Micro Electro Mechanical Systems or MEMS is a term coined around 1989 by Prof. R. Howe and others to describe an emerging research, where mechanical elements, like cantilevers or membranes, had been manufactured at a scale more akin to microelectronics circuit than to lathe machining. But MEMS is not the only term used to describe this and from its multicultural origin it is also known as Micromachines, a term often used in Japan, or more broadly as Microsystem Technology (MST), in Europe.
However, if the etymology of the word is more or less well known, the dictionaries are still mum about an exact definition. Actually, what could link an inkjet printer head, a video projector DLP system, a disposable bio-analysis chip and an airbag crash sensor – yes, they are all MEMS, but what is MEMS?
It appears that these devices share the presence of features below 100 micro metre that are not machined using standard machining but using other techniques globally called micro-fabrication technology. Of course, this simple definition would also include microelectronics, but there is a characteristic that electronic circuits do not share with MEMS. While electronic circuits are inherently solid and compact structures, MEMS have holes, cavity, channels, cantilevers, membranes, etc, and, in some way, imitate `mechanical’ parts. This has a direct impact on their manufacturing process. Actually, even when MEMS are based on silicon, microelectronics process needs to be adapted to cater for thicker layer deposition, deeper etching and to introduce special steps to free the mechanical structures. Then, many more MEMS are not based on silicon and can be manufactured in polymer, in glass, in quartz or even in metals [5, 6].
Thus, if similarities between MEMS and microelectronics exist, they now clearly are two distinct. Actually, MEMS needs a completely different set of mind, where next to electronics, mechanical and material knowledge plays a fundamental role.
1.2 MEMS technology
The development of a MEMS component has a cost that should not be misevaluated but the technology has the possibility to bring unique benefits. The reasons that prompt the use of MEMS technology can be classified broadly in three classes:
a) Miniaturization of existing devices, like for example the production of silicon based gyroscope which reduced existing devices weighting several kg and with a volume of 1000 cm3 to a chip of a few grams contained in a 0.5 cm3 package.
b) Development of new devices based on principles that do not work at larger scale. A typical example is given by the biochips where electrical are use to pump the reactant around the chip. This so called electro-osmotic effect based on the existence of a drag force in the fluid works only in channels with dimension of a fraction of one mm, that is, at micro-scale.
c) Development of new tools to interact with the micro-world. In 1986 H. Rohrer and G. Binnig at IBM were awarded the Nobel price in physics for their work on scanning tunneling microscope. This work heralded the development of a new class of microscopes (atomic force microscope, scanning near optical microscope…) that shares the presence of micro machined sharp micro-tips with radius below 50 nm. This micro-tool was used to position atoms in complex arrangement, writing Chinese character or helping verify some prediction of quantum mechanics. Another example of this class of MEMS devices at a slightly larger scale would be the development of micro-grippers to handle cells for analysis.
2.1 History of Micromirror :
In recent years, deformable mirror devices (DMDs) have emerged as a new micro-electromechanical (MEM) technology with tremendous potential for future applications. As shown in Fig. 1-1, the concept of deformable mirrors was developed and utilized as early as 211 BC by Greek soldiers to destroy enemy ships .
However, it was not until 1973 that serious development of micromirror devices began to emerge. Currently, several designs of deformable mirrors have been fabricated, some before a practical use had been identified. It is these devices that are now receiving serious attention as optical communication and related fields are expanding.
Mirror devices are a specific type of spatial light modulator (SLM).Spatial light modulators are devices that can alter the phase, amplitude, and/or the direction of propagation of an incident beam of light. Deformable mirror devices do this by moving a reflective surface to achieve the desired effect. Currently, two distinct types of micro-mirrors are used . Continuous surface devices use one large reflective membrane that is locally controlled by individual actuators to form a continuous reflective surface. Circus “fun house” mirrors are an example of such a device. Segmented devices, on the other hand, use a mirror surface that is divided into numerous individually controllable smaller mirrors. Greek soldiers used segmented mirrors to form a parabolic reflective surface which was used to focus sunlight onto enemy ships.
Segmented devices are used today in the formation of large parabolic mirrors. As shown in Figure 1-2, the primary mirror of many modern optical telescope systems is comprised of segmented deformable mirrors. In the past, the size-limiting factor in such systems has been the size of the primary mirror which had to be mechanically stable yet light enough to move to various positions throughout a full field of view. Larger mirrors were frequently damaged or caused damage to other components of the telescope when movement was attempted. With the application of segmented deformable mirror technology, the practical limit in telescopic primary mirror size can be extended since much lighter and smaller mirrors can be individually anchored, controlled, and placed adjacent to each other to form the necessary parabolic mirror.
The segmented mirrors are not only placed at a slight angle to each other, but are shaped by the segmented actuators and are free to bend to form smaller parabolically curved surfaces. The segmented actuators are manipulated by the control electronics which receive information from the laser figure sensor and the edge computer which is then translated into a necessary change in the position or shape of the mirrors. These monitoring devices continually check the status of the segmented mirrors to maintain the parabolic form of the entire device and to ensure that no gaps or severe discontinuities are present in the surface of the primary mirror which would result in a distorted image or a loss in image resolution.
The basic principles of this macroscopic technology can also be used in microscopic applications which involve fabricating deformable mirrors on integrated circuits. Several forms of micromirrors have emerged that combine on-chip addressing electronics with the micro-mechanical mirrors . The geometric and material variations of these devices demonstrate that deformable mirrors can be designed and implemented for a variety of specific uses. The micromirror devices currently used are segmented surface devices in which the actuation of a small reflective mirror is controlled by a single address electrode. The metallized mirror and the address electrode of the device form a parallel plate capacitor. The voltage between the mirror and the electrode creates an electrostatic force acting on the mirror in the downward direction. The flexures holding the mirror are designed to deform, allowing the mirror to move vertically with applied voltage. The resulting spring force of the flexures acts on the mirror in the upward direction, countering the electrostatic force of the capacitor.
3.MICROMIRROR ACTUATION METHODS FOR SENSING
3.1 Electromagnetic Actuation:
A micromirror can be deflected in two ways by electromagnetic actuation. First, by using Lorentz force to move a patterned coil by exerting external magnetic field. Second, by repulsive/attractive forces to repel/attract the magnetic material attached to the mirror from/to the actuator. Advances in material fabrication to provide thick film deposition of magnetic material on the surface of micro actuators should reduce voltage and current requirements. Magnetic MEMS can offer non- contact operation, and can induce mechanical resonance by magnetic element excitation. However, thermal budget imposed by the current CMOS technology limits the fabrication of the magnetic film on the substrate from reaching the desired characteristics .
3.2 Piezoelectric Actuation:
The piezoelectric actuation takes advantage of the corresponding physical deformation to applied electrical voltage property . It has relatively lower operation voltage (3-20 Volt DC) with low power consumption, better linearity, and fast switching time 0.1 to 1.0 milliseconds .
3.3 Thermal Actuation:
The main advantage of thermal actuation is the simplicity of the fabrication method. However, in general, thermal actuation tends to have higher power consumption and slow response time.
The out-of-plane thermal micro actuator uses thermal expansion due to ohmic heating. A thin arm and wide arm configuration with one end fixed to the substrate has nonlinear property due to temperature dependency .
3.4 Electrostatic Actuation:
Despite suffering from the pull-in effect, nonlinear behavior, and higher operating voltage, the electrostatic actuation’s fast response time (less than 0.1 ms), low power consumption, and the easiness of integration and testing with electrical control system make the electrostatic actuation one of the preferred choices for micromirror actuation .
The operation voltage of the micromirror can be lowered while achieving more angular deflection if the stiffness of torsion bar is reduced. However, when the stiffness is lowered, the natural frequency of the micromirror also decreases, thereby reducing operational bandwidth.
Say w, v, d scales as L1.
Maximum Electrostatic Potential Energy Stored is given by:
Permitivity of vacuum and relative permitivity remains unchanged with scaling.
Assume Vb scales linearly with d (Out of Paschen effect range), then
Electrostatic Forces Found to Scale as Square of L.
Since mass and hence inertial forces scale as cube of L, Electrostatic Actuators are advantageous in Scaled Down Sizes .
Paschen Effect: Breakdown of continuum theory
Figure 3 -Vb v/s P,d
Paschen Effect: Breakdown of continuum theory:
a) Vb scales non linearly in Paschen effect range.
b) Vb increases in Paschen effect range.
c) Higher Vb implies higher storage of energy and so larger force.
4.Summary of Advantages and Disadvantages of Each Actuation Mechanism
– Low actuation voltage
– Relatively large angular deflection with lower driving power
– Difficult to assemble permanent magnets and coils with current CMOS technology
– Challenge in minimizing the size of device
– Higher switching speed
– Low power consumption
– Short actuation range
– Ease of fabrication (require only one composite beam) for bulk production
-High power consumption
– Slow response time
– Fatigue due to thermal cycle
– Low power consumption
– Fast switching
– Ease of integration and testing with electrical control circuitry
– Nonlinear characteristics
– Limited by the pull-in effect
– High actuation voltage
– Fabrication complexity
5.1 ANALYTICAL MODEL OF THE STACKED MICROMIRRORS
In this section, micromirrors of different configurations are presented and compared in terms of their deflection angle and actuation voltage. The conceptual schematics of the three configurations analyzed are shown below. Figure 1(a) shows a conventional micromirror configuration. Figure 1(b) shows a unique configuration of the stacked micromirror also denoted as the first stacked mirror configuration, and Figure 1(c) shows a novel configuration of the stacked micromirror with an offset, which is also known as the second stacked micromirror configuration .
Figure 1. Schematics of Three Different Micromirror Configurations.
The moving electrode (middle plate) in the stacked configurations is designed to be identical to the micromirror in size and material. Solutions for the following analytical model are independent of the shape and size of the plate (micromirror) as long as the dimensions of each layer are identical.
First, an analytical model of the micromirror is derived to better understand the relationship between each parameter of the micromirror. The torque created by the electrostatic force between the micromirror and its electrodes, as denoted by M for each configuration, is derived from the following dynamic Equation (1):
I (d2O/dt2) + C (dO/dt) + kO = M —-(1)
I is the moment of the inertia.
C is the damping coefficient representing the squeeze-film.
k is the torsional stiffness of the rotated serpentine spring.
M is the torque created by the electrostatic force between the micromirror and its electrodes.
The moment of the inertia of the micromirror along the y-axis is equal to (1/12)*ml2.
Second, the value for damping coefficient, c, representing the squeeze-film damping of the micromirror is derived from the linearized Reynold’s equation  and presented in Equation (2).
C= -(48w3)/(Ï€6(b2+4)D3) —– (2)
Î¼ is the dynamic viscosity of the air.
l is equal to the half length of the micromirror, .
w is the width of the micromirror.
b is the ratio of the width to the length of the micromirror.
D is the initial air gap between the micromirror and its electrodes.
Third, the torsional stiffness, k, of the rotated serpentine spring
K= (G Jp)/(2NLp+3Lp) —–(3)
G is the shear modulus of the material used in the rotated serpentine spring.
Jp is the torsion factor of a beam with rectangular cross-section  and can be derived from the Equation (4) below.
N is the number of the loops or turns in the rotated serpentine spring.
Lp is the length of the rotated serpentine spring segment that is parallel to the rotation axis.
Jp= (tw3/3)*(1-(192w/3t)*âˆ‘t=1,2,3….1/t3* tanh(tÏ€t/2w)) —–(4)
Fourth, for the sake of simplicity, the micromirror is considered to be a rigid body and the deflection of the rotated serpentine spring in the Z axis is assumed to be negligible. In order to find the torque created by the electrostatic force between the micromirror and its electrodes, the parallel plate capacitor theory is used to derive the differential force that acts on a small segment of the micromirror and its electrodes:
dF = 1â„®V2 (wdx)/(D-x2 ——-(5) where,
â„® denotes the permittivity of air and V represents the potential difference.
The torque, M, for each configuration is simplified with the normalized angle as represented by the following Equation (6), (7) and (8):
MO = 0.5 â„®wV2 (L2/D2 o2)*(o/1-o + ln(1-o)) ————(6)
M1 = 0.5 â„®wV2 (L2/D2 4o2)*(2o/1-2o + ln(1-2o)) ————(7)
M2 = 0.5 â„®wV2 (L2/D2 2)*(1/(1-2o+o2)) ————(8)
M0 represents the torque created in the single mirror configuration. M1 and M2 denote the torque generated in the first and second stacked mirror configurations, respectively. To simplify the analysis, the fixed bottom electrodes are not used to actuate the micromirrors in both stacked configurations .
Figure-2. Torque versus Angle Comparison Plot for Three Micromirror Configurations.
To visualize the magnitude of torques against the normalized angles, the normalized torques of M0, M1, and M2 are plotted in the Figure 2. The red line shows an exponential increase in the normalized torque as the normalized angle grows. The black line (conventional single mirror configuration) shows relatively gradual increase. As expected, while the deflection angle is small there are negligible differences between the three configurations in terms of the torque created by the same actuation voltage. However, as the deflection angle increases, the torque acting on the first stacked mirror grows exponentially. On the other hand, the second stacked mirror configuration shows a 50% increase in torque when compared to the single mirror configuration.
The size and geometry of the micromirror are determined by the diameter of the optical beam as well as its application. For example, a micromirror used in an endoscope would require a smaller form factor. The micromirror discussed here is designed to be 1 mm in length, 1 mm in width and 10 Î¼m in thickness. Also, it is assumed to be made of polysilicon that has a Young’s modulus of 160 GPa, Poisson’s ratio of 0.22
and density of 2330 kg/m3. Normally, the micromirror is designed to be suspended over a cavity by two torsion bars. Even though a straight torsion bar is simple to design and fabricate, it suffers from residual stress, which alters the stiffness of a torsion bar and the micromirror’s frequency response. Furthermore, modification of the physical or geometric properties of the straight torsion bar is not straightforward since the geometry of the torsion bar such as the width and thickness are limited by the fabrication process. Hence, two rotated serpentine springs are chosen to hold the micromirror in place while the micromirror rotates. The serpentine springs’ stiffness can be easily customized regardless of the fabrication process. Thus, a rotated serpentine spring is employed in this analysis. The rotated serpentine spring used in this analysis is 4 Î¼m wide, 10 Î¼m thick, and 100 Î¼m in length
from one end to another end. The gap between each turn is 4 Î¼m. Figure.3 (a) shows the expanded view of the rotated serpentine spring, and Figure.3 (b) shows the relative size and location of the spring on the micromirror.
Figure 3. (a) Rotated Serpentine Spring Torsion Bar and (b) the Micromirror.
Two different configurations of the micromirror are presented in Figure 4. To simplify modeling and analysis, the geometry and material of the plates (micromirrors) are kept identical except the stacking configuration. As shown in Figure 4(a), a micromirror is placed 250 Î¼m directly above another square plate along the z-axis. In Figure 4(b), a micromirror is placed above another mirror with a 250 Î¼m gap in the z axis and a 500 Î¼m offset along the x- axis. The top plate is the micromirror, and the bottom plate is used as moving electrodes .
The micromirror and its moving counterpart have two electrodes located on their bottom. The electrodes are assumed to be made of 1 Î¼m aluminium thin film. The rotated serpentine springs provide electrical connection between the electrodes and control circuitry.
Figure-4. Stacked Micromirror Configurations.
5.3 Flexure Beam Micro-Mirror
Figure-5: Flexure Beam Micromirror
In order to develop the characteristic model of the Flexure-Beam micromirror device, it must first be characterized by equating the electrostatic actuation force of the parallel plate capacitor with the mechanical restoring force of the spring. Figure-6 shows a Flexure-Beam device in the resting ( V = 0 ) and active ( V > 0 ) modes where Zm represents the vertical height of the mirror above the address electrode. It is initially assumed that when no electrode potential is applied, the mirror rests firmly in the resting position, Z0, where the deflection distance, d, at all points on the mirror is zero .
Figure-6: Forces acting in flexure Beam Micromirror
The Flexure-Beam device is a “phase-only” device since the direction of motion of the mirror is orthogonal to the reflective surface. Therefore, the optical path length can be altered while the direction of propagation remains unchanged. This makes the piston device very appealing for phase modulated filters or for adaptive phase correcting optics.
Figure-7: Cloverleaf Micromirror
One design improvement is another cantilever device known as the Cloverleaf. As shown in Figure, the flexures holding the reflective surfaces are placed in the center of the geometry. This takes the basic design of the Inverted Cloverleaf and reduces some of the negative effects observed. Also, the electrodes are located directly beneath each mirror which allows the cantilever surfaces to be individually addressable.
Moving the support for the mirrors to the center of the pixel cell allows for better use of overall space. Now, the pixels can be placed so that adjacent cells nearly touch each other with only a small gap required between the mirrors of one cell and the mirrors of another. Most of the total surface area of the device is reserved for the active elements with the exception of the posts which hold the mirrors in place. This increases the active area of the device to as much as 86% which is similar to the remaining devices described in this chapter. This device, however, maintains the side effect of redirecting an incident beam of light in four distinct directions.
Figure-8 The Quad-Cantilever deformable micromirror device
The significant advantage over the Cloverleaf devices is that the mirrors are aligned so that the redirection of the incident beam of light is in a common direction. This allows the device to be capable of switching or redirecting the incident light with little loss in amplitude. One characteristic similar to the Inverted Cloverleaf and Cloverleaf devices is the slanted behavior of the deflected mirror. This behavior is typical with cantilever devices and creates a non-uniform phase response across the surface of each mirror .
In order to compute the electrostatic force on the mirror, it must first be determined by which means this force will be calculated. More specifically, it must be decided whether the charge distribution, which is not uniform over the mirror surface, will be considered. The charge distribution will change with the position of the mirror surface and will also be altered by any mirror surface deformations or discontinuities such as etch holes. This leads to a complicated solution when integrating across the mirror.
As an alternative, since both the charge distribution of the mirror and the applied electrode voltage are related to the electric field within the device, it is possible to express the potential energy, of the electric charge distribution solely in terms of this field:
Where, a is the surface charge distribution on the mirror, V is the actuation voltage between the mirror and address electrode, A is the area of the mirror, e0 is the free space dielectric constant and E is the electric field intensity at any point in the volume v within the device .
By assigning an electric energy density of V-2coloumbs to each point in space within the device, the physical effect of the charge distribution on the mirror surface is preserved. From this approach it is easy to see that the non-uniform charge distribution on the mirror surface and the fringing effects of electric fields around the edges of the mirror are complementary descriptions of the same electrical phenomenon.
5.4 Dual Axis Micro-Mirror
Figure-9: Dual-Axis micromirror
Micromirror working principle
The micromirror is made up by a circular polysilicon micromirror plate that is connected to a gimbal frame by a pair of polysilicon torsion springs (Fig. 9). The gimbal frame is supported by a pairs of polysilicon springs too. The structure is a dual axis micromirror: the slow axis works at the resonance frequency of 300 Hz while the fast axis works at the resonance frequency of 30 kHz. The fast axis allows the micromirror to be tilted around y direction while the slow axis allows the micromirror to be tilted around x direction. Both the two axis are actuated by electrostatic vertical comb drives. Vertical comb drives provide a motion in and out of the plane and present several advantages if compared to lateral comb drives. First of all, they generate a vertical force larger than lateral comb drives ,then they achieve larger scan angle at high resonance frequencies and finally they directly apply the torque to the micromirror without needing any hinges to couple their linear motion into torsional micromirror motion .
Each vertical comb drive consists of a set of moving mechanical polysilicon electrodes and a set of rigid electrodes suspended over an etched pit. The rigid electrodes are bound to the substrate, while the movable electrodes are linked to the axis. When a voltage is applied between the fixed fingers and the movable fingers, an electrostatic Torque arises between the two electrodes . Consequently the movable fingers rotate around the torsional axis until the Electrostatic Torque (Te) and the Mechanical restoring Torque (Tm) of the springs are equal. These two torques can be expressed by (1) and (2).
Figure-10: Forces acting in a Dual-Axis Micromirror
5.5 Micromirror with Hidden Vertical Comb Drives
The actuators and the torsion springs are hidden underneath the mirror to achieve high-fill factor in micromirror arrays. In this case, the fringing capacitance is significant and cannot be ignored . The total capacitance as a function of angle can be calculated by integrating over the finger length. Fig. 11 shows the 3-D design of this:
Figure-11: Hidden Vertical-Comb Drive Micromirror
In this report, the first three phase of the project have been completed. The different actuation principles , their advantages and disadvantages have been discussed. Also four designs have been proposed and analytical study of them has been done. We can now move on to the next phase which comprises of modeling as well as analysis of the designs chosen.
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