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采用Tiersten方程研究了环形ZnO薄膜谐振器中横模寄生问题, 获得了环(圆)形薄膜谐振器的横模振动方程, 求得横模位移场解和频率色散方程; 然后采用电磁学模式合成理论进行分析, 发现环形薄膜谐振器横模频率与环形电极的内外径之比a/b有关, 振动模式可由圆形薄膜谐振器横模模式合成得到, 通过控制a/b能够抑制横模模式数和调控基膜频率. 采用外差激光干涉仪和网络矢量分析仪测量并比较了同批次的圆形和环形薄膜谐振器的上电极横模振动图样和电阻抗曲线. 振动图样显示环形薄膜谐振器振动模式可由半径为a和半径为b的圆形薄膜谐振器振动模式合成, 仅存在节圆数大于0的横模振动, 等于0的横模模式被抑制; 电阻抗曲线显示当a/b为0.436时, 环形薄膜谐振器的基频(约1217 MHz)和圆形的(0, 1)模式频率相等. 测量数据验证了模式合成理论的分析结果正确性, 为薄膜谐振器的横模抑制研究提供了理论基础和新方法.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
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[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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