An Overview of MEMS Inertial Sensing Technology

February 1, 2003By: Jonathan Bernstein

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Whileaccelerometers are the current leaders in commercially successful MEMStechnology, other inertial devices such as rate gyroscopes are poisedfor a similar success. In addition to high-volume markets forautomotive crash sensors, there are niche markets for high-resolutionseismic sensing and high-g sensors. This article presents an overviewof the designs and operating principles of some MEMS inertial devices.

Accelerometers

Accelerometers are the stars of the MEMS show [1],with millions bought each year by the automotive industry. Devices withintegral electronics offer readout electronics and self-testcapability, and cost far less than accelerometers of decades ago. Thephysical mechanisms underlying MEMS accelerometers include capacitive,piezoresistive, electromagnetic, piezoelectric, ferroelectric, optical,and tunneling. The most successful types are based on capacitivetransduction; the reasons are the simplicity of the sensor elementitself, no requirement for exotic materials, low power consumption, andgood stability over temperature. Although many capacitive transducershave a nonlinear capacitance vs. displacement characteristic, feedbackis commonly used to convert the signal to a linear output. The outputcan be analog, digital, ratiometric to the supply voltage, or any ofvarious types of pulse modulation. Sensors with digital output areconvenient when the data must be transmitted without further noisedegradation.

Among the specifications to consider when choosing an accelerometer arebandwidth, noise floor, cross-axis sensitivity, drift, linearity,dynamic range, shock survivability, and power consumption. Resonantfrequency is also important because the sensor's upper useful frequencyrange is usually some fraction of its resonant frequency, which alsodetermines its sensitivity and displacement per g of acceleration:

 

(1)

where:

 

d_g  = displacement per g M and k_sp  = mass and spring constant of the device g  = 9.8 m/s² ₀  = angular resonant frequency

In general, the displacement of a sensing element is an essential part of the sensing process, and d_gis part of the open-loop gain of the sensor, so there tends to be astrong inverse relationship between sensitivity and bandwidth for anyclass of sensors.

Noise. There are many contributors to noise in anaccelerometer—the sensor itself, the readout electronics, mechanicaldamping, and all electrical resistances. MEMS sensors are so small thatthe Johnson noise of the devices' mechanical resistance must beconsidered, while it is usually ignored in larger sensors. Just asBrownian motion agitates bacteria and dust motes, it can be a largeforce on a tiny MEMS component. The Brownian force is [2,3]:

 

(2)

which causes Brownian motion of the proof mass, x_B:

 

(3)

where:

 

D  = damping coefficient of proof mass M supported by spring constant k_sp

Solving for the acceleration that generates the same motion, x_B, and substituting:

 

 

gives the Brownian equivalent acceleration noise in g/ Hz:

 

(4)

From Equation 4 we see that a large mass and a high Q (low damping)help achieve a low noise floor. To achieve a large mass in amicromachined sensor typically requires a wafer-thick proof mass carvedout of the sensor chip. For absolute minimum noise, the dampingconstant must be reduced by suspending the proof mass in a vacuum frompurely elastic springs. Feedback prevents the sensor from ringing atits resonant frequency.

Examples. Analog Devices manufactures a family of surface micromachined accelerometers with polysilicon as the structural and

Figure 1. In the Analog Devices ADXL 50 accelerometer, the electronics occupy the majority of the 3 mm 2 chip area. The 2-axis device is not only extremely small, but also modest in power requirements and can measure both static and dynamic acceleration.

proof mass elements. The 2-micron-thick polysilicon layer is deposited on a sacrificial layer of SiO₂ thatis removed in a final release step with hydrofluoric acid. Oneadvantage of this technique is that it can be combined with a CMOS orBiMOS process, allowing the entire system (electronics plus sensor) tobe inexpensively integrated on one chip. The ADXL202E (see Figure 1), alow-cost, low-power (2 µA per axis), 2-axis accelerometer with a rangeof ±2 g, can measure both dynamic (vibration) and static acceleration(gravity). The outputs are duty cycle modulated signals, with dutycycles proportional to the acceleration in each of the two sensitiveaxes.

The surface micromachining process developed at U.C. Berkeley in theearly 1980s was at the time restricted to about two microns ofstructural polysilicon. In response to the stress and stress gradientsthat limited the size and flatness of these MEMS structures,alternative fabrication techniques were developed that yielded higherprecision devices. They included thick polysilicon processes (epi-poly [4] and thick silane based deposition), the dissolved wafer process, and processes based on SOI (silicon-on-insulator) wafers.

 

Figure 2. Developed at Draper Laboratory, this MEMS accelerometer features a 20 micron thick single-crystal comb structure whose precision and flatness provide high performance while the glass substrate ensures very low stray capacitance. Low stray capacitance is essential to achieving low noise, high sensitivity, and high dynamic range. The structure was fabricated by the dissolved wafer process.

The dissolved wafer process [5]begins with a heavily boron-doped etch-stop layer on a silicon wafer.The desired features (e.g., combs, springs) are etched into theetch-stop layer and then it is anodically bonded to a glass wafer withmetal surface electrodes. Finally, the bulk of the wafer is dissolvedaway, leaving just the boron-doped structures (see Figure 2).

High-g Accelerometers. There is a niche market foraccelerometers that read out very high g's for crash tests, impacts,and missile and artillery shell launches. Charles Stark DraperLaboratory has produced an accelerometer reading out 100,000 g's.Similar devices will almost certainly be commercialized in time.

Angular Accelerometers.MEMS angular accelerometers are usedprimarily to compensate for angular shock and vibration in diskread/write head assemblies. These devices, while similar to linearaccelerometers in terms of design, fabrication, and readout, aredesigned with zero pendulosity (i.e., the center of gravity is locatedat the centroid of the support springs), and are compliant torotational motion yet stiff with respect to linear motion. Delphi andST Microelectronics, manufacturers of angular accelerometers, usecapacizive MEMS sensors and custom CMOS ASICs. Some of thespecifications for two angular accelerometers are given in Figure 3.

Figure 3 Angular Accelerometer COTS Components
Manufacturer

Part #

BW (Hz)

Max (R/s²)

Output

ST Microelectronics

LIS1R02

30-800

200

7-bit A/D

Delphi

RV200L

10-800

100-400

Analog

Geophones. Geophones can be thought of as accelerometers withvery high sensitivity and no DC output requirement. With no drift orbias stability specifications, geophone design can be optimized to givethe lowest noise floor. Applications include seismic sensing, machineryvibration and failure prediction, tracking and identification ofvehicles or personnel, and underwater pressure gradient sensing.

Conventional geophones incorporate permanent magnets and fine wire coils to measure velocity above their fundamental resonance [6]. This is in contrast to capacitive accelerometers, which measure acceleration below their fundamental resonance.

Figure 4. In this cross section of an Applied MEMS device can be seen the wafer-thick proof mass between the upper and lower stationary wafers. A narrow sense gap, large area, low damping, and low resonant frequency all contribute to an extremely low noise floor.

There are also piezoelectric and ferroelectric accelerometers.Micromachined sensors can offer size and weight advantages overconventional sensors, as well as a digital output which is easilytransmitted noise free.

One MEMS geophone that has been commercialized by Applied MEMS Inc.(see Figures 4 and 5) incorporates a three-wafer stack in which thecenter wafer forms the proof mass. Referring again to Equation 4, thelargest mass available in most MEMS devices is the wafer itself, and avacuum package reduces Brownian noise to a negligible level. The deviceis read out using a custom CMOS mixed-signal ASIC with a loop operating in force-feedback mode.

 

Figure 5. The upper and lower lids of these Applied MEMS devices have been removed to show the proof mass. These devices are much smaller than the conventional geophones they are replacing.

To achieve the maximum sensitivity, the spring constants (andresonant frequency) are reduced so that the maximum acceleration is 0.2g's over a frequency range of 3–200 Hz. Minimum resolvable accelerationis 30 ng/Hzfor a dynamic range of 115 dB. To avoid saturating the A/D converter,the device must be oriented such that the sensitive axis is horizontal.The noise floor of this device is about 66 times lower than that ofmost "high-resolution" surface micromachined accelerometers.

Gyroscopes

All MEMS gyroscopes take advantage of the Coriolis effect. In a reference frame rotating at angular velocity , a mass M moving with velocity v sees a force:

 

(5)

Many types of MEMS gyroscopes have appeared in the literature, withmost falling into the categories of tuning-fork gyros, oscillatingwheels, Foucault pendulums, and wine glass resonators. Conventional(non-MEMS) spinning wheel gyros are common, but levitation and rotationof a MEMS device with no springs has not yet been commercialized.

Tuning Fork Gyroscopes. Tuning fork gyros contain a pair ofmasses that are driven to oscillate with equal amplitude but inopposite directions. When rotated, the Coriolis force creates anorthogonal vibration that can be sensed by a variety of mechanisms. TheDraper Lab gyro [7-9] shown in Figure 6 uses comb-type structures to drive the tuning fork into resonance.

 

Figure 6. The first working prototype of the Draper Lab comb drive tuning fork gyro is shown here in an SEM image. Due to the superior mechanical properties of single-crrystal silicon, a much better performance was achieved using single-crystal silicon with the dissolved wafer process.

Rotation causes the proof masses to vibrate out of plane, and thismotion is sensed capacitively with a custom CMOS ASIC. The technologyhas been licensed to Rockwell, Boeing, Honeywell, and others.

The resonant modes of a MEMS inertial sensor are extremely important.In a gyro, there is typically a vibration mode that is driven and asecond mode for output sensing. In some cases, the input and outputmodes are degenerate or nearly so. If the I/O modes are chosen suchthat they are separated by ~10%, the open-loop sensitivity will beincreased due to the resonance effect. It is also critical that noother resonant modes be close to the I/O resonant frequencies.

Samsung Corp. has put a large effort into inertial sensors forautomotive and consumer electronics applications. Gyroscopicstabilization of camcorders has been shown to improve picture quality,and gyroscopes are enhancing vehicular safety in multiple ways [10]. With gyros costing as little as $10.00 per sensed axis, they should soon claim a sizeable market share.

Vibrating-Wheel Gyroscopes. Many reports of vibrating-wheel gyros also have been published [4].In this type of gyro, the wheel is driven to vibrate about its axis ofsymmetry, and rotation about either in-plane axis results in thewheel's tilting, a change that can be detected with capacitiveelectrodes under the wheel (see Figure 7).

 

Figure 7. The vibrating wheel gyro made by Bosch Corp. [10], with capacitive sensing under the wheel, can be used to detect two in-plane rotational axes.

It is possible to sense two axes of rotation with a single vibratingwheel. A surface micromachined polysilicon vibratingwheel gyro (seeFigure 8) has been designed at the U.C. Berkeley Sensors and ActuatorsCenter.

 

Figure 8. This polysilicon surface-micromachined vibrating wheel gyro was designed at the Berkeley Sensors and Actuators Center. The potential for combining the mechanical resonator and sense and drive electronics on a single chip permits extreme miniaturization.

Wine Glass Resonator Gyroscopes. A third type of gyro is thewine glass resonator. Fabricated from fused silica, this device is alsoknown as a hemispherical resonant gyro. Researchers at the Universityof Michigan have fabricated resonant-ring gyros in planar form [11]. In a wine glass gyro, the resonant ring is driven to resonance and the positions of the nodal points

Figure 9. The Silicon Sensing Systems gyro is fabricated from single-crystal silicon with metal added for higher conductivity. This device measures 29 by 29 by 18 mm and is used to stabilize the Segway Human Transporter.

indicate the rotation angle. The input and output modes arenominally degenerate, but due to imperfect machining some tuning isrequired. The output signal is monitored and nulled, yielding a rategyro.

Silicon Sensing Systems, a joint venture between Sumitomo and BritishAerospace, has brought to market an electromagnetically driven andsensed MEMS gyro (see Figures 9 and 10). A permanent magnet sits abovethe MEMS device. Current passing through the conducting legs creates aforce that resonates the ring. This Coriolis-induced ring motion isdetected by induced voltages as the legs cut the magnetic field.

Analog Devices has been working on MEMS gyros for many years, and has patented [12,13] several concepts based on modified tuning forks.

 

Figure 10. The resonant ring at the heart of the Silicon Sensing Systems gyro is shown here as an SEM image. Both electromagnetic drive and sensing are accomplished with a permanent magnet in the center (not shown).

The company has recently introduced the ADXRS family of integratedangular rate-sensing gyros, in which the mass is tethered to apolysilicon frame that allows it to resonate in only one direction.Capacitive silicon sensing elements interdigitated with stationarysilicon beams attached to the substrate measure the Coriolis-induceddisplacement of the resonating mass and its frame (see Figure 11).

 

Figure 11. The iMEMS ADXRS angular rate-sensing gyro from Analog Devices integrates an angular rate sensor and signal processing electronics onto a single piece of silicon. Based on the Coriolis effect, its very low noise output makes it a good choice for GPS receivers, where critical location information is required during temporary disruptions of GPS signals.

Foucault Pendulum Gyroscopes. These devices are based on a vibrating rod that is typically oriented out of the plane of the chip [14,15].They are therefore challenging to build with planar fabrication tools,but recent advances in MEMS technology allow very high aspect ratioMEMS that make it possible to fabricate the pendulum without handassembly of the rod.

Summary

MEMS inertial sensing is an established industry, withperformance-to-cost rapidly improving each year. Gyroscopes and angularaccelerometers are entering the marketplace and will soon make manynon-MEMS components obsolete. They should also open up new applicationsdue to their small size and weight, modest power consumption and cost,and high reliability.

References

1. N. Yazdi, F. Ayazi, and K. Najafi. Aug. 1998. "Micromachined Inertial Sensors," Proc IEEE, Vol. 86, No. 8.

2. T.B. Gabrielson. May 1993. "Mechanical-thermal noise in micromachined acoustic and vibration sensors," IEEE Trans, Electron. Devices, Vol. 40:903-909.

3. J. Bernstein et al. 8 June 1998. "Low Noise MEMS Vibration Sensor for Geophysical Applications," Proc 1998 Solid State Sensor and Actuator Workshop, Hilton Head Island, SC:55-58. Extended version also in IEEE JMEMS Dec. 1999.

4. M. Lutz et al. June 1997. "A precision yaw rate sensor in sillicon micromachining," Tech Dig 9th Intl. Conf Solid State Sensors and Actuators (Transducers '97), Chicago, IL:847-850.

5. Y. Gianchandani and K. Najafi. June 1992. "A bulk silicon dissolved wafer process for microelectromechanical systems," J Microelectromech Syst:77-85.

6. GS-14 geophone. Geospace Inc. 7334 N. Gessner Rd., Houston, TX 77040.

7. J. Bernstein et al. Feb. 1993. "A micromachined comb-drive tuning fork rate gyroscope," Proc IEEE Micro Electro Mechanical Systems Workshop (MEMS '93), Fort Lauderdale, FL:143-148.

8. J.J. Bernstein and M.S. Weinberg. 5 March 1996. U.S. Patent#5,496,436, "Comb-Drive Micromechanical Tuning Fork Gyro FabricationMethod."

9. J.J. Bernstein and M.S. Weinberg. U.S. Patent

#5,349,855, "Comb-Drive Micromechanical Tuning Fork Gyro."

10. C. Song. June 1997. "Commercial vision of silicon based inertial sensors," Tech Dig 9th Intl. Conf Solid State Sensors and Actuators.

11. M.W. Putty. March 1995. "A micromachined vibrating ring gyroscope,"Ph.D. dissertation, University of Michigan, Ann Arbor, MI.

12. J. Geen. 3 June 1997. US Patent #5,635,638, "Coupling for multiple masses in a micromachined device."

13. J. Geen. 3 June 1997. U.S. Patent #5,635,640, "Micromachined device with rotationally vibrated masses."

14. J.J. Bernstein. U.S. Patent #5,203,208, "Symmetrical Micromechanical Gyroscope."

15. T.K. Tang et al. 1997. "A packaged silicon MEMS vibratory gyroscope for micro-spacecraft," Proc IEEE Micro Electro Mechanical Systems Workshop (MEMS '97), Japan:500-505.

 

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