- Email: [email protected]
Capacitive type surface-micromachined silicon accelerometer with stiffness tuning capability
Sensors and Actuators 73 Ž1999. 109–116
Capacitive type surface-micromachined silicon accelerometer with stiffness tuning capability Kyu-Yeon Park b
a,)
, Chong-Won Lee b, Hyun-Suk Jang a , Yongsoo Oh c , Byeoungju Ha
c
a R & D Center, Samsung Electro-Mechanics, 314, Maetan-dong, Paldal-ku, Suwon, South Korea Center for Noise and Vibration Control, Department of Mechanical Engineering, KAIST, South Korea c Microsystems Lab., Samsung AdÕanced Institute of Technology, South Korea
Received 13 April 1998; accepted 7 October 1998
Abstract A surface-micromachined silicon accelerometer with a novel concept, which has a stiffness tuning capability to improve the sensor resolution, is developed. Imposing an electrostatic force to the electrodes reduces the stiffness of the sensor structure. By adopting the stiffness tuning, the initially stiff structure guarantees the stability of fabrication, and the reduced stiffness, only along the sensing direction, produces the improved resolution. One of the major improvements in the developed accelerometer is the branched comb-finger type electrode which senses the relative position between the mass and the electrode. Maintaining the same capacitance variation, such electrodes allow a larger initial gap between the mass and the electrode, so that the clash problem can be easily eliminated. The accelerometer was successfully fabricated with the active size of 650 = 530 mm2 , the 7-mm thick polysilicon structure, and a proof mass of about 1 mg. Experimental results show that the equivalent noise level of the accelerometer is improved by 30 dB through the stiffness tuning. The accelerometer has the bandwidth of 350 Hz, linearity of 0.3% FS, and sensing range of 50 g. q 1999 Elsevier Science S.A. All rights reserved. Keywords: Surface-micromachined; Silicon accelerometer; Stiffness tuning capability
1. Introduction Since the resolution of an accelerometer with a given seismic mass is proportional to the square of the natural frequency or, equivalently, the stiffness of the sensor structure along the sensing direction, the natural frequency must be lowered to improve the resolution, requiring the use of a bigger mass and longer beam springs for the sensor structure w1x. However, the compliance of the accelerometer structure tends to cause the sticking problem between sensor elements in the surface micromachining process w2x and increases the undesired-cross sensitivity. The sticking occurring in the wet etching process is known to be crucial to the yield of surface-micromachined accelerometers. In this paper, in order to lower the natural frequency along the sensing axis w3x, the stiffness of the
)
Corresponding author. Tel.: q82-331-280-8276; Fax: q82-331-2806955; E-mail: [email protected]
sensor structure is reduced by providing the electrostatic force only along the sensing direction. The strength of the original sensor structure is kept high enough to overcome the surface-tension between the structure and substrate or the interdigitated structures, so that the stability of the surface micromachining process is ensured. While a tuned accelerometer with a low natural frequency has an improved resolution, the sensing frequency range and the dynamic range can also be enhanced by using an electrostatic force-balancing technique w4,5x. The idea of electrostatic negative stiffness has already been successfully implemented in the vibratory microgyroscope so that the natural frequency along the sensing direction is properly tuned w6x. In this paper, the capacitive accelerometers were fabricated on silicon wafers. The fabrication process includes the realization of a free-standing seismic mass and beam springs by means of RIE and a sacrificial PSG wet etching. Compared with the accelerometer without stiffness tuning, the resolution of the tuned accelerometer was improved by
0924-4247r99r$ - see front matter q 1999 Elsevier Science S.A. All rights reserved. PII: S 0 9 2 4 - 4 2 4 7 Ž 9 8 . 0 0 2 6 2 - 3
K.-Y. Park et al.r Sensors and Actuators 73 (1999) 109–116
110
to the sensor natural frequency, and z s crŽ 2 Ž mk .1r2 . is the damping ratio. Where the frequency range of the accelerometer is far below the natural frequency, i.e., v < vn , Eq. Ž2. reduces to: HŽ v . (y
Fig. 1. Dynamic model of accelerometer.
30 dB, showing a good electrodynamic stability in the fabrication process and operating states.
1
vn2
.
Ž 3.
Fig. 2 shows the electrostatic force balancing loop w4,5x which is used to improve the bandwidth, linearity and dynamic range. The white noise NeŽ v . simulates the major sensing noise present in the capacitance-to-voltage converter. The resolution between the input acceleration, AŽ v ., and the output voltage, VaŽ v ., can be written as: DV mG
Va Ž v . s
2. Design of accelerometer 2.1. Dynamic consideration
DC D Fe mqHŽ v . G Ž jv K d q K p . D x DC DVe DC DV
DC The typical dynamic model of an accelerometer is shown in Fig. 1. The equation of motion for the accelerometer can be written as: mx¨ Ž t . q cx˙ Ž t . q kx Ž t . s yma Ž t . , x Ž t . s y Ž t . y z Ž t . , a Ž t . s z¨ Ž t . ,
Ž 1.
where m is the seismic mass, c is the damping coefficient, k is the spring constant, z Ž t . is the displacement of the base, y Ž t . is the absolute displacement of the seismic mass, and x Ž t . is the relative displacement between the seismic mass and the base. The frequency response function between aŽ t . and x Ž t . can be written as: HŽ v. s
XŽ v.
1 sy
AŽ v .
1
vn2 1 y r 2 q j2 z r
,
Ž 2.
= HŽ v.
Dx
A Ž v . q Ne Ž v .
Ž 4.
where G is the amplifier gain, Fe and Ve are the force and voltage from the force-balancing, respectively, and K d and K p are the derivative and proportional feedback gains, respectively. From Eqs. Ž3. and Ž4., the equivalent noise level, A r Ž v ., can be defined as: Ar Ž v . '
Ne Ž v . Ne Ž v . ( vn2 . DC DC HŽ v. Dx Dx
Ž 5.
Finally, we can clearly find that the accelerometer with more compliant structure has more accurate resolution if it uses same displacement sensing element.
where 2.2. Design of structure xŽ t. sX Ž v . e
jv 1
, z Ž t . s ZŽ v . e
jv 1
,
2
A Ž v . s yv Z Ž v . . Here, vn s Ž krm.1r2 is the natural frequency, r s vrvn is the frequency ratio of the acceleration frequency
A schematic of the accelerometer is shown in Fig. 3. The accelerometer consists of a planar proof mass with branched comb-fingers, differential capacitive type electrodes to sense the relative displacement between the
Fig. 2. Force-balancing loop.
K.-Y. Park et al.r Sensors and Actuators 73 (1999) 109–116
111
Fig. 3. Schematics of accelerometer.
seismic mass and the electrodes themselves, tuning electrodes to reduce the stiffness of the structure by generating electrostatic force, and four folded type beam springs. The black squares are the anchors that fix the sensor structure to the substrate.
Each dimension and shape was carefully designed to account for fabrication and operation. The area of the sensor structure was limited to within 1 = 1 mm2 due to the production cost and reliability, while the thickness of the polysilicon structure was limited to within 10 mm for
Fig. 4. Electrodes for position-sensing. Ža. Straight comb-finger type. Žb. Branched comb-finger type.
K.-Y. Park et al.r Sensors and Actuators 73 (1999) 109–116
112
the stability in the fabrication process and the structural stability such as the damage of a crystal tube of LPCVD process and the residual stress. 2.3. Sensing of relatiÕe displacement Various types of the electrodes were considered to sense the gap between the seismic mass and the electrode itself. The capacitive type was selected because of the fair accuracy, good frequency characteristics and simplicity in the fabrication process. The comb-finger type of capacitive sensing element that is commonly used in surface-micromachined accelerometers, is shown in Fig. 4a, where the variations of the capacitances C1 and C2 are reversed in sign. The performance of the differential capacitive sensing type electrode can be improved by reducing the gap between the seismic mass and electrode, and by increasing the sensing area. On the other hand, in this electrode, the electrostatic stability deteriorates with better sensitivity especially in the accelerometer with a high resolution. The probability of clash between mass and electrode increases because of its low stiffness. In this work, in order to overcome such clash problem, branched comb-fingers were introduced, as shown in Fig. 4b and Fig. 5. The gap along the sensing direction d bo of a branched comb-finger can be larger than that of a straight comb-finger, while maintaining the capacitance variation and occupied wafer area unchanged. The sticking problem can then be resolved with lager gap. The gap g c along the perpendicular axis to the sensing direction can be made much smaller than d bo , because the stiffness of folded spring along the perpendicular axis to the sensing direction is much higher than that of the sensing direction. Actually, the minimum gap g c is limited normally by the performance of dry etching.
Fig. 6. Electrodes for stiffness tuning. Ža. Straight-finger type. Žb. Branched-finger type.
On the other hand, the complexity in the shape of the branched comb-finger necessitates the calculation of the capacitance variation with the gap varied, obtained by a field emission microscopy ŽFEM. electric field simulation package. In order to design an accurate accelerometer, the shape of the electrode should be determined such that the value DCrD x is maximized for the fabrication and size given. 2.4. Stiffness tuning To improve the resolution of accelerometer, electrostatic negative stiffness was introduced so that the natural frequency of the sensor structure along the sensing axis is lowered w3x. The stiffness of the original sensor structure was kept high enough to guarantee the stability of the surface micromachining process. The potential energy U stored in a capacitor is: 1 U s CtVt 2 , Ž 6. 2 where Ct is the capacitance and Vt is the applied voltage to the capacitor. The effective electrostatic stiffness k n is then calculated as: 1 2 E2 s y V C. Ž 7. 2 t E x2 t E x2 Note that, the effective electrostatic stiffness is normally negative w2,6x. For the widely adopted electrodes with straight fingers shown in Fig. 6a, the negative stiffness kXn can be written as: kn s y
kXn s y Fig. 5. Branched comb-finger type electrode for position-sensing.
E 2U
2 ´ A tVt 2 g t3
,
Ž 8.
K.-Y. Park et al.r Sensors and Actuators 73 (1999) 109–116
113
Fig. 7. The FEM modal analysis Žby ANSYS.. Ža. First mode Ž5.2 kHz.. Žb. Second mode Ž15.6 kHz.. Žc. Third mode Ž23.8 kHz..
where ´ is the permittivity of air, A t is the facing area of a pair of electrodes and g t is the gap between the electrodes. As discussed previously, since a narrow gap may cause a clash problem with straight finger type electrodes, the branched finger in Fig. 6b was introduced. On the other hand, the complexity in the shape of the branched finger necessitates the calculation of the optimal negative stiffness by a FEM electric field simulation package. The shape optimization was achieved such that the tension is small enough not to cause the clash problem and the negative stiffness is large enough to effectively tune the natural frequency. The natural frequency of the tuned accelerometer f n can be written as: fn s
(
km q kn m
as the structural stiffness, implying the tuned natural frequency ranges from zero to the initial natural frequency. 2.5. Design of suspension In a one-axis accelerometer, the suspension must have only one directional flexibility, no residual stress under the clamping situation and a low structural stress coupling in compression and bending. To meet these requirements, a folded beam spring was adopted for suspension. The FEM modal analysis as shown in Fig. 7 suggested the final dimensions of the beam spring. 3. Fabrication
,
Ž 9.
where k m is the structural stiffness. The FEM field analysis gives that the negative stiffness is about 1 Nrm for the designed electrodes when the tuning voltage is 10 V. For the seismic mass of 1 mg and the initial natural frequency of 5 kHz, the negative stiffness becomes almost the same
The microstructure of the accelerometer was fabricated with five mask processes. A significant advantage of this technology is that the critical features are defined with one mask, eliminating errors due to mask-to-mask misalignment. The critical features of the accelerometer are the widths of the springs, the shape of the branched comb-
Fig. 8. Cross-sectional view of accelerometer.
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K.-Y. Park et al.r Sensors and Actuators 73 (1999) 109–116
Fig. 11. Frequency response. Fig. 9. The scanning electron microscopy ŽSEM. photography of accelerometer.
fingers and the tuning electrodes. They determine the natural frequency of the sensing mode, the sensitivity, and the tuning performance. The cross-sectional view of the accelerometer is shown in Fig. 8. The fabricated accelerometer shown in Fig. 9 has the active size of 650 = 530 mm2 , the 7-mm thick polysilicon structure, and the seismic mass of 1 mg. Silicon wafer is used for the substrate; phosphor silicate glass for the sacrificial layer; silicon nitride and silicon oxide for the insulator; thin polysilicon film for the electric interconnection; aluminum for the wire bonding pad and the thick polysilicon for the active structure and the electrodes.
4. Characterization 4.1. Force-balanced capacitiÕe sensing Fig. 10 shows the schematic diagram of the circuit for the accelerometer which consists of an oscillator, charge
amplifiers, a demodulator, a stiffness tuner, and a forcebalancing feedback block. The moving seismic mass is driven by the oscillatorŽ1 Vp – p , 50 kHz carrier.. A charge signal proportional to the relative displacement between the mass and the electrodes is induced on the positionsensing electrodes w7x. The charge signal is differential amplified after the gain balancing. The gain balancing is essential because the two facing electrodes may not be identical, due to the difference in the initial gaps and the gains of the charge amplifiers. The differential amplified signal is rectified and low pass filtered to yield a low frequency acceleration signal. The amplified acceleration signal is fed back to the seismic mass to improve the linearity and the dynamic range. The bandwidth of the accelerometer is determined by the low pass filter frequency of the demodulator and the feedback gain. 4.2. Calibration The measured force-balanced frequency response of the accelerometer is shown in Fig. 11. The sensitivity and bandwidth Žy3 dB. of the accelerometer are found to be
Fig. 10. Schematics of force-balanced capacitive sensing.
K.-Y. Park et al.r Sensors and Actuators 73 (1999) 109–116
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cated, and calibrated. It was found that the resolution of the accelerometer was improved by 30 dB trough the stiffness tuning, while the clash problem was removed by introducing a new type of electrodes.
Acknowledgements
Fig. 12. Accelerometer output to a 100-Hz 1 g p–p sinusoidal acceleration Žwithout stiffness tuning..
The authors would like to thank the members of Microsystems Lab. of Samsung-AIT for their dedication in the fabrication and testing and the R & D center of Samsung Electro-Mechanics for providing the SEM facility. They also greatly acknowledge the help of the ISCR of Seoul National University in the Si-processes.
References
Fig. 13. Accelerometer output to a-100 Hz 1 g p–p sinusoidal acceleration Žwith stiffness tuning..
39 mVrg and 370 Hz, respectively. The frequency response of the tuned accelerometer remained almost the same as that without tuning, by properly adjusting the electrostatic feedback gain. The measured nonlinearity of the accelerometer was 0.3% FS with the maximum range of 50 g, indicating that the highly linear characteristics can be achieved by the electrostatic force-balancing. The effect of stiffness tuning is clearly shown in Figs. 12 and 13. Through the stiffness tuning, the equivalent noise level of the accelerometer was improved by 30 dB, and a good electrodynamic stability was maintained in the fabrication process and the operating states. The untuned and tuned natural frequencies of the accelerometer were 5.12 kHz and 950 Hz, respectively.
5. Conclusion A capacitive force-balanced accelerometer with a stiffness tuning capability was successfully designed, fabri-
w1x K.Y. Park, C.W. Lee, H.S. Jang, Y.S. Oh, B.J. Ha, Capacitive sensing type surface-micromachined silicon accelerometer with a stiffness tuning capability, Digest of IEEErASME MEMS Workshop, Heidelberg, Germany Ž1998. pp. 637–642. w2x C. Liu, A high-yield drying process for surface microstructures using active levitation, Digest of 1997 International Conference on Solidstate Sensors and Actuators ŽTransducer ’97., Chicago, USA Ž1997. pp. 241–244. w3x S.G. Adams, F. Bertsch et al., Capacitance-based tunable micromechanical resonators, Digest of 1995 International Conference on Solid-state Sensors and Actuators ŽTransducer ’95., Stockholm, Sweden Ž1995. pp. 438–441. w4x K.H.L. Chau, S.R. Lewis, Y. Zhao, R.T. Howe, S.F. Bart, R.G. Marcheselli, An integrated force-balanced capacitive accelerometer for low-g application, Sensors and Actuators A ŽPhysical. Ž1995. 472–476. w5x L. Zimmermann, J.Ph. Ebersohl, F. Le Hung, J.P. Berry, F. Baillieu, P. Rey, B. Diem, S. Renard, P. Caillat, Airbag application: a microsystem including a silicon capacitive accelerometer, CMOS switched capacitor electronics and true self-test capability, Sensors and Actuators A ŽPhysical. Ž1995. 190–195. w6x K.Y. Park, C.W. Lee, Y.S. Oh, Y.H. Cho, Laterally oscillated and force-balanced micro vibratory gyroscope supported by fish hook shape springs, Sensors and Actuators A ŽPhysical. 64 Ž1998. 69–76. w7x B.E. Boser, Electronics for micromachined inertial sensors, Digest of 1997 International Conference on Solid-state Sensors and Actuators ŽTransducer ’97., Chicago, USA Ž1997. pp. 1169–1172.
Kyu-Yeon Park received his BSME from Korea University in 1988 and MSME from Korea Advanced Institute of Science and Technology ŽKAIST. in 1990. He has worked for Samsung Electro-Mechanics since 1988. In 1994, he joined the Center for Noise and Vibration Control ŽNo ViC., KAIST as the PhD candidate. At KAIST, he developed piezoelectric accelerometer, piezoelectric singlermultiple-axis force transducer, square-beam shape piezoelectric vibratory gyro, surface-micromachined accelerometer and vibratory gyro. In 1998, he returned to his company and has developed microdevices for vehicles and household electric appliances. His interests are in the vibration analysis and the design of micromachined structures.
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Chong-Won Lee received the BS and MS degrees in mechanical engineering from Seoul National University, Korea, in 1970 and 1972, respectively, the MS degree in applied mechanics from Yale University in 1975, and the PhD in mechanical engineering from University of California, Berkeley, in 1980. Since then, he has been a member of the faculty of the mechanical engineering department, KAIST, Korea. His main interests are in the areas of the analytical and experimental modal analysis of, in particular, rotating machinery; the active control of vibration and motion using magnetic bearings, controllable fluids and piezoelectric actuators; the parameter identification and diagnosis of rotating machines. He is a member of ASME, SEM, SAE, IIAV, KSME, KSAS and KSAE, vice president of KSNVE, and the author of the book, Vibration Analysis of Rotors, Kluwer Academic Publishers, 1993. Hyun-Suk Jang received his BSME from Hanyang University in 1995 and MSME from Korea Advanced Institute of Science and Technology ŽKAIST. in 1997. He has worked for Samsung Electro-Mechanics since 1997. His interests are in the vibration analysis and the design of ink jet printer head.
Yongsoo Oh received his MS degree and doctoral Engineering degree from Hanyang University, Korea, in 1983 and Nagaoka University of Technology, Japan, in 1993, respectively. From 1986 to 1990, he worked at central research center, Chichibu cement, in Japan. Since 1994, he has been working for Samsung Advanced Institute of Technology in Korea. He is currently engaged in the research and development of microsensors.
Byeoungju Ha received his MS degree from the Seoul City University in 1993. He studied silicon pressure sensor at the Korea Institute of Science and Technology in 1991–1993. He has been working at Samsung Advanced Institute of Technology in Korea since 1993. In 1996, he researched inertial sensors as a Visiting Scholar at the University of Michigan in USA. He is currently engaged in the research and the development of microsensors.
Capacitive type surface-micromachined silicon accelerometer with stiffness tuning capability Kyu-Yeon Park b
a,)
, Chong-Won Lee b, Hyun-Suk Jang a , Yongsoo Oh c , Byeoungju Ha
c
a R & D Center, Samsung Electro-Mechanics, 314, Maetan-dong, Paldal-ku, Suwon, South Korea Center for Noise and Vibration Control, Department of Mechanical Engineering, KAIST, South Korea c Microsystems Lab., Samsung AdÕanced Institute of Technology, South Korea
Received 13 April 1998; accepted 7 October 1998
Abstract A surface-micromachined silicon accelerometer with a novel concept, which has a stiffness tuning capability to improve the sensor resolution, is developed. Imposing an electrostatic force to the electrodes reduces the stiffness of the sensor structure. By adopting the stiffness tuning, the initially stiff structure guarantees the stability of fabrication, and the reduced stiffness, only along the sensing direction, produces the improved resolution. One of the major improvements in the developed accelerometer is the branched comb-finger type electrode which senses the relative position between the mass and the electrode. Maintaining the same capacitance variation, such electrodes allow a larger initial gap between the mass and the electrode, so that the clash problem can be easily eliminated. The accelerometer was successfully fabricated with the active size of 650 = 530 mm2 , the 7-mm thick polysilicon structure, and a proof mass of about 1 mg. Experimental results show that the equivalent noise level of the accelerometer is improved by 30 dB through the stiffness tuning. The accelerometer has the bandwidth of 350 Hz, linearity of 0.3% FS, and sensing range of 50 g. q 1999 Elsevier Science S.A. All rights reserved. Keywords: Surface-micromachined; Silicon accelerometer; Stiffness tuning capability
1. Introduction Since the resolution of an accelerometer with a given seismic mass is proportional to the square of the natural frequency or, equivalently, the stiffness of the sensor structure along the sensing direction, the natural frequency must be lowered to improve the resolution, requiring the use of a bigger mass and longer beam springs for the sensor structure w1x. However, the compliance of the accelerometer structure tends to cause the sticking problem between sensor elements in the surface micromachining process w2x and increases the undesired-cross sensitivity. The sticking occurring in the wet etching process is known to be crucial to the yield of surface-micromachined accelerometers. In this paper, in order to lower the natural frequency along the sensing axis w3x, the stiffness of the
)
Corresponding author. Tel.: q82-331-280-8276; Fax: q82-331-2806955; E-mail: [email protected]
sensor structure is reduced by providing the electrostatic force only along the sensing direction. The strength of the original sensor structure is kept high enough to overcome the surface-tension between the structure and substrate or the interdigitated structures, so that the stability of the surface micromachining process is ensured. While a tuned accelerometer with a low natural frequency has an improved resolution, the sensing frequency range and the dynamic range can also be enhanced by using an electrostatic force-balancing technique w4,5x. The idea of electrostatic negative stiffness has already been successfully implemented in the vibratory microgyroscope so that the natural frequency along the sensing direction is properly tuned w6x. In this paper, the capacitive accelerometers were fabricated on silicon wafers. The fabrication process includes the realization of a free-standing seismic mass and beam springs by means of RIE and a sacrificial PSG wet etching. Compared with the accelerometer without stiffness tuning, the resolution of the tuned accelerometer was improved by
0924-4247r99r$ - see front matter q 1999 Elsevier Science S.A. All rights reserved. PII: S 0 9 2 4 - 4 2 4 7 Ž 9 8 . 0 0 2 6 2 - 3
K.-Y. Park et al.r Sensors and Actuators 73 (1999) 109–116
110
to the sensor natural frequency, and z s crŽ 2 Ž mk .1r2 . is the damping ratio. Where the frequency range of the accelerometer is far below the natural frequency, i.e., v < vn , Eq. Ž2. reduces to: HŽ v . (y
Fig. 1. Dynamic model of accelerometer.
30 dB, showing a good electrodynamic stability in the fabrication process and operating states.
1
vn2
.
Ž 3.
Fig. 2 shows the electrostatic force balancing loop w4,5x which is used to improve the bandwidth, linearity and dynamic range. The white noise NeŽ v . simulates the major sensing noise present in the capacitance-to-voltage converter. The resolution between the input acceleration, AŽ v ., and the output voltage, VaŽ v ., can be written as: DV mG
Va Ž v . s
2. Design of accelerometer 2.1. Dynamic consideration
DC D Fe mqHŽ v . G Ž jv K d q K p . D x DC DVe DC DV
DC The typical dynamic model of an accelerometer is shown in Fig. 1. The equation of motion for the accelerometer can be written as: mx¨ Ž t . q cx˙ Ž t . q kx Ž t . s yma Ž t . , x Ž t . s y Ž t . y z Ž t . , a Ž t . s z¨ Ž t . ,
Ž 1.
where m is the seismic mass, c is the damping coefficient, k is the spring constant, z Ž t . is the displacement of the base, y Ž t . is the absolute displacement of the seismic mass, and x Ž t . is the relative displacement between the seismic mass and the base. The frequency response function between aŽ t . and x Ž t . can be written as: HŽ v. s
XŽ v.
1 sy
AŽ v .
1
vn2 1 y r 2 q j2 z r
,
Ž 2.
= HŽ v.
Dx
A Ž v . q Ne Ž v .
Ž 4.
where G is the amplifier gain, Fe and Ve are the force and voltage from the force-balancing, respectively, and K d and K p are the derivative and proportional feedback gains, respectively. From Eqs. Ž3. and Ž4., the equivalent noise level, A r Ž v ., can be defined as: Ar Ž v . '
Ne Ž v . Ne Ž v . ( vn2 . DC DC HŽ v. Dx Dx
Ž 5.
Finally, we can clearly find that the accelerometer with more compliant structure has more accurate resolution if it uses same displacement sensing element.
where 2.2. Design of structure xŽ t. sX Ž v . e
jv 1
, z Ž t . s ZŽ v . e
jv 1
,
2
A Ž v . s yv Z Ž v . . Here, vn s Ž krm.1r2 is the natural frequency, r s vrvn is the frequency ratio of the acceleration frequency
A schematic of the accelerometer is shown in Fig. 3. The accelerometer consists of a planar proof mass with branched comb-fingers, differential capacitive type electrodes to sense the relative displacement between the
Fig. 2. Force-balancing loop.
K.-Y. Park et al.r Sensors and Actuators 73 (1999) 109–116
111
Fig. 3. Schematics of accelerometer.
seismic mass and the electrodes themselves, tuning electrodes to reduce the stiffness of the structure by generating electrostatic force, and four folded type beam springs. The black squares are the anchors that fix the sensor structure to the substrate.
Each dimension and shape was carefully designed to account for fabrication and operation. The area of the sensor structure was limited to within 1 = 1 mm2 due to the production cost and reliability, while the thickness of the polysilicon structure was limited to within 10 mm for
Fig. 4. Electrodes for position-sensing. Ža. Straight comb-finger type. Žb. Branched comb-finger type.
K.-Y. Park et al.r Sensors and Actuators 73 (1999) 109–116
112
the stability in the fabrication process and the structural stability such as the damage of a crystal tube of LPCVD process and the residual stress. 2.3. Sensing of relatiÕe displacement Various types of the electrodes were considered to sense the gap between the seismic mass and the electrode itself. The capacitive type was selected because of the fair accuracy, good frequency characteristics and simplicity in the fabrication process. The comb-finger type of capacitive sensing element that is commonly used in surface-micromachined accelerometers, is shown in Fig. 4a, where the variations of the capacitances C1 and C2 are reversed in sign. The performance of the differential capacitive sensing type electrode can be improved by reducing the gap between the seismic mass and electrode, and by increasing the sensing area. On the other hand, in this electrode, the electrostatic stability deteriorates with better sensitivity especially in the accelerometer with a high resolution. The probability of clash between mass and electrode increases because of its low stiffness. In this work, in order to overcome such clash problem, branched comb-fingers were introduced, as shown in Fig. 4b and Fig. 5. The gap along the sensing direction d bo of a branched comb-finger can be larger than that of a straight comb-finger, while maintaining the capacitance variation and occupied wafer area unchanged. The sticking problem can then be resolved with lager gap. The gap g c along the perpendicular axis to the sensing direction can be made much smaller than d bo , because the stiffness of folded spring along the perpendicular axis to the sensing direction is much higher than that of the sensing direction. Actually, the minimum gap g c is limited normally by the performance of dry etching.
Fig. 6. Electrodes for stiffness tuning. Ža. Straight-finger type. Žb. Branched-finger type.
On the other hand, the complexity in the shape of the branched comb-finger necessitates the calculation of the capacitance variation with the gap varied, obtained by a field emission microscopy ŽFEM. electric field simulation package. In order to design an accurate accelerometer, the shape of the electrode should be determined such that the value DCrD x is maximized for the fabrication and size given. 2.4. Stiffness tuning To improve the resolution of accelerometer, electrostatic negative stiffness was introduced so that the natural frequency of the sensor structure along the sensing axis is lowered w3x. The stiffness of the original sensor structure was kept high enough to guarantee the stability of the surface micromachining process. The potential energy U stored in a capacitor is: 1 U s CtVt 2 , Ž 6. 2 where Ct is the capacitance and Vt is the applied voltage to the capacitor. The effective electrostatic stiffness k n is then calculated as: 1 2 E2 s y V C. Ž 7. 2 t E x2 t E x2 Note that, the effective electrostatic stiffness is normally negative w2,6x. For the widely adopted electrodes with straight fingers shown in Fig. 6a, the negative stiffness kXn can be written as: kn s y
kXn s y Fig. 5. Branched comb-finger type electrode for position-sensing.
E 2U
2 ´ A tVt 2 g t3
,
Ž 8.
K.-Y. Park et al.r Sensors and Actuators 73 (1999) 109–116
113
Fig. 7. The FEM modal analysis Žby ANSYS.. Ža. First mode Ž5.2 kHz.. Žb. Second mode Ž15.6 kHz.. Žc. Third mode Ž23.8 kHz..
where ´ is the permittivity of air, A t is the facing area of a pair of electrodes and g t is the gap between the electrodes. As discussed previously, since a narrow gap may cause a clash problem with straight finger type electrodes, the branched finger in Fig. 6b was introduced. On the other hand, the complexity in the shape of the branched finger necessitates the calculation of the optimal negative stiffness by a FEM electric field simulation package. The shape optimization was achieved such that the tension is small enough not to cause the clash problem and the negative stiffness is large enough to effectively tune the natural frequency. The natural frequency of the tuned accelerometer f n can be written as: fn s
(
km q kn m
as the structural stiffness, implying the tuned natural frequency ranges from zero to the initial natural frequency. 2.5. Design of suspension In a one-axis accelerometer, the suspension must have only one directional flexibility, no residual stress under the clamping situation and a low structural stress coupling in compression and bending. To meet these requirements, a folded beam spring was adopted for suspension. The FEM modal analysis as shown in Fig. 7 suggested the final dimensions of the beam spring. 3. Fabrication
,
Ž 9.
where k m is the structural stiffness. The FEM field analysis gives that the negative stiffness is about 1 Nrm for the designed electrodes when the tuning voltage is 10 V. For the seismic mass of 1 mg and the initial natural frequency of 5 kHz, the negative stiffness becomes almost the same
The microstructure of the accelerometer was fabricated with five mask processes. A significant advantage of this technology is that the critical features are defined with one mask, eliminating errors due to mask-to-mask misalignment. The critical features of the accelerometer are the widths of the springs, the shape of the branched comb-
Fig. 8. Cross-sectional view of accelerometer.
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Fig. 11. Frequency response. Fig. 9. The scanning electron microscopy ŽSEM. photography of accelerometer.
fingers and the tuning electrodes. They determine the natural frequency of the sensing mode, the sensitivity, and the tuning performance. The cross-sectional view of the accelerometer is shown in Fig. 8. The fabricated accelerometer shown in Fig. 9 has the active size of 650 = 530 mm2 , the 7-mm thick polysilicon structure, and the seismic mass of 1 mg. Silicon wafer is used for the substrate; phosphor silicate glass for the sacrificial layer; silicon nitride and silicon oxide for the insulator; thin polysilicon film for the electric interconnection; aluminum for the wire bonding pad and the thick polysilicon for the active structure and the electrodes.
4. Characterization 4.1. Force-balanced capacitiÕe sensing Fig. 10 shows the schematic diagram of the circuit for the accelerometer which consists of an oscillator, charge
amplifiers, a demodulator, a stiffness tuner, and a forcebalancing feedback block. The moving seismic mass is driven by the oscillatorŽ1 Vp – p , 50 kHz carrier.. A charge signal proportional to the relative displacement between the mass and the electrodes is induced on the positionsensing electrodes w7x. The charge signal is differential amplified after the gain balancing. The gain balancing is essential because the two facing electrodes may not be identical, due to the difference in the initial gaps and the gains of the charge amplifiers. The differential amplified signal is rectified and low pass filtered to yield a low frequency acceleration signal. The amplified acceleration signal is fed back to the seismic mass to improve the linearity and the dynamic range. The bandwidth of the accelerometer is determined by the low pass filter frequency of the demodulator and the feedback gain. 4.2. Calibration The measured force-balanced frequency response of the accelerometer is shown in Fig. 11. The sensitivity and bandwidth Žy3 dB. of the accelerometer are found to be
Fig. 10. Schematics of force-balanced capacitive sensing.
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cated, and calibrated. It was found that the resolution of the accelerometer was improved by 30 dB trough the stiffness tuning, while the clash problem was removed by introducing a new type of electrodes.
Acknowledgements
Fig. 12. Accelerometer output to a 100-Hz 1 g p–p sinusoidal acceleration Žwithout stiffness tuning..
The authors would like to thank the members of Microsystems Lab. of Samsung-AIT for their dedication in the fabrication and testing and the R & D center of Samsung Electro-Mechanics for providing the SEM facility. They also greatly acknowledge the help of the ISCR of Seoul National University in the Si-processes.
References
Fig. 13. Accelerometer output to a-100 Hz 1 g p–p sinusoidal acceleration Žwith stiffness tuning..
39 mVrg and 370 Hz, respectively. The frequency response of the tuned accelerometer remained almost the same as that without tuning, by properly adjusting the electrostatic feedback gain. The measured nonlinearity of the accelerometer was 0.3% FS with the maximum range of 50 g, indicating that the highly linear characteristics can be achieved by the electrostatic force-balancing. The effect of stiffness tuning is clearly shown in Figs. 12 and 13. Through the stiffness tuning, the equivalent noise level of the accelerometer was improved by 30 dB, and a good electrodynamic stability was maintained in the fabrication process and the operating states. The untuned and tuned natural frequencies of the accelerometer were 5.12 kHz and 950 Hz, respectively.
5. Conclusion A capacitive force-balanced accelerometer with a stiffness tuning capability was successfully designed, fabri-
w1x K.Y. Park, C.W. Lee, H.S. Jang, Y.S. Oh, B.J. Ha, Capacitive sensing type surface-micromachined silicon accelerometer with a stiffness tuning capability, Digest of IEEErASME MEMS Workshop, Heidelberg, Germany Ž1998. pp. 637–642. w2x C. Liu, A high-yield drying process for surface microstructures using active levitation, Digest of 1997 International Conference on Solidstate Sensors and Actuators ŽTransducer ’97., Chicago, USA Ž1997. pp. 241–244. w3x S.G. Adams, F. Bertsch et al., Capacitance-based tunable micromechanical resonators, Digest of 1995 International Conference on Solid-state Sensors and Actuators ŽTransducer ’95., Stockholm, Sweden Ž1995. pp. 438–441. w4x K.H.L. Chau, S.R. Lewis, Y. Zhao, R.T. Howe, S.F. Bart, R.G. Marcheselli, An integrated force-balanced capacitive accelerometer for low-g application, Sensors and Actuators A ŽPhysical. Ž1995. 472–476. w5x L. Zimmermann, J.Ph. Ebersohl, F. Le Hung, J.P. Berry, F. Baillieu, P. Rey, B. Diem, S. Renard, P. Caillat, Airbag application: a microsystem including a silicon capacitive accelerometer, CMOS switched capacitor electronics and true self-test capability, Sensors and Actuators A ŽPhysical. Ž1995. 190–195. w6x K.Y. Park, C.W. Lee, Y.S. Oh, Y.H. Cho, Laterally oscillated and force-balanced micro vibratory gyroscope supported by fish hook shape springs, Sensors and Actuators A ŽPhysical. 64 Ž1998. 69–76. w7x B.E. Boser, Electronics for micromachined inertial sensors, Digest of 1997 International Conference on Solid-state Sensors and Actuators ŽTransducer ’97., Chicago, USA Ž1997. pp. 1169–1172.
Kyu-Yeon Park received his BSME from Korea University in 1988 and MSME from Korea Advanced Institute of Science and Technology ŽKAIST. in 1990. He has worked for Samsung Electro-Mechanics since 1988. In 1994, he joined the Center for Noise and Vibration Control ŽNo ViC., KAIST as the PhD candidate. At KAIST, he developed piezoelectric accelerometer, piezoelectric singlermultiple-axis force transducer, square-beam shape piezoelectric vibratory gyro, surface-micromachined accelerometer and vibratory gyro. In 1998, he returned to his company and has developed microdevices for vehicles and household electric appliances. His interests are in the vibration analysis and the design of micromachined structures.
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Chong-Won Lee received the BS and MS degrees in mechanical engineering from Seoul National University, Korea, in 1970 and 1972, respectively, the MS degree in applied mechanics from Yale University in 1975, and the PhD in mechanical engineering from University of California, Berkeley, in 1980. Since then, he has been a member of the faculty of the mechanical engineering department, KAIST, Korea. His main interests are in the areas of the analytical and experimental modal analysis of, in particular, rotating machinery; the active control of vibration and motion using magnetic bearings, controllable fluids and piezoelectric actuators; the parameter identification and diagnosis of rotating machines. He is a member of ASME, SEM, SAE, IIAV, KSME, KSAS and KSAE, vice president of KSNVE, and the author of the book, Vibration Analysis of Rotors, Kluwer Academic Publishers, 1993. Hyun-Suk Jang received his BSME from Hanyang University in 1995 and MSME from Korea Advanced Institute of Science and Technology ŽKAIST. in 1997. He has worked for Samsung Electro-Mechanics since 1997. His interests are in the vibration analysis and the design of ink jet printer head.
Yongsoo Oh received his MS degree and doctoral Engineering degree from Hanyang University, Korea, in 1983 and Nagaoka University of Technology, Japan, in 1993, respectively. From 1986 to 1990, he worked at central research center, Chichibu cement, in Japan. Since 1994, he has been working for Samsung Advanced Institute of Technology in Korea. He is currently engaged in the research and development of microsensors.
Byeoungju Ha received his MS degree from the Seoul City University in 1993. He studied silicon pressure sensor at the Korea Institute of Science and Technology in 1991–1993. He has been working at Samsung Advanced Institute of Technology in Korea since 1993. In 1996, he researched inertial sensors as a Visiting Scholar at the University of Michigan in USA. He is currently engaged in the research and the development of microsensors.