Linear Acoustic B Suppression in P Bandgap Arrays for Spuri ...
Linear Acoustic B Bandgap Arrays for Spuriious Mode Suppression in P Piezoelectric MEMS Resonators Logann Sorenson, Jenna Fu, and Farrokh Ayazi Schoool of Electrical and Computer Engineering Georgia Institute of Technology Atlanta, Georgia, USA [email protected] Abstract— In this work, we present a techn nique that utilizes arrays of coupled-ring linear acoustic bandgap (LAB) structures, which exhibit characteristic frequeency stop bands, to reduce spurious modes in the wide-band resp ponse of AlN-on-Si lateral mode resonators. Aggressive LAB tetheering (one support per finger) of high-order modes yields an increase in atmospheric quality factor (Q) from 1860 to 2890 for the designed peak at 209 MHz, compared too resonators with traditional tethers. Spurious modes from 0 to 360 MHz are suppressed by at least 30 dB relative to the maain peak. The LAB structures presented achieve this goal through h a combination of complete acoustic bandgaps and deaf bands.
I.
INTRODUCTION
Today’s mobile devices are becom ming increasingly powerful as a result of the incorporation of multiple wireless frequency standards into a single handheld uunit. Applications such as wireless internet, GSM/CDMA voicce networks, GPS navigation, and BlueTooth/ZigBee interdevicce networking are already included in many mobile phones. Fuuture applications will be enabled by emerging frequency stanndards (e.g., IEEE 802.15 wireless personal area networks [1]). Mobile phones may soon feature personal health monitoriing through body area networks (BANs) [2]. To support integration of these standardds into consumer products, microelectromechanical systtems (MEMS) resonators, which offer several advantages foor RF applications including small size, high mechanical qualitty factor (Q), and low loss, can be configured in the locall oscillators of a wireless transceiver. Furthermore, lithogrraphically-defined frequencies of certain MEMS resonators enable multiple frequency standards to be implemented on thhe same substrate. A typical MEMS oscillator consists of a MEMS resonator connected in the feedback path of a transimppedance amplifier (TIA) (Fig. 1a). While piezoelectric MEMS resonatorss can be easily interfaced with low-power electronics, thhe appearance of sufficiently strong low-Q spurious modes nnear the designed operation frequency can cause degrraded oscillator performance. Oscillator phase and gain condditions may cause the spurious mode to become preferred over the desired mode during start-up, causing the oscillator to lockk into the spurious mode. Additionally, feedthrough and couppling between the desired and the spurious modes can degrrade phase noise
(a)
(b)
Figure 1. (a) Schematic of MEMS oscillato or with resonator in feedback with CMOS TIA; (b) Transmission plot rep presentation showing negative feedthrough and coupling effects of a spuriou us mode occurring close to the desired resonance peak.
performance and increase frequency y instability, depending on the proximity of the spur (Fig. 1b) [3]. Therefore, it is essential to elim minate wide-band spurious modes in piezoelectric micromechan nical resonators for use in oscillators [4]. The linear acoustic bandgap b (LAB) structures presented in this work may be used d to achieve this goal by creating support structures that utilize u a combination of complete acoustic bandgaps [5] and deaf bands [6] to suppress the spurious modes without loweriing the Q of the desired mode. II.
NDGAP STRUCTURES LINEAR ACOUSTIC BAN
LAB structures are one-dimen nsional phononic crystals (PCs) with small cross-sectional dim mensions perpendicular to the axis of the 1D lattice. The cou upled-ring LAB structure presented in this work is a linear ch hain of rings connected by narrow beams, repeated at a characteeristic distance a known as the lattice constant (Fig. 2). This perriodically-repeated section is termed the basis of the 1D PC. The ring inner and outer w and layer thicknesses di radii (ri , ro), coupling beam width w, parameterize the basis dimensions. The periodic nature of the 1D PC combined with large acoustic mismatch at the solid/air interface creates acoustic bandgaps, or frequencies of no allowed acoustic propagation (shaded blue in Fig. 3). In additiion to complete acoustic bandgaps, “deaf bands” [6] can also o be found in the coupledring LAB structure dispersion chaaracteristic. These bands
PML
PML
QSupport = 1484
Figure 2. Schematic and 3D view of coupled-ring LAB structure with AlNon-Si stack (a = 20 µm, ri = 4 µm, ro = 8 µm, w = 2 µm, dSi = 10 µm, dAlN = 1 µm, dMo = 100 nm).
(a) PML
PML
Frequency [MHz] R
0
100
200
300
400
(a)
QSupport = 331,805 (b)
X
Figure 4. COMSOL PML simulation for a device with three support pairs; (a) simple tethers; (b) LAB tethers. PML
PML
QSupport = 21,723
(b)
(c)
Figure 3. (a) Acoustic dispersion curve for AlN-on-Si coupled-ring linear acoustic bandgap (LAB) structure (bandgaps shaded blue); (b, c) mode shapes of indicated bands showing displacement polarization orthogonal to the axis of the LAB structure.
demonstrate minimal coupling to the LAB structure when waves from the acoustic source exhibit orthogonal polarization to the mode of the LAB structure at the boundary between the two components. The mode shapes of two such deaf bands are depicted in Fig. 3, where the acoustic source is a longitudinal acoustic wave propagating orthogonally to the axis of the coupled-ring LAB structure. For these modes, displacement corresponding to the polarization of the longitudinal wave is effectively zero on the exposed faces of the coupling beam, meaning these bands of the LAB structure are deaf to the longitudinal waves propagating in this direction. Thus, LAB structures and integrated devices must be carefully designed to maximize the attenuation effects provided by complete acoustic bandgaps as well as deaf bands. III.
DEVICE DESIGN AND FABRICATION
LAB structures can serve as Q-enhancing support elements for MEMS resonators by tailoring bandgaps and deaf bands to confine acoustic energy within the device at the desired operation frequency. This confinement of energy enables an aggressive tethering approach using LAB structures, where one pair of tethers is used for each finger of the interdigitated transducer, to simultaneously improve the support loss component of Q (Qsupport) and provide significant attenuation of spurious modes which lie outside of the designed bandgaps. A. Qsupport Enhancement via Aggressive LAB Tethering The perfectly matched layer (PML) method was employed in COMSOL finite element software to study the effect of aggressive tethering on resonator support loss [7]. PMLs are
PML
(a)
PML
QSupport = 2,489,724 (b)
Figure 5. COMSOL PML simulation for an infinite order device; periodic boundary conditions are applied to the appropriate faces of the device to emulate infinite extent; (a) simple tethers; (b) LAB tethers.
additional artificial domains attached to the device which absorb incoming acoustic waves and emulate loss of acoustic energy into the substrate surrounding the device. In this way, PMLs give an estimation of the theoretical lower bound on Qsupport. Figure 4 shows the results of applying PMLs to an 11th order, 20 μm pitch, 220 μm wide AlN-on-Si resonator, comparing both traditional simple beam support tethers and six periods of coupled-ring LAB supports. For both designs, three pairs of support tethers are used to minimize the number of parallel acoustic leakage paths while maintaining sufficient structural support. To avoid acoustic mismatch, the PML domains were created by extending the cross-section of the support tethers by a certain distance known as the PML length. In addition to this length, there are several parameters in the PML implementation of COMSOL which must be swept to obtain accurate values for the support loss. Additionally, a sufficiently fine mesh is needed to ensure convergence of the support loss value. Sweeping these parameters enables exploration of the PML design space to determine the lower bound of Qsupport. Because reflections and confinement of acoustic energy due to material mismatch are neglected in simulation, the PML result underestimates the value of Qsupport (i.e., the values obtained from the PML method are lower than those obtained in reality).
Figure 6. SEM image of fabricated LAB ring tether array.
With these considerations in mind, the Qsupport for the 11thorder resonator with three pairs of simple teethers is estimated to be 1484 (Fig. 4a), while a Qsupport of 331,8805 is obtained for the same device with LAB tethers, showinng over 200-fold improvement of support loss (Fig. 4b). Noote that the mode shape in Fig. 4a shows deterioration, and a wave-like pattern develops along the supported edge off the resonator. Comparison of these results with other sets of PML parameters shows that as Qsupport is increasedd, the mode shape of the design in Fig. 4a approaches that of F Fig. 4b, where the rippling along the supported edge is less appparent, suggesting that the support loss can have localizedd impact on the resonator mode shape. Figure 5 studies a device that uses onee pair of support tethers per finger of the interdigitated transdducer structure. In addition to the PML method, periodic bounddary conditions are employed to reduce the number of fingeers to two. This effectively models an infinite order resonnator and greatly reduces required computation time to calcuulate Qsupport (each support contributes a large number of elem ments). The high number of support tethers confines the modde more closely to the resonator body and nearly eliminates thee waves along the supported edge. The confinement also reducces the number of possible resonance modes in the vicinity of tthe desired mode, which translates into higher Qsupport, even in the traditional tether case. Over 100-fold improvementt is obtained in simulation by employing aggressive LAB tetthers, boosting the estimated Qsupport from 21,723 to 2,489,724 (F Fig. 5). B. Fabrication Process Flow Devices were fabricated on a silicon-oon-insulator (SOI) substrate with 10-µm device layer thickkness (dSi). The piezoelectric stack, which consists of 100-nnm Mo electrodes and 1-µm thick AlN, was deposited directtly on the silicon device layer and subsequently patterned to ddefine the top Mo and provide access to the bottom Mo forr grounding. The resonator shape, including LAB ring tetherss, was defined by RIE etching the piezoelectric stack and B Bosch etching the device layer to maintain straight sidewalls. The devices were released by etching the handle silicon layer and removing the EM image of an buried oxide (BOX) layer. A close-up SE aggressive LAB tether array is shown in Figg. 6. SEM images of fabricated devices with simple tethers and LAB tether
Figure 7. SEM images of 11th-order, 20 μm μ pitch AlN-on-Si resonators fabricated on 10 μm SOI wafers: (left) 3 paiirs of traditional beam supports (20 μm x 2 μm); (right) 11 pairs of 6 period coupled-ring c LAB supports.
L resonators arrays are shown in Fig. 7. The LAB-supported have six periods per support tether. Because the LAB support array provides Q enhancement of inssertion loss (IL), the width of the resonator body was decreased.. IV.
EXPERIMENTA AL RESULTS
To quantify the impact of the LAB support array, the devices of Fig. 7 were measured on a Cascade Microtech Summit 12000 M probe station at atmospheric pressure and room temperature. The data weree taken with an Agilent N5241a PNA-X network analyzer in two-port configuration. bserve the wide-spectrum A 1 GHz span was measured to ob response of both devices (Fig. 8). All A spurious modes below 360 MHz are suppressed by at leaast 30 dB relative to the desired mode, which lies near 209.5 MHz. A few spurs are Hz as a result of acoustic amplified in the range 150-250 MH confinement introduced by the LAB B support array; however, they are not large enough to impact oscillator operation at the desired peak. pression in the vicinity of In addition to spurious mode supp the desired peak, at least 25 dB of suppression s is obtained at higher frequencies between 360 MHz M and 680 MHz. The cluster of spurious modes near 370 MHz M is well-suppressed in IL compared to the reference deevice. There is also an acoustically quiet section of the freq quency spectrum from 380 MHz to 480 MHz in the LAB-su upported resonator, when compared to several spurious modes in the reference response. M in the LAB-supported A spurious mode is found at 680 MHz case. It is not clear if a relationship exists between this mode n that vicinity; however, it and the reference spurious modes in may indicate a bandgap or deaf band b introduced by LAB structures at that frequency. c about the desired Figure 9 shows a 50 MHz span centered mode. The LAB array has completeely removed a spur on the high-frequency side of the referencee device peak. Underlying modes are boosted by the LAB tetthers but remain near the noise floor and will have minim mal effect on oscillator performance. Finally, Figure 10 givees a narrow-span (2 MHz) measurement of the main peaks forr both reference and LAB array devices. The LAB array is fou und to improve the device Q by almost 60% from 1860 to 2890.
Desired mo ode > 25 dB suppression
> 30 dB suppression
S Simple tethers
LAB ring tethers
Figure 8. Measured S21 response showing wide-bandd spurious suppression. Below 360 MHz, spurious modes are suppressed d at least 30 dB relative to the desired mode. Betweenn 360 MHz and 680 MHz, spurious modes are suppressed at least 25 dB..
S Simple tethers
LAB ring tethers
Figure 9. Medium-span (50 MHz) response for booth devices at 210 MHz.
V.
DISCUSSION
Comparison of the measured Q value withh the QSupport value predicted by COMSOL finite element PML L simulations for the simple tether case (Fig. 10 vs. Figg. 4a) yields the conclusion that support loss simulations are accurate to about 20%. However, this particular case ignoress reflections back into the resonator body from materiall and geometry mismatches in the support structure. In that context, COMSOL PML simulations predict the lower boundd of the Q value, which is accurate for support loss limited resoonators.
Figure 10. Narrow-span (2 MHz) responsee for both devices at 210 MHz.
However, the predicted QSupportt for the LAB-enhanced resonator was in the millions, whereaas the measured value was still limited to a few thousand (Fig. 10 vs. Fig. 5b). In highorder piezoelectric MEMS resonato ors, a large component of the dissipation can be attributeed to the piezoelectric transduction stack [8]. LAB array supports nearly eliminate support loss, which causes other facctors to become dominant in the expression of the overall Q:
ܳ ൌ ொ
ଵ
ೄೠೝ
ொ
ଵ ೀೝ
ିଵ
൨
(1)
Finally, the enhanced Q of the LAB supported device also improves the device IL, enabling a reduced transduction area for similar levels of IL. Thus, LAB structures can be incorporated into MEMS resonators without significantly increasing device area. VI.
CONCLUSION
In this work, we have presented aggressive tethering of MEMS resonators with LAB arrays to control and suppress spurious modes which negatively impact MEMS oscillator performance. We have also used the PML method to predict the lower bound of support loss contribution to overall resonator Q, and demonstrated that this approach agrees well with measured experimental values when the resonator is support-loss limited. ACKNOWLEDGMENT This work was supported by Integrated Device Technology, Inc. The authors would like to thank the OEM Group for AlN deposition, the staff at the Georgia Tech NRC for fabrication support, and Dr. Saeed Mohammadi for helpful discussions.
REFERENCES [1]
[2] [3] [4]
[5]
[6]
[7] [8]
IEEE Std 802.15.1™-2005, "IEEE Standard for Information technology—Telecommunications and information exchange between systems—Local and metropolitan area networks—Specific requirements; Part 15.1: Wireless medium access control (MAC) and physical layer (PHY) specifications for wireless personal area networks (WPANs)," ed, 2005. T.G. Zimmerman, "Personal area networks: near-field intrabody communication," IBM Systems Journal, vol. 35, 1996, pp. 609-617. M.E. Tobar, "Effects of spurious modes in resonant cavities," Journal of Physics D: Applied Physics, vol. 26, 1993, p. 2022. R. Abdolvand, H. Lavasani, G. Ho, and F. Ayazi, "Thin-film piezoelectric-on-silicon resonators for high-frequency reference oscillator applications," IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control, vol. 55, 2008, pp. 2596-2606. S. Mohammadi, AA Eftekhar, A. Khelif, H. Moubchir, R. Westafer, WD Hunt, and A. Adibi, "Complete phononic bandgaps and bandgap maps in two-dimensional silicon phononic crystal plates," Electronics Letters, vol. 43, 2007, pp. 898-899. Fu-Li Hsiao, Abdelkrim Khelif, Hanane Moubchir, Abdelkrim Choujaa, Chii-Chang Chen, and Vincent Laude, "Complete band gaps and deaf bands of triangular and honeycomb water-steel phononic crystals," Journal of Applied Physics, vol. 101, 2007, pp. 044903-5. W. Chu and Q. Liu, "Perfectly matched layers for elastodynamics: A new absorbing boundary condition," J. Comp. Acoustics, vol. 4, 1996, pp. 341–359. Farrokh Ayazi, Logan Sorenson, and Roozbeh Tabrizian, "Energy Dissipation in Micromechanical Resonators," in Proc. SPIE, 2011, pp. 1-13.
I.
INTRODUCTION
Today’s mobile devices are becom ming increasingly powerful as a result of the incorporation of multiple wireless frequency standards into a single handheld uunit. Applications such as wireless internet, GSM/CDMA voicce networks, GPS navigation, and BlueTooth/ZigBee interdevicce networking are already included in many mobile phones. Fuuture applications will be enabled by emerging frequency stanndards (e.g., IEEE 802.15 wireless personal area networks [1]). Mobile phones may soon feature personal health monitoriing through body area networks (BANs) [2]. To support integration of these standardds into consumer products, microelectromechanical systtems (MEMS) resonators, which offer several advantages foor RF applications including small size, high mechanical qualitty factor (Q), and low loss, can be configured in the locall oscillators of a wireless transceiver. Furthermore, lithogrraphically-defined frequencies of certain MEMS resonators enable multiple frequency standards to be implemented on thhe same substrate. A typical MEMS oscillator consists of a MEMS resonator connected in the feedback path of a transimppedance amplifier (TIA) (Fig. 1a). While piezoelectric MEMS resonatorss can be easily interfaced with low-power electronics, thhe appearance of sufficiently strong low-Q spurious modes nnear the designed operation frequency can cause degrraded oscillator performance. Oscillator phase and gain condditions may cause the spurious mode to become preferred over the desired mode during start-up, causing the oscillator to lockk into the spurious mode. Additionally, feedthrough and couppling between the desired and the spurious modes can degrrade phase noise
(a)
(b)
Figure 1. (a) Schematic of MEMS oscillato or with resonator in feedback with CMOS TIA; (b) Transmission plot rep presentation showing negative feedthrough and coupling effects of a spuriou us mode occurring close to the desired resonance peak.
performance and increase frequency y instability, depending on the proximity of the spur (Fig. 1b) [3]. Therefore, it is essential to elim minate wide-band spurious modes in piezoelectric micromechan nical resonators for use in oscillators [4]. The linear acoustic bandgap b (LAB) structures presented in this work may be used d to achieve this goal by creating support structures that utilize u a combination of complete acoustic bandgaps [5] and deaf bands [6] to suppress the spurious modes without loweriing the Q of the desired mode. II.
NDGAP STRUCTURES LINEAR ACOUSTIC BAN
LAB structures are one-dimen nsional phononic crystals (PCs) with small cross-sectional dim mensions perpendicular to the axis of the 1D lattice. The cou upled-ring LAB structure presented in this work is a linear ch hain of rings connected by narrow beams, repeated at a characteeristic distance a known as the lattice constant (Fig. 2). This perriodically-repeated section is termed the basis of the 1D PC. The ring inner and outer w and layer thicknesses di radii (ri , ro), coupling beam width w, parameterize the basis dimensions. The periodic nature of the 1D PC combined with large acoustic mismatch at the solid/air interface creates acoustic bandgaps, or frequencies of no allowed acoustic propagation (shaded blue in Fig. 3). In additiion to complete acoustic bandgaps, “deaf bands” [6] can also o be found in the coupledring LAB structure dispersion chaaracteristic. These bands
PML
PML
QSupport = 1484
Figure 2. Schematic and 3D view of coupled-ring LAB structure with AlNon-Si stack (a = 20 µm, ri = 4 µm, ro = 8 µm, w = 2 µm, dSi = 10 µm, dAlN = 1 µm, dMo = 100 nm).
(a) PML
PML
Frequency [MHz] R
0
100
200
300
400
(a)
QSupport = 331,805 (b)
X
Figure 4. COMSOL PML simulation for a device with three support pairs; (a) simple tethers; (b) LAB tethers. PML
PML
QSupport = 21,723
(b)
(c)
Figure 3. (a) Acoustic dispersion curve for AlN-on-Si coupled-ring linear acoustic bandgap (LAB) structure (bandgaps shaded blue); (b, c) mode shapes of indicated bands showing displacement polarization orthogonal to the axis of the LAB structure.
demonstrate minimal coupling to the LAB structure when waves from the acoustic source exhibit orthogonal polarization to the mode of the LAB structure at the boundary between the two components. The mode shapes of two such deaf bands are depicted in Fig. 3, where the acoustic source is a longitudinal acoustic wave propagating orthogonally to the axis of the coupled-ring LAB structure. For these modes, displacement corresponding to the polarization of the longitudinal wave is effectively zero on the exposed faces of the coupling beam, meaning these bands of the LAB structure are deaf to the longitudinal waves propagating in this direction. Thus, LAB structures and integrated devices must be carefully designed to maximize the attenuation effects provided by complete acoustic bandgaps as well as deaf bands. III.
DEVICE DESIGN AND FABRICATION
LAB structures can serve as Q-enhancing support elements for MEMS resonators by tailoring bandgaps and deaf bands to confine acoustic energy within the device at the desired operation frequency. This confinement of energy enables an aggressive tethering approach using LAB structures, where one pair of tethers is used for each finger of the interdigitated transducer, to simultaneously improve the support loss component of Q (Qsupport) and provide significant attenuation of spurious modes which lie outside of the designed bandgaps. A. Qsupport Enhancement via Aggressive LAB Tethering The perfectly matched layer (PML) method was employed in COMSOL finite element software to study the effect of aggressive tethering on resonator support loss [7]. PMLs are
PML
(a)
PML
QSupport = 2,489,724 (b)
Figure 5. COMSOL PML simulation for an infinite order device; periodic boundary conditions are applied to the appropriate faces of the device to emulate infinite extent; (a) simple tethers; (b) LAB tethers.
additional artificial domains attached to the device which absorb incoming acoustic waves and emulate loss of acoustic energy into the substrate surrounding the device. In this way, PMLs give an estimation of the theoretical lower bound on Qsupport. Figure 4 shows the results of applying PMLs to an 11th order, 20 μm pitch, 220 μm wide AlN-on-Si resonator, comparing both traditional simple beam support tethers and six periods of coupled-ring LAB supports. For both designs, three pairs of support tethers are used to minimize the number of parallel acoustic leakage paths while maintaining sufficient structural support. To avoid acoustic mismatch, the PML domains were created by extending the cross-section of the support tethers by a certain distance known as the PML length. In addition to this length, there are several parameters in the PML implementation of COMSOL which must be swept to obtain accurate values for the support loss. Additionally, a sufficiently fine mesh is needed to ensure convergence of the support loss value. Sweeping these parameters enables exploration of the PML design space to determine the lower bound of Qsupport. Because reflections and confinement of acoustic energy due to material mismatch are neglected in simulation, the PML result underestimates the value of Qsupport (i.e., the values obtained from the PML method are lower than those obtained in reality).
Figure 6. SEM image of fabricated LAB ring tether array.
With these considerations in mind, the Qsupport for the 11thorder resonator with three pairs of simple teethers is estimated to be 1484 (Fig. 4a), while a Qsupport of 331,8805 is obtained for the same device with LAB tethers, showinng over 200-fold improvement of support loss (Fig. 4b). Noote that the mode shape in Fig. 4a shows deterioration, and a wave-like pattern develops along the supported edge off the resonator. Comparison of these results with other sets of PML parameters shows that as Qsupport is increasedd, the mode shape of the design in Fig. 4a approaches that of F Fig. 4b, where the rippling along the supported edge is less appparent, suggesting that the support loss can have localizedd impact on the resonator mode shape. Figure 5 studies a device that uses onee pair of support tethers per finger of the interdigitated transdducer structure. In addition to the PML method, periodic bounddary conditions are employed to reduce the number of fingeers to two. This effectively models an infinite order resonnator and greatly reduces required computation time to calcuulate Qsupport (each support contributes a large number of elem ments). The high number of support tethers confines the modde more closely to the resonator body and nearly eliminates thee waves along the supported edge. The confinement also reducces the number of possible resonance modes in the vicinity of tthe desired mode, which translates into higher Qsupport, even in the traditional tether case. Over 100-fold improvementt is obtained in simulation by employing aggressive LAB tetthers, boosting the estimated Qsupport from 21,723 to 2,489,724 (F Fig. 5). B. Fabrication Process Flow Devices were fabricated on a silicon-oon-insulator (SOI) substrate with 10-µm device layer thickkness (dSi). The piezoelectric stack, which consists of 100-nnm Mo electrodes and 1-µm thick AlN, was deposited directtly on the silicon device layer and subsequently patterned to ddefine the top Mo and provide access to the bottom Mo forr grounding. The resonator shape, including LAB ring tetherss, was defined by RIE etching the piezoelectric stack and B Bosch etching the device layer to maintain straight sidewalls. The devices were released by etching the handle silicon layer and removing the EM image of an buried oxide (BOX) layer. A close-up SE aggressive LAB tether array is shown in Figg. 6. SEM images of fabricated devices with simple tethers and LAB tether
Figure 7. SEM images of 11th-order, 20 μm μ pitch AlN-on-Si resonators fabricated on 10 μm SOI wafers: (left) 3 paiirs of traditional beam supports (20 μm x 2 μm); (right) 11 pairs of 6 period coupled-ring c LAB supports.
L resonators arrays are shown in Fig. 7. The LAB-supported have six periods per support tether. Because the LAB support array provides Q enhancement of inssertion loss (IL), the width of the resonator body was decreased.. IV.
EXPERIMENTA AL RESULTS
To quantify the impact of the LAB support array, the devices of Fig. 7 were measured on a Cascade Microtech Summit 12000 M probe station at atmospheric pressure and room temperature. The data weree taken with an Agilent N5241a PNA-X network analyzer in two-port configuration. bserve the wide-spectrum A 1 GHz span was measured to ob response of both devices (Fig. 8). All A spurious modes below 360 MHz are suppressed by at leaast 30 dB relative to the desired mode, which lies near 209.5 MHz. A few spurs are Hz as a result of acoustic amplified in the range 150-250 MH confinement introduced by the LAB B support array; however, they are not large enough to impact oscillator operation at the desired peak. pression in the vicinity of In addition to spurious mode supp the desired peak, at least 25 dB of suppression s is obtained at higher frequencies between 360 MHz M and 680 MHz. The cluster of spurious modes near 370 MHz M is well-suppressed in IL compared to the reference deevice. There is also an acoustically quiet section of the freq quency spectrum from 380 MHz to 480 MHz in the LAB-su upported resonator, when compared to several spurious modes in the reference response. M in the LAB-supported A spurious mode is found at 680 MHz case. It is not clear if a relationship exists between this mode n that vicinity; however, it and the reference spurious modes in may indicate a bandgap or deaf band b introduced by LAB structures at that frequency. c about the desired Figure 9 shows a 50 MHz span centered mode. The LAB array has completeely removed a spur on the high-frequency side of the referencee device peak. Underlying modes are boosted by the LAB tetthers but remain near the noise floor and will have minim mal effect on oscillator performance. Finally, Figure 10 givees a narrow-span (2 MHz) measurement of the main peaks forr both reference and LAB array devices. The LAB array is fou und to improve the device Q by almost 60% from 1860 to 2890.
Desired mo ode > 25 dB suppression
> 30 dB suppression
S Simple tethers
LAB ring tethers
Figure 8. Measured S21 response showing wide-bandd spurious suppression. Below 360 MHz, spurious modes are suppressed d at least 30 dB relative to the desired mode. Betweenn 360 MHz and 680 MHz, spurious modes are suppressed at least 25 dB..
S Simple tethers
LAB ring tethers
Figure 9. Medium-span (50 MHz) response for booth devices at 210 MHz.
V.
DISCUSSION
Comparison of the measured Q value withh the QSupport value predicted by COMSOL finite element PML L simulations for the simple tether case (Fig. 10 vs. Figg. 4a) yields the conclusion that support loss simulations are accurate to about 20%. However, this particular case ignoress reflections back into the resonator body from materiall and geometry mismatches in the support structure. In that context, COMSOL PML simulations predict the lower boundd of the Q value, which is accurate for support loss limited resoonators.
Figure 10. Narrow-span (2 MHz) responsee for both devices at 210 MHz.
However, the predicted QSupportt for the LAB-enhanced resonator was in the millions, whereaas the measured value was still limited to a few thousand (Fig. 10 vs. Fig. 5b). In highorder piezoelectric MEMS resonato ors, a large component of the dissipation can be attributeed to the piezoelectric transduction stack [8]. LAB array supports nearly eliminate support loss, which causes other facctors to become dominant in the expression of the overall Q:
ܳ ൌ ொ
ଵ
ೄೠೝ
ொ
ଵ ೀೝ
ିଵ
൨
(1)
Finally, the enhanced Q of the LAB supported device also improves the device IL, enabling a reduced transduction area for similar levels of IL. Thus, LAB structures can be incorporated into MEMS resonators without significantly increasing device area. VI.
CONCLUSION
In this work, we have presented aggressive tethering of MEMS resonators with LAB arrays to control and suppress spurious modes which negatively impact MEMS oscillator performance. We have also used the PML method to predict the lower bound of support loss contribution to overall resonator Q, and demonstrated that this approach agrees well with measured experimental values when the resonator is support-loss limited. ACKNOWLEDGMENT This work was supported by Integrated Device Technology, Inc. The authors would like to thank the OEM Group for AlN deposition, the staff at the Georgia Tech NRC for fabrication support, and Dr. Saeed Mohammadi for helpful discussions.
REFERENCES [1]
[2] [3] [4]
[5]
[6]
[7] [8]
IEEE Std 802.15.1™-2005, "IEEE Standard for Information technology—Telecommunications and information exchange between systems—Local and metropolitan area networks—Specific requirements; Part 15.1: Wireless medium access control (MAC) and physical layer (PHY) specifications for wireless personal area networks (WPANs)," ed, 2005. T.G. Zimmerman, "Personal area networks: near-field intrabody communication," IBM Systems Journal, vol. 35, 1996, pp. 609-617. M.E. Tobar, "Effects of spurious modes in resonant cavities," Journal of Physics D: Applied Physics, vol. 26, 1993, p. 2022. R. Abdolvand, H. Lavasani, G. Ho, and F. Ayazi, "Thin-film piezoelectric-on-silicon resonators for high-frequency reference oscillator applications," IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control, vol. 55, 2008, pp. 2596-2606. S. Mohammadi, AA Eftekhar, A. Khelif, H. Moubchir, R. Westafer, WD Hunt, and A. Adibi, "Complete phononic bandgaps and bandgap maps in two-dimensional silicon phononic crystal plates," Electronics Letters, vol. 43, 2007, pp. 898-899. Fu-Li Hsiao, Abdelkrim Khelif, Hanane Moubchir, Abdelkrim Choujaa, Chii-Chang Chen, and Vincent Laude, "Complete band gaps and deaf bands of triangular and honeycomb water-steel phononic crystals," Journal of Applied Physics, vol. 101, 2007, pp. 044903-5. W. Chu and Q. Liu, "Perfectly matched layers for elastodynamics: A new absorbing boundary condition," J. Comp. Acoustics, vol. 4, 1996, pp. 341–359. Farrokh Ayazi, Logan Sorenson, and Roozbeh Tabrizian, "Energy Dissipation in Micromechanical Resonators," in Proc. SPIE, 2011, pp. 1-13.
