Characteristics of AlN Lamb Wave Resonators with Various Bottom Electrode Configurations

Transcription

1 Characteritic of AlN Lamb Wave Reonator with Variou Bottom Electrode Configuration Chih-Ming Lin 1, Ventilav Yantchev, Yung-Yu Chen 3, Valery V. Felmetger 4, and Albert P. Piano 1 1 Department of Mechanical Engineering, Univerity of California, Berkeley, California, USA Department of Solid State Electronic, Uppala Univerity, Uppala, Sweden 3 Department of Mechanical Engineering, Tatung Univerity, Taipei, Taiwan 4 PVD Product Group, OEM Group Incorporated, Gilbert, Arizona, USA Abtract The characteritic of aluminum nitride (AlN) Lamb wave reonator utilizing the lowet ymmetric (S ) mode with grounded, floating, and open bottom urface configuration are theoretically and experimentally invetigated. The Lamb wave reonator without the bottom electrode exhibit a quality factor (Q) a high a,573 but a low effective coupling of.18% at MHz. On the contrary, the Lamb wave reonator with a floating bottom electrode how an effective coupling of 1.5% but a low Q of 85 at 85.3 MHz becaue the imperfect interface between the AlN plate and bottom electrode uually degrade the Q. Limited by the larger tatic capacitance, in contrat to the floating bottom electrode, the Lamb wave reonator with a grounded bottom electrode how a maller effective coupling of.78% and a low Q of 8 at 85.5 MHz. Thee reult ugget that the reonator with a floating bottom urface i uitable for filter application, wherea that with an open bottom urface i preferred for enor and ocillator application. h AlN Electric field bottom urface bottom urface (a) (b) (c) Keyword Lamb Wave Reonator, Aluminum Nitride, Quality Factor, Electromechanical Coupling, Bottom Electrode I. INTRODUCTION Recently, there are a large number of long-term evolution (LTE) frequency band that are being deignated a the poibilitie for the third generation (3G) and the fourth generation (4G) wirele mobile ytem. For the frequency diviion duplex (FDD) and time diviion duplex (TDD) technologie, mot of the LTE frequency band are allocated within the ultra-high-frequency (UHF) region. Several LTE frequency band have deignated with the narrow bandwidth between.75% and % [1]. In recent year, a new cla of aluminum nitride (AlN) Lamb wave reonator utilizing the lowet ymmetric (S ) mode i being widely explored [] [7]. The AlN Lamb wave reonator uually exhibit a high phae velocity around 1, m/ and a moderate electromechanical coupling, very uitable for the high-frequency and narrowband wirele tranmiion ytem. During the pat ix year, two ditinct deign of S mode Lamb wave reonator are imultaneouly developing. One i baed on the Lamb wave excitation from the interdigital tranducer () and the reflection from the periodic grating bottom urface Figure 1. Illutration of the cro-ection of AlN Lamb wave reonator with grounded, floating, and open bottom urface configuration. on the AlN membrane (the grating-type reflector) [], [3]; intead, the other one i baed on the Lamb wave excitation from the and the reflection from the upended free edge of the AlN membrane (the edge-type reflector) [4] [7]. Furthermore, the robut temperature compenation for the two type of S mode Lamb wave reonator ha been theoretically analyzed and experimentally demontrated [8] [1]. Thee aforementioned reult reveal the potential of Lamb wave reonator for the future narrowband wirele tranmiion ytem becaue thi technology can reliably provide a wide frequency range from hundred MHz to everal GHz on the ingle ilicon chip and imultaneouly offer the high quality factor (Q) a well a the low motional reitance ( ) in air. In thi work, the S mode Lamb wave reonator utilizing the edge-type reflector with the variou bottom urface configuration are tudied. A hown in Fig. 1, the electric field ditribution in the AlN membrane would dominate the performance of the reonator with grounded, floating, and open bottom urface configuration. Baed on the ame Thi work wa upported by the DARPA Chip-Scale Mechanical Spectrum Analyzer (CSSA) award (Grant No. NGC ) under the DARPA Microytem Technology Office (MTO) /11/$6. 11 IEEE 55

2 Electromechanical coupling, k (%) (%) Normalized AlN thickne AlN thickne, h AlN / λh AlN /λ Figure. The diperive electromechanical coupling coefficient of the lowet ymmetric (S ) mode Lamb wave in the AlN membrane with the non-metallized and metallized bottom urface. deign, the AlN Lamb wave reonator with a floating bottom electrode provide a larger effective coupling (k eff) of 1.5%, preenting a 1.35 increae in k eff over that with a grounded bottom electrode becaue the floating bottom electrode make a maller tatic capacitance in the membrane. However, the electrode-to-reonator interface tre caue the degradation in Q. In contrat to the metallized bottom urface, the Lamb wave reonator with the non-metallized bottom urface (i.e. the open bottom urface) provide a Q a high a,573 but a mall k eff of.18% due to the weak electric field in the 1.5- μm-thick AlN membrane. II. FININTE ELEMENT ANALYSIS OF ONE-PORT LAMB WAVE RESONATORS WITH VARIOUS BOTTOM SURFACES By uing Adler approach [11] or finite element analyi (FEA) method [1], the diperive electromechanical coupling in the piezoelectric plate can be theoretically calculated. In the imulation, the S mode Lamb wave propagate in the plane normal to the c-axi of the AlN membrane and the bottom electrode i aumed to be infinitely thin. A illutrated in Fig., the dahed and olid line repreent the electromechanical coupling diperion of the S mode Lamb wave in the AlN membrane with the non-metallized and metallized bottom urface, repectively. In general, the metallized bottom urface enhance the electromechanical coupling coefficient becaue the electric field trength through the AlN thin plate i higher than that between the electrode. However, the electromechanical coupling calculated uing Adler approach i identical for the both grounded and floating bottom urface becaue the hort-circuited boundary condition i conidered in the two configuration. Thi i not true for the real Lamb wave reonator ince the parallel frequency and the effective coupling are ignificantly influenced by the tatic and paraitic capacitance in the reonator. Therefore, the actual effective coupling for the grounded and floating bottom electrode are different becaue of the ditinct tatic capacitance in the two configuration. C U U/ -U/ C C U A hown in Fig. 3, a imple phyical model can be ued to illutrate the effect of capacitive feedthrough to ground in the one-port Lamb wave reonator and the tatic capacitance (C ) in the modified Butterworth-Van dyke (MBVD) model for the electrically grounded, floating, and open bottom urface. For the grounded bottom urface in Fig. 3(a), the lateral and vertical electric field induce the in-line capacitance ( ) and cro-field capacitance (C ) o the C i imply aumed to be the ummation of and C. A for the floating bottom urface in Fig. 3(b), the electric potential in the bottom electrode i preumed to be zero and the electric potential in the electrode are equivalent to be U/ and U/ becaue of the ymmetric electric filed. A a reult, the C i imply aumed to be the ummation of and C / for the floating bottom urface. A illutrated in Fig. 3(c), C i imply equal to the in-line capacitance,, in the open bottom urface. The excitation efficiency of the with grounded and floating bottom urface would be the ame and larger than that with an open bottom urface becaue the backide metallization trongly enhance the vertical electric field in the AlN plate. In addition, C in the open bottom urface i the mallet among the three configuration; C in the floating bottom urface i maller than C in the grounded bottom urface, reulting in a larger k eff for the reonator with a floating bottom electrode. In order to verify the above phyical model, a hown in Fig. 4, the two-dimenional (D) model in COMSOL FEA oftware i ued to imulate the frequency pectra of one-port AlN Lamb wave reonator with the grounded, floating, and open bottom urface. With the ame 11 electrode deign but different electric condition in the bottom urface, the D COMSOL FEA model predict that the floating bottom electrode provide a 1.8 time larger k eff than the grounded bottom electrode on a 1.5-μm-thick AlN plate. The imulation reult alo confirm that the tranduction efficiency of the with grounded and floating bottom electrode would be C = +C (a) C = +C / (b) (c) C = C C C Figure 3. A imple phyical model for the capacitive feedthrough to ground in the one-port Lamb wave reonator and the equivalent C in the modified Butterworth-Van dyke (MBVD) model for the electrically (a) grounded, (b) floating, and (c) open bottom urface. R R R 56

3 Admittance (db) Relative Frequency frequency (%) (%) identical when the ame even electrode pair and acoutic lo condition are conidered in the imulation. III. EXPERIMENTAL RESULT AND DISCUSSION In order to tudy the effect of the bottom electric condition on the reonator performance, the AlN Lamb wave reonator with electrically grounded, floating, and open bottom urface are deigned a ummarized in Table I. The micro-fabrication proce ha been preented in [6] o it i not further conidered in thi work. To diminih the experimental error reulted from the fabrication proce, the reonator were fabricated on the ame wafer and placed in the vicinity. Lamb wave reonator were all teted in air and S 11 parameter were extracted uing an Agilent E571B network analyzer. The meaured Q wa extracted from the admittance plot by dividing the reonance frequency by the 3 db bandwidth. The k eff of the meaured device i defined a k eff Figure 4. Simulated admittance plot of the one-port AlN Lamb wave reonator with the grounded, floating, and open bottom urface uing the two-dimenional (D) model in COMSOL. TABLE I. GEOMETRIC DIMENSIONS OF LAMB WAVE RESONATORS Deign 1 Deign Deign 3 electrode Aperture 1 μm 1 μm 1 μm Electrode width.77 μm.77 μm.77 μm Pt electrode thickne 1 nm 1 nm 1 nm Pt bottom electrode thkickne 1 nm 1 nm - AlN membrane thkickne 1.5 μm 1.5 μm 1.5 μm Bottom electric condition π f p f 4 f p where f and f p are the erie frequency and parallel frequency, repectively. Fig. 5 preent the meaured frequency pectra of one-port AlN Lamb wave reonator with the grounded, floating, and (1) Admittance (db) (S) Relative Frequency frequency (MHz) (%) Figure 5. Meaured admittance plot of the one-port AlN Lamb wave reonator with the grounded, floating, and open bottom urface. open bottom urface. With the ame 11 electrode but different bottom electric condition a lited in Table I, the Lamb wave reonator with the open bottom urface exhibit the mallet k eff of.18% and tranduction efficiency a expected. However, it exhibit a loaded Q a high a,573 among the three reonator deign. The tranduction efficiency and effective coupling of the reonator with an open bottom urface can be enhanced by increaing the electrode or thickening the AlN membrane [13]. On the other hand, the Lamb wave reonator with a floating bottom electrode how the highet k eff of 1.5%, preenting a 1.35 enhancement in k eff over that with a grounded bottom electrode, wherea the preence of additional bottom electrode decreae the Q to 85 becaue of the high tre level in the interface. In addition, the extracted C in the AlN plate with the floating and grounded bottom electrode are 195 ff and 355 ff, repectively. The reult confirm that the floating bottom electrode efficiently reduce C and boot k eff in the one-port AlN Lamb wave reonator. Moreover, the employment of the floating bottom electrode alo make the micro-fabrication proce eaier becaue the electrical contact via i no longer needed. In the D COMSOL FEA model, the imulated C ratio of the grounded bottom electrode to the floating bottom electrode i approximately equal to for the ame deign parameter lited in Table I. However, the meaured C ratio i equal to 1.8 becaue ome additional ignificant paraitic capacitance occur and influence the experimental C ratio. In fact, thee additional paraitic capacitance are dead and do not take the reponibility for the Lamb wave excitation, but only decreae the parallel frequency and conequently reduce the k eff for a given AlN plate thickne. In addition to k eff and C, the experimental tranduction efficiency of the Lamb wave reonator with grounded and floating bottom electrode i of interet. For thi purpoe, the coupling-of-mode (COM) tranduction coefficient, α(ω ), which i reponible for the excitation efficiency of the, 57

4 Conductance (S).6.4. Δf / f (ppm) Frequency (MHz) Figure 6. Meaured conductance plot of the one-port AlN Lamb wave reonator with the grounded and floating bottom electrode Temperature ( C) (ºC) Figure 7. Meaured frequency variation v. temperature of the Lamb wave reonator with the electrically grounded, floating, and open bottom urface. TABLE II. can be introduced to compare the excitation efficiency of the with grounded and floating bottom electrode. The COM tranduction coefficient α(ω ) i derived a [14] ( ) WΓ QF β ω α( ω ) =, () Λ where Λ T i the wavelength of tranduction, Q F (β) i the elemental charge denity function, β=π/λ T i the acoutic wave number, ω i the reonance angular frequency, W i the aperture, and Γ i expreed a [14], [15] T k Γ =, (3) ε (, βh ) where k =(v oc -v c )/v oc i the intrinic electromechanical coupling coefficient in Fig., v oc and v c are the S mode Lamb wave velocitie at the open-circuited and hort-circuited urface, repectively, ε (, βh AlN ) i the effective permittivity for infinite lowne (the effective tatic permittivity), and h AlN i the AlN thickne. Moreover, the acoutic conductance at the reonance frequency ω of a reflector-le having an aperture W and N P pair of electrode i defined a [15], [16] G PERFORMANCE OF LAMB WAVE RESONATORS f [MHz] Q Motional reitance, [Ω] Motional capacitance, C m [ff] Static capacitance, C [ff] k eff [%] Figure of merit, k eff Q TCF [ppm/ C] a AlN ( ) ( ) ω ω W Q β N = Γ. (4) F p The latter can be preented a a function of the COM tranduction coefficient a: ( ) = Λ ( ) Ga ω Tα ω N p, (5) revealing further the phyical meaning of the COM tranduction coefficient. The latter i directly related to the conductance which in turn i proportional to the radiated acoutic power. When comparing the performance of the Lamb wave reonator, one hould bear in mind that (5) become more general. The conductance at reonance depend not only on the COM tranduction and the length but alo on the acoutic loe ince the latter determine the Q. Accordingly, only comparing the reonator with the ame topology could reveal the information about the tranduction efficiency. Here we compare the Lamb wave reonator of the ame topology with the electrically grounded and floating bottom urface, repectively. A hown in Fig. 6, both the AlN Lamb wave reonator how quite imilar conductance characteritic. The conductance ratio between the reonator with floating and grounded bottom electrode i equal to.88, reulting in a tranduction efficiency ratio of.94, which i very cloe to the imulated ratio,.91, obtained from the D COMSOL FEA model. The different tranduction efficiency for grounded and floating bottom electrode i caued by the unymmetrical electric filed in the 11 electrode, while the experimental tranduction efficiency ratio i 1.1 for 1 electrode. A dicued above, when imulating the tranduction efficiency ratio, all remaining contribution to the conductance hould be kept the ame except for the bottom electric condition. The reult further confirm our preliminary obervation that the excitation efficiency i the ame for the with electrically grounded and floating bottom urface, wherea the larger tatic capacitance in the AlN Lamb wave reonator with a grounded bottom electrode reult in the maller k eff. Fig. 7 how the plot of meaured fractional frequency variation for the Lamb wave reonator lited in Table I from 58

5 room temperature to 1 C. A expected, the AlN Lamb wave reonator without the bottom electrode exhibit a maller firtorder temperature coefficient of frequency (TCF) of 5.9 ppm/ C becaue the platinum (Pt) bottom electrode ha a large negative TCF and decreae the overall TCF accordingly. The reonator with the electrically grounded and floating bottom electrode how the firt-order TCF of 7. ppm/ C and 6.6 ppm/ C, repectively. Table II compare the meaured performance of the AlN Lamb wave reonator with grounded, floating, and open bottom urface. All in all, the experimental reult are in qualitative agreement with the imulated concluion from the D COMSOL FEA model. It i noted that the Q and k eff reported in thi work are not optimal by far. The better reonator deign, micro-fabrication proce, and thin film tre control can improve the figure of merit (FOM) to a large extent. IV. CONCLUSION Baed on a 1.5-μm-thick AlN plate and the ame deign, the characteritic of one-port Lamb wave reonator with the electrically grounded, floating, and open bottom urface are theoretically analyzed uing the FEA method and experimentally invetigated. The employment of the floating bottom electrode imultaneouly provide a larger effective coupling, an eaier micro-fabrication proce, and a higher FOM than the grounded bottom electrode without acrificing the tranduction efficiency much. In particular, the Lamb wave reonator with the floating bottom electrode how the highet FOM which i mot uitable for the filter application. The high phae velocity, moderate electromechanical coupling, weak diperion, and ability to tune the effective coupling (i.e. the bandwidth) by changing the bottom electric condition alo how the potential of AlN Lamb wave reonator for the future high-frequency and narrowband wirele tranmiion ytem. On the contrary, the reonator with the open bottom urface configuration uually provide a higher Q which i mot uitable for the ocillator and enor application. REFERENCES [1] [] J. Bjurtröm, I. Katardjiev, and V. Yantchev, Lateral-field-excited thin-film Lamb wave reonator, in Appl. Phy. Lett., vol. 86, Apr. 5. [3] V. Yantchev, and I. Katardjiev, Micromachined thin film plate acoutic reonator utilizing the lowet order ymmetric Lamb wave mode, IEEE Tran. Ultraon. Ferroelect. Freq. Control, vol. 54, pp , Jan. 7. [4] A. Volatier, G. Caruyer, D. P. Tanon, P. Ancey, E. Defay, and B. Dubu, UHF/VHF reonator uing Lamb wave co-integrated with bulk acoutic wave reonator, in Proc. IEEE Ultraonic Symp., 5, pp [5] H. Matumoto, A. Iobe and K. Aai, Multilayer film piezoelectric Lamb wave reonator for everal GHz application, in Proc. IEEE Intl. Freq. Contr. Symp., 6, pp [6] G. Piazza, P. J. Stephanou, and A. P. Piano, One and two port piezoelectric higher order contour-mode MEMS reonator for mechanical ignal proceing, Solid-State Electron., vol. 51, pp , Nov. 7. [7] M. Rinaldi, C. Zuniga, C. Zuo, and G. Piazza, Super-high-frequency two-port AlN contour-mode reonator for RF application, IEEE Tran. Ultraon. Ferroelectr. Freq. Control, vol 57, pp , Jan. 1. [8] G. Wingqvit, L. Arapan, V. Yantchev, and I. Katardjiev, A micromachined thermally compenated thin film Lamb wave reonator for frequency control and ening application, J. Micromech. Microeng., vol. 19, 3518, Mar. 9. [9] C.-M. Lin, T.-T. Yen, Y.-J. Lai, V. V. Felmetger, M. A. Hopcroft, J. H. Kuyper, and A. P. Piano, Temperature-compenated aluminum nitride Lamb wave reonator, IEEE Tran. Ultraon. Ferroelectr. Freq. Control, vol. 57, pp , Mar. 1. [1] C.-M. Lin, T.-T. Yen, V. V. Felmetger, M. A. Hopcroft, J. H. Kuyper, and A. P. Piano, Thermally compenated aluminum nitride Lamb wave reonator for high temperature application, Appl. Phy. Lett., vol. 97, 8351, Aug. 1. [11] E. L. Adler, Electromechanical coupling to Lamb and hearhorizontal mode in piezoelectric plate IEEE Tran. Ultraon. Ferroelectr. Freq. Control, vol. 36, pp. 3-3, Mar [1] F. Di Pietrantonio, M. Benetti, D. Cannatà, R. Beccherelli, and E. Verona, Guided Lamb wave electroacoutic device on micromachined AlN/Al plate, IEEE Tran. Ultraon. Ferroelectr. Freq. Control, vol. 57, pp , May 1. [13] C. Zuo, J. Van der Spiegel, and G. Piazza 1.5-GHz CMOS ocillator baed on lateral-field-excited piezoelectric AlN contour-mode MEMS reonator, IEEE Tran. Ultraon. Ferroelect. Freq. Control, vol. 57, pp. 8-87, Jan. 1. [14] B. P. Abbott, C.-S. Hartmann, and D. C. Malocha, Tranduction magnitude and phae for COM modeling of SAW device, IEEE Tran. Ultraon. Ferroelect. Freq. Control, vol. 39, pp. 54-6, Jan [15] V. Yantchev, Coupling-of-mode analyi of thin film plate acoutic wave reonator utilizing the S Lamb mode, IEEE Tran. Ultraon. Ferroelect. Freq. Control, vol. 57, pp , Apr. 1. [16] D. P. Morgan, Surface-wave device for ignal proceing, 1t ed., Amterdam, New York: Elevier,