Whole-Angle MEMS Gyroscopes. Doruk Senkal

Figure 2.2 Misalignment in principal axes of (a) elasticity and (b) damping ...Figure 2.3 Elliptical orbit of a CVG and the canonical variables.

      3 Chapter 3Figure 3.1 Quadrature signal can be separated from Coriolis signal via synch...Figure 3.2 Open‐loop mechanization utilizes no feedback loop in the sense mo...Figure 3.3 Force‐to‐rebalance utilizes feedback loops in both the drive (

) ...Figure 3.4 Whole‐angle gyroscope control with (optional) parametric drive.

      4 Chapter 4Figure 4.1 Traditional silicon MEMS encapsulation process consists of: (a) f...Figure 4.2 Integrated MEMS/CMOS fabrication process consists of: (a) pre‐etc...Figure 4.3 Epitaxial Silicon Encapsulation (EpiSeal) process consists of: (a...

      5 Chapter 5Figure 5.1 Ring/disk gyroscopes can be anchored (a) at the outer perimeter o...Figure 5.2 A 100k

‐factor, epitaxial silicon encapsulated Toroidal Ring Gyr...Figure 5.3 In this implementation, the central electrode assembly consists o...Figure 5.4 Due to the distributed suspension system vibrational energy is tr...Figure 5.5 Frequency sweep showing the

wineglass modes with

‐factor above...Figure 5.6 Electrostatic tuning with 3.26 and 0.5 V resulted in

(

at

)....Figure 5.7 Scale factor of Toroidal Ring Gyroscope in force‐to‐rebalance mod...Figure 5.8 Allan Variance of gyroscope in the force‐to‐rebalance mechanizati...Figure 5.9 Experimental demonstration of rate integrating operation under pa...Figure 5.10 Comparison of residual errors of conventional drive and parametr...Figure 5.11 Wineglass modes of axisymmetric architectures, such as ring/disk...Figure 5.12 Dual Foucault Pendulum (DFP) gyroscope consists of two mechanica...Figure 5.13 Vibration immunity and anchor loss mitigation are provided by an...Figure 5.14 FEA showing

–

symmetric anti‐phase operation. Device is anchor...Figure 5.15 Image of fabricated gyroscope with closeups of the shuttle assem...Figure 5.16 High‐vacuum test‐bed with nonevaporable getter pump provided

To...Figure 5.17 Ring‐down experiment showing energy decay time constant (

) of 3...Figure 5.18 Rate characterization with

s step input showed a FRB scale fact...Figure 5.19 Allan Variance of the gyroscope's zero rate output, showing ARW ...Figure 5.20 Polar plots showing the pattern angle dependence of four main cl...Figure 5.21 Spooling of the whole‐angle gyro output over 2 h of continuous r...

      6 Chapter 6Figure 6.1 Northrop Grumman HRG uses a double‐stemmed fused silica wineglass...Figure 6.2 SAGEM HRG uses a mushroom/bell type fused silica resonator [88]....Figure 6.3 Cross‐sectional view of various micro‐shell resonator geometries:...Figure 6.4 Micro‐shell fabrication processes can be categorized into two mai...Figure 6.5 Arrays of spherical shells were created by bonding borosilicate g...Figure 6.6 3‐D metal traces can be fabricated on the surface of glass shells...Figure 6.7 Bulk metallic glass shell structures are inherently conductive, e...Figure 6.8 Blow‐torch molded birdbath shell resonator [103].Figure 6.9 Fused silica spheres were micro‐machined into 3‐D shell structure...Figure 6.10 Silicon dioxide shells were formed by isotropic etching of silic...Figure 6.11 Hemispherical shell structures were fabricated by isotropically ...Figure 6.12 SEM image of arrays of 1 mm diameter released polycrystalline di...Figure 6.13 Cylindrical polycrystalline diamond shells can be created if the...Figure 6.14 SEM image of an all‐dielectric cylindrical shell [116].Figure 6.15 Diamond hemisphere deposited into a pre‐etched glass cavity and ...Figure 6.16 Thin film sputtered ULE (Ultra Low Expansion Glass) shells were ...Figure 6.17 Hemitoroidal polycrystalline diamond shell structure [123].Figure 6.18 SEM image of extremely small (200 μm diameter) cenosphere‐derive...Figure 6.19 Highly doped silicon electrodes adjacent to a

micro‐shell, fri...Figure 6.20 Blow‐torch molded fused silica micro‐shell resonator with silico...Figure 6.21 Polydiamond micro‐shell resonator with integrated electrodes [11...Figure 6.22 Bulk Metallic Glass (BMG) micro‐shell resonator with integrated ...Figure 6.23 Micro‐shell resonator with polysilicon electrodes [111]. The ele...Figure 6.24 Silicon electrodes for “Poached Egg” micro‐shell resonators [118...

      7 Chapter 7Figure 7.1 ULE TSG/fused silica micro‐glassblowing process, consists of: (a)...Figure 7.2 Small central post diameters create solid stem structures (left),...Figure 7.3 Geometric parameters of an inverted‐wineglass structure: Minor ra...Figure 7.4 Analytical solution of etch depth (

), wineglass diameter (

) ver...Figure 7.5 Boundary conditions for finite element analysis: (a) before glass...Figure 7.6 Transient FEA of micro‐glassblowing process showing the formation...Figure 7.7 Finite element predictions and cross‐sectional SEM shots of fabri...Figure 7.8 Wineglass structures with (a) 1.2 mm outer diameter and 600 μm st...Figure 7.9 Mode shapes and minimal electrode configuration required for

(a...Figure 7.10 Polar plots showing the first four harmonics of thickness imperf...Figure 7.11 Sketch of an ideal wineglass (perfectly spherical), showing

as...Figure 7.12 Plot showing wineglass thickness versus thickness imperfections ...Figure 7.13 The effect of thickness variation of the fourth harmonic on freq...Figure 7.14 Surface tension‐induced pressure differential depends on geometr...Figure 7.15 Custom‐built micro‐glassblowing furnace with process capability ...Figure 7.16 Optical photograph of glassblown fused silica inverted‐wineglass...Figure 7.17 Optical photograph of fused silica spherical shell structures, g...Figure 7.18 Optical photograph of inverted‐wineglass, released along the per...Figure 7.19 AFM surface profiles of TSG, (a) before and (b) after glassblowi...Figure 7.20 Slow cooling of TSG (

8 h) causes recrystallization [13].Figure 7.21 Glassblowing with rapid cooling of TSG (

1 min) prevents recrys...Figure 7.22 EDS spectral analysis of TSG and fused silica reveals that compo...

      8 Chapter 8Figure 8.1 Electrodes are fabricated separately on an SOI stack, bonded to t...Figure 8.2 SEM image of an adjustable electrode with 400 μm maximum displace...Figure 8.3 Ratchet mechanism acting on the electrode structure, the electrod...Figure 8.4 Released wineglass structure with 4.2 mm diameter, 50 μm thicknes...Figure 8.5 Electrode structures assembled onto a micro‐glassblown wineglass ...Figure 8.6 Electrostatic frequency sweep using adjustable electrode assembly...Figure 8.7 A glassblown spherical resonator with assembled electrodes. Diame...Figure 8.8 Process flow for fabrication of micro‐glassblown wineglass resona...Figure 8.9 SEM image of a stand‐alone micro‐wineglass structure after releas...Figure 8.10 Metallized micro‐wineglass structure with integrated electrodes....Figure 8.11 Packaged and wirebonded micro‐wineglass resonator. Diameter 4.4 ...Figure 8.12 Laser Doppler Vibrometer was used to scan along the perimeter of...Figure 8.13 Measured velocity amplitude distribution (mm/s) identifying (a) Figure 8.14 Experimental frequency sweeps of

and