A 2000 o/s Dynamic Range Bulk Mode Dodecagon Gyro for a Commercial SOI Technology

Mohannad Elsayed1, Frederic Nabki2, Mourad El-Gamal1

1McGill University, Montréal, Québec, H3A2A7, CANADA 2Université du Québec à Montréal, Montréal, Québec, H3C3P8, CANADA

Abstract—This paper reports on the design and suggested fabrication steps of a bulk mode dodecagon disk gyroscope. A major contribution of this work, compared to prior art, is that it enables the fabrication of this important class of gyroscopes in commercially available and low-cost SOI technologies – e.g. MEMSCAP’s SOIMUMPs. The structure was simulated using COMSOL, operates at 8.14 MHz, and exhibits a competitive rate sensitivity of ~2.3 pA/o/s, a high dynamic range of 2000 o/s, and a mechanical noise of 1 o/√hr, for a quality factor of 10,000.

I. INTRODUCTION Micro-machined gyroscopes are receiving more and more

attention in the sensing community. This is due to their small sizes, which enable their use in numerous consumer electronics applications (e.g., image stabilization in digital cameras, motion sensing etc.). Gyros are also used in navigation systems for robotic, military, aeronautic and space applications, providing a significant opportunity for the growth of their micro-machined implementations.

As highlighted in [1], bulk mode gyroscopes are capable of achieving superior performance compared to flexural mode gyroscopes. These gyros operate in higher order resonant modes, and thus their frequencies of operation are in the MHz range, three orders of magnitude higher than flexural mode ones. Higher order modes experience less thermoelastic damping as they involve less mechanical motion. Moreover, they can achieve very high quality factors (~50,000) even in atmospheric pressure, as air damping has little impact on their operation. Also, bulk mode gyroscopes exhibit orders of magnitude higher bandwidths than flexural mode gyroscopes. This relaxes the need for drive-sense mode matching and expensive vacuum packaging, which are crucial for the operation of flexural mode gyroscopes. The mechanical noise of a vibratory gyroscope is given by (1) [2].

( )0

41 Bz Brownian

drive effect sense

k Tq MQω −

Ω ∝ (1)

where qdrive is the drive mode vibration amplitude, kB is the Boltzmann constant, T is the absolute temperature, ω0 is the resonance frequency, M is the mass, and Qeffect-sense is the effective quality factor. From (1), it is clear that raising the

resonance frequency and the quality factor improves the noise performance of a gyroscope significantly.

Bulk mode gyroscopes presented in the literature [1]-[4] typically require very narrow transducer gaps which are complex to fabricate. As was previously mentioned, gyros are more and more common in motion sensing systems present in consumer electronics. As such, low-cost fabrication is paramount. This paper aims at designing a bulk mode gyro that is suited to low-cost micro-fabrication technologies.

In [1]-[3], a circular disk architecture was introduced in “100” and “111” silicon. In [4], a circular disk gyro with spokes was introduced. The latter combines both flexural and bulk modes and achieves a large dynamic range. These gyros utilize very small gaps (~200nm) between the center resonating element and the electrodes. Such narrow gaps are expected to increase the complexity, cost of fabrication, and reduce the reliability significantly. In fact, the fabrication technology involves a high aspect ratio combined poly and single crystal silicon process (HARPSS) which is relatively complex. Alternatively in [5], a double mass tuning fork flexural mode gyroscope was presented. It was fabricated in a simpler 3.3 µm gap technology. However, a very small bandwidth of 10 Hz was achieved which is typical for flexural mode gyroscopes. Very good noise performance of 0.1 o/hr/√Hz ~ 0.002 o/√hr is achieved using very complex mode matching circuitry, which increases the design complexity of the sensing system for such a gyro.

In this work, a dodecagon disk bulk mode gyroscope is presented. The sensor was designed and sent for fabrication in commercial SOI technology (SOIMUMPs from MEMSCAP), which has lower cost in comparison with many of the technologies used for state-of-the-art bulk mode gyroscopes. The design exhibits a theoretical mechanical noise floor of 1o/√hr. Modal simulation shows a rate sensitivity of 2.3 pA/o/s and a dynamic range of 2000 o/s with a DC biasing voltage of 25 V. A worst case quality factor of 10,000 was assumed in all simulations. Furthermore, a bandwidth of 810 Hz is achieved, mitigating the need for complex mode matching circuitry. The design is first described, and simulation results are reported. Then, the layout is presented, followed by a discussion and conclusion.

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II. DESIGN In bulk mode gyroscopes, the resonating structure vibrates

at higher order bulk modes. For the SOIMUMPs technology, the device layer is “100” single crystalline silicon (SCS), which is anisotropic. In a disk, the first order bulk mode exhibits a 1 MHz split between the drive and sense modes. Therefore, in order to have closer matching of the drive and sense modes, the second order bulk mode of a dodecagon (12 sides) structure is favored, providing a drive-sense mode separation of only 100 Hz. The drive and sense modes for the second order mode are spatially separated by 30º. Therefore, the polygon needs 12 sides in order to have 30º between its vertices so that the second order maxima coincide with the disk vertices.

The proposed design is shown in Figure 1. The structure is composed of a central dodecagon structure with a 730 µm face to face distance and a 25 µm thickness. The central structure is surrounded by electrodes. The electrodes marked as “D” are used to electrostatically drive the structure, while the electrodes marked as “S” are used to sense the output signal. The central pad is used to connect the necessary DC bias voltage to the disk structure. This precludes the need for suspended upper traces as used in [1]-[4] or for a lower metallization that would result in a more complex fabrication process.

In order to release the structure, 10 µm diameter and 25 µm spaced release holes are added. The release holes are distributed around the structure in a symmetric manner, in order to mitigate any frequency split that may arise due to these holes. Then, the release will be performed in-house by timed hydrofluoric acid (HF) wet etching. An etch rate of 1.6 µm/min is stated in [6] for SOIMUMPs, using 48% aqueous HF and Triton X-100 surfactant. To validate this etch rate, HF etch tests were performed in-house on similar SOI wafers and an etch rate of ~1 µm/min using 49% aqueous HF was measured. Careful timing is essential so as to avoid etching below the center pad, which may lead to the structural failure of the disk while wire bonding to the center pad.

III. SIMULATION RESULTS The COMSOL multiphysics finite element simulation

package is used for all simulations. In order to accurately simulate the performance of the proposed structure, taking into consideration the anisotropic elastic properties of “100” SCS, the orthotropic elastic model stated in [7] is used in all finite element simulations. This model provides the elasticity constants in the frame of reference of a standard “100” SCS wafer as shown in (2)–(5). 169 , 130 (2) 0.36, 0.28, 0.064 (3) 79.6 , 50.9 (4) 165.7 63.9 63.963.9 165.7 63.963.9 63.9 165.7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 79.6 0 00 79.6 00 0 79.6

(5)

where Ei is the Young’s modulus in direction i, vij is the Poisson’s ratio between directions i and j, Gij is the shear modulus between directions i and j, and C is the stiffness matrix.

Eigen frequency analysis was performed for the structure and the second order bulk modes were obtained. The drive and sense resonance frequencies were found to be 8.135626 MHz and 8.135742 MHz respectively, spatially separated by 30º, as shown in Figure 2.

Generally, it is very difficult to obtain accurate estimates for the quality factor of resonating structures by simulation, and the quality factor is obtained by measurements of the fabricated devices. Therefore, a worst case quality factor of 10,000 was assumed to obtain the drive and sense resonance characteristics of the sensor and its angular rate sensitivity using harmonic analysis. This is a pessimistic value in comparison with state-of-the-art structures reported in the literature (e.g., [2], [3]). Figure 3 shows the drive and sense resonance curves. From Figure 3, the 3-dB bandwidth of the sensor is calculated to be ~810 Hz. This value is two orders of magnitude higher than that typically achieved in flexural mode gyroscopes. This wide bandwidth relaxes the requirement for electronic mode matching between the drive and sense modes, and consequently simplifies the circuitry as mentioned earlier.

By performing harmonic analysis, qdrive was found to be 3.5 nm. Then, by applying a coriolis force load, and running a sweep for the angular rate input, the displacement of the sense vertices was found to be 7.5×10-13 m/º/s. According to (6) and (7), this is equivalent to capacitance and current sensitivities of 0.002 aF/º/s and 2.3 pA/º/s per electrode, respectively. The response of the gyroscope to an input angular rate is shown in Figure 4, showing a dynamic range of ±2000 o/s.

02

electrodeAC disp

gapε

Δ ≈ ⋅ Δ (6)

0( )

.DCDC

d CVI C V

dtω= ≈ Δ ⋅ (7)

Figure 1. Schematic of the proposed dodecagon bulk mode gyroscope.

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where ∆C and ∆disp vary harmonically wequal to the resonance frequency (ω0) in reactuation voltage.

According to (8) and (9) [8], the angular mechanical noise of the sensor were foun1 o/√hr, respectively for a quality factor of 10

0

4sense g drive zQq A qω

= Ω

( ) .0

414

Bradz Brownian s Hz

g drive effect sense

k TA q MQω

⎡ ⎤⎢ ⎥⎢ ⎥⎣ ⎦

−

Ω =

(a)

Figure 2. (a) Drive mode at 8.135626 MHz, and 8.135742 MHz of the proposed dodecagon bulk m730 µm face to face distance and 25 µm thickness.

(a)

(b) Figure 3. (a) Amplitude of the drive vertices veloc

(b) amplitude of the sense vertices velocity squared,

with a frequency sponse to the AC

r gain (Ag) and the nd to be 0.3 and 0,000.

(8)

(9)

(b) (b) sense mode at

mode gyroscope with

city squared, and against frequency.

Figure 4.Angular rate response of the propgyroscope.

IV. DEVICE LA

Layout of the gyro was made ussoftware. It was sent for fabrtechnology. Figure 5 shows the laystructure will need a post processingholes with 10 µm diameter are addethis purpose. A 3 μm transducer gapstructure from the electrodes. The elenough so as not to fail as a result ooccur during the HF release. Moreothe center pad and the nearest releensure that the device is well reletching would occur beneath the ceto the structural failure of the disk up

V. DISCUSS

Table I summarizes the performaproposed design and compares ipublished in the literature. It is clearis expected to achieve a higher dcompared to [4], which however quality factor of 1,000 due to its use

Figure 5. Layout of the dodecagon bulk modeface distance.

posed dodecagon bulk mode

AYOUT sing the Cadence Virtuoso rication in SOIMUMPs yout of the structure. The g HF release step. Release ed to the disk structure for p separates the resonating lectrodes were made thick of the under etch that will over, the distance between ease holes is designed to leased before any under nter pad, which may lead

pon wirebonding.

ION ance characteristics of the it to others, previously r that the proposed sensor dynamic range except as exhibits a relatively low of flexural elements.

e gyroscope with 730 µm face to .

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The larger 3 μm transducer gap of the SOIMUMPs technology used, limits rate sensitivity and noise performance as qdrive is understandably lower than that of thinner transducer gap devices. For instance, in [1]-[4], a qdrive of 10-20 nm at 5-10 V operating voltage was achieved, while in the proposed design, a qdrive of 2.5 nm was obtained at 25 V. This could be increased by further raising the operating voltage or by being able to achieve a smaller transducer gap size, resulting in increased fabrication complexity. A significant advantage of the larger gap size however is the significantly high dynamic range achieved. This makes this gyro interesting in high angular rate applications, while being suited to low-cost fabrication. Moreover, the improvement in device noise performance is still present with a smaller qdrive, because as seen in (1), the increases in quality factor and resonant frequency overcome the negative impact of the lower drive amplitude on noise performance.

The presented simulations were performed for a somewhat conservative quality factor of 10,000. In reality, the quality factor is expected to be higher, as the disk structure is composed of SCS and operates in a bulk mode of resonance. As such, once fabricated, this design should exhibit performance that is somewhat improved in comparison with the presented simulation results.

VI. CONCLUSION In this work, a dodecagon disk bulk mode gyroscope is

presented. The disk structure has a face to face distance of 730 μm and a thickness of 25 μm. The sensor operates at 8.14 MHz. By using a worst case quality factor of 10,000 and with a basing voltage of 25 V, finite element simulation results show a rate sensitivity of 2.3 pA/o/s, a dynamic range of 2000 o/s and a 3-dB bandwidth of 810 Hz. Furthermore, mechanical noise for the device is calculated to be 1o/√hr. The device is currently being fabricated in the SOIMUMPs technology, which is a simpler and lower cost technology compared to those typically used for state-of-the-art bulk mode gyroscopes.

ACKNOWLEDGMENT The authors would like to thank the Canadian

Microelectronics Corporation (CMC) for providing the layout design tools needed, and for the device fabrication in the SOIMUMPs technology.

REFERENCES [1] F. Ayazi, H. Johari, “Capacitive Bulk Acoustic Wave Disk

Gyroscopes,” US Patent 7,543,496 B2, June 2009. [2] H. Johari, F. Ayazi, “Capacitive Bulk Acoustic Wave Silicon Disk

Gyroscopes,” Proc. IEEE Electron Devices Meeting, pp. 1-4, Dec. 2006.

[3] H. Johari, F. Ayazi, “High Frequency Capacitive Disk Gyroscopes in (100) and (111) Silicon,” Proc. IEEE Conf. on MEMS, pp. 47-50, Jan. 2007.

[4] W. Sung, M. Dalal, F. Ayazi, “A 3MHz Spoke Gyroscope with Wide Bandwidth and Large Dynamic Range,” Proc. IEEE Conf. on MEMS, pp. 104-107, Jan. 2010.

[5] A. Sharma, M. Zaman, F. Ayazi, “A Sub-0.2 o/hr Bias Drift Micromechanical Silicon Gyroscope With Automatic CMOS Mode-Matching,” IEEE Journal of Solid-State Circuits, vol. 44, no. 5, pp. 1593-1608, May 2009.

[6] D. Miller, B. Boyce, M. Dugger, T. Buchheit, K. Gall, “Characteristics of Commercially Available Silicon-on-Insulator MEMS Material,” Journal of Sensors and Actuators, vol. 138, no. 1, pp. 130-144, 2007.

[7] M. Hopcroft, W. Nix, T. Kenny, “What is the Young’s Modulus of Silicon?” IEEE Journal of MEMS, vol. 19, no.2, pp. 229-238, April 2010.

[8] F. Ayazi and K. Najafi, ‘‘A HARPSS Polysilicon Vibrating Ring Gyroscope,’’IEEE Journal of MEMS, vol. 10, no.2,pp. 169-179, June 2001.

[9] M. Zaman, A.Sharma, F. Ayazi, “The Resonating Star Gyroscope: A Novel Multiple-Shell Silicon Gyroscope with Sub-5 deg/hr Allan Deviation Bias Instability,” IEEE Journal of Sensors, vol. 9, no. 6, pp. 616-624, June 2009.

TABLE I. COMPARISON BETWEEN THE DODECAGON GYROSCOPE PRESENTED HERE AND OTHER STATE-OF-THE-ART GYROSCOPES

[2] [3] [4] [5] [9] This work

Size (mm) 0.8 1.2 1.12 4 2.5 0.73

Gap (µm) 0.25 0.18 0.2 3.3 4 3

Thickness (µm) 50 35 60 60 40 25

f (MHz) 5.88 2.917 3.12 0.015 0.09 8.14

VDC (V) 5 5 10 40 ±40 25

Q (,000) 12 66 1 36 30 10

Mech. Noise (o/√hr) 0.174 0.0442 0.002 0.04 1

Rate Sensitivity

(aF/o/s) 4.367 80 0.002

Rate Sensitivity

(pA/o/s) 420 2.73 2.3

Dynamic Range (o/s)

measurements limited to 100 30000

meas. limited to

10

meas. limited to

70 2000

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