Tunable Silicon Bulk Acoustic Resonators with ... - Semantic Scholar
Tunable Silicon Bulk Acoustic Resonators with Multi-Face AlN Transduction Roozbeh Tabrizian and Farrokh Ayazi School of Electrical and Computer Engineering Georgia Institute of Technology Atlanta, USA [email protected]; [email protected]
Abstract—This paper presents tunable width-extensional mode bulk acoustic resonators that are piezoelectrically-actuated and sensed using thin layers of AlN on the sidewalls as well as the top surface. By using both longitudinal and transverse piezoelectric effects of conformally-sputtered AlN layers on sidewalls and top surface of a 20 m thick resonator, a low motional resistance of ~35 Ω was achieved for a 100 MHz silicon resonator operating in air. The motional resistance is improved by at least 10x compared to similar devices with capacitive transduction. Furthermore, it is shown that the resonance frequency of these piezoelectrically-transduced devices can be tuned by varying the electric signal power from 0 to 7 dBm.
I. INTRODUCTION Lateral bulk acoustic wave (BAW) resonators implemented in single crystal silicon (SCS) are of great interest for signal processing applications. Since the resonance frequencies of such resonators are defined lithographically, devices with multiple frequencies can be implemented in the same batch and integrated with CMOS circuitry. Furthermore, superior acoustic properties of SCS such as high bulk acoustic wave velocity, small intrinsic dissipation in different frequency regimes [1, 2] and extended linear-elastic region alleviate the implementation of resonators with small form factor, improved power handling, and high quality factor (Q). Although advances in micromachining techniques (i.e., fabrication of small capacitive gaps, deposition of high quality piezoelectric thin films, etc.) have enabled the realization of high-frequency SCS BAW resonators [2], large motional resistance of these devices remains a major obstacle to utilize them in low insertion loss filters. Most transduction techniques that have been used to actuate and sense silicon BAW resonators [3-5] require a relatively large DC polarization voltage (Vp) to provide sufficient electromechanical coupling required for low motional resistances. Piezoelectric transduction, on the other hand, has the advantage of high electromechanical coupling without requiring Vp. However, all demonstrations of lateral micromechanical resonators have so far used the transverse piezoelectric coefficient e31 of a planar piezoelectric layer such as AlN [6-9]. While low motional resistances have been demonstrated using this technique for AlN-on-Si resonators [6], achieving low resistances (< 50 Ω) has been challenging due to limited transverse piezoelectric coupling, which is
mainly a result of smaller e31 compared to e33 and small transduction area. To overcome this limitation, high-order modes are used in high-frequency lateral BAW resonators to increase the transduction area, which in turn leads to a larger die area [8]. Moreover, the efficiency of transverse piezoelectric transduction of silicon lateral BAW resonators is significantly degraded by the increase in proportional thickness of silicon in the resonator stack. However, thick silicon substrates are desirable for improvement of Q, power handling and linearity. Furthermore, the resonance frequency of BAW devices with transverse piezoelectric transduction cannot be tuned without sacrificing transduction area and considerably degrading the motional resistance. Using the technique presented here, in addition to the AlN layer on top surface of the resonator AlN layers on the vertical sidewalls of the resonator are simultaneously used to employ the larger longitudinal piezoelectric coefficient e33 to actuate and sense bulk acoustic waves through the resonator sidewalls. In this configuration since Mo electrodes on the sidewalls connect equi-stress areas of AlN layers, charge cancellation is substantially reduced. Moreover, since transduction occurs on two sidewalls in addition to the top surface, it is scalable with resonator thickness which makes this method preferable for high-frequency resonators with small width (frequency-determining dimension). Because the sidewall AlN layers are mainly responsible for actuation and sensing, the top AlN layer can be dedicated to tuning purposes without a considerable reduction in effective transduction area. II.
MULTI-FACE ALN TRANSDUCTION
Figure 1 shows the cross-section of a silicon BAW resonator with multi-face AlN transduction. Since the top and bottom Mo electrodes are conformally deposited over the resonator surface, an input voltage signal results in electric fields ETop and ESW perpendicular to the top surface and sidewalls, respectively. ETop and ESW induce transverse and longitudinal mechanical stress in top and sidewall AlN layers, respectively (Fig. 1a), which results in excitation of the width-extensional bulk acoustic mode (Fig. 2). This resonance mode has an amplified strain in the AlN films on
top and sidewall of the resonator and induces electric charge on the Mo electrodes (Fig. 1b).
TL=e33.ESW
TT =e33.ETop
TL=e33.ESW
(a)
Figure 1: Silicon Bulk Acoustic Resonator (SiBAR) with Mo/AlN/Mo on top surface and sidewalls: (a) actuation mechanism; (b) sense mechanism; (c) resonator cross-section; ETop and ESW are applied electric fields and DT and DL are excited electric-displacement on top and sidewall AlN layers, respectively.
Figure 3: Electrical equivalent circuit for general SiBAR with multi-face AlN considering three ports for electromechanical transduction. V1, V2 and V3 are shorted if the top Mo layer is continuous over the sidewall and top surfaces of the device, resulting in a one-port resonator.
where ASW is the sidewall surface area and AAlN,Top represents the area of the vertical cross-section of top AlN layer. Since the top Mo layer is conformally deposited on the sidewall and top surfaces (Fig. 1), all three ports are electrically connected together; hence, the resonator can be treated as a one-port device. The resonator motional resistance Rm can be estimated from (2):
Rm
Figure 2: Stress field (T) and deformation in two half-cycles of resonance for a SiBAR with multi-face AlN transduction.
III. MODELING Considering each AlN layer (two sidewall layers and one top layer) as a separate electromechanical transducer, a SiBAR with multi-face AlN transduction can be modeled as a three-port device. Figure 3 shows the general form electrical equivalent circuit of the resonator around the first widthextensional mode. In this model, transformers represent the two piezoelectric transduction mechanisms with longitudinal (η1) and transverse (η2) coupling coefficients. In the equivalent circuit of Fig. 3, D1, K1, and M1, and D2, K2, and M2 represent equivalent damping, stiffness and mass of the SiBAR with top AlN and sidewall AlN, respectively. CSW and CTop are the capacitances of sidewall and top AlN layers, respectively. The ratio between η1 and η2 can be estimated from (1):
1 e33 A SW 2 e31 AAlN ,Top
(1)
Dtot (21 2 )2
(2)
where Dtot represents the total mechanical damping in the resonator. Since |e33| ≈ 3|e31| and ASW is much larger than AAlN,Top, η1 is much larger than η2 (in this work η1 ≈ 100η2), implying that actuation and sensing of the bulk acoustic resonance is more efficient using piezoelectric films on the sidewalls rather than the top surface. Thus, bulk acoustic resonators with sidewall piezoelectric transduction should provide a considerably lower Rm than those employing top surface AlN actuation and sensing. Additionally, since η1 is directly proportional to ASW, Rm can be further reduced by increasing resonator thickness. This is a superior advantage of sidewall transduction over top surface transduction, where a piezoelectric layer with large surface area is required to achieve small values of Rm. IV. FABRICATION PROCESS The fabrication process of one-port SiBARs with multi-face AlN layers consists of two masks and three steps (schematically shown in Fig. 4). First, the resonator body is patterned in the silicon device layer of a thick SOI wafer using the Bosch DRIE process. This is followed by thermal oxidation and annealing in N2 ambient at 1100°C to improve the smoothness of sidewalls surface after Bosch DRIE. The BOX layer is then partially etched in HF to prevent deposition of Mo/AlN on the BOX layer in the next step. This is done to allow access of HF to the BOX layer during the final release step. Silicon structures are then covered with RF sputter deposition of a thin AlN layer sandwiched between top and
(a)
(b)
(c)
Bottom Mo
Si resonator body
Ein
Partially etched BOX layer Equi-stress surface
Bottom Mo
AlN
Ein
Top Mo
e31.Ein Ein e33.Ein
Figure 4: Resonator fabrication process: (a) patterning Si device layer and partially etching the BOX layer; (b) deposition of Mo/AlN/Mo layers, etching top Mo and AlN on one pad to expose ground contact; (c) releasing device in HF.
bottom Mo electrodes on the top surface and sidewalls. Then, the top Mo and AlN layers are etched from one pad to access the bottom Mo which serves as an electrical signal ground. Finally, the device is released by etching the BOX layer in HF. Figure 5 shows an SEM image of a fabricated one-port SiBAR with multi-face AlN and schematic of the electrical interface for measurement.
Figure 8 shows the quality and uniformity of sidewall AlN towards the bottom of the resonator. Uniform thickness of the AlN sidewall film results in efficient actuation of the desired width-extensional resonance mode over the entire thickness of the resonator and eliminates charge cancellation in the sensing mechanism.
Figure 5: SEM image of the resonator and electrical interface scheme for measurement.
Figure 7: Continuity of AlN and Mo films from the top surface to sidewalls at the resonator edges.
Figure 6 is the cross-sectional SEM picture of the resonator before release in HF. Figure 7 shows the continuity of AlN and Mo films from the top surface to sidewalls at the edges of the resonator, with sidewall AlN thicknesses approximately half of the top surface AlN.
Mo/AlN/Mo stack
Partially etched BOX layer
Figure 8: Close-up SEM image, detailing the quality and uniformity of sidewall AlN towards the bottom of the resonator.
V. Figure 6: SEM image of the device cross-section; BOX layer partially etched to enable full release in HF.
MEASUREMENT RESULTS
Experimental results are obtained using a vector network analyzer. Fig 9 shows the measured reflection coefficient
(S11) as well as the resonator impedance extracted from S11 response of the one-port resonator of Fig. 5. A quality factor (Q) of 3500 can be extracted from [10]:
Q
X 2R
(3)
where ω is the angular frequency and R and X are the real and imaginary components of resonator impedance, respectively. An Rm of 35 Ω has been achieved at 99.85 MHz, which is at least ten times less than its capacitive and transverse piezoelectric counterparts [3-6].
VI.
CONCLUSION
This work presents very low motional resistance tunable silicon bulk acoustic resonators with piezoelectric AlN layers on the sidewalls and top surface of the resonator. Exploiting the larger longitudinal piezoelectric coefficient of sidewall AlN layers as well as the substantially reduced charge cancellation as a result of the electrode configuration, this technique demonstrates very high transduction efficiency for silicon bulk acoustic resonators. The electrical equivalent model is presented to demonstrate the advantage of this transduction technique as well as the possibility of efficiency improvement by using thick silicon substrates. Resonators with Rm values as low as 35 Ω have been implemented at 100 MHz using a two-mask, three-step fabrication process. The feasibility of tuning these devices without degrading Rm has been demonstrated by sweeping the applied signal power from 0 to 7 dBm. ACKNOWLEDGMENT This work was supported by Integrated Device Technology (IDT). The authors wish to thank the OEM Group for AlN film deposition and the staff at the Nanotechnology Research Center (NRC) at the Georgia Institute of Technology for assistance with microfabrication. REFERENCES
Figure 9: Reflection coefficient (|S11|) of the resonator in Fig. 5; (insets) |S11| resonator impedance and response over a 10 MHz span.
Pin< 0 dbm 2 dbm 4 dbm
4.7 dbm 5 dbm
6 dbm
7 dbm
|S11|(db)
Figure 10 shows the resonator frequency shift for input powers higher than 0 dBm, where leakage current increases in sidewall AlN thin layers [11]. This leakage current changes the electric field boundary condition in the top AlN layer as a result of the finite resistance of the excitation source (schematically shown in the equivalent circuit of Fig. 10 inset). As shown in Fig. 10, tuning does not degrade the amplitude of reflection coefficient (|S11|) and the motional resistance of the one-port device.
Top Mo/AlN/Mo Single Crystal Silicon Sidewall Mo/AlN/Mo
Rleakage
Frequency (MHz) Figure 10: Tuning of AlN-on-Si resonator with input power levels from 0 to 7 dBm; inset shows tuning concept.
[1]
R. Tabrizian, M. Rais-zadeh and F. Ayazi, “Effect of Phonon Interactions on Limiting the f.Q product of micromechanical resonators”, IEEE International Conference on Solid-state Sensors, Actuators and Microsystems (TRANSDUCERS’09), Denver, CO, June 2009, pp. 2131-2134. [2] F. Ayazi, L. Sorenson, and R. Tabrizian, "Energy Dissipation in Micromechanical Resonators," in Proc. SPIE, 2011, pp. 1-13. [3] A. K. Samarao and F. Ayazi, “Quality Factor Sensitivity to Crystallographic Misalignments in Silicon Micromechanical Resonators”, Solid-State Sensors, Actuators, and Microsystems Workshop (Hilton Head 2010), Hilton Head Island, SC, June 2010, pp. 479-482. [4] S. A. Bhave and R. T. Howe, “Internal electrostatic transduction for bulk-mode MEMS resonators”, Solid-State Sensors, Actuators, and Microsystems Workshop (Hilton Head 2004), Hilton Head Island, SC, June, 2004, pp. 59-60. [5] A. Rahafrooz, et al., “Thermal actuation, a suitable mechanism for high-frequency electromechanical resonators”, Proc. 23st IEEE MEMS, Hong Kong, China, Jan. 2010, pp. 200-203. [6] W. Pan and F. Ayazi, “Thin-film piezoelectric-on-substrate resonators with Q enhancement and TCF reduction”, 23rd IEEE MEMS, pp 72730, 2010. [7] M. Rinaldi, et al., “Super-high-frequency two-port AlN contour-mode resonators for RF applications”, Ultrasonic, Ferroelectrics and Frequency Control IEEE Transactions, vol. 57, pp. 38-45, 2010. [8] B. P. Harrington, et al., “Toward ultimate performance in GHz MEMS resonators: Low impedance and high”, Proc. IEEE Micro Electro Mechanical Systems Conference, Jan. 2010, pp. 707–710. [9] G. K. Ho, et al., “Piezoelectric-on-Silicon Lateral Bulk Acoustic Wave Micromechanical Resonators”, IEEE Journal of Microelectromechanical Systems, Vol. 17, No. 2, April 2008, pp. 512520. [10] C.G. Montgomery, et al., “Principles of Microwave Circuits”, New York, McGraw-Hill (1948). [11] F. Martin, P. Muralt, M. A. Dubois, and A. Pezous, “Thickness Dependence of Properties of Highly C-Axis Textured AlN Thin Films”, J. Vac. Sci. Technol. A 22, 361 (2004).
Abstract—This paper presents tunable width-extensional mode bulk acoustic resonators that are piezoelectrically-actuated and sensed using thin layers of AlN on the sidewalls as well as the top surface. By using both longitudinal and transverse piezoelectric effects of conformally-sputtered AlN layers on sidewalls and top surface of a 20 m thick resonator, a low motional resistance of ~35 Ω was achieved for a 100 MHz silicon resonator operating in air. The motional resistance is improved by at least 10x compared to similar devices with capacitive transduction. Furthermore, it is shown that the resonance frequency of these piezoelectrically-transduced devices can be tuned by varying the electric signal power from 0 to 7 dBm.
I. INTRODUCTION Lateral bulk acoustic wave (BAW) resonators implemented in single crystal silicon (SCS) are of great interest for signal processing applications. Since the resonance frequencies of such resonators are defined lithographically, devices with multiple frequencies can be implemented in the same batch and integrated with CMOS circuitry. Furthermore, superior acoustic properties of SCS such as high bulk acoustic wave velocity, small intrinsic dissipation in different frequency regimes [1, 2] and extended linear-elastic region alleviate the implementation of resonators with small form factor, improved power handling, and high quality factor (Q). Although advances in micromachining techniques (i.e., fabrication of small capacitive gaps, deposition of high quality piezoelectric thin films, etc.) have enabled the realization of high-frequency SCS BAW resonators [2], large motional resistance of these devices remains a major obstacle to utilize them in low insertion loss filters. Most transduction techniques that have been used to actuate and sense silicon BAW resonators [3-5] require a relatively large DC polarization voltage (Vp) to provide sufficient electromechanical coupling required for low motional resistances. Piezoelectric transduction, on the other hand, has the advantage of high electromechanical coupling without requiring Vp. However, all demonstrations of lateral micromechanical resonators have so far used the transverse piezoelectric coefficient e31 of a planar piezoelectric layer such as AlN [6-9]. While low motional resistances have been demonstrated using this technique for AlN-on-Si resonators [6], achieving low resistances (< 50 Ω) has been challenging due to limited transverse piezoelectric coupling, which is
mainly a result of smaller e31 compared to e33 and small transduction area. To overcome this limitation, high-order modes are used in high-frequency lateral BAW resonators to increase the transduction area, which in turn leads to a larger die area [8]. Moreover, the efficiency of transverse piezoelectric transduction of silicon lateral BAW resonators is significantly degraded by the increase in proportional thickness of silicon in the resonator stack. However, thick silicon substrates are desirable for improvement of Q, power handling and linearity. Furthermore, the resonance frequency of BAW devices with transverse piezoelectric transduction cannot be tuned without sacrificing transduction area and considerably degrading the motional resistance. Using the technique presented here, in addition to the AlN layer on top surface of the resonator AlN layers on the vertical sidewalls of the resonator are simultaneously used to employ the larger longitudinal piezoelectric coefficient e33 to actuate and sense bulk acoustic waves through the resonator sidewalls. In this configuration since Mo electrodes on the sidewalls connect equi-stress areas of AlN layers, charge cancellation is substantially reduced. Moreover, since transduction occurs on two sidewalls in addition to the top surface, it is scalable with resonator thickness which makes this method preferable for high-frequency resonators with small width (frequency-determining dimension). Because the sidewall AlN layers are mainly responsible for actuation and sensing, the top AlN layer can be dedicated to tuning purposes without a considerable reduction in effective transduction area. II.
MULTI-FACE ALN TRANSDUCTION
Figure 1 shows the cross-section of a silicon BAW resonator with multi-face AlN transduction. Since the top and bottom Mo electrodes are conformally deposited over the resonator surface, an input voltage signal results in electric fields ETop and ESW perpendicular to the top surface and sidewalls, respectively. ETop and ESW induce transverse and longitudinal mechanical stress in top and sidewall AlN layers, respectively (Fig. 1a), which results in excitation of the width-extensional bulk acoustic mode (Fig. 2). This resonance mode has an amplified strain in the AlN films on
top and sidewall of the resonator and induces electric charge on the Mo electrodes (Fig. 1b).
TL=e33.ESW
TT =e33.ETop
TL=e33.ESW
(a)
Figure 1: Silicon Bulk Acoustic Resonator (SiBAR) with Mo/AlN/Mo on top surface and sidewalls: (a) actuation mechanism; (b) sense mechanism; (c) resonator cross-section; ETop and ESW are applied electric fields and DT and DL are excited electric-displacement on top and sidewall AlN layers, respectively.
Figure 3: Electrical equivalent circuit for general SiBAR with multi-face AlN considering three ports for electromechanical transduction. V1, V2 and V3 are shorted if the top Mo layer is continuous over the sidewall and top surfaces of the device, resulting in a one-port resonator.
where ASW is the sidewall surface area and AAlN,Top represents the area of the vertical cross-section of top AlN layer. Since the top Mo layer is conformally deposited on the sidewall and top surfaces (Fig. 1), all three ports are electrically connected together; hence, the resonator can be treated as a one-port device. The resonator motional resistance Rm can be estimated from (2):
Rm
Figure 2: Stress field (T) and deformation in two half-cycles of resonance for a SiBAR with multi-face AlN transduction.
III. MODELING Considering each AlN layer (two sidewall layers and one top layer) as a separate electromechanical transducer, a SiBAR with multi-face AlN transduction can be modeled as a three-port device. Figure 3 shows the general form electrical equivalent circuit of the resonator around the first widthextensional mode. In this model, transformers represent the two piezoelectric transduction mechanisms with longitudinal (η1) and transverse (η2) coupling coefficients. In the equivalent circuit of Fig. 3, D1, K1, and M1, and D2, K2, and M2 represent equivalent damping, stiffness and mass of the SiBAR with top AlN and sidewall AlN, respectively. CSW and CTop are the capacitances of sidewall and top AlN layers, respectively. The ratio between η1 and η2 can be estimated from (1):
1 e33 A SW 2 e31 AAlN ,Top
(1)
Dtot (21 2 )2
(2)
where Dtot represents the total mechanical damping in the resonator. Since |e33| ≈ 3|e31| and ASW is much larger than AAlN,Top, η1 is much larger than η2 (in this work η1 ≈ 100η2), implying that actuation and sensing of the bulk acoustic resonance is more efficient using piezoelectric films on the sidewalls rather than the top surface. Thus, bulk acoustic resonators with sidewall piezoelectric transduction should provide a considerably lower Rm than those employing top surface AlN actuation and sensing. Additionally, since η1 is directly proportional to ASW, Rm can be further reduced by increasing resonator thickness. This is a superior advantage of sidewall transduction over top surface transduction, where a piezoelectric layer with large surface area is required to achieve small values of Rm. IV. FABRICATION PROCESS The fabrication process of one-port SiBARs with multi-face AlN layers consists of two masks and three steps (schematically shown in Fig. 4). First, the resonator body is patterned in the silicon device layer of a thick SOI wafer using the Bosch DRIE process. This is followed by thermal oxidation and annealing in N2 ambient at 1100°C to improve the smoothness of sidewalls surface after Bosch DRIE. The BOX layer is then partially etched in HF to prevent deposition of Mo/AlN on the BOX layer in the next step. This is done to allow access of HF to the BOX layer during the final release step. Silicon structures are then covered with RF sputter deposition of a thin AlN layer sandwiched between top and
(a)
(b)
(c)
Bottom Mo
Si resonator body
Ein
Partially etched BOX layer Equi-stress surface
Bottom Mo
AlN
Ein
Top Mo
e31.Ein Ein e33.Ein
Figure 4: Resonator fabrication process: (a) patterning Si device layer and partially etching the BOX layer; (b) deposition of Mo/AlN/Mo layers, etching top Mo and AlN on one pad to expose ground contact; (c) releasing device in HF.
bottom Mo electrodes on the top surface and sidewalls. Then, the top Mo and AlN layers are etched from one pad to access the bottom Mo which serves as an electrical signal ground. Finally, the device is released by etching the BOX layer in HF. Figure 5 shows an SEM image of a fabricated one-port SiBAR with multi-face AlN and schematic of the electrical interface for measurement.
Figure 8 shows the quality and uniformity of sidewall AlN towards the bottom of the resonator. Uniform thickness of the AlN sidewall film results in efficient actuation of the desired width-extensional resonance mode over the entire thickness of the resonator and eliminates charge cancellation in the sensing mechanism.
Figure 5: SEM image of the resonator and electrical interface scheme for measurement.
Figure 7: Continuity of AlN and Mo films from the top surface to sidewalls at the resonator edges.
Figure 6 is the cross-sectional SEM picture of the resonator before release in HF. Figure 7 shows the continuity of AlN and Mo films from the top surface to sidewalls at the edges of the resonator, with sidewall AlN thicknesses approximately half of the top surface AlN.
Mo/AlN/Mo stack
Partially etched BOX layer
Figure 8: Close-up SEM image, detailing the quality and uniformity of sidewall AlN towards the bottom of the resonator.
V. Figure 6: SEM image of the device cross-section; BOX layer partially etched to enable full release in HF.
MEASUREMENT RESULTS
Experimental results are obtained using a vector network analyzer. Fig 9 shows the measured reflection coefficient
(S11) as well as the resonator impedance extracted from S11 response of the one-port resonator of Fig. 5. A quality factor (Q) of 3500 can be extracted from [10]:
Q
X 2R
(3)
where ω is the angular frequency and R and X are the real and imaginary components of resonator impedance, respectively. An Rm of 35 Ω has been achieved at 99.85 MHz, which is at least ten times less than its capacitive and transverse piezoelectric counterparts [3-6].
VI.
CONCLUSION
This work presents very low motional resistance tunable silicon bulk acoustic resonators with piezoelectric AlN layers on the sidewalls and top surface of the resonator. Exploiting the larger longitudinal piezoelectric coefficient of sidewall AlN layers as well as the substantially reduced charge cancellation as a result of the electrode configuration, this technique demonstrates very high transduction efficiency for silicon bulk acoustic resonators. The electrical equivalent model is presented to demonstrate the advantage of this transduction technique as well as the possibility of efficiency improvement by using thick silicon substrates. Resonators with Rm values as low as 35 Ω have been implemented at 100 MHz using a two-mask, three-step fabrication process. The feasibility of tuning these devices without degrading Rm has been demonstrated by sweeping the applied signal power from 0 to 7 dBm. ACKNOWLEDGMENT This work was supported by Integrated Device Technology (IDT). The authors wish to thank the OEM Group for AlN film deposition and the staff at the Nanotechnology Research Center (NRC) at the Georgia Institute of Technology for assistance with microfabrication. REFERENCES
Figure 9: Reflection coefficient (|S11|) of the resonator in Fig. 5; (insets) |S11| resonator impedance and response over a 10 MHz span.
Pin< 0 dbm 2 dbm 4 dbm
4.7 dbm 5 dbm
6 dbm
7 dbm
|S11|(db)
Figure 10 shows the resonator frequency shift for input powers higher than 0 dBm, where leakage current increases in sidewall AlN thin layers [11]. This leakage current changes the electric field boundary condition in the top AlN layer as a result of the finite resistance of the excitation source (schematically shown in the equivalent circuit of Fig. 10 inset). As shown in Fig. 10, tuning does not degrade the amplitude of reflection coefficient (|S11|) and the motional resistance of the one-port device.
Top Mo/AlN/Mo Single Crystal Silicon Sidewall Mo/AlN/Mo
Rleakage
Frequency (MHz) Figure 10: Tuning of AlN-on-Si resonator with input power levels from 0 to 7 dBm; inset shows tuning concept.
[1]
R. Tabrizian, M. Rais-zadeh and F. Ayazi, “Effect of Phonon Interactions on Limiting the f.Q product of micromechanical resonators”, IEEE International Conference on Solid-state Sensors, Actuators and Microsystems (TRANSDUCERS’09), Denver, CO, June 2009, pp. 2131-2134. [2] F. Ayazi, L. Sorenson, and R. Tabrizian, "Energy Dissipation in Micromechanical Resonators," in Proc. SPIE, 2011, pp. 1-13. [3] A. K. Samarao and F. Ayazi, “Quality Factor Sensitivity to Crystallographic Misalignments in Silicon Micromechanical Resonators”, Solid-State Sensors, Actuators, and Microsystems Workshop (Hilton Head 2010), Hilton Head Island, SC, June 2010, pp. 479-482. [4] S. A. Bhave and R. T. Howe, “Internal electrostatic transduction for bulk-mode MEMS resonators”, Solid-State Sensors, Actuators, and Microsystems Workshop (Hilton Head 2004), Hilton Head Island, SC, June, 2004, pp. 59-60. [5] A. Rahafrooz, et al., “Thermal actuation, a suitable mechanism for high-frequency electromechanical resonators”, Proc. 23st IEEE MEMS, Hong Kong, China, Jan. 2010, pp. 200-203. [6] W. Pan and F. Ayazi, “Thin-film piezoelectric-on-substrate resonators with Q enhancement and TCF reduction”, 23rd IEEE MEMS, pp 72730, 2010. [7] M. Rinaldi, et al., “Super-high-frequency two-port AlN contour-mode resonators for RF applications”, Ultrasonic, Ferroelectrics and Frequency Control IEEE Transactions, vol. 57, pp. 38-45, 2010. [8] B. P. Harrington, et al., “Toward ultimate performance in GHz MEMS resonators: Low impedance and high”, Proc. IEEE Micro Electro Mechanical Systems Conference, Jan. 2010, pp. 707–710. [9] G. K. Ho, et al., “Piezoelectric-on-Silicon Lateral Bulk Acoustic Wave Micromechanical Resonators”, IEEE Journal of Microelectromechanical Systems, Vol. 17, No. 2, April 2008, pp. 512520. [10] C.G. Montgomery, et al., “Principles of Microwave Circuits”, New York, McGraw-Hill (1948). [11] F. Martin, P. Muralt, M. A. Dubois, and A. Pezous, “Thickness Dependence of Properties of Highly C-Axis Textured AlN Thin Films”, J. Vac. Sci. Technol. A 22, 361 (2004).
