORMANCE E NHANCEMENT Several avenues of device-performance enhancement exist in the M2 -TFG design. By ensuring a larger proof-mass, drive amplitude, and improved sense-gap aspect ratio, it is possible to improve the device Brownian noise floor and sensitivity and reduce operating voltage requirements. Table IV summarizes a list of optimizations made to the M2 -TFG design on a 60-μm SOI substrate. Another critical aspect of the new prototypes was the sense-capacitance enhancements as shown in Fig. 20. The mode-matched resonant peak of the 60-μm-thick M2 -TFG prototype in vacuum is shown in Fig. 21. By optimizing the flexural dimensions, it is possible to maintain the same operating frequency regime, thereby ensuring
Rate-sensitivity plot of the 60-μm SOI M2 -TFG.
high-Q mode-matched operation demonstrated from its 40-μmthick predecessors. The scale-factor plot of the 60-μm-thick SOI M2 -TFG, shown in Fig. 22, displays a measured sensitivity of approximately 83 mV/◦ /s (with post-TIA gain stage of four). Owing to increased drive amplitude (5 μm), high QEFF (36 000), and larger aspect ratio sense gaps (∼17 : 1), the sense-channel output displays nonlinearity at rates approaching ±5◦ /s. Allan variance analysis was performed with ZRO data collected over a period of 12 h and at three constant-temperature settings. In each case, the 60-μm-thick SOI M2 -TFG prototype was operated under mode-matched operation with drive amplitude of 5 μm. As shown in Fig. 23, the device has a bias instability of 0.15◦ /hr at room temperature (25 ◦ C), which is the best reported for a MEMS vibratory gyroscope to date. The bias instability degraded at 50 ◦ C, which is primarily caused by reduction of the device quality factor at elevated temperatures. At 5 ◦ C, the M2 -TFG prototype displayed an enhanced bias instability of only 0.09◦ /hr. Sub-0.1◦ /hr bias drift allows integration of MEMS gyroscopes into high-precision applications such as gyrocompassing—something that has been challenging in the past due to performance limitations.
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Fig. 23. Root Allan variance plot of the 60-μm M2 -TFG at three different temperature settings.
VII. C ONCLUSION This paper has presented the design, implementation, and characterization of a subdegree-per-hour MEMS gyroscope ideal for gyrocompassing and potentially compatible with short-range navigation and guidance systems. The in-plane silicon M2 -TFG has an optimized design which employs two high-Q resonant modes operating under matched-mode condition. The M2 -TFG represents the first reported implementation of perfect mode matching (zero-hertz frequency split) in vibratory gyroscopes operating under nondegenerate resonant modes. The M2 -TFG design has all the required attributes for a high-precision gyroscope—a large resonant mass enabled by the fabrication process, high-Q resonant modes through optimized flexural design, and increased drive amplitude via combdrive electrodes. Prototype devices were fabricated on 40- and 60-μm-thick silicon device layers of SOI substrates. Characterization of a 40-μm-thick M2 -TFG under varying-frequency split-mode operation was performed to highlight the significance of mode matching. Finally, an optimized version of the M2 -TFG design implemented using 60-μm-thick SOI substrate displayed a bias drift of 0.15◦ /hr which is the best performance reported to date for micromachined silicon vibratory gyroscope. ACKNOWLEDGMENT The authors would like to thank the staff at the Georgia Tech Microelectronics Research Center for their support and Dr. B. Vakili Amini and M. Zurcher for their helpful discussions and suggestions pertaining to the project. R EFERENCES [1] N. Yazdi, F. Ayazi, and K. Najafi, “Micromachined inertial sensors,” Proc. IEEE, vol. 86, no. 8, pp. 1640–1659, Aug. 1998. [2] J. Bernstein et al., “A micromachined comb-drive tuning fork rate gyroscope,” in Proc. IEEE MEMS, 1993, pp. 143–148. [3] H. Xie and G. Fedder, “A DRIE CMOS–MEMS gyroscope,” in Proc. IEEE Sensors, 2002, pp. 1413–1416.
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[4] S. Bhave et al., “An integrated, vertical-drive, in-plane-sense microgyroscope,” in Proc. IEEE Transducers, 2003, pp. 171–174. [5] IEEE Standard Specification Format Guide and Test Procedure for Coriolis Vibratory Gyros. IEEE Standard 1431–2004. [6] M. F. Zaman, A. Sharma, and F. Ayazi, “High performance matched-mode tuning fork gyroscope,” in Proc. IEEE MEMS, 2006, pp. 66–69. [7] O. Schwarzelbach et al., “New approach for resonant frequency matching of tuning fork gyroscopes by using a non-linear drive concept,” in Proc. IEEE Transducers, 2001, pp. 464–467. [8] Y. Mochida, M. Tamura, and K. Ohwada, “A micromachined vibrating rate gyroscope with independent beams for the drive and detection modes,” in Proc. IEEE MEMS, 1999, pp. 618–623. [9] F. Ayazi and K. Najafi, “A HARPSS polysilicon vibrating ring gyroscope,” J. Microelectromech. Syst., vol. 10, no. 2, pp. 169–179, Jun. 2001. [10] M. F. Zaman et al., “The resonating star gyroscope,” in Proc. IEEE MEMS, 2005, pp. 355–358. [11] K. Park et al., “Laterally oscillated and force-balanced micro vibratory rate gyroscope supported by fish-hook-shaped springs,” Sens. Actuators A, Phys., vol. 64, no. 1, pp. 69–76, Jan. 1998. [12] A. Sharma, M. F. Zaman, and F. Ayazi, “A 104-dB dynamic range transimpedance-based CMOS ASIC for tuning fork microgyroscopes,” IEEE J. Solid-State Circuits, vol. 42, no. 8, pp. 1790–1802, Aug. 2007. [13] A. Sharma, M. F. Zaman, and F. Ayazi, “A 0.2◦ /hr micro-gyroscope with automatic CMOS mode matching,” in Proc. ISSCC, 2007, pp. 386–387. [14] Z. Hao et al., “Energy loss mechanisms in a bulk-micromachined tuning fork gyroscope,” in Proc. IEEE Sensors, 2006, pp. 1333–1336. [15] Z. Hao, A. Erbil, and F. Ayazi, “An analytical model for support loss in micromachined beam resonators with in-plane flexural vibrations,” Sens. Actuators A, Phys., vol. 109, no. 1, pp. 156–164, Dec. 2003. [16] S. McAuley et al., “Silicon micromachining using a high-density plasma source,” J. Phys. D, Appl. Phys., vol. 34, no. 18, pp. 2769–2774, Sep. 2001. [17] K. Miller et al., SOIMUMPS Design Handbook. [Online]. Available: http://www.memscap.com/mumps/documents/SOIMUMPs.dr.v4.pdf [18] W. A. Clark, “Micromachined vibratory rate gyroscopes,” Ph.D. dissertation, Univ. California, Berkeley, CA, 1997. [19] B. Kim et al., “Temperature dependence of quality factor in MEMS resonators,” in Proc. IEEE MEMS, 2006, pp. 590–593. [20] G. Beck, Navigation Systems. New York: Van Nostrand, 1979. [21] A. Sharma, M. F. Zaman, and F. Ayazi, “A smart angular rate sensor system,” in IEEE Sensors Conf. Tech. Dig., Atlanta, GA, Oct. 2007, pp. 1116–1119.
Mohammad Faisal Zaman (S’98–M’08) received the B.S. (with high honors) and Ph.D. degrees in electrical and computer engineering from Georgia Institute of Technology, Atlanta, in 2002 and 2008, respectively. His doctoral work encompassed the design, fabrication, and analysis of high-precision MEMS inertial sensors. He is currently a Microelectromechanical System Engineer with Qualtré Inc., Atlanta, GA. Dr. Zaman is a member of the Eta Kappa Nu.
Ajit Sharma (S’01–M’08) received the B.E. (Hons.) degree in electrical engineering from the Birla Institute of Technology and Science, Pilani, India, in 2001, the M.S. degree in electrical engineering from Oregon State University, Corvallis, in 2003, and the Ph.D. degree in electrical engineering from the Georgia Institute of Technology, Atlanta, in 2007. He is currently an IC Designer with the MixedSignal Automotive Group of Texas Instruments Incorporated, Dallas, TX. He has held co-op positions at Infineon Technologies, Singapore, Biotronik Inc., Lake Oswego, OR, and Texas Instruments Incorporated, Dallas, TX. His master’s research focused on the prediction of substrate noise coupling in mixed-signal SOCs and his doctoral work involved the design of low-power and low-noise mixed-signal CMOS systems for high-precision MEMS inertial sensors. His research interests are in the areas of analog circuits, smart sensors, microsystem modeling/simulation, and MEMS-based systems-on-chip. Dr. Sharma is a recipient of the Texas Instruments Analog Fellowship for the years 2003–2007 and the IEEE Sensors 2007 Best Student Paper Award.
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Zhili Hao (M’02) received the B.S. and M.S. degrees in mechanical engineering from Shanghai Jiao Tong University, Shanghai, China, in 1994 and 1997, respectively, and the Ph.D. degree from the Department of Mechanical, Materials and Aerospace Engineering, University of Central Florida, Orlando, in 2000. Following graduation, she worked as a MEMS Engineer in industry for two years and was involved in the development of optical MEMS and microfluidic products. From December 2002 to June 2006, she was with the Integrated MEMS Laboratory, School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta. She is currently an Assistant Professor in the Department of Mechanical Engineering, Old Dominion University, Norfolk, VA. Her research interests are in the investigation of micromechanics, such as energy loss mechanisms in MEMS resonators, and the development of various MEMS devices for inertial sensing, bio/chemical sensing, and wireless communications.
Farrokh Ayazi (S’96–M’00–SM’05) received the B.S. degree in electrical engineering from the University of Tehran, Tehran, Iran, in 1994, and the M.S. and Ph.D. degrees in electrical engineering from the University of Michigan, Ann Arbor, in 1997 and 2000, respectively. Since December 1999, he has been with the faculty of Georgia Institute of Technology, Atlanta, where he is currently an Associate Professor with the School of Electrical and Computer Engineering. He is a Cofounder and the Chief Technical Officer of Qualtré Inc., Atlanta, which is a spinout of his research laboratory that commercializes three-axis microgyroscopes and six-degrees-of-freedom motion sensors for consumer electronics and personal navigation devices. His research interests are in the areas of integrated micro- and nanoelectromechanical resonators, IC design for microelectromechanical system (MEMS) and sensors, RF MEMS, inertial sensors, and microfabrication techniques. Prof. Ayazi is an Editor of the JOURNAL OF MICROELECTROMECHANICAL SYSTEMS and serves on the Technical Program Committees of the IEEE International Solid State Circuits Conference (ISSCC) and the International Conference on Solid State Sensors, Actuators and Microsystems (Transducers). He was the recipient of the National Science Foundation CAREER Award in 2004, the 2004 Richard M. Bass Outstanding Teacher Award (determined by the vote of the ECE senior class), and the Georgia Tech College of Engineering Cutting Edge Research Award for 2001–2002. He was also a recipient of the Rackham Predoctoral Fellowship from the University of Michigan for 1998–1999.
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A Mode-Matched Silicon-Yaw Tuning-Fork Gyroscope With Subdegree-Per-Hour Allan Deviation Bias Instability Mohammad Faisal Zaman, Member, IEEE, Ajit Sharma, Member, IEEE, Zhili Hao, Member, IEEE, Member, ASME, and Farrokh Ayazi, Senior Member, IEEE
Abstract—In this paper, we report on the design, fabrication, and characterization of an in-plane mode-matched tuning-fork gyroscope (M2 -TFG). The M2 -TFG uses two high-quality-factor (Q) resonant flexural modes of a single crystalline silicon microstructure to detect angular rate about the normal axis. Operating the device under mode-matched condition, i.e., zero-hertz frequency split between drive and sense modes, enables a Q-factor mechanical amplification in the rate sensitivity and also improves the overall noise floor and bias stability of the device. The M2 -TFG is fabricated on a silicon-on-insulator substrate using a combination of device and handle-layer silicon etching that precludes the need for any release openings on the proof-mass, thereby maximizing the mass per unit area. Experimental data indicate subdegree-per-hour Brownian noise floor with a measured Allan deviation bias instability of 0.15◦ /hr for a 60-μm-thick 1.5 mm × 1.7 mm footprint M2 -TFG prototype. The gyroscope exhibits an open-loop rate sensitivity of approximately 83 mV/◦ /s in vacuum. [2007-0100] Index Terms—Mode-matching, silicon-on-insulator (SOI), tuning fork, vibratory microgyroscope.
I. I NTRODUCTION
M
ICROMACHINED gyroscopes constitute one of the fastest growing segments of the microsensor market. The application domain of these devices is rapidly expanding from automotive to consumer electronics and personal navigation systems. Small form factor, light weight, and low power consumption make micromachined gyroscopes ideal for use in handheld applications, many of which require multiaxis sensitivity. Gaming consoles, image stabilization in digital cameras, and traction control systems in automobiles represent applications in which angular-rate resolution on the order of Manuscript received May 11, 2007; revised November 16, 2007, April 28, 2008, and July 21, 2008. First published September 30, 2008; current version published December 4, 2008. This work was supported by the DARPA HERMIT Program under Contract W31P4Q-04-1-R001. Subject Editor G. K. Fedder. M. F. Zaman was with the School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0250 USA. He is now with Qualtré, Inc., Atlanta, GA 30308 USA (e-mail: [email protected]). A. Sharma is with Texas Instruments Incorporated, Dallas, TX 75243 USA (e-mail: [email protected]). Z. Hao is with the Department of Mechanical Engineering, Old Dominion University, Norfolk, VA 23529-0246 USA (e-mail: [email protected]). F. Ayazi is with the School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0250 USA, and also with Qualtré, Inc., Atlanta, GA 30308 USA (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/JMEMS.2008.2004794
0.1◦ /s is sufficient. Microelectromechanical-system (MEMS) gyroscopes, however, have yet to break into the high-precision market that requires sub-0.1◦ /hr resolution and bias stability. Applications in this area include gyrocompassing, the process of utilizing the Earth’s rotation to determine the direction of true north. Other applications include short-range navigation (in the absence of the GPS signal) and guidance deployed in autonomous vehicles [1]. Micromachined vibratory gyroscopes are based on the Coriolis induced transfer of energy between two vibration modes of a microstructure. They can operate in either mode-matched or split-mode condition. Under mode-matched condition, the sense mode is designed to have the same (or nearly the same) resonant frequency as the drive mode. Hence, the rotationinduced Coriolis signal is amplified by the mechanical quality factor of the sense mode. In split-mode condition, the drive and sense modes are separated in resonant frequency. The sense mode is then a controlled mode that operates similar to an accelerometer and measures the Coriolis acceleration [2]–[4]. Due to Q-factor amplification, gyroscopes operated under mode-matched configuration offer higher sensitivity and better resolution. Resonant-matched devices are themselves further classified into two types, depending upon the nature of their operating modes [5]. Class-I devices rely on nondegenerate vibration modes for driving and sensing. Tuning-fork and frame gyroscopes are examples of class-I gyroscopes [6]–[8]. Class-II devices, such as shell-type gyroscopes, on the other hand, function with degenerate vibration modes [9], [10]. Gyroscope resolution, along with bias stability, sensitivity, and bandwidth, play an important role in defining its application area. A review of the noise expressions in [9] highlights the key parameters that affect performance. In order to attain the subdegree-per-hour noise performance, a vibratory gyroscope must attain high-Q mode-matched operation, large resonant proof-mass, and large drive amplitude. In this paper, the authors introduce the mode-matched tuning-fork gyroscope (M2 -TFG): an in-plane single crystalline silicon yaw-rate tuning-fork device that incorporates all the earlier specifications within a single framework. The concept and operation of the M2 -TFG is discussed in Section II. Section III describes the micromachining processes involved in the fabrication of prototype devices. Characterization results of the operating resonant modes of the M2 -TFG are the subject of Section IV, while Section V deals with the examination of microsystem performance. This paper
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Fig. 1. SEM overview of an M2 -TFG implemented on 40-μm-thick SOI substrate.
concludes with the performance summary of an optimized M2 TFG design in Section VI. II. D ESIGN The M2 -TFG, as shown in the SEM image in Fig. 1, is comprised of two proof-masses, supported by a network of flexural springs, and anchored at a central post. A collection of capacitive control electrodes is symmetrically distributed around the proof-masses. The operating principle is based upon a standard tuning fork’s response to rotation. The two proof-masses are analogous to tines and driven in-plane into resonance along the x-axis using electrostatic comb-drive electrodes. An input rotation signal normal to the device plane (along z-axis) causes a Coriolis induced transfer of energy to the sense vibration mode. The resulting in-plane displacement is sensed capacitively at sense electrodes located along the y-axis. The operating mode shapes of the M2 -TFG may be viewed as shown in Fig. 2. An advantage in utilizing a symmetric tuning-fork architecture is the inherent differential nature of the sense mode. As a result, linear acceleration is rejected as common mode signal without the need for complex electronics. The anchor design of the M2 -TFG satisfies two critical properties: mechanical coupling and resonant-mode isolation. The mechanical coupling, promoted by the central ladder-shaped anchor structure, allows synchronization of the phases of the proof-masses even in the presence of minor fabrication imperfections. The second important function enabled by the anchor is the isolation of the in-plane operating modes from the two other existing inplane resonant modes. These are the pseudodrive mode (both proof-masses vibrate along the drive axis in the same direction) and the pseudosense mode (both proof-masses vibrate along the sense axis in the same direction). These two modes correspond to the symmetric and antisymmetric modes of a tuning-fork structure and are also influenced by Coriolis acceleration. In the current M2 -TFG design, these modes occur at least 200 Hz away from the operating modes of interest.
Fig. 2. Resonant in-plane operating modes of the M2 -TFG (motion exaggerated for clarity).
The flexural-spring design must satisfy a host of critical properties. The ideal spring design must ensure large mobility along both axes. To this effect, a fishhook architecture was adopted which ensures that the mode shapes have two directional flexibility [11]. The current spring structure enables 4–6-μm drive-mode displacements. The second important criterion is to ensure that the two operating-mode frequencies lie in close proximity to one another while remaining isolated from the out-of-plane resonant modes. Detailed finite-element analysis simulations of the flexural springs and anchor were performed in ANSYS to optimize the dimensions to allow the sense mode to occur 50–150 Hz higher than the drive mode. Upon fabrication, the sense-mode frequency is electrostatically tuned to match the drive-mode frequency. A key performance parameter of vibratory gyroscopes is the mechanical quality factor (Q) of its operating modes. In order to achieve higher sensitivity and better rate resolution and drift, the design of gyroscopes with large sense-mode Q is pursued. A large drive-mode Q is also necessary for improved bias stability as well as ensuring large drive amplitudes using small drive voltages—a desirable feature required in low-power CMOS interfacing [12], [13]. The energy-dissipation mechanisms associated with the M2 -TFG design are air damping, support loss, thermoelastic damping (TED), surface loss, and the intrinsic loss of silicon. Hence, the overall mechanical Q for an operating mode is expressed as the sum of all these contributions. 1 1 1 1 = + + Q QAir Damping QSupport QTED 1 1 + + . (1) QSurface QIntrinsic Among them, the effect of air damping may be eliminated by operating the gyroscope in vacuum, while the contribution of
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Fig. 3. Outline of the fabrication process flow for SOI M2 -TFG.
Fig. 4. (a) Close-up of the drive and sense gaps and (b) view of the anchor support posts (as seen from handle layer) for a 40-μm-thick SOI prototype.
surface loss can be made negligible through optimized processing. With QIntrinsic being very high in silicon, this leaves TED and support loss as the primary loss mechanisms in the M2 -TFG design. By simplifying the structure, one may identify basic trends required to operate in a region of high QTED . As shown in Fig. 2, during the flexural vibrations in the operating resonant modes, the proof-masses only undergo translational motion. The spring structures, unlike the proof-masses, experience structural deformation. Half the tuning-fork structure in each operating mode may be viewed as a beamlike resonator with an added proof-mass symmetric with respect to the centerline. This simplified model was utilized to estimate the TED of the structure [14]. The mechanism responsible for TED in solids is the lack of thermal equilibrium between various parts of the vibrating solid. Based on the theory of linear thermoelasticity, the governing equations for thermoelastic uncoupled flexuralmode vibrations in a beamlike resonator with added proofmass are the same as that of a simple flexural beam. The addition of the proof-mass modifies the resonant frequency (ω0 ). The QTED in the M2 -TFG structure may be estimated from the equation of a simple flexural beam expressed in [14]. The QTED is a function of the flexural-spring width (b) and the operating frequency (ω0 ). In the current M2 -TFG design, the flexural-spring dimensions and operating-frequency regime were tactically selected to operate in a region away from the Debye peak of the QTED curve. During resonant flexural vibrations, the proof-masses exert a time-harmonic load on the support structure. Acting as an excitation source, this time-harmonic load excites elastic waves propagating through the support. The vibration energy dissipated through elastic-wave propagation in the support media represents the support loss. The complexity of the anchor geometry and composition prevented an accurate analysis of the
support loss. However, the flexural beams were designed with high-aspect ratio to minimize support loss [15]. III. F ABRICATION The prototype M2 -TFGs are implemented on an silicon-oninsulator (SOI) substrate. The fabrication-process flow is shown in Fig. 3. The moving sections of the structure and the area under the comb drives are first released from the rear by etching the handle silicon layer through to the buried-oxide layer using the Bosch process. The buried oxide is then removed in a reactive-ion-etching system. Finally, the device layer is patterned all the way through; leaving behind a suspended structure whose anchor is supported to the substrate via support posts. SEM images of fabricated M2 -TFG are shown in Figs. 1 and 4. The device-layer silicon etching was performed using the advanced-silicon-etch process developed by surface technology systems. At high plasma densities, the silicon-etch profile tends to have a high lateral etch rate at the Si−SiO2 interface, an effect commonly referred to as notching. Eliminating the buriedoxide layer underneath the M2 -TFG area prevents structural damage via notching (as shown in Fig. 5). However, it does not prevent notching from occurring at the oxide interface in the electrode boundaries. The resultant accumulation of silicon debris compromises electrical isolation. Notching arises as a result of deflection of incoming ions onto the sidewalls due to charge build-up at the surface of the buried oxide. By reducing the operating RF frequency from 13.56 MHz to 380 kHz, it is possible to generate a surplus of low-energy ions. These low-energy ions are able to neutralize the excess charge build-up resulting in debris-free electrode trenches [16]. By ramping RF platen power and adjusting etchant flow rates, it was possible to attain a trench aspect ratio as high as 18 : 1
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Fig. 5.
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View of the flexural springs observed from the handle-layer openings.
with the low-frequency RF module. A short HF etch was performed to release areas under the anchor support posts shown in Fig. 4(b). The fabrication process, an improvization of the SOI– MUMPS process [17], is simple and precludes the requirement of any perforations in the proof-mass, resulting in a larger mass per unit area. The simultaneous elimination of the ground plane under the comb drives prevents the excitation of the out-of-plane modes and detrimental effects associated with comb levitation. The fact that all the electrodes and the structure are defined using a single mask ensures that there are no horizontal misalignment errors of actuation/ sense gaps. IV. D EVICE C HARACTERIZATION Preliminary open-loop characterization of the M2 -TFG is performed using dedicated analog front-end electronics (AFE) implemented by means of discrete amplifiers. The M2 -TFG die is mounted on the AFE board and wire bonded to pads that interface with transimpedance amplifiers. This AFE board is then placed in the vacuum chamber, and device characterization is performed. The devices were characterized in 1-mtorr vacuum, and an Agilent 4395A network analyzer was used to measure the frequency response. The measured drive and sense resonant modes for a prototype 40-μm-thick M2 -TFG are shown in Fig. 6. In this particular device, the driveand sense-mode Q’s were measured as 78 000 and 45 000, respectively. As shown in Fig. 2, the vibrations in the drive resonant mode effectively ensure force cancellation at the anchor. However, the vibrations in the sense resonant mode introduce forces to the anchor regions. These forces are offcenter and lead to a net torque along the support structure. As a result, the drivemode Q is expected to be higher than the sense-mode Q due to effective torque cancellation. This fact has been verified in Table I which tabulates the average Q values recorded over five samples in two batches of 40-μm-thick M2 -TFGs. In addition, as predicted from [14], a device with larger beamwidth displays lower Q-factor operating modes. A. Mode Matching and Quadrature Nulling Mode matching is performed by increasing the dc polarization voltage (VP ) on the MEMS structure until electrostatic
Fig. 6. Measured (top) drive and (bottom) sense resonant-mode Q. TABLE I MEASURED FREQUENCY AND Q FOR TWO BATCHES OF M2 -TFGs
spring softening decreases the sense-mode frequency to become equal to the drive-mode frequency. The capacitive clearance between the drive-mode flexures and the sense electrodes are large enough to ensure that the drive mode remains relatively constant as shown in Fig. 7. Despite an optimized flexural design, in practice, fabrication imperfections can lead to nonzero offdiagonal elements in the spring stiffness and damping-coefficient matrices. This results in an undesirable zero-rate output (ZRO) signal commonly referred to as quadrature. Quadrature error prevents perfect overlap of the drive and sense resonant modes. Only through the minimization of this error component will near-perfect mode matching be possible [18]. Unlike Coriolis acceleration, which is proportional to the proof-mass velocity, quadrature errors are
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B. Temperature Characterization
Fig. 7. Calculated tuning characteristics of M2 -TFG sense and drive modes.
In order to ensure high performance, it is essential that mode matching is maintained over temperature. The M2 -TFG was tested under both matched- and split-mode conditions to accurately determine the effects of temperature on the operating modes. Fig. 10 shows the measured frequency variation of the individual unmatched resonant modes of a M2 -TFG prototype (beamwidth ∼ 21 μm, f0 ∼ 18.4 kHz) as a function of temperature. Such frequency variation is attributed to the temperature dependence of Young’s modulus of single crystalline silicon substrate. The drive-mode temperature coefficient of frequency (TCF) is measured to be—21.75 ppm/◦ C. The TCF of the drive and sense resonant modes vary by less than 1 ppm/◦ C. Table II highlights Q-factor degradation in individual operating resonant modes at increased temperatures. This observation is attributed to elevated TED [19]. A separate M2 -TFG device under mode-matched condition (operating at 15 kHz) was also subjected to the TCF measurement test (see Fig. 11). Mode matching is maintained over the temperature range of 25–100 ◦ C (without requiring any closed-loop quadrature compensation or frequency tuning). Hence, a single temperature-compensation circuit will suffice to maintain mode matching over temperature. A mode-matched Q-factor degradation was observed at elevated temperature similar to the split-mode characterization.
V. P ERFORMANCE A NALYSIS
Fig. 8. View of the quadrature minimization electrodes of the 40-μm-thick SOI M2 -TFG prototype.
accelerations attributed to the proof-mass position. Quadratureminimization electrodes are situated at corners of each proofmass. Reducing quadrature error requires electrostatic forces which are in phase with the motion of the proof-mass while in drive-mode resonance. The forcing function can be accomplished by slightly unbalancing the bias voltages applied to the structure for mode matching (as shown in Fig. 8). This force is directly proportional to the proof-mass displacement (i.e., a time-varying force). By adjusting VQ at one of the two electrodes, it is possible to align the proof-masses by reducing the offdiagonal components of the stiffness matrix of the system [13]. In the current mode-matching implementation, typical values of VQ and |VP ± VQ | are approximately ±20 and 10–20 V, respectively. From an initial separation of approximately 60 Hz, the drive and sense frequencies were matched electronically by varying the polarization voltage and adjusting the appropriate quadrature voltages as shown in Fig. 9. Mode matching is achieved to within the precision of the measurement setup and equipment (better than 0.1 Hz). The M2 -TFG is the first reported high-Q mode-matched implementation (i.e., zero-hertz frequency split) of a class-I vibratory microgyroscope [6].
In order to extract the rotation-rate information from the sense electrodes, a considerable amount of signal processing is required. The signal-processing circuitry shown in Fig. 12 has been implemented using discrete electronic components and consists of two main blocks: 1) drive loop to maintain resonance in the drive mode and 2) sense channel that extracts the rotation rate from the output at the sense electrodes. The drive loop uses a digital phase-locked loop (PLL) to lock to the drive resonant frequency and supplies the actuation voltage to the drive-comb electrodes. The variable gain amplifier maintains constant drive amplitude and prevents overdriving the sensor. The front-end of the M2 -TFG sense channel is comprised of two discrete transimpedance amplifier chains that process signals from a pair of mechanically differential-sense electrodes, as shown in Fig. 12. There is an additional adjustable gain stage immediately beyond the transimpedance front-end (not shown). Any offset that manifests itself on each signal chain is cancelled before being fed into the differential amplifier. The sense channel further consists of a synchronous demodulator to extract the rate signal from the sensor output. The PLL generates a signal that is in phase with the drive velocity. This square wave is used in a synchronous demodulator and mixed with the incoming signal from the sensor and, subsequently, low passed filtered to obtain the rate signal. A synchronous demodulator maintains inherent phase information while demodulating the AM signal. This phase relationship is used to distinguish between the rotation rate and quadrature signal. A customized
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Fig. 9.
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Collection of plots showing mode matching of the 40-μm-thick SOI M2 -TFG prototype.
Fig. 10. Temperature variation of the individual operating resonant modes. TABLE II MEASURED OPERATING-MODE Q-FACTOR WITH TEMPERATURE Fig. 11. Temperature variation of the mode-matched resonant peak.
CMOS–IC implementing the drive and sense loop of the M2 -TFG has been demonstrated in [12]. A. Scale-Factor Measurements The setup used to measure the rotation rate sensitivity of the M2 -TFG device is shown in Fig. 13. An ideal Aerosmith singleaxis rate table (Model 1291 BR) was used to generate rotation signals at various rates. The rotation rate sensitivity response of a 40-μm-thick M2 -TFG under mode-matched operation and a fully differential configuration (using four sense electrodes) are shown in Fig. 14. The inset shows the signal observed at one sense electrode. The perfectly mode-matched device with QEFF of 42 000 exhibits a rate sensitivity of 20 mV/◦ /s (with post-TIA gain stage of ten). Fig. 15 shows the response of the M2 -TFG to a 6◦ /s 100-mHz sinusoidal input rotation signal. B. Allan Variance Analysis The scale factor of the M2 -TFG is a direct function of the mode-matched Q and its stability over time. It was experi-
mentally verified that the measured QEFF remained constant at the initial value of 42 000 over an extended period of time (under constant temperature and vacuum). The ZRO of a modematched M2 -TFG was sampled every 100 ms for a period of 12 h. The normalized bias value of the gyroscope is shown in Fig. 16. The initial 1 h of data were rejected to allow the system to stabilize at the set temperature. The remaining data were used for Allan variance analysis to characterize the long-term stability of the mode-matched device (interfaced with discrete electronics). The root Allan variance plot of the M2 -TFG is shown in Fig. 17. From this graph, the estimated angle random walk is determined to be 0.045◦ /hr while the measured bias instability of the system, without applying any prewhitening or filtering, is 0.96◦ /hr [20]. C. Dynamic Range and Bandwidth Control At perfect mode-matched operation, the linear dynamic range of the 40-μm device is ±20◦ /s for the drive-mode amplitude (xdrive ) of 3 μm, and the effective sensor bandwidth is 0.5 Hz. Such specifications are compatible with high-precision measurement and calibration functions such as gyrocompassing and platform stabilization [20]. While perfect mode matching provides exceptional enhancements in bias stability, it places certain limitations on the dynamic range
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Fig. 12. Schematic of the interface signal-processing circuitry for the M2 -TFG.
Fig. 14. Rate sensitivity plot for the M2 -TFG under mode-matched operation. (Inset) Signal at one sense electrode. Fig. 13. Experimental setup of the M2 -TFG.
and sensor bandwidth—critical parameters to other gyroscope applications such as commercial/automotive electronics and navigation/guidance systems. The advantage of the M2 -TFG mode-matching scheme is that the high gain that is achieved by leveraging the QEFF can be traded off for increased linear dynamic range and sensor bandwidth. Equation (2) gives the expression for the current measured at the sense channel in response to a rotation signal ISENSE =
2VP Cs0 QEFF Xdrive Ωz ds0
(2)
with other parameters such as polarization voltage (VP ), initial rest gap (ds0 ), and operating frequency kept relatively constant; the scale factor can be controlled by varying the QEFF . As
Fig. 15.
Device response to sinusoidal input rotation signal.
described in [13], this may be accomplished by introducing a controlled mismatch between the drive and sense resonantmode frequencies by slightly varying the VP . Fig. 18 shows
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Fig. 19. Scale-factor comparison under two different matched conditions. Fig. 16. Time-domain plot of the ZRO (recorded at 25
◦ C).
TABLE III PERFORMANCE COMPARISON OF 40-μm M2 -TFG UNDER TWO DIFFERENT MATCHING CONDITIONS
TABLE IV PARAMETER COMPARISON OF M2 -TFG IMPROVEMENTS
Fig. 17. Root Allan variance plot of the 40-μm M2 -TFG prototype.
Fig. 18. Near mode-matched operation. (Inset) Two-hertz frequency split.
the frequency response of a second 40-μm M2 -TFG device with similar resonant-mode Q’s but operated with a 2-Hz mode mismatch (i.e., Δf ∼ 2 Hz). As shown, the QEFF is
now ∼10 000, which is still significantly higher than other micromachined gyroscopes conventionally operated with a few percent of mode mismatch. Fig. 19 shows a comparison of the scale-factor plots for the sensor with a frequency split of 2 Hz and the mode-matched case. While the linear operating range for the mode-matched case is limited to under ±50◦ /s, it is increased to ±150◦ /s when the bandwidth is increased to 2 Hz (both measurements done at reduced drive amplitude of approximately 1 μm). The scale factor has decreased to 7.2 mV/◦ /s. It must be noted that the scale factors observed in this graph have been electronically compensated (post-TIA gain of 36) to account for reduction in drive amplitude. The bias drift for the M2 -TFG under both the conditions were compared using the Allan variance technique. Due to the reduction in QEFF , the bias drift for the 2-Hz bandwidth case was 4.1◦ /hr as compared to approximately 1◦ /hr recorded for the perfectly mode-matched case (when operated using drive amplitude approaching 3 μm). The topic of bandwidth control
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Fig. 20. (Left) SEM overview of the 60-μm-thick M2 -TFGs. (Right) Sense capacitance area enhancement in detail.
Fig. 22.
Fig. 21. Measured mode-matched Q for the 60-μm SOI M2 -TFG.
of the M2 -TFG is currently under investigation. In [21], the authors attempt to enhance device bandwidth by introducing a controlled mode splitting. Table III compares performance metrics of two M2 -TFGs operating under varying mode-matched conditions. VI. D EVICE -P ERFORMANCE E NHANCEMENT Several avenues of device-performance enhancement exist in the M2 -TFG design. By ensuring a larger proof-mass, drive amplitude, and improved sense-gap aspect ratio, it is possible to improve the device Brownian noise floor and sensitivity and reduce operating voltage requirements. Table IV summarizes a list of optimizations made to the M2 -TFG design on a 60-μm SOI substrate. Another critical aspect of the new prototypes was the sense-capacitance enhancements as shown in Fig. 20. The mode-matched resonant peak of the 60-μm-thick M2 -TFG prototype in vacuum is shown in Fig. 21. By optimizing the flexural dimensions, it is possible to maintain the same operating frequency regime, thereby ensuring
Rate-sensitivity plot of the 60-μm SOI M2 -TFG.
high-Q mode-matched operation demonstrated from its 40-μmthick predecessors. The scale-factor plot of the 60-μm-thick SOI M2 -TFG, shown in Fig. 22, displays a measured sensitivity of approximately 83 mV/◦ /s (with post-TIA gain stage of four). Owing to increased drive amplitude (5 μm), high QEFF (36 000), and larger aspect ratio sense gaps (∼17 : 1), the sense-channel output displays nonlinearity at rates approaching ±5◦ /s. Allan variance analysis was performed with ZRO data collected over a period of 12 h and at three constant-temperature settings. In each case, the 60-μm-thick SOI M2 -TFG prototype was operated under mode-matched operation with drive amplitude of 5 μm. As shown in Fig. 23, the device has a bias instability of 0.15◦ /hr at room temperature (25 ◦ C), which is the best reported for a MEMS vibratory gyroscope to date. The bias instability degraded at 50 ◦ C, which is primarily caused by reduction of the device quality factor at elevated temperatures. At 5 ◦ C, the M2 -TFG prototype displayed an enhanced bias instability of only 0.09◦ /hr. Sub-0.1◦ /hr bias drift allows integration of MEMS gyroscopes into high-precision applications such as gyrocompassing—something that has been challenging in the past due to performance limitations.
ZAMAN et al.: SILICON-YAW M2 -TFG WITH SUBDEGREE-PER-HOUR ALLAN DEVIATION BIAS INSTABILITY
Fig. 23. Root Allan variance plot of the 60-μm M2 -TFG at three different temperature settings.
VII. C ONCLUSION This paper has presented the design, implementation, and characterization of a subdegree-per-hour MEMS gyroscope ideal for gyrocompassing and potentially compatible with short-range navigation and guidance systems. The in-plane silicon M2 -TFG has an optimized design which employs two high-Q resonant modes operating under matched-mode condition. The M2 -TFG represents the first reported implementation of perfect mode matching (zero-hertz frequency split) in vibratory gyroscopes operating under nondegenerate resonant modes. The M2 -TFG design has all the required attributes for a high-precision gyroscope—a large resonant mass enabled by the fabrication process, high-Q resonant modes through optimized flexural design, and increased drive amplitude via combdrive electrodes. Prototype devices were fabricated on 40- and 60-μm-thick silicon device layers of SOI substrates. Characterization of a 40-μm-thick M2 -TFG under varying-frequency split-mode operation was performed to highlight the significance of mode matching. Finally, an optimized version of the M2 -TFG design implemented using 60-μm-thick SOI substrate displayed a bias drift of 0.15◦ /hr which is the best performance reported to date for micromachined silicon vibratory gyroscope. ACKNOWLEDGMENT The authors would like to thank the staff at the Georgia Tech Microelectronics Research Center for their support and Dr. B. Vakili Amini and M. Zurcher for their helpful discussions and suggestions pertaining to the project. R EFERENCES [1] N. Yazdi, F. Ayazi, and K. Najafi, “Micromachined inertial sensors,” Proc. IEEE, vol. 86, no. 8, pp. 1640–1659, Aug. 1998. [2] J. Bernstein et al., “A micromachined comb-drive tuning fork rate gyroscope,” in Proc. IEEE MEMS, 1993, pp. 143–148. [3] H. Xie and G. Fedder, “A DRIE CMOS–MEMS gyroscope,” in Proc. IEEE Sensors, 2002, pp. 1413–1416.
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[4] S. Bhave et al., “An integrated, vertical-drive, in-plane-sense microgyroscope,” in Proc. IEEE Transducers, 2003, pp. 171–174. [5] IEEE Standard Specification Format Guide and Test Procedure for Coriolis Vibratory Gyros. IEEE Standard 1431–2004. [6] M. F. Zaman, A. Sharma, and F. Ayazi, “High performance matched-mode tuning fork gyroscope,” in Proc. IEEE MEMS, 2006, pp. 66–69. [7] O. Schwarzelbach et al., “New approach for resonant frequency matching of tuning fork gyroscopes by using a non-linear drive concept,” in Proc. IEEE Transducers, 2001, pp. 464–467. [8] Y. Mochida, M. Tamura, and K. Ohwada, “A micromachined vibrating rate gyroscope with independent beams for the drive and detection modes,” in Proc. IEEE MEMS, 1999, pp. 618–623. [9] F. Ayazi and K. Najafi, “A HARPSS polysilicon vibrating ring gyroscope,” J. Microelectromech. Syst., vol. 10, no. 2, pp. 169–179, Jun. 2001. [10] M. F. Zaman et al., “The resonating star gyroscope,” in Proc. IEEE MEMS, 2005, pp. 355–358. [11] K. Park et al., “Laterally oscillated and force-balanced micro vibratory rate gyroscope supported by fish-hook-shaped springs,” Sens. Actuators A, Phys., vol. 64, no. 1, pp. 69–76, Jan. 1998. [12] A. Sharma, M. F. Zaman, and F. Ayazi, “A 104-dB dynamic range transimpedance-based CMOS ASIC for tuning fork microgyroscopes,” IEEE J. Solid-State Circuits, vol. 42, no. 8, pp. 1790–1802, Aug. 2007. [13] A. Sharma, M. F. Zaman, and F. Ayazi, “A 0.2◦ /hr micro-gyroscope with automatic CMOS mode matching,” in Proc. ISSCC, 2007, pp. 386–387. [14] Z. Hao et al., “Energy loss mechanisms in a bulk-micromachined tuning fork gyroscope,” in Proc. IEEE Sensors, 2006, pp. 1333–1336. [15] Z. Hao, A. Erbil, and F. Ayazi, “An analytical model for support loss in micromachined beam resonators with in-plane flexural vibrations,” Sens. Actuators A, Phys., vol. 109, no. 1, pp. 156–164, Dec. 2003. [16] S. McAuley et al., “Silicon micromachining using a high-density plasma source,” J. Phys. D, Appl. Phys., vol. 34, no. 18, pp. 2769–2774, Sep. 2001. [17] K. Miller et al., SOIMUMPS Design Handbook. [Online]. Available: http://www.memscap.com/mumps/documents/SOIMUMPs.dr.v4.pdf [18] W. A. Clark, “Micromachined vibratory rate gyroscopes,” Ph.D. dissertation, Univ. California, Berkeley, CA, 1997. [19] B. Kim et al., “Temperature dependence of quality factor in MEMS resonators,” in Proc. IEEE MEMS, 2006, pp. 590–593. [20] G. Beck, Navigation Systems. New York: Van Nostrand, 1979. [21] A. Sharma, M. F. Zaman, and F. Ayazi, “A smart angular rate sensor system,” in IEEE Sensors Conf. Tech. Dig., Atlanta, GA, Oct. 2007, pp. 1116–1119.
Mohammad Faisal Zaman (S’98–M’08) received the B.S. (with high honors) and Ph.D. degrees in electrical and computer engineering from Georgia Institute of Technology, Atlanta, in 2002 and 2008, respectively. His doctoral work encompassed the design, fabrication, and analysis of high-precision MEMS inertial sensors. He is currently a Microelectromechanical System Engineer with Qualtré Inc., Atlanta, GA. Dr. Zaman is a member of the Eta Kappa Nu.
Ajit Sharma (S’01–M’08) received the B.E. (Hons.) degree in electrical engineering from the Birla Institute of Technology and Science, Pilani, India, in 2001, the M.S. degree in electrical engineering from Oregon State University, Corvallis, in 2003, and the Ph.D. degree in electrical engineering from the Georgia Institute of Technology, Atlanta, in 2007. He is currently an IC Designer with the MixedSignal Automotive Group of Texas Instruments Incorporated, Dallas, TX. He has held co-op positions at Infineon Technologies, Singapore, Biotronik Inc., Lake Oswego, OR, and Texas Instruments Incorporated, Dallas, TX. His master’s research focused on the prediction of substrate noise coupling in mixed-signal SOCs and his doctoral work involved the design of low-power and low-noise mixed-signal CMOS systems for high-precision MEMS inertial sensors. His research interests are in the areas of analog circuits, smart sensors, microsystem modeling/simulation, and MEMS-based systems-on-chip. Dr. Sharma is a recipient of the Texas Instruments Analog Fellowship for the years 2003–2007 and the IEEE Sensors 2007 Best Student Paper Award.
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Zhili Hao (M’02) received the B.S. and M.S. degrees in mechanical engineering from Shanghai Jiao Tong University, Shanghai, China, in 1994 and 1997, respectively, and the Ph.D. degree from the Department of Mechanical, Materials and Aerospace Engineering, University of Central Florida, Orlando, in 2000. Following graduation, she worked as a MEMS Engineer in industry for two years and was involved in the development of optical MEMS and microfluidic products. From December 2002 to June 2006, she was with the Integrated MEMS Laboratory, School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta. She is currently an Assistant Professor in the Department of Mechanical Engineering, Old Dominion University, Norfolk, VA. Her research interests are in the investigation of micromechanics, such as energy loss mechanisms in MEMS resonators, and the development of various MEMS devices for inertial sensing, bio/chemical sensing, and wireless communications.
Farrokh Ayazi (S’96–M’00–SM’05) received the B.S. degree in electrical engineering from the University of Tehran, Tehran, Iran, in 1994, and the M.S. and Ph.D. degrees in electrical engineering from the University of Michigan, Ann Arbor, in 1997 and 2000, respectively. Since December 1999, he has been with the faculty of Georgia Institute of Technology, Atlanta, where he is currently an Associate Professor with the School of Electrical and Computer Engineering. He is a Cofounder and the Chief Technical Officer of Qualtré Inc., Atlanta, which is a spinout of his research laboratory that commercializes three-axis microgyroscopes and six-degrees-of-freedom motion sensors for consumer electronics and personal navigation devices. His research interests are in the areas of integrated micro- and nanoelectromechanical resonators, IC design for microelectromechanical system (MEMS) and sensors, RF MEMS, inertial sensors, and microfabrication techniques. Prof. Ayazi is an Editor of the JOURNAL OF MICROELECTROMECHANICAL SYSTEMS and serves on the Technical Program Committees of the IEEE International Solid State Circuits Conference (ISSCC) and the International Conference on Solid State Sensors, Actuators and Microsystems (Transducers). He was the recipient of the National Science Foundation CAREER Award in 2004, the 2004 Richard M. Bass Outstanding Teacher Award (determined by the vote of the ECE senior class), and the Georgia Tech College of Engineering Cutting Edge Research Award for 2001–2002. He was also a recipient of the Rackham Predoctoral Fellowship from the University of Michigan for 1998–1999.
