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In this paper, we analytically study the spurious lateral mode of the ring (circular) thin-film bulk acoustic resonator (FBAR) by using Tiersten equation. The lateral mode displacement field and frequency dispersion equation are obtained. According to the electromagnetic mode analysis, we find that the mode frequency and spurious electrical responses relate to the ratio of inner radius to outer radius (a/b) of the ring resonator, and its lateral vibration mode can be obtained by coupling other circular FBAR modes. The ring electrode can greatly reduce the number of spurious electrical responses caused by lateral resonances. Suppressing lateral mode and adjusting fundamental frequency can be achieved by controlling a/b. In this paper, the experiments for the same batch of ring and circular FBARs are carried out by using a heterodyne interferometer and a vector network analyzer, including the measurements of acoustic wave fields and eigenmode spectra, which can provide the information about vibration localization and coupling between lateral mode and thickness extensional mode. The data indicate that the lateral vibration mode of ring FBAR can be obtained by coupling the two modes of circular FBARs, whose radii are a and b, respectively, and the lateral mode pattern of n' = 0 is suppressed. When the ring resonator is designed with an a/b ratio of 0.436, the fundamental frequency (～ 1217 MHz) is the same as the (0, 1) mode frequency of the circular FBAR. Based on this observation, the acoustic wave field images and electrical spurious responses can accurately describe the lateral modes, and the obtained results accord well with the analyses of theoretical electromagnetic modes. This phenomenon may be found to have applications in the design and theoretical analysis of the resonators.
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Keywords:
- thin-film bulk acoustic resonators /
- lateral mode /
- mode coupling /
- zinc oxide
[1] Weigel R, Morgan D P, Owens J M, Ballato A, Lakin K M, Hashimoto K, Ruppel C C 2002 IEEE Trans. Microw. Theory Technol. 50 738
[2] Kim Y D, Sunwoo K H, Sul S C, Lee J H, Kim D H, Song I S, Choa S H, Yook J G 2006 IEEE Trans. Microw. Theory Technol. 54 1218
[3] Su Q X, Kirby P, Komuro E, Imura M, Zhang Q, Whatmore R 2001 IEEE Trans. Microw. Theory Technol. 49 769
[4] Zhou Z K, Wei L M, Feng J 2013 Acta Phys. Sin. 62 104601 (in Chinese) [周振凯, 韦利明, 丰杰 2013 62 104601]
[5] Chen D, Wang J J, Xu Y, Li D H, Zhang L Y, Liu W H 2013 J. Micromech. Microeng. 23 095032
[6] Link M, Schreiter M, Weber J, Primig R, Pitzer D, Gabl R 2006 IEEE Trans. Ultrason. Ferroelect. Freq. Control 53 492
[7] Zhang H, Zhang S Y, Fan L 2011 Chin. Phys. Lett. 28 114301
[8] Chao M C, Huang Z N, Pao S Y, Wang Z, Lam C S 2002 IEEE International Ultrasonics Symposium Munich, Germany, October 8-11, 2002 p973
[9] Bradley P D, Ruby III R C, Larson J D, Oshmyansky Y, Figueredo D A 2001 IEEE MTT-S Int. Microwave Symp. Dig. 1 367
[10] Larson III J D, Ruby R C, Bradley P D 2001 US Patent 6 215 375 B1 [2001-4-10]
[11] Ruby R C, Bradley P D, Oshmyansky Y, Figueredo D A 2004 US Patent 6 714 102 B2 [2004-03-30]
[12] Kaitila J, Ylilammi M, Ella J 2001 International Patent WO 2001006647 A1 [2001-1-25]
[13] Cushman D, Crawford J D 2002 US Patent 6381820 B1 [2002-05-07]
[14] Larson III J D, Bradley P D, Wartenberg S, Ruby R C 2000 IEEE Ultrasonics Symposium San Juan, Puerto Rico, October 22-25, 2000 p863
[15] Makkonen T, Holappa A, Ell J, Salomaa M 2001 2001 IEEE Trans. IEEE Trans. Ultrason. Ferroelect. Freq. Control. 48 1240
[16] Kokkonen K, Meltaus J, Pensala T, Kaivola M 2012 IEEE Trans. Ultrason. Ferroelect. Freq. Control 59 557
[17] Tiersten H F, Stevens D S 1983 J. Appl. Phys. 54 5893
[18] Kokkonen K, Pensala T, Kaivola M 2011 IEEE Trans. Ultrason. Ferroelect. Freq. Control 58 215
[19] Leissa A W 2001 Int. J. Solids Struct. 38 3341
[20] Pors A, Moreno E, Martin-Moreno L, Pendry J B, Garcia-Vidal F J 2012 Phys. Rev. Lett. 108 223905
[21] Flax L, Dragonette L R, berall H 1978 J. Acoust. Soc. Am. 63 723
[22] Chew W C 1995 Waves Fields in Inhomogenous Media (New York: Wiley-IEEE Press) pp161-167
[23] Wong W O, Yam L H, Li Y Y, Law L Y, Chan K T 2000 J. Sound Vib. 232 807
[24] Murphy J D, Breitenbach E D, berall H 1978 J. Acoust. Soc. Am. 64 677
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[1] Weigel R, Morgan D P, Owens J M, Ballato A, Lakin K M, Hashimoto K, Ruppel C C 2002 IEEE Trans. Microw. Theory Technol. 50 738
[2] Kim Y D, Sunwoo K H, Sul S C, Lee J H, Kim D H, Song I S, Choa S H, Yook J G 2006 IEEE Trans. Microw. Theory Technol. 54 1218
[3] Su Q X, Kirby P, Komuro E, Imura M, Zhang Q, Whatmore R 2001 IEEE Trans. Microw. Theory Technol. 49 769
[4] Zhou Z K, Wei L M, Feng J 2013 Acta Phys. Sin. 62 104601 (in Chinese) [周振凯, 韦利明, 丰杰 2013 62 104601]
[5] Chen D, Wang J J, Xu Y, Li D H, Zhang L Y, Liu W H 2013 J. Micromech. Microeng. 23 095032
[6] Link M, Schreiter M, Weber J, Primig R, Pitzer D, Gabl R 2006 IEEE Trans. Ultrason. Ferroelect. Freq. Control 53 492
[7] Zhang H, Zhang S Y, Fan L 2011 Chin. Phys. Lett. 28 114301
[8] Chao M C, Huang Z N, Pao S Y, Wang Z, Lam C S 2002 IEEE International Ultrasonics Symposium Munich, Germany, October 8-11, 2002 p973
[9] Bradley P D, Ruby III R C, Larson J D, Oshmyansky Y, Figueredo D A 2001 IEEE MTT-S Int. Microwave Symp. Dig. 1 367
[10] Larson III J D, Ruby R C, Bradley P D 2001 US Patent 6 215 375 B1 [2001-4-10]
[11] Ruby R C, Bradley P D, Oshmyansky Y, Figueredo D A 2004 US Patent 6 714 102 B2 [2004-03-30]
[12] Kaitila J, Ylilammi M, Ella J 2001 International Patent WO 2001006647 A1 [2001-1-25]
[13] Cushman D, Crawford J D 2002 US Patent 6381820 B1 [2002-05-07]
[14] Larson III J D, Bradley P D, Wartenberg S, Ruby R C 2000 IEEE Ultrasonics Symposium San Juan, Puerto Rico, October 22-25, 2000 p863
[15] Makkonen T, Holappa A, Ell J, Salomaa M 2001 2001 IEEE Trans. IEEE Trans. Ultrason. Ferroelect. Freq. Control. 48 1240
[16] Kokkonen K, Meltaus J, Pensala T, Kaivola M 2012 IEEE Trans. Ultrason. Ferroelect. Freq. Control 59 557
[17] Tiersten H F, Stevens D S 1983 J. Appl. Phys. 54 5893
[18] Kokkonen K, Pensala T, Kaivola M 2011 IEEE Trans. Ultrason. Ferroelect. Freq. Control 58 215
[19] Leissa A W 2001 Int. J. Solids Struct. 38 3341
[20] Pors A, Moreno E, Martin-Moreno L, Pendry J B, Garcia-Vidal F J 2012 Phys. Rev. Lett. 108 223905
[21] Flax L, Dragonette L R, berall H 1978 J. Acoust. Soc. Am. 63 723
[22] Chew W C 1995 Waves Fields in Inhomogenous Media (New York: Wiley-IEEE Press) pp161-167
[23] Wong W O, Yam L H, Li Y Y, Law L Y, Chan K T 2000 J. Sound Vib. 232 807
[24] Murphy J D, Breitenbach E D, berall H 1978 J. Acoust. Soc. Am. 64 677
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