Patent Publication Number: US-8117915-B1

Title: GRA MEMS accelerometer

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
     This application is a continuation in part of application Ser. No. 11/460,115, filed on Jul. 26, 2006, which itself claimed priority of provisional application Ser. No. 60/702,422 filed on Jul. 26, 2005. The disclosures of these two prior applications are incorporated herein by reference. 
    
    
     STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH 
     This invention was made with government support under contract number HQ0006-05-C-2718 issued by the MDA. The government has certain rights in this invention. 
    
    
     FIELD OF THE INVENTION 
     This invention relates to accelerometer designs. 
     BACKGROUND OF THE INVENTION 
     Closed loop MEMS pendulous accelerometers typically use torque rebalance with a voltage-controlled capacitive actuator to hold the pendulum at null. Assuming the actuator is stable, the voltage applied is proportional to acceleration. The accelerometers are calibrated to obtain the scale factor (acceleration to voltage proportionality). In the present implementation, the torque applied is not measured directly. The voltage is but the actuator may change and therefore the actual applied torque is not known. The accuracy and stability of the accelerometer will be dependent on the accuracy and stability of the applied voltage and the actuator functional stability, thereby limiting scale factor accuracy if only the voltage is measured. To rectify this problem and thereby increase performance especially of the MEMS accelerometers, the stability in the components becomes more critical. In the GRA the instability in the components is largely overcome by measuring the applied torque rebalance by directly measuring the actuator functions. 
     In the Pendulous Integrating Gyro Accelerometer (PIGA), a single degree-of-freedom (SDF) gyro is mounted onto a rotating platform that allows the gyro to be rotated about its Input Axis. The gyro contains a wheel that spins about the SRA (Spin Reference Axis). The wheel is mounted to a gimbal that can rotate about the Output Axis (OA). The gimbal is mounted within a case that is in turn attached to the rotating platform via a post. The SRA and OA are orthogonal. During operation, in response to a rotation of the case about the gyro Input Axis, the gyro gimbal responds with a rotation about the Output Axis. By rotating the platform, the same gimbal rotation will result. 
     To make a PIGA, the gyro is made purposely unbalanced by the addition of a mass along the SRA axis, to convert the gimbal into a pendulum. Under acceleration, the unbalanced mass generates a torque that tends to rotate the gimbal about the OA. By rotation of the platform (servo member) in the appropriate direction, the gimbal can be returned to its null position. Note that the pendulous torque and the gyro torque act on a common member, the gimbal. For this reason the gimbal is referred to as a Torque Summing Member (TSM). 
     The PIGA equation of motion for the gimbal rotation angle θ is given by
 
 I{umlaut over (θ)}+D{dot over (θ)}+Kθ=H   spin   {dot over (φ)}−Pa   (1)
 
where H spin {dot over (φ)} is the gyro torque; Pa is the pendulous torque; H spin =I wheel {dot over (α)} spin  is the wheel angular momentum; I wheel  is the wheel moment of inertia about the spin axis;
 
{dot over (φ)} is the rotation rate of the platform; {dot over (α)} spin  is the spin rate of the wheel; P is the pendulosity; and
 
α is the input acceleration. In closed loop operation, the gyro torque is equal to the pendulous torque, H spin {dot over (φ)}=Pa. The acceleration is then given by
 
                   a   =         H   spin     P     ⁢     ϕ   .               (   2   )               
where
 
               H   spin     P         
is the Scale Factor.
 
     One unique attribute of the PIGA is that when both sides of equation (2) are integrated, the following expression is obtained 
                   v   =         H   spin     P     ⁢   ϕ             (   3   )               
This expression represents the mechanical integration of acceleration, and the velocity is given directly by the Servo Member angle. The significance of this is that numerical integration is not required and a source of random walk in velocity is eliminated.
 
     A second PIGA attribute is that the accuracy of the measurement only depends on the measurement of the platform angle for the velocity read-out or the rate of the platform rotation for the acceleration read-out, since the wheel speed is maintained constant by a synchronous drive motor whose speed is determined by the drive frequency only, and not on the magnitude of the voltages/currents applied to spin the wheel and rotate the platform. This attribute is possible because a very stable gyroscope is used to provide a very accurate rebalance torque. 
     The Gyro-Rebalanced Accelerometer (GRA) is intended to overcome the instability of torque rebalance components by applying a gyroscopic torque that can be measured directly. The principle has been shown in U.S. Pat. Nos. 5,457,993, 5,691,470 and 5,712,426. The disclosures of each of these patents are incorporated herein by reference. The significance of this approach is that the acceleration-produced torque is balanced by a gyroscopic torque; both are inertial torques. 
     SUMMARY OF THE INVENTION 
     This invention relates to designs and implementations of a Gyro Rebalanced Accelerometer (GRA). 
     This invention further relates to planar GRA designs capable of being fabricated with MEMS processing technologies. 
     This invention further relates to the components of the design and how they provide the functionality of the GRA. 
     This invention also relates to open-loop operation of the GRA. 
     This invention also relates to two GRA designs optimized for MEMS fabrication processes. These are referred to as GRA and GRA 2 . 
     This invention also relates to offset operation of the GRA as defined by the frequency difference between the Rotor and Servo Member natural frequencies. The preferred offset is zero. Non-zero offset requires that the frequency difference is small to minimize the drive power. 
     This invention also relates to monolithic constructions of the GRA to minimize structural instability. Because of this, the structure is electrically connected to ground. 
     This invention features an accelerometer, termed GRA, that lies generally in a plane, for detecting acceleration along an input axis, comprising a substrate, a generally planar Servo Member (SM) flexibly coupled to the substrate such that it is capable of oscillatory motion about a servo axis that lies in the plane, a generally planar Torque Summing Member (TSM) coplanar with and flexibly coupled to the SM such that the TSM is capable of rotary motion relative to the SM about an output axis that is in the plane and orthogonal to the servo axis, wherein the TSM is mass-imbalanced relative to the output axis, and a generally planar rotor coplanar with and flexibly coupled to the TSM such that it is capable of rotary oscillatory motion relative to the TSM about a rotor axis that is orthogonal to the plane. There are one or more rotor drives for oscillating the rotor about the rotor axis, and one or more SM drives for oscillating the SM about the servo axis. There are also one or more rotor output sensors that detect oscillation of the rotor about the rotor axis, one or more SM output sensors that detect oscillation of the SM about the servo axis, and one or more TSM output sensors that detect rotation of the TSM about the output axis. 
     The rotor and SM drives preferably comprise capacitive drives. The SM drive may comprise plates. There may be at least one SM drive on each side of the servo axis. The rotor output sensors may comprise capacitive sensors, which may be comb sensors. The comb sensors may comprise sectors that are radially arranged around the output axis. There may be two pairs of adjacent comb sectors, one pair for sensing and one pair for driving. The TSM output sensors may comprise capacitive plate sensors. 
     The accelerometer may further comprise a controller, responsive to the rotor output sensors, for maintaining the amplitude and phase of the rotor constant. The rotor may oscillate at essentially the same frequency as the SM oscillation frequency. The rotor may be flexibly coupled to the TSM by a plurality of rotor flexures. The rotor may be circular, in which case the rotor flexures may be spaced evenly about its periphery. The rotor flexures may each comprise two bending “U” flexures, and may further comprise stress relief features comprising a bend in the flexure. The SM may be flexibly coupled to the substrate by a pair of SM linear flexures. 
     The rotor may be located within the TSM, and the TSM may be located within the SM. The rotor may be coupled to the TSM by flexures that are radial relative to the rotor axis. The rotor may oscillate at resonance. 
     The accelerometer may further comprise a controller, responsive to the SM output sensors, for maintaining the amplitude and phase of the SM constant. The accelerometer may further comprise a controller, responsive to the TSM output sensors, for causing the rotor drive to vary the phase of the rotor oscillation. The accelerometer may further comprise a controller, responsive to the TSM output sensors, for causing the SM drive to vary the phase of the SM oscillation. The accelerometer may further comprise at least one phase-lock loop control that locks onto the resonance of at least one of the rotor and SM. The accelerometer may comprise two controllers for each of the rotor and SM, one a phase-lock loop and the second an amplitude control loop. 
     This invention also features an accelerometer, termed the GRA 2 , that lies generally in a plane, for detecting acceleration along an input axis, comprising a substrate, a generally planar Servo Member (SM) flexibly coupled to the substrate such that it is capable of oscillatory motion about a servo axis that is normal to (orthogonal to) the plane, a generally planar Torque Summing Member (TSM) coplanar with and flexibly coupled to the SM such that the TSM is capable of rotary motion relative to the SM about an output axis that is in the plane and orthogonal to the servo axis, wherein the TSM is mass-imbalanced relative to the output axis, and a generally planar rotor coplanar with and flexibly coupled to the TSM such that it is capable of rotary oscillatory motion relative to the TSM about a rotor axis that lies in the plane. There are one or more rotor drives for oscillating the rotor about the rotor axis, and one or more SM drives for oscillating the SM about the Servo Axis. There are also one or more rotor output sensors that detect oscillation of the rotor about the Rotor Axis, one or more SM output sensors that detect oscillation of the SM about the Servo Axis, and one or more TSM output sensors that detect rotation of the TSM about the Output Axis. 
     The rotor and SM drives of the GRA 2  preferably comprise capacitive drives. The rotor drive may comprise capacitive plates. There may be at least one rotor capacitive drive plate on each side of the Rotor Axis. The SM drive may comprise rotary comb capacitors that may further comprise sectors (quadrants) that are radially arranged around the Servo Axis. 
     The SM output sensors of the GRA 2  may comprise capacitive sensors, which may be comb sensors. The comb sensors may comprise sectors (quadrants) that are radially arranged around the Servo Axis. There may be two pairs of adjacent comb sectors, one pair for sensing and one pair for driving. The TSM output sensors may comprise capacitive plate sensors. 
     The GRA 2  accelerometer may further comprise a controller, responsive to the SM output sensors, for maintaining the amplitude and phase of the SM oscillation constant. The SM may oscillate at essentially the same frequency as the rotor oscillation frequency. 
     The TSM of the GRA 2  may be flexibly coupled to the SM by two collinear TSM flexures that define the TSM Output Axis which is orthogonal to the Servo Axis. The SM flexures flexibly couple the SM to the substrate. The SM may be circular and the flexures may be spaced evenly about its periphery. Each flexure may comprise two bending “U” flexures, and may further comprise stress relief features comprising a bend in the flexure. The rotor may be coupled to the TSM by a pair of rotor linear flexures aligned orthogonal to the TSM Axis. 
     The GRA 2  rotor may be located within the TSM, and the TSM may be located within the SM. The TSM may be coupled to the SM by flexures that are radial relative to the SM axis. The SM may be driven to oscillate at resonance. 
     The GRA 2  accelerometer may further comprise a controller, responsive to the TSM output sensors, for causing the rotor drive to vary the phase of the rotor oscillation. The accelerometer may further comprise a controller, responsive to the TSM output sensors, for causing the SM drive to vary the phase of the SM oscillation. The accelerometer may further comprise at least one phase-lock loop control that locks onto the resonance frequency of at least one of the rotor and SM. The accelerometer may comprise two controllers for each of the rotor and SM, one an amplitude control loop for the rotor and the second an amplitude control loop for the SM. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       Other objects, features and advantages will occur to those skilled in the art from the following description of the preferred embodiments, and the accompanying drawings, in which: 
         FIGS. 1A ,  1 B and  1 C schematically depict the inventive planar GRA concept based on the oscillatory gyro and the simple pendulum accelerometer. 
         FIG. 2  is a graph of the GRA scale factor as a function of phase, δ, between the Servo and Rotor Members for the invention. 
         FIG. 3  is a top schematic view of the mechanical design of one embodiment of the inventive GRA. 
         FIG. 4  is a close-up view of the W-flexure design of  FIG. 3 . 
         FIG. 5  shows the rotary comb design of  FIG. 3 . 
         FIG. 6  shows neighboring comb segments of the rotary comb design of  FIG. 5 . 
         FIG. 7  shows the GRA metallization layout for the design of  FIG. 3 . 
         FIG. 8  is a view similar to that of  FIG. 3  for an alternative embodiment of a GRA with square TSM geometry. 
         FIG. 9  is a functional block diagram of the preferred GRA electronics for the embodiments of  FIGS. 3 and 8 . 
         FIG. 10  is a top schematic view of the mechanical design of another embodiment of the invention, termed the GRA 2 . 
         FIG. 11  is a close-up view of the W-flexure design of  FIG. 10 . 
         FIG. 12  shows the rotary comb design of  FIG. 10 . 
         FIG. 13  shows neighboring comb quadrants of the rotary comb design of  FIG. 12 . 
         FIG. 14  shows the GRA 2  metallization layout for the embodiment of  FIG. 10 . 
         FIG. 15  is a functional block diagram of the preferred GRA 2  electronics for the embodiment of  FIG. 10 . 
         FIG. 16  schematically depicts the preferred Dissolved Wafer Process steps used to fabricate the various embodiments of the GRA. 
         FIG. 17  is a schematic side-view of a completed GRA device after the silicon substrate is etched away. 
     
    
    
     PREFERRED EMBODIMENTS OF THE INVENTION 
     The GRA is similar in operation to the PIGA. By understanding the PIGA, the description of the GRA is simplified. 
     Like the PIGA, the GRA is based on the use of a stable gyroscope. Because the rotor and Servo Member in the GRA are oscillatory, the measurement and control of their amplitudes and drive frequency eliminates the instability in the actuators and the voltages applied. Therefore a stable and accurate scale factor will also be obtained for the GRA. 
     GRA Description/Principle of Operation 
     The GRA is a planar device with two oscillating members and a pendulum.  FIGS. 1A-1C  show how the gyroscope and pendulum are combined in one instrument for one configuration of the GRA. The GRA  2  changes the geometry of the members and the orientation of the three axes relative to the plane. The description is equivalent. The simple pendulum accelerometer,  FIG. 1A , contains an annular disk with a pendulous mass. The disk is attached to the substrate with two in-line torsional flexures. The gyroscope,  FIG. 1B , contains a rotor in the center of a balanced annular disk. The disk is also attached to the substrate with two, in-line torsional flexures. The gyro is operated by oscillating the rotor about the axis normal to the plane. In response to rotation rate about the Input Axis, the annular disk (the output member) oscillates about the Output Axis, which is aligned with the torsional flexures. Radial flexures (not shown in this drawing) suspend the rotor from the inner diameter of the ring. 
     The GRA,  FIG. 1C , is formed by functionally combining the two instruments. The annular disk (the TSM) is the common member. The pendulous mass generates rotation of the disk about the Output Axis in response to acceleration. The rotor causes oscillation of the disk when the gyro is rotated about its Input Axis. When the gyro is oscillated about its Input Axis and at the same frequency as the Rotor, the disk is rotated (not oscillated) to counter the rotation of the pendulum. To enable the oscillation of the gyro, a third member (the Servo Member or SM) is added to the outside of the Rotor and Disk. Because the gyro and pendulous mass both produce torques on the disk, the disk is called the Torque Summing Member (TSM). 
     The GRA equation of motion is that of the TSM (annular disk) angle of rotation subject to gyro and pendulosity torques.
 
 I{umlaut over (θ)}+D{dot over (θ)}+Kθ=H   osc {dot over (φ)} osc   −Pa   (4)
 
where H osc {dot over (φ)} osc  is the gyro torque, Pa is the pendulous torque, H osc =I rotor {dot over (α)} osc  is the rotor angular momentum, I rotor  is the rotor moment of inertia about the oscillation axis, {dot over (φ)} osc  is the oscillation rate of the platform (TSM or disk), {dot over (α)} osc  is the oscillation rate of the rotor, P is the pendulosity, and α is the input acceleration. In closed loop operation, the gyro torque at steady state is equal to the pendulous torque, H osc {dot over (φ)} osc =Pa. The acceleration is then given by
 
     
       
         
           
             
               
                 
                   a 
                   = 
                   
                     
                       
                         H 
                         osc 
                       
                       P 
                     
                     ⁢ 
                     
                       
                         ϕ 
                         . 
                       
                       osc 
                     
                   
                 
               
               
                 
                   ( 
                   5 
                   ) 
                 
               
             
           
         
       
     
     To obtain a more useful expression we substitute for H osc =I rotor {dot over (α)} osc , {dot over (α)} osc =ω{tilde over (α)} osc  cos ωt, {dot over (φ)} osc =ω{tilde over (φ)} osc  cos(ωt−δ) where {tilde over (α)} osc  is the rotor oscillation amplitude; {tilde over (φ)} is the servo oscillation amplitude; ω is the oscillation frequency and δ is the phase between the Rotor and Servo Member oscillators. The more relevant expression for acceleration becomes 
                   a   =           I   rotor     ⁢     ω   2     ⁢     α   ~     ⁢     ϕ   ~         2   ⁢   P       ⁢   cos   ⁢           ⁢   δ             (   6   )               
where
 
                 I   rotor     ⁢     ω   2     ⁢       α   ~     osc     ⁢       ϕ   ~     osc         2   ⁢   P           
is the Scale Factor and cos δ is the control variable for closed-loop operation. The amplitudes of oscillation are not required to be equal, but to maintain a constant scale factor, they must be held constant. To change the magnitude of the Scale Factor, the inertia, operating frequency and the oscillation amplitudes can be changed.
 
       FIG. 2  is a plot of the Scale Factor for a maximum acceleration of 1 g. For practical operation, the nearly linear operating range bounded by ±60 degrees is selected. 
     According to equation (6), the accuracy of the scale factor depends primarily on the measurement accuracy of the oscillation amplitude and not on the stability of the actuator or the applied drive voltages. The measurement accuracy of acceleration is also dependent on phase measurements, which are highly accurate and not on how the phase is varied. The resolution and bias stability will depend on the smallest measurable phase between the oscillators, which is dependent on the magnitude of the scale factor and the noise. 
     Unlike the simple pendulum, for which the accuracy and stability of the accelerometer depends on the accuracy and stability of the pick-off and actuator, the accuracy and stability of the GRA is dependent on the accuracy and stability of the pick-offs alone, which measure the oscillation amplitudes and the frequency of oscillation. Gyroscopic rebalance essentially provides a more stable and accurate Scale Factor over simple accelerometers. 
     Practical Mode of Operation 
     The ideal GRA will operate with matched Rotor and Servo Member natural frequencies. In the practical case, however, the frequency match is difficult to obtain. Therefore, after the difference (offset) is made small, the GRA is operated by phase-locking the drive frequency to the Rotor or the Servo Member. The second oscillator will then be driven at the same frequency. 
     Advanced Mode of Operation 
     The Rotor and Servo Members are mechanical oscillators that are coupled by the overall structure. By actively phase-locking the separate oscillators, the two will lock and oscillate at the same frequency if they are sufficiently close and the feedback amplitude is also sufficient. 
     GRA Embodiment 
     Mechanical design 
     The mechanical design of the preferred embodiment of inventive GRA  10  is shown in  FIG. 3 . The rectangular shapes on each end are bonding pads  12  used to bond the device to the Pyrex substrate  14 . Two co-linear torsional flexures  16 ,  17  connect the Servo Member (SM)  18  to the bonding pads. The flexures are stress-relieved by the oval cutouts  20 ,  21  in the bonding pads. The square SM shape allows the placement of sufficiently large capacitive plates underneath the SM for actuation. Capacitive sense plates are used to measure the motion of the SM. The Rotor  22  is an annular disk connected to the TSM  8  with four W-shaped flexures  24 ,  25 ,  26 ,  27 . 
     The W-flexure design  42 , shown in  FIG. 4 , is made up of two U-shaped flexures  43 ,  44 . One end of each is connected to the TSM  8  and the other to the Rotor  45  through an L-shaped segment  47 ,  48  essentially tangent to the rotor disk curvature. The L-shaped segment is added to enable the U-structure to bend with Rotor rotation and to absorb stress between the TSM and Rotor. The radial alignment of the flexures along diagonals across the Rotor disk makes a symmetric arrangement with each flexure experiencing the equivalent stress. 
     The TSM is connected to the Servo Member with two torsional flexures  76  and  77 . The pendulosity is caused by the hole  78  cut into the TSM. 
     The working gap between the gyro structure and the Pyrex substrate is 10 microns but the gap used depends on several factors: geometry, actuation capacity, sensitivity, and fabrication constraints. The gap is fabricated by etching a well in the silicon and a well in the Pyrex, as explained below. 
     The use of Pyrex is dependent on the need to anodically bond epitaxial silicon to a substrate as described in the DWP process. Other fabrication processes are possible. It is preferred to use a substrate that has similar thermal characteristics to the device material, which in this case is silicon. An option is to also use silicon as the substrate for close thermal match and to enable anodic bonding with a deposited Pyrex-equivalent film added to the substrate silicon. This would also preserve the electrical isolation between devices. 
     It is preferred for the device to be monolithic for mechanical stability and to connect it to electrical ground. 
     On the inside diameter of the Rotor is constructed a continuous radial comb  30  around the circumference. The comb fingers are aligned radially with the rotor center of rotation about rotor axis  4 . Four sets of stator mating combs are constructed on four separate quadrants, fixed separately to the substrate, two of which actuate the Rotor and two sense its rotation. The stators are connected electrically to pads by crimping the trace between the Pyrex and the silicon during anodic bonding. 
     The GRA is operated by oscillating the Rotor about the Rotor Axis  4  (about the normal to the plane), oscillating the Servo Member about the Servo Axis  5  and sensing the rotation of the TSM about the GRA Output Axis  6 . The GRA Input Axis is the same as the Rotor Axis. 
     Rotary Comb Capacitive Sensor 
     The rotary comb design  30  is illustrated in  FIG. 5 . It is separated into four quadrants  32 ,  33 ,  34 ,  35 . For each quadrant, the comb is divided into a stator with stator comb fingers  36  attached to the substrate  14  and a rotor with rotor comb fingers  38  that are part of the moving Rotor disk  40 . The stator fingers and rotor fingers are aligned radially with the center of rotation of the disk. For each rotor finger there is a stator finger with the two separated by a small gap. They make up a comb finger pair. Pairs of comb fingers are separated by a large gap. A number of comb finger pairs make up each quadrant. The sensitivity of the comb sensor scales with the number of comb finger pairs. By reducing the small gap between the comb finger pairs, the sensitivity is increased. 
     Neighboring quadrants  33 ,  34  are designed symmetrically about the axis that separates them as shown in  FIG. 6 . For rotation of the rotor in either direction, the small gap  37  of comb finger pairs in one quadrant decreases while the small gap of comb finger pairs in the other quadrant increases. The purpose of the rotary design based on neighboring quadrants is that when the signals from the comb finger pairs located on two neighboring quadrants are differenced, the signals add and the common-mode noise subtracts; this is differential operation. At zero rotation of the IM, the output is also zero. The other two quadrants  32 ,  35  are used to actuate the rotor. 
     Metallization Design 
     The metallization design  50  is shown in  FIG. 7 . It consists of capacitive plates, connecting traces and pads. Capacitive plates  51  and  52  are located under part of the SM on one side of the Servo Axis. They are connected by a trace. Capacitive plates  53 ,  54  are located on the other side. They are connected by a trace. Drive voltages are applied to the actuator plates to predominantly pull down on one side of the SM during the first half of the drive cycle and to predominantly pull down on the other side of the SM during the second half of the drive cycle. The result is an oscillatory motion of the SM about the Servo Axis. The sensing of the SM motion is accomplished with two capacitive plates  55 ,  56 . The outputs are connected differentially since for any motion, the gap for one increases and the gap for the other decreases. 
     Capacitive plates  70 ,  71 ,  72  and  73  are used to sense the rotation of the TSM. 
     Trace  57  connects capacitive plates  51 ,  52  to the pad  58 , for example. 
     Stators of the rotary comb are connected to pads with traces  59  that are crimped between the stator structure and the Pyrex substrate during anodic bonding. The GRA monolithic structure containing the SM, Rotor and TSM is connected to electrical ground with trace  63  crimped between the mounting structures  12  and the Pyrex substrate. 
     Traces also act as capacitive sensing plates when they are located beneath the moving structure, and this needs to be taken into consideration. A rule is to make the lengths under the moving parts equal and symmetric. Pick-up between plates is also a consideration. Design practices known in the art apply. Electrical pick-up can be a source of quadrature in the gyro output. 
     Electrical Leads 
     Electrical leads or traces connect the capacitive sensors and actuators to the termination pads on the periphery of the instrument. The gyro is grounded by a trace that is crimped under the supporting mesa during anodic bonding. Stator combs are connected similarly by crimping traces under their mesas. Plates are connected directly to the pads. 
     Several considerations apply: 
     
         
         
           
             traces that pass under silicon structures add stray capacitance, therefore this transit should be minimized, 
             traces that are required to pass under silicon structures should be symmetric so that the influence of any leakage capacitance will cancel under differential operation of the pick-off (capacitive sensors) and actuators, and 
             traces should be routed to minimize capacitive coupling between them.
 
Flexures
 
           
         
       
    
     The purposes of flexures are to:
         set orientational alignment between members,   govern rotation of the members about prescribed axes, and   provide support for the structures.       

     The orientational alignment between members is an especially important consideration for the gyroscope because it will introduce mechanical coupling between the OM oscillation and the Output Member to generate quadrature error. 
     The ideal flexure allows only motion about one axis. 
     The support capability is especially important when considering shock capability. Through a combination of the necessary design weight and flexure design, there is a maximum possible shock capability. Modeling can be used to find structurally-weak points and strengthen them. 
     SM Flexure Relief Structure 
     The stress relief absorbs the tension on the flexure that is due to the differential thermal expansion between the Pyrex and epitaxially-doped silicon, while cooling from the elevated anodic bonding temperature. If a different process is used, the stress relief may not be necessary. Without the stress relief, the tension on the flexure will cause a potato chip deformation of the SM structure that introduces stress between the SM and the TSM and rotor, inhibiting their proper operation. 
     Rotor Flexure 
     The W-flexure enables rotation of the IM about the normal to the plane. Four are used in this design. Each W-flexure is composed of two bending U-flexures with a stress relief in each. For cases where the OM applies a tension or compression to the W-flexure, the stress relief can bend and absorb the stress. In this way, the flexure does not kink and inhibit rotation of the IM. 
     Design Modification 
     A second design of the first iteration is shown in  FIG. 8 . It modifies shape of the TSM from circular to square. One reason is to reduce the mechanical coupling with the Rotor. The greater inertia and the larger area would also provide greater capacitive pick-off sensitivity and a larger proof-mass. The downside is that the Servo Member surface area is smaller and the capacitive drive and sense efficiency is reduced. 
     Description of GRA Preferred Electronics 
     The preferred GRA electronics are described with a block schematic in  FIG. 9 . A rotary capacitive comb actuator is used to drive the rotor member into oscillation at the SM frequency or at a small offset from the SM frequency. A rotary capacitive comb pick-off (sensor) is used to sense the oscillation amplitude and phase of the rotor. An amplitude control loop is used to hold the rotor amplitude constant. The phase of the rotor motion is used with a phase control loop to vary the phase of the rotor member to change the feedback variable that holds the TSM at null. 
     A capacitive plate actuator is used to drive the SM into oscillation. A capacitive plate pick-off (sensor) is used to sense the oscillation amplitude and phase of the SM. An amplitude control loop is used to hold the SM amplitude constant. The phase of the SM is used with a phase-lock loop to hold the SM oscillation frequency at resonance. The rotor member may be designed to oscillate at the same frequency as the servo member for one embodiment. Capacitive plate actuators and pick-offs (sensors) are used for the servo member because its motion is towards and away from the plane. 
     Under acceleration input, the TSM is caused to rotate. The TSM signal is used with a phase control loop to vary the phase of either the Rotor or Servo Member to apply gyroscope torque to counter the motion of the pendulum and bring it back to null. Only rotor phase control is shown in  FIG. 9 . The cosine of the phase change is proportional to the acceleration input. 
     The maximum operating range of the GRA is set to the most linear segment of the cos δ control variable. The optimum resolution depends on the smallest equivalent phase that can be resolved, which depends on the sensor sensitivity and the electronics noise as determined by the Allan Deviation and Scale Factor and other resolution measurement means. 
     GRA 2  Embodiment 
     Mechanical Design 
     The mechanical design of the preferred embodiment of inventive GRA 2   110  is shown in  FIG. 10 . It comprises three planar members concentrically arranged and with a common center. All three are flexurally connected to each other with the outermost member connected to the substrate. All three members rotate about three mutually orthogonal axes. The outermost member is the servo member  118  (SM). It is flexurally connected to four bonding pads  112  with four W-flexures  124 ,  125 ,  126 ,  127 . The bonding pads are bonded to the Pyrex substrate  114 . The SM member has an annular disk shape. Within the inner diameter of the SM is flexurally connected the TSM  108  with two collinear flexures  176 ,  177 . The TSM has a circular outer diameter to maximize its size. The rotor  122  has a near rectangular shape and it is located within a cut-out in the TSM. The rotor is flexurally connected to the TSM with two collinear torsional flexures  116 ,  117 . Cuts  178  into the TSM and the rotor on one side of the TSM Axis form the pendulosity necessary for accelerometer sensitivity. The rotor and TSM flexures define the Rotor Axis  104  and TSM Axis  106  which are orthogonal to each other and to the SM Axis  105 . 
     On the outer diameter of the SM annular disk is constructed a continuous radial comb  130  around the circumference. The comb fingers are aligned radially with the SM annular disk center of rotation about the Servo Axis. Four sets of stator mating combs are constructed on four separate quadrants, fixed separately to the substrate, two of which actuate the SM and two sense its rotation. The stators are connected electrically to electrical connecting pads by crimping a trace between the Pyrex and the silicon during anodic bonding. 
     The GRA 2  is operated by oscillating the SM about the Servo Axis (about the normal to the plane); because of the coupling of the TSM to the SM, and the rotor to the TSM, this also oscillates the TSM and the rotor about the Servo Axis. The rotation of the TSM about the GRA 2  Output Axis is sensed. The GRA 2  Input Axis is the same as the Servo Axis. The rotor is independently oscillated by itself about the Rotor Axis  104  at the same frequency as the SM. 
     The W-flexure design  142 , shown in  FIG. 11 , is made up of two U-shaped flexures  143 ,  144 . One end of each is connected to the bonding pad  112  and the other to the SM  146  through L-shaped segments  147 ,  148  essentially tangent to the SM annular disk curvature. The L-shaped segment is added to enable the U-structure to bend with SM rotation and to absorb stress between the bonding pads and the SM. The radial alignment of the flexures along diagonals across the SM annular disk makes a symmetric arrangement with each flexure experiencing similar stress. A stress relief  120  cut into the bonding pads further relieves the stress applied to the SM. 
     The working gap between the GRA 2  structure and the Pyrex substrate is 10 microns but the required gap depends on several factors: geometry, actuation capacity, sensitivity, and fabrication constraints. The gap is fabricated by etching a well in the silicon for a portion of the gap and a matching well in the Pyrex for the remainder depth, as explained below. 
     The use of Pyrex is dependent on the need to anodically bond epitaxial silicon to a substrate as described in the DWP process. Other fabrication processes are possible. It is preferred to use a substrate that has similar thermal characteristics to the device material, which in this case is silicon. An option is to also use silicon as the substrate for close thermal match and to enable anodic bonding with a deposited Pyrex-equivalent film added to the substrate silicon. This film would also preserve the electrical isolation between devices. 
     It is preferred for the device to be monolithic for mechanical stability and to connect it to electrical ground. 
     Rotary Comb Capacitive Sensor 
     The rotary comb design  130  is illustrated in  FIG. 12 . It is separated into four quadrants  132 ,  133 ,  134 ,  135 . For each quadrant, the comb is divided into a stator with stator comb  138  attached to the substrate  114  and a rotor with a single rotor comb  136  that is part of the moving servo member annular disk  118 . The stator fingers and rotor fingers are aligned radially with the center of rotation of the SM annular disk. For each SM finger there is a mating stator finger with the two separated by a small gap. They make up a comb finger pair  140 . Pairs of comb fingers are separated by a large gap. A number of comb finger pairs make up each quadrant. The sensitivity of the comb sensor scales with the number of comb finger pairs. By reducing the small gap between the comb finger pairs, the sensitivity is increased. The actuation capability is also dependent on the number of comb finger pairs and the dimension of the small gap. 
     Neighboring quadrants  132 ,  133  are designed symmetrically about the radial axis that separates them as shown in  FIG. 13 . For rotation of the SM in either direction, the small gap  137  of comb finger pairs in one quadrant decreases while the small gap of comb finger pairs in the other quadrant increases. The purpose of the rotary design based on neighboring quadrants is that when the signals from the comb finger pairs located on two neighboring quadrants are differenced, the signals add and the common-mode noise subtracts; this is differential operation. At zero rotation of the SM, the output is also zero. The other two quadrants  134 ,  135  are used to actuate the SM. 
     Metallization Design 
     The metallization design  150  for the GRA 2  is shown in  FIG. 14 . It consists of capacitive plates, connecting traces and electrically connecting pads. Capacitive actuator plate  151  is located on the substrate surface under part of the rotor on one side of the Rotor Axis. Capacitive actuator plate  152  is located on the other side. Drive voltages are applied to the actuator plates to predominantly pull down on one side of the rotor during the first half of the rotor drive cycle and to predominantly pull down on the other side of the rotor during the second half of the rotor drive cycle. The result is an oscillatory motion of the rotor by itself about the Rotor Axis. The sensing of the rotor motion is accomplished with two capacitive plates  153 ,  154  located on either side of the Rotor Axis. The sense outputs are connected differentially since for any motion, the gap for one increases and the gap for the other decreases. 
     Capacitive plates  170 ,  171 ,  172 ,  173  are used to sense the rotation of the TSM (together with the rotor) about the TSM axis, using plates  170 ,  172  located on one side of the TSM Axis and plates  171 ,  173  located on the other side. In the full sensing mode, the signals from plates  170 ,  172  are added and plates  171 ,  173  are added. For an alternate use of the TSM plates, plates  170 ,  171  can be used for sensing and plates  172 ,  173  can be used for actuation of the TSM. Actuation of the TSM can be used to test the open loop operation of the TSM by using DC voltages to rotate the TSM to simulate the action of acceleration on the TSM proof mass, which is caused by the holes in the TSM. 
     Trace  157  connects capacitive plate  171  to the pad  158 , for an example of the connection of a capacitive plate to the electrically connecting pad. 
     The example for electrically connecting the quadrants of the rotary comb stators to output pads is shown with trace  159 . The trace is crimped between the stator structure and the Pyrex substrate during anodic bonding. The GRA monolithic silicon structure containing the SM, rotor and TSM is connected to electrical ground with trace  163  crimped between the mounting structure  112  and the Pyrex substrate. 
     Traces also act as capacitive sensing plates when they are located beneath the moving structure, and this needs to be taken into consideration. A rule is to make the lengths under the moving parts equal and symmetric. Pick-up between plates is also a consideration. Design practices known in the art apply. Electrical pick-up can be a source of quadrature in the gyro output. 
     Description of GRA  2  Preferred Electronics 
     The preferred GRA 2  electronics are described with a block schematic in  FIG. 15 . A rotary capacitive comb actuator is used to drive the servo member (and the TSM and rotor) into oscillation about the servo axis at the resonant frequency for the three members together, for low power consumption. A rotary capacitive comb pick-off (sensor) is used to sense the oscillation amplitude and phase. An amplitude control loop is used to hold the SM (and TSM and rotor) oscillation amplitude constant. The phase of the SM motion is used with a phase-lock loop to hold the SM on resonance. Similar electronics are used for the rotor member except a phase-lock loop is not needed since the rotor is driven at the same frequency as the SM in this case. Capacitive plate actuators and pick-offs (sensors) are used for the rotor member because its motion is towards and away from the plane. 
     Under acceleration input, the TSM (and because of coupling, the rotor along with the TSM) is caused to rotate about the TSM (output) axis. The TSM signal is used with a phase control loop to vary the phase of either the rotor or SM, to apply gyroscope torque to counter the rotation of the TSM and bring it back to null. Only rotor phase control is shown in  FIG. 15 . The cosine of the phase change is proportional to the acceleration input. 
     The maximum operating range of the GRA 2  is set to the most linear segment of the cos δ control variable. The optimum resolution depends on the smallest equivalent phase that can be resolved, which depends on the sensor sensitivity and the electronics noise as determined by the Allan Deviation and Scale Factor and other resolution measurement methods. 
     Optional Open-Loop Mode of Operation 
     The GRA 2  can also be operated open loop; the phase control loop is removed. In this case the rotor and the SM are driven in the same way: at the same frequency and with constant amplitudes. The difference for open-loop operation is that, as the pendulum (the TSM) is acted upon by acceleration input, the TSM is allowed to rotate. The response is a phase change between the oscillators. The phase change is the output. 
     Dissolved Wafer Processing 
     Dissolved Wafer Processing (DWP) is a MEMS fabrication process for making relatively large parts with good flatness and square profiles. The process requires two wafers: the first Pyrex and the second silicon with a boron-doped epitaxial layer. The combination of materials enables the two wafers to be anodically bonded. The thickness of the epitaxy determines the final device thickness, while boron doping of the epitaxial layer inhibits EDP etching. 
     Typical dimensions include: device size of about 3 mm in the plane, device thickness of 40 microns, smallest flexure thickness of 5 microns and gaps between comb fingers of 5 microns. Other dimensions are of course possible depending on the required dynamics of the members. 
     Four process masks are needed: two for processing the silicon and two for the Pyrex. Instrument functions are distributed between the two layers: the mechanical structure and comb components are fabricated in the doped silicon layer and the electrical connections and flat capacitive plate components are deposited onto the Pyrex layer. A detailed description of the process follows. 
     Process Steps 
     The process steps are described with reference to  FIG. 16 . The starting silicon wafer includes a grown epitaxial layer with heavy boron diffusion of 43-micron thickness. In step  1 , the epitaxial layer is etched to form mesas that support the silicon structures on the Pyrex as patterned by Mask  1 . The mesa thickness also sets part of the gap between the device and the substrate that allows motion of parts. In step  2 , deep reactive ion etching is used to etch through the epitaxial layer to form the device geometry that includes the structure, mass and combs as patterned with Mask  2 . In step  3 , wells are formed in the Pyrex to form the rest of the required gap using Mask  3 . With Mask  4  (step  4 ), metal deposited on the Pyrex is patterned to form capacitive plates for driving and sensing out of plane motions. In addition, Mask  4  patterns traces (conductors) that connect the structure, capacitive plates and the comb stators to the pads. In step  5 , the silicon wafer is anodically bonded to the Pyrex wafer at the mesas. In step  6  the wafer is cut with a saw along outlines (streets) that separate devices. Each device is then EDP (Ethylene-Diamene-Pyrocatechol) etched to remove the silicon, leaving behind epitaxial devices with movable parts. The thickness of the devices is equal to the epitaxial thickness minus the mesa thickness, approximately 40 microns for the present devices. A conceptual side view of the finished device is shown in  FIG. 17 . 
     Advantages/Disadvantages of DWP 
     DWP has several advantages:
         devices are made of one material (doped silicon) for greater thermal stability,   Pyrex serves as a robust substrate since it can be made as thick as desired,   multiple devices can be fabricated on the same Pyrex substrate, while making them physically separate,   thicker doped silicon devices can be made subject to the epitaxial process,   the process is a relatively low-temperature process, thereby generating low internal stresses.       

     The disadvantages of DWP are not limiting, but can contribute to cost of fabrication and greater design complication. They include:
         epitaxial growth limits the device thickness and introduces stresses,   chemical etching of most of the silicon wafer by EDP,   induced stresses from differential expansion of the silicon and Pyrex from the anodic bonding operation, and   reactive ion etching produces some tapering which makes it difficult to assign a resonance frequency.       

     It is important to form flexures with precise geometry and having a rectangular cross-section. A small variation in the wall verticality can greatly affect the stiffness and hence the dynamics. A conical cross-section would also have the effect of changing the rotation axis of the suspended member, and perhaps the orthogonality between the members. This misalignment leads to “quadrature error” in gyroscopes—the inadvertent drive of one member by one of the other members. 
     Since certain changes that would be apparent to one skilled in the art may be made in the above described embodiments of the invention without departing from the scope thereof, it is intended that all matter contained herein be interpreted in an illustrative and not a limiting sense. 
     Other embodiments will occur to those skilled in the art and are within the following claims.