3-d micromachined hemispherical shell resonators ... - Semantic Scholar
3-D MICROMACHINED HEMISPHERICAL SHELL RESONATORS WITH INTEGRATED CAPACITIVE TRANSDUCERS L. D. Sorenson, X. Gao, and F. Ayazi Georgia Institute of Technology, Atlanta, Georgia, USA
ABSTRACT We present a self-aligned fabrication method developed for three-dimensional (3-D) microscale hemispherical shell resonators with integrated capacitive transducers and a center post for electrical access to the shell. The self-aligned process preserves the axisymmetry for robust, balanced resonators that can potentially reach very high-Q due to suppressed anchor loss. High-Q operation of a thin polycrystalline silicon shell resonator is verified by exciting devices capacitively into a breathing resonance mode, with measured Q of 8,000 at 412 kHz in vacuum. This process can be further optimized to batch-fabricate micro-hemispherical resonator gyroscopes for portable inertial navigation.
INTRODUCTION The hemispherical resonator gyroscope (HRG) has shown very high performance and robustness over the years for inertial navigation. However, the existing HRG has relatively large size and very high manufacturing cost, limiting its use to demanding air- and spacecraft navigation and orientation applications [1]. An advantage of the HRG is its ability to operate in two modes: force-rebalance (or rate) and whole-angle (or rate-integrating) mode [2]. Typically, vibratory MEMS gyroscopes produce angular velocity or rate output [3]. Whole-angle mode gyroscopes using conventional planar silicon micromachining with low dissipation have recently been demonstrated [4]. Alternatively, emerging fabrication techniques have focused on producing 3-D balanced and isotropic shells for operation similar to HRG;; these techniques include wafer-scale glassblowing [5±8], and assembly and micromachining of prefabricated glass spheres [9]. Creation of hemispherical shells using isotropically-etched molds in silicon has also been explored as early as 1979, but for the purpose of creating fuel pellets for thermonuclear fusion research [10]. Although capacitive transducers situated on adjacent satellite shells have been co-fabricated for glass-blown shell resonators [6], wafer-level control over the dimension of the capacitive air gap has yet to be demonstrated. Further, no techniques have been proposed for self-aligned central support and electrical connection to a micro-hemisphere via a narrow support stem, to truly resemble a wineglass HRG microstructure. In this work, we present batch-processed micro- hemispherical shell resonators (ȝHSRs) which can potentially be a cost-effective alternative to macroscale HRGs. A novel 3-D fabrication process is developed which, in the spirit of [10], takes advantage of isotropic silicon micromachining to produce hemispherical molds, into which sacrificial and shell layers can be deposited. Boron doping is used to form electrodes surrounding the rim of the shell, which are isolated from the n-type substrate via the resulting PN junctions. The thickness of
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Figure 1: SEM view of a batch-fabricated polysilicon micro-hemispherical shell resonator (ȝHSR). The n-type silicon substrate was purposefully cleaved to reveal the embedded shell. P-doped electrodes formed by boron doping surround the rim of the shell, enabling actuation, sensing, and control for gyroscope application. the sacrificial layer yields a controllable and uniform gap size, while the doped electrodes follow the curvature of the shell, enhancing transducer efficiency. The ȝHSR presented here consists of a thin polysilicon hemisphere with an oxide support post, backside access plug for polarization voltage (Vp) connection, and doped capacitive electrodes (Fig. 1).
ENERGY DISSIPATION IN MICRO-HSR The macroscale HRG achieves its impressive performance due to ultra-low energy dissipation, which is demonstrated by quality factors (Q) in excess of 10 million [1]. An understanding of energy dissipation PHFKDQLVPV LV WKHUHIRUH NH\ WR UHSOLFDWLQJ WKH +5*¶V performance on the microscale, especially for the whole- angle mode where the Q directly impacts the decay time constant and must be large to sustain operation with minimal interruptions. Of the possible dissipation mechanisms enumerated in [11], the critical dissipation factors in ȝHSRs (assuming operation in high vacuum to remove air losses) are expected to be thermoelastic damping (TED), anchor loss through the support post, scattering from imperfections in the shell (surface roughness and deviation from a geometrically perfect hemisphere), and intrinsic material loss (which includes grain boundary scattering in the case of polysilicon). Of particular interest to gyroscope operation of the ȝHSR are the elliptical modes, especially the m=2 ³wineglass´ mode. Due to the nature of the hemispherical shell, in which the elliptical mode acoustic energy is concentrated around the VKHOO¶V rim far from the support, the ȝHSR can be expected to have low support loss even
MEMS 2012, Paris, FRANCE, 29 January - 2 February 2012
for finite support dimensions. Mitigating losses from the shell imperfections is done by producing an ultra-smooth mold with low imperfections and high symmetry. Polysilicon is an established MEMS material with well- known properties;; therefore, deposition of high-quality polysilicon with uniform grain size and smooth surface is easily achievable [12]. The only remaining concern when using polysilicon as the shell material is TED. To determine the expected TED losses in the ȝHSR, the coupled equations of thermoelasticity were formulated and implemented in COMSOL Multiphysics, and predicted QTED of 10.3 million was obtained for a polysilicon shell of 2 mm diameter and 500 nm thickness with an m=2 resonance frequency of 1 kHz, leading to an estimated decay time constant of almost 3400 seconds. Hence, with these positive attributes, polysilicon was selected to create the first ȝHSR prototypes.
FABRICATION PROCESS Devices are fabricated on 500-1000 ȝP (depending on desired shell diameter) low-resistivity antimony-doped n-type (100) single-crystal silicon (SCS) substrates, as shown in Figure 2. First, 2 ȝm thermal SiO2 (oxide) is patterned to mask the wafer during subsequent boron doping and annealing at 1050°C, which creates capacitive actuation and sense electrodes that are isolated from the substrate by PN junctions (Fig. 2a,b). The resonating shell, excluding the electrodes, is created by layer stacking in a micromachined silicon mold formed by two etching steps: the top hemispherical part of the mold is formed by isotropic etching, while the lower pyramidal part is anisotropically wet-etched from the backside. A 5 ȝm PECVD oxide layer is patterned to form the isotropic etch mask (Fig. 2c). Sulfur hexafluoride (SF6) plasma etches the hemispherical mold (Fig. 2d), which gives a smoother surface and better hemispherical profile than that created using xenon difluoride (XeF 2) reported in [13]. An LPCVD low-stress silicon nitride layer is patterned to mask the topside and backside during KOH etching, which forms the backside plug mold (Fig. 2e,f). This part must be thoroughly etched to reach the top mold to enable electrical access for polarization voltage. The oxide sacrificial layer, followed by the polysilicon shell layer, is conformally coated, allowing simultaneous formation of the topside shell and backside plug. While the shells are protected by photoresist, the polysilicon layer on the wafer surface is removed in a short dry etching step with SF6 plasma. The polysilicon is then doped and annealed (Fig. 2g). The shells are released in HF and dried using supercritical dryer (Fig. 2h). The oxide support is formed by etching the sacrificial layer during the HF release, which forces its outer edge to be self-aligned to the polysilicon shell. As long as the oxide support fully encloses the neck of the backside plug within its diameter, small misalignment between the top and bottom molds is tolerable. The support diameter can be controlled by the release time.
Figure 2 (color online): Fabrication process flow on n- type substrate: (a) growth and patterning of thermal oxide for (b) subsequent boron doping to form p-doped electrode regions isolated from the substrate via PN junctions;; (c) PECVD oxide is deposited and patterned to form the hard mask for (d) SF6 isotropic etching of the hemispherical mold;; (e) deposition and backside patterning of low-stress LPCVD silicon nitride for protection of the hemispherical mold during (f) KOH etching of the backside plug mold;; (g) thermal oxidation and subsequent polysilicon deposition to form the sacrificial and shell layers, respectively;; (h) release of the sacrificial oxide in HF and supercritical drying to form the final free-standing polysilicon ȝHSR structure with integrated capacitive air gap and electrodes.
169
(a) (a)
(b)
(b) Figure 4: Least squares fit to circle of (a) original ȝHSR SEM (b) overlain to show high symmetry of the shell. (c)
(d)
Figure 3: SEM views of ȝHSR components: (a) cross- section cut of silicon mold showing top-side hemisphere and bottom side plug;; (b) tilted view of exposed ȝHSR showing backside plug opening;; (c) 3.5 ȝP x 3.5 ȝP square hole viewed from the top-side;; (d) close up of the ȝHSR rim showing the 2 ȝP capacitive air gap. (a)
PROCESS CHARACTERIZATION Figure 3 provides SEM views of additional details during the fabrication process. The cross-section of the top-side hemispherical and backside plug molds shows that the isotropic SF6 etch creates a nearly hemispherical profile (Fig. 3a). The mold is observed to become reentrant near the top rim due to undercut of the oxide hard mask. Although it is not necessarily harmful, and can indeed be beneficial by lowering the resonance frequency of the shell, this can be controlled by increasing the size of the hard mask opening [10] or thinning the wafer post isotropic etch. The backside plug is pyramidal in shape, and is encompassed by the oxide support (Fig. 3b). At the neck of the plug, where the top-side polysilicon meets the EDFNVLGHRSHQLQJVDVVPDOODVȝP[ȝPKDYHEHHQ achieved (Fig. 3c). The free-standing polysilicon shell is surrounded by a uniform capacitive air gap (Fig. 3d, typically 2-3 ȝP 7KHURXJKQHVVRIWKHPROGLVREVHUYHG to be at least partially transferred to the shell. It should be noted that the sacrificial oxide layer in this case was created by thermally oxidizing a blanket polysilicon deposition before deposition of the shell polysilicon layer. Therefore, additional smoothing of the mold is possible using a thin direct thermal oxidation, or via other methods
170
(b) Figure 5: Circularity characterization of the polysilicon shell based on the fit in Figure 4b. (a) raw (red) plus sinusoidal fit (blue);; (b) corrected for possible SEM tilt. such as hydrogen annealing or a quick dip in HNA (HF, Nitric, and Acetic acid). The boron-doped electrodes are ~9 ȝPLQWKLFNQHVV For the whole angle mode, symmetry of the shell about a central axis is important to the dynamic operation of the device, since it allows the vibrational energy to transfer from one degree-of-freedom (e.g, X) to the other (e.g., Y) with the least loss or disturbance. To support the
analysis of fabricated axisymmetric shells, a software program was developed to analyze top-view SEM images, such as Figure 4a. The program proceeds by performing an edge detection algorithm on the raw SEM data, which is subsequently analyzed using a least squares fit to a circle (Fig. 4b). The least squares fit is assumed to represent the ideal circularity of the shell, and the mean radius can be determined. The deviation of the true radius from the ideal can be plotted as a function of angle about the axis (Fig. 5a). This technique is promising, but comes with some caveats. First, if the SEM view is not perfectly aligned with the axis of symmetr\ WKH VKHOO¶V SURMHFWLRQ would become slightly ellipsoidal. To correct for this, a sinusoidal fit can be made to the radial deviation, from which the tilt angle can be determined. The data can then be corrected (Fig. 5b). More accuracy in determining the tilt angle can be obtained by using lithographically- defined features in the SEM, such as the p-doped electrodes surrounding the shell. The resolution and contrast of the SEM also affect the accuracy of the result. Image analysis of the prototype ȝHSR in Figure 4a demonstrates that the final shells exhibit high symmetry and have a radial standard deviation of better than 2 ȝP for the uncorrected ~ ȝP UDGLXV VKHOO data (0.66%), and the radial deviation would be bettHU WKDQ ȝP (0.41%) if corrected for the estimated tilt angle.
EXPERIMENTAL RESULTS We have successfully excited and sensed early prototypes of the ȝHSR in vacuum by applying AC and DC electrical signals to the silicon substrate, the polysilicon shell, and the boron-doped electrodes. For a device with a polysilicon shell thickness of only 660 nm and widest diameter of ~1.2 mm, a resonance peak at 412 kHz was observed (Fig. 6). This peak displays tunability with the polarization voltage and was confirmed to be the 3-D breathing mode using COMSOL (Fig. 7). Tuning of the mode confirms that the resonance peak originates with the device. A quality factor of approximately 8,000 indicates the potential of higher Q values at lower frequency modes, e.g., elliptical modes.
CONCLUSION A self-aligned fabrication method was developed for 3-D ȝHSRs with integrated capacitive transducers and a self-aligned center post for electrical access to the shell, preserving the shell axisymmetry for robust, balanced resonators. High-Q operation of a thin polysilicon shell resonator was verified by exciting devices capacitively into a breathing resonance mode, with measured Q of 8,000 at 412kHz. This process can be further optimized to batch-fabricate ȝHRGs for portable inertial navigation.
ACKNOWLEDGMENTS This work was supported by the DARPA Microsystems Technology Office, Microscale Rate Integrating Gyroscope (MRIG) program under contract #HR0011-00-C-0032 led by Northrop Grumman. The authors would like to thank the cleanroom staff at Georgia 7HFK¶V 1Dnoelectronics Research Center for fabrication support.
171
Figure 6: Frequency response of a 1.2 mm diameter ȝHSR at a polarization voltage of 2V.
Figure 7: (left) Finite element simulation of breathing mode shape for 1.2 mm diameter ȝHSR. (right) Tuning characteristic of the 412 kHz breathing mode with polarization voltage. The mode tunes from 412.17 kHz at VP = 2 V to 412.10 kHz at VP = 8 V, a downward shift of 159.6 ppm.
REFERENCES [1] D. M. Rozelle, in Proc. 19th AAS/AIAA Space Flight Mechanics Meeting, Feb. 2009, pp. 1157±1178. [2] A. Matthews, IEEE Aerospace and Electronic Systems Magazine, vol. 7, no. 5, pp. 40-46, May 1992. [3] N. Yazdi, Proc. IEEE, vol. 86, no. 8, pp. 1640-1659, Aug. 1998. [4] A. A. Trusov, IEEE Sensors Journal, vol. 11, pp. 2763-2770, Nov. 2011. [5] E. J. Eklund, J. Microelectromech. Syst., vol. 16, pp. 232-239, Apr. 2007. [6] I. P. Prikhodko, J. Microelectromech. Syst., vol. 20, pp. 691-701, Jun. 2011. [7] D. Senkal, in Technologies for Future Micro-Nano Manufacturing, Napa, California, USA, Aug. 2011. [8] B. Sarac, J. Microelectromech. Syst., vol. 20, no. 1, pp. 28-36, Feb. 2011. [9] K. Visvanathan, in IEEE MEMS 2011, Jan. 2011, pp. 45-48. [10] K. D. Wise, J. Vac. Sci. Technol., vol. 16, p. 936, May 1979. [11] F. Ayazi, in Micro- and Nanotechnology Sensors, Systems, and Applications III, Orlando, Florida, USA, May 2011, vol. 8031, pp. 803119-13. [12] R. Abdolvand, J. Microelectromech. Syst., vol. 15, no. 3, pp. 471-478, 2006. [13] L. C. Fegely, in 75$16'8&(56¶, Jun. 2011, pp. 2295-2298.
CONTACT *L D. Sorenson, tel: +1-404-385-6691;; [email protected]
ABSTRACT We present a self-aligned fabrication method developed for three-dimensional (3-D) microscale hemispherical shell resonators with integrated capacitive transducers and a center post for electrical access to the shell. The self-aligned process preserves the axisymmetry for robust, balanced resonators that can potentially reach very high-Q due to suppressed anchor loss. High-Q operation of a thin polycrystalline silicon shell resonator is verified by exciting devices capacitively into a breathing resonance mode, with measured Q of 8,000 at 412 kHz in vacuum. This process can be further optimized to batch-fabricate micro-hemispherical resonator gyroscopes for portable inertial navigation.
INTRODUCTION The hemispherical resonator gyroscope (HRG) has shown very high performance and robustness over the years for inertial navigation. However, the existing HRG has relatively large size and very high manufacturing cost, limiting its use to demanding air- and spacecraft navigation and orientation applications [1]. An advantage of the HRG is its ability to operate in two modes: force-rebalance (or rate) and whole-angle (or rate-integrating) mode [2]. Typically, vibratory MEMS gyroscopes produce angular velocity or rate output [3]. Whole-angle mode gyroscopes using conventional planar silicon micromachining with low dissipation have recently been demonstrated [4]. Alternatively, emerging fabrication techniques have focused on producing 3-D balanced and isotropic shells for operation similar to HRG;; these techniques include wafer-scale glassblowing [5±8], and assembly and micromachining of prefabricated glass spheres [9]. Creation of hemispherical shells using isotropically-etched molds in silicon has also been explored as early as 1979, but for the purpose of creating fuel pellets for thermonuclear fusion research [10]. Although capacitive transducers situated on adjacent satellite shells have been co-fabricated for glass-blown shell resonators [6], wafer-level control over the dimension of the capacitive air gap has yet to be demonstrated. Further, no techniques have been proposed for self-aligned central support and electrical connection to a micro-hemisphere via a narrow support stem, to truly resemble a wineglass HRG microstructure. In this work, we present batch-processed micro- hemispherical shell resonators (ȝHSRs) which can potentially be a cost-effective alternative to macroscale HRGs. A novel 3-D fabrication process is developed which, in the spirit of [10], takes advantage of isotropic silicon micromachining to produce hemispherical molds, into which sacrificial and shell layers can be deposited. Boron doping is used to form electrodes surrounding the rim of the shell, which are isolated from the n-type substrate via the resulting PN junctions. The thickness of
978-1-4673-0325-5/12/$31.00 ©2012 IEEE
168
Figure 1: SEM view of a batch-fabricated polysilicon micro-hemispherical shell resonator (ȝHSR). The n-type silicon substrate was purposefully cleaved to reveal the embedded shell. P-doped electrodes formed by boron doping surround the rim of the shell, enabling actuation, sensing, and control for gyroscope application. the sacrificial layer yields a controllable and uniform gap size, while the doped electrodes follow the curvature of the shell, enhancing transducer efficiency. The ȝHSR presented here consists of a thin polysilicon hemisphere with an oxide support post, backside access plug for polarization voltage (Vp) connection, and doped capacitive electrodes (Fig. 1).
ENERGY DISSIPATION IN MICRO-HSR The macroscale HRG achieves its impressive performance due to ultra-low energy dissipation, which is demonstrated by quality factors (Q) in excess of 10 million [1]. An understanding of energy dissipation PHFKDQLVPV LV WKHUHIRUH NH\ WR UHSOLFDWLQJ WKH +5*¶V performance on the microscale, especially for the whole- angle mode where the Q directly impacts the decay time constant and must be large to sustain operation with minimal interruptions. Of the possible dissipation mechanisms enumerated in [11], the critical dissipation factors in ȝHSRs (assuming operation in high vacuum to remove air losses) are expected to be thermoelastic damping (TED), anchor loss through the support post, scattering from imperfections in the shell (surface roughness and deviation from a geometrically perfect hemisphere), and intrinsic material loss (which includes grain boundary scattering in the case of polysilicon). Of particular interest to gyroscope operation of the ȝHSR are the elliptical modes, especially the m=2 ³wineglass´ mode. Due to the nature of the hemispherical shell, in which the elliptical mode acoustic energy is concentrated around the VKHOO¶V rim far from the support, the ȝHSR can be expected to have low support loss even
MEMS 2012, Paris, FRANCE, 29 January - 2 February 2012
for finite support dimensions. Mitigating losses from the shell imperfections is done by producing an ultra-smooth mold with low imperfections and high symmetry. Polysilicon is an established MEMS material with well- known properties;; therefore, deposition of high-quality polysilicon with uniform grain size and smooth surface is easily achievable [12]. The only remaining concern when using polysilicon as the shell material is TED. To determine the expected TED losses in the ȝHSR, the coupled equations of thermoelasticity were formulated and implemented in COMSOL Multiphysics, and predicted QTED of 10.3 million was obtained for a polysilicon shell of 2 mm diameter and 500 nm thickness with an m=2 resonance frequency of 1 kHz, leading to an estimated decay time constant of almost 3400 seconds. Hence, with these positive attributes, polysilicon was selected to create the first ȝHSR prototypes.
FABRICATION PROCESS Devices are fabricated on 500-1000 ȝP (depending on desired shell diameter) low-resistivity antimony-doped n-type (100) single-crystal silicon (SCS) substrates, as shown in Figure 2. First, 2 ȝm thermal SiO2 (oxide) is patterned to mask the wafer during subsequent boron doping and annealing at 1050°C, which creates capacitive actuation and sense electrodes that are isolated from the substrate by PN junctions (Fig. 2a,b). The resonating shell, excluding the electrodes, is created by layer stacking in a micromachined silicon mold formed by two etching steps: the top hemispherical part of the mold is formed by isotropic etching, while the lower pyramidal part is anisotropically wet-etched from the backside. A 5 ȝm PECVD oxide layer is patterned to form the isotropic etch mask (Fig. 2c). Sulfur hexafluoride (SF6) plasma etches the hemispherical mold (Fig. 2d), which gives a smoother surface and better hemispherical profile than that created using xenon difluoride (XeF 2) reported in [13]. An LPCVD low-stress silicon nitride layer is patterned to mask the topside and backside during KOH etching, which forms the backside plug mold (Fig. 2e,f). This part must be thoroughly etched to reach the top mold to enable electrical access for polarization voltage. The oxide sacrificial layer, followed by the polysilicon shell layer, is conformally coated, allowing simultaneous formation of the topside shell and backside plug. While the shells are protected by photoresist, the polysilicon layer on the wafer surface is removed in a short dry etching step with SF6 plasma. The polysilicon is then doped and annealed (Fig. 2g). The shells are released in HF and dried using supercritical dryer (Fig. 2h). The oxide support is formed by etching the sacrificial layer during the HF release, which forces its outer edge to be self-aligned to the polysilicon shell. As long as the oxide support fully encloses the neck of the backside plug within its diameter, small misalignment between the top and bottom molds is tolerable. The support diameter can be controlled by the release time.
Figure 2 (color online): Fabrication process flow on n- type substrate: (a) growth and patterning of thermal oxide for (b) subsequent boron doping to form p-doped electrode regions isolated from the substrate via PN junctions;; (c) PECVD oxide is deposited and patterned to form the hard mask for (d) SF6 isotropic etching of the hemispherical mold;; (e) deposition and backside patterning of low-stress LPCVD silicon nitride for protection of the hemispherical mold during (f) KOH etching of the backside plug mold;; (g) thermal oxidation and subsequent polysilicon deposition to form the sacrificial and shell layers, respectively;; (h) release of the sacrificial oxide in HF and supercritical drying to form the final free-standing polysilicon ȝHSR structure with integrated capacitive air gap and electrodes.
169
(a) (a)
(b)
(b) Figure 4: Least squares fit to circle of (a) original ȝHSR SEM (b) overlain to show high symmetry of the shell. (c)
(d)
Figure 3: SEM views of ȝHSR components: (a) cross- section cut of silicon mold showing top-side hemisphere and bottom side plug;; (b) tilted view of exposed ȝHSR showing backside plug opening;; (c) 3.5 ȝP x 3.5 ȝP square hole viewed from the top-side;; (d) close up of the ȝHSR rim showing the 2 ȝP capacitive air gap. (a)
PROCESS CHARACTERIZATION Figure 3 provides SEM views of additional details during the fabrication process. The cross-section of the top-side hemispherical and backside plug molds shows that the isotropic SF6 etch creates a nearly hemispherical profile (Fig. 3a). The mold is observed to become reentrant near the top rim due to undercut of the oxide hard mask. Although it is not necessarily harmful, and can indeed be beneficial by lowering the resonance frequency of the shell, this can be controlled by increasing the size of the hard mask opening [10] or thinning the wafer post isotropic etch. The backside plug is pyramidal in shape, and is encompassed by the oxide support (Fig. 3b). At the neck of the plug, where the top-side polysilicon meets the EDFNVLGHRSHQLQJVDVVPDOODVȝP[ȝPKDYHEHHQ achieved (Fig. 3c). The free-standing polysilicon shell is surrounded by a uniform capacitive air gap (Fig. 3d, typically 2-3 ȝP 7KHURXJKQHVVRIWKHPROGLVREVHUYHG to be at least partially transferred to the shell. It should be noted that the sacrificial oxide layer in this case was created by thermally oxidizing a blanket polysilicon deposition before deposition of the shell polysilicon layer. Therefore, additional smoothing of the mold is possible using a thin direct thermal oxidation, or via other methods
170
(b) Figure 5: Circularity characterization of the polysilicon shell based on the fit in Figure 4b. (a) raw (red) plus sinusoidal fit (blue);; (b) corrected for possible SEM tilt. such as hydrogen annealing or a quick dip in HNA (HF, Nitric, and Acetic acid). The boron-doped electrodes are ~9 ȝPLQWKLFNQHVV For the whole angle mode, symmetry of the shell about a central axis is important to the dynamic operation of the device, since it allows the vibrational energy to transfer from one degree-of-freedom (e.g, X) to the other (e.g., Y) with the least loss or disturbance. To support the
analysis of fabricated axisymmetric shells, a software program was developed to analyze top-view SEM images, such as Figure 4a. The program proceeds by performing an edge detection algorithm on the raw SEM data, which is subsequently analyzed using a least squares fit to a circle (Fig. 4b). The least squares fit is assumed to represent the ideal circularity of the shell, and the mean radius can be determined. The deviation of the true radius from the ideal can be plotted as a function of angle about the axis (Fig. 5a). This technique is promising, but comes with some caveats. First, if the SEM view is not perfectly aligned with the axis of symmetr\ WKH VKHOO¶V SURMHFWLRQ would become slightly ellipsoidal. To correct for this, a sinusoidal fit can be made to the radial deviation, from which the tilt angle can be determined. The data can then be corrected (Fig. 5b). More accuracy in determining the tilt angle can be obtained by using lithographically- defined features in the SEM, such as the p-doped electrodes surrounding the shell. The resolution and contrast of the SEM also affect the accuracy of the result. Image analysis of the prototype ȝHSR in Figure 4a demonstrates that the final shells exhibit high symmetry and have a radial standard deviation of better than 2 ȝP for the uncorrected ~ ȝP UDGLXV VKHOO data (0.66%), and the radial deviation would be bettHU WKDQ ȝP (0.41%) if corrected for the estimated tilt angle.
EXPERIMENTAL RESULTS We have successfully excited and sensed early prototypes of the ȝHSR in vacuum by applying AC and DC electrical signals to the silicon substrate, the polysilicon shell, and the boron-doped electrodes. For a device with a polysilicon shell thickness of only 660 nm and widest diameter of ~1.2 mm, a resonance peak at 412 kHz was observed (Fig. 6). This peak displays tunability with the polarization voltage and was confirmed to be the 3-D breathing mode using COMSOL (Fig. 7). Tuning of the mode confirms that the resonance peak originates with the device. A quality factor of approximately 8,000 indicates the potential of higher Q values at lower frequency modes, e.g., elliptical modes.
CONCLUSION A self-aligned fabrication method was developed for 3-D ȝHSRs with integrated capacitive transducers and a self-aligned center post for electrical access to the shell, preserving the shell axisymmetry for robust, balanced resonators. High-Q operation of a thin polysilicon shell resonator was verified by exciting devices capacitively into a breathing resonance mode, with measured Q of 8,000 at 412kHz. This process can be further optimized to batch-fabricate ȝHRGs for portable inertial navigation.
ACKNOWLEDGMENTS This work was supported by the DARPA Microsystems Technology Office, Microscale Rate Integrating Gyroscope (MRIG) program under contract #HR0011-00-C-0032 led by Northrop Grumman. The authors would like to thank the cleanroom staff at Georgia 7HFK¶V 1Dnoelectronics Research Center for fabrication support.
171
Figure 6: Frequency response of a 1.2 mm diameter ȝHSR at a polarization voltage of 2V.
Figure 7: (left) Finite element simulation of breathing mode shape for 1.2 mm diameter ȝHSR. (right) Tuning characteristic of the 412 kHz breathing mode with polarization voltage. The mode tunes from 412.17 kHz at VP = 2 V to 412.10 kHz at VP = 8 V, a downward shift of 159.6 ppm.
REFERENCES [1] D. M. Rozelle, in Proc. 19th AAS/AIAA Space Flight Mechanics Meeting, Feb. 2009, pp. 1157±1178. [2] A. Matthews, IEEE Aerospace and Electronic Systems Magazine, vol. 7, no. 5, pp. 40-46, May 1992. [3] N. Yazdi, Proc. IEEE, vol. 86, no. 8, pp. 1640-1659, Aug. 1998. [4] A. A. Trusov, IEEE Sensors Journal, vol. 11, pp. 2763-2770, Nov. 2011. [5] E. J. Eklund, J. Microelectromech. Syst., vol. 16, pp. 232-239, Apr. 2007. [6] I. P. Prikhodko, J. Microelectromech. Syst., vol. 20, pp. 691-701, Jun. 2011. [7] D. Senkal, in Technologies for Future Micro-Nano Manufacturing, Napa, California, USA, Aug. 2011. [8] B. Sarac, J. Microelectromech. Syst., vol. 20, no. 1, pp. 28-36, Feb. 2011. [9] K. Visvanathan, in IEEE MEMS 2011, Jan. 2011, pp. 45-48. [10] K. D. Wise, J. Vac. Sci. Technol., vol. 16, p. 936, May 1979. [11] F. Ayazi, in Micro- and Nanotechnology Sensors, Systems, and Applications III, Orlando, Florida, USA, May 2011, vol. 8031, pp. 803119-13. [12] R. Abdolvand, J. Microelectromech. Syst., vol. 15, no. 3, pp. 471-478, 2006. [13] L. C. Fegely, in 75$16'8&(56¶, Jun. 2011, pp. 2295-2298.
CONTACT *L D. Sorenson, tel: +1-404-385-6691;; [email protected]
