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An Introduction to MEMS Optical Switchesprepared forPenny BeebeEngineering Communications ProgramJoseph M. BallantyneSchool of Electrical and Computer EngineeringbyMeng Fai TungSchool of Electrical and Computer EngineeringDecember 13, 2001 2001 Meng Fai Tung

CONTENTSLIST OF FIGURESiiI. GLOSSARY1II. LIST OF SYMBOLS AND ABBREVIATIONS5III. INTRODUCTION7IV. SOURCES7V. DISCUSSION8A. Background8B. Two-Dimensional and Three-Dimensional Architectures for MEMS10Optical SwitchesC. The Two-Dimensional 2x2 MEMS Optical Switch by Marxer et al.13D. Micromirrors14E. Actuating Mechanisms16F. V-Grooves21G. Insertion Loss21H. Other Two-Dimensional MEMS Optical Switches24I. Applications of MEMS Optical Switches25J. Advantages and Disadvantages of MEMS Optical Switches25VI. CONCLUSION27VII. WORKS CITED29VIII. APPENDICES32Appendix A: Structure and operation of the Marxer et al. optical switch32Appendix B: Fabrication of the Marxer et al. optical switch33Appendix C: Two-dimensional MEMS optical switch based on pop-up mirrors34i

LIST OF FIGURESFigure 1Three basic steps in micromachining9Figure 2Patterning process9Figure 3A two-dimensional 4x4 MEMS optical switch11Figure 4Two-axis tilting micromirror11Figure 5Arrays of tilting micromirrors in action12Figure 6Micromirror reflectivity as a function of metal coating thickness14Figure 7Coupling loss as a function of mirror angle for four different mirror16thicknessesFigure 8Operation of electrostatic comb drive actuator18Figure 9Inner and outer comb drives19Figure 10Transmitted power as a function of voltage applied on the outer comb20driveFigure 11Holding structures for mounting optical fibers21Figure 12Mode coupling between optical fibers23ii

I. GLOSSARYactuator:a device that causes movement of parts in amachineactuating:causing movement of parts in a machineall-optical network:an optical network environment that exploits multiple channel wavelengths forswitching, routing or distribution, usinglight to the almost total exclusion of electronics (Bates, 2001, p. 273)bar state:the state in which, a light beam is allowedto pass straight through from one opticalfiber to anotherbeam divergence:the spreading of a light beam as it exits asmall aperturebulk micromachining:micromachining that involves directly etching the silicon substrateburied oxide:the layer of oxide that is buried beneath athin silicon top layercollimator:a device that makes divergent or convergent rays more nearly parallelcoupling:the act of transferring energy from one optical component to anothercoupling loss:the loss that occurs when transferring energy from one optical component to anothercrosstalk:the undesired coupling of a signal from onechannel to anothercross state:the state in which, a light beam is deflectedfrom one optical fiber into another perpendicular optical fiberdeep reactive ion etching (DRIE):an etching process that allows for veryhigh-aspect-ratio etching of silicon1

electromagnetic actuation:the movement of machine parts by electromagnetic forcesthe movement of machine parts by electrostatic forces of attractionelectrostatic actuation:electrostatic comb drive actuator:an electrostatic actuator that uses a largenumber of interdigitated fingersfree-space microoptical bench (FS-MOB):a scheme whereby micro-optical elements,micropositioners and microactuators areattached to on the same substrate, but thelight beams travel in airFresnel reflection:the reflection of part of the incident light atthe sharp boundary between two mediawith different refractive indices (AmericanNational , 2000)fringe fields:electromagnetic fields at the edges of conductorshysteresis behavior:the dependence on prior history of a difference in a stateinsertion loss:the total optical power loss caused by insertion of an optical component in an opticalfiber systemintegrated circuit (IC):a semiconductor chip which contains dozens to millions of transistorslaser diode:a semiconductor device that emits lightwhen an electrical current is appliedmask:a template containing the patterns of a layerMEMS optical switch:an optical switch implemented with MEMStechnologymicroelectromechanical systems (MEMS):micron-size mechanical components suchas levers, plates and hinges which areformed on a substrate (usually silicon) andactuated by electrical meansmicromachining:machining of structures at the microscale,often in silicon2

micromirror:a tiny mirror fabricated in silicon usingMEMS technologymode:a pattern of electric and magnetic fieldshaving a physical size (Crisp, 2001, p. 61)mode coupling:the transfer of energy from one mode oftransmission to anotheroptical add/drop multiplexer:an optical network component that letsspecific channels of a multi-channel opticaltransmission system to be dropped and/oradded without affecting the other signalchannels that are to be transported throughthe network node (Bates, 2001, p.284)optical cross connect (OXC):a large optical switch capable of simultaneously switching many input optical signalsto any output portsoptical-electronic-optical (O-E-O) switch:a switch that first converts optical signalsinto electrical signals to perform theswitching function, and then converts theelectrical signal back into an optical signalfor further transmissionoptical fiber:a cylindrical optical waveguide for transmitting lightoptical switch:a device that switches an optical signalfrom one optical fiber to another, withouthaving to first convert the optical signalinto an electrical signalphotodetector:a device that detects light and generates anelectrical signalphotoresist (resist):a light-sensitive material that is used in thepatterning processpolarization:the direction of the electric field in electromagnetic wavesport count:the number of input and output ports in anoptical switch3

rise time:the time taken for the light intensity to increase from 10% to 90% of its final levelrotary electrostatic actuator:an electrostatic actuator capable of causingrotationshielding:insulating from the effects of electrical ormagnetic fieldssilicon-on-insulator (SOI):silicon wafer with a layer of buried oxidebeneath a thin silicon surface layersilicon substrate (bulk):a thin slice (wafer) of siliconsilicon wafer:see silicon substratesingle mode fiber:an optical fiber with only one mode oftransmissionsynchronous optical network (SONET):a standard for transmitting digital information over optical networks (Bates, 2001, p.288)surface micromachining:micromachining that involves selectivelyetching the additional layers deposited onthe silicon substratev-groove:a V-shaped trench used to hold and alignoptical fibers4

II. LIST OF SYMBOLS AND ABBREVIATIONSSYMBOLSAamplitude (in section on insertion loss)ACplate area (in section on actuatingmechanisms)capacitance Cchange in capacitance Lchange in overlap length of fingersεopermittivity of free spaceεrrelative permittivity of dielectricmaterialFattractive force between plateshheight of fingersLoverlap length of fingersλwavelength of lightnnumber of fingers in lower comb (in sectionon actuating mechanisms)nrefractive index (in section on insertion loss)Poptical power deliveredPscatflux of light scattered awayPtottotal reflected fluxσroot mean square surface roughnessθiangle of incidenceVdifferential voltagewbeam radius5

Wenergy stored by a parallel-plate capacitorxseparation between plates (in actuatingmechanisms)ABBREVIATIONSDRIEdeep reactive ion etchingICintegrated circuitMarxer et al. optical switchtwo-dimensional 2x2 MEMS optical switchby Marxer et al.MEMSmicroelectromechanical systemsO-E-Ooptical-electronic-opticalOXCoptical cross connectSEMscanning electron microscopeSOIsilicon-on-insulatorSONETsynchronous optical networkFS-MOBfree-space microoptical bench6

III. INTRODUCTIONThe purpose of my library research has been to study Microelectromechanical Systems(MEMS) optical switches, and to introduce this topic to newly graduated engineers whoare unfamiliar with this area. Optical switches are components in a fiber-optic communications network that direct light beams from one optical fiber to another. Throughout thispaper, the term “optical switch” shall refer only to switches that manipulate light beamsdirectly. Switches that perform the switching function by converting the optical signal toan electrical signal are not included. MEMS technology (used to create microscale systems in silicon) is used to implement the optical switches that I have studied. I have focused on two-dimensional MEMS optical switches, and have chosen the two-dimensional2x2 MEMS optical switch by Marxer et al. (1997, pp. 277-285) as an example for introducing some key features of two-dimensional MEMS optical switches.IV. SOURCESThe major sources for my library research have been journal articles and conference proceedings. I have been using articles mainly from the Journal of MicroelectromechanicalSystems and Laser Focus World. I have also used conference papers written for the Optical Fiber Communication Conference and Exhibit. The IEEE Xplore website has alsoprovided a number of useful on-line articles relevant to MEMS optical switches. For anunderstanding of fundamental concepts in MEMS and fiber-optics, I have relied on anumber of introductory as well as advanced textbooks such as, Introduction to Fiber Optics by Crisp and Micromachined Transducers Sourcebook by Kovacs. I have also spokenwith Cornell University Professors Ballantyne, Kan, Pollock and Lipson about varioussections of this paper.7

V. DISCUSSIONA. Background Information(a) MEMSAccording to Maluf (2000, pp. 3-4), MEMS is a very broad term that can refer to “techniques and processes to design and create miniature systems [at the microscale].” MEMShas been used to create miniaturized sensors, actuators and structures (often in silicon) fora variety of applications. A common example is the crash sensor used in automotivesafety. The airbag deployment systems in automobiles have miniaturized sensors thatmonitor acceleration, and will produce a signal to activate the airbag deployment mechanism in the event of a crash. (Maluf, 2000, pp. 4-5) Despite having being discovered asearly as the 1960’s, MEMS is still finding its way into new applications, ranging fromgenetic and chemical analysis to telecommunications.(b) Basic Micromachining ProcessesMicromachining literally is the machining of structures at the microscale. MEMS products are usually made by micromachining silicon, which is the primary material used inthe manufacture of integrated circuits (ICs). Hence, many of the processes inmicromachining came from IC fabrication. (Maluf, 2000, p. 41) Micromachining iscomplex and involves several disciplines, including those of material science andchemistry. It is beyond the scope of this library research project to give a detailedtreatment of micromachining. The intent in this section is to provide basic information, sothat the process of fabricating MEMS optical switches may be understood.The fabrication of MEMS products may involve several process steps. However, thesesteps can be grouped into three basic processes – deposition, patterning and etching. Figure 1 depicts these steps together with the cross-section of a silicon wafer. In deposition,layers of material are added on top of the silicon substrate (or bulk). The materials deposited include thin films of polysilicon, silicon dioxide, silicon nitrides and metals, such asaluminum, copper and tungsten. Photoresist (or resist) is a special type of material, similar to film used in photography. In the patterning step, the photoresist is exposed to light8

passing through a mask (a template containing the patterns of a layer) and is subsequentlydeveloped. Figure 2 illustrates thepatterning process. A series of masksdefines how to build the structureslayer by layer. In etching, the undeveloped parts of the photoresist actas a protective layer, so that chemicals applied to the surface only remove material from the exposed reFigure 1: Three basic steps in micromachining(adapted from Maluf, 2000, p. 43)gions. Hence, patterning and subsequently etching achieve selectiveremoval of material. By repeating the three basic steps using different materials andchemicals, miniature structures are fashioned outof the silicon. (Maluf, 2000, pp. 42-69)Generally, two classes of micromachining areavailable for making MEMS products. In surfacemicromachining, layers of material are added tothe surface of the silicon and are selectively etchedto produce the structures. However, bulk micromachining involves directly etching the siliconbulk to form the structures. Thus, bulk micromachining does not add additional layers of mate-Figure 2: Patterning process(adapted from Maluf, 2000, p. 52)rial other than photoresist, which is required for patterning. (Neukermans and Ramaswami, 2001, p. 63)(c) The need for optical switchesOptical switches have become important because of the telecommunications industry’sfocus on all-optical networks. According to Bates (2001, p. 273), all-optical networks are“optical network environments that exploit multiple channel wavelengths for switching,routing or distribution, using light to the almost total exclusion of electronics.” The moti-9

vation for all-optical networks is evident from the bandwidth of an optical communication link. Today’s optical fibers have an effective bandwidth of approximately 25THz (aunit of frequency equal to 1012 cycles per second). This amount of bandwidth can be regarded as infinite for today’s applications. However, the optical-electronic-optical (O-EO) switches that are currently being used to switch optical signals are limiting the use ofthe wide bandwidth of optical fibers. O-E-O switches first convert the input optical signalto an electronic signal using a high-speed photo-detector (a device that detects light andgenerates an electrical signal). Electronic circuits in the switch then perform the switching function, directing the electronic signal to the appropriate output port. Finally, a laserdiode (a device that emits light when an electrical current is applied) converts the electronic signal back into an optical signal for further transmission on the optical fiber network. (Bates, 2001, p. 135) The O-E-O switches are unable to match the higher data rateof the optical fibers because of this conversion process, and they slow down the operationof the optical fiber communication link (Morris, 2001, p. 47).As demand for bandwidth grows, due to increased Internet traffic and the advent of dataand video-centric networks, the need to eliminate this bottleneck at the switches becomesmore critical. Optical switches that manipulate optical signals directly without convertingthe optical signal to an electronic signal have been developed to replace the O-E-Oswitches. One approach has been the use of MEMS technology to fabricate tiny mirrorsthat perform the switching function. These tiny mirrors (micromirrors) switch optical signals by reflecting the light beams, and switches using these tiny mirrors are known asMEMS optical switches.B. Two-Dimensional and Three-Dimensional Architectures for MEMS OpticalSwitchesGenerally, two approaches are taken in implementing MEMS optical switches. In thetwo-dimensional or digital approach, an array of micromirrors and the optical fibers arearranged so that the optical plane is parallel to the surface of the silicon substrate. Themicromirrors can assume one of two states at any given time. (Husain, 2001, p. wx1-2) In10

the cross state, the micromirror moves into the path of the light beam and reflects thelight beam, whereas in the bar state, it allows the light beam to pass straight through. Figure 3 is a diagram of a simplified two-dimensional 4x4 MEMS optical switch. The shortdiagonal lines represent micromirrors. The darkened mirrors are in the cross state whilethe grayed out micromirrors are in the bar state.Input light beams 1, 2, 3 and 4 are directed tooutput ports 3, 1, 4 and 2 respectively. With individual micromirrors in the cross state or barstate in the array, any input port can be connected to any output port. (Barthel and Chuh,2001, p. 93)In the three-dimensional or analog approach,the micromirrors are not limited to just two positions. They are able to vary their position overa continuous range of angles and in two direc-Figure 3: A two-dimensional 4x4MEMS optical switch(adapted from Barthel and Chuh,2001, p. 93)tions, which allows a single micromirror to direct an input light beam to more than onepossible output port (Hecht, 2001, p. 126). In contrast, in the two-dimensional approach,the micromirror in row one, column three for example, is able to direct only input lightbeam 1 to output port 3. According to Hecht(2001, pp. 125-126), a common threedimensional micromirror is the two-axis tilting micromirror (see Figure 4). The circularmicromirror “pivots on one axis between apair of posts attached to a surrounding ring.The ring, in turn, pivots on a perpendicularaxis on a pair of posts connected to a surFigure 4: Two-axis tilting micromirror(Hecht, 2001, p. 125)rounding framework, which is fixed in placeabove the surface.” Figure 5 depicts two ar-rays of these tilting micromirrors, used in an NxN MEMS optical switch. The light beamsfrom an array of input ports fall onto the first array of tilting micromirrors, which reflects11

the light beams onto a second array. The second array then reflects the light beams intoan array of output ports. Each micromirror on the first array is able to reach any of themicromirrors on the second array and vice-versa. (Hecht, 2001, p. 126)For an NxN switch, the two-dimensional approach requires N2 micromirrors, while thethree-dimensional approach requires only 2N micromirrors. The three-dimensional approach scales much better with port count, as it is linear in N. Hence, as port count increases, the three-dimensional approach results in more compact designs than the twodimensional approach. The two-dimensional approach also suffers from an increasingpropagation distance for light as port counts grow. When the light beam exits the opticalFigure 5: Arrays of tilting micromirrors in action(adapted from Hecht, 2001, p. 126)fiber, it begins to spread. The longer the distance traveled, the greater the beam’s diameter becomes, resulting in the need for greater collimator (device that makes divergent orconvergent rays more nearly parallel) performance. However, the two-dimensional approach has the advantage of being simpler and less sensitive to noise. The micromirrorsin the three-dimensional approach have to be very precise. A small amount of noise present in the control circuit can cause an error in the tilt angle of the micromirror, leading tomisdirection to the wrong port. (Husain, 2001, pp. wx1-2 – wx1-3)12

C. The Two-Dimensional 2x2 MEMS Optical Switch by Marxer et al.Appendix A shows the structure and operation of a simplified version of the twodimensional 2x2 MEMS optical switch by Marxer et al. (1997, pp. 277-285). This opticalswitch (subsequently referred to specifically as the “Marxer et al. optical switch”) uses asliding vertical micromirror whose movement is controlled by an electrostatic comb driveactuator. The vertical micromirror is found at the intersection of two perpendicularalignment grooves. The optical fibers (only one is shown) lie in the alignment grooves. In(1), the optical switch is in the cross state and the vertical micromirror moves into thelight path. The light beam from input 1 is reflected into output 2, and the light beam frominput 2 is reflected to output 1. The optical switch is in the bar-state in (2). The verticalmicromirror is retracted, and the light beams from inputs 1 and 2 are allowed to passstraight through into their respective outputs. (Maluf, 2000, pp. 187-190)Appendix B explains the fabrication of the Marxer et al. optical switch. Bulk micromachining with a silicon-on-insulator (SOI) wafer (silicon wafer with a layer of buriedoxide beneath the silicon bulk) is used. Photoresist is applied, and patterning is performedas shown in (1). A single mask is used that contains the patterns for the micromirror, theoptical fiber alignment grooves, the electrostatic comb drive actuator and the suspensionsprings. The left side of the cross-section corresponds to the electrostatic comb drive actuator and the right side to the optical fiber alignment groove. An etching process knownas Deep Reactive Ion Etching (DRIE) is then used to obtain the deep trenches shown in(2). DRIE is capable of very high-aspect-ratio silicon etching of up to 200:1 aspect ratios.For a detailed discussion of DRIE, see pages 66 to 70 of Maluf’s book. Etching stopswhen the buried oxide is exposed because the chemistry changes. In (3), hydrofluoricacid, which does not etch silicon, is applied to remove the buried oxide. By controllingthe duration and rate of etching, the hydrofluoric acid does not etch away all the buriedoxide in the SOI wafer. The movable structures are freed while the rest remain anchored.Finally, in (d), the optical fiber is placed into the alignment groove and the micromirror iscoated with aluminum. (Maluf, 2000, pp. 66-70; Marxer et al., 1997, p. 279)13

Two-dimensional 2x2 optical switches such as the Marxer et al. optical switch are thebasic building blocks for two-dimensional optical switches of higher port count. Typically, these larger two-dimensional optical switches are formed by cascading a number oftwo-dimensional 2x2 optical switches in a matrix. Therefore, many of the features oftwo-dimensional MEMS optical switches are illustrated in the Marxer et al. opticalswitch presented above.D. MicromirrorsMicromirrors are the centerpieces of MEMS optical switches. They are tiny mirrors fabricated in silicon using MEMS technology. The switching function is performed bychanging the position of a micromirror to deflect an incoming light beam into the appropriate outgoing optical fiber. The three important properties of micromirrors are reflectivity, light transmission, and surface roughness. Coating its surface with metal can increasethe reflectivity of a micromirror. Figure 6 shows a plot of micromirror reflectivity versusthe thickness of metal coating forfour different metals. The wavelength of light used was 1.3 µmand the measurements were takenfor normal incidence. The micromirrorreflectivityincreaseswith increasing thickness of metalcoating, and saturates at a maximum value. Coating the micromirror with aluminum appears to beFigure 6: Micromirror reflectivity as a function of metal coating thickness(adapted from Marxer et al., 1997, p. 278)the best option, giving the micromirror a maximum reflectivityof 97% at a thickness of 40 nm. Agold coating is also a good option, but the micromirror reflectivity only saturates to itsmaximum value at 60 nm. If the angle of incidence is non-normal, the reflectivity of themicromirror is dependent on the polarization of light. Polarization refers to the direction14

of the electric field in electromagnetic waves. The dependence varies for different metalcoatings. For a 45o angle of incidence, the aluminum-coated micromirror demonstrates apolarization dependence of only 1.1%, whereas for chrome and nickel, the polarizationdependence is greater than 11%. (Marxer et al., 1997, pp. 277-278)Ideally, the micromirror should only reflect light, but a small amount of light is alsotransmitted. The light transmission should be attenuated as far as possible so that no lightpasses through the micromirror. Otherwise, crosstalk into an undesired fiber would occur.It has been found that the light transmission is attenuated below 1 ppm for an aluminumcoating thickness of 100 nm. Gold, chrome and nickel coatings all require a thickness inexcess of 170 nm to achieve the same result. (Marxer et al., 1997, pp. 277-278)If the surface of the micromirror is not smooth, light is scattered, resulting in light loss.The total amount of scattered light for a micromirror may be estimated using the equationPscat 1 ePtot 4πσ cos θ i λ 2where Pscat is the flux of light scattered away from the specular direction, Ptot is the totalreflected flux, θi is the incidence angle, λ is the wavelength and σ is the root mean squaresurface roughness. This relationship is only valid for gently sloped surfaces with a Gaussian distribution of surface height (Marxer et al., 1997, p. 278). Zhu and Kahn (2001, pp.185-186) provide a more advanced treatment of light loss due to micromirror surfaceroughness.In the case of the Marxer et al. optical switch, additional properties of concern are micromirror verticality and thickness. The effect of a micromirror’s verticality and nonzerothickness on coupling loss (the loss that occurs when energy is transferred from one optical fiber to another) has been studied. The mirror introduces an angular offset, as it is notexactly 90o to the substrate. A traverse beam offset is also present due to the nonzerothickness. Figure 7 is a plot of coupling loss versus micromirror angle for four differentmicromirror thicknesses. The plot shows that the thickness of the micromirror should be15

kept below 3.5 µm for a 90o micromirror, and at most, 2 µm for an angle error of 0.7o, inFigure 7: Coupling loss as a function of mirror angle for four differentmirror thicknesses(adapted from Marxer et al., 1997, p. 279)order to achieve a coupling loss below 2dB. (Marxer et al., 1997, p. 279)E. Actuating Mechanisms(a) Electromagnetic ActuationIn electromagnetic actuation, electromagnetic forces are used to move the micromirror.An electromagnetic 2x2 MEMS optical switch has been successfully developed by Milleret al. (1997, pp. 89-92). The micromirror was fabricated on top of a silicon plate supported by cantilever beams. A copper coil is found on the bottom side of the silicon plate.The application of an electric current through the coil, in the presence of a magnetic field,exerts a force on the silicon plate. The force causes the cantilever supports to bend,thereby altering the position of the micromirror. Magnetic actuation can provide largerforces, but it suffers from high power consumption and problems with shieldingneighboring objects from the magnetic fields (Kovacs, 1998, p. 649).16

(b) Electrostatic ActuationElectrostatic actuation relies on the attraction between two oppositely charged plates, andhas the benefits of repeatability, no shielding requirements, and well-studied behavior(Husain, 2001, p. WX1-2). According to Kovacs (1998, p. 277), electrostatic actuatorsare also “very low power” and “simple to fabricate”. Electrostatic actuation is the methodemployed in the Marxer et al. optical switch, and will be discussed further.Using a parallel-plate capacitor approximation, the force supplied by electrostatic actuation can be estimated to first order. The approximation holds only for simple geometriesand very small angles (in the case of cantilevers). Neglecting fringe fields (fields at theedges of the plates), the energy stored by a parallel-plate capacitor, C, with plate area, A,and voltage, V, across its terminals is given by11 ε ε AV 2W CV 2 r o22xwhere x is the separation between the plates, εr, the relative permittivity of the dielectricmaterial and εo, the permittivity of free space. Taking the derivative of W with respect tox yields the force between the plates:F dW1 ε r ε o AV 2 2dxx2This equation states that the force versus separation distance and force versus voltage relationships are non-linear (Kovacs, 1998, p. 278). Maluf (2000, p. 92) mentioned that theelectrostatic force generated for a spacing of one µm, an applied voltage of 5V, and a“reasonable area” of 1,000 µm2 is “merely” 0.11 µN. To obtain relatively large movements in the plane of the substrate, electrostatic comb drive actuators are used in theMarxer et al. optical switch. Electrostatic comb drive actuators are a type of electrostaticactuator that makes use of a large number of “interdigitated fingers” (Kovacs, 1998, pp.282-283).Figure 8(a) shows a simplified diagram of an electrostatic comb drive actuator in the unactuated state. The upper comb is held rigid while the lower comb is free to move. Thecapacitance of the electrostatic comb drive is approximately17

C 2nε r ε o Lhxwhere n is the number of fingers in the lower comb (n is four in Figure 1), x is the separation between the fingers, L is the overlap length of the fingers and h (not shown in the(a) Unactuated(b) ActuatedFigure 8: Operation of electrostatic comb drive actuator(adapted from Böhringer, 1999)figure) is the height of the fingers. When a differential voltage, V, is applied, the lowercomb experiences an attractive force given by1dCF V22dLin the vertical direction (with respect to the orientation in the figure). The lower combdoes not move in the horizontal direction, as each finger on the lower comb experiencesan equal force of attraction in both the left and right directions. The actuated state isshown in Figure 8(b). The change in capacitance, C, when the lower comb moves by Lis given by C 2nε r ε o h LxTherefore,F nε r ε o hV 2xand F is independent of L, suggesting that F is due mainly to fringing fields as opposedto parallel-plate fields. (Böhringer, 1999) The above equation shows that the force supplied by an electrostatic comb drive increases linearly with the number of fingers on the18

lower comb. Hence, the electrostatic force generated can be made much larger than 0.11µN by using a large number of fingers.Other types of electrostatic actuators for moving micromirrors have been fabricated. Rotary electrostatic actuators have been demonstrated by Grade and Jerman (2001, pp.WX2-1-WX2-3). These rotary electrostatic actuators consist of special arrangements ofmodified comb drives, which enable rotation of the micromirror.(C) Actuating Mechanism of the Marxer et al. Optical SwitchTo minimize the switching time, the Marxer et a

tems in silicon) is used to implement the optical switches that I have studied. I have fo-cused on two-dimensional MEMS optical switches, and have chosen the two-dimensional 2x2 MEMS optical switch by Marxer et al. (1997, pp. 277-285) as an example for intro-ducing some key features of two-dimensional MEMS optical switches. IV. SOURCES

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