P2G-2 Capacitively Coupled VHF Silicon Bulk ... - Semantic Scholar
Capacitively Coupled VHF Silicon Bulk Acoustic Wave Filters Qishu Qin, Siavash Pourkamali*, and Farrokh Ayazi School of Electrical & Computer Engineering Georgia Institute of Technology, Atlanta, GA USA 30332 (*Now an Assistant Professor with the Department of Electrical Engineering, University of Denver, Denver, CO, USA 80208) Abstract—This work reports on the implementation of VHF MEMS bandpass filters by capacitive coupling of Silicon Bulk Acoustic wave Resonators (SiBAR) fabricated using the HARPSS-on-SOI fabrication process. Such resonators operate in their horizontal width extensional modes with quality factors (Q) in the range of 10,000~100,000. With the comparatively large electrode area and deep submicron capacitive transduction gaps these resonators have also exhibited relatively low impedances. Compared with existing technologies such as quartz crystals, SAW filters, capacitively-coupled SiBARs have demonstrated the smallest form factor high-Q filters in the VHF range that can be integrated with silicon electronics on a common substrate. Filters with center frequencies up to 150MHz are demonstrated by coupling of two SiBAR resonators in their fundamental widthextensional modes. Tuning of the filter bandwidth by varying the DC polarization voltages on the resonators is investigated. Keywords-bulk acoustic wave filter; quality factor; capacitive coupling; bandwidth tuning
I. INTRODUCTION Silicon-based MEMS resonators with their high quality factors, low cost batch fabrication, small sizes and IC compatibility have a great potential as frequency selective components (i.e. frequency references and filters) in modern, highly integrated electronic systems. A variety of high frequency silicon micromechanical resonator technologies are currently under development to provide viable replacements for the existing technologies such as bulk quartz and surface acoustic wave (SAW) [1]. Among the most successful newly developed technologies are film bulk acoustic wave resonators (FBAR) [2], miniaturized quartz resonators, piezoelectric in plane resonators, and capacitive silicon resonators. The concept of silicon bulk acoustic resonators (SiBAR) and fabrication and characterization results for such devices was presented in [3, 4]. It was shown that due to much larger signal transduction areas, SiBARs can provide significantly lower motional resistances while maintaining the high quality factors. Sub-kilo ohm or lower impedances have been demonstrated for the SiBARs operating in the VHF band. Despite high quality factors in the order of tens of thousands, a single SiBAR is a first-order resonant system providing limited frequency selectivity. When used as bandpass filters, in order to provide higher selectivity, higher order resonant systems comprising of a number of coupled SiBARs are required. This work presents capacitive coupling
techniques for the implementation of 2nd order bandpass filters from individual SiBAR resonators. Filters consisting of different variations of resonators are introduced. Two different filter bandwidth tuning techniques utilizing changing DC polarization voltages and coupling capacitor size are discussed and demonstrated. II.
DEVICE DESIGN, FABRICATION AND OPERATION
In the structure of the SiBAR, the pure silicon resonating member (Figure 1a) is placed in between two electrodes that are separated from the resonator by very small capacitive gaps to operate the resonator electrostatically in its horizontal width extensional mode (Figure 1b). This horizontal dimension known as “the width” determines the frequency of the extensional bulk resonant mode of the SiBAR. Therefore a high operating frequency can be maintained while extending the other dimensions to provide a larger transduction area and consequently lower the equivalent impedance. Using the HARPSS [5] fabrication technology, while increasing the resonator length, one can extend the resonator thickness in the vertical direction as well to achieve a total of tens to hundreds of times larger transduction area compared to previously demonstrated disk resonators [6]. SiBAR Electrodes
w
Capacitive Gaps
t
L
Figure 1(a). Schematic diagram of a Vertical Capacitive SiBAR
Figure 1(b). Mode shape of a 27µm wide, 10µm thick SiBAR
Equation 1 gives the electrical equivalent resistance for a two-port in plane capacitive block resonator:
Rm =
γ KM g 4 γg 4 ∝ Qε 0 2 Le 2t 2V p 2 Q.V p 2 . Le 2 .t
(1)
where K and M are the effective mechanical mass and stiffness of the resonator, g is the capacitive gap size, Q is the quality factor of the resonator, Vp is the applied DC polarization voltage, Le is the physical electrode length, t is the thickness (height) of the structure, and γ is a coupling coefficient indicating how effective the electromechanical coupling
This work is supported by the DARPA Analog Spectral Processor project.
US Government Work Not Protected by US Copyright
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2007 IEEE Ultrasonics Symposium
between the resonator and the electrodes is. The value of γ varies from 1 for a completely uniform mode shape with flat resonator sidewalls, to 0 for a wavy mode shape with complete cancellation.
in the midpoint of the resonator width, and the rectangular openings in the electrode pads are etched during the last lithography and etching step to facilitate and accelerate resonator undercut in HF.
Equation 2 gives the resonance frequency for a thin and narrow block resonator:
n E ⋅ (2) n ρ 2W where n is the width extensional mode number, which is an integer (n = 1,2,…), W is the width (frequency determining dimension) of the block and E and ρ are the Young’s modulus and density of the structural material respectively. SiBARs are long and thick block resonators operating in a similar resonance mode, therefore the same equation can be used to calculate resonance frequency of SiBARs with good approximation. To determine the exact resonance frequency for SiBARs finite element modal analysis need to be performed for each specific set of dimensions. f
f=102.1MHz IL=20dB Q=61K
=
The process flow used to fabricate SiBARs is the HARPSSon-SOI process and is shown in Figure 2 and consists of only three lithography steps and a number of thin film deposition and etching steps. The process starts with patterning a 0.5~1.5µm thick oxide mask on the substrate. Deep trenches are etched through the device layer of the SOI to define the resonating SCS structures. A thin layer of sacrificial LPCVD oxide is deposited to form the capacitive gaps, and subsequently trenches are filled with LPCVD polysilicon. Next, the polysilicon is etched back to expose the oxide mask and this oxide mask was patterned on the surface. Then another LPCVD polysilicon layer is deposited. After patterning the polysilicon on the surface to define the pads, polysilicon inside the trenches as well as parts of the silicon substrate are removed using the Bosch process to define the electrodes. Finally, the device is released in HF.
(a) Grow and pattern initial oxide.
(b) Etch trenches, deposit LPCVD sacrificial oxide etch back oxide.
Fig 3(a). SEM view of a 40µm wide, 240µm long, 20µm thick SiBAR fabricated using the HARPSS process.
Fig 3(b). Measured frequency response of a 102.1MHz SiBAR.
Figure 3b shows the measured frequency response of the fabricated SiBAR using a network analyzer with 50Ω input and output termination. A very clear resonance peak was observed for this resonator by applying polarization voltages of 17V and quality factor of 61,000 in vacuum was measured for the first width extensional bulk mode of this resonator at 102.1MHz. The motional resistance extracted is only 980Ω. Electrostatic tuning of parallel plate capacitive resonators is a well known method of frequency tuning. Tuning slope for a capacitive SiBAR [4] assuming a non-distorted mode shape is given by Equation 3:
2V p fεAe ∂f =− ∂V p Kg 3
(3)
where f is the resonance frequency of the resonator, Ae is the electrode area (area of one electrode only) and K is the effective stiffness as used in Equation 1. In order to implement a 2nd order filter system, two SiBARs with the same resonance frequency are placed side by side and coupled by a capacitor. Figure 4 shows this capacitive coupling approach. As illustrated, two SiBARs share one electrode which will act as the coupling capacitor. This capacitor interacts with the resonators resulting in an additional resonance mode for the system and consequently a 2nd order bandpass frequency response.
(c) Pattern silicon substrate and (d) HF release. polysilicon inside the trenches. Fig 2. Process flow of the three-mask HARPSS-on-SOI approach used for fabrication of the SiBAR. Fig 4. Schematic diagram of a capacitively coupled SiBAR filter.
Figure 3a is the SEM view of a fabricated 40µm wide, 240µm long, 20µm long SiBAR. The resonator is supported on the two sides by tiny support beams. Support beams are placed
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Due to the variations during the fabrication process, there is always be some difference between the resonance frequencies of the two resonators, thus two different polarization voltages
2007 IEEE Ultrasonics Symposium
were applied to the two resonators in order to tune their center frequencies to equal values. To avoid extra biasing elements for the coupling capacitor, which may cause extra capacitance on the coupling node, polarization voltages with opposite polarities were applied to the two resonators causing the coupling capacitor to have a DC value equal to the average of the two polarization voltages, which is close to zero. Figure 5 and 6 show the SEM views of the fabricated SiBAR capacitive filters at 61.9MHz and 145.6MHz and their measured frequency response using a network analyzer with 50Ω terminations. It is clear in these measurement results that the peaks of the two individual resonators are coupled together by the coupling capacitor to form a filter. The filters both show very high-Q at VHF range. f=61.9MHz BW=3.3 KHz IL=35dB Q=18,600
to a half circuit with one resonator and a series capacitor Cc/2 to ground. The series capacitor reduces the total capacitance of the RLC tank, causing the second resonance mode to have a higher frequency given by Equation 4:
f1 = f 0 1 +
2C Cc
(4)
where f0 is the mechanical resonant frequency of the individual resonators, and C is the resonator equivalent series capacitance.
Fig 7(a). Electrical schematic diagram of a SiBAR resonator
Fig 7(b). Electrical schematic diagram of a capacitively-coupled SiBAR filter Fig 5(a). SEM view of a capacitive filter consisting of two coupled 68µm x 544µm x 20µm resonators
Fig 5(b). Measured frequency response of a 61.9MHz capacitive SiBAR filter in vacuum. f=145.6MHz BW=10.9 KHz IL=52dB Q=13,300
Fig 6(a). SEM view of a capacitive filter consisting of two coupled 27µm x 270µm x 20µm resonators
Fig 6(b). Measured frequency response of a 145.6MHz capacitive SiBAR filter in air.
III. ELECTRICAL EQUIVALENT CIRCUIT Figure 7a shows the equivalent circuit model of a two-port SiBAR resonator, where Ci and Co are the drive and sense electrode capacitance respectively. This is a simple series RLC tank where L and C are cancelled out at resonance. Figure 7b shows the model of a 2nd order coupled filter, where Cc is the coupling capacitor [7]. Looking at the frequency response of this two-resonator system, the first resonance occurs at the mechanical resonant frequency of the individual resonators. At the 1st resonance, as shown in Figure 7c, the two resonators resonate in phase and the coupling capacitor has negligible contribution (while Cc is being charged by the first resonator, the other resonator is discharging it). At the 2nd resonance, as shown in Figure 7d, the two resonators operate with a 180° phase difference and hence the coupling capacitor comes into play (it is being charged and discharged at the same time by both resonators). Under ideal conditions, the two SiBARs act exactly similar in this mode. Due to this symmetry, the system can be reduced
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Fig 7(c). 1st resonance mode of capacitive SiBAR filter
Fig 7(d). 2nd resonance mode of capacitive SiBAR filter
In practice under non-ideal conditions, the system is not always symmetric. In most situations the two SiBARs will have slightly different RLC parameters. Electrostatic tuning of the resonator center frequency by applying different DC polarization voltages can compensate the frequency difference to some extent, but for higher frequency bulk mode resonators frequency mismatch compensation could require very high polarization voltage values making it non-practical. In such cases a perfect coupling between the two resonators can not be achieved and two distinctive peaks from the resonators will be observed. From Equation 4 we can see that a large coupling capacitor will cause the two peaks to be closer to each other, and it is still true in the non-ideal situation assuming that the only thing changed is the coupling capacitor. IV. FILTER BANDWIDTH TUNING A major advantage of electrical based resonator coupling techniques compared to the mechanical approach is the higher tunability provided by the bias voltages. As shown in [7] both filter center frequency and separation of the two resonance modes (and therefore filter bandwidth) can be tuned by changing the polarization voltages. Figure 8 shows the measurement results of a SiBAR filter and the effect of change in polarization voltages on it. This filter consists of two 27µm wide, 20µm thick resonators and its center frequency is around 145.6MHz. Three different sets of DC polarization voltages were applied to the device. By
2007 IEEE Ultrasonics Symposium
increasing the polarization voltages, the two peaks of this filter gradually come closer to each other and then overlap, causing the bandwidth of the system shrinks from 23KHz to 11KHz.
(a)
BW=23KHz Q=6,300 IL=63dB
V. CONCLUSION AND FUTURE WORK This work reported on high-Q capacitively-coupled VHF SiBAR filters with center frequency up to 145MHz. Preliminary measurement results identified that changing the DC polarization voltages on individual resonators is an effective technique for tuning the filter bandwidth. Future work includes further investigations on electrostatic tuning of the filter bandwidth and detailed functions of the coupling capacitor, as well as reducing the insertion loss of the filter system by impedance matching and parasitic capacitance cancellation.
Vp1=24V, Vp2=-18V
(b)
However, the shift in the frequency of the resonator with the larger voltage is larger and one peak moves faster than the other under the same amount of change in polarization voltages, which will cause these two peaks to eventually overlap.
BW=20KHz Q=7,400 IL=61dB
ACKNOWLEDGMENT The authors would like to thank the staff at the Georgia Tech Microelectronics Research Center for their assistance. REFERENCES [1]
Vp1=28V, Vp2=-20V
(c)
[2]
BW=11KHz Q=13,300 IL=52dB
[3]
[4]
[5]
Vp1=32V, Vp2=-28V Fig 8. Filter bandwidth tuning measurement results in air with 50Ω terminations by changing polarization voltages.
[6]
It is obvious that the electrostatic tuning should drive both the two peaks towards the same direction based on Equation 3, and we see that both center frequencies of the peaks decrease by increasing the polarization voltages in our measurements.
1652
[7]
“Ultra-miniaturized and high performance PCS SAW duplexer with steep cut-off filters”, MTT-S 2004, Vol. 2, pp.913-916. R. C. Ruby, et al, “Thin film bulk wave acoustic resonators (FBAR) for wireless applications”, Ultrasonics Symposium, 2001, Vol. 1, pp. 813– 821. S. Pourkamali, G. K. Ho and F. Ayazi, “Low-Impedance VHF and UHF Capacitive Silicon Bulk Acoustic Wave Resonators—Part I: Concept and Fabrication,” IEEE Transactions on Electron Devices, Vol. 54, Issue: 8, Aug. 2007, pp. 2017 – 2023. S. Pourkamali, G. K. Ho and F. Ayazi, “Low-Impedance VHF and UHF Capacitive Silicon Bulk Acoustic Wave Resonators—Part II: Measurement and Characterization,” IEEE Transactions on Electron Devices, Vol. 54, Issue: 8, Aug. 2007, pp. 2024 – 2030. S. Pourkamali, et al, “High-Q single crystal silicon HARPSS capacitive beam resonators with self-aligned sub-100nm transduction gaps,” Journal of Micro Electro Mechanical Systems, Vol. 12, Issue 4, August 2003, pp. 487-496. S. Pourkamali, et al, “VHF single crystal silicon capacitive elliptic bulkmode disk resonators part II: implementation and characterization”, Journal of Micro Electro Mechanical Systems, Vol. 13, Issue 6, December 2004, pp. 1054-1062. S. Pourkamali and F. Ayazi, "Electrically Coupled MEMS Bandpass Filters Part I: With Coupling Element," Journal of Sensors and Actuators A, Aug. 2005, pp. 307-316.
2007 IEEE Ultrasonics Symposium
I. INTRODUCTION Silicon-based MEMS resonators with their high quality factors, low cost batch fabrication, small sizes and IC compatibility have a great potential as frequency selective components (i.e. frequency references and filters) in modern, highly integrated electronic systems. A variety of high frequency silicon micromechanical resonator technologies are currently under development to provide viable replacements for the existing technologies such as bulk quartz and surface acoustic wave (SAW) [1]. Among the most successful newly developed technologies are film bulk acoustic wave resonators (FBAR) [2], miniaturized quartz resonators, piezoelectric in plane resonators, and capacitive silicon resonators. The concept of silicon bulk acoustic resonators (SiBAR) and fabrication and characterization results for such devices was presented in [3, 4]. It was shown that due to much larger signal transduction areas, SiBARs can provide significantly lower motional resistances while maintaining the high quality factors. Sub-kilo ohm or lower impedances have been demonstrated for the SiBARs operating in the VHF band. Despite high quality factors in the order of tens of thousands, a single SiBAR is a first-order resonant system providing limited frequency selectivity. When used as bandpass filters, in order to provide higher selectivity, higher order resonant systems comprising of a number of coupled SiBARs are required. This work presents capacitive coupling
techniques for the implementation of 2nd order bandpass filters from individual SiBAR resonators. Filters consisting of different variations of resonators are introduced. Two different filter bandwidth tuning techniques utilizing changing DC polarization voltages and coupling capacitor size are discussed and demonstrated. II.
DEVICE DESIGN, FABRICATION AND OPERATION
In the structure of the SiBAR, the pure silicon resonating member (Figure 1a) is placed in between two electrodes that are separated from the resonator by very small capacitive gaps to operate the resonator electrostatically in its horizontal width extensional mode (Figure 1b). This horizontal dimension known as “the width” determines the frequency of the extensional bulk resonant mode of the SiBAR. Therefore a high operating frequency can be maintained while extending the other dimensions to provide a larger transduction area and consequently lower the equivalent impedance. Using the HARPSS [5] fabrication technology, while increasing the resonator length, one can extend the resonator thickness in the vertical direction as well to achieve a total of tens to hundreds of times larger transduction area compared to previously demonstrated disk resonators [6]. SiBAR Electrodes
w
Capacitive Gaps
t
L
Figure 1(a). Schematic diagram of a Vertical Capacitive SiBAR
Figure 1(b). Mode shape of a 27µm wide, 10µm thick SiBAR
Equation 1 gives the electrical equivalent resistance for a two-port in plane capacitive block resonator:
Rm =
γ KM g 4 γg 4 ∝ Qε 0 2 Le 2t 2V p 2 Q.V p 2 . Le 2 .t
(1)
where K and M are the effective mechanical mass and stiffness of the resonator, g is the capacitive gap size, Q is the quality factor of the resonator, Vp is the applied DC polarization voltage, Le is the physical electrode length, t is the thickness (height) of the structure, and γ is a coupling coefficient indicating how effective the electromechanical coupling
This work is supported by the DARPA Analog Spectral Processor project.
US Government Work Not Protected by US Copyright
1649
2007 IEEE Ultrasonics Symposium
between the resonator and the electrodes is. The value of γ varies from 1 for a completely uniform mode shape with flat resonator sidewalls, to 0 for a wavy mode shape with complete cancellation.
in the midpoint of the resonator width, and the rectangular openings in the electrode pads are etched during the last lithography and etching step to facilitate and accelerate resonator undercut in HF.
Equation 2 gives the resonance frequency for a thin and narrow block resonator:
n E ⋅ (2) n ρ 2W where n is the width extensional mode number, which is an integer (n = 1,2,…), W is the width (frequency determining dimension) of the block and E and ρ are the Young’s modulus and density of the structural material respectively. SiBARs are long and thick block resonators operating in a similar resonance mode, therefore the same equation can be used to calculate resonance frequency of SiBARs with good approximation. To determine the exact resonance frequency for SiBARs finite element modal analysis need to be performed for each specific set of dimensions. f
f=102.1MHz IL=20dB Q=61K
=
The process flow used to fabricate SiBARs is the HARPSSon-SOI process and is shown in Figure 2 and consists of only three lithography steps and a number of thin film deposition and etching steps. The process starts with patterning a 0.5~1.5µm thick oxide mask on the substrate. Deep trenches are etched through the device layer of the SOI to define the resonating SCS structures. A thin layer of sacrificial LPCVD oxide is deposited to form the capacitive gaps, and subsequently trenches are filled with LPCVD polysilicon. Next, the polysilicon is etched back to expose the oxide mask and this oxide mask was patterned on the surface. Then another LPCVD polysilicon layer is deposited. After patterning the polysilicon on the surface to define the pads, polysilicon inside the trenches as well as parts of the silicon substrate are removed using the Bosch process to define the electrodes. Finally, the device is released in HF.
(a) Grow and pattern initial oxide.
(b) Etch trenches, deposit LPCVD sacrificial oxide etch back oxide.
Fig 3(a). SEM view of a 40µm wide, 240µm long, 20µm thick SiBAR fabricated using the HARPSS process.
Fig 3(b). Measured frequency response of a 102.1MHz SiBAR.
Figure 3b shows the measured frequency response of the fabricated SiBAR using a network analyzer with 50Ω input and output termination. A very clear resonance peak was observed for this resonator by applying polarization voltages of 17V and quality factor of 61,000 in vacuum was measured for the first width extensional bulk mode of this resonator at 102.1MHz. The motional resistance extracted is only 980Ω. Electrostatic tuning of parallel plate capacitive resonators is a well known method of frequency tuning. Tuning slope for a capacitive SiBAR [4] assuming a non-distorted mode shape is given by Equation 3:
2V p fεAe ∂f =− ∂V p Kg 3
(3)
where f is the resonance frequency of the resonator, Ae is the electrode area (area of one electrode only) and K is the effective stiffness as used in Equation 1. In order to implement a 2nd order filter system, two SiBARs with the same resonance frequency are placed side by side and coupled by a capacitor. Figure 4 shows this capacitive coupling approach. As illustrated, two SiBARs share one electrode which will act as the coupling capacitor. This capacitor interacts with the resonators resulting in an additional resonance mode for the system and consequently a 2nd order bandpass frequency response.
(c) Pattern silicon substrate and (d) HF release. polysilicon inside the trenches. Fig 2. Process flow of the three-mask HARPSS-on-SOI approach used for fabrication of the SiBAR. Fig 4. Schematic diagram of a capacitively coupled SiBAR filter.
Figure 3a is the SEM view of a fabricated 40µm wide, 240µm long, 20µm long SiBAR. The resonator is supported on the two sides by tiny support beams. Support beams are placed
1650
Due to the variations during the fabrication process, there is always be some difference between the resonance frequencies of the two resonators, thus two different polarization voltages
2007 IEEE Ultrasonics Symposium
were applied to the two resonators in order to tune their center frequencies to equal values. To avoid extra biasing elements for the coupling capacitor, which may cause extra capacitance on the coupling node, polarization voltages with opposite polarities were applied to the two resonators causing the coupling capacitor to have a DC value equal to the average of the two polarization voltages, which is close to zero. Figure 5 and 6 show the SEM views of the fabricated SiBAR capacitive filters at 61.9MHz and 145.6MHz and their measured frequency response using a network analyzer with 50Ω terminations. It is clear in these measurement results that the peaks of the two individual resonators are coupled together by the coupling capacitor to form a filter. The filters both show very high-Q at VHF range. f=61.9MHz BW=3.3 KHz IL=35dB Q=18,600
to a half circuit with one resonator and a series capacitor Cc/2 to ground. The series capacitor reduces the total capacitance of the RLC tank, causing the second resonance mode to have a higher frequency given by Equation 4:
f1 = f 0 1 +
2C Cc
(4)
where f0 is the mechanical resonant frequency of the individual resonators, and C is the resonator equivalent series capacitance.
Fig 7(a). Electrical schematic diagram of a SiBAR resonator
Fig 7(b). Electrical schematic diagram of a capacitively-coupled SiBAR filter Fig 5(a). SEM view of a capacitive filter consisting of two coupled 68µm x 544µm x 20µm resonators
Fig 5(b). Measured frequency response of a 61.9MHz capacitive SiBAR filter in vacuum. f=145.6MHz BW=10.9 KHz IL=52dB Q=13,300
Fig 6(a). SEM view of a capacitive filter consisting of two coupled 27µm x 270µm x 20µm resonators
Fig 6(b). Measured frequency response of a 145.6MHz capacitive SiBAR filter in air.
III. ELECTRICAL EQUIVALENT CIRCUIT Figure 7a shows the equivalent circuit model of a two-port SiBAR resonator, where Ci and Co are the drive and sense electrode capacitance respectively. This is a simple series RLC tank where L and C are cancelled out at resonance. Figure 7b shows the model of a 2nd order coupled filter, where Cc is the coupling capacitor [7]. Looking at the frequency response of this two-resonator system, the first resonance occurs at the mechanical resonant frequency of the individual resonators. At the 1st resonance, as shown in Figure 7c, the two resonators resonate in phase and the coupling capacitor has negligible contribution (while Cc is being charged by the first resonator, the other resonator is discharging it). At the 2nd resonance, as shown in Figure 7d, the two resonators operate with a 180° phase difference and hence the coupling capacitor comes into play (it is being charged and discharged at the same time by both resonators). Under ideal conditions, the two SiBARs act exactly similar in this mode. Due to this symmetry, the system can be reduced
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Fig 7(c). 1st resonance mode of capacitive SiBAR filter
Fig 7(d). 2nd resonance mode of capacitive SiBAR filter
In practice under non-ideal conditions, the system is not always symmetric. In most situations the two SiBARs will have slightly different RLC parameters. Electrostatic tuning of the resonator center frequency by applying different DC polarization voltages can compensate the frequency difference to some extent, but for higher frequency bulk mode resonators frequency mismatch compensation could require very high polarization voltage values making it non-practical. In such cases a perfect coupling between the two resonators can not be achieved and two distinctive peaks from the resonators will be observed. From Equation 4 we can see that a large coupling capacitor will cause the two peaks to be closer to each other, and it is still true in the non-ideal situation assuming that the only thing changed is the coupling capacitor. IV. FILTER BANDWIDTH TUNING A major advantage of electrical based resonator coupling techniques compared to the mechanical approach is the higher tunability provided by the bias voltages. As shown in [7] both filter center frequency and separation of the two resonance modes (and therefore filter bandwidth) can be tuned by changing the polarization voltages. Figure 8 shows the measurement results of a SiBAR filter and the effect of change in polarization voltages on it. This filter consists of two 27µm wide, 20µm thick resonators and its center frequency is around 145.6MHz. Three different sets of DC polarization voltages were applied to the device. By
2007 IEEE Ultrasonics Symposium
increasing the polarization voltages, the two peaks of this filter gradually come closer to each other and then overlap, causing the bandwidth of the system shrinks from 23KHz to 11KHz.
(a)
BW=23KHz Q=6,300 IL=63dB
V. CONCLUSION AND FUTURE WORK This work reported on high-Q capacitively-coupled VHF SiBAR filters with center frequency up to 145MHz. Preliminary measurement results identified that changing the DC polarization voltages on individual resonators is an effective technique for tuning the filter bandwidth. Future work includes further investigations on electrostatic tuning of the filter bandwidth and detailed functions of the coupling capacitor, as well as reducing the insertion loss of the filter system by impedance matching and parasitic capacitance cancellation.
Vp1=24V, Vp2=-18V
(b)
However, the shift in the frequency of the resonator with the larger voltage is larger and one peak moves faster than the other under the same amount of change in polarization voltages, which will cause these two peaks to eventually overlap.
BW=20KHz Q=7,400 IL=61dB
ACKNOWLEDGMENT The authors would like to thank the staff at the Georgia Tech Microelectronics Research Center for their assistance. REFERENCES [1]
Vp1=28V, Vp2=-20V
(c)
[2]
BW=11KHz Q=13,300 IL=52dB
[3]
[4]
[5]
Vp1=32V, Vp2=-28V Fig 8. Filter bandwidth tuning measurement results in air with 50Ω terminations by changing polarization voltages.
[6]
It is obvious that the electrostatic tuning should drive both the two peaks towards the same direction based on Equation 3, and we see that both center frequencies of the peaks decrease by increasing the polarization voltages in our measurements.
1652
[7]
“Ultra-miniaturized and high performance PCS SAW duplexer with steep cut-off filters”, MTT-S 2004, Vol. 2, pp.913-916. R. C. Ruby, et al, “Thin film bulk wave acoustic resonators (FBAR) for wireless applications”, Ultrasonics Symposium, 2001, Vol. 1, pp. 813– 821. S. Pourkamali, G. K. Ho and F. Ayazi, “Low-Impedance VHF and UHF Capacitive Silicon Bulk Acoustic Wave Resonators—Part I: Concept and Fabrication,” IEEE Transactions on Electron Devices, Vol. 54, Issue: 8, Aug. 2007, pp. 2017 – 2023. S. Pourkamali, G. K. Ho and F. Ayazi, “Low-Impedance VHF and UHF Capacitive Silicon Bulk Acoustic Wave Resonators—Part II: Measurement and Characterization,” IEEE Transactions on Electron Devices, Vol. 54, Issue: 8, Aug. 2007, pp. 2024 – 2030. S. Pourkamali, et al, “High-Q single crystal silicon HARPSS capacitive beam resonators with self-aligned sub-100nm transduction gaps,” Journal of Micro Electro Mechanical Systems, Vol. 12, Issue 4, August 2003, pp. 487-496. S. Pourkamali, et al, “VHF single crystal silicon capacitive elliptic bulkmode disk resonators part II: implementation and characterization”, Journal of Micro Electro Mechanical Systems, Vol. 13, Issue 6, December 2004, pp. 1054-1062. S. Pourkamali and F. Ayazi, "Electrically Coupled MEMS Bandpass Filters Part I: With Coupling Element," Journal of Sensors and Actuators A, Aug. 2005, pp. 307-316.
2007 IEEE Ultrasonics Symposium
