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TECHNOLOGY BRIEF 15: MICROMECHANICAL SENSORS AND ACTUATORS 337

Technology Brief 15Micromechanical Sensors andActuators

Energy is stored in many different forms in the worldaround us. The conversion of energy from one formto another is called transduction. Each of our fivesenses, for example, transduces a specific form ofenergy into electrochemical signals: tactile transducerson the skin convert mechanical and thermal energy; theeye converts electromagnetic energy; smell and tastereceptors convert chemical energy; and our ears convertthe mechanical energy of pressure waves. Any device,whether natural or man-made, that converts energysignals from one form to another is a transducer.

Most modern man-made systems are designed to ma-nipulate signals (i.e., information) using electrical energy.Computation, communication, and storage of informationare examples of functions performed mostly with electricalcircuits. Most systems also perform a fourth class ofsignal manipulation: the transduction of energy from theenvironment into electrical signals that circuits can usein support of their intended application. If a transducerconverts external signals into electrical signals, it is calleda sensor.The charge-coupled device (CCD) chip on yourcamera is a sensor that converts electromagnetic energy(light) into electrical signals that can be processed, stored,and communicated by your camera circuits. Some trans-ducers perform the reverse function, namely to convert acircuit’s electrical signal into an environmental excitation.Such a transducer then is called an actuator. The com-ponents that deploy the airbag in your car are actuators:given the right signal from the car’s microcontroller,the actuators convert electrical energy into mechanicalenergy and the airbag is released and inflated.

Microelectromechanical Systems (MEMS)

Micro- and nanofabrication technology have begun torevolutionize many aspects of sensor and actuator design.Humans increasingly are able to embed transducersat very fine scales into their environment. This isleading to big changes, as our computational elementsare becoming increasingly aware of their environment.Shipping containers that track their own accelerationprofiles, laptops that scan fingerprints for routine login,cars that detect collisions, and even office suites thatmodulate energy consumption based on human activityare all examples of this transduction revolution. In this

technology brief, we will focus on a specific type ofmicroscale transducers that lend themselves to directintegration with silicon ICs. Collectively, devices ofthis type are called microelectromechanical systems(MEMS) or microsystems technologies (MST); the twonames are used interchangeably.

A Capacitive Sensor: The MEMSAccelerometer

According to Eq. (5.21), the capacitance C of a parallelplate capacitor varies directly with A, the effective area ofoverlap between its two conducting plates, and inverselywith d, the spacing between the plates. By capitalizing onthese two attributes, capacitors can be made into motionsensors that can measure velocity and acceleration alongx, y, and z.

Figure TF15-1 illustrates two mechanisms for trans-lating motion into a change of capacitance. The firstgenerally is called the gap-closing mode, while thesecond one is called the overlap mode. In the gap-closingmode, A remains constant, but if a vertical force is appliedonto the upper plate, causing it to be displaced from itsnominal position at height d above the lower plate to anew position (d − z), then the value of capacitance Czwill change in accordance with the expression givenin Fig. TF15-1(a). The sensitivity of Cz to the verticaldisplacement is given by dCz/dz.

The overlap mode (Fig. TF15-1(b)) is used to measurehorizontal motion. If a horizontal force causes one ofthe plates to shift by a distance y from its nominalposition (where nominal position corresponds to a 100percent overlap), the decrease in effective overlap areawill lead to a corresponding change in the magnitude ofcapacitance Cy. In this case, d remains constant, butthe width of the overlapped areas changes from w to(w − y). The expression for Cy given in Fig. TF15-1(b)is reasonably accurate (even though it ignores the effectsof the fringing electric field between the edges of thetwo plates) so long as y � w. To measure and amplifychanges in capacitance, the capacitor can be integratedinto an appropriate op-amp circuit whose output voltage isproportional to C. As we shall see shortly, a combinationof three capacitors, one to sense vertical motion andtwo to measure horizontal motion along orthogonal axes,can provide complete information on both the velocityand acceleration vectors associated with the appliedforce. The capacitor configurations shown in Fig. TF15-1illustrate the basic concept of how a capacitor is usedto measure motion, although more complex capacitor

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338 TECHNOLOGY BRIEF 15: MICROMECHANICAL SENSORS AND ACTUATORS

Gap-Closing Mode

εwld − zCz =

εwl

(d − z)2dCzdz =

Capacitance:

Sensitivity:

z Fd

w

Nominal position(no force)

Metalplates

l

Overlap Mode

ε(w − y)ldCy =

εld

dCydy = −

Capacitance:

Sensitivity:

Metalplates

F

d

y

wl

Figure TF15-1: Basic capacitive measurement modes. For (b), the expressions hold only for small displacements such thaty � w.

geometries also are possible, particularly for sensingangular motion.

To convert the capacitor-accelerometer concept into apractical sensor—such as the automobile accelerometerthat controls the release of the airbag—let us consider thearrangement shown in Fig. TF15-2(b). The lower plateis fixed to the body of the vehicle, and the upper platesits on a plane at a height d above it. The upper plate isattached to the body of the vehicle through a spring witha spring constant k. When no horizontal force is actingon the upper plate, its position is such that it provides a100 percent overlap with the lower plate, in which casethe capacitance will be a maximum at Cy = εW�/d. If thevehicle accelerates in the y-direction with acceleration ay,the acceleration force Facc will generate an opposingspring force Fsp of equal magnitude.

Equating the two forces leads to an expressionrelating the displacement y to the acceleration ay, asshown in the figure. Furthermore, the capacitance Cyis directly proportional to the overlap area �(w − y) andtherefore is proportional to the acceleration ay. Thus, bymeasuring Cy, the accelerometer determines the valueof ay. A similar overlap-mode capacitor attached to thevehicle along the x-direction can be used to measure ax.Through a similar analysis for the gap-closing modecapacitor shown in Fig. TF15-2(a), we can arrive at afunctional relationship that can be used to determine thevertical acceleration az by measuring capacitance Cz.

For example, if we designate the time when the ignitionstarts the engine as t = 0, we then can set the initial

conditions on both the velocity u of the vehicle and itsacceleration a as zero at t = 0. That is, u(0) = a(0) = 0.The capacitor accelerometers measure continuous-timewaveforms ax(t), ay(t), and az(t).Each waveform then canbe used by an op-amp integrator circuit to calculate thecorresponding velocity waveform. For ux, for example,

ux(t) =t∫

0

ax(t) dt,

and similar expressions apply to uy and uz.

Commercial MEMS Accelerometers

Figure TF15-3 shows the Analog Devices ADXL202accelerometer which uses the gap-closing mode todetect accelerations on a tiny micromechanical capacitorstructure that works on the same principle describedabove, although slightly more complicated geometrically.Commercial accelerometers, such as this one, make useof negative feedback to prevent the plates from physicallymoving. When an acceleration force attempts to movethe plate, an electric negative-feedback circuit applies avoltage across the plates to generate an electrical forcebetween the plates that counteracts the acceleration forceexactly, thereby preventing any motion by the plate. Themagnitude of the applied voltage becomes a measure ofthe acceleration force that the capacitor plate is subjectedto. Because of their small size and low power consump-tion, chip-based microfabricated silicon accelerometers

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TECHNOLOGY BRIEF 15: MICROMECHANICAL SENSORS AND ACTUATORS 339

(a) The ADXL202 accelerometer employs many gap-closing capacitor sensors to detect acceleration. (Courtesy Analog Devices.)

(b) A silicon sensor that uses overlap mode fingers. Thewhite arrow shows the direction of motion of the movingmass and its fingers in relation to the fixed anchors. Notethat the moving fingers move into and out of the fixedfingers on either side of the mass during motion. (Courtesy of the Adriatic Research Institute.)

Spring constant k

Mass m z

d

Fsp

Facc

Fsp = Facc

kz = maz

mazkz =

Cz =εwl

mazkd −( )

Spring

yw

d

FspFacc

Facc = Fsp

may = kymay

ky =

Cy = = d

εlmay

kw −( )εl(w − y)d

Figure TF15-2: Adding a spring to a movable plate capacitor makes an accelerometer.

are used in most modern cars to activate the releasemechanism of airbags.They also are used heavily in manytoy applications to detect position, velocity and accelera-tion.The Nintendo Wii, for example, uses accelerometersin each remote to detect orientation and acceleration.Incidentally, a condenser microphone operates much likethe device shown in Fig.TF15-2(a): as air pressure waves

(sound) hit the spring-mounted plate, it moves and thechange in capacitance can be read and recorded.

A Capacitive Actuator: MEMS ElectrostaticResonators

Not surprisingly, we can drive the devices discussedpreviously in reverse to obtain actuators. Consider again

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340 TECHNOLOGY BRIEF 15: MICROMECHANICAL SENSORS AND ACTUATORS

FigureTF15-3: The complete ADXL202 accelerometer chip.The center region holds the micromechanical sensor; the majorityof the chip space is used for the electronic circuits that measure the capacitance change, provide feedback, convert themeasurement into a digital signal, and perform self-tests. (Courtesy of Analog Devices.)

the configuration in Fig. TF15-2(a). If the device is notexperiencing any external forces and we apply a voltage Vacross the two plates, an attractive force F will developbetween the plates. This is because charges of oppositepolarity on the two plates give rise to an electrostaticforce between them.This, in fact, is true for all capacitors.In the case of our actuator, however, we replace thenormally stiff, dielectric material with air (since air isitself a dielectric) and attach it to a spring as before.With this modification, an applied potential generates anelectrostatic force that moves the plates.

This basic idea can be applied to a variety ofapplications. A classic application is the digital lightprojector (DLP) system that drives most digital projectors

used today. In the DLP, hundreds of thousands ofcapacitor actuators are arranged in a 2-D array on achip, with each actuator corresponding to a pixel onan image displayed by the projector. One capacitiveplate of each pixel actuator (which is mirror smoothand can reflect light exceedingly well) is connectedto the chip via a spring. In order to brighten ordarken a pixel, a voltage is applied between theplates, causing the mirror to move into or out ofthe path of the projected light. These same de-vices have been used for many other applications,including microfluidic valves and tiny force sensorsused to measure forces as small as a zeptonewton(1 zeptonewton = 10−21 newtons).