Research ArticleTheoretical Simulation and Optimization on MaterialParameters of Thin Film Bulk Acoustic Resonator

Tao Zhang12 Fujun Liang1 Min Li1 Shaorong Li1 Huafeng Pang1 Sufang Wang1

Huaze Zhu1 Zhengxin Yan1 and Shenggui Zhao1

1College of Science Xirsquoan University of Science and Technology Xirsquoan 710054 China2Laboratory of Modern Acoustics Institute of Acoustics Nanjing University Nanjing 210093 China

Correspondence should be addressed to Tao Zhang tzhang psuyahoocom

Received 20 June 2015 Accepted 6 September 2015

Academic Editor Jun Chen

Copyright copy 2015 Tao Zhang et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

The resonance frequency 119891119904 and the effective electromechanical coupling factor 1198962eff of thin film bulk acoustic resonators (FBARs)

are derived by transfer matrix method The effects of thickness and density of electrode on 119891119904and 1198962eff with different piezoelectric

layers are investigated by numerical calculationmethodThe results show that thickness and density of electrode affect119891119904obviously

especially in large thickness and density area Moreover the effects of thickness density and acoustic velocity of electrode on 1198962eff ofFBAR were also studied The results show that there is a maximum 1198962eff corresponding to the composition of thickness and densityof electrode which is about 20 over the original electromechanical factor of piezoelectric film 1198962eff is in the direct proportion tothe density 120588

119890and V

119890of electrode respectively The electrode thickness affects 1198962eff small with high V

119890 moreover when V

119890is high

enough then 1198962eff has almost nothing to do with 119889119890 1198962eff always rises with electrode thickness first and then descends with its rising

and the thickness corresponding to the maximum 1198962eff is different with different electrode but it always locates in the special areaAll above results indicate that the thickness density and acoustic velocity of electrode are so important that these results can beapplied to design FBAR

1 Introduction

The thin film bulk acoustic resonators (FBARs) are exten-sively applied for filters resonators and sensors since theywere first realized with the resonance frequency of 19 GHzin 1999 such as MEMS biosensors and gas sensors [1ndash8]It is a kind of important device in electronic equipmentand so many kinds of FBARs with high frequency andsmall dimension have been fabricated during recent ten yearsfor the demand of the industry [9 10] The FBARs areespecially expected to be investigated and applied by manysemiconductor companies such as Agilent Philip Murataand TDK because of their excellent merits

Most of researchers focus on the fabrications and theapplications of FBAR and there also are a few researchesabout numerical simulation and optimization of FBAR Chaoet al studied the electrode effects of FBAR by Butterworth-van Dyke (BVD) equivalent circuit [11] and Chen and

Wang calculated the effective electromechanical couplingcoefficient of FBAR [12] and Zhang et al applied resonantspectrummethod to characterize piezoelectric films in FBAR[13] Besides our research group published the research aboutthe electrode effect of FBAR [14] and Naumenko analyzedthe propagation of acoustic wave in FBAR with FiniteElement Method [15] and Kvasov and Tagantsev calculatedthe nonlinear electrostrictive coefficient with first principles[16] All of above researches aim at the excellent FBARperformance because the resonance frequency the effectivecoupling coefficient and the accurate optimization for thedesign of FBAR are the key points for FBAR performance

As a kind of bulk acoustic resonator (BAR) the figure ofmerit of an FBAR can be defined by119872 = 1198962eff sdot 119876119878(1 minus 119896

2

eff )and 119876

119878is the resonance quality factor which is obviously

controlled by the piezoelectric layer and electrode effectand the special research has been done by our researchgroup [14] and so we deeply discuss the material parameter

Hindawi Publishing CorporationJournal of NanomaterialsVolume 2015 Article ID 413687 8 pageshttpdxdoiorg1011552015413687

2 Journal of Nanomaterials

Piezofilm

Top electrode

Bottom electrode

d

l

e

de

Figure 1 A typical FBAR structure

u9984001

F9984001

E1

u1 u2

F1

P

I U Z2Z1

Zin

F2

E2

u9984002

F9984002

Figure 2 Transfer matrix schematic diagram

effects of electrode on the resonance frequency the effectiveelectromechanical coupling factor and the theoretical opti-mization consideration of FBAR in this paper consideringthe regularity among the density 120588

119890 the thickness 119889

119890 the

acoustic velocity V119890of electrode and the FBAR performance

parameters 119891119904and 1198962eff The transmission matrix method

was used in this research and the following research pointsand corresponding simulation results are presented (1) thetransfer matrix method being used to derive the inputimpedance equation (2) effects of 120588

119890and 119889

119890on 119891119904 (3) effects

of 120588119890and 119889

119890on 1198962eff (4) effects of V119890 and 119889119890 on 119896

2

eff and (5)the two cases with the piezoelectric films of ZnO and AlNrespectively being compared for discussion

2 Simulation Method and Procedures

For the FBAR shown in Figure 1 its transfermatrix schematicdiagram is shown in Figure 2 P part represents the piezoelec-tric layer E1 and E2 parts represent top electrode and bottomelectrode respectively 119880 and 119868 represent electronic voltageand current port respectively119865 and 119906 represent the force andvibration velocity respectively and 119885in represents the inputacoustic impedance of this system Sowe can get the followingtransfer equation [13]

[119880

119868] = [119861] sdot [

119865

119906] (1)

The piezoelectric transfer matrix [119861] can be given as [13]

[119861]

=1

120601119867[

[

11198951206012

1205961198620

1198951205961198620

0

]

]

sdot[[

[

cos 120574 + 119895119885119864sin 120574 119885

0(119885119864cos 120574 + 119895119885

119864sin 120574)

119895 sin 1205741198850

2 (cos 120574 minus 1) + 119895119885119864sin 120574

]]

]

(2)

where 120601 = 119896211990511986201198850119897119881 is Mason equivalent circuit transfer

ratio 1198962119905is the electromechanical coupling factor of piezoelec-

tric film 1198620= 12057611987833119878119897 is the clamped capacitor with area of 119878

12057611987833

is the dielectric constant with the vertical direction 119897 isthe thickness of piezoelectric film 119885

0= 120588119881119878 is the acoustic

impedance of piezoelectric film with the density of 120588119881 is thelongitudinal wave velocity 120574 = 120596119897119881 is the phase delay in thepiezoelectric film 120596 = 2120587119891 is angular frequency and 119885

119864is

the acoustic impedance of electrodesWe take the electrode material as isotropic and then we

can get the matrix as

[1198651

1199061

] =[[

[

cos 1205741198901

1198951198851198901sin 1205741198901

119895 sin 1205741198901

1198851198901

cos 1205741198901

]]

]

sdot [11986510158401

11990610158401

] (3)

where 11986510158401is zero because of the free top acoustic port 120574

1198901=

12059611989711989011198811198901

is the phase delay in the top electrode 1198971198901

is thethickness of top electrode 119881

1198901is the acoustic velocity of top

electrode 1198851198901= 12058811989011198811198901119878 is the acoustic impedance of top

electrode and 1205881198901is the density of top electrode

We can get 1198851from (3)

1198851=1198650

1199060

= 1198951198851198901tan 1205741198901 (4)

Similarly we can get the acoustic impedance of bottomelectrode

1198852=1198652

1199062

= 1198951198851198902tan 1205741198902 (5)

So the total input acoustic impedance can be given as [13]

119885in =119880

119868=

1

1198951205961198620

sdot [1 minus1198962119905

120574

sdot(1199111+ 1199112) sdot sin 120574 + 119895 sdot 2 sdot (1 minus cos 120574)

(1199111+ 1199112) sdot cos 120574 + 119895 sdot (1 + 119911

1sdot 1199112) sdot sin 120574

]

(6)

Inside (6) 1199111= 11988511198850 1199112= 11988521198850 We take the top

electrode and bottom electrode as the same so the inputimpedance (119885in) can be given as (7) with a transfer matrixmethod [12 14]

119885in =1

1198951205961198620

[1 minus1198962119905

120574

119911 sin 120574 + 119895 (1 minus cos 120574)119911 cos 120574 + (1198952) (1 + 1199112) sin 120574

] (7)

Journal of Nanomaterials 3

120574 = 120596119897119881 is the phase shift in the piezofilm and 119911 = 1198851198850

is the characteristic impedance ratio of the electrodes to thepiezofilm as the top and bottom electrodes with the samematerial and thicknessThe series resonance frequency119891

119904and

the parallel resonance frequency 119891119901can be obtained by (7)

and then the effective electromechanical coupling factor ofFBAR can be demonstrated with the known 119891

119904and 119891

119901

1198962eff =(1198912119901minus 1198912119904)

1198912119901

cong 2 sdot(119891119901minus 119891119904)

119891119901

(8)

Based on the definition published in the IEEE Std176-1987 [17] 119891

119904is the frequency corresponding with the

maximum conductance Then 119891119904can be calculated by (7)

and 1198962eff can be evaluated by (8) However 1198962eff is not onlydetermined by 1198962

119905but also closely related with the electrode

and resonator structureIn the calculation of the resonance frequency 119891

119904with

(7) the dielectric the piezoelectric and the elastic constantsof the piezoelectric film and the elastic constants of theelectrodes generally are complex values but all others suchas 1198962119905 are considered as real values [12] In addition for a

given piezofilm 1198620is a constant The complex velocity

119897in

piezofilms or electrodes was given by a complex expression[12]

= [(119862101584033+ 1198951198621015840101584033)

120588]

12

cong 1198811015840 [1 +119895

(2119876119898)] (9)

1198811015840 = radic119862101584033120588 is the real part 11988110158401015840 = radic11986210158401015840

33120588 is the imaginary

part and 119862101584033

and 1198621015840101584033

are the real part and imaginary partof elastic constant 119862

33 where 11986210158401015840

33is responsible for the

mechanical losses and 119876119898= 119862101584011986210158401015840 cong 1198811015840211988110158401015840 is the

mechanical quality factor of the piezofilm or the electrodeSo the resonance frequency and the effective electrome-

chanical coupling coefficient of FBAR can be obtained andanalyzed by above definitions and equations

3 Effects of Material Quality Factors onEffective Coupling Factor

The effect of electrode on FBAR performance is studied andshown in the following parts and the thickness 119889

119890 the

density 120588119890 on the resonance frequency 119891

119904 and the effec-

tive electromechanical coupling factor 1198962eff are investigatedbesides the acoustic velocity V

119890on 1198962eff is also done The

different piezoelectric films of ZnO and AlN with thicknessof 2 120583m are used in this research and they both are typicalexamples in the realistic applications and the constants ofmaterial used in the calculation are shown in Table 1

31 Effects of 120588119890and 119889

119890on 119891119904of FBAR The resonance

frequency is very important parameter for frequency devicesespecially for the acoustic device with vibration such asFBAR In general the frequency of FBAR is the basicparameter which should be considered during the design ofFBAR and so it is why we began with it

Table 1 Data of material properties

Material Density(kgm3)

Velocity(ms)

Impedance(106 kgm3s) 1198962

119905

ZnO 5606 6350 356 750AlN 3300 11050 365 625

The resonance frequency definitions are stated in theIEEE Std 176-1987 that 119891

119904is defined as the frequency of

maximum conductance [17] So we can calculate119891119904by setting

the conductance maximum with (7) In the calculations wetake the different piezoelectric films with ZnO and AlN andtake all other parameters as constants except the density andthe thickness of electrode We can take the different densityas different electrode material and study what will happen tothe resonance frequency of FBAR if we change the thicknessof the same material electrode which is very valuable for thedesign of FBAR devices

The results of 119891119904changing with 120588

119890and 119889

119890of FBAR based

on ZnO and AlN piezoelectric films were obtained andthe three-dimensional (3D) figures were shown as Figures3(a) and 4(a) respectively and the two-dimensional (2D)figures were shown as Figures 3(b) and 4(b) respectivelyIt can be obtained that the resonance frequency decreaseswith the thickness and the density of electrode increasingby the 3D figures and this rule becomes more typical withthe thin electrode or the high density and it is the mostobvious when both thickness and density of electrode appearin large value area So we can choose proper material withsmall density and thin electrode for high resonance frequencyby these results even though there still are some otherparameters which should also be considered such as acousticvelocity However if the acoustic velocity in the electrode is aconstant then this result can be effectively used to design andevaluate the resonance frequency according to the applicationrequirementThe above results can also be proved by the two2D figures Besides we also can get that the FBAR decreasedover half of resonance frequency just with the thicknesschange of 04 120583m and so the thickness effect of electrodeon the resonance frequency are very distinct which becomessmoother in the smaller thickness area

32 Effects of 120588119890and 119889

119890on 1198962119890119891119891

of FBAR Based on thedefinition published in the IEEE Std 176-1987 [17] 119891

119904is the

frequency of maximum conductance and 119891119901is the frequency

of maximum resistance Then 119891119904and 119891

119901can be calculated

by (7) and 1198962eff can be evaluated by (8) 1198962eff is not onlydetermined by 1198962

119905but also determined by the electrode and

resonator structureWe calculated 1198962eff changing with the thickness and the

density of electrode and the 3D figures and 2D figures weregiven in Figures 5 and 6 with ZnO and AlN piezoelectricfilms respectively

It can be obtained by Figures 5(a) and 6(a) that thereis the maximum 1198962eff corresponding to some compositionsof thickness and density of electrode which is near thethin electrode and high density area 1198962eff increases and then

4 Journal of Nanomaterials

00511520 01 02 03 04 05 06 07 08 09 104

06

08

1

12

14

16

05 06 07 08 09 1 11 12 13 14 15

fs

(Hz)

de (120583m)

times109

times109

120588e (104 kgm3 )

(a)

04 06 08 1 12 14 16 18

010203040506070809

1

5 6 7 8 9 10 11 12 13 14

de

(120583m

)

times108

120588e (104 kgm3)

(b)

Figure 3 119891119904of FBAR versus the thickness and the density of electrode with ZnO piezoelectric film

00511520 01 02 03 04 05 06 07 08 09 1456789

1011

5 6 7 8 9 10

fs

(Hz)

de (120583m)

times108

times108

120588e(10

4 kgm3 )

(a)

04 06 08 1 12 14 16 18

010203040506070809

1

45 5 55 6 65 7 75 8 85 9 95 10

de

(120583m

)

times108

120588e (104 kgm3)

(b)

Figure 4 119891119904of FBAR versus the thickness and the density of electrode with AlN piezoelectric film

01

2

001020304050607080910055

006

0065

007

0075

0056 0058 006 0062 0064 0066 0068 007 0072

k2 eff

de (120583m) 120588 e(10

4 kgm

3 )

(a)

04 06 08 1 12 14 16 18

010203040506070809

1

0056 0058 006 0062 0064 0066 0068 007

de

(120583m

)

120588e (104 kgm3)

(b)

Figure 5 1198962eff of FBAR versus the thickness and the density of electrode with ZnO piezoelectric film

Journal of Nanomaterials 5

0 051 15

2

00102030405060708091005

0052

0054

0056

0058

006

0062

0052 0053 0054 0055 0056 0057 0058 0059 006

k2 eff

de (120583m) 120588 e(10

4 kgm3 )

(a)

04 06 08 1 12 14 16 18

010203040506070809

1

0052 0053 0054 0055 0056 0057 0058 0059 006

de

(120583m

)

120588e (104 kgm3)

(b)

Figure 6 1198962eff of FBAR versus the thickness and the density of electrode with AlN piezoelectric film

decreases with the thickness increasing and the increasingratio can reach to 20 over original value of piezoelectricfilm However 1198962eff mostly increases with the density ofelectrode 1198962eff changes fast with the thickness of electrodewhen the density of electrode is small and vice versa TheFBAR with the ZnO layer shows that 1198962eff changes morequickly than the case of AlN and the thickness effect is moreobvious too especially for the small density of electrode casesFurthermore we can also get the same witness from the 2Dfigures of Figures 5(b) and 6(b)

A very interesting result is obtained from 2D figures that1198962eff will arrive at a maximum area with special thicknessvalues for any density of electrode and the correspondingthickness area is very obvious at the center such as the FBARwith ZnO The thickness beginning with the maximum 1198962effarea is nearby 037 120583m and the thickness is nearby 05 120583m forthe AlN case This is a very interesting and important resultand it means the effect of thickness on 1198962eff has a strong rulewhich is affected little by the density of electrode materialWe analyzed this phenomenon that it is the thickness wherestanding wave appears and the difference between thesetwo piezoelectric film cases should be attributed to thedifferent piezoelectric thin films Moreover it confirms thatthe standing wave exists in the FBAR and the thickness ofelectrode should be optimized with this merit point which iseffective for all kinds of electrode materials

33 Effects of V119890and119889119890on 1198962119890119891119891

of FBAR For overall evaluationof 1198962eff the effects of V

119890and 119889

119890on 1198962eff were conducted

with the 2 120583m thick piezoelectric film and the 2D and 3Dfigures with four different electrode density choices weregiven for contrasting The 3D 1198962eff versus V

119890and 119889

119890curves

based on ZnO and AlN were shown in Figures 7 and 9respectively and the 2D results were shown in Figures 8and 10 correspondingly The key parameters and results weremarked on the 3D figures We can get that 1198962eff always riseswith the density of electrode for the ZnO case in Figure 7

0 05 12468101214

002

003

004

005

006

007

008k2 eff

Number 1 120588e = 19 times 104 kgm3

(e = 145 times 103 ms de = 055120583m)

Number 2 120588e = 13 times 104 kgm3

(e = 145 times 103 ms de = 06 120583m)

eNumber 3 120588 = 7 times 103

103kgm3

(e = 145 times ms de = 065120583m)

Number 4 120588e = 2 times 103

103kgm3

(e = 145 times ms de = 08 120583m)

e (103 ms) de(120583m)

max k = 0074156

max k = 007372

max k = 0072642

max k = 007028

Figure 7 1198962eff of FBAR versus the thickness and the acoustic velocityof electrode with ZnO piezoelectric film and different density (3Dcurves)

which also can be observed in above section results andthe maximum 1198962eff always appears at the maximum acousticvelocity during our calculation range The AlN case is thesame behavior as the ZnO FBAR in Figure 9 Moreover 1198962effrises more obviously with V

119890in the large electrode thickness

area and vice versa and 1198962eff changes little with V119890among the

small electrode thickness area and especially least in the highdensity electrode material area On the other hand 1198962eff risesdistinctlywith the electrode thickness in the low velocity areabut it almost does not change in the high velocity space

6 Journal of Nanomaterials

01 02 03 04 05 06 07 08 09 1

4

6

8

10

12

14

003

004

005

006

007

e(103

ms

)

de (120583m)

(a) 120588119890= 2 times 10

3 kgm3

0035004004500500550060065007

01 02 03 04 05 06 07 08 09 1

4

6

8

10

12

14

e(103

ms

)

de (120583m)

(b) 120588119890= 7 times 10

3 kgm3

005

0055

006

0065

01 02 03 04 05 06 07 08 09 1

4

6

8

10

12

14

e(103

ms

)

de (120583m)

(c) 120588119890= 13 times 10

4 kgm3

0055

006

0065

007

01 02 03 04 05 06 07 08 09 1

4

6

8

10

12

14

e(103

ms

)de (120583m)

(d) 120588119890= 19 times 10

4 kgm3

Figure 8 1198962eff of FBAR versus the thickness and the acoustic velocity of electrode with ZnO piezoelectric film (2D curves)

005

1

24681012140025

003

0035

004

0045

005

0055

006

0065

k2 eff

e (103 ms) de(120583m)

4 3Number 1 120588e = 19 times 10 kgm(e = 145 times 103 ms de = 08 120583m)

Number 2 120588e = 13 times 104 kgm3

(e = 145 times 103 ms de = 09 120583m)Number 3 120588e = 7 times 103 kgm3

e e( = 145 times 103 ms d = 095120583m)Number 4 120588e = 2 times 103 kgm3

(e = 145 times 103 ms de = 105 120583m)

max k = 0061397

max k = 0060458

max k = 0058439

max k = 0061766

Figure 9 1198962eff of FBAR versus the thickness and the acoustic velocityof electrode with AlN piezoelectric film and different density (3Dcurves)

We can conclude that 1198962eff is in the direct proportion tothe density 120588

119890here and the acoustic velocity of electrode has

a similar effect too and 1198962eff dominantly rises with V119890 The

electrode thickness affects small 1198962eff with high V119890 moreover

when V119890is high enough then 1198962eff has almost nothing to do

with 119889119890 But 1198962eff changes fast with 119889

119890when V

119890is small and

1198962eff rises with electrode thickness first and then descendswithits rising which was also observed in the former sectionThe thickness corresponding to themaximum 1198962eff is differentwith different electrode density however it descends withdensity ascending which also proves the special value 120588

119890119889119890

corresponding with the maximum 1198962eff of FBAR even thoughwe cannot get this result directly by these figures becausethere are not so many piezoelectric film parameters consid-ered for proving [14] All these behaviors are similar for bothZnO and AlN based FBARs

The density acoustic velocity and thickness of electrodeof FBAR can be optimized by above results for special 119891

119904and

1198962eff need We can get the higher 1198962eff with the higher electrodedensity and it is also the same to acoustic velocity of electrodematerialThe best thickness of electrode is decided by densityand especially acoustic velocity however the thickness effectsare obvious when the acoustic velocity is small but it almostdoes not change if the acoustic velocity is very big Moreoverthe best thickness corresponding to the maximum 1198962eff isdifferent with different cases but the values are in the specialarea comparing with the distinctly variable V

119890and 120588119890 and it is

because we take most of the parameters of piezoelectric thinfilm as constants even though these results can be observedin both ZnO and AlN FBARs in this research

4 Conclusions

In this paper the following research and results have beengiven

Journal of Nanomaterials 7

003

0035

004

0045

005

0055

01 02 03 04 05 06 07 08 09 14

6

8

10

12

14 e

(103

ms

)

de (120583m)

(a) 120588119890= 2 times 10

3 kgm3

004

0045

005

0055

006

01 02 03 04 05 06 07 08 09 14

6

8

10

12

14

e(103

ms

)

de (120583m)

(b) 120588119890= 7 times 10

3 kgm3

0045

005

0055

006

01 02 03 04 05 06 07 08 09 14

6

8

10

12

14

e(103

ms

)

de (120583m)

(c) 120588119890= 13 times 10

4 kgm3

005

0052

0054

0056

0058

01 02 03 04 05 06 07 08 09 14

6

8

10

12

14

e(103

ms

)de (120583m)

(d) 120588119890= 19 times 10

4 kgm3

Figure 10 1198962eff of FBAR versus the thickness and the acoustic velocity of electrode with AlN piezoelectric film and different density (2Dcurves)

(i) Firstly we derived the input acoustic impedanceequation with transfer matrix method and the sim-plified impedance equation of FBAR with the sametop and bottom electrode is obtained This equationcan be applied extensively to calculate the resonancefrequency the effective electromechanical couplingfactor themechanical quality factor and themerit fig-ure of FBAR which makes the theoretical calculationand optimization easy

(ii) Secondly the effect of thickness and density ofelectrode on the resonance frequency of FBAR wasinvestigated and it can be obtained that the thicknessand the density of electrode affect the resonancefrequency obviously especially at the large thicknessand density area This result shows that the thicknessand the material of electrode are very key parametersfor the resonance frequency design of FBAR

(iii) Finally the effects of thickness density and acousticvelocity on the effective electromechanical couplingfactor were studied respectivelyThe results show that1198962eff is in the direct proportion to both density 120588

119890and

V119890of electrode The electrode thickness affects small

1198962eff with high V119890 moreover when V

119890is high enough

then 1198962eff has almost nothing to do with 119889119890 1198962eff rises

with electrode thickness first and then descends withits rising and the thickness corresponding to themaximum 1198962eff is different with different electrodedensity and V

119890 but they almost locate in the special

area

All above results indicate that the thickness density andacoustic velocity of electrode are very important and they canbe applied to optimize and design different kind of FBARs

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This work is supported by the National Natural ScienceFoundation of China (nos 61201088 11404257 and 11504291)Shaanxi Province Innovation Project for Science and Tech-nology Overall Planning (no 2012KTCL01-12) Industrial-ization Foundation of Shaanxi Educational Committee (no2011JG10) and Xirsquoan Technology Transferring and PromotingProject (CXY1342(5) CX1253(2))

References

[1] J D Larson III R Ruby P Bradley and Y Oshmyansky ldquoBAWantenna duplex for the 1900MHz PCS bandrdquo in Proceedings ofthe IEEE Ultrasonics Symposium pp 887ndash890 Caesars TahoeNV USA October 1999

[2] R Ruby P Bradley J D Larson III and Y Oshmyansky ldquoPCS1900MHz duplexer using thin film bulk acoustic resonators(FBARs)rdquo Electronics Letters vol 35 no 10 pp 794ndash796 1999

[3] R C Ruby P Bradley Y Oshmyansky A Chien and J DLarson III ldquoThin film bulk wave acoustic resonators (FBAR)for wireless applicationsrdquo in Proceedings of the UltrasonicsSymposium pp 813ndash821 October 2001

8 Journal of Nanomaterials

[4] K M Lakin J Belsick J F McDonald and K T McCarronldquoImproved bulk wave resonator coupling coefficient for widebandwidth filtersrdquo inProceedings of the IEEEUltrasonics Sympo-sium vol 1 pp 827ndash831 IEEE Atlanta Ga USA October 2001

[5] I Voiculescu and A N Nordin ldquoAcoustic wave based MEMSdevices for biosensing applicationsrdquo Biosensors and Bioelectron-ics vol 33 no 1 pp 1ndash9 2012

[6] F T Chu C Li Z Z Wang and X Z Liu ldquoAluminum NitrideThin films on molybdenumpolyimide heterostructure for bulkacoustic resonatorsrdquo Rare Metal Materials and Engineering vol42 no 10 pp 2023ndash2026 2013

[7] A J Festschrift J K Luo Y Q Fu et al ldquoZnO based SAWand FBAR devices for bio-sensing applicationsrdquo Journal of Non-Newtonian Fluid Mechanics vol 222 pp 209ndash216 2015

[8] H Zhang G Jiang Z Liu S Zhang and L Fan ldquoOptimizationsof composited acoustic sensors with a microfluidic channelrdquoJournal of Applied Physics vol 115 no 13 Article ID 1335022014

[9] A Vorobiev and S Gevorgian ldquoIntrinsically switchable thinfilm bulk acoustic wave resonatorsrdquo Applied Physics Letters vol104 no 22 Article ID 222905 2014

[10] H J Lee K A Hyun and H I Jung ldquoA high-Q resonator usingbiocompatible materials at microwave frequenciesrdquo AppliedPhysics Letters vol 104 no 2 Article ID 023509 2014

[11] M-C Chao Z-N Huang S-Y Pao Z Wang and C S LamldquoModified BVD-equivalent circuit of FBARby taking electrodesinto accountrdquo inProceedings of the IEEEUltrasonics Symposiumpp 973ndash976 October 2002

[12] Q Chen and Q-M Wang ldquoThe effective electromechani-cal coupling coefficient of piezoelectric thin-film resonatorsrdquoApplied Physics Letters vol 86 no 2 Article ID 022904 2005

[13] Y Zhang Z Wang and J D N Cheeke ldquoResonant spectrummethod to characterize piezoelectric films in composite res-onatorsrdquo IEEE Transactions on Ultrasonics Ferroelectrics andFrequency Control vol 50 no 3 pp 321ndash333 2003

[14] T Zhang H Zhang Z-Q Wang and S-Y Zhang ldquoEffects ofelectrodes on performance figures of thin film bulk acousticresonatorsrdquo Journal of the Acoustical Society of America vol 122no 3 pp 1646ndash1651 2007

[15] N F Naumenko ldquoAdvanced numerical technique for analysisof surface and bulk acoustic waves in resonators using periodicmetal gratingsrdquo Journal of Applied Physics vol 116 no 10 ArticleID 104503 2014

[16] A Kvasov and A K Tagantsev ldquoThin film bulk acoustic waveresonators tuning from first principlesrdquo Journal of AppliedPhysics vol 113 no 20 Article ID 204104 2013

[17] IEEE ldquoIEEE standard on piezoelectricityrdquo Tech Rep 176-1987 IEEE Transactions on Ultrasonics Ferroelectrics andFrequency Control 1996 43719

Submit your manuscripts athttpwwwhindawicom

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Nano

materials

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Journal ofNanomaterials

2 Journal of Nanomaterials

Piezofilm

Top electrode

Bottom electrode

d

l

e

de

Figure 1 A typical FBAR structure

u9984001

F9984001

E1

u1 u2

F1

P

I U Z2Z1

Zin

F2

E2

u9984002

F9984002

Figure 2 Transfer matrix schematic diagram

effects of electrode on the resonance frequency the effectiveelectromechanical coupling factor and the theoretical opti-mization consideration of FBAR in this paper consideringthe regularity among the density 120588

119890 the thickness 119889

119890 the

acoustic velocity V119890of electrode and the FBAR performance

parameters 119891119904and 1198962eff The transmission matrix method

was used in this research and the following research pointsand corresponding simulation results are presented (1) thetransfer matrix method being used to derive the inputimpedance equation (2) effects of 120588

119890and 119889

119890on 119891119904 (3) effects

of 120588119890and 119889

119890on 1198962eff (4) effects of V119890 and 119889119890 on 119896

2

eff and (5)the two cases with the piezoelectric films of ZnO and AlNrespectively being compared for discussion

2 Simulation Method and Procedures

For the FBAR shown in Figure 1 its transfermatrix schematicdiagram is shown in Figure 2 P part represents the piezoelec-tric layer E1 and E2 parts represent top electrode and bottomelectrode respectively 119880 and 119868 represent electronic voltageand current port respectively119865 and 119906 represent the force andvibration velocity respectively and 119885in represents the inputacoustic impedance of this system Sowe can get the followingtransfer equation [13]

[119880

119868] = [119861] sdot [

119865

119906] (1)

The piezoelectric transfer matrix [119861] can be given as [13]

[119861]

=1

120601119867[

[

11198951206012

1205961198620

1198951205961198620

0

]

]

sdot[[

[

cos 120574 + 119895119885119864sin 120574 119885

0(119885119864cos 120574 + 119895119885

119864sin 120574)

119895 sin 1205741198850

2 (cos 120574 minus 1) + 119895119885119864sin 120574

]]

]

(2)

where 120601 = 119896211990511986201198850119897119881 is Mason equivalent circuit transfer

ratio 1198962119905is the electromechanical coupling factor of piezoelec-

tric film 1198620= 12057611987833119878119897 is the clamped capacitor with area of 119878

12057611987833

is the dielectric constant with the vertical direction 119897 isthe thickness of piezoelectric film 119885

0= 120588119881119878 is the acoustic

impedance of piezoelectric film with the density of 120588119881 is thelongitudinal wave velocity 120574 = 120596119897119881 is the phase delay in thepiezoelectric film 120596 = 2120587119891 is angular frequency and 119885

119864is

the acoustic impedance of electrodesWe take the electrode material as isotropic and then we

can get the matrix as

[1198651

1199061

] =[[

[

cos 1205741198901

1198951198851198901sin 1205741198901

119895 sin 1205741198901

1198851198901

cos 1205741198901

]]

]

sdot [11986510158401

11990610158401

] (3)

where 11986510158401is zero because of the free top acoustic port 120574

1198901=

12059611989711989011198811198901

is the phase delay in the top electrode 1198971198901

is thethickness of top electrode 119881

1198901is the acoustic velocity of top

electrode 1198851198901= 12058811989011198811198901119878 is the acoustic impedance of top

electrode and 1205881198901is the density of top electrode

We can get 1198851from (3)

1198851=1198650

1199060

= 1198951198851198901tan 1205741198901 (4)

Similarly we can get the acoustic impedance of bottomelectrode

1198852=1198652

1199062

= 1198951198851198902tan 1205741198902 (5)

So the total input acoustic impedance can be given as [13]

119885in =119880

119868=

1

1198951205961198620

sdot [1 minus1198962119905

120574

sdot(1199111+ 1199112) sdot sin 120574 + 119895 sdot 2 sdot (1 minus cos 120574)

(1199111+ 1199112) sdot cos 120574 + 119895 sdot (1 + 119911

1sdot 1199112) sdot sin 120574

]

(6)

Inside (6) 1199111= 11988511198850 1199112= 11988521198850 We take the top

electrode and bottom electrode as the same so the inputimpedance (119885in) can be given as (7) with a transfer matrixmethod [12 14]

119885in =1

1198951205961198620

[1 minus1198962119905

120574

119911 sin 120574 + 119895 (1 minus cos 120574)119911 cos 120574 + (1198952) (1 + 1199112) sin 120574

] (7)

Journal of Nanomaterials 3

120574 = 120596119897119881 is the phase shift in the piezofilm and 119911 = 1198851198850

is the characteristic impedance ratio of the electrodes to thepiezofilm as the top and bottom electrodes with the samematerial and thicknessThe series resonance frequency119891

119904and

the parallel resonance frequency 119891119901can be obtained by (7)

and then the effective electromechanical coupling factor ofFBAR can be demonstrated with the known 119891

119904and 119891

119901

1198962eff =(1198912119901minus 1198912119904)

1198912119901

cong 2 sdot(119891119901minus 119891119904)

119891119901

(8)

Based on the definition published in the IEEE Std176-1987 [17] 119891

119904is the frequency corresponding with the

maximum conductance Then 119891119904can be calculated by (7)

and 1198962eff can be evaluated by (8) However 1198962eff is not onlydetermined by 1198962

119905but also closely related with the electrode

and resonator structureIn the calculation of the resonance frequency 119891

119904with

(7) the dielectric the piezoelectric and the elastic constantsof the piezoelectric film and the elastic constants of theelectrodes generally are complex values but all others suchas 1198962119905 are considered as real values [12] In addition for a

given piezofilm 1198620is a constant The complex velocity

119897in

piezofilms or electrodes was given by a complex expression[12]

= [(119862101584033+ 1198951198621015840101584033)

120588]

12

cong 1198811015840 [1 +119895

(2119876119898)] (9)

1198811015840 = radic119862101584033120588 is the real part 11988110158401015840 = radic11986210158401015840

33120588 is the imaginary

part and 119862101584033

and 1198621015840101584033

are the real part and imaginary partof elastic constant 119862

33 where 11986210158401015840

33is responsible for the

mechanical losses and 119876119898= 119862101584011986210158401015840 cong 1198811015840211988110158401015840 is the

mechanical quality factor of the piezofilm or the electrodeSo the resonance frequency and the effective electrome-

chanical coupling coefficient of FBAR can be obtained andanalyzed by above definitions and equations

3 Effects of Material Quality Factors onEffective Coupling Factor

The effect of electrode on FBAR performance is studied andshown in the following parts and the thickness 119889

119890 the

density 120588119890 on the resonance frequency 119891

119904 and the effec-

tive electromechanical coupling factor 1198962eff are investigatedbesides the acoustic velocity V

119890on 1198962eff is also done The

different piezoelectric films of ZnO and AlN with thicknessof 2 120583m are used in this research and they both are typicalexamples in the realistic applications and the constants ofmaterial used in the calculation are shown in Table 1

31 Effects of 120588119890and 119889

119890on 119891119904of FBAR The resonance

frequency is very important parameter for frequency devicesespecially for the acoustic device with vibration such asFBAR In general the frequency of FBAR is the basicparameter which should be considered during the design ofFBAR and so it is why we began with it

Table 1 Data of material properties

Material Density(kgm3)

Velocity(ms)

Impedance(106 kgm3s) 1198962

119905

ZnO 5606 6350 356 750AlN 3300 11050 365 625

The resonance frequency definitions are stated in theIEEE Std 176-1987 that 119891

119904is defined as the frequency of

maximum conductance [17] So we can calculate119891119904by setting

the conductance maximum with (7) In the calculations wetake the different piezoelectric films with ZnO and AlN andtake all other parameters as constants except the density andthe thickness of electrode We can take the different densityas different electrode material and study what will happen tothe resonance frequency of FBAR if we change the thicknessof the same material electrode which is very valuable for thedesign of FBAR devices

The results of 119891119904changing with 120588

119890and 119889

119890of FBAR based

on ZnO and AlN piezoelectric films were obtained andthe three-dimensional (3D) figures were shown as Figures3(a) and 4(a) respectively and the two-dimensional (2D)figures were shown as Figures 3(b) and 4(b) respectivelyIt can be obtained that the resonance frequency decreaseswith the thickness and the density of electrode increasingby the 3D figures and this rule becomes more typical withthe thin electrode or the high density and it is the mostobvious when both thickness and density of electrode appearin large value area So we can choose proper material withsmall density and thin electrode for high resonance frequencyby these results even though there still are some otherparameters which should also be considered such as acousticvelocity However if the acoustic velocity in the electrode is aconstant then this result can be effectively used to design andevaluate the resonance frequency according to the applicationrequirementThe above results can also be proved by the two2D figures Besides we also can get that the FBAR decreasedover half of resonance frequency just with the thicknesschange of 04 120583m and so the thickness effect of electrodeon the resonance frequency are very distinct which becomessmoother in the smaller thickness area

32 Effects of 120588119890and 119889

119890on 1198962119890119891119891

of FBAR Based on thedefinition published in the IEEE Std 176-1987 [17] 119891

119904is the

frequency of maximum conductance and 119891119901is the frequency

of maximum resistance Then 119891119904and 119891

119901can be calculated

by (7) and 1198962eff can be evaluated by (8) 1198962eff is not onlydetermined by 1198962

119905but also determined by the electrode and

resonator structureWe calculated 1198962eff changing with the thickness and the

density of electrode and the 3D figures and 2D figures weregiven in Figures 5 and 6 with ZnO and AlN piezoelectricfilms respectively

It can be obtained by Figures 5(a) and 6(a) that thereis the maximum 1198962eff corresponding to some compositionsof thickness and density of electrode which is near thethin electrode and high density area 1198962eff increases and then

4 Journal of Nanomaterials

00511520 01 02 03 04 05 06 07 08 09 104

06

08

1

12

14

16

05 06 07 08 09 1 11 12 13 14 15

fs

(Hz)

de (120583m)

times109

times109

120588e (104 kgm3 )

(a)

04 06 08 1 12 14 16 18

010203040506070809

1

5 6 7 8 9 10 11 12 13 14

de

(120583m

)

times108

120588e (104 kgm3)

(b)

Figure 3 119891119904of FBAR versus the thickness and the density of electrode with ZnO piezoelectric film

00511520 01 02 03 04 05 06 07 08 09 1456789

1011

5 6 7 8 9 10

fs

(Hz)

de (120583m)

times108

times108

120588e(10

4 kgm3 )

(a)

04 06 08 1 12 14 16 18

010203040506070809

1

45 5 55 6 65 7 75 8 85 9 95 10

de

(120583m

)

times108

120588e (104 kgm3)

(b)

Figure 4 119891119904of FBAR versus the thickness and the density of electrode with AlN piezoelectric film

01

2

001020304050607080910055

006

0065

007

0075

0056 0058 006 0062 0064 0066 0068 007 0072

k2 eff

de (120583m) 120588 e(10

4 kgm

3 )

(a)

04 06 08 1 12 14 16 18

010203040506070809

1

0056 0058 006 0062 0064 0066 0068 007

de

(120583m

)

120588e (104 kgm3)

(b)

Figure 5 1198962eff of FBAR versus the thickness and the density of electrode with ZnO piezoelectric film

Journal of Nanomaterials 5

0 051 15

2

00102030405060708091005

0052

0054

0056

0058

006

0062

0052 0053 0054 0055 0056 0057 0058 0059 006

k2 eff

de (120583m) 120588 e(10

4 kgm3 )

(a)

04 06 08 1 12 14 16 18

010203040506070809

1

0052 0053 0054 0055 0056 0057 0058 0059 006

de

(120583m

)

120588e (104 kgm3)

(b)

Figure 6 1198962eff of FBAR versus the thickness and the density of electrode with AlN piezoelectric film

decreases with the thickness increasing and the increasingratio can reach to 20 over original value of piezoelectricfilm However 1198962eff mostly increases with the density ofelectrode 1198962eff changes fast with the thickness of electrodewhen the density of electrode is small and vice versa TheFBAR with the ZnO layer shows that 1198962eff changes morequickly than the case of AlN and the thickness effect is moreobvious too especially for the small density of electrode casesFurthermore we can also get the same witness from the 2Dfigures of Figures 5(b) and 6(b)

A very interesting result is obtained from 2D figures that1198962eff will arrive at a maximum area with special thicknessvalues for any density of electrode and the correspondingthickness area is very obvious at the center such as the FBARwith ZnO The thickness beginning with the maximum 1198962effarea is nearby 037 120583m and the thickness is nearby 05 120583m forthe AlN case This is a very interesting and important resultand it means the effect of thickness on 1198962eff has a strong rulewhich is affected little by the density of electrode materialWe analyzed this phenomenon that it is the thickness wherestanding wave appears and the difference between thesetwo piezoelectric film cases should be attributed to thedifferent piezoelectric thin films Moreover it confirms thatthe standing wave exists in the FBAR and the thickness ofelectrode should be optimized with this merit point which iseffective for all kinds of electrode materials

33 Effects of V119890and119889119890on 1198962119890119891119891

of FBAR For overall evaluationof 1198962eff the effects of V

119890and 119889

119890on 1198962eff were conducted

with the 2 120583m thick piezoelectric film and the 2D and 3Dfigures with four different electrode density choices weregiven for contrasting The 3D 1198962eff versus V

119890and 119889

119890curves

based on ZnO and AlN were shown in Figures 7 and 9respectively and the 2D results were shown in Figures 8and 10 correspondingly The key parameters and results weremarked on the 3D figures We can get that 1198962eff always riseswith the density of electrode for the ZnO case in Figure 7

0 05 12468101214

002

003

004

005

006

007

008k2 eff

Number 1 120588e = 19 times 104 kgm3

(e = 145 times 103 ms de = 055120583m)

Number 2 120588e = 13 times 104 kgm3

(e = 145 times 103 ms de = 06 120583m)

eNumber 3 120588 = 7 times 103

103kgm3

(e = 145 times ms de = 065120583m)

Number 4 120588e = 2 times 103

103kgm3

(e = 145 times ms de = 08 120583m)

e (103 ms) de(120583m)

max k = 0074156

max k = 007372

max k = 0072642

max k = 007028

Figure 7 1198962eff of FBAR versus the thickness and the acoustic velocityof electrode with ZnO piezoelectric film and different density (3Dcurves)

which also can be observed in above section results andthe maximum 1198962eff always appears at the maximum acousticvelocity during our calculation range The AlN case is thesame behavior as the ZnO FBAR in Figure 9 Moreover 1198962effrises more obviously with V

119890in the large electrode thickness

area and vice versa and 1198962eff changes little with V119890among the

small electrode thickness area and especially least in the highdensity electrode material area On the other hand 1198962eff risesdistinctlywith the electrode thickness in the low velocity areabut it almost does not change in the high velocity space

6 Journal of Nanomaterials

01 02 03 04 05 06 07 08 09 1

4

6

8

10

12

14

003

004

005

006

007

e(103

ms

)

de (120583m)

(a) 120588119890= 2 times 10

3 kgm3

0035004004500500550060065007

01 02 03 04 05 06 07 08 09 1

4

6

8

10

12

14

e(103

ms

)

de (120583m)

(b) 120588119890= 7 times 10

3 kgm3

005

0055

006

0065

01 02 03 04 05 06 07 08 09 1

4

6

8

10

12

14

e(103

ms

)

de (120583m)

(c) 120588119890= 13 times 10

4 kgm3

0055

006

0065

007

01 02 03 04 05 06 07 08 09 1

4

6

8

10

12

14

e(103

ms

)de (120583m)

(d) 120588119890= 19 times 10

4 kgm3

Figure 8 1198962eff of FBAR versus the thickness and the acoustic velocity of electrode with ZnO piezoelectric film (2D curves)

005

1

24681012140025

003

0035

004

0045

005

0055

006

0065

k2 eff

e (103 ms) de(120583m)

4 3Number 1 120588e = 19 times 10 kgm(e = 145 times 103 ms de = 08 120583m)

Number 2 120588e = 13 times 104 kgm3

(e = 145 times 103 ms de = 09 120583m)Number 3 120588e = 7 times 103 kgm3

e e( = 145 times 103 ms d = 095120583m)Number 4 120588e = 2 times 103 kgm3

(e = 145 times 103 ms de = 105 120583m)

max k = 0061397

max k = 0060458

max k = 0058439

max k = 0061766

Figure 9 1198962eff of FBAR versus the thickness and the acoustic velocityof electrode with AlN piezoelectric film and different density (3Dcurves)

We can conclude that 1198962eff is in the direct proportion tothe density 120588

119890here and the acoustic velocity of electrode has

a similar effect too and 1198962eff dominantly rises with V119890 The

electrode thickness affects small 1198962eff with high V119890 moreover

when V119890is high enough then 1198962eff has almost nothing to do

with 119889119890 But 1198962eff changes fast with 119889

119890when V

119890is small and

1198962eff rises with electrode thickness first and then descendswithits rising which was also observed in the former sectionThe thickness corresponding to themaximum 1198962eff is differentwith different electrode density however it descends withdensity ascending which also proves the special value 120588

119890119889119890

corresponding with the maximum 1198962eff of FBAR even thoughwe cannot get this result directly by these figures becausethere are not so many piezoelectric film parameters consid-ered for proving [14] All these behaviors are similar for bothZnO and AlN based FBARs

The density acoustic velocity and thickness of electrodeof FBAR can be optimized by above results for special 119891

119904and

1198962eff need We can get the higher 1198962eff with the higher electrodedensity and it is also the same to acoustic velocity of electrodematerialThe best thickness of electrode is decided by densityand especially acoustic velocity however the thickness effectsare obvious when the acoustic velocity is small but it almostdoes not change if the acoustic velocity is very big Moreoverthe best thickness corresponding to the maximum 1198962eff isdifferent with different cases but the values are in the specialarea comparing with the distinctly variable V

119890and 120588119890 and it is

because we take most of the parameters of piezoelectric thinfilm as constants even though these results can be observedin both ZnO and AlN FBARs in this research

4 Conclusions

In this paper the following research and results have beengiven

Journal of Nanomaterials 7

003

0035

004

0045

005

0055

01 02 03 04 05 06 07 08 09 14

6

8

10

12

14 e

(103

ms

)

de (120583m)

(a) 120588119890= 2 times 10

3 kgm3

004

0045

005

0055

006

01 02 03 04 05 06 07 08 09 14

6

8

10

12

14

e(103

ms

)

de (120583m)

(b) 120588119890= 7 times 10

3 kgm3

0045

005

0055

006

01 02 03 04 05 06 07 08 09 14

6

8

10

12

14

e(103

ms

)

de (120583m)

(c) 120588119890= 13 times 10

4 kgm3

005

0052

0054

0056

0058

01 02 03 04 05 06 07 08 09 14

6

8

10

12

14

e(103

ms

)de (120583m)

(d) 120588119890= 19 times 10

4 kgm3

Figure 10 1198962eff of FBAR versus the thickness and the acoustic velocity of electrode with AlN piezoelectric film and different density (2Dcurves)

(i) Firstly we derived the input acoustic impedanceequation with transfer matrix method and the sim-plified impedance equation of FBAR with the sametop and bottom electrode is obtained This equationcan be applied extensively to calculate the resonancefrequency the effective electromechanical couplingfactor themechanical quality factor and themerit fig-ure of FBAR which makes the theoretical calculationand optimization easy

(ii) Secondly the effect of thickness and density ofelectrode on the resonance frequency of FBAR wasinvestigated and it can be obtained that the thicknessand the density of electrode affect the resonancefrequency obviously especially at the large thicknessand density area This result shows that the thicknessand the material of electrode are very key parametersfor the resonance frequency design of FBAR

(iii) Finally the effects of thickness density and acousticvelocity on the effective electromechanical couplingfactor were studied respectivelyThe results show that1198962eff is in the direct proportion to both density 120588

119890and

V119890of electrode The electrode thickness affects small

1198962eff with high V119890 moreover when V

119890is high enough

then 1198962eff has almost nothing to do with 119889119890 1198962eff rises

with electrode thickness first and then descends withits rising and the thickness corresponding to themaximum 1198962eff is different with different electrodedensity and V

119890 but they almost locate in the special

area

All above results indicate that the thickness density andacoustic velocity of electrode are very important and they canbe applied to optimize and design different kind of FBARs

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This work is supported by the National Natural ScienceFoundation of China (nos 61201088 11404257 and 11504291)Shaanxi Province Innovation Project for Science and Tech-nology Overall Planning (no 2012KTCL01-12) Industrial-ization Foundation of Shaanxi Educational Committee (no2011JG10) and Xirsquoan Technology Transferring and PromotingProject (CXY1342(5) CX1253(2))

References

[1] J D Larson III R Ruby P Bradley and Y Oshmyansky ldquoBAWantenna duplex for the 1900MHz PCS bandrdquo in Proceedings ofthe IEEE Ultrasonics Symposium pp 887ndash890 Caesars TahoeNV USA October 1999

[2] R Ruby P Bradley J D Larson III and Y Oshmyansky ldquoPCS1900MHz duplexer using thin film bulk acoustic resonators(FBARs)rdquo Electronics Letters vol 35 no 10 pp 794ndash796 1999

[3] R C Ruby P Bradley Y Oshmyansky A Chien and J DLarson III ldquoThin film bulk wave acoustic resonators (FBAR)for wireless applicationsrdquo in Proceedings of the UltrasonicsSymposium pp 813ndash821 October 2001

8 Journal of Nanomaterials

[4] K M Lakin J Belsick J F McDonald and K T McCarronldquoImproved bulk wave resonator coupling coefficient for widebandwidth filtersrdquo inProceedings of the IEEEUltrasonics Sympo-sium vol 1 pp 827ndash831 IEEE Atlanta Ga USA October 2001

[5] I Voiculescu and A N Nordin ldquoAcoustic wave based MEMSdevices for biosensing applicationsrdquo Biosensors and Bioelectron-ics vol 33 no 1 pp 1ndash9 2012

[6] F T Chu C Li Z Z Wang and X Z Liu ldquoAluminum NitrideThin films on molybdenumpolyimide heterostructure for bulkacoustic resonatorsrdquo Rare Metal Materials and Engineering vol42 no 10 pp 2023ndash2026 2013

[7] A J Festschrift J K Luo Y Q Fu et al ldquoZnO based SAWand FBAR devices for bio-sensing applicationsrdquo Journal of Non-Newtonian Fluid Mechanics vol 222 pp 209ndash216 2015

[8] H Zhang G Jiang Z Liu S Zhang and L Fan ldquoOptimizationsof composited acoustic sensors with a microfluidic channelrdquoJournal of Applied Physics vol 115 no 13 Article ID 1335022014

[9] A Vorobiev and S Gevorgian ldquoIntrinsically switchable thinfilm bulk acoustic wave resonatorsrdquo Applied Physics Letters vol104 no 22 Article ID 222905 2014

[10] H J Lee K A Hyun and H I Jung ldquoA high-Q resonator usingbiocompatible materials at microwave frequenciesrdquo AppliedPhysics Letters vol 104 no 2 Article ID 023509 2014

[11] M-C Chao Z-N Huang S-Y Pao Z Wang and C S LamldquoModified BVD-equivalent circuit of FBARby taking electrodesinto accountrdquo inProceedings of the IEEEUltrasonics Symposiumpp 973ndash976 October 2002

[12] Q Chen and Q-M Wang ldquoThe effective electromechani-cal coupling coefficient of piezoelectric thin-film resonatorsrdquoApplied Physics Letters vol 86 no 2 Article ID 022904 2005

[13] Y Zhang Z Wang and J D N Cheeke ldquoResonant spectrummethod to characterize piezoelectric films in composite res-onatorsrdquo IEEE Transactions on Ultrasonics Ferroelectrics andFrequency Control vol 50 no 3 pp 321ndash333 2003

[14] T Zhang H Zhang Z-Q Wang and S-Y Zhang ldquoEffects ofelectrodes on performance figures of thin film bulk acousticresonatorsrdquo Journal of the Acoustical Society of America vol 122no 3 pp 1646ndash1651 2007

[15] N F Naumenko ldquoAdvanced numerical technique for analysisof surface and bulk acoustic waves in resonators using periodicmetal gratingsrdquo Journal of Applied Physics vol 116 no 10 ArticleID 104503 2014

[16] A Kvasov and A K Tagantsev ldquoThin film bulk acoustic waveresonators tuning from first principlesrdquo Journal of AppliedPhysics vol 113 no 20 Article ID 204104 2013

[17] IEEE ldquoIEEE standard on piezoelectricityrdquo Tech Rep 176-1987 IEEE Transactions on Ultrasonics Ferroelectrics andFrequency Control 1996 43719

Submit your manuscripts athttpwwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CeramicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CompositesJournal of

NanoparticlesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Biomaterials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

CrystallographyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MetallurgyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

MaterialsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nano

materials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofNanomaterials

Journal of Nanomaterials 3

120574 = 120596119897119881 is the phase shift in the piezofilm and 119911 = 1198851198850

is the characteristic impedance ratio of the electrodes to thepiezofilm as the top and bottom electrodes with the samematerial and thicknessThe series resonance frequency119891

119904and

the parallel resonance frequency 119891119901can be obtained by (7)

and then the effective electromechanical coupling factor ofFBAR can be demonstrated with the known 119891

119904and 119891

119901

1198962eff =(1198912119901minus 1198912119904)

1198912119901

cong 2 sdot(119891119901minus 119891119904)

119891119901

(8)

Based on the definition published in the IEEE Std176-1987 [17] 119891

119904is the frequency corresponding with the

maximum conductance Then 119891119904can be calculated by (7)

and 1198962eff can be evaluated by (8) However 1198962eff is not onlydetermined by 1198962

119905but also closely related with the electrode

and resonator structureIn the calculation of the resonance frequency 119891

119904with

(7) the dielectric the piezoelectric and the elastic constantsof the piezoelectric film and the elastic constants of theelectrodes generally are complex values but all others suchas 1198962119905 are considered as real values [12] In addition for a

given piezofilm 1198620is a constant The complex velocity

119897in

piezofilms or electrodes was given by a complex expression[12]

= [(119862101584033+ 1198951198621015840101584033)

120588]

12

cong 1198811015840 [1 +119895

(2119876119898)] (9)

1198811015840 = radic119862101584033120588 is the real part 11988110158401015840 = radic11986210158401015840

33120588 is the imaginary

part and 119862101584033

and 1198621015840101584033

are the real part and imaginary partof elastic constant 119862

33 where 11986210158401015840

33is responsible for the

mechanical losses and 119876119898= 119862101584011986210158401015840 cong 1198811015840211988110158401015840 is the

mechanical quality factor of the piezofilm or the electrodeSo the resonance frequency and the effective electrome-

chanical coupling coefficient of FBAR can be obtained andanalyzed by above definitions and equations

3 Effects of Material Quality Factors onEffective Coupling Factor

The effect of electrode on FBAR performance is studied andshown in the following parts and the thickness 119889

119890 the

density 120588119890 on the resonance frequency 119891

119904 and the effec-

tive electromechanical coupling factor 1198962eff are investigatedbesides the acoustic velocity V

119890on 1198962eff is also done The

different piezoelectric films of ZnO and AlN with thicknessof 2 120583m are used in this research and they both are typicalexamples in the realistic applications and the constants ofmaterial used in the calculation are shown in Table 1

31 Effects of 120588119890and 119889

119890on 119891119904of FBAR The resonance

frequency is very important parameter for frequency devicesespecially for the acoustic device with vibration such asFBAR In general the frequency of FBAR is the basicparameter which should be considered during the design ofFBAR and so it is why we began with it

Table 1 Data of material properties

Material Density(kgm3)

Velocity(ms)

Impedance(106 kgm3s) 1198962

119905

ZnO 5606 6350 356 750AlN 3300 11050 365 625

The resonance frequency definitions are stated in theIEEE Std 176-1987 that 119891

119904is defined as the frequency of

maximum conductance [17] So we can calculate119891119904by setting

the conductance maximum with (7) In the calculations wetake the different piezoelectric films with ZnO and AlN andtake all other parameters as constants except the density andthe thickness of electrode We can take the different densityas different electrode material and study what will happen tothe resonance frequency of FBAR if we change the thicknessof the same material electrode which is very valuable for thedesign of FBAR devices

The results of 119891119904changing with 120588

119890and 119889

119890of FBAR based

on ZnO and AlN piezoelectric films were obtained andthe three-dimensional (3D) figures were shown as Figures3(a) and 4(a) respectively and the two-dimensional (2D)figures were shown as Figures 3(b) and 4(b) respectivelyIt can be obtained that the resonance frequency decreaseswith the thickness and the density of electrode increasingby the 3D figures and this rule becomes more typical withthe thin electrode or the high density and it is the mostobvious when both thickness and density of electrode appearin large value area So we can choose proper material withsmall density and thin electrode for high resonance frequencyby these results even though there still are some otherparameters which should also be considered such as acousticvelocity However if the acoustic velocity in the electrode is aconstant then this result can be effectively used to design andevaluate the resonance frequency according to the applicationrequirementThe above results can also be proved by the two2D figures Besides we also can get that the FBAR decreasedover half of resonance frequency just with the thicknesschange of 04 120583m and so the thickness effect of electrodeon the resonance frequency are very distinct which becomessmoother in the smaller thickness area

32 Effects of 120588119890and 119889

119890on 1198962119890119891119891

of FBAR Based on thedefinition published in the IEEE Std 176-1987 [17] 119891

119904is the

frequency of maximum conductance and 119891119901is the frequency

of maximum resistance Then 119891119904and 119891

119901can be calculated

by (7) and 1198962eff can be evaluated by (8) 1198962eff is not onlydetermined by 1198962

119905but also determined by the electrode and

resonator structureWe calculated 1198962eff changing with the thickness and the

density of electrode and the 3D figures and 2D figures weregiven in Figures 5 and 6 with ZnO and AlN piezoelectricfilms respectively

It can be obtained by Figures 5(a) and 6(a) that thereis the maximum 1198962eff corresponding to some compositionsof thickness and density of electrode which is near thethin electrode and high density area 1198962eff increases and then

4 Journal of Nanomaterials

00511520 01 02 03 04 05 06 07 08 09 104

06

08

1

12

14

16

05 06 07 08 09 1 11 12 13 14 15

fs

(Hz)

de (120583m)

times109

times109

120588e (104 kgm3 )

(a)

04 06 08 1 12 14 16 18

010203040506070809

1

5 6 7 8 9 10 11 12 13 14

de

(120583m

)

times108

120588e (104 kgm3)

(b)

Figure 3 119891119904of FBAR versus the thickness and the density of electrode with ZnO piezoelectric film

00511520 01 02 03 04 05 06 07 08 09 1456789

1011

5 6 7 8 9 10

fs

(Hz)

de (120583m)

times108

times108

120588e(10

4 kgm3 )

(a)

04 06 08 1 12 14 16 18

010203040506070809

1

45 5 55 6 65 7 75 8 85 9 95 10

de

(120583m

)

times108

120588e (104 kgm3)

(b)

Figure 4 119891119904of FBAR versus the thickness and the density of electrode with AlN piezoelectric film

01

2

001020304050607080910055

006

0065

007

0075

0056 0058 006 0062 0064 0066 0068 007 0072

k2 eff

de (120583m) 120588 e(10

4 kgm

3 )

(a)

04 06 08 1 12 14 16 18

010203040506070809

1

0056 0058 006 0062 0064 0066 0068 007

de

(120583m

)

120588e (104 kgm3)

(b)

Figure 5 1198962eff of FBAR versus the thickness and the density of electrode with ZnO piezoelectric film

Journal of Nanomaterials 5

0 051 15

2

00102030405060708091005

0052

0054

0056

0058

006

0062

0052 0053 0054 0055 0056 0057 0058 0059 006

k2 eff

de (120583m) 120588 e(10

4 kgm3 )

(a)

04 06 08 1 12 14 16 18

010203040506070809

1

0052 0053 0054 0055 0056 0057 0058 0059 006

de

(120583m

)

120588e (104 kgm3)

(b)

Figure 6 1198962eff of FBAR versus the thickness and the density of electrode with AlN piezoelectric film

decreases with the thickness increasing and the increasingratio can reach to 20 over original value of piezoelectricfilm However 1198962eff mostly increases with the density ofelectrode 1198962eff changes fast with the thickness of electrodewhen the density of electrode is small and vice versa TheFBAR with the ZnO layer shows that 1198962eff changes morequickly than the case of AlN and the thickness effect is moreobvious too especially for the small density of electrode casesFurthermore we can also get the same witness from the 2Dfigures of Figures 5(b) and 6(b)

A very interesting result is obtained from 2D figures that1198962eff will arrive at a maximum area with special thicknessvalues for any density of electrode and the correspondingthickness area is very obvious at the center such as the FBARwith ZnO The thickness beginning with the maximum 1198962effarea is nearby 037 120583m and the thickness is nearby 05 120583m forthe AlN case This is a very interesting and important resultand it means the effect of thickness on 1198962eff has a strong rulewhich is affected little by the density of electrode materialWe analyzed this phenomenon that it is the thickness wherestanding wave appears and the difference between thesetwo piezoelectric film cases should be attributed to thedifferent piezoelectric thin films Moreover it confirms thatthe standing wave exists in the FBAR and the thickness ofelectrode should be optimized with this merit point which iseffective for all kinds of electrode materials

33 Effects of V119890and119889119890on 1198962119890119891119891

of FBAR For overall evaluationof 1198962eff the effects of V

119890and 119889

119890on 1198962eff were conducted

with the 2 120583m thick piezoelectric film and the 2D and 3Dfigures with four different electrode density choices weregiven for contrasting The 3D 1198962eff versus V

119890and 119889

119890curves

based on ZnO and AlN were shown in Figures 7 and 9respectively and the 2D results were shown in Figures 8and 10 correspondingly The key parameters and results weremarked on the 3D figures We can get that 1198962eff always riseswith the density of electrode for the ZnO case in Figure 7

0 05 12468101214

002

003

004

005

006

007

008k2 eff

Number 1 120588e = 19 times 104 kgm3

(e = 145 times 103 ms de = 055120583m)

Number 2 120588e = 13 times 104 kgm3

(e = 145 times 103 ms de = 06 120583m)

eNumber 3 120588 = 7 times 103

103kgm3

(e = 145 times ms de = 065120583m)

Number 4 120588e = 2 times 103

103kgm3

(e = 145 times ms de = 08 120583m)

e (103 ms) de(120583m)

max k = 0074156

max k = 007372

max k = 0072642

max k = 007028

Figure 7 1198962eff of FBAR versus the thickness and the acoustic velocityof electrode with ZnO piezoelectric film and different density (3Dcurves)

which also can be observed in above section results andthe maximum 1198962eff always appears at the maximum acousticvelocity during our calculation range The AlN case is thesame behavior as the ZnO FBAR in Figure 9 Moreover 1198962effrises more obviously with V

119890in the large electrode thickness

area and vice versa and 1198962eff changes little with V119890among the

small electrode thickness area and especially least in the highdensity electrode material area On the other hand 1198962eff risesdistinctlywith the electrode thickness in the low velocity areabut it almost does not change in the high velocity space

6 Journal of Nanomaterials

01 02 03 04 05 06 07 08 09 1

4

6

8

10

12

14

003

004

005

006

007

e(103

ms

)

de (120583m)

(a) 120588119890= 2 times 10

3 kgm3

0035004004500500550060065007

01 02 03 04 05 06 07 08 09 1

4

6

8

10

12

14

e(103

ms

)

de (120583m)

(b) 120588119890= 7 times 10

3 kgm3

005

0055

006

0065

01 02 03 04 05 06 07 08 09 1

4

6

8

10

12

14

e(103

ms

)

de (120583m)

(c) 120588119890= 13 times 10

4 kgm3

0055

006

0065

007

01 02 03 04 05 06 07 08 09 1

4

6

8

10

12

14

e(103

ms

)de (120583m)

(d) 120588119890= 19 times 10

4 kgm3

Figure 8 1198962eff of FBAR versus the thickness and the acoustic velocity of electrode with ZnO piezoelectric film (2D curves)

005

1

24681012140025

003

0035

004

0045

005

0055

006

0065

k2 eff

e (103 ms) de(120583m)

4 3Number 1 120588e = 19 times 10 kgm(e = 145 times 103 ms de = 08 120583m)

Number 2 120588e = 13 times 104 kgm3

(e = 145 times 103 ms de = 09 120583m)Number 3 120588e = 7 times 103 kgm3

e e( = 145 times 103 ms d = 095120583m)Number 4 120588e = 2 times 103 kgm3

(e = 145 times 103 ms de = 105 120583m)

max k = 0061397

max k = 0060458

max k = 0058439

max k = 0061766

Figure 9 1198962eff of FBAR versus the thickness and the acoustic velocityof electrode with AlN piezoelectric film and different density (3Dcurves)

We can conclude that 1198962eff is in the direct proportion tothe density 120588

119890here and the acoustic velocity of electrode has

a similar effect too and 1198962eff dominantly rises with V119890 The

electrode thickness affects small 1198962eff with high V119890 moreover

when V119890is high enough then 1198962eff has almost nothing to do

with 119889119890 But 1198962eff changes fast with 119889

119890when V

119890is small and

1198962eff rises with electrode thickness first and then descendswithits rising which was also observed in the former sectionThe thickness corresponding to themaximum 1198962eff is differentwith different electrode density however it descends withdensity ascending which also proves the special value 120588

119890119889119890

corresponding with the maximum 1198962eff of FBAR even thoughwe cannot get this result directly by these figures becausethere are not so many piezoelectric film parameters consid-ered for proving [14] All these behaviors are similar for bothZnO and AlN based FBARs

The density acoustic velocity and thickness of electrodeof FBAR can be optimized by above results for special 119891

119904and

1198962eff need We can get the higher 1198962eff with the higher electrodedensity and it is also the same to acoustic velocity of electrodematerialThe best thickness of electrode is decided by densityand especially acoustic velocity however the thickness effectsare obvious when the acoustic velocity is small but it almostdoes not change if the acoustic velocity is very big Moreoverthe best thickness corresponding to the maximum 1198962eff isdifferent with different cases but the values are in the specialarea comparing with the distinctly variable V

119890and 120588119890 and it is

because we take most of the parameters of piezoelectric thinfilm as constants even though these results can be observedin both ZnO and AlN FBARs in this research

4 Conclusions

In this paper the following research and results have beengiven

Journal of Nanomaterials 7

003

0035

004

0045

005

0055

01 02 03 04 05 06 07 08 09 14

6

8

10

12

14 e

(103

ms

)

de (120583m)

(a) 120588119890= 2 times 10

3 kgm3

004

0045

005

0055

006

01 02 03 04 05 06 07 08 09 14

6

8

10

12

14

e(103

ms

)

de (120583m)

(b) 120588119890= 7 times 10

3 kgm3

0045

005

0055

006

01 02 03 04 05 06 07 08 09 14

6

8

10

12

14

e(103

ms

)

de (120583m)

(c) 120588119890= 13 times 10

4 kgm3

005

0052

0054

0056

0058

01 02 03 04 05 06 07 08 09 14

6

8

10

12

14

e(103

ms

)de (120583m)

(d) 120588119890= 19 times 10

4 kgm3

Figure 10 1198962eff of FBAR versus the thickness and the acoustic velocity of electrode with AlN piezoelectric film and different density (2Dcurves)

(i) Firstly we derived the input acoustic impedanceequation with transfer matrix method and the sim-plified impedance equation of FBAR with the sametop and bottom electrode is obtained This equationcan be applied extensively to calculate the resonancefrequency the effective electromechanical couplingfactor themechanical quality factor and themerit fig-ure of FBAR which makes the theoretical calculationand optimization easy

(ii) Secondly the effect of thickness and density ofelectrode on the resonance frequency of FBAR wasinvestigated and it can be obtained that the thicknessand the density of electrode affect the resonancefrequency obviously especially at the large thicknessand density area This result shows that the thicknessand the material of electrode are very key parametersfor the resonance frequency design of FBAR

(iii) Finally the effects of thickness density and acousticvelocity on the effective electromechanical couplingfactor were studied respectivelyThe results show that1198962eff is in the direct proportion to both density 120588

119890and

V119890of electrode The electrode thickness affects small

1198962eff with high V119890 moreover when V

119890is high enough

then 1198962eff has almost nothing to do with 119889119890 1198962eff rises

with electrode thickness first and then descends withits rising and the thickness corresponding to themaximum 1198962eff is different with different electrodedensity and V

119890 but they almost locate in the special

area

All above results indicate that the thickness density andacoustic velocity of electrode are very important and they canbe applied to optimize and design different kind of FBARs

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This work is supported by the National Natural ScienceFoundation of China (nos 61201088 11404257 and 11504291)Shaanxi Province Innovation Project for Science and Tech-nology Overall Planning (no 2012KTCL01-12) Industrial-ization Foundation of Shaanxi Educational Committee (no2011JG10) and Xirsquoan Technology Transferring and PromotingProject (CXY1342(5) CX1253(2))

References

[1] J D Larson III R Ruby P Bradley and Y Oshmyansky ldquoBAWantenna duplex for the 1900MHz PCS bandrdquo in Proceedings ofthe IEEE Ultrasonics Symposium pp 887ndash890 Caesars TahoeNV USA October 1999

[2] R Ruby P Bradley J D Larson III and Y Oshmyansky ldquoPCS1900MHz duplexer using thin film bulk acoustic resonators(FBARs)rdquo Electronics Letters vol 35 no 10 pp 794ndash796 1999

[3] R C Ruby P Bradley Y Oshmyansky A Chien and J DLarson III ldquoThin film bulk wave acoustic resonators (FBAR)for wireless applicationsrdquo in Proceedings of the UltrasonicsSymposium pp 813ndash821 October 2001

8 Journal of Nanomaterials

[4] K M Lakin J Belsick J F McDonald and K T McCarronldquoImproved bulk wave resonator coupling coefficient for widebandwidth filtersrdquo inProceedings of the IEEEUltrasonics Sympo-sium vol 1 pp 827ndash831 IEEE Atlanta Ga USA October 2001

[5] I Voiculescu and A N Nordin ldquoAcoustic wave based MEMSdevices for biosensing applicationsrdquo Biosensors and Bioelectron-ics vol 33 no 1 pp 1ndash9 2012

[6] F T Chu C Li Z Z Wang and X Z Liu ldquoAluminum NitrideThin films on molybdenumpolyimide heterostructure for bulkacoustic resonatorsrdquo Rare Metal Materials and Engineering vol42 no 10 pp 2023ndash2026 2013

[7] A J Festschrift J K Luo Y Q Fu et al ldquoZnO based SAWand FBAR devices for bio-sensing applicationsrdquo Journal of Non-Newtonian Fluid Mechanics vol 222 pp 209ndash216 2015

[8] H Zhang G Jiang Z Liu S Zhang and L Fan ldquoOptimizationsof composited acoustic sensors with a microfluidic channelrdquoJournal of Applied Physics vol 115 no 13 Article ID 1335022014

[9] A Vorobiev and S Gevorgian ldquoIntrinsically switchable thinfilm bulk acoustic wave resonatorsrdquo Applied Physics Letters vol104 no 22 Article ID 222905 2014

[10] H J Lee K A Hyun and H I Jung ldquoA high-Q resonator usingbiocompatible materials at microwave frequenciesrdquo AppliedPhysics Letters vol 104 no 2 Article ID 023509 2014

[11] M-C Chao Z-N Huang S-Y Pao Z Wang and C S LamldquoModified BVD-equivalent circuit of FBARby taking electrodesinto accountrdquo inProceedings of the IEEEUltrasonics Symposiumpp 973ndash976 October 2002

[12] Q Chen and Q-M Wang ldquoThe effective electromechani-cal coupling coefficient of piezoelectric thin-film resonatorsrdquoApplied Physics Letters vol 86 no 2 Article ID 022904 2005

[13] Y Zhang Z Wang and J D N Cheeke ldquoResonant spectrummethod to characterize piezoelectric films in composite res-onatorsrdquo IEEE Transactions on Ultrasonics Ferroelectrics andFrequency Control vol 50 no 3 pp 321ndash333 2003

[14] T Zhang H Zhang Z-Q Wang and S-Y Zhang ldquoEffects ofelectrodes on performance figures of thin film bulk acousticresonatorsrdquo Journal of the Acoustical Society of America vol 122no 3 pp 1646ndash1651 2007

[15] N F Naumenko ldquoAdvanced numerical technique for analysisof surface and bulk acoustic waves in resonators using periodicmetal gratingsrdquo Journal of Applied Physics vol 116 no 10 ArticleID 104503 2014

[16] A Kvasov and A K Tagantsev ldquoThin film bulk acoustic waveresonators tuning from first principlesrdquo Journal of AppliedPhysics vol 113 no 20 Article ID 204104 2013

[17] IEEE ldquoIEEE standard on piezoelectricityrdquo Tech Rep 176-1987 IEEE Transactions on Ultrasonics Ferroelectrics andFrequency Control 1996 43719

Submit your manuscripts athttpwwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CeramicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CompositesJournal of

NanoparticlesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Biomaterials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

CrystallographyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MetallurgyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

MaterialsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nano

materials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofNanomaterials

4 Journal of Nanomaterials

00511520 01 02 03 04 05 06 07 08 09 104

06

08

1

12

14

16

05 06 07 08 09 1 11 12 13 14 15

fs

(Hz)

de (120583m)

times109

times109

120588e (104 kgm3 )

(a)

04 06 08 1 12 14 16 18

010203040506070809

1

5 6 7 8 9 10 11 12 13 14

de

(120583m

)

times108

120588e (104 kgm3)

(b)

Figure 3 119891119904of FBAR versus the thickness and the density of electrode with ZnO piezoelectric film

00511520 01 02 03 04 05 06 07 08 09 1456789

1011

5 6 7 8 9 10

fs

(Hz)

de (120583m)

times108

times108

120588e(10

4 kgm3 )

(a)

04 06 08 1 12 14 16 18

010203040506070809

1

45 5 55 6 65 7 75 8 85 9 95 10

de

(120583m

)

times108

120588e (104 kgm3)

(b)

Figure 4 119891119904of FBAR versus the thickness and the density of electrode with AlN piezoelectric film

01

2

001020304050607080910055

006

0065

007

0075

0056 0058 006 0062 0064 0066 0068 007 0072

k2 eff

de (120583m) 120588 e(10

4 kgm

3 )

(a)

04 06 08 1 12 14 16 18

010203040506070809

1

0056 0058 006 0062 0064 0066 0068 007

de

(120583m

)

120588e (104 kgm3)

(b)

Figure 5 1198962eff of FBAR versus the thickness and the density of electrode with ZnO piezoelectric film

Journal of Nanomaterials 5

0 051 15

2

00102030405060708091005

0052

0054

0056

0058

006

0062

0052 0053 0054 0055 0056 0057 0058 0059 006

k2 eff

de (120583m) 120588 e(10

4 kgm3 )

(a)

04 06 08 1 12 14 16 18

010203040506070809

1

0052 0053 0054 0055 0056 0057 0058 0059 006

de

(120583m

)

120588e (104 kgm3)

(b)

Figure 6 1198962eff of FBAR versus the thickness and the density of electrode with AlN piezoelectric film

decreases with the thickness increasing and the increasingratio can reach to 20 over original value of piezoelectricfilm However 1198962eff mostly increases with the density ofelectrode 1198962eff changes fast with the thickness of electrodewhen the density of electrode is small and vice versa TheFBAR with the ZnO layer shows that 1198962eff changes morequickly than the case of AlN and the thickness effect is moreobvious too especially for the small density of electrode casesFurthermore we can also get the same witness from the 2Dfigures of Figures 5(b) and 6(b)

A very interesting result is obtained from 2D figures that1198962eff will arrive at a maximum area with special thicknessvalues for any density of electrode and the correspondingthickness area is very obvious at the center such as the FBARwith ZnO The thickness beginning with the maximum 1198962effarea is nearby 037 120583m and the thickness is nearby 05 120583m forthe AlN case This is a very interesting and important resultand it means the effect of thickness on 1198962eff has a strong rulewhich is affected little by the density of electrode materialWe analyzed this phenomenon that it is the thickness wherestanding wave appears and the difference between thesetwo piezoelectric film cases should be attributed to thedifferent piezoelectric thin films Moreover it confirms thatthe standing wave exists in the FBAR and the thickness ofelectrode should be optimized with this merit point which iseffective for all kinds of electrode materials

33 Effects of V119890and119889119890on 1198962119890119891119891

of FBAR For overall evaluationof 1198962eff the effects of V

119890and 119889

119890on 1198962eff were conducted

with the 2 120583m thick piezoelectric film and the 2D and 3Dfigures with four different electrode density choices weregiven for contrasting The 3D 1198962eff versus V

119890and 119889

119890curves

based on ZnO and AlN were shown in Figures 7 and 9respectively and the 2D results were shown in Figures 8and 10 correspondingly The key parameters and results weremarked on the 3D figures We can get that 1198962eff always riseswith the density of electrode for the ZnO case in Figure 7

0 05 12468101214

002

003

004

005

006

007

008k2 eff

Number 1 120588e = 19 times 104 kgm3

(e = 145 times 103 ms de = 055120583m)

Number 2 120588e = 13 times 104 kgm3

(e = 145 times 103 ms de = 06 120583m)

eNumber 3 120588 = 7 times 103

103kgm3

(e = 145 times ms de = 065120583m)

Number 4 120588e = 2 times 103

103kgm3

(e = 145 times ms de = 08 120583m)

e (103 ms) de(120583m)

max k = 0074156

max k = 007372

max k = 0072642

max k = 007028

Figure 7 1198962eff of FBAR versus the thickness and the acoustic velocityof electrode with ZnO piezoelectric film and different density (3Dcurves)

which also can be observed in above section results andthe maximum 1198962eff always appears at the maximum acousticvelocity during our calculation range The AlN case is thesame behavior as the ZnO FBAR in Figure 9 Moreover 1198962effrises more obviously with V

119890in the large electrode thickness

area and vice versa and 1198962eff changes little with V119890among the

small electrode thickness area and especially least in the highdensity electrode material area On the other hand 1198962eff risesdistinctlywith the electrode thickness in the low velocity areabut it almost does not change in the high velocity space

6 Journal of Nanomaterials

01 02 03 04 05 06 07 08 09 1

4

6

8

10

12

14

003

004

005

006

007

e(103

ms

)

de (120583m)

(a) 120588119890= 2 times 10

3 kgm3

0035004004500500550060065007

01 02 03 04 05 06 07 08 09 1

4

6

8

10

12

14

e(103

ms

)

de (120583m)

(b) 120588119890= 7 times 10

3 kgm3

005

0055

006

0065

01 02 03 04 05 06 07 08 09 1

4

6

8

10

12

14

e(103

ms

)

de (120583m)

(c) 120588119890= 13 times 10

4 kgm3

0055

006

0065

007

01 02 03 04 05 06 07 08 09 1

4

6

8

10

12

14

e(103

ms

)de (120583m)

(d) 120588119890= 19 times 10

4 kgm3

Figure 8 1198962eff of FBAR versus the thickness and the acoustic velocity of electrode with ZnO piezoelectric film (2D curves)

005

1

24681012140025

003

0035

004

0045

005

0055

006

0065

k2 eff

e (103 ms) de(120583m)

4 3Number 1 120588e = 19 times 10 kgm(e = 145 times 103 ms de = 08 120583m)

Number 2 120588e = 13 times 104 kgm3

(e = 145 times 103 ms de = 09 120583m)Number 3 120588e = 7 times 103 kgm3

e e( = 145 times 103 ms d = 095120583m)Number 4 120588e = 2 times 103 kgm3

(e = 145 times 103 ms de = 105 120583m)

max k = 0061397

max k = 0060458

max k = 0058439

max k = 0061766

Figure 9 1198962eff of FBAR versus the thickness and the acoustic velocityof electrode with AlN piezoelectric film and different density (3Dcurves)

We can conclude that 1198962eff is in the direct proportion tothe density 120588

119890here and the acoustic velocity of electrode has

a similar effect too and 1198962eff dominantly rises with V119890 The

electrode thickness affects small 1198962eff with high V119890 moreover

when V119890is high enough then 1198962eff has almost nothing to do

with 119889119890 But 1198962eff changes fast with 119889

119890when V

119890is small and

1198962eff rises with electrode thickness first and then descendswithits rising which was also observed in the former sectionThe thickness corresponding to themaximum 1198962eff is differentwith different electrode density however it descends withdensity ascending which also proves the special value 120588

119890119889119890

corresponding with the maximum 1198962eff of FBAR even thoughwe cannot get this result directly by these figures becausethere are not so many piezoelectric film parameters consid-ered for proving [14] All these behaviors are similar for bothZnO and AlN based FBARs

The density acoustic velocity and thickness of electrodeof FBAR can be optimized by above results for special 119891

119904and

1198962eff need We can get the higher 1198962eff with the higher electrodedensity and it is also the same to acoustic velocity of electrodematerialThe best thickness of electrode is decided by densityand especially acoustic velocity however the thickness effectsare obvious when the acoustic velocity is small but it almostdoes not change if the acoustic velocity is very big Moreoverthe best thickness corresponding to the maximum 1198962eff isdifferent with different cases but the values are in the specialarea comparing with the distinctly variable V

119890and 120588119890 and it is

because we take most of the parameters of piezoelectric thinfilm as constants even though these results can be observedin both ZnO and AlN FBARs in this research

4 Conclusions

In this paper the following research and results have beengiven

Journal of Nanomaterials 7

003

0035

004

0045

005

0055

01 02 03 04 05 06 07 08 09 14

6

8

10

12

14 e

(103

ms

)

de (120583m)

(a) 120588119890= 2 times 10

3 kgm3

004

0045

005

0055

006

01 02 03 04 05 06 07 08 09 14

6

8

10

12

14

e(103

ms

)

de (120583m)

(b) 120588119890= 7 times 10

3 kgm3

0045

005

0055

006

01 02 03 04 05 06 07 08 09 14

6

8

10

12

14

e(103

ms

)

de (120583m)

(c) 120588119890= 13 times 10

4 kgm3

005

0052

0054

0056

0058

01 02 03 04 05 06 07 08 09 14

6

8

10

12

14

e(103

ms

)de (120583m)

(d) 120588119890= 19 times 10

4 kgm3

Figure 10 1198962eff of FBAR versus the thickness and the acoustic velocity of electrode with AlN piezoelectric film and different density (2Dcurves)

(i) Firstly we derived the input acoustic impedanceequation with transfer matrix method and the sim-plified impedance equation of FBAR with the sametop and bottom electrode is obtained This equationcan be applied extensively to calculate the resonancefrequency the effective electromechanical couplingfactor themechanical quality factor and themerit fig-ure of FBAR which makes the theoretical calculationand optimization easy

(ii) Secondly the effect of thickness and density ofelectrode on the resonance frequency of FBAR wasinvestigated and it can be obtained that the thicknessand the density of electrode affect the resonancefrequency obviously especially at the large thicknessand density area This result shows that the thicknessand the material of electrode are very key parametersfor the resonance frequency design of FBAR

(iii) Finally the effects of thickness density and acousticvelocity on the effective electromechanical couplingfactor were studied respectivelyThe results show that1198962eff is in the direct proportion to both density 120588

119890and

V119890of electrode The electrode thickness affects small

1198962eff with high V119890 moreover when V

119890is high enough

then 1198962eff has almost nothing to do with 119889119890 1198962eff rises

with electrode thickness first and then descends withits rising and the thickness corresponding to themaximum 1198962eff is different with different electrodedensity and V

119890 but they almost locate in the special

area

All above results indicate that the thickness density andacoustic velocity of electrode are very important and they canbe applied to optimize and design different kind of FBARs

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This work is supported by the National Natural ScienceFoundation of China (nos 61201088 11404257 and 11504291)Shaanxi Province Innovation Project for Science and Tech-nology Overall Planning (no 2012KTCL01-12) Industrial-ization Foundation of Shaanxi Educational Committee (no2011JG10) and Xirsquoan Technology Transferring and PromotingProject (CXY1342(5) CX1253(2))

References

[1] J D Larson III R Ruby P Bradley and Y Oshmyansky ldquoBAWantenna duplex for the 1900MHz PCS bandrdquo in Proceedings ofthe IEEE Ultrasonics Symposium pp 887ndash890 Caesars TahoeNV USA October 1999

[2] R Ruby P Bradley J D Larson III and Y Oshmyansky ldquoPCS1900MHz duplexer using thin film bulk acoustic resonators(FBARs)rdquo Electronics Letters vol 35 no 10 pp 794ndash796 1999

[3] R C Ruby P Bradley Y Oshmyansky A Chien and J DLarson III ldquoThin film bulk wave acoustic resonators (FBAR)for wireless applicationsrdquo in Proceedings of the UltrasonicsSymposium pp 813ndash821 October 2001

8 Journal of Nanomaterials

[4] K M Lakin J Belsick J F McDonald and K T McCarronldquoImproved bulk wave resonator coupling coefficient for widebandwidth filtersrdquo inProceedings of the IEEEUltrasonics Sympo-sium vol 1 pp 827ndash831 IEEE Atlanta Ga USA October 2001

[5] I Voiculescu and A N Nordin ldquoAcoustic wave based MEMSdevices for biosensing applicationsrdquo Biosensors and Bioelectron-ics vol 33 no 1 pp 1ndash9 2012

[6] F T Chu C Li Z Z Wang and X Z Liu ldquoAluminum NitrideThin films on molybdenumpolyimide heterostructure for bulkacoustic resonatorsrdquo Rare Metal Materials and Engineering vol42 no 10 pp 2023ndash2026 2013

[7] A J Festschrift J K Luo Y Q Fu et al ldquoZnO based SAWand FBAR devices for bio-sensing applicationsrdquo Journal of Non-Newtonian Fluid Mechanics vol 222 pp 209ndash216 2015

[8] H Zhang G Jiang Z Liu S Zhang and L Fan ldquoOptimizationsof composited acoustic sensors with a microfluidic channelrdquoJournal of Applied Physics vol 115 no 13 Article ID 1335022014

[9] A Vorobiev and S Gevorgian ldquoIntrinsically switchable thinfilm bulk acoustic wave resonatorsrdquo Applied Physics Letters vol104 no 22 Article ID 222905 2014

[10] H J Lee K A Hyun and H I Jung ldquoA high-Q resonator usingbiocompatible materials at microwave frequenciesrdquo AppliedPhysics Letters vol 104 no 2 Article ID 023509 2014

[11] M-C Chao Z-N Huang S-Y Pao Z Wang and C S LamldquoModified BVD-equivalent circuit of FBARby taking electrodesinto accountrdquo inProceedings of the IEEEUltrasonics Symposiumpp 973ndash976 October 2002

[12] Q Chen and Q-M Wang ldquoThe effective electromechani-cal coupling coefficient of piezoelectric thin-film resonatorsrdquoApplied Physics Letters vol 86 no 2 Article ID 022904 2005

[13] Y Zhang Z Wang and J D N Cheeke ldquoResonant spectrummethod to characterize piezoelectric films in composite res-onatorsrdquo IEEE Transactions on Ultrasonics Ferroelectrics andFrequency Control vol 50 no 3 pp 321ndash333 2003

[14] T Zhang H Zhang Z-Q Wang and S-Y Zhang ldquoEffects ofelectrodes on performance figures of thin film bulk acousticresonatorsrdquo Journal of the Acoustical Society of America vol 122no 3 pp 1646ndash1651 2007

[15] N F Naumenko ldquoAdvanced numerical technique for analysisof surface and bulk acoustic waves in resonators using periodicmetal gratingsrdquo Journal of Applied Physics vol 116 no 10 ArticleID 104503 2014

[16] A Kvasov and A K Tagantsev ldquoThin film bulk acoustic waveresonators tuning from first principlesrdquo Journal of AppliedPhysics vol 113 no 20 Article ID 204104 2013

[17] IEEE ldquoIEEE standard on piezoelectricityrdquo Tech Rep 176-1987 IEEE Transactions on Ultrasonics Ferroelectrics andFrequency Control 1996 43719

Submit your manuscripts athttpwwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CeramicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CompositesJournal of

NanoparticlesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Biomaterials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

CrystallographyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MetallurgyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

MaterialsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nano

materials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofNanomaterials

Journal of Nanomaterials 5

0 051 15

2

00102030405060708091005

0052

0054

0056

0058

006

0062

0052 0053 0054 0055 0056 0057 0058 0059 006

k2 eff

de (120583m) 120588 e(10

4 kgm3 )

(a)

04 06 08 1 12 14 16 18

010203040506070809

1

0052 0053 0054 0055 0056 0057 0058 0059 006

de

(120583m

)

120588e (104 kgm3)

(b)

Figure 6 1198962eff of FBAR versus the thickness and the density of electrode with AlN piezoelectric film

decreases with the thickness increasing and the increasingratio can reach to 20 over original value of piezoelectricfilm However 1198962eff mostly increases with the density ofelectrode 1198962eff changes fast with the thickness of electrodewhen the density of electrode is small and vice versa TheFBAR with the ZnO layer shows that 1198962eff changes morequickly than the case of AlN and the thickness effect is moreobvious too especially for the small density of electrode casesFurthermore we can also get the same witness from the 2Dfigures of Figures 5(b) and 6(b)

A very interesting result is obtained from 2D figures that1198962eff will arrive at a maximum area with special thicknessvalues for any density of electrode and the correspondingthickness area is very obvious at the center such as the FBARwith ZnO The thickness beginning with the maximum 1198962effarea is nearby 037 120583m and the thickness is nearby 05 120583m forthe AlN case This is a very interesting and important resultand it means the effect of thickness on 1198962eff has a strong rulewhich is affected little by the density of electrode materialWe analyzed this phenomenon that it is the thickness wherestanding wave appears and the difference between thesetwo piezoelectric film cases should be attributed to thedifferent piezoelectric thin films Moreover it confirms thatthe standing wave exists in the FBAR and the thickness ofelectrode should be optimized with this merit point which iseffective for all kinds of electrode materials

33 Effects of V119890and119889119890on 1198962119890119891119891

of FBAR For overall evaluationof 1198962eff the effects of V

119890and 119889

119890on 1198962eff were conducted

with the 2 120583m thick piezoelectric film and the 2D and 3Dfigures with four different electrode density choices weregiven for contrasting The 3D 1198962eff versus V

119890and 119889

119890curves

based on ZnO and AlN were shown in Figures 7 and 9respectively and the 2D results were shown in Figures 8and 10 correspondingly The key parameters and results weremarked on the 3D figures We can get that 1198962eff always riseswith the density of electrode for the ZnO case in Figure 7

0 05 12468101214

002

003

004

005

006

007

008k2 eff

Number 1 120588e = 19 times 104 kgm3

(e = 145 times 103 ms de = 055120583m)

Number 2 120588e = 13 times 104 kgm3

(e = 145 times 103 ms de = 06 120583m)

eNumber 3 120588 = 7 times 103

103kgm3

(e = 145 times ms de = 065120583m)

Number 4 120588e = 2 times 103

103kgm3

(e = 145 times ms de = 08 120583m)

e (103 ms) de(120583m)

max k = 0074156

max k = 007372

max k = 0072642

max k = 007028

Figure 7 1198962eff of FBAR versus the thickness and the acoustic velocityof electrode with ZnO piezoelectric film and different density (3Dcurves)

which also can be observed in above section results andthe maximum 1198962eff always appears at the maximum acousticvelocity during our calculation range The AlN case is thesame behavior as the ZnO FBAR in Figure 9 Moreover 1198962effrises more obviously with V

119890in the large electrode thickness

area and vice versa and 1198962eff changes little with V119890among the

small electrode thickness area and especially least in the highdensity electrode material area On the other hand 1198962eff risesdistinctlywith the electrode thickness in the low velocity areabut it almost does not change in the high velocity space

6 Journal of Nanomaterials

01 02 03 04 05 06 07 08 09 1

4

6

8

10

12

14

003

004

005

006

007

e(103

ms

)

de (120583m)

(a) 120588119890= 2 times 10

3 kgm3

0035004004500500550060065007

01 02 03 04 05 06 07 08 09 1

4

6

8

10

12

14

e(103

ms

)

de (120583m)

(b) 120588119890= 7 times 10

3 kgm3

005

0055

006

0065

01 02 03 04 05 06 07 08 09 1

4

6

8

10

12

14

e(103

ms

)

de (120583m)

(c) 120588119890= 13 times 10

4 kgm3

0055

006

0065

007

01 02 03 04 05 06 07 08 09 1

4

6

8

10

12

14

e(103

ms

)de (120583m)

(d) 120588119890= 19 times 10

4 kgm3

Figure 8 1198962eff of FBAR versus the thickness and the acoustic velocity of electrode with ZnO piezoelectric film (2D curves)

005

1

24681012140025

003

0035

004

0045

005

0055

006

0065

k2 eff

e (103 ms) de(120583m)

4 3Number 1 120588e = 19 times 10 kgm(e = 145 times 103 ms de = 08 120583m)

Number 2 120588e = 13 times 104 kgm3

(e = 145 times 103 ms de = 09 120583m)Number 3 120588e = 7 times 103 kgm3

e e( = 145 times 103 ms d = 095120583m)Number 4 120588e = 2 times 103 kgm3

(e = 145 times 103 ms de = 105 120583m)

max k = 0061397

max k = 0060458

max k = 0058439

max k = 0061766

Figure 9 1198962eff of FBAR versus the thickness and the acoustic velocityof electrode with AlN piezoelectric film and different density (3Dcurves)

We can conclude that 1198962eff is in the direct proportion tothe density 120588

119890here and the acoustic velocity of electrode has

a similar effect too and 1198962eff dominantly rises with V119890 The

electrode thickness affects small 1198962eff with high V119890 moreover

when V119890is high enough then 1198962eff has almost nothing to do

with 119889119890 But 1198962eff changes fast with 119889

119890when V

119890is small and

1198962eff rises with electrode thickness first and then descendswithits rising which was also observed in the former sectionThe thickness corresponding to themaximum 1198962eff is differentwith different electrode density however it descends withdensity ascending which also proves the special value 120588

119890119889119890

corresponding with the maximum 1198962eff of FBAR even thoughwe cannot get this result directly by these figures becausethere are not so many piezoelectric film parameters consid-ered for proving [14] All these behaviors are similar for bothZnO and AlN based FBARs

The density acoustic velocity and thickness of electrodeof FBAR can be optimized by above results for special 119891

119904and

1198962eff need We can get the higher 1198962eff with the higher electrodedensity and it is also the same to acoustic velocity of electrodematerialThe best thickness of electrode is decided by densityand especially acoustic velocity however the thickness effectsare obvious when the acoustic velocity is small but it almostdoes not change if the acoustic velocity is very big Moreoverthe best thickness corresponding to the maximum 1198962eff isdifferent with different cases but the values are in the specialarea comparing with the distinctly variable V

119890and 120588119890 and it is

because we take most of the parameters of piezoelectric thinfilm as constants even though these results can be observedin both ZnO and AlN FBARs in this research

4 Conclusions

In this paper the following research and results have beengiven

Journal of Nanomaterials 7

003

0035

004

0045

005

0055

01 02 03 04 05 06 07 08 09 14

6

8

10

12

14 e

(103

ms

)

de (120583m)

(a) 120588119890= 2 times 10

3 kgm3

004

0045

005

0055

006

01 02 03 04 05 06 07 08 09 14

6

8

10

12

14

e(103

ms

)

de (120583m)

(b) 120588119890= 7 times 10

3 kgm3

0045

005

0055

006

01 02 03 04 05 06 07 08 09 14

6

8

10

12

14

e(103

ms

)

de (120583m)

(c) 120588119890= 13 times 10

4 kgm3

005

0052

0054

0056

0058

01 02 03 04 05 06 07 08 09 14

6

8

10

12

14

e(103

ms

)de (120583m)

(d) 120588119890= 19 times 10

4 kgm3

Figure 10 1198962eff of FBAR versus the thickness and the acoustic velocity of electrode with AlN piezoelectric film and different density (2Dcurves)

(i) Firstly we derived the input acoustic impedanceequation with transfer matrix method and the sim-plified impedance equation of FBAR with the sametop and bottom electrode is obtained This equationcan be applied extensively to calculate the resonancefrequency the effective electromechanical couplingfactor themechanical quality factor and themerit fig-ure of FBAR which makes the theoretical calculationand optimization easy

(ii) Secondly the effect of thickness and density ofelectrode on the resonance frequency of FBAR wasinvestigated and it can be obtained that the thicknessand the density of electrode affect the resonancefrequency obviously especially at the large thicknessand density area This result shows that the thicknessand the material of electrode are very key parametersfor the resonance frequency design of FBAR

(iii) Finally the effects of thickness density and acousticvelocity on the effective electromechanical couplingfactor were studied respectivelyThe results show that1198962eff is in the direct proportion to both density 120588

119890and

V119890of electrode The electrode thickness affects small

1198962eff with high V119890 moreover when V

119890is high enough

then 1198962eff has almost nothing to do with 119889119890 1198962eff rises

with electrode thickness first and then descends withits rising and the thickness corresponding to themaximum 1198962eff is different with different electrodedensity and V

119890 but they almost locate in the special

area

All above results indicate that the thickness density andacoustic velocity of electrode are very important and they canbe applied to optimize and design different kind of FBARs

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This work is supported by the National Natural ScienceFoundation of China (nos 61201088 11404257 and 11504291)Shaanxi Province Innovation Project for Science and Tech-nology Overall Planning (no 2012KTCL01-12) Industrial-ization Foundation of Shaanxi Educational Committee (no2011JG10) and Xirsquoan Technology Transferring and PromotingProject (CXY1342(5) CX1253(2))

References

[1] J D Larson III R Ruby P Bradley and Y Oshmyansky ldquoBAWantenna duplex for the 1900MHz PCS bandrdquo in Proceedings ofthe IEEE Ultrasonics Symposium pp 887ndash890 Caesars TahoeNV USA October 1999

[2] R Ruby P Bradley J D Larson III and Y Oshmyansky ldquoPCS1900MHz duplexer using thin film bulk acoustic resonators(FBARs)rdquo Electronics Letters vol 35 no 10 pp 794ndash796 1999

[3] R C Ruby P Bradley Y Oshmyansky A Chien and J DLarson III ldquoThin film bulk wave acoustic resonators (FBAR)for wireless applicationsrdquo in Proceedings of the UltrasonicsSymposium pp 813ndash821 October 2001

8 Journal of Nanomaterials

[4] K M Lakin J Belsick J F McDonald and K T McCarronldquoImproved bulk wave resonator coupling coefficient for widebandwidth filtersrdquo inProceedings of the IEEEUltrasonics Sympo-sium vol 1 pp 827ndash831 IEEE Atlanta Ga USA October 2001

[5] I Voiculescu and A N Nordin ldquoAcoustic wave based MEMSdevices for biosensing applicationsrdquo Biosensors and Bioelectron-ics vol 33 no 1 pp 1ndash9 2012

[6] F T Chu C Li Z Z Wang and X Z Liu ldquoAluminum NitrideThin films on molybdenumpolyimide heterostructure for bulkacoustic resonatorsrdquo Rare Metal Materials and Engineering vol42 no 10 pp 2023ndash2026 2013

[7] A J Festschrift J K Luo Y Q Fu et al ldquoZnO based SAWand FBAR devices for bio-sensing applicationsrdquo Journal of Non-Newtonian Fluid Mechanics vol 222 pp 209ndash216 2015

[8] H Zhang G Jiang Z Liu S Zhang and L Fan ldquoOptimizationsof composited acoustic sensors with a microfluidic channelrdquoJournal of Applied Physics vol 115 no 13 Article ID 1335022014

[9] A Vorobiev and S Gevorgian ldquoIntrinsically switchable thinfilm bulk acoustic wave resonatorsrdquo Applied Physics Letters vol104 no 22 Article ID 222905 2014

[10] H J Lee K A Hyun and H I Jung ldquoA high-Q resonator usingbiocompatible materials at microwave frequenciesrdquo AppliedPhysics Letters vol 104 no 2 Article ID 023509 2014

[11] M-C Chao Z-N Huang S-Y Pao Z Wang and C S LamldquoModified BVD-equivalent circuit of FBARby taking electrodesinto accountrdquo inProceedings of the IEEEUltrasonics Symposiumpp 973ndash976 October 2002

[12] Q Chen and Q-M Wang ldquoThe effective electromechani-cal coupling coefficient of piezoelectric thin-film resonatorsrdquoApplied Physics Letters vol 86 no 2 Article ID 022904 2005

[13] Y Zhang Z Wang and J D N Cheeke ldquoResonant spectrummethod to characterize piezoelectric films in composite res-onatorsrdquo IEEE Transactions on Ultrasonics Ferroelectrics andFrequency Control vol 50 no 3 pp 321ndash333 2003

[14] T Zhang H Zhang Z-Q Wang and S-Y Zhang ldquoEffects ofelectrodes on performance figures of thin film bulk acousticresonatorsrdquo Journal of the Acoustical Society of America vol 122no 3 pp 1646ndash1651 2007

[15] N F Naumenko ldquoAdvanced numerical technique for analysisof surface and bulk acoustic waves in resonators using periodicmetal gratingsrdquo Journal of Applied Physics vol 116 no 10 ArticleID 104503 2014

[16] A Kvasov and A K Tagantsev ldquoThin film bulk acoustic waveresonators tuning from first principlesrdquo Journal of AppliedPhysics vol 113 no 20 Article ID 204104 2013

[17] IEEE ldquoIEEE standard on piezoelectricityrdquo Tech Rep 176-1987 IEEE Transactions on Ultrasonics Ferroelectrics andFrequency Control 1996 43719

Submit your manuscripts athttpwwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CeramicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CompositesJournal of

NanoparticlesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Biomaterials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

CrystallographyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MetallurgyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

MaterialsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nano

materials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofNanomaterials

6 Journal of Nanomaterials

01 02 03 04 05 06 07 08 09 1

4

6

8

10

12

14

003

004

005

006

007

e(103

ms

)

de (120583m)

(a) 120588119890= 2 times 10

3 kgm3

0035004004500500550060065007

01 02 03 04 05 06 07 08 09 1

4

6

8

10

12

14

e(103

ms

)

de (120583m)

(b) 120588119890= 7 times 10

3 kgm3

005

0055

006

0065

01 02 03 04 05 06 07 08 09 1

4

6

8

10

12

14

e(103

ms

)

de (120583m)

(c) 120588119890= 13 times 10

4 kgm3

0055

006

0065

007

01 02 03 04 05 06 07 08 09 1

4

6

8

10

12

14

e(103

ms

)de (120583m)

(d) 120588119890= 19 times 10

4 kgm3

Figure 8 1198962eff of FBAR versus the thickness and the acoustic velocity of electrode with ZnO piezoelectric film (2D curves)

005

1

24681012140025

003

0035

004

0045

005

0055

006

0065

k2 eff

e (103 ms) de(120583m)

4 3Number 1 120588e = 19 times 10 kgm(e = 145 times 103 ms de = 08 120583m)

Number 2 120588e = 13 times 104 kgm3

(e = 145 times 103 ms de = 09 120583m)Number 3 120588e = 7 times 103 kgm3

e e( = 145 times 103 ms d = 095120583m)Number 4 120588e = 2 times 103 kgm3

(e = 145 times 103 ms de = 105 120583m)

max k = 0061397

max k = 0060458

max k = 0058439

max k = 0061766

Figure 9 1198962eff of FBAR versus the thickness and the acoustic velocityof electrode with AlN piezoelectric film and different density (3Dcurves)

We can conclude that 1198962eff is in the direct proportion tothe density 120588

119890here and the acoustic velocity of electrode has

a similar effect too and 1198962eff dominantly rises with V119890 The

electrode thickness affects small 1198962eff with high V119890 moreover

when V119890is high enough then 1198962eff has almost nothing to do

with 119889119890 But 1198962eff changes fast with 119889

119890when V

119890is small and

1198962eff rises with electrode thickness first and then descendswithits rising which was also observed in the former sectionThe thickness corresponding to themaximum 1198962eff is differentwith different electrode density however it descends withdensity ascending which also proves the special value 120588

119890119889119890

corresponding with the maximum 1198962eff of FBAR even thoughwe cannot get this result directly by these figures becausethere are not so many piezoelectric film parameters consid-ered for proving [14] All these behaviors are similar for bothZnO and AlN based FBARs

The density acoustic velocity and thickness of electrodeof FBAR can be optimized by above results for special 119891

119904and

1198962eff need We can get the higher 1198962eff with the higher electrodedensity and it is also the same to acoustic velocity of electrodematerialThe best thickness of electrode is decided by densityand especially acoustic velocity however the thickness effectsare obvious when the acoustic velocity is small but it almostdoes not change if the acoustic velocity is very big Moreoverthe best thickness corresponding to the maximum 1198962eff isdifferent with different cases but the values are in the specialarea comparing with the distinctly variable V

119890and 120588119890 and it is

because we take most of the parameters of piezoelectric thinfilm as constants even though these results can be observedin both ZnO and AlN FBARs in this research

4 Conclusions

In this paper the following research and results have beengiven

Journal of Nanomaterials 7

003

0035

004

0045

005

0055

01 02 03 04 05 06 07 08 09 14

6

8

10

12

14 e

(103

ms

)

de (120583m)

(a) 120588119890= 2 times 10

3 kgm3

004

0045

005

0055

006

01 02 03 04 05 06 07 08 09 14

6

8

10

12

14

e(103

ms

)

de (120583m)

(b) 120588119890= 7 times 10

3 kgm3

0045

005

0055

006

01 02 03 04 05 06 07 08 09 14

6

8

10

12

14

e(103

ms

)

de (120583m)

(c) 120588119890= 13 times 10

4 kgm3

005

0052

0054

0056

0058

01 02 03 04 05 06 07 08 09 14

6

8

10

12

14

e(103

ms

)de (120583m)

(d) 120588119890= 19 times 10

4 kgm3

Figure 10 1198962eff of FBAR versus the thickness and the acoustic velocity of electrode with AlN piezoelectric film and different density (2Dcurves)

(i) Firstly we derived the input acoustic impedanceequation with transfer matrix method and the sim-plified impedance equation of FBAR with the sametop and bottom electrode is obtained This equationcan be applied extensively to calculate the resonancefrequency the effective electromechanical couplingfactor themechanical quality factor and themerit fig-ure of FBAR which makes the theoretical calculationand optimization easy

(ii) Secondly the effect of thickness and density ofelectrode on the resonance frequency of FBAR wasinvestigated and it can be obtained that the thicknessand the density of electrode affect the resonancefrequency obviously especially at the large thicknessand density area This result shows that the thicknessand the material of electrode are very key parametersfor the resonance frequency design of FBAR

(iii) Finally the effects of thickness density and acousticvelocity on the effective electromechanical couplingfactor were studied respectivelyThe results show that1198962eff is in the direct proportion to both density 120588

119890and

V119890of electrode The electrode thickness affects small

1198962eff with high V119890 moreover when V

119890is high enough

then 1198962eff has almost nothing to do with 119889119890 1198962eff rises

with electrode thickness first and then descends withits rising and the thickness corresponding to themaximum 1198962eff is different with different electrodedensity and V

119890 but they almost locate in the special

area

All above results indicate that the thickness density andacoustic velocity of electrode are very important and they canbe applied to optimize and design different kind of FBARs

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This work is supported by the National Natural ScienceFoundation of China (nos 61201088 11404257 and 11504291)Shaanxi Province Innovation Project for Science and Tech-nology Overall Planning (no 2012KTCL01-12) Industrial-ization Foundation of Shaanxi Educational Committee (no2011JG10) and Xirsquoan Technology Transferring and PromotingProject (CXY1342(5) CX1253(2))

References

[1] J D Larson III R Ruby P Bradley and Y Oshmyansky ldquoBAWantenna duplex for the 1900MHz PCS bandrdquo in Proceedings ofthe IEEE Ultrasonics Symposium pp 887ndash890 Caesars TahoeNV USA October 1999

[2] R Ruby P Bradley J D Larson III and Y Oshmyansky ldquoPCS1900MHz duplexer using thin film bulk acoustic resonators(FBARs)rdquo Electronics Letters vol 35 no 10 pp 794ndash796 1999

[3] R C Ruby P Bradley Y Oshmyansky A Chien and J DLarson III ldquoThin film bulk wave acoustic resonators (FBAR)for wireless applicationsrdquo in Proceedings of the UltrasonicsSymposium pp 813ndash821 October 2001

8 Journal of Nanomaterials

[4] K M Lakin J Belsick J F McDonald and K T McCarronldquoImproved bulk wave resonator coupling coefficient for widebandwidth filtersrdquo inProceedings of the IEEEUltrasonics Sympo-sium vol 1 pp 827ndash831 IEEE Atlanta Ga USA October 2001

[5] I Voiculescu and A N Nordin ldquoAcoustic wave based MEMSdevices for biosensing applicationsrdquo Biosensors and Bioelectron-ics vol 33 no 1 pp 1ndash9 2012

[6] F T Chu C Li Z Z Wang and X Z Liu ldquoAluminum NitrideThin films on molybdenumpolyimide heterostructure for bulkacoustic resonatorsrdquo Rare Metal Materials and Engineering vol42 no 10 pp 2023ndash2026 2013

[7] A J Festschrift J K Luo Y Q Fu et al ldquoZnO based SAWand FBAR devices for bio-sensing applicationsrdquo Journal of Non-Newtonian Fluid Mechanics vol 222 pp 209ndash216 2015

[8] H Zhang G Jiang Z Liu S Zhang and L Fan ldquoOptimizationsof composited acoustic sensors with a microfluidic channelrdquoJournal of Applied Physics vol 115 no 13 Article ID 1335022014

[9] A Vorobiev and S Gevorgian ldquoIntrinsically switchable thinfilm bulk acoustic wave resonatorsrdquo Applied Physics Letters vol104 no 22 Article ID 222905 2014

[10] H J Lee K A Hyun and H I Jung ldquoA high-Q resonator usingbiocompatible materials at microwave frequenciesrdquo AppliedPhysics Letters vol 104 no 2 Article ID 023509 2014

[11] M-C Chao Z-N Huang S-Y Pao Z Wang and C S LamldquoModified BVD-equivalent circuit of FBARby taking electrodesinto accountrdquo inProceedings of the IEEEUltrasonics Symposiumpp 973ndash976 October 2002

[12] Q Chen and Q-M Wang ldquoThe effective electromechani-cal coupling coefficient of piezoelectric thin-film resonatorsrdquoApplied Physics Letters vol 86 no 2 Article ID 022904 2005

[13] Y Zhang Z Wang and J D N Cheeke ldquoResonant spectrummethod to characterize piezoelectric films in composite res-onatorsrdquo IEEE Transactions on Ultrasonics Ferroelectrics andFrequency Control vol 50 no 3 pp 321ndash333 2003

[14] T Zhang H Zhang Z-Q Wang and S-Y Zhang ldquoEffects ofelectrodes on performance figures of thin film bulk acousticresonatorsrdquo Journal of the Acoustical Society of America vol 122no 3 pp 1646ndash1651 2007

[15] N F Naumenko ldquoAdvanced numerical technique for analysisof surface and bulk acoustic waves in resonators using periodicmetal gratingsrdquo Journal of Applied Physics vol 116 no 10 ArticleID 104503 2014

[16] A Kvasov and A K Tagantsev ldquoThin film bulk acoustic waveresonators tuning from first principlesrdquo Journal of AppliedPhysics vol 113 no 20 Article ID 204104 2013

[17] IEEE ldquoIEEE standard on piezoelectricityrdquo Tech Rep 176-1987 IEEE Transactions on Ultrasonics Ferroelectrics andFrequency Control 1996 43719

Submit your manuscripts athttpwwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CeramicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CompositesJournal of

NanoparticlesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Biomaterials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

CrystallographyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MetallurgyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

MaterialsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nano

materials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofNanomaterials

Journal of Nanomaterials 7

003

0035

004

0045

005

0055

01 02 03 04 05 06 07 08 09 14

6

8

10

12

14 e

(103

ms

)

de (120583m)

(a) 120588119890= 2 times 10

3 kgm3

004

0045

005

0055

006

01 02 03 04 05 06 07 08 09 14

6

8

10

12

14

e(103

ms

)

de (120583m)

(b) 120588119890= 7 times 10

3 kgm3

0045

005

0055

006

01 02 03 04 05 06 07 08 09 14

6

8

10

12

14

e(103

ms

)

de (120583m)

(c) 120588119890= 13 times 10

4 kgm3

005

0052

0054

0056

0058

01 02 03 04 05 06 07 08 09 14

6

8

10

12

14

e(103

ms

)de (120583m)

(d) 120588119890= 19 times 10

4 kgm3

Figure 10 1198962eff of FBAR versus the thickness and the acoustic velocity of electrode with AlN piezoelectric film and different density (2Dcurves)

(i) Firstly we derived the input acoustic impedanceequation with transfer matrix method and the sim-plified impedance equation of FBAR with the sametop and bottom electrode is obtained This equationcan be applied extensively to calculate the resonancefrequency the effective electromechanical couplingfactor themechanical quality factor and themerit fig-ure of FBAR which makes the theoretical calculationand optimization easy

(ii) Secondly the effect of thickness and density ofelectrode on the resonance frequency of FBAR wasinvestigated and it can be obtained that the thicknessand the density of electrode affect the resonancefrequency obviously especially at the large thicknessand density area This result shows that the thicknessand the material of electrode are very key parametersfor the resonance frequency design of FBAR

(iii) Finally the effects of thickness density and acousticvelocity on the effective electromechanical couplingfactor were studied respectivelyThe results show that1198962eff is in the direct proportion to both density 120588

119890and

V119890of electrode The electrode thickness affects small

1198962eff with high V119890 moreover when V

119890is high enough

then 1198962eff has almost nothing to do with 119889119890 1198962eff rises

with electrode thickness first and then descends withits rising and the thickness corresponding to themaximum 1198962eff is different with different electrodedensity and V

119890 but they almost locate in the special

area

All above results indicate that the thickness density andacoustic velocity of electrode are very important and they canbe applied to optimize and design different kind of FBARs

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This work is supported by the National Natural ScienceFoundation of China (nos 61201088 11404257 and 11504291)Shaanxi Province Innovation Project for Science and Tech-nology Overall Planning (no 2012KTCL01-12) Industrial-ization Foundation of Shaanxi Educational Committee (no2011JG10) and Xirsquoan Technology Transferring and PromotingProject (CXY1342(5) CX1253(2))

References

[1] J D Larson III R Ruby P Bradley and Y Oshmyansky ldquoBAWantenna duplex for the 1900MHz PCS bandrdquo in Proceedings ofthe IEEE Ultrasonics Symposium pp 887ndash890 Caesars TahoeNV USA October 1999

[2] R Ruby P Bradley J D Larson III and Y Oshmyansky ldquoPCS1900MHz duplexer using thin film bulk acoustic resonators(FBARs)rdquo Electronics Letters vol 35 no 10 pp 794ndash796 1999

[3] R C Ruby P Bradley Y Oshmyansky A Chien and J DLarson III ldquoThin film bulk wave acoustic resonators (FBAR)for wireless applicationsrdquo in Proceedings of the UltrasonicsSymposium pp 813ndash821 October 2001

8 Journal of Nanomaterials

[4] K M Lakin J Belsick J F McDonald and K T McCarronldquoImproved bulk wave resonator coupling coefficient for widebandwidth filtersrdquo inProceedings of the IEEEUltrasonics Sympo-sium vol 1 pp 827ndash831 IEEE Atlanta Ga USA October 2001

[5] I Voiculescu and A N Nordin ldquoAcoustic wave based MEMSdevices for biosensing applicationsrdquo Biosensors and Bioelectron-ics vol 33 no 1 pp 1ndash9 2012

[6] F T Chu C Li Z Z Wang and X Z Liu ldquoAluminum NitrideThin films on molybdenumpolyimide heterostructure for bulkacoustic resonatorsrdquo Rare Metal Materials and Engineering vol42 no 10 pp 2023ndash2026 2013

[7] A J Festschrift J K Luo Y Q Fu et al ldquoZnO based SAWand FBAR devices for bio-sensing applicationsrdquo Journal of Non-Newtonian Fluid Mechanics vol 222 pp 209ndash216 2015

[8] H Zhang G Jiang Z Liu S Zhang and L Fan ldquoOptimizationsof composited acoustic sensors with a microfluidic channelrdquoJournal of Applied Physics vol 115 no 13 Article ID 1335022014

[9] A Vorobiev and S Gevorgian ldquoIntrinsically switchable thinfilm bulk acoustic wave resonatorsrdquo Applied Physics Letters vol104 no 22 Article ID 222905 2014

[10] H J Lee K A Hyun and H I Jung ldquoA high-Q resonator usingbiocompatible materials at microwave frequenciesrdquo AppliedPhysics Letters vol 104 no 2 Article ID 023509 2014

[11] M-C Chao Z-N Huang S-Y Pao Z Wang and C S LamldquoModified BVD-equivalent circuit of FBARby taking electrodesinto accountrdquo inProceedings of the IEEEUltrasonics Symposiumpp 973ndash976 October 2002

[12] Q Chen and Q-M Wang ldquoThe effective electromechani-cal coupling coefficient of piezoelectric thin-film resonatorsrdquoApplied Physics Letters vol 86 no 2 Article ID 022904 2005

[13] Y Zhang Z Wang and J D N Cheeke ldquoResonant spectrummethod to characterize piezoelectric films in composite res-onatorsrdquo IEEE Transactions on Ultrasonics Ferroelectrics andFrequency Control vol 50 no 3 pp 321ndash333 2003

[14] T Zhang H Zhang Z-Q Wang and S-Y Zhang ldquoEffects ofelectrodes on performance figures of thin film bulk acousticresonatorsrdquo Journal of the Acoustical Society of America vol 122no 3 pp 1646ndash1651 2007

[15] N F Naumenko ldquoAdvanced numerical technique for analysisof surface and bulk acoustic waves in resonators using periodicmetal gratingsrdquo Journal of Applied Physics vol 116 no 10 ArticleID 104503 2014

[16] A Kvasov and A K Tagantsev ldquoThin film bulk acoustic waveresonators tuning from first principlesrdquo Journal of AppliedPhysics vol 113 no 20 Article ID 204104 2013

[17] IEEE ldquoIEEE standard on piezoelectricityrdquo Tech Rep 176-1987 IEEE Transactions on Ultrasonics Ferroelectrics andFrequency Control 1996 43719

Submit your manuscripts athttpwwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CeramicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CompositesJournal of

NanoparticlesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Biomaterials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

CrystallographyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MetallurgyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

MaterialsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nano

materials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofNanomaterials

8 Journal of Nanomaterials

[4] K M Lakin J Belsick J F McDonald and K T McCarronldquoImproved bulk wave resonator coupling coefficient for widebandwidth filtersrdquo inProceedings of the IEEEUltrasonics Sympo-sium vol 1 pp 827ndash831 IEEE Atlanta Ga USA October 2001

[5] I Voiculescu and A N Nordin ldquoAcoustic wave based MEMSdevices for biosensing applicationsrdquo Biosensors and Bioelectron-ics vol 33 no 1 pp 1ndash9 2012

[6] F T Chu C Li Z Z Wang and X Z Liu ldquoAluminum NitrideThin films on molybdenumpolyimide heterostructure for bulkacoustic resonatorsrdquo Rare Metal Materials and Engineering vol42 no 10 pp 2023ndash2026 2013

[7] A J Festschrift J K Luo Y Q Fu et al ldquoZnO based SAWand FBAR devices for bio-sensing applicationsrdquo Journal of Non-Newtonian Fluid Mechanics vol 222 pp 209ndash216 2015

[8] H Zhang G Jiang Z Liu S Zhang and L Fan ldquoOptimizationsof composited acoustic sensors with a microfluidic channelrdquoJournal of Applied Physics vol 115 no 13 Article ID 1335022014

[9] A Vorobiev and S Gevorgian ldquoIntrinsically switchable thinfilm bulk acoustic wave resonatorsrdquo Applied Physics Letters vol104 no 22 Article ID 222905 2014

[10] H J Lee K A Hyun and H I Jung ldquoA high-Q resonator usingbiocompatible materials at microwave frequenciesrdquo AppliedPhysics Letters vol 104 no 2 Article ID 023509 2014

[11] M-C Chao Z-N Huang S-Y Pao Z Wang and C S LamldquoModified BVD-equivalent circuit of FBARby taking electrodesinto accountrdquo inProceedings of the IEEEUltrasonics Symposiumpp 973ndash976 October 2002

[12] Q Chen and Q-M Wang ldquoThe effective electromechani-cal coupling coefficient of piezoelectric thin-film resonatorsrdquoApplied Physics Letters vol 86 no 2 Article ID 022904 2005

[13] Y Zhang Z Wang and J D N Cheeke ldquoResonant spectrummethod to characterize piezoelectric films in composite res-onatorsrdquo IEEE Transactions on Ultrasonics Ferroelectrics andFrequency Control vol 50 no 3 pp 321ndash333 2003

[14] T Zhang H Zhang Z-Q Wang and S-Y Zhang ldquoEffects ofelectrodes on performance figures of thin film bulk acousticresonatorsrdquo Journal of the Acoustical Society of America vol 122no 3 pp 1646ndash1651 2007

[15] N F Naumenko ldquoAdvanced numerical technique for analysisof surface and bulk acoustic waves in resonators using periodicmetal gratingsrdquo Journal of Applied Physics vol 116 no 10 ArticleID 104503 2014

[16] A Kvasov and A K Tagantsev ldquoThin film bulk acoustic waveresonators tuning from first principlesrdquo Journal of AppliedPhysics vol 113 no 20 Article ID 204104 2013

[17] IEEE ldquoIEEE standard on piezoelectricityrdquo Tech Rep 176-1987 IEEE Transactions on Ultrasonics Ferroelectrics andFrequency Control 1996 43719

Submit your manuscripts athttpwwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CeramicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CompositesJournal of

NanoparticlesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Biomaterials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

CrystallographyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MetallurgyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

MaterialsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nano

materials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofNanomaterials

Submit your manuscripts athttpwwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CeramicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CompositesJournal of

NanoparticlesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Biomaterials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

CrystallographyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MetallurgyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

MaterialsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nano

materials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofNanomaterials