We studied thickness-shear vibration frequencies and modes in a rectangular AT-cut quartz plate resonator with ring electrodes. The electrodes are also rectangular, with their central parts missing and thus form rectangular ring electrodes. It was found that the vibration tends to be trapped in the electrode area and decays away from the electrode edges. By properly designing the electrode dimensions, the vibration can be made nearly uniform in the central part of the plate. This is particularly suitable for resonator-based sensor applications where the sensitivity is determined theoretically from the uniform vibration distribution of pure thickness-shear modes in an unbounded plate.
ZhangT., WangY., LiuW.L., ChengJ.G., SongZ.T., FengS.L., Chan-WongL.H. and ChoyC.L., Fabrication and characterization of zno-based film bulk acoustic resonator with a high working frequency, Chin Phys Lett22 (2005), 694-696.
2.
WangW.Y., ZhangC., ZhangZ.T., LiuY. and FengG.P., Lateral-field-excitation properties of LiNbO3 single crystal, Chin Phys B18 (2009), 795-802.
3.
MaT.F., ZhangC., FengG.P. and JiangX.N., Lateral field excitation properties of langasite single crystal, Chin Phys B19 (2010), 087701.
4.
MaT.F., ZhangC., JianX.N. and FengG.P., Thickness shear mode quartz crystal resonators with optimized elliptical electrodes, Chin Phys B20 (2011), 047701.
5.
ZhangH.F., TurnerJ.A. and KosinskiJ.A., Experimental measurements of the force - frequency effect of thickness-mode langasite resonators, IEEE Trans Ultrason, Ferroelect, Freq Contr60 (2013), 1475-1478.
6.
XiaB.G., ZhangH.D., ZhaoX., YiM. and HuangJ., Design and implementation of sub-reflector for Ka band antenna based on quartz wafer coating technology, Acta Phys Sin62 (2013), 204103.
7.
LiuY.Y., DongL., WuH.P., ZhengH.D., MaW.G., ZhangL., YinW.B. and JiaS.T., All optical quartz-enhanced photoacoustic spectroscopy, Acta Phys Sin62 (2013), 220701.
8.
GuY., LiQ., TianF.F. and XuB.J., Structure and absorbability of a nanometer nonmetallic polymer thin film coating on quartz used in piezoelectric sensors, Chin Phys Lett30 (2013), 108101.
9.
OlssonR.H., HattarK., HomeijerS.J., WiwicM., EichenfieldaM., BranchdD.W., BakeraM.S., NguyenaJ., ClarkbB., BauercT. and FriedmanncaT.A., A high electromechanical coupling coefficient SH0 Lamb wave lithiumniobate micromechanical resonator and a method for fabrication, Sensors and Actuators A-Physical209 (2014), 183-190.
10.
KoW. and JeonS., An electrodeless quartz crystal resonator integrated with UV/Vis spectroscopy for the investigation of the photodecomposition of methylene blue, Sensors and Actuator-B Chemical193 (2014), 774-777.
11.
Cao-PazA., Rodriguez-PardoL. and FarinaJ., Temperature compensation of QCM sensors in liquid media, Sensors and Actuator-B Chemical193 (2014), 78-81.
12.
GuY., LiQ., XuB.J., and ZhaoZ., Vibration analysis of a new polymer quartz piezoelectric crystal sensor for detecting characteristic materials of volatility liquid, Chin Phys B23 (2014), 017804.
13.
GuY. and LiQ., Application of the new pattern recognition system in the new e-nose to detecting Chinese spirits, Chin, Phys B23 (2014), 044213.
14.
SauerbreyG., Verwendung von schwingquarzen zur wägung dünner schichten und zur mikrowägung, Zeitschrift für Physik155 (1959), 206-222.
15.
KanazawaK.K.and Gordon IIJ.G., The oscillation frequency of a quartz resonator in contact with a liquid, Anal Chem Acta175 (1985), 99-105.
16.
KogaI., Thickness vibrations of piezoelectric oscillating crystals, Physics3 (1932), 70-80.
MindlinR.D., High frequency vibrations of plated, crystal plates, in: Prog in Appl Mech, New York: Macmillan, (1963), 73-84.
19.
MillerJ.G. and BolefD.J., Acoustic wave analysis of the operation of quartz-crystal film-thickness monitors, J Appl Phys39 (1968), 5815-5816.
20.
BoersmaF. and van BallegooyenE.C., Rotated Y-cut quartz crystal with two different electrodes treated as a one-dimensional acoustic composite resonator, J Acoust Soc Am62 (1977), 335-340.
21.
ReedC.E., KanazawaK.K. and KaufmanJ.H., Physical description of a viscoelastically loaded AT-cut quartz resonator, J Acoust Soc Am68 (1990), 1993-2001.
22.
MartinS.J., GranstaffV.E. and FryeG.C., Characterization of a quartz crystal microbalance with simultaneous mass and liquid loading, Anal Chem63 (1991), 2272-2281.
23.
Duncan-HewittW.C. and ThompsonM., Four-layer theory for the acoustic shear wave sensor in liquids incorporating interface slip and liquid structure, Anal Chem64 (1992), 94-105.
24.
FerranteF., KiplingA.L. and ThompsonM., Molecular slip at the solid-liquid interface of an acoustic-wave sensor, J Appl Phys76 (1994), 3448-3462.
25.
BenesE., GröschlM., BurgerW. and SchmidM., Sensors based on piezoelectric resonators, Sens Actuat A48 (1995), 1-21.
26.
KosinskiJ.A., Thickness vibration of flat piezoelectric plates with massy electrodes of unequal thickness, in: Proc IEEE Ultrasonics Symp, Prague, Czech Republic, (2003), 70-73.
27.
YangJ.S., ZhouH.G. and ZhangW.P., Thickness-shear vibration of rotated Y-cut quartz plates with relatively thick electrodes of unequal thickness, IEEE Trans Ultrason, Ferroelect, Freq Contr52 (2005), 918-922.
28.
WangJ. and ShenL.J., Exact thickness-shear resonance frequency of electroded piezoelectric crystal plates, J Zhejiang Univ SCI6A (2005), 980-985.
29.
YangJ.S., HuY.T., ZengY. and FanH., Thickness-shear vibration of rotated Y-cut quartz plates with imperfectly bounded surface mass layers, IEEE Trans Ultrason, Ferroelect, Freq Contr53 (2006), 241-245.
30.
JingY., ChenJ., ChenX. and GongX., Frequency shift of thickness-shear vibrations of AT-cut quartz resonators due to a liquid layer with the electrode stiffness considered, IEEE Trans Ultrason, Ferroelect, Freq Contr54 (2007), 1290-1292.
31.
LiuB., JiangQ. and YangJ.S., Fluid-induced frequency shift in a piezoelectric plate driven by lateral electric fields, Int J Appl Electrom34 (2010), 171-180.
32.
LiuB., JiangQ. and YangJ.S., Frequency shifts in a quartz plate piezoelectric resonator in contact with a viscous fluid under a separated electrode, Int J Appl Electrom35 (2011), 177-187.
33.
BottomV.E., Introduction to quartz crystal unit design, Van Nostrand Reinhold Co., Inc.,1982.
34.
VigJ.R. and BallatoA., Comments about the effects of nonuniform mass loading on a quartz crystal microbalance, IEEE Trans Ultrason, Ferroelect, Freq Contr45 (1998), 1123-1124.
35.
NakamuraK., YasuikeR., HiramaK. and ShimizuH., Trapped-energy piezoelectric resonators with elliptical ring electrodes, in: Proc 44th Annual Symposium on Frequency Control, Baltimore, MD, (1990), 372-377.
36.
RichardsonA., BhethanabotlaV.R., SmithA.L. and JosseF., Patterned electrodes for thickness shear mode quartz resonators to achieve uniform mass sensitivity distribution, IEEE Sensors Journal12 (2009), 1772-1777.
37.
TierstenH.F., Analysis of intermodulation in thickness-shear and trapped energy resonators, J Acoust Soc Am57 (1975), 667-681.
38.
TierstenH.F., Analysis of trapped-energy resonators operating in overtones of coupled thickness-shear and thickness-twist, J Acoust Soc Am59 (1976), 879-888.
39.
TierstenH.F. and SmytheR.C., An analysis of contoured crystal resonators operating in overtones of coupled thickness shear and thickness twist, J Acoust Soc of Am65 (1979), 1455-1460.
40.
TierstenH.F. and SmytheR.C., Coupled thickness-shear and thickness-twist vibrations of unelectroded AT-cut quartz plates, J Acoust Soc of Am78 (1985), 1684-1689.
41.
StevensD.S. and TierstenH.F., An analysis of doubly rotated quartz resonators utilizing essentially thickness modes with transverse variation, J Acoust Soc Am79 (1986), 1811-1826.
42.
ShiJ.J., FanC.Y., ZhaoM.H. and YangJ.S., Variational formulation of the Stevens-Tiersten equation and application in the analysis of rectangular trapped-energy quartz resonators, J Acoust Soc Am135 (2014), 175-181.
43.
ShiJ.J., FanC.Y., ZhaoM.H. and YangJ.S., Variational analysis of thickness-shear vibrations of a quartz piezoelectric plate with two pairs of electrodes as an acoustic wave filter, Int J Appl Electrom47 (2015), 951-961.
