Actuators for alltypes of MEMS devices are covered in Chapter 5, but the most common actuator types for surface micro-machines — electrostatic and thermal — are also covered here.. The s
Trang 1The phenomenon of buckling is much different than that of bending A beam will begin to bend assoon as any moment (bending load) is present In contrast, a column will not exhibit any lateral deflec-tion until the critical or buckling load is reached Above the critical load, additional loading causes largeincreases in lateral deflection Because of the tensile properties of polysilicon, it is possible to design a col-umn to buckle without exceeding the yield strength If yield does not occur, the column will return to itsoriginal straight position after the load is removed If designed appropriately, a buckling column can beused as an out-of-plane flexure [Garcia 1998].
Buckling is a complex nonlinear problem and predicting the shape of the buckled structure is beyondthe scope of this text It is, however, covered in several references including Timoshenko and Gere (1961),Brush and Almroth (1975), Hutchinson and Koiter (1970), and Fang and Wickert (1994) However, theequation for predicting the onset of buckling is relatively straightforward For a column with one endfixed and the other free to move in any direction (i.e., a cantilever), the critical load to cause buckling is:
It is important to remember that the critical load for buckling cannot exceed the maximum force ported by the material In other words, if the load needed to cause buckling is larger than the load needed
sup-to exceed the compressive strength, the column will fail by rupture before buckling
4.4.1.9 Hinges and Hubs
A different type of rigid-body-mode machine is a vertical axis hinge These hinges are used in surfacemicromachining to create three-dimensional structures out of a two-dimensional surface micromachin-ing process In the surface micromachining process, hinges are constructed by stapling one layer of poly-silicon over another layer of polysilicon with a sacrificial layer between them A cross section of a simplehinge is illustrated in Figure 4.16 A more complex hinge is shown in Figure 4.17 Hinges have some
Trang 2mid-advantages over flexible joints One advantage is that no stress is transmitted to the hinged part so greaterangles of rotation are possible Also, the performance of hinged structures is not influenced by the thick-ness of the material and deformation of the machine is not required The limitations of hinged structuresare that the sacrificial layers must be thick enough for the hinge pin to rotate and at least two released lay-ers of material are required Hinges are also susceptible to problems with friction, wear, and the associ-ated reliability problems The same limitations and advantages are true for structures that rotate parallel
to the plane of the substrate such as gears and wheels A cross section of a simple hub and gear is shown
in Figure 4.18 and a complex hub structure is shown in Figure 4.4
4.4.1.10 Actuators
There are several different actuation techniques for surface micromachine mechanisms Actuators for alltypes of MEMS devices are covered in Chapter 5, but the most common actuator types for surface micro-machines — electrostatic and thermal — are also covered here Electrostatic actuators harness the attrac-tive Coulomb force between charged bodies For a constant voltage between two parallel plates, the energystored between the plates is given by:
where ε0is the dielectric constant of free space (8.854 1012F/m), εris the relative dielectric constant,
for air it is 1.0, A is the area, V is the voltage, and y is the distance The force between the plates is attractive
and given by:
Trang 3The derivative of energy with respect to position is force.
Note that this force is not dependent on the lateral position x Comb-drive actuators utilize these
tan-gential forces with banks of comb fingers The surface micromachined comb-drive in Figure 4.20 typicallyoperates at voltages of 90 V and has output forces of around 10 µN Comb-drives can operate at speeds
up to 10 s of kHz and consume only the power necessary to charge and discharge their capacitive plates
Tangential forces Area
Normal forces
FIGURE 4.19 Illustration of normal and tangential forces in an electrostatic actuator.
FIGURE 4.20 Electrostatic comb-drive actuator fabricated in the SUMMiT V TM process at Sandia National Laboratories.
Trang 4Because the output force of an electrostatic comb-drive is proportional to the square of the applied voltage,these devices are often operated at higher voltages than most analog and digital integrated circuits Thishas complicated their implementation into systems It should be noted that Equations 4.37 through 4.40are for electrostatic actuators connected to a power supply and in constant voltage mode.
Example
The plate in Figure 4.19 is 50 µm long, 6 µm thick, and 3 µm wide It has a neighboring electrode that
is 1 µm away If 80 V are applied between the electrode and its identical neighbor and fringing is ignored,what are the forces in the normal and tangential directions if the combs are aligned in the width dimen-sion and overlap by 40 µm and 10 µm in the length dimension? How much does the force change in bothdirections if the distance is reduced to 0.1 µm? If there are 30 electrodes at 80 V interlaced with 31 elec-trodes at 0 V as in Figure 4.20with a separation of 1 µm between the electrodes what is the net tangentialforce? Assume that εr 1.0
Parallel plate electrostatic forces for the 40 µm of overlap case are:
and for the 10 µm case:
For the tangential force, the lateral dimension, x, is not included in Equation 4.40 so both calculations
yield the same result
The reader should note that the parallel plate force is much higher than tangential force If the separation
is reduced to 0.1 µm, then the normal force is increased by a factor of 100 to 440 µN and the tangentialforce is increased by a factor of 10 to 1.7 µN For 30 energized electrodes and 31 non-energized electrodes,the tangential force is multiplied by the number of energized electrodes and then doubled to account forboth faces of the electrode:
F 30 fingers 170 nN 30 2 10 µNNote that the parallel plate force of one electrode engaged 40 µm is still higher than the tangential force
of 30 electrodes However, the tangential force comb-drive has a force that is independent of position,while the parallel plate case falls off rapidly with distance However, the high forces at small separationsmakes parallel plate actuators useful for electrical contact switches
Thermal actuators have higher forces (hundreds of µN up to a few mN) and operate at lower voltages(1 V to 15 V) than electrostatic actuators They operate by passing current through a thermally isolatedactuator The actuator increases in temperature through resistive heating and expands, thus moving theload One type of thermal actuator has two beams that expand different amounts relative to each other[Guckel et al, 1992; Comtois, 1998] These pseudo bimorph or differential actuators use a wide beam and
a narrow beam that are electrically resistors in series and mechanically flexures in parallel Because thenarrow beam has a higher resistance than the wide beam, it expands more and bends the actuator in anarc around the anchors
Another type of thermal actuator uses two beams that are at a shallow angle Bent beam thermal ators generally have strokes of between 5 µm and 50 µm [Que et al., 2001; Cragun and Howell, 1999].Unlike the pseudo bimorph devices, they move in a straight line instead of an arc Like the pseudo bimorphactuators, they have an output force that falls off quickly with displacement Both types of thermal actua-tors are shown in Figure 4.21
Trang 54.5 Packaging
This section covers only aspects of packaging that are especially relevant to surface micromachines One
of the challenges of packaging surface micromachines is that the packaging is application specific andvaries greatly between different types of devices This is one reason that packaging tends to be the mostexpensive part of surface micromachined devices Therefore it is very important that designers of surfacemicromachines understand packaging and collaborate with engineers specializing in packaging whiledesigning their device Some of the main purposes of packages for surface micromachines include elec-trical and mechanical connections to the next assembly and protection from the environment
The mechanical attachment between a die and a package can be achieved in several different ways Themain criteria for choosing a die-attach method include: the temperature used during the die-attachprocess; the amount of stress the die-attach process induces on the die; the electrical and thermal prop-erties of the die-attach; the preparation of the die for the die-attach process; and the amount of out-gassing that is emitted by the die-attach Die-attach methods that do not outgas include silver-filledglasses and eutectics (gold–silicon) Both of these induce a large amount of stress onto the die as well asrequiring temperatures of around 400°C Epoxy-based die-attaches use much lower temperatures (up to150°C) and induce lower stress on the die than eutectics or silver-filled glasses The low stress means thatthey can be used for larger die However, depending on the type of epoxy, they do outgas water and cor-rosive chemicals such as ammonia As an alternative, flip-chip processes combine the process of die-attach and electrical interconnection by mounting the die upside-down on solder balls A note of caution:surface micromachines are strongly influenced by coatings and contamination or removal of these coat-ings, which can happen during temperature cycling, is detrimental to the micromachine
Electrical interconnect to surface micromachines is typically accomplished by wire bonding.Wirebonders use a combination of heat, force, and ultrasonic energy to weld a wire (normally aluminum
or gold) to a bondpad on the surface micromachined die The other end of the wire is welded to the age Although, wirebonds in high volume production have been done on less than 50 µm centers, for lowvolume applications it is easier if the bondpads are fairly large Metal coated bond pads that are 125 µm
pack-or larger on a side with 250 µm center-to-center spacing allow rewpack-orking of the wire bonds and fpack-or automated wire bonding equipment to be used These numbers are on the conservative side but could befollowed in the absence of process specific information.Figure 4.22 shows an Analog Devices ADXL50surface micromachined accelerometer with its wirebonds and epoxy die-attach
non-Cold Hot
Electrical current
Absolute actuator
actuator
Motion Motion
Cold
FIGURE 4.21 Drawings of absolute and differential thermal actuators.
Trang 6While electrical and mechanical connections to surface micromachines are similar to other types ofmicromachines and integrated circuits, the mechanical protection aspects of the packaging can be quitedifferent The package must protect the surface micromachine from handling by people or machines,from particles and dust that might mechanically interfere with the device, and from water vapor that caninduce stiction Packages for some resonant devices must maintain a vacuum and all packages must keepout dust and soot in the air However, sensor packages must allow the MEMS device to interact with itsenvironment Because surface micromachines are very delicate and fragile after release, even a carefulpackaging process can damage a released die Therefore, one of the trends in packaging is to encapsulateand mechanically protect the devices as early as possible in the manufacturing process Henry Guckel atthe University of Wisconsin was one of the first developers of an integrated encapsulation technique[Guckel, 1991] In this design, the surface micromachine was covered by an additional layer of structuralmaterial during the fabrication process This last structural layer completely encapsulates the surfacemicromachine with the exception of a hole used to permit removal of the sacrificial layer by the releaseetchant After the release etch, the hole is sealed with materials ranging from LPCVD films, to sputteredfilms, to solders There is a good summary of this and other sealing techniques in Hsu (2004).
Another method of encapsulating the device is to use wafer bonding In this technique a cap wafer isbonded to the device wafer forming a protective cover One common method involves anodic bonding of
a glass cover wafer over the released surface micromachines A second involves the use of intermediatelayers such as glass frit, silicon gold eutectic, and aluminum The wafer bonding techniques are moreindependent of the fabrication process than the wafer level deposition processes Because of the lack ofstiction forces between the cap and the substrate and because film stresses in the cap are not a problem,bonded caps can be used for larger devices than deposited caps A package formed by Corning 7740 glass(pyrex) bonded to a surface micromachine is shown in Figure 4.23
Conventional packaging such as ceramic or metal packages also protect surface micromachines fromthe environment In this case, the package provides electrical and mechanical interconnections to the nextassembly as well as mechanical protection These types of packages tend to be more expensive than plas-tic packages, which can be used if encapsulation is done on the wafer level These packages are typicallysealed using either a welding operation that keeps the surface micromachine at room temperature or a
FIGURE 4.22 Analog Devices accelerometer after the package lid has been removed The epoxy die-attach and wire bonds are clearly visible This device had its package lid removed at Sandia National Laboratories (Photograph cour- tesy of Jon Custer of Sandia National Laboratories.)
Trang 7belt sealing operation that elevates the temperature of the entire assembly to several hundred degreesCentigrade.
4.6 Applications
The applications section of this chapter will present some surface micromachined mechanisms and cuss them with regard to some of the mechanical concepts discussed earlier The chapter concludes withsome design rules and lessons learned in the design of surface micromachined devices
One example of a surface micromachined mechanism is the countermeshing gear discriminator that wasinvented by Polosky et al (1998) This device has two large wheels with coded gear teeth Counter-rotationpawls restrain each wheel so that it can rotate counterclockwise and is prevented from rotating clockwise.The wheels have three levels of teeth that are designed so they will interfere if the wheels are rotated inthe incorrect sequence Only the correct sequence of drive signals will allow the wheels to rotate and open
an optical shutter If mechanical interference occurs, the mechanism is immobilized in the wise direction by the interfering gear teeth and by the counter-rotation pawls in the clockwise direction
counterclock-A drawing of the device and a close-up of the teeth are shown in Figures 4.24 and 4.25, respectively Thewheels have three levels of intermeshing gear teeth that will allow only one sequence of rotations out ofthe more than the 16 million that are possible Because the gear teeth on one level are not intended tointerfere with gear teeth on another level and because the actuators must remain meshed with the codewheels, the vertical displacement of the code wheels must be restricted This was accomplished with dim-ples on the underside of the coded wheels that limited the vertical displacement to 0.5 µm Warpage ofthe large 1.9-mm-diameter coded wheels is reduced by adding ribs with an additional layer of polysilicon.The large coded wheels are prevented from rotating backward by the counter-rotation pawls Thesedevices must be compliant in one direction and capable of preventing rotation in the other direction Thenext example discusses counter-rotation pawls
FIGURE 4.23 A surface micromachine encapsulated by a piece of glass Comb-drives can be seen through the right side of the mechanically machined cap This process can be accomplished either on a die or wafer basis (Photograph courtesy of A Oliver, Sandia National Laboratories).
Trang 8Figure 4.26 shows a counter-rotation pawl The spring is 180 µm long from the anchor to a stop
(labeled as l) and 20 µm long from the stop to the end of the flexible portion (denoted as a), with a width of
2 µm and a thickness of 3 µm The Young’s modulus is 155 GPa Assume that the tooth on the free end of
FIGURE 4.24 The countermeshing gear discriminator The two code wheels are the large gears with five spokes in the center of the drawing; the counter-rotation pawls are connected to the comb-drives; and the long beams in the upper right and lower left portion of the photograph (Drawing courtesy of M.A Polosky, Sandia National Laboratories.)
FIGURE 4.25 Teeth in the countermeshing gear discriminator The gear tooth on the left is on the top level of icon and the gear tooth on the right is on the bottom layer If the gears do not tilt or warp, the teeth should pass with- out interfering with each other (Photograph courtesy of Sandia National Laboratories.)
Trang 9polysil-the beam does not affect polysil-the stiffness and that polysil-the width of polysil-the stop is negligible Find polysil-the spring constant
of the pawl if the gear is rotated in the counterclockwise direction Comment on the spring constant ifthe gear is rotated in the clockwise direction
In the counterclockwise direction, the spring constant k is:
using a length l a of 200 µm In the clockwise direction, it is tempting to redefine the spring length as
20 µm The resulting spring constant is 116 N/m Unfortunately, this is an oversimplification because the
beam will deform around the stop The exact equation is in Timoshenko’s Strength of Materials
[Timoshenko, 1958] and in Equation 4.41:
This equation results in a spring constant of 15 N/m, which is still very stiff but not as stiff as the results
of the oversimplified calculation
One important element of many polysilicon mechanism designs is the microengine This device, described
by Garcia and Sniegowski (1995) and shown in Figures 4.27 to 4.29, uses an electrostatic comb-drive
FIGURE 4.26 Example of a simple counter-rotation pawl The stop is assumed to have a width of 0.
Trang 10connected to a pinion gear by a slider-crank mechanism with a second comb-drive to move the pinionpast the top and bottom dead center Two comb-drives are necessary because the torque on a pinion pro-duced by a single actuator has a dependence on angle and is given by the following equation:
X
Y
FIGURE 4.27 Mechanical representation of a microengine.
FIGURE 4.28 Drawing of a microengine The actuator measures 2.2 mm 2.2 mm and produces approximately
55 pN-m of torque.
Trang 11where F 0is the force of the comb-drive, θ describes the angle between hub of the output gear and the
link-age, and r is the distance between the hub and the linkage The torque produced by the “Y” actuator has a
similar dependence on angle The inertia of the rotating pinion gear is not great enough to rotate the gearpast the top and bottom dead center One important feature of this device is that the conversion from linearmotion to rotary motion requires the beams between the actuator and the driven gear to bend The bending
is permitted by a polysilicon linkage that is 40 µm in length and 1.5 µm in width with a thickness of 2.5 µm
Example
The comb-drive labeled “X” inFigure 4.27 has an actuator arm that must bend 17 µm in the lateraldirection as the gear rotates from 0° to 90° The gear is connected to the comb-drive via a 50-µm-widebeam that is 500 µm long in series with a thin flexible link that is 1.5 µm wide and 45 µm long The thinlink is connected to the comb-drive actuator and both beams have a Young’s modulus of 155 GPa Giventhat both beams are 2.5 µm thick, approximately how much force does it take to bend to the flexible link-age to rotate the gear from q 0 to q 90° if friction and surface forces are neglected? A drawing of thislinkage is shown in Figure 4.29
Assume that each segment is a cantilever beam spring that has one end fixed while the other end isundergoing a small deflection For each beam:
Trang 12and for the short beam:
Because the majority of the bending occurs in the thin flexible link the desired slope of the flexible link
at its end is:
of the bending occurs in the long flexible beam and not in the plate or the anchor beams The next examplediscusses the buckling criteria
Example
Determine how much axial force is needed for a micromachined polysilicon mirror to buckle given thefollowing dimensions The main beam is 300 µm long, 4 µm wide, and 1 µm thick with a Young’s modu-lus of 155 GPa Assume that the beam can be simplified to be a cantilever Neglect the buckling of theanchors and the mirror
Trang 13The moment of inertia for this situation is:
mir-is impossible to determine if the beam will initially buckle toward or away from the substrate If the beambuckles away from the substrate, it will continue to deflect away from the substrate If it initially bucklestoward the substrate, it will contact the substrate and further compression of the beam will result in thestructure buckling away from the substrate
Example
For the mechanism shown in Figure 4.31, how much mechanical force is made available by the mission if the microengine output gear has a diameter of 50 µm and an applied torque of 50 pN-m, thelarge spoked wheel has a diameter of 1600 µm, and the pin joint that links the spoked wheel to the mirror
FIGURE 4.30 A flexible pop-up mirror that operates via buckling In this photograph the buckling is out of the plane of the substrate (Photograph courtesy of E.J Garcia of Sandia National Laboratories.) A further description of
this device can be found in Garcia, E.J (1998) “Micro-Flex Mirror and Instability Actuation Technique,” in Proc 1998 IEEE Conf on Micro Electro Mechanical Systems (MEMS ’98), pp 470–474.
Trang 14is 100 µm from the hub? Determine the maximum force in the direction of the mirror at the pin joint,neglecting friction, if there is a gap of 0.5 µm between the linkage and the pin joint.
The torque available at the pin joint is:
where θ is the angle between a line connecting the pin joint and the mirror and a line connecting the pin
joint and the hub However, there is a gap or slop in the pin joint Sin(θ) is given by:
F radial
sin(θ)
FIGURE 4.31 A flexible mirror in its initial state and a large gear with spokes The spoked wheel acts as a sion and is used to gain enough mechanical advantage to buckle the beam Two important features are the hinge joint and guides which convert the off-axis motion of the “c-shaped” linkage to motion that is aligned with the mirror The c-shaped linkage was designed to avoid fabricating the linkage above the rotating joint and thus causing fabrication problems (Photograph courtesy of E.J Garcia, Sandia National Laboratories.)
Trang 15transmis- 5180For a mirror that is 150 µm 150 µm the force required is:
F area 5180 (150 106m)2 120 µNFor a mirror with dimples:
F area 5180 4 (2 µm)2 83 nNNote that the adhesive forces due to stiction are much smaller when dimples are used
For most practioners, the field of MEMS and surface micromachines has a steep learning curve Often thelearning occurs through repeated iterations of the same design, but this can be very time consuming andexpensive because the time between design completion and testing is usually measured in months and theprice per fabrication run is many thousands of dollars This section describes some failures in surfacemicromachined mechanisms The hope is that the reader will gain a deeper appreciation for the com-plexities of surface micromachined mechanism design and learn about some of the pitfalls
Surface micromachined parts typically have a thickness that is very small in relationship to their width orbreadth In the out-of-plane direction, the thickness is limited to a few micrometers due to the limiteddeposition rates of deposition systems and the stresses in the deposited films In the plane of the sub-strate, structures can be millimeters across These factors typically lead to surface micromachined struc-tures that have a very small aspect ratio as well as stiffness issues in the out-of-plane direction due to thelimited thickness of the parts The result is that designers of surface micromachines need to design struc-tures in three dimensions and account for potential movements out of the plane of the substrate Apotential problem occurs when two gears fabricated in the same structural layer of polysilicon fail tomesh because one or both of the gears are tilted Another is when structures moving above or belowanother structure mechanically interfere with each other when it was intended for them to not touch eachother Both of these instances will be examined separately
An example of the out-of-plane movement of gears is illustrated in Figure 4.32 In this instance, thedriven gear in the top of the figure has been wedged underneath the large load gear at the bottom of thephotograph The way to prevent this situation is to understand the forces that create the out-of-plane motionand to reduce or restrain them One way of reducing the relative vertical motion of meshed gears is toincrease the ratio of the radius of the hub to the radius of the gear Mathematically, the maximum dis-placement of the outside edge of a gear from its position parallel to the plane of the substrate is: