A heterodyne laser interferometer is used to study acoustic wave fields excited in a 1.8 GHz AlN thin film bulk acoustic waveresonator. The electrical response of the resonator exhibits a strong thickness resonance onto which spurious modes, caused by lateral standing plate waves, are superposed. Optical interferometermeasurements are used to extract dispersion curves of the laterally propagating waves responsible for the spurious responses. A discrete eigenmode spectrum due to the finite lateral dimensions of the resonator is observed. An equivalent circuit model for a multimode resonator is fitted to the mechanical resonator response extracted along a single curve in the dispersion diagram, and is used to determine properties, such as Q-values, of the individual lateral eigenmodes.Measuredwave field images, extracted dispersion curves, and the eigenmode spectrum with the model fitting results are presented.Peer reviewe

Fattinger G. G.

Graebner J. E.

Johanna Meltaus

Kaitila J.

Kimmo Kokkonen

Marksteiner S.

Matti Kaivola

Meltaus J.

Telschow K. L.

Tuomas Pensala

Crossref

Extraction of lateral eigenmode properties in thin film bulk acoustic wave resonator from interferometric measurements

Kokkonen, Kimmo

Pensala, Tuomas

Meltaus, Johanna

Kaivola, Matti

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This is an electronic reprint of the original article.This reprint may differ from the original in pagination and typographic detail.Author(s): Kokkonen, Kimmo & Pensala, Tuomas & Meltaus, Johanna &Kaivola, MattiTitle: Extraction of lateral eigenmode properties in thin film bulk acousticwave resonator from interferometric measurementsYear: 2010Version: Final published versionPlease cite the original version:Kokkonen, Kimmo & Pensala, Tuomas & Meltaus, Johanna & Kaivola, Matti. 2010.Extraction of lateral eigenmode properties in thin film bulk acoustic wave resonator frominterferometric measurements. Applied Physics Letters. Volume 96, Issue 17. 173502.ISSN 0003-6951 (printed). DOI: 10.1063/1.3299012.Rights: © 2010 American Intitute of Physics (AIP). This article may be downloaded for personal use only. Any otheruse requires prior permission of the author and the American Institute of Physics.http://scitation.aip.org/content/aip/journal/aplAll material supplied via Aaltodoc is protected by copyright and other intellectual property rights, andduplication or sale of all or part of any of the repository collections is not permitted, except that material maybe duplicated by you for your research use or educational purposes in electronic or print form. You mustobtain permission for any other use. Electronic or print copies may not be offered, whether for sale orotherwise to anyone who is not an authorised user.Powered by TCPDF (www.tcpdf.org)Extraction of lateral eigenmode properties in thin film bulk acoustic wave resonatorfrom interferometric measurementsKimmo Kokkonen, Tuomas Pensala, Johanna Meltaus, and Matti Kaivola  Citation: Applied Physics Letters 96, 173502 (2010); doi: 10.1063/1.3299012 View online: http://dx.doi.org/10.1063/1.3299012 View Table of Contents: http://scitation.aip.org/content/aip/journal/apl/96/17?ver=pdfcov Published by the AIP Publishing  Articles you may be interested in Selective normal mode excitation in multilayer thin film bulk acoustic wave resonators Appl. Phys. Lett. 105, 162910 (2014); 10.1063/1.4899067  Intrinsically switchable thin film bulk acoustic wave resonators Appl. Phys. Lett. 104, 222905 (2014); 10.1063/1.4881141  Effect of interface roughness on acoustic loss in tunable thin film bulk acoustic wave resonators J. Appl. Phys. 110, 024116 (2011); 10.1063/1.3610513  Shear mode bulk acoustic wave resonator based on c -axis oriented AlN thin film J. Appl. Phys. 104, 084508 (2008); 10.1063/1.2996319  Laser Acoustic Imaging of Film Bulk Acoustic Resonator (FBAR) Lateral Mode Dispersion AIP Conf. Proc. 760, 251 (2005); 10.1063/1.1916685    This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:130.233.216.240 On: Tue, 19 May 2015 08:54:54Extraction of lateral eigenmode properties in thin film bulk acoustic waveresonator from interferometric measurementsKimmo Kokkonen,1,a Tuomas Pensala,2 Johanna Meltaus,2 and Matti Kaivola11Department of Applied Physics, Helsinki University of Technology, Espoo 02150, Finland2VTT Technical Research Centre of Finland, P. O. Box 1000, 02044 VTT, FinlandReceived 15 September 2009; accepted 6 January 2010; published online 26 April 2010A heterodyne laser interferometer is used to study acoustic wave fields excited in a 1.8 GHz AlNthin film bulk acoustic wave resonator. The electrical response of the resonator exhibits a strongthickness resonance onto which spurious modes, caused by lateral standing plate waves, aresuperposed. Optical interferometer measurements are used to extract dispersion curves of thelaterally propagating waves responsible for the spurious responses. A discrete eigenmode spectrumdue to the finite lateral dimensions of the resonator is observed. An equivalent circuit model for amultimode resonator is fitted to the mechanical resonator response extracted along a single curve inthe dispersion diagram, and is used to determine properties, such as Q-values, of the individuallateral eigenmodes. Measured wave field images, extracted dispersion curves, and the eigenmodespectrum with the model fitting results are presented. © 2010 American Institute of Physics.doi:10.1063/1.3299012Laser interferometry is a versatile, noncontact opticalmethod that provides direct information on the mechanicalwave fields excited in microacoustic structures. Optical prob-ing of gigahertz-range bulk-acoustic waves BAWs1–7 hasproven to be very useful for studying the operation of BAWdevices, revealing their loss mechanisms, helping to refinesimulation models and for obtaining materials parameters.The fields can be measured with a lateral resolution betterthan 1 m and with smallest detectable vibration amplitudesin the subpicometer range.The so-called solidly mounted resonator under studyhere is composed of a piezoelectric thin film sandwichedbetween metal electrodes and of an acoustic Bragg reflectorthat serves to acoustically isolate the device from the sub-strate. The resonator operates in the lowest order longitudinalthickness LT1 mode, in which about half an acoustic wave-length is contained within the thickness formed by the piezo-electric film and the metal electrodes. Since the LT1 modecan also propagate horizontally as a plate wave, standingwaves are formed within the laterally finite-sized resonator.These lateral eigenmodes induce ripple in the electrical re-sponse near the main resonance. For use in frequency controlapplications and in filtering, effective suppression of thesespurious electrical responses is desired. Therefore, the prop-erties of the lateral eigenresonances are of great interest, toenable deeper understanding of the device physics and tofurther develop modeling.8–11In this letter, extraction of detailed information on indi-vidual lateral eigenmodes from the measured acoustical re-sponse is demonstrated. We present interferometric measure-ments of the acoustic wave fields on a 1.8 GHz AlN thin filmBAW resonator. Plate wave dispersion curves are calculatedfrom the measured wave fields, and the vibration amplitudesextracted along the LT1 dispersion curve are presented as afunction of frequency. Individual resonances are character-ized by fitting a mechanical resonator equivalent circuitmodel to the measured vibration data.The experimental method is demonstrated with a 1820MHz AlN based resonator utilizing an acoustic reflector con-sisting of five alternating layers of W and SiO2 for substrateisolation. The reflector is optimized for high Q according tothe method of Marksteiner et al.12 and for obtaining a desiredtype of plate wave dispersion13 to ensure lateral energy trap-ping. The resonator structure is schematically presented inaElectronic mail: Kimmo.Kokkonen@tkk.fi.TiW 10 nmAlN 1960 nmMo 296 nmW 507 nmW 505 nmSiAl 106 nm(b)SiO2 1029 nmSiO2 621 nmSiO2 786 nm-2-1.5-1-0.500.511.51700 1800 1900Frequency (MHz)(d)Phase (Z11)100101102103104Frequency (MHz)fs = 1818 MHzfp = 1861 MHzQs > 1100(c)Abs (Z11)1700 1800 1900(a)Outside regionActive areaBond wire100 µmFIG. 1. Color online a Microscope image of the sample wire-bonded toa jig for interferometric measurements. b Schematic cross sectional viewof the layer stack of the sample with measured layer thicknesses SEM. cand d Magnitude and phase of impedance obtained with wafer level mea-surement. Main figures of merit are provided as an inset in c. The electricalresponse features spurious resonances.APPLIED PHYSICS LETTERS 96, 173502 20100003-6951/2010/9617/173502/3/$30.00 © 2010 American Institute of Physics96, 173502-1 This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:130.233.216.240 On: Tue, 19 May 2015 08:54:54Fig. 1, along with a photograph and an electrical responsemeasured on wafer. The electrical response features a strongresonance-antiresonance behavior, onto which sharp spuriousoscillations are superposed, making direct extraction of theelectrical figures of merit for the main resonance difficult.Approximate values are indicated in Fig. 1.Interferometric measurements of the resonator were car-ried out with a scanning heterodyne laser interferometer.5The heterodyne concept enables acquisition of the absoluteamplitude of the surface vibration independently of the localoptical surface reflectance. The heterodyne signal also carriesphase information of the acoustic wave field, measured si-multaneously with the amplitude data at each measurementpoint.The wave field measurements feature an area of 248.49248.49 m2, including the circular active area of the reso-nator and some outer region. A lateral scan step of 0.99 mwas used, resulting in scans of 252252 63 504 datapoints. In order to study the acoustic frequency response indetail, the interferometer measurements were carried out atfrequencies ranging from 1600 to 2000 MHz. The frequencyrange was covered using three different frequency steps: astep of 1 MHz between 1600–1800 MHz and 1950–2000MHz, 0.5 MHz between 1800–1815 MHz and 1860–1950MHz, and a finer 0.25 MHz step between 1815–1860 MHzin order to provide better resolution near the resonance fre-quency fs and the frequencies of the first LT1 eigenmodes.The sample was driven with a nominal input power of+5 dBm from a 50  transmission line.Carrying out interferometric measurements at a numberof frequencies allows us to apply Fourier transform tech-niques to the measured wave fields at each frequency andthereby to determine the mode spectrum of the resonator as afunction of frequency and present it as a plate wave disper-sion diagram.6,14–17 The measured dispersion diagram isshown in Fig. 2. The LT1-dispersion curve is identified as thebright red curve emerging at just above 1820 MHz, forwhich the frequency increases monotonically with the lateralwave number k. For a simulation of the dispersion prop-erties, see Ref. 18. Furthermore, quantization of the LT1wave into lateral high-Q eigenmodes due to the finite lateralsize of the resonator results in a chain of discrete maximaseen along the dispersion curve. The lower bright red curveis identified as the second harmonic shear thickness modeST2. In addition, weaker modes with higher k are alsoexcited.The measured dispersion diagram can be further used toinvestigate the details of the LT1 resonances by extractingthe amplitude values ALT1f along a single dispersioncurve see Fig. 3. The dispersion diagram presents a decom-position of the measured wave motion to the different eigen-modes at each frequency, and therefore, by following asingle dispersion curve, the contribution of those particulareigenmodes can be isolated and further investigated.The electrical behavior of a multimode resonator is oftenpresented with a modified Butterworth van Dyke equivalentcircuit with several resonance legs.19 There is a mechanicalanalog to the electrical circuit, where the current drawn bythe circuit is proportional to the mechanical vibration ampli-tude, and can be expressed as1where C0 is the static capacitance, a resonator-geometry-related constant that is independent of the eigenmode p, V isthe driving voltage, kp the electromechanical coupling coef-ficient, Qp the quality factor and p the angular resonancefrequency of the eigenmode p. The shape of the resonancepeak is determined by the part labeled Fm, whereas thepart Ap is a mode-dependent constant. To demonstrate theextraction of the parameters, the properties of the 6 firsteigenresonances of the LT1 dispersion curve are determinedby fitting Eq. 1 to the extracted LT1 amplitude data, keep-ing the first term as a free offset parameter Boffset,2000160017001800190019501850175016500 1 2 30.5 1.5 2.5Frequency(MHz)|k||| (1/µm)LT11823 MHz 1831.5 MHz 1841.5 MHz(dB)−70−60−50−40−30−20−101852 MHz 1863.5 MHz 1874.5 MHz(dB)−70−60−50−40−30−20−10−10−60−50−40−80−70(dB)−20−30ST2FIG. 2. Color Dispersion diagram calculated from the measured vibration data and measured amplitude distributions most closely corresponding to the fitted6 first eigenfrequencies. Due to the finite lateral dimensions and high-Q resonances, the LT1 dispersion curve marked with dashed black line is seen in thedispersion diagram as a chain of discrete maxima.173502-2 Kokkonen et al. Appl. Phys. Lett. 96, 173502 2010 This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/ter sconditions. Downloaded to IP:130.233.216.240 On: Tue, 19 May 2015 08:54:54M = Boffset + p=16Ap11 + Qpp2−2jp. 2The resulting resonance frequencies fp and values of Qp areshown along with the original data ALT1f, solid line andthe function fit circles in Fig. 3. The measured amplitudedistributions corresponding to the 6 first LT1 eigenfrequen-cies are shown in Fig. 2.There is an excellent correspondence between the LT1amplitude line profile extracted from the dispersion curvesand the fitted M, validating the equivalent circuit basedrepresentation of the multimode resonator. It is to be notedthat the left-hand-side of the first peak in Fig. 3 lies belowthe cutoff frequency of the LT1 mode, where the vibrationconsists of mainly forced k0 vibration, whereas the righthand side is above the cutoff, where lateral propagation ispossible. This explains the asymmetric shape of the firstpeak. The approximate Q-value of Q1100 of the mainresonance determined from the electrical frequency responsecorresponds well to the Q-value of 1300 obtained via theinterferometer measurements. The Q-values of the followingresonances Q2−Q6 range from 670 to 820, which is clearlylower than that for the main resonance. The Q-values of theindividual lateral resonances are affected by several lossmechanisms, such as electrical and viscous losses, acousticleakage laterally and through the reflector, etc. A deeperanalysis of these effects is beyond the scope of this letter.The acoustic wave fields excited in a 1820 MHz AlNsolidly mounted BAW resonator were measured in detail.The discrete set of lateral eigenmodes excited in the resona-tor is seen in the measured dispersion curve as a chain ofmaxima rather than as a continuous mode branch. Followinga measured dispersion curve enables us to determine theproperties of the individual eigenmodes resonances by fit-ting a mechanical response function to the measured vibra-tion data. This approach facilitates direct experimental ex-traction of the eigenfrequencies, Q-values, and relativestrengths of these resonances. The relative strengths of thecoupling coefficients, kp, are available from the modelthrough the Ap parameter, but obtaining their absolute valueswould require exact knowledge of the relation between themechanical amplitude and the resonator current and leads toconsiderations beyond the scope of this letter. This directcharacterization of the LT1 eigenmodes yields valuable in-formation on the underlying device physics and also feed-back to the component designers.K. Kokkonen thanks the Finnish Cultural Foundationand the Nokia Foundation for scholarships.1J. V. Knuuttila, P. T. Tikka, and M. M. Salomaa, Opt. Lett. 25, 613 2000.2J. E. Graebner, B. P. Barber, P. L. Gammel, S. Gopani, and D. S. Greywall,Appl. Phys. Lett. 78, 159 2001.3G. G. Fattinger and P. T. Tikka, Appl. Phys. Lett. 79, 290 2001.4K. L. Telschow, V. A. Deason, D. L. Cottle, and J. D. Larson, IEEE Trans.Ultrason. Ferroelectr. Freq. Control 50, 1279 2003.5K. Kokkonen and M. Kaivola, Appl. Phys. Lett. 92, 063502 2008.6T. Fujikura, O. Matsuda, D. M. Profunser, O. B. Wright, J. Masson, and S.Ballandras, Appl. Phys. Lett. 93, 261101 2008.7K.-Y. Hashimoto, K. Kashiwa, T. Omori, M. Yamaguchi, O. Takano, S.Meguro, and K. Akahane, Microwave Symposium Digest, 2008 IEEEMTT-S International, 15–20 June, Atlanta, Georgia IEEE, New Jersey,2008, p 854.8J. D. Larson III, R. C. Ruby, and P. Bradley, U.S. Patent No. 6,215,375B1, 10 April 2001.9A. Link, E. Schmidhammer, H. Heinze, M. Mayer, B. Bader, and R.Weigel, Microwave Symposium Digest, 2006 IEEE, New Jersey, 2006,pp. 394–397.10D. Rosén, J. Bjurström, and I. Katardjiev, IEEE Trans. Ultrason. Ferro-electr. Freq. Control 52, 1189 2005.11J. Kaitila, M. Ylilammi, J. Ellä, and R. Aigner, Proc. - IEEE Ultrason.Symp. 1, 84 2003.12S. Marksteiner, J. Kaitila, G. G. Fattinger, and R. Aigner, Proc. - IEEEUltrason. Symp. 1, 329 2005.13G. G. Fattinger, S. Marksteiner, J. Kaitila, and R. Aigner, Proc. - IEEEUltrason. Symp. 2, 1175 2005.14J. E. Graebner, H. F. Safar, B. Barber, P. L. Gammel, G. J. Herbsommer,L. A. Fetter, J. Pastalan, H. A. Huggins, and R. E. Miller, Proc. - IEEEUltrason. Symp. 1, 635 2000.15G. G. Fattinger and P. T. Tikka, IEEE MTT-S Int. Microwave Symp. Dig.1, 371 2001.16T. Makkonen, T. Pensala, J. Vartiainen, J. V. Knuuttila, J. Kaitila, and M.M. Salomaa, IEEE Trans. Ultrason. Ferroelectr. Freq. Control 51, 422004.17K. L. Telschow and J. D. Larson, Proc. - IEEE Ultrason. Symp. 1, 2802003.18J. Meltaus, T. Pensala, and K. Kokkonen, Proc. - IEEE Ultrason. Symp. 1,1544 2008.19B. A. Auld, Acoustic Fields and Waves in Solids, 2nd ed. Robert E.Krieger, Malabar, FL, 1990, Vol. 2, pp. 260–261.1820 1840 1860 1900 1920Frequency (MHz)Amplitudeinlinearscale(a.u.)1234651880Q1 = 1300Q2 = 730Q3 = 670Q4 = 710Q5 = 670Q6 = 820f1 = 1822.8 MHzf2 = 1831.6 MHzf3 = 1841.4 MHzf4 = 1852.1 MHzf5 = 1863.3 MHzf6 = 1874.7 MHzFIG. 3. Color online Extracted vibration amplitudes ALT1 along the LT1dispersion curve as a function of frequency solid line, along with theresults of the mechanical equivalent circuit model fitted to the 6 first eigen-modes circles. The resulting eigenfrequencies and Q-values are presentedas an inset. There is an excellent correspondence between the extractedmechanical response and the function fit, indicating that the LT1 dispersioncurve may be described as a sum of a discrete set of independenteigenmodes.173502-3 Kokkonen et al. Appl. Phys. Lett. 96, 173502 2010 This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:130.233.216.240 On: Tue, 19 May 2015 08:54:54

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This is an electronic reprint of the original article.
This reprint may differ from the original in pagination and typographic detail.
Author(s): Kokkonen, Kimmo & Pensala, Tuomas & Meltaus, Johanna &
Kaivola, Matti
Title: Extraction of lateral eigenmode properties in thin film bulk acoustic
wave resonator from interferometric measurements
Year: 2010
Version: Final published version
Please cite the original version:
Kokkonen, Kimmo & Pensala, Tuomas & Meltaus, Johanna & Kaivola, Matti. 2010.
Extraction of lateral eigenmode properties in thin film bulk acoustic wave resonator from
interferometric measurements. Applied Physics Letters. Volume 96, Issue 17. 173502.
ISSN 0003-6951 (printed). DOI: 10.1063/1.3299012.
Rights: © 2010 American Intitute of Physics (AIP). This article may be downloaded for personal use only. Any other
use requires prior permission of the author and the American Institute of Physics.
http://scitation.aip.org/content/aip/journal/apl
All material supplied via Aaltodoc is protected by copyright and other intellectual property rights, and
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Powered by TCPDF (www.tcpdf.org)
Extraction of lateral eigenmode properties in thin film bulk acoustic wave resonator
from interferometric measurements
Kimmo Kokkonen, Tuomas Pensala, Johanna Meltaus, and Matti Kaivola 
 
Citation: Applied Physics Letters 96, 173502 (2010); doi: 10.1063/1.3299012 
View online: http://dx.doi.org/10.1063/1.3299012 
View Table of Contents: http://scitation.aip.org/content/aip/journal/apl/96/17?ver=pdfcov 
Published by the AIP Publishing 
 
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130.233.216.240 On: Tue, 19 May 2015 08:54:54
Extraction of lateral eigenmode properties in thin film bulk acoustic wave
resonator from interferometric measurements
Kimmo Kokkonen,1,a Tuomas Pensala,2 Johanna Meltaus,2 and Matti Kaivola1
1Department of Applied Physics, Helsinki University of Technology, Espoo 02150, Finland
2VTT Technical Research Centre of Finland, P. O. Box 1000, 02044 VTT, Finland
Received 15 September 2009; accepted 6 January 2010; published online 26 April 2010
A heterodyne laser interferometer is used to study acoustic wave fields excited in a 1.8 GHz AlN
thin film bulk acoustic wave resonator. The electrical response of the resonator exhibits a strong
thickness resonance onto which spurious modes, caused by lateral standing plate waves, are
superposed. Optical interferometer measurements are used to extract dispersion curves of the
laterally propagating waves responsible for the spurious responses. A discrete eigenmode spectrum
due to the finite lateral dimensions of the resonator is observed. An equivalent circuit model for a
multimode resonator is fitted to the mechanical resonator response extracted along a single curve in
the dispersion diagram, and is used to determine properties, such as Q-values, of the individual
lateral eigenmodes. Measured wave field images, extracted dispersion curves, and the eigenmode
spectrum with the model fitting results are presented. © 2010 American Institute of Physics.
doi:10.1063/1.3299012
Laser interferometry is a versatile, noncontact optical
method that provides direct information on the mechanical
wave fields excited in microacoustic structures. Optical prob-
ing of gigahertz-range bulk-acoustic waves BAWs1–7 has
proven to be very useful for studying the operation of BAW
devices, revealing their loss mechanisms, helping to refine
simulation models and for obtaining materials parameters.
The fields can be measured with a lateral resolution better
than 1 m and with smallest detectable vibration amplitudes
in the subpicometer range.
The so-called solidly mounted resonator under study
here is composed of a piezoelectric thin film sandwiched
between metal electrodes and of an acoustic Bragg reflector
that serves to acoustically isolate the device from the sub-
strate. The resonator operates in the lowest order longitudinal
thickness LT1 mode, in which about half an acoustic wave-
length is contained within the thickness formed by the piezo-
electric film and the metal electrodes. Since the LT1 mode
can also propagate horizontally as a plate wave, standing
waves are formed within the laterally finite-sized resonator.
These lateral eigenmodes induce ripple in the electrical re-
sponse near the main resonance. For use in frequency control
applications and in filtering, effective suppression of these
spurious electrical responses is desired. Therefore, the prop-
erties of the lateral eigenresonances are of great interest, to
enable deeper understanding of the device physics and to
further develop modeling.8–11
In this letter, extraction of detailed information on indi-
vidual lateral eigenmodes from the measured acoustical re-
sponse is demonstrated. We present interferometric measure-
ments of the acoustic wave fields on a 1.8 GHz AlN thin film
BAW resonator. Plate wave dispersion curves are calculated
from the measured wave fields, and the vibration amplitudes
extracted along the LT1 dispersion curve are presented as a
function of frequency. Individual resonances are character-
ized by fitting a mechanical resonator equivalent circuit
model to the measured vibration data.
The experimental method is demonstrated with a 1820
MHz AlN based resonator utilizing an acoustic reflector con-
sisting of five alternating layers of W and SiO2 for substrate
isolation. The reflector is optimized for high Q according to
the method of Marksteiner et al.12 and for obtaining a desired
type of plate wave dispersion13 to ensure lateral energy trap-
ping. The resonator structure is schematically presented in
aElectronic mail: Kimmo.Kokkonen@tkk.fi.
TiW 10 nm
AlN 1960 nm
Mo 296 nm
W 507 nm
W 505 nm
Si
Al 106 nm
(b)
SiO2 1029 nm
SiO2 621 nm
SiO2 786 nm
-2
-1.5
-1
-0.5
0
0.5
1
1.5
1700 1800 1900
Frequency (MHz)
(d)
Phase (Z11)
100
101
102
103
104
Frequency (MHz)
fs = 1818 MHz
fp = 1861 MHz
Qs > 1100
(c)
Abs (Z11)
1700 1800 1900
(a)
Outside region
Active area
Bond wire
100 µm
FIG. 1. Color online a Microscope image of the sample wire-bonded to
a jig for interferometric measurements. b Schematic cross sectional view
of the layer stack of the sample with measured layer thicknesses SEM. c
and d Magnitude and phase of impedance obtained with wafer level mea-
surement. Main figures of merit are provided as an inset in c. The electrical
response features spurious resonances.
APPLIED PHYSICS LETTERS 96, 173502 2010
0003-6951/2010/9617/173502/3/$30.00 © 2010 American Institute of Physics96, 173502-1
 This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:
130.233.216.240 On: Tue, 19 May 2015 08:54:54
Fig. 1, along with a photograph and an electrical response
measured on wafer. The electrical response features a strong
resonance-antiresonance behavior, onto which sharp spurious
oscillations are superposed, making direct extraction of the
electrical figures of merit for the main resonance difficult.
Approximate values are indicated in Fig. 1.
Interferometric measurements of the resonator were car-
ried out with a scanning heterodyne laser interferometer.5
The heterodyne concept enables acquisition of the absolute
amplitude of the surface vibration independently of the local
optical surface reflectance. The heterodyne signal also carries
phase information of the acoustic wave field, measured si-
multaneously with the amplitude data at each measurement
point.
The wave field measurements feature an area of 248.49
248.49 m2, including the circular active area of the reso-
nator and some outer region. A lateral scan step of 0.99 m
was used, resulting in scans of 252252 63 504 data
points. In order to study the acoustic frequency response in
detail, the interferometer measurements were carried out at
frequencies ranging from 1600 to 2000 MHz. The frequency
range was covered using three different frequency steps: a
step of 1 MHz between 1600–1800 MHz and 1950–2000
MHz, 0.5 MHz between 1800–1815 MHz and 1860–1950
MHz, and a finer 0.25 MHz step between 1815–1860 MHz
in order to provide better resolution near the resonance fre-
quency fs and the frequencies of the first LT1 eigenmodes.
The sample was driven with a nominal input power of
+5 dBm from a 50  transmission line.
Carrying out interferometric measurements at a number
of frequencies allows us to apply Fourier transform tech-
niques to the measured wave fields at each frequency and
thereby to determine the mode spectrum of the resonator as a
function of frequency and present it as a plate wave disper-
sion diagram.6,14–17 The measured dispersion diagram is
shown in Fig. 2. The LT1-dispersion curve is identified as the
bright red curve emerging at just above 1820 MHz, for
which the frequency increases monotonically with the lateral
wave number k. For a simulation of the dispersion prop-
erties, see Ref. 18. Furthermore, quantization of the LT1
wave into lateral high-Q eigenmodes due to the finite lateral
size of the resonator results in a chain of discrete maxima
seen along the dispersion curve. The lower bright red curve
is identified as the second harmonic shear thickness mode
ST2. In addition, weaker modes with higher k are also
excited.
The measured dispersion diagram can be further used to
investigate the details of the LT1 resonances by extracting
the amplitude values ALT1f along a single dispersion
curve see Fig. 3. The dispersion diagram presents a decom-
position of the measured wave motion to the different eigen-
modes at each frequency, and therefore, by following a
single dispersion curve, the contribution of those particular
eigenmodes can be isolated and further investigated.
The electrical behavior of a multimode resonator is often
presented with a modified Butterworth van Dyke equivalent
circuit with several resonance legs.19 There is a mechanical
analog to the electrical circuit, where the current drawn by
the circuit is proportional to the mechanical vibration ampli-
tude, and can be expressed as
1
where C0 is the static capacitance, a resonator-geometry-
related constant that is independent of the eigenmode p, V is
the driving voltage, kp the electromechanical coupling coef-
ficient, Qp the quality factor and p the angular resonance
frequency of the eigenmode p. The shape of the resonance
peak is determined by the part labeled Fm, whereas the
part Ap is a mode-dependent constant. To demonstrate the
extraction of the parameters, the properties of the 6 first
eigenresonances of the LT1 dispersion curve are determined
by fitting Eq. 1 to the extracted LT1 amplitude data, keep-
ing the first term as a free offset parameter Boffset,
2000
1600
1700
1800
1900
1950
1850
1750
1650
0 1 2 30.5 1.5 2.5
Fr
eq
ue
nc
y
(M
H
z)
|k||| (1/µm)
LT1
1823 MHz 1831.5 MHz 1841.5 MHz
(dB)
−70
−60
−50
−40
−30
−20
−10
1852 MHz 1863.5 MHz 1874.5 MHz
(dB)
−70
−60
−50
−40
−30
−20
−10
−10
−60
−50
−40
−80
−70
(dB)
−20
−30
ST2
FIG. 2. Color Dispersion diagram calculated from the measured vibration data and measured amplitude distributions most closely corresponding to the fitted
6 first eigenfrequencies. Due to the finite lateral dimensions and high-Q resonances, the LT1 dispersion curve marked with dashed black line is seen in the
dispersion diagram as a chain of discrete maxima.
173502-2 Kokkonen et al. Appl. Phys. Lett. 96, 173502 2010
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M = Boffset + 
p=1
6
Ap
1
1 + Qpp
2
−2
jp
. 2
The resulting resonance frequencies fp and values of Qp are
shown along with the original data ALT1f, solid line and
the function fit circles in Fig. 3. The measured amplitude
distributions corresponding to the 6 first LT1 eigenfrequen-
cies are shown in Fig. 2.
There is an excellent correspondence between the LT1
amplitude line profile extracted from the dispersion curves
and the fitted M, validating the equivalent circuit based
representation of the multimode resonator. It is to be noted
that the left-hand-side of the first peak in Fig. 3 lies below
the cutoff frequency of the LT1 mode, where the vibration
consists of mainly forced k0 vibration, whereas the right
hand side is above the cutoff, where lateral propagation is
possible. This explains the asymmetric shape of the first
peak. The approximate Q-value of Q1100 of the main
resonance determined from the electrical frequency response
corresponds well to the Q-value of 1300 obtained via the
interferometer measurements. The Q-values of the following
resonances Q2−Q6 range from 670 to 820, which is clearly
lower than that for the main resonance. The Q-values of the
individual lateral resonances are affected by several loss
mechanisms, such as electrical and viscous losses, acoustic
leakage laterally and through the reflector, etc. A deeper
analysis of these effects is beyond the scope of this letter.
The acoustic wave fields excited in a 1820 MHz AlN
solidly mounted BAW resonator were measured in detail.
The discrete set of lateral eigenmodes excited in the resona-
tor is seen in the measured dispersion curve as a chain of
maxima rather than as a continuous mode branch. Following
a measured dispersion curve enables us to determine the
properties of the individual eigenmodes resonances by fit-
ting a mechanical response function to the measured vibra-
tion data. This approach facilitates direct experimental ex-
traction of the eigenfrequencies, Q-values, and relative
strengths of these resonances. The relative strengths of the
coupling coefficients, kp, are available from the model
through the Ap parameter, but obtaining their absolute values
would require exact knowledge of the relation between the
mechanical amplitude and the resonator current and leads to
considerations beyond the scope of this letter. This direct
characterization of the LT1 eigenmodes yields valuable in-
formation on the underlying device physics and also feed-
back to the component designers.
K. Kokkonen thanks the Finnish Cultural Foundation
and the Nokia Foundation for scholarships.
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1820 1840 1860 1900 1920
Frequency (MHz)
A
m
pl
itu
de
in
lin
ea
rs
ca
le
(a
.u
.)
1
2
3
4
65
1880
Q1 = 1300
Q2 = 730
Q3 = 670
Q4 = 710
Q5 = 670
Q6 = 820
f1 = 1822.8 MHz
f2 = 1831.6 MHz
f3 = 1841.4 MHz
f4 = 1852.1 MHz
f5 = 1863.3 MHz
f6 = 1874.7 MHz
FIG. 3. Color online Extracted vibration amplitudes ALT1 along the LT1
dispersion curve as a function of frequency solid line, along with the
results of the mechanical equivalent circuit model fitted to the 6 first eigen-
modes circles. The resulting eigenfrequencies and Q-values are presented
as an inset. There is an excellent correspondence between the extracted
mechanical response and the function fit, indicating that the LT1 dispersion
curve may be described as a sum of a discrete set of independent
eigenmodes.
173502-3 Kokkonen et al. Appl. Phys. Lett. 96, 173502 2010
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130.233.216.240 On: Tue, 19 May 2015 08:54:54


English

A heterodyne laser interferometer is used to study acoustic wave fields excited in a 1.8 GHz AlN thin film bulk acoustic wave resonator. The electrical response of the resonator exhibits a strong thickness resonance onto which spurious modes, caused by lateral standing plate waves, are superposed. Optical interferometer measurements are used to extract dispersion curves of the laterally propagating waves responsible for the spurious responses. A discrete eigenmode spectrum due to the finite lateral dimensions of the resonator is observed. An equivalent circuit model for a multimode resonator is fitted to the mechanical resonator response extracted along a single curve in the dispersion diagram, and is used to determine properties, such as Q-values, of the individual lateral eigenmodes. Measured wave field images, extracted dispersion curves, and the eigenmode spectrum with the model fitting results are presented

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Extraction of lateral eigenmode properties in thin film bulk acoustic wave resonator from interferometric measurements

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