(a) (b) COLOR FIGURE 2.1 Examples of two high-volume accelerometer products. Example (a) is the top view micro- graph of the Analog Devices, Inc. ADXL250 two-axis lateral monolithically-integrated accelerometer. Example (b) is a perspective view of the Freescale Semiconductor, Inc. wafer-scale packaged accelerometer and control chips stack- mounted on a lead frame prior to plastic injection molding. (Photos courtesy of Analog Devices, Inc. and Freescale Semiconductor, Inc.) COLOR FIGURE 2.4 Top view micrograph of a Z-axis accelerometer quadrant showing a folded spring and sacri- ficial etch holes designed into the proof-mass structure. (Photo courtesy Freescale Semiconductor, Inc.) © 2006 by Taylor & Francis Group, LLC 0 1 2 3 4 5 6 0 0.5 1 1.5 2 Damping ratio Normalized frequency (/n) Frequency response (x) ξ = 0.1 ξ = 0.3 ξ = 0.65 ξ = 1.0 CMOS Device area Poly 2 P-tub Poly 1 Pad N-tub PE nitride Metal 1 Field oxide Sac oxide BPSG TEOS PETEOS Nitride poly stud Mechanical poly Nitride Arsenic-doped epitaxial layer MM poly 0 n-type silicon substrate Micromechanical device area COLOR FIGURE 2.13 Cross-sectional diagram of the IMEMS process developed at Sandia National Laboratories demonstrating the transducer formed in a recessed moat and sealed prior to the commencement of the high density CMOS process. (Photo courtesy Sandia National Laboratories.) COLOR FIGURE 2.6 The frequency response x ෆ versus normalized frequency ratio ω / ω n . © 2006 by Taylor & Francis Group, LLC COLOR FIGURE 2.14 Top view micrograph of a Z-axis capacitive accelerometer in three polysilicon layers. The design allows for high inertial sensitivity with a low temperature sensitivity. (Photo courtesy Freescale Semiconductor, Inc.) 0.00 0.05 0.10 0.15 0.20 0.25 0.30 r/w 3.0 2.8 2.6 2.4 2.2 2.0 1.8 1.6 1.4 K t F F W W r W/w = 1.5 W/w = 2 COLOR FIGURE 4.10 Stress concentrations for a flat plate loaded axially with two different widths and fillet radius r. The maximum stress is located around the fillets. © 2006 by Taylor & Francis Group, LLC COLOR FIGURE 4.32 The gear teeth of the small gear are wedged underneath the teeth of the large diameter gear. In this case, gear misalignment is about 2.5 mm in the vertical direction. F F F F V cos t V cos t −V cos t −V cos t V cos t V cos t −V cos t −V cos t (a) (b) (c) (d) COLOR FIGURE 9.4 Schematic illustration of the capacitive charging: (a) and (b) demonstrate the electric field, and F represents time averaged Maxwell force; (c) and (d) demonstrate the flow profile. © 2006 by Taylor & Francis Group, LLC F F F F V cos t V cos t −V cos t −V cos t V cos t V cos t −V cos t −V cos t (a) (b) (c) (d) COLOR FIGURE 9.5 Schematic illustration of the Faradaic charging: (a) and (b) on the left, anions are driven to the same electrode surface where cations are produced by a Faradaic anodic reaction during the half-cycle when the electrode potential is positive; (c) and (d) the flow directions are opposite to those in Figure 9.4. (b) (a) COLOR FIGURE 9.7 Particle focusing lines along the stagnation points for capacitive charging. The vertical force toward the electrode is a weak DEP or gravitational force. The circulation is opposite for Faradaic charging. An actual image of the assembled particles is shown below. © 2006 by Taylor & Francis Group, LLC (a) (c) (b) (d) 1Vrms 2,2Vrms COLOR FIGURE 9.8 The writing and erasure processes for Au electrodes at ω ϭ 100 Hz. The frames are taken at 0 s, 5 s, 10 s, and 15s after the field is turned on. The initial voltage is 1.0 Vrms and is increased to 2.2 Vrms at 7.0s. Particles on the electrode in the first two frames (a) and (b) move in directions consistent with electro-osmotic flow due to capacitive charging and assemble into lines. They are erased by Faradaic charging in the next two frames (c) and (d). The arrows demonstrate the direction of particle motion. The dashed lines are located at the theoretical L / ͙ 2 ෆ . COLOR FIGURE 9.9 Bacteria trapping by AC electroosmotic flow. © 2006 by Taylor & Francis Group, LLC COLOR FIGURE 10.11 Bubble volume variation versus time for three different heater designs under same heat flux of 1.2 GW/m 2 , courtesy Yang, et al. (2004). COLOR FIGURE 11.7 Silicon wafer into which an array of micro heat pipes has been fabricated. © 2006 by Taylor & Francis Group, LLC 0 40 80 120 160 200 240 280 0 5 10 15 20 25 30 35 40 45 50 Power input (W) Temperature difference (°C) With working fluid Without working fluid COLOR FIGURE 11.10 Temperature difference of micro heat pipe arrays with or without working fluid. (Reprinted with permission from Wang, Y., Ma, H.B., and Peterson, G.P. (2001) “Investigation of the Temperature Distributions on Radiator Fins with Micro Heat Pipes,” AIAA J. Thermophysics and Heat Transfer 15(1), pp. 42–49.) 0 500 1000 1500 2000 2500 3000 3500 0 20 40 60 80 100 120 140 Power input (W) Effective conductivity (W/mK) Test article No.2 (Exp. average) Test article No.1 Test article No.3 MHP without working fluid COLOR FIGURE 11.11 Effective thermal conductivity of micro heat pipe arrays. (Reprinted with permission from Wang, Y., Ma, H.B., and Peterson, G.P. (2001) “Investigation of the Temperature Distributions on Radiator Fins with Micro Heat Pipes,” AIAA J. Thermophysics and Heat Transfer 15(1), pp. 42–49.) © 2006 by Taylor & Francis Group, LLC tunneling tip, as well as low frequency noise sources, remain [Grade et al., 1996]. Recently, Shashkin et al. (2004) proposed that Fowler–Nordheim tunneling-based inertial sensing could provide a more stable alter- native using parallel electrodes resulting in high sensitivity. As tunneling-based technologies expand in application, researchers will find solutions to mitigate the current limitations of the methodology. 2.5 Rotational Inertial Sensor Parameters Linear and rotational inertial sensors have much in common; for example, both exhibit a structure com- prising a specific mass as well as a flexible means by which this structure is anchored to the substrate, and both types of sensors are often manufactured through the same or similar technologies. Unlike a linear iner- tial sensor, however, the transducer of an angular rate sensor needs to be driven into oscillation in order to generate a measurable signal (in most cases). This requirement comes from the coupling of vibratory motion by the Coriolis Effect to produce a positional shift sufficient for sensing. The requirement adds both transducer and circuit complexity to the system.Upon a rotation of the transducer about its sense axis,aCoriolis force is generated in the presence of arotational velocity of the reference frame, which in turn drives the trans- ducer structure orthogonally as given in Equation 2.4. This means that a minimum of two orthonormal axes of motion is required in order to suitably measure the small Coriolis force exerted on a resonating proof- mass during rotation. Rollover sensors typically resonate in plane and measure normal to the surface. Axes of sensitivity for gyroscopic sensors are shown in Figure 2.8. The scalar governing equation of motionfora gyroscopic device with a resonating mass in the Y-axis, rotated about the Z-axis is given by Equation 2.14, ϩ 2 ξω n ϩ ω 2 n x ϭ 2Ω z (2.14) where Ω z is the rate of rotation and y is linear velocity of the structure due to the drive. One may make an analogy between rotational and linear sensors if the Coriolis term (2 Ω z dy/dt) is considered an accel- eration. According to a typical automotive spec where the full range of angular velocity is 100 deg/sec an equivalent acceleration, a, is given by Equation 2.15, a ϭ 3.5 (2.15) In general, the driving frequency is near resonance and the vibration amplitude of the transducer struc- ture is about 1 µm. Assuming a natural frequency of 10 kHz, the resulting Coriolis acceleration of Equation 2.15 has a value of 0.022mg, demonstrating that this force-induced acceleration is very small. dy ᎏ dt dy ᎏ dt dx ᎏ dt d 2 x ᎏ dt 2 Inertial Sensors 2-13 mass z x y Resonant mode Coriolis Accele ration z x y about x Coriolis Acceleration about y Mass Resonant mode about z (a) (b) FIGURE 2.8 Reference frames for rotational gyroscopes based on the Coriolis effect showing axes of sensing for (a) yaw and (b) roll applications. © 2006 by Taylor & Francis Group, LLC For most applications, a single axis angular rotation measurement is required. Such a single axis rate sensor can be built by sensing induced displacement from an oscillating rotor or from a linearly oscillating structure. Although these two types of rate sensor designs appear to be very different, the operation principles are the same. In both cases, when the reference frame (or device substrate) experiences a rotation along the input axis, the oscillating mass (either translational or rotary),in a direction perpendicular to the input axis (referred to as the drive axis), would induce a Coriolis force or torque in a direction perpendicular to both the input axis and the drive axis.With the amplitude of the drive oscillation fixed and controlled, the amplitude of the sensing oscillation is proportional to the rate of rotation of the mounting foundation. Feng and Gore (2004) show a mathematical model for the dynamic behavior of vibratory gyroscopes. Because the coupling of the Coriolis Effect is orthogonal to the vibratory motion in a micromachined device, two degrees of mechanical freedom are required. One degree of freedom is utilized for the excitation of the vibratory motion, and the second degree of freedom orthogonal to the first is required for sensing. This requirement couples tightly into the technology choice for rotational inertial sensors, because the axis of sensitivity defines which mechanical degrees of freedom are required to sense it. For example, a very thick high aspect ratio technology — as is possible with direct wafer bonded structures — might not be the most suitable for a device that is required to move out of the plane of the wafer.However,as with their linear counterparts,most technologies and sensing methodologies have been applied to vibratory sensors with new combinations of methodologies always under consideration. Putty and Najafi (1994) provide a discussion of the varieties of rotational inertial sensors, including vibrat- ing prismatic beams [Greiff et al., 1991], tuning fork designs [Voss et al., 1997; Hiller et al., 1998], coupled accelerometers [Lutz et al., 1997; Kobayashi et al., 1999; Park et al., 1999], and vibrating shells [Putty and Najafi, 1994; McNie et al., 1999]. As illustrated in Figure 2.9, He and Najafi (2002) demonstrate an all- silicon vibrating ring gyroscope with very good performance. Multiple-axis systems have also been demonstrated [Juneau et al.,1997; Fujita et al., 1997]. In all cases, the vibrating structure is displaced orthog- onally to the direction of the vibrating motion. This configuration can lead to system errors related to the transducer structure and the electronics. The primary error related to the transducer is called quadrature error and is discussed in the next sub-section. As an alternative to single proof-mass designs, a concept involving two coupled oscillating masses has emerged, with one mass for driving and one mass for sensing. One of the first such designs is documented by Hsu et al. (1999), who used an outer ring as the drive mass and an inner disk as the sense mass. The driving mass is actuated by a set of rotary comb structures and oscillates about the Z-axis (or the vertical axis). The sensing disk is anchored to the substrate in such a way that the stiffness about the Z-axis is significantly greater 2-14 MEMS: Applications FIGURE 2.9 Perspective view scanning electron micrograph of a single-crystalline silicon vibratory ring gyroscope. (Photo courtesy K. Najafi, University of Michigan.) © 2006 by Taylor & Francis Group, LLC [...]... system © 20 06 by Taylor & Francis Group, LLC 2- 2 2 MEMS: Applications 20 Maximum deflection (µm) Damping Ratio 15 ξ = 0.0 ξ = 0 .1 ξ = 1. 0 ξ = 1. 5 10 5 0 10 0 11 0 12 0 13 0 14 0 15 0 Beam length (µm) FIGURE 2 . 12 Calculation of the maximum beam displacement, zmax, for a 2 µm thick cantilever beam with different damping ratios and lengths (Li and Shanasky) 2. 8 .1 System Partitioning: One-Chip or Multi-Chip The sense... of 1. 5 (over damped), the equivalent acceleration is 14 ,000 g These values of acceleration would be doubled if the package impact with the floor is elastic (r ϭ 1) Nevertheless, it is clear that the drop-induced acceleration is large, much larger than one normally expects to encounter during normal operation © 20 06 by Taylor & Francis Group, LLC Inertial Sensors 2- 2 1 30 Equivalent acceleration (10 3g)... tolerance levels Therefore, each MEMS package must be uniquely designed and evaluated to meet special requirements [Dickerson and Ward, 19 97; Tang et al., 19 97] © 20 06 by Taylor & Francis Group, LLC 2- 2 0 MEMS: Applications 0 .2 Out-of-plane displacement (µm) Temperature T = 90°C T = 25 °C T = −40°C 0 .15 0 .1 0.05 0 1 −0.5 0 0.5 1 Distance from die center (mm) FIGURE 2 .10 Die deformation due to a chip-packaging... Sensors 2 -1 5 than stiffness about the other axes The outer ring and the inner disk are connected by a set of flexible beams or linkages When there is no input of angular rotation, the oscillation of the drive mass about the Z-axis has virtually no impact on the motion of the sense disk When the device experiences a rotation about either the X- or Y-axis, the Coriolis force-induced torque drives the inner... (10 3g) 25 20 15 10 Damping Ratio 5 ξ = 0.0 ξ = 0.5 ξ = 1. 0 ξ = 1. 5 0 −5 0 0.5 1 1.5 Drop Test Height (meters) FIGURE 2 .11 Calculation of the equivalent g load on an accelerometer due to an inelastic drop shock for several damping ratios The device conditions are: m ϭ 0.6 µg, k ϭ 5 N/m, r ϭ 0 The analysis on a lumped mass and spring model helps to provide a picture regarding the magnitude of proof-mass... Metal 1 TEOS Field oxide P-tub Poly 1 N-tub Arsenic-doped epitaxial layer Nitride BPSG Sac oxide poly stud Mechanical poly Nitride MM poly 0 n-type silicon substrate FIGURE 2 .13 (See color insert following page 2 -1 2. ) Cross-sectional diagram of the IMEMS process developed at Sandia National Laboratories demonstrating the transducer formed in a recessed moat and sealed prior to the commencement of the. .. [Li and Shemansky, 20 00] The motion of the microstructure as a result of the impact is governed by a second order ordinary differential equation of a standard form, as in Equation 2 .11 [Meirovitch, 19 75] Equation 2 .17 gives the maximum displacement, zmax ϭ Ί 2mgh ᎏ d0(ξ, r) k (2 .16 ) where d0(ξ, r) is a unit-less scaling function only of the damping ratio, ξ, and the elasticity of the collision as defined... and their implementation using a © 20 06 by Taylor & Francis Group, LLC 2- 2 6 MEMS: Applications FIGURE 2 .14 (See color insert following page 2 -1 2. ) Top view micrograph of a Z-axis capacitive accelerometer in three polysilicon layers The design allows for high inertial sensitivity with a low temperature sensitivity (Photo courtesy Freescale Semiconductor, Inc.) FIGURE 2 .15 Perspective view scanning electron... Vegas, NV Noell, W., Clerc, P.-A., Dellmann, L., Guldimann, B., Herzig, H.-P., Manzardo, O., Marxer, C.R., Weible, K.J., Dändliker, R., and de Rooij, N (20 02) Applications of SOI-based Optical MEMS, ” IEEE J Select Top Quant Electron., 8 (1) , pp 14 8–54 Noworolski, J .M., and Judy, M (19 99) “VHARM: Sub-Micrometer Electrostatic MEMS, ” Technical Digest IEEE International Conference on Solid-State Sensors... K.D (19 94) “Low-Temperature Silicon Wafer-to-Wafer Bonding using Gold at Eutectic Temperature,” Sensors Actuators A, 43, pp 22 3 29 Wu, J., Fedder, G.K., and Carley, L.R (20 04) “A Low-Noise Low-Offset Capacitive Sensing Amplifier for a Hz 5 0- g/͙ෆෆ Monolithic CMOS MEMS Accelerometer,” IEEE J Solid-State Circuits, 39(5), pp 722 –30 Wycisk, M., Tönnesen, T., Binder, J., Michaelis, S., and Timme, H.–J (19 99) . In monolithically integrated technology, the 2- 2 2 MEMS: Applications 0 5 10 15 20 10 0 11 0 12 0 13 0 14 0 15 0 Damping Ratio ξ = 0.0 ξ = 0 .1 ξ = 1. 0 ξ = 1. 5 Beam length ( m) Maximum deflection ( m) FIGURE. Shemansky (20 00), the maximum displacement, z max , for a2 m thick polysilicon cantilever is graphically shown in Figure 2 . 12 , where h ϭ 1. 2m, E ϭ 16 1,000MPa, I ϭ 4/3 m 4 , r ϭ 0.5. Assuming there is. system. Inertial Sensors 2- 2 1 −5 0 5 10 15 20 25 30 0 0.5 1 Damping Ratio 1. 5 ξ = 0.0 ξ = 0.5 ξ = 1. 0 ξ = 1. 5 Drop Test Height (meters) Equivalent acceleration (10 3 g) FIGURE 2 .11 Calculation of the equivalent