Achieving Below 200ppm Scale Factor Temperature Stability in an am Gyroscope with On-Chip Stress Sensing

ACHIEVING BELOW 200PPM SCALE FACTOR TEMPERATURE STABILITY IN AN AM GYROSCOPE WITH ON-CHIP STRESS SENSING Mehran Hosseini-Pishrobat1, Derin Erkan1, and Erdinc Tatar1,2 1Dept. of Electrical and Electronics Engineering, Bilkent University, Ankara, TURKEY and 2National Nanotechnology Research Center (UNAM), Bilkent University, Ankara, TURKEY ABSTRACT For the first time, we demonstrate a stress-based compensation that improves the scale factor stability of an AM, mode split gyroscope by more than 15x compared to the common temperature calibration. We test our gyroscope by exposing it to controlled temperature cycles within the 25-90°C range while maintaining a dithered rate table input. We have equipped our double-ring, 3.2mm-diameter, 58kHz gyroscope with eight 45°-apart capacitive stress sensors. This arrangement allows us to measure the nonuniform distribution of the stresses across the device as well as their residuals over temperature. Thanks to stress sensing, the proposed compensation captures the hysteresis effects induced by the residual stresses, achieving 125ppm (peak-to-peak) and singledigit ppm Allan deviation scale factor temperature stability. KEYWORDS MEMS gyroscope; Calibration; Scale factor stability; Stress sensor INTRODUCTION Emerging application areas such as autonomous navigation and the Internet of Things (IoT) demand improvement in the long-term performance of MEMS gyroscopes. Environmental temperature and stress are the main obstacles to realizing such improvements. Accordingly, as a crucial performance metric, the temperature stability of scale factor (SF) has been a central research theme for MEMS gyroscopes. A multiparameter fitting algorithm incorporating drive frequency/amplitude, split, and sense mode’s phase error with temperature was presented in [1], demonstrating 8ppm/°C SF-temperature sensitivity. An automatic modematching scheme was presented in [2] that limits the SF variations over temperature to 130ppm/°C. In [3], the frequency change-to-drive force ratio was used to stabilize the SF (achieving 4ppm/°C) around room temperatures. In [4], it is shown that compensating for the phase error mitigates the SF nonlinearity over temperature. The effects of temperature in MEMS gyroscopes can be understood via two core mechanisms [5]: 1) temperature variations of the silicon’s thermosmechanical properties, notably -60ppm/°C change in Young’s modulus, and 2) thermal stresses. Unlike the first one, the latter is a much more complex factor that involves thermal interactions of all the device’s constituent components, including MEMS, die-attach, packaging, and PCB, as well as the response of the structure of the gyroscope itself to thermal deformations. Additionally, while the first mechanism tends to induce stiffness softening, the second can affect the stiffness distribution among the gyroscope’s modes in more intricate and unpredictable ways. For example, there could be stress components that induce hardening, electrostatic gaps could change nonuniformly [6], and residual stresses might accumulate over temperature fluctuations, leading to hysteresis [7]. Perturbation in mechanical and electrostatic states of the gyroscope could deteriorate the SF stability as it depends on both mechanical and capacitive gains of the drive and sense modes. The open-loop SF is given by SF = 𝐴 𝑔 . 𝑋 . Ω Δ ω × Cap . Gain × Electronics Gain . (1) Here, 𝐴𝑔 is the angular gain, 𝑋 is the drive mode amplitude, Ω is the rate, and Δ𝜔 is the mode split, which is much larger than the bandwidth, Δ𝜔 ≫ 𝐵𝑊/2. Thermal stresses, therefore, affect the SF primarily through their impact on the gyroscope’s stiffness (Δ𝜔) and electrostatic gaps (Cap. Gain). That being said, these stresses cannot be captured by the temperature alone. In light of the above discussion, combined stresstemperature has shown promising results for the bias drift compensation [8], e.g., 3-4x improvement over pure temperature calibration [9]. As the main contribution, we will capitalize on the potential of stress-temperature calibration for SF stability. Compared with the cited works, we examine the following gaps: 1) full temperature cycling, which can reveal residual stress/hysteretic effects, has been ignored; 2) these studies overlook thermal stresses, which, as we discussed, taking them into account is essential for achieving robust SF stability. GYROSCOPE AND TEST SETUP Figure 1 shows the SEM of the double ring AM gyroscope with the outer ring (as the main vibrating component) having 3.2mm diameter. We have placed 16 pairs of electrodes around the outer ring for differential drive, sense, frequency tuning, and force-rebalance control purposes. The gyroscope operates at ~58kHz 𝑛 = 2 wineglass mode (cos (2𝜃): drive, sin (2𝜃): sense) with 110Hz frequency split. The device was fabricated by a silicon-on-glass (SOG) process. As shown in Figure 2, we have eight stress sensors surrounding the ring with 45° symmetry. The working principle of stress sensors is briefly explained in Figure 3-(a). Each of these sensors is a capacitive strain gauge where a mechanically imbalanced structure amplifies displacement in the xdirection by a gain (~6.5), transferring it to the ydirection. This configuration enables us to measure stresses at the stress sensors’ anchors. We should note that the stress sensors are only sensitive to mechanical strains and do not respond when the whole structure expands freely; compare the displacement gradients of (a) and (b) 979-8-3315-0889-0/25/$31.00 ©2025 IEEE 44 IEEE MEMS 2025, Kaohsiung, Taiwan 19-23 January 2025 2025 IEEE 38th International Conference on Micro Electro Mechanical Systems (MEMS) | 979-8-3315-0889-0/25/$31.00 ©2025 IEEE | DOI: 10.1109/MEMS61431.2025.10917391 Authorized licensed use limited to: ULAKBIM UASL - Bilkent University. Downloaded on April 19,2025 at 20:24:49 UTC from IEEE Xplore. Restrictions apply. Figure 5: Temperature cycles for Tests#1. in Figure 3. These mechanical strains mainly stem from the coefficient of thermal expansion (CTE) mismatches between different layers (PCB, packaging, die-attach, and MEMS). Our temperature test setup is shown in Figure 4- (a). We have a PCB heater on the daughter board to cycle the temperature by heating the MEMS die independent of the electronics. An underneath PTAT sensor records the temperature. We applied a dithered 2s-long, ±40°/s rate inputs during the tests (see Figure 4-(b)). We report the results of two tests from the same device: Test#1 (forcerebalanced closed-loop sense mode) and Test#2 (conventional open-loop sense mode). As Figure 5 shows, each test has two temperature cycles generated by ±1.5°C/min ramps. During both tests, the quadrature channel was nulled using a PI controller while the inphase channel, in conjunction with the applied rate, was used to calculate the SF online. The data collection (with 1Hz sampling rate), and the drive, sense, and quadrature control loops were implemented in a digital lock-in amplifier. The stress sensors’ outputs were multiplexed, periodically sampling each sensor every eight seconds. Sample measured strains from Test#1 are presented in Figure 6. We have a maximum value of 60 micro-strains with a distribution including both compressive and tensile regions. These measurements hint at complex stress regimes that could develop in the substrate due to the CTE differences described above. Additionally, hysteresis loops in the plots indicate residual stresses form over the temperature cycles. These stresses are attributable to the viscoelastic behavior of the die-attach epoxy. Furthermore, as Figure 7 shows, hysteresis loops manifest in the temperature variations of the drive mode’s frequency as well. Similar effects are expected to pervade the sense mode’ frequency and the mode split. Based on these observations, the hysteresis phenomenon, which is captured by on-chip stress sensing, affects the temperature sensitivity of SF. We argue that this factor constitutes a distinct advantage of stress over temperature for calibration. CALIBRATION RESULTS Figure 8 summarizes the calibration results for both tests by reporting the peak-to-peak values of the compensated SF residuals. Figure 1: SEM of the double ring gyroscope (58kHz) with 16 pairs of electrodes. Figure 2: Arrangement of Stress sensors (45° apart) while the ring assumes its cos(2θ) mode shape. Figure 3: Displacement (nm) across stress sensor under pure thermal expansion (a) and Δx=50nm mechanical load applied to anchors (b); the highlights in bold explain the working principle. Figure 4: (a) Test setup including the rate table and PCB heater; (b) dithered rate input (2s-long, ±40°/s) applied during the temperature tests. 45 Authorized licensed use limited to: ULAKBIM UASL - Bilkent University. Downloaded on April 19,2025 at 20:24:49 UTC from IEEE Xplore. Restrictions apply. Considering the uncompensated SF, temperature-only calibration yields a modest improvement: 1.8x for Test#1 and 1.6x for Test#2. Stress-only calibration significantly improves upon these values (again, with respect to the uncompensated case): 28x for Test#1 and 13x for Test#2. Stress is, therefore, more efficacious than temperature in capturing the thermo-mechanical effects that underlie the SF variations, especially regarding the hysteresis behavior discussed in the previous section. Similarly, combined stress-temperature linear fitting improves temperatureonly fitting by more than 15x and 8x for Tests#1 and 2, respectively. Considering both tests, a second-order (multivariable) polynomial in temperature and stress gives the best compensation results by achieving below 200ppm peak-to-peak SF error (128ppm for Test#1 and 168ppm for Test#2). Interestingly, inverse temperature and stress (1/T,1/σ) result in better SF stability than mere linear fitting. We explain this by noting that SF inversely depends on the frequency split, which is linearly correlated with stress (see Equation (1)). Test#1, overall, has better SF stability than Test#2. We link this to the force-rebalance control that diminishes electrostatic nonlinearity in the sense mode. Figure 9 provides the Allan deviation plots based on the residual SFs in Figure 8. The compensation by the second-order polynomial reaches single-digit stability with eliminated long-term effects. Moreover, the associated (almost) straight Allan deviation line reveals that the calibration may be limited by the gyroscope noise and/or rate table stability. Although our setup cannot go to lower temperatures, we expect the calibration to hold since the residues in Figure 8 do not exhibit any particular test-dependent patterns. Table 1 gives a comparative summary of our achieved SF stability with respect to the literature. This comparison highlights the potential of the presented calibration method, especially regarding the commercial ring gyroscopes [10]. Concerning the other references in Table 1, we again remark that temperature cycling is an important aspect that was not investigated in these studies. Figure 6: Sampled measured strains during Test#1 (numbers indicate the angular positions of the sensors). Figure 7: hysteresis in temperature variations of drive mode’s frequency. Figure 8: Scale factor compensation results for different fitting schemes (p2p: peak-to-peak, Poly(T,σ): second-order polynomial in T,σ); closed-loop refers to force-rebalance. 46 Authorized licensed use limited to: ULAKBIM UASL - Bilkent University. Downloaded on April 19,2025 at 20:24:49 UTC from IEEE Xplore. Restrictions apply. Table 1: Different SF stability data. Reference This study Silicon Sensing [10] Ref. [1]* Ref. [2]* Ref. [3]* SF variation (ppm) 125 3000 800 13000 61 *Temperature was not cycled in these studies. CONCLUSION We studied the scale factor stability of a ring gyroscope using on-chip stress sensing. Our results showed that stress encapsulates certain essential thermomechanical effects that temperature alone cannot capture. These effects perturb the symmetry of the structural stiffness and electrostatic gaps, leading to variations in the gyroscope’s mechanical and capacitive gains. We discussed that full cycling of the temperature is imperative for observing such effects, especially hysteresis loops that could form in the frequencies. On this basis, combining temperature with stress demonstrated encouraging potential to attain below 200ppm scale factor stability. Force rebalance operation tends to have better stability because of reduced electrostatic nonlinearity. As a future direction, we will focus on developing analytical models that mathematically describe the link from stress-temperature to scale factor and bias stability. Such models would be helpful in understanding the physics behind the drift phenomenon. ACKNOWLEDGEMENTS This work was supported by the European Union’s European Research Council (ERC) Starting Grant under the grant agreement 101116162–0-drift–ERC-2023-STG. Views and opinions expressed are however those of the authors only and do not necessarily reflect those of European Union. REFERENCES [1] J. Cui, Q. Zhao, Z. Bai, and G. Yan, “An 8PPM/°C Temperature Sensitivity of the Scale Factor in MEMS Gyroscope Based on Multi Parameters Fusion Compensation Method,” in MEMS 2019, Seoul, South Korea, Jan. 27-31, 2019, pp. 696–699. [2] S. Sonmezoglu, S. E. Alper, and T. Akin, “A high performance automatic mode-matched MEMS gyroscope with an improved thermal stability of the scale factor,” in TRANSDUCERS 2013, Barcelona, Spain, June 16-20, 2013, pp. 2519–2522. [3] B. Eminoglu, M. H. Kline, I. Izyumin, Y.-C. Yeh, and B. E. Boser, “Background calibrated MEMS gyroscope,” in 2014 IEEE SENSORS, Valencia, Spain, Nov. 02-05, 2014, pp. 922–925. [4] Y. Kuang, Z. Hou, G. Liu, D. Xiao, and X. Wu, “Real-Time Phase Compensation for Scale Factor Nonlinearity Improvement Over Temperature Variations for MEMS Gyroscope,” J. Microelectromech. Syst. vol. 32, no. 4, pp. 305–313, Aug. 2023. [5] M. Hosseini-Pishrobat, D. Erkan, and E. Tatar, “On Temperature Effects in a MEMS Ring Gyroscope,” in INERTIAL 2024, Hiroshima, Japan, Mar. 25-28, 2024, pp. 1–4. [6] M. Hosseini-Pishrobat, D. Erkan, and E. Tatar, “Analytical and experimental study of stress effects in a MEMS ring gyroscope,” Sens. Actuators A: Phys., vol. 362, p. 114639, Nov. 2023. [7] E. Tatar, “MEMS Sensor Drift Compensation with On-Chip Stress Sensing,” in Transducers 2023, Kyoto, Japan, June 25-29, 2023, pp. 292–297. [8] B. E. Uzunoglu, D. Erkan, and E. Tatar, “A Ring Gyroscope With On-Chip Capacitive Stress Compensation,” J. Microelectromech. Syst., vol. 31, no. 5, pp. 741–752, Oct. 2022. [9] D. Erkan and E. Tatar, “Improving the Temperature Stability of MEMS Gyroscope Bias with on-chip Stress Sensors,” in INERTIAL 2024, Hiroshima, Japan, March 25-28, 2024, pp. 1–4. [10] “CRH03 - Silicon Sensing.”, Datasheet, 2024. Available: https://siliconsensing.com/product/crh03 CONTACT M. Hosseini-Pishrobat, tel: +90-312-2901219; [email protected] Figure 9: Allan deviations for the residual scale factors. 47 Authorized licensed use limited to: ULAKBIM UASL - Bilkent University. Downloaded on April 19,2025 at 20:24:49 UTC from IEEE Xplore. Restrictions apply.