dual-mode vertical membrane resonant pressure ... - Semantic Scholar
DUAL-MODE VERTICAL MEMBRANE RESONANT PRESSURE SENSOR Roozbeh Tabrizian and Farrokh Ayazi Georgia Institute of Technology, Atlanta, USA coupled microresonators (Figure 1). Inertial loading of gas molecules [4] on thin vertical membranes driven by silicon bulk acoustic resonators (SiBAR) into their transverse flexural resonance are used in contrast with pressureinsensitive extensional modes to realize absolute air pressure measurement without a need for a reference pressure.
ABSTRACT This paper presents a novel dual-mode resonant pressure sensor operating based on mass loading of air molecules on transversely resonating vertical silicon membranes. Two silicon bulk acoustic resonators (SiBAR) are acoustically coupled through thin vertical membranes, resulting in two high-Q resonance modes with small frequency split, but large difference in pressure sensitivity. The membranes are designed to couple 180° out-of-phase vibrations of piezoelectrically-transduced SiBARs through pressure-insensitive extensional Lamb waves and without changing their resonance frequency. The in-phase vibrations, on the other hand, induce a high-order pressuresensitive transverse flexural resonance in vertical membranes while slightly changing the resonance frequency of SiBAR due to stiffness and mass loading. A combinatorial of the two modes is used as a pressure sensor with an amplified sensitivity. A proof-of-concept device implemented on a 20m silicon substrate and activated by a thin aluminum nitride film shows a combinatorial beat frequency (fb) of 1.3 MHz with a linear pressure sensitivity of 346 ppm/kPa over 0-100kPa range.
Figure 1: Schematic view of the dual-mode vertical membrane resonant pressure sensor with aluminum nitride (AlN) film transduction.
INTRODUCTION
RESONANT PRESSURE SENSING
The majority of MEMS pressure sensors require lowpressure hermetic encapsulation to exploit the pressure difference between inside and outside of a package as an input force deflecting a thin membrane [1]. While realization of such encapsulation adds into the overall cost of the device, the membrane may experience large stress in operation, which can degrade their performance; hence necessitating co-integration of stress sensors on the same die for extraction and consequent compensation of packaginginduced effects [2]. Furthermore, additional calibration steps may be required to determine the reference pressure level inside the encapsulated volume. Therefore, absolute pressure sensing techniques which obviate the need for hermetic packaging are desirable.
The acoustic interaction between solid resonant structure and its ambient fluid molecules at their interface gives rise into energy dissipation [5, 6] and inertial-loading [6, 7] of the resonator. Such effects will be amplified as surface to volume ratio of the resonant structure increases. Furthermore, depending on the particle polarization at solidfluid interface and frequency of vibration, different resonance modes of a single structure experience different Q and f0 loading when operated in fluids: while transversely polarized resonance modes interact efficiently with surrounding molecules resulting in radiation of compression waves in fluid, shear-based vibrations do not couple into propagating waves and their frequency remains nearly constant.
Besides several advantages offered by miniaturized resonant sensors, acoustic engineering of microstructures can further provide promising opportunities for realization of in-situ physical relative references. This can be accomplished by formation of synthesized resonant modes with largely different sensitivities to physical/environmental signals in a single structure. A combinatorial of these modes can result in a frequency with an amplified sensitivity to the physical input of interest. The authors have recently shown an application of such techniques for highly-sensitive resonant temperature sensing [3].
Pressure Sensitive Flexural Membranes Thin membranes resonating in their transverse flexural modes are specifically sensitive to their surrounding fluid. Such sensitivity can be used to implement simple resonant pressure sensors. For a rectangular membrane operating in nth flexural mode, the resonance frequency when operating in an arbitrary fluid of finite density can be estimated as [6]: ≈
In this paper we report, for the first time, on a combinatorial resonant pressure sensor using acoustically
978-1-4799-3509-3/14/$31.00 ©2014 IEEE
,
∙ 1− ∙
(1)
Here fn,vac is the resonance frequency in vacuum; A is
120
MEMS 2014, San Francisco, CA, USA, January 26 - 30, 2014
corresponding coupled mode a good relative pressure reference. Furthermore, although thin membranes coupling bulk acoustic resonators are operating in a high-order tone with reduced pressure sensitivity compared to fundamental transverse flexural mode, the PCFb can be considerably increased by proper design for frequency split reduction.
the surface area of membrane lateral cross-section and 0 is the mass density of the membrane; and is the added mass per unit length as a result of inertial loading of fluid molecules carried along by membrane vibration which can be estimated from [4]: ≈ ∙
∙
(2)
RESONATOR DESIGN Two identical SiBARs with characteristic length of L are connected through thin vertical membranes with a length of 2L, resulting in creation two coupled resonance modes when SiBARs are resonating in their 3rd length-extensional mode (Figure 2).
Here f is the fluid density and t is the vertical membrane depth. For a membrane resonating in air, (2) can be re-written as a function of ambient pressure and temperature using the ideal gas law: ≈ ∙
∙
(3)
∙
where P and T are absolute pressure and temperature; and Rspecific is the specific gas constant of air. Using (1-3), the pressure coefficient of frequency (PCF) of the flexural modes can be written as: ∙
≈− ∙
∙
∙
∙
(4) Figure 2: Mode shapes of (a) pressure insensitive CM1; and (b) pressure sensitive CM2.
It can be concluded from (4) that PCF of the flexural modes can be improved by opting for thin membranes (i.e. small w) with large depth (t). This, on the other hand, results in placement of lower-order flexural modes in lowfrequencies resulting in significant air damping [8, 9] especially for high-pressure applications. This is undesirable since realization of any accurate resonant-based sensor requires implementation of low phase-noise oscillator, which in turn needs high Q of the resonance mode, consistent over the entire sensing range. On the other hand, although the Q of higher-order flexural modes are less affected by air damping, their PCF cannot be approximated accurately using (4) since Euler-Bernoulli beam theory is not valid for modeling of flexural resonance of beams/membranes with small aspect ratios (= ).
The 180° out-of-phase coupling of SiBARs excites an extensional Lamb wave with a wavelength of =2L/3 at the same frequency in thin membranes of length 3 resulting in mode CM1 (Figure 2a). In this case, vertical membranes do not load the equivalent stiffness/mass of the SiBARs. On the other hand, since the in-phase coupling of LE3 modes in SiBARs results in anti-periodic stress at two terminations of the membranes, extensional wave cannot be excited since the length of the membrane is an integer number of . Therefore, the vibration of the beam will be purely flexural, and load the resonance of SiBARs resulting in slight shift in their frequency (mode CM2, figure 2b). While the longitudinal polarization of the membrane in CM1 makes this mode insensitive to the gas mass loading, the transverse vibration of the membrane in CM2 makes it pressure sensitive. Figure 3 shows a simplified electrical equivalent circuit for the single-input, double-output electromechanical transduction configuration (Figure 1).
Dual-Mode Pressure Sensor In this paper, acoustic coupling of vertical membranes with bulk acoustic wave resonators is used to generate two high Q coupled resonance modes (CM1,2) with small frequency split (fres=fres,1 – fres,2) but large PCF difference (PCF). A combinatorial beat frequency generated from the two modes shows an amplified PCF: ≈
,
∆
∙∆
(5)
The large (PCF) of the coupled modes is due to different polarization of the vibrations induced in vertical membranes when coupling SiBARs in-phase and 180°-outof-phase. While the former excites a high-order transverse flexure in membranes, the latter results in pressureinsensitive extensional Lamb waves making the
Figure 3: Electrical equivalent model of the dual-mode resonant pressure sensor. Here Mi, Ki and Di (i ϵ{LE3, ext, flx}) are the equivalent mass, spring and damping of LE3 mode in SiBARs and
121
extensional and flexural modes in vertical membranes. is the piezoelectric transduction coefficient per single finger electrode (Figure 1), and and are the acoustic coupling efficiency between LE3 mode in SiBARs mode with extensional and flexural modes in vertical membranes respectively. Pressure sensitive fluid mass and damping loading are shown by M(P) and D(P) in the model. Proper acoustic engineering guarantees = ≠ . Therefore, fb can be formulated as: + 2∙
≈ 3
+
3 2 ∙(
+∆ ( ))
−
3
(6)
3
It’s worth to note the absolute sign in (6). The frequency sequence of the two coupled modes depends on the membrane thickness, resulting in placement of transverse flexural resonance frequency before or after that of extensional mode. Also considering the electrical equivalent model, since the main portion of acoustic energy is concentrated in high-frequency SiBARs (i.e. small and ), the effect of air damping (D(P)) on overall Q of the modes remains negligible over the entire pressure range from vacuum to atmospheric level. Figure 4 shows the COMSOL simulated pressure characteristic of the resonance frequency for the two coupled modes at 30°C.
Figure 5: (a) Block diagram required for extraction of fb. (b) Simulated pressure sensitivity of fb.
DEVICE FABRICATION A proof-of-concept design consisting of high frequency SiBARs operating in their LE3 at ~120 MHz and coupled through two vertical membranes of 2m thickness, has been implemented on AlN-on-Si acoustic platform using TPoS fabrication process [10] and a 20m SOI wafer. A 0.5m AlN film sandwiched between metal electrodes used to provide efficient and selective electromechanical transduction for the two modes. Figure 6 shows the SEM image of the device. A single-input double-output configuration of top electrodes has been used to facilitate implementation of two electrically-isolated oscillators locking separately into the two modes.
Figure 4: Simulated pressure characteristic of the two resonance modes of figure 2. An amplified pressure sensitivity can be realized by generating a combinatorial beat frequency from subtraction of reference (CM1) from pressure sensing mode (CM2) using a system with a block diagram schematically shown in figure 5a. Figure 5b shows the pressure characteristic of fb extracted from coupled modes in figure 4. The small frequency split of 453 kHz and large PCF has resulted in a large pressure sensitivity of ~2900 ppm/kPa. Considering (4), since the mass-loading effect of fluid molecules linearly increases with the depth of the vertical membranes, thick silicon substrates can be used to further increase the pressure sensitivity.
Figure 6: SEM image of the dual-mode vertical membrane resonant pressure sensor.
122
DEVICE CHARACTERIZATION
CONCLUSION
Figure 7 shows the measured transmission frequency response for both S21 and S31 configurations.
A dual-mode resonant pressure sensor has been implemented based on gas mass loading of vertical thin membranes operating in their transverse flexural mode. The membranes are driven using two identical SiBARs operating in 3rd length-extensional bulk acoustic mode. SiBAR and membrane dimensions are designed to provide two acoustically coupled resonance modes with small frequency split but large difference in their pressure sensitivity. This facilitated extraction of a combinatorial beat frequency with amplified pressure sensitivity. A high pressure sensitivity of 346 ppm/kPa has been measured over the vacuum to atmospheric pressure range, while the Q of fb constituent modes remained consistently high over the entire pressure range.
Figure 7: Measured frequency response of the dual-mode resonant pressure sensor.
REFERENCES
An fb of ~1.3 MHz extracted from subtraction of the two modes shows a linear pressure sensitivity of ~346 ppm/kPa over the pressure range of 0-100 kPa (Figure 8).
[1] W. P. Eaton, et. al., "Micromachined pressure sensors: review and recent developments," Smart Materials and Structures 6.5 (1997), pp. 530-539. [2] C. F. Chiang, et. al., "Resonant pressure sensor with onchip temperature and strain sensors for error correction," in Proc. IEEE Int. Conf. MEMS, 2013, pp. 45-48. [3] R. Tabrizian and F. Ayazi, "Acoustically-Engineered multi-port AlN-on-Silicon resonators for accurate temperature sensing," to be presented at IEEE International Electron Devices Meeting (IEDM 2013), Washington, DC, Dec. 2013. [4] W. K. Blake, "The radiation from free-free beams in air and in water," Journal of Sound and Vibration, vol. 33. No. 4, 1974, pp. 427-450. [5] Y.-H. Cho, A. P. Pisano, and R. T. Howe, "Viscous damping model for laterally oscillating microstructures", J. Microelectromech. Syst., vol. 3, no. 2, pp.81 -87 1994. [6] M. Christen, "Air and gas damping of quartz tuning forks," Sensors and Actuators, vol. 4, No. 4, 1983, pp. 555-564. [7] L. Chen, and M. Tabib-Azar, "Air and gas damping of quartz tuning forks," IEEE Sensors 2011, pp. 740-742. [8] W. E. Newell, "Miniaturization of tuning forks," Science 161, no. 3848, 1968, pp. 1320-1326. [9] W. Zhang and K. Turner, "Frequency dependent fluid damping of micro/nano flexural resonators: Experiment, model and analysis," Sensors and Actuators A: Physical 134, no. 2, 2007, pp. 594-599. [10] W. Pan and F. Ayazi, "Thin-Film Piezoelectric-onSubstrate Resonators with Q Enhancement and TCF Reduction," IEEE International Conference on Micro Electro Mechanical Systems (MEMS 2010), Hong Kong, 2010, pp. 104-107.
Figure 8: Pressure characteristics of fb measured at 30°C, over 0-100 kPa pressure range. The smaller measured pressure sensitivity compared to simulated value (Figure 5b) is due to the larger fb of the device resulted from fabrication processing imperfections. Figure 9 shows the pressure characteristic of the Q for the two coupled modes. The Q of the two modes remains consistent across the entire pressure range with a maximum drop of ~9% for the pressure sensitive mode CM2, highlighting the role of SiBARs to store the main portion of acoustic energy, and hence minimizing the effect of air damping on resonance Q.
CONTACT Figure 9: Measured pressure characteristics of Q for CM1,2.
*R. Tabrizian, tel: +1-404-259-7322; [email protected]
123
ABSTRACT This paper presents a novel dual-mode resonant pressure sensor operating based on mass loading of air molecules on transversely resonating vertical silicon membranes. Two silicon bulk acoustic resonators (SiBAR) are acoustically coupled through thin vertical membranes, resulting in two high-Q resonance modes with small frequency split, but large difference in pressure sensitivity. The membranes are designed to couple 180° out-of-phase vibrations of piezoelectrically-transduced SiBARs through pressure-insensitive extensional Lamb waves and without changing their resonance frequency. The in-phase vibrations, on the other hand, induce a high-order pressuresensitive transverse flexural resonance in vertical membranes while slightly changing the resonance frequency of SiBAR due to stiffness and mass loading. A combinatorial of the two modes is used as a pressure sensor with an amplified sensitivity. A proof-of-concept device implemented on a 20m silicon substrate and activated by a thin aluminum nitride film shows a combinatorial beat frequency (fb) of 1.3 MHz with a linear pressure sensitivity of 346 ppm/kPa over 0-100kPa range.
Figure 1: Schematic view of the dual-mode vertical membrane resonant pressure sensor with aluminum nitride (AlN) film transduction.
INTRODUCTION
RESONANT PRESSURE SENSING
The majority of MEMS pressure sensors require lowpressure hermetic encapsulation to exploit the pressure difference between inside and outside of a package as an input force deflecting a thin membrane [1]. While realization of such encapsulation adds into the overall cost of the device, the membrane may experience large stress in operation, which can degrade their performance; hence necessitating co-integration of stress sensors on the same die for extraction and consequent compensation of packaginginduced effects [2]. Furthermore, additional calibration steps may be required to determine the reference pressure level inside the encapsulated volume. Therefore, absolute pressure sensing techniques which obviate the need for hermetic packaging are desirable.
The acoustic interaction between solid resonant structure and its ambient fluid molecules at their interface gives rise into energy dissipation [5, 6] and inertial-loading [6, 7] of the resonator. Such effects will be amplified as surface to volume ratio of the resonant structure increases. Furthermore, depending on the particle polarization at solidfluid interface and frequency of vibration, different resonance modes of a single structure experience different Q and f0 loading when operated in fluids: while transversely polarized resonance modes interact efficiently with surrounding molecules resulting in radiation of compression waves in fluid, shear-based vibrations do not couple into propagating waves and their frequency remains nearly constant.
Besides several advantages offered by miniaturized resonant sensors, acoustic engineering of microstructures can further provide promising opportunities for realization of in-situ physical relative references. This can be accomplished by formation of synthesized resonant modes with largely different sensitivities to physical/environmental signals in a single structure. A combinatorial of these modes can result in a frequency with an amplified sensitivity to the physical input of interest. The authors have recently shown an application of such techniques for highly-sensitive resonant temperature sensing [3].
Pressure Sensitive Flexural Membranes Thin membranes resonating in their transverse flexural modes are specifically sensitive to their surrounding fluid. Such sensitivity can be used to implement simple resonant pressure sensors. For a rectangular membrane operating in nth flexural mode, the resonance frequency when operating in an arbitrary fluid of finite density can be estimated as [6]: ≈
In this paper we report, for the first time, on a combinatorial resonant pressure sensor using acoustically
978-1-4799-3509-3/14/$31.00 ©2014 IEEE
,
∙ 1− ∙
(1)
Here fn,vac is the resonance frequency in vacuum; A is
120
MEMS 2014, San Francisco, CA, USA, January 26 - 30, 2014
corresponding coupled mode a good relative pressure reference. Furthermore, although thin membranes coupling bulk acoustic resonators are operating in a high-order tone with reduced pressure sensitivity compared to fundamental transverse flexural mode, the PCFb can be considerably increased by proper design for frequency split reduction.
the surface area of membrane lateral cross-section and 0 is the mass density of the membrane; and is the added mass per unit length as a result of inertial loading of fluid molecules carried along by membrane vibration which can be estimated from [4]: ≈ ∙
∙
(2)
RESONATOR DESIGN Two identical SiBARs with characteristic length of L are connected through thin vertical membranes with a length of 2L, resulting in creation two coupled resonance modes when SiBARs are resonating in their 3rd length-extensional mode (Figure 2).
Here f is the fluid density and t is the vertical membrane depth. For a membrane resonating in air, (2) can be re-written as a function of ambient pressure and temperature using the ideal gas law: ≈ ∙
∙
(3)
∙
where P and T are absolute pressure and temperature; and Rspecific is the specific gas constant of air. Using (1-3), the pressure coefficient of frequency (PCF) of the flexural modes can be written as: ∙
≈− ∙
∙
∙
∙
(4) Figure 2: Mode shapes of (a) pressure insensitive CM1; and (b) pressure sensitive CM2.
It can be concluded from (4) that PCF of the flexural modes can be improved by opting for thin membranes (i.e. small w) with large depth (t). This, on the other hand, results in placement of lower-order flexural modes in lowfrequencies resulting in significant air damping [8, 9] especially for high-pressure applications. This is undesirable since realization of any accurate resonant-based sensor requires implementation of low phase-noise oscillator, which in turn needs high Q of the resonance mode, consistent over the entire sensing range. On the other hand, although the Q of higher-order flexural modes are less affected by air damping, their PCF cannot be approximated accurately using (4) since Euler-Bernoulli beam theory is not valid for modeling of flexural resonance of beams/membranes with small aspect ratios (= ).
The 180° out-of-phase coupling of SiBARs excites an extensional Lamb wave with a wavelength of =2L/3 at the same frequency in thin membranes of length 3 resulting in mode CM1 (Figure 2a). In this case, vertical membranes do not load the equivalent stiffness/mass of the SiBARs. On the other hand, since the in-phase coupling of LE3 modes in SiBARs results in anti-periodic stress at two terminations of the membranes, extensional wave cannot be excited since the length of the membrane is an integer number of . Therefore, the vibration of the beam will be purely flexural, and load the resonance of SiBARs resulting in slight shift in their frequency (mode CM2, figure 2b). While the longitudinal polarization of the membrane in CM1 makes this mode insensitive to the gas mass loading, the transverse vibration of the membrane in CM2 makes it pressure sensitive. Figure 3 shows a simplified electrical equivalent circuit for the single-input, double-output electromechanical transduction configuration (Figure 1).
Dual-Mode Pressure Sensor In this paper, acoustic coupling of vertical membranes with bulk acoustic wave resonators is used to generate two high Q coupled resonance modes (CM1,2) with small frequency split (fres=fres,1 – fres,2) but large PCF difference (PCF). A combinatorial beat frequency generated from the two modes shows an amplified PCF: ≈
,
∆
∙∆
(5)
The large (PCF) of the coupled modes is due to different polarization of the vibrations induced in vertical membranes when coupling SiBARs in-phase and 180°-outof-phase. While the former excites a high-order transverse flexure in membranes, the latter results in pressureinsensitive extensional Lamb waves making the
Figure 3: Electrical equivalent model of the dual-mode resonant pressure sensor. Here Mi, Ki and Di (i ϵ{LE3, ext, flx}) are the equivalent mass, spring and damping of LE3 mode in SiBARs and
121
extensional and flexural modes in vertical membranes. is the piezoelectric transduction coefficient per single finger electrode (Figure 1), and and are the acoustic coupling efficiency between LE3 mode in SiBARs mode with extensional and flexural modes in vertical membranes respectively. Pressure sensitive fluid mass and damping loading are shown by M(P) and D(P) in the model. Proper acoustic engineering guarantees = ≠ . Therefore, fb can be formulated as: + 2∙
≈ 3
+
3 2 ∙(
+∆ ( ))
−
3
(6)
3
It’s worth to note the absolute sign in (6). The frequency sequence of the two coupled modes depends on the membrane thickness, resulting in placement of transverse flexural resonance frequency before or after that of extensional mode. Also considering the electrical equivalent model, since the main portion of acoustic energy is concentrated in high-frequency SiBARs (i.e. small and ), the effect of air damping (D(P)) on overall Q of the modes remains negligible over the entire pressure range from vacuum to atmospheric level. Figure 4 shows the COMSOL simulated pressure characteristic of the resonance frequency for the two coupled modes at 30°C.
Figure 5: (a) Block diagram required for extraction of fb. (b) Simulated pressure sensitivity of fb.
DEVICE FABRICATION A proof-of-concept design consisting of high frequency SiBARs operating in their LE3 at ~120 MHz and coupled through two vertical membranes of 2m thickness, has been implemented on AlN-on-Si acoustic platform using TPoS fabrication process [10] and a 20m SOI wafer. A 0.5m AlN film sandwiched between metal electrodes used to provide efficient and selective electromechanical transduction for the two modes. Figure 6 shows the SEM image of the device. A single-input double-output configuration of top electrodes has been used to facilitate implementation of two electrically-isolated oscillators locking separately into the two modes.
Figure 4: Simulated pressure characteristic of the two resonance modes of figure 2. An amplified pressure sensitivity can be realized by generating a combinatorial beat frequency from subtraction of reference (CM1) from pressure sensing mode (CM2) using a system with a block diagram schematically shown in figure 5a. Figure 5b shows the pressure characteristic of fb extracted from coupled modes in figure 4. The small frequency split of 453 kHz and large PCF has resulted in a large pressure sensitivity of ~2900 ppm/kPa. Considering (4), since the mass-loading effect of fluid molecules linearly increases with the depth of the vertical membranes, thick silicon substrates can be used to further increase the pressure sensitivity.
Figure 6: SEM image of the dual-mode vertical membrane resonant pressure sensor.
122
DEVICE CHARACTERIZATION
CONCLUSION
Figure 7 shows the measured transmission frequency response for both S21 and S31 configurations.
A dual-mode resonant pressure sensor has been implemented based on gas mass loading of vertical thin membranes operating in their transverse flexural mode. The membranes are driven using two identical SiBARs operating in 3rd length-extensional bulk acoustic mode. SiBAR and membrane dimensions are designed to provide two acoustically coupled resonance modes with small frequency split but large difference in their pressure sensitivity. This facilitated extraction of a combinatorial beat frequency with amplified pressure sensitivity. A high pressure sensitivity of 346 ppm/kPa has been measured over the vacuum to atmospheric pressure range, while the Q of fb constituent modes remained consistently high over the entire pressure range.
Figure 7: Measured frequency response of the dual-mode resonant pressure sensor.
REFERENCES
An fb of ~1.3 MHz extracted from subtraction of the two modes shows a linear pressure sensitivity of ~346 ppm/kPa over the pressure range of 0-100 kPa (Figure 8).
[1] W. P. Eaton, et. al., "Micromachined pressure sensors: review and recent developments," Smart Materials and Structures 6.5 (1997), pp. 530-539. [2] C. F. Chiang, et. al., "Resonant pressure sensor with onchip temperature and strain sensors for error correction," in Proc. IEEE Int. Conf. MEMS, 2013, pp. 45-48. [3] R. Tabrizian and F. Ayazi, "Acoustically-Engineered multi-port AlN-on-Silicon resonators for accurate temperature sensing," to be presented at IEEE International Electron Devices Meeting (IEDM 2013), Washington, DC, Dec. 2013. [4] W. K. Blake, "The radiation from free-free beams in air and in water," Journal of Sound and Vibration, vol. 33. No. 4, 1974, pp. 427-450. [5] Y.-H. Cho, A. P. Pisano, and R. T. Howe, "Viscous damping model for laterally oscillating microstructures", J. Microelectromech. Syst., vol. 3, no. 2, pp.81 -87 1994. [6] M. Christen, "Air and gas damping of quartz tuning forks," Sensors and Actuators, vol. 4, No. 4, 1983, pp. 555-564. [7] L. Chen, and M. Tabib-Azar, "Air and gas damping of quartz tuning forks," IEEE Sensors 2011, pp. 740-742. [8] W. E. Newell, "Miniaturization of tuning forks," Science 161, no. 3848, 1968, pp. 1320-1326. [9] W. Zhang and K. Turner, "Frequency dependent fluid damping of micro/nano flexural resonators: Experiment, model and analysis," Sensors and Actuators A: Physical 134, no. 2, 2007, pp. 594-599. [10] W. Pan and F. Ayazi, "Thin-Film Piezoelectric-onSubstrate Resonators with Q Enhancement and TCF Reduction," IEEE International Conference on Micro Electro Mechanical Systems (MEMS 2010), Hong Kong, 2010, pp. 104-107.
Figure 8: Pressure characteristics of fb measured at 30°C, over 0-100 kPa pressure range. The smaller measured pressure sensitivity compared to simulated value (Figure 5b) is due to the larger fb of the device resulted from fabrication processing imperfections. Figure 9 shows the pressure characteristic of the Q for the two coupled modes. The Q of the two modes remains consistent across the entire pressure range with a maximum drop of ~9% for the pressure sensitive mode CM2, highlighting the role of SiBARs to store the main portion of acoustic energy, and hence minimizing the effect of air damping on resonance Q.
CONTACT Figure 9: Measured pressure characteristics of Q for CM1,2.
*R. Tabrizian, tel: +1-404-259-7322; [email protected]
123
