04460876j

ieee transactions on ultrasonics, ferroelectrics, and frequency control, vol. 55, no. 2, february 2008 421

Modeling for Temperature Compensation andTemperature Characterizations of BAW

Resonators at GHz FrequenciesBrice Ivira, Philippe Benech, Rene Fillit, Fabien Ndagijimana, Pascal Ancey, and Guy Parat

Abstract—This paper deals with the temperature de-pendence of electrical and physical features of variouskinds of solidly mounted resonators (SMR). The presentedbulk acoustic wave (BAW) devices are designed for the2 GHz application. The temperature coefficient of frequency(TCF) is determined from measurements well above thetemperature range defined for wireless telecommunicationsystem specifications. Therefore, evolution of electrome-chanical coupling factors and quality factors at resonanceand antiresonance are also monitored. Results of character-izations show the trend for a subsequent theoretical tem-perature compensation study by using analytical modeling.To improve accuracy of modeling, an attempt to extracttemperature dependence of dielectric permittivity 33 andpiezoelectric coefficient e33 is made. Finally, a well-knownanalytical model is modified to take into account the tem-perature dependence of length, density, stiffness coefficient,dielectric permittivity, and piezoelectric coefficient. Model-ing highlights the need to deposit a material with positivetemperature coefficient of stiffness on the top electrode. Re-alistic thickness of such a layer is determined. At the sametime, it is necessary to adjust piezoelectric and electrodethin film thicknesses for simultaneously keeping a constantantiresonance frequency, reaching a zero temperature coef-ficient of frequency for antiresonance, and minimizing thedecrease in the coupling factor because of the mass-loadingdeposition.

I. Introduction

The recent growing interest in bulk acoustic wave(BAW) resonators aims to improve performances in

term of miniaturization, power handling, and thermal sta-bility of radio-frequency (RF) filtering functions in wirelesstelecommunication systems. At the same time, the numberof functions provided by these systems (image and audiodata processing) is steadily increasing. As a result, inte-gration of more and more functionality is space consumingand requires ultimate miniaturization of the RF circuits. Inthis context, BAW resonators were first evolved for on-chipintegration with RF CMOS and biCMOS in the above-ICapproach. The feasibility of such a design is demonstrated

Manuscript received June 21, 2007; accepted October 1, 2007. Thiswork is funded by the Rhone-Alpes Regional council, France.

B. Ivira, P. Benech, and F. Ndagijimana are with the Instituteof Microelectronics, Electromagnetism and Photonics, INPG/UJF,CNRS, Grenoble, France (email: [email protected]).

R. Y. Fillit is with the Ecole Nationale Superieure des Mines deSt-Etienne, Saint Etienne, France.

P. Ancey is with STMicroelectronics, Crolles, France.G. Patat is with CEA-LETI, Grenoble, France.Digital Object Identifier 10.1109/TUFFC.2008.660

[1]–[3], but a separated process still remains cheaper thanthe combined process at this point [4].

As guard band requirements of RF filters are very strin-gent, temperature dependence of electrical characteristicshas to be accurately measured. According to the giventemperature coefficient of frequency in the literature, itappears clearly that BAW resonators can be temperaturecompensated to render RF filters always more competitivethan surface acoustic wave (SAW) and dielectric ceramicfilters on the market. For studying temperature impacton electrical features, this work first presents RF char-acterizations on a wide range of temperature for manykinds of solidly mounted resonators (SMR) having vari-ous properties. Indeed, thickness pairs of piezoelectric andelectrode thin films vary to target an antiresonance fre-quency of 2.14 GHz at room temperature. Moreover, res-onators have different sizes (from 100 × 100 µm2 up to400× 400 µm2). Therefore, several resonators have a massloading of SiO2, and two types of acoustic reflectors, eitherW/SiO2 or SiN/SiOC, are studied. Comparison betweenthe different kinds of resonators allowed us to determinethe best way for reducing TCF. Based on experimental re-sults, we next investigated temperature compensation bymodifying a well-known analytical model. The work is spe-cially focused on a single resonator because it is the smallerconstitutive element of a filter and it contains ample infor-mation for subsequent filter design.

II. Samples

A schematic presentation of an SMR cross section isgiven in Fig. 1. The studied devices are composed of anAlN piezoelectric thin film sandwiched between two metal-lic electrodes in Mo of equal thickness, and the bottomone is deposited on an acoustic reflector. Therefore, someof the top electrodes are apodized to minimize spuriousmodes [5]. Antiresonance frequency is mainly determinedby the thickness of the AlN layer and decreases with in-creasing thickness. To realize the acoustic reflector, twotypes of Bragg reflectors were deposited onto the sub-strate, and layer thicknesses were designed for a targetedantiresonance frequency of 2.14 GHz. The Bragg reflectoris composed of a succession of quarter wave length layers(λ/4) of high and low acoustic impedance, either W/SiO2or SiN/SiOC [6]. Moreover, some resonators were mass-loaded by a thin SiO2 layer of about hundred nanometers

0885–3010/$25.00 c© 2008 IEEE

422 ieee transactions on ultrasonics, ferroelectrics, and frequency control, vol. 55, no. 2, february 2008

Fig. 1. Schematic cross section of SMR.

thick deposited on the top electrode, with the purpose todecrease (∼3% of the carrier frequency [7]) locally andadjust their resonance frequencies for subsequent ladderor lattice filter designs. A final process involves deposit-ing a Au/Ti thin film on Mo pads to improve electricaland mechanical contacts with RF probes for characteri-zation. Finally, a SiN passivation layer protects some ofresonators.

III. Temperature Dependence of Fundamental

1-D Equations

Modeling is investigated to find the best way for re-ducing the TCF of SMR structures. This study is basi-cally focused on frequency and coupling factor variations.While keeping constant the antiresonance frequency, weexamined the impact of different AlN/Mo thickness ratiosand a variable SiO2 thickness on the top electrode as itspositive temperature coefficient of stiffness is well knownfor temperature compensation. Therefore, because of themass-loading by SiO2 on the top electrode, we optimizethe SiO2/AlN/Mo stack thickness to minimize the cou-pling factor decrease. The model is obtained by solving thelinear equations of piezoelectricity for the one-dimensionalcase for the thickness vibration mode [8]. Thus, the electri-cal impedance of a resonator is expressed by the followingrelationship where ω is the angular frequency:

Z = (1/jωC0)1 − k2t [(tan ϕ)/ϕ)][((zr + zl) cos2 ϕ

+ j sin 2ϕ)/((zr + zl)cos2ϕ + j(zrzl + 1) sin 2ϕ)], (1)

where zr and zl are loading acoustic impedances nor-malized by the piezoelectric film acoustic impedanceZa(AlN) according to the top and bottom electrode acousticimpedances Zn(Mo Top,Bot):

zr,l = Zn(Mo Top,Bot)/Za(AlN). (2)

To know the acoustic impedance of each layer exceptthe piezoelectric one, Zn gives the terminating acousticimpedance of a nonpiezoelectric layer as a function of thepreceding one Zn−1. Za is the acoustic impedance of theconsidered medium:

Zn = Za[(Zn−1 cos θ + jZa sin θ)/(Za cos θ + jZn−1 sin θ)].(3)

Phase across the piezoelectric film ϕ depends on the prop-agation constant k and the thickness d of the consideredmedium:

ϕ = (kd)/2. (4)

In contrast, phase across a nonpiezoelectric layer θ uses thefollowing relationship according to the considered medium:

θ = kd. (5)

An important point is to define mechanical losses to getrealistic and finite quality factors at resonance and an-tiresonance (∼1000). Mechanical losses can be introducedon different parameters such as the stiffness coefficient:c = clossless(1 + j/Qm) [9] where Qm is the mechanicalquality factor or c = creal + j2πfη [10] where η is theacoustic viscosity. Rosenbaum [11] shows how introducingmechanical losses on the propagation constant k such as:k = ω/νa(1+ jα) with α = (ηω)/(2ρνa) and α 1, whereρ is the mass density and νa the acoustic velocity. Becauseit is difficult to gather the acoustic viscosity of each layerfrom the literature, we prefer using expression developedby R. Lanz [12] where mechanical losses are introducedas a complex part into phase. Consequently, phase acrossAlN and other materials are defined by (6) and (7), re-spectively, where Qm values are defined in Table III:

ϕ = ϕlossless[1 − j/(2QAlN)], (6)θ = θlossless[1 − j/(2Qm)]. (7)

Regarding dielectric losses of AlN, they are very weak andlikely inferior to 0.02 according to references [13], [14].Therefore, temperature dependence of dielectric and evenmechanical losses is still unknown, and no particular trendof quality factors has been found from measures under vari-able temperature as it is described later in Section V. Forthese reasons, we do not consider the impact of dielectriclosses on quality factors because it does not bring moreinformation on the targeted analysis.

To render the model temperature dependant and forthe considered isotropic materials (Si, W, SiO2 and Mo),we suppose a linear variation around room temperature T0(25C) of stiffness c, thickness d, and density ρ accordingto (8), (9), and (11), respectively. One has to notice thatdensity is linked to thermal expansion [11], [15] by using(10), and we consider (11):

c(T ) = c(T0)[1 + Tc(T − T0)], (8)d(T ) = d(T0)[1 + α(T − T0)], (9)

dρ/dT = −3αρ(T0), (10)ρ(T ) = ρ(T0)[1 − 3α(T − T0)]. (11)

ivira et al.: modeling for temperature compensation and characterization of baw resonators 423

TABLE IStiffness Coefficients c and Temperature Coefficients of

Stiffness Tc.

Material c (109 Pa) Tc (10−4/C)

AlN 395 [16] −0.6 [17];−0.37 [15];−0.23 (from

−23C to +127C) [18]

SiO2 74 [16] +2.39 [17];+2.74 (“Bulk modulus” from

+25C to +150C) [19];

Mo 276 −1.3 [17];−0.8 (“Bulk modulus” from

−13C to +25C) [20];

W 400 −0.99 (“Bulk modulus” from−13C to +25C) [20];

−0.58 (“Bulk modulus” from+24C to +200C) [21]

Si 165 −0.75 [22]

The variable temperature, the temperature coefficient ofstiffness, and the thermal expansion coefficient are de-fined by T , Tc, and α, respectively. Regarding piezoelectricAlN thin film, anisotropic properties involve changing theabovementioned expressions. We then replace c with c33 in(8), α with α33 in (9), and 3α with α11 +α22 +α33 in (10)and (11). For AlN, area S (S(T0) = Length(T0)Width(T0))is also considered for subsequent static capacitance deter-mination. We then define (12). Dielectric ε33 and piezo-electric e33 coefficient variations are described by (13) and(14), respectively. Consequently, static capacitance C0 isexpressed by the well-known relationship (15) for eachtemperature. Regarding the coupling factor k2

t , we use thewell-known physical expression (16) for each temperature.

S(T ) = S(T0)[1 + α11(T − T0)][1 + α22(T − T0)],(12)

e33(T ) = e33(T0)[1 + Te33(T − T0)], (13)ε33(T ) = ε33(T0)[1 + Tε33(T − T0)], (14)C0(T ) = ε33(T )S(T )/d(T ), (15)

k2t (T ) = e2

33(T )/[ε33(T )c33(T )], (16)

where Te33 and Tε33 are the temperature coefficients ofpiezoelectricity and dielectric permittivity, respectively.Despite difficulties for finding temperature dependence ofdielectric permittivity ε33 and piezoelectric coefficient e33in the literature, we tried to extract Te33 and Tε33 fromour measurements and by using basic equations, as de-tailed in the next section.

In addition, all physical properties of materials consti-tutive stack used in equations and modeling are defined inTables I, II, and III. In Table I, some temperature coeffi-cients of stiffness are calculated from data points found inthe literature and extracted for the temperature range ofinterest.

TABLE IIThermal Expansion α and Density ρ.

Material α (10−6/C) ρ (kg/m3)

AlN α11 = 5.27 [16]; α33 = 4.15 [16] 3260 [16]SiO2 0.54 [23] 2200 [16]Mo 5.1 [23] 10220 [23]W 4.7 [23] 19300 [23]Si 4.7 [23] 2340 [23]

TABLE IIIMechanical Quality Factors Qm.

Material Qm (without unit)

AlN 1500 [17]; 2000 [12]SiO2 2000 [17]; 500 [12]Mo 1500 [17]; 300 [12]W 300Si 3000 [17]; 500 [12]

IV. Temperature Dependence of Piezoelectric

Coefficient (e33) and Dielectric

Permittivity (ε33)

To improve accuracy of modeling, we attempted to ex-tract Te33 and Tε33 values after linearization from +10Cto +127C. For this experiment, six SMR were processedon two different wafers (waf1 and waf2). These six samplespresent various shapes (apodized or not), sizes and sev-eral resonators have a mass-loading of SiO2 on the topelectrode. The measurement procedure will be detailedin Section V. First, the imaginary part of the resonatorsimpedance ImIMP(T) was measured far from resonances atvery low frequency for each temperature T , and then weextracted the static capacitance C0 by the following ex-pression:

C0(T ) = 1/(ImIMP(T)2πf), (17)

where f is the frequency. As dielectric losses are alreadyvery low at the operating frequency, we do not considertheir impact in static capacitance extractions for such alow frequency. Fig. 2 illustrates static capacitance evolu-tion with respect to the temperature between −80C and+127C. Static capacitance increases when temperatureincreases. To know which parameter is prominent on thecapacitance variation, either the thermal expansion or thedielectric permittivity variation, we first consider that di-electric permittivity does not vary according to the tem-perature as we search its thermal dependence. In this case,only linear variation of thickness and surface is consideredfor static capacitance calculation. Afterwards, the calcu-lated slopes are compared to the slopes directly fitted tostatic capacitance variation with respect to the tempera-ture. As a result, for the six measures, the impact of ther-mal expansion does not exceed 6% of the full static ca-pacitance variation. We can conclude that more than 90%


Fig. 2. Static capacitances evolution of various SMR having differ-ent shapes and sizes of active area, with and without mass-loading,without passivation, with respect to the temperature.

TABLE IVTemperature Coefficients Tε33 and Te33 of SMR Having

Different Sizes of Active Area, With and Without SiO2 of

Mass-Loading, Without Passivation.

Active area (µm2) Tε33(/C) Te33(/C)

400 × 400 waf1 1.88.10−4 −0.19.10−4

400 × 400 + SiO2 waf1 1.79.10−4 2.4.10−4

350 × 350 + SiO2 waf1 1.85.10−4 −0.01.10−4

400 × 400 waf2 1.40.10−4 0.23.10−4

400 × 400 + SiO2 waf2 1.45.10−4 0.36.10−4

350 × 350 + SiO2 waf2 1.57.10−4 −1.14.10−4

of the static capacitance variation is due to the dielectricpermittivity variation with respect to the temperature.

From the viewpoint of dielectric permittivity and con-sidering ε33(T0) = 9.5.10−11 F/m [16], we calculate Tε33by solving (9), (12), (14), (15), and (17). Then, the cou-pling factor is extracted from antiresonance and resonancefrequencies measurements by using the classical formula(18). One has to notice that antiresonance (fa) and res-onance (fr) frequencies correspond to the maximum andminimum of the measured impedance, respectively.

k2t (T ) = (π2/4)[(fa(T ) − fr(T ))/fa(T )]. (18)

From the known Tε33 and by considering e33(T0) =1.55 C/m2 [16], the equations (8), (13), (14), (16) and(18) allow the system of equations to be solved, and Te33is then extracted. The extracted temperature coefficientof dielectric permittivity Tε33 and piezoelectric coefficientTe33 of AlN are given in Table IV. The Te33 can be eitherpositive or negative, which is due to the square of e33 inequation (16) of the coupling factor. From a physical view-point, it is clear that Te33 is positive or negative but notboth as in the mathematical way. However, no techniquein the literature gives the trend of such a parameter in

TABLE VTemperature Coefficients Used in Our Model.

Temperature coefficientMaterial (10−4/C)

AlN −0.6 (Tc); +1.5 (Tε33); +0.1 (Te33)SiO2 +2.39 (Tc)Mo −1.3 (Tc)W −0.91 (Tc)Si −0.75 (Tc)

respect to temperature. Therefore, compared to Tε33, re-producible values of Te33 are more difficult to get with thistechnique. Nevertheless, one has to notice the coefficientsare in the same order than those of ZnO piezoelectric thinfilm [24].

Owing to the various aforementioned temperature coef-ficients, we decided to consider the ones defined in Table Vand the thermal expansion coefficients cited in Table II.

V. Model Fitting to Electrical

Characterizations Under Variable

Temperature Environment

Performed beyond wireless telecommunication systemspecification (−40C to +85C), the temperature depen-dence on coupling factor, antiresonance, resonance fre-quencies, and quality factors is accurately determinedin a temperature-controlled vacuum chamber (PMC150,SussMicrotec SA, Saint Jeoire, France). A heater chuckand liquid nitrogen system ensures an accurate tempera-ture in the device environment. Inside the chamber, spe-cific RF |Z|Probes were designed for probing from −265Cup to +300C under small signal (< 1 W). The open, short,and especially load (50 Ω) standards of the associated cal-ibration substrate are designed to exhibit a very high ac-curacy well above the temperature range of our experi-ments. Therefore, to avoid condensation inside chamber,that is, on probes, calibration substrate, devices, and otherinstruments, a pressure as low as 2.10−6 mbar is attainedfor temperatures below 0C. Moreover, we performed theOSL calibration procedure of our vector network analyzer(8720ES, Agilent Technologies, Santa Clara, CA), at eachtemperature to correct properly the mismatches of thetest-set. Furthermore, an open de-embedding structure,which is the same structure as the resonator but with-out the top electrode, allows parallel parasitic capacitancesgenerated by RF pad contribution around the resonatorto be removed from the resonators response. The TCF atantiresonance (TCFa) is determined by the following ex-pression:

TCFa = (1/fa(T0))(dfa/dt), (19)

where fa(T0) is the antiresonance frequency at room tem-perature (25C). From measurements, dfa/dt is the fittedslope of antiresonance frequency with respect to the tem-perature. Likewise, the same relationship is used for TCF


Fig. 3. Impedance at room temperature of measurement and model ofa resonator having the same features, with respect to the frequency.

Fig. 4. Antiresonance and resonance frequencies for the resonatordefined in Fig. 3, with respect to the temperature.

at resonance (TCFr). The measured coupling factor is de-fined by (18) for each temperature. The quality factor atantiresonance Qa is obtained from antiresonance frequencyand the −3 dB frequency band measurements according to(20). The same expression is used for resonance.

Qa = fa/∆f(−3dB). (20)

For the first step, we compared the model and measureda resonator with the same layer thickness and same ac-tive area size; the impedance at room temperature is illus-trated in Fig. 3. The resonance and antiresonance frequen-cies with respect to the temperature for the same resonatorare superimposed in Fig. 4. As a result, one can see thatsuch a model fits very well with the experiment in terms ofimpedance and drifts of resonance, antiresonance frequen-cies, and coupling factor.

At least 54 SMR with various physical properties interms of thickness, mass-loading, passivation layer, and

Fig. 5. Antiresonance frequencies of various SMR having differentsizes of active area without mass-loading and passivation, with re-spect to the temperature.

Fig. 6. Resonance frequencies of various SMR having different shapesand sizes of active area without mass-loading and passivation, withrespect to the temperature.

material type for Bragg reflectors have been probed. Figs. 5and 6 show some antiresonance and resonance frequen-cies, respectively, of two kinds of SMR based on the sameW/SiO2 Bragg reflector. The thickness (in µm) of the firststack Mo/AlN/Mo is 0.3/1.06/0.3, while the second oneis 0.2/1.453/0.2. The two kinds of stacks are not exactlycharacterized at the same temperature, but the results aresuperimposed on the same Figs. 5 and 6. The resonators ofthe first stack were first probed from +25C up to +108Cat atmospheric pressure ensured by ambient nitrogen gas.Second, the vacuum was performed up to 2.10−6 mbar,and samples were probed from −150C up to +25C. Forthe second stack, the procedure consisted of probing sam-ples subsequently from −100C up to +127C and from−190C up to −115C after, both measurements were car-ried out in a vacuum of 2.10−6 mbar and not at atmo-spheric pressure.


By using the appropriate fitting method as least meanssquare, all TCF are extracted from a linear temperaturerange as −40C to +85C for the first stack and −40Cto +127C for the second one. Regarding the first stack,the overall TCFa is −21.6 ppm/C and −17.3 ppm/Cfor TCFr. The second stack presents an average TCFa of−14.5 ppm/C and −11.5 ppm/C for TCFr. In this laststack, the measurements indicate that most of resonatorshaving SiO2 for mass-loading (thickness: 150 nm) exhibitbetter TCFr and TCFa of about 2–3 ppm/C than res-onators without this mass-loading. This point is not vis-ible in any of the figures. Comparison between the twodifferent stacks clearly indicates that increasing AlN whilereducing Mo thickness reduces temperature dependenceof fa and fr if the same frequency application is tar-geted. Because TCFr is always smaller than TCFa for res-onators based on a W/SiO2 Bragg reflector, the couplingfactor slightly decreases when temperature increases. Fromviewpoint of analytical modeling, resonance frequency ispurely due to mechanical phenomena, and antiresonancefrequency is due to both mechanical and electrical phe-nomena. Consequently, these two different resonances donot depend on the same coefficients, and temperature doesnot affect them in the same way. As Pinkett et al. [25], wefind no particular trend for quality factors with respect tothe temperature for each resonator. We think that spuriousmodes could hamper the resonances, and the properties ofspurious modes are very difficult to control, especially withrespect to the temperature. Moreover, it is also difficult tomeasure very accurate quality factors under ambient con-ditions, and then temperature does not facilitate its mea-surement. Consequently, we think that quality factor is nota relevant parameter under temperature for this study. Atvery low temperatures, resonance and antiresonance fre-quency behaviors are nonlinear and TCF is positive be-tween −190C and −150C. The main reasons that couldexplain such an effect at low temperatures are nonlinearvariations of intrinsic parameters such as stiffness coeffi-cient, piezoelectric coefficient, and dielectric permittivity.Nevertheless, no applications of BAW resonators are tar-geted at such low temperatures right now.

Finally, a last generation of SMR deposited onto aSiN/SiOC Bragg reflector and processed on 200 mm wafersallows us to study again the effect of different AlN/Mothickness ratios and SiO2 for mass-loading. The samplesare first measured and TCF extracted from −40C up to+125C at a pressure as low as 2.10−6 mbar. Figs. 7 and8 illustrate the typical antiresonance and resonance fre-quencies, respectively, with respect to the temperature forseveral resonators having the same Bragg reflector.

All measurements indicate that resonators having SiO2on the top electrode exhibit a better TCF than bare res-onators, as previously observed on SMR based on W/SiO2Bragg reflector. Furthermore, comparison between SMRwith the two different Mo/AlN/Mo thickness ratios re-veals that a thin film ratio of 0.15/1.566/0.15 yields a bet-ter TCF than 0.5/0.521/0.5 ratio when the same antires-onance frequency is targeted. Consequently, it is observed

Fig. 7. Antiresonance frequencies of various SMR (150×150 µm2 foractive area) with and without mass-loading and but no passivation,with respect to the temperature.

Fig. 8. Resonance frequencies of various SMR (150 × 150 µm2 foractive area) with and without mass-loading and but no passivation,with respect to the temperature.

again that increasing AlN while reducing Mo thickness ispreferable to reduce TCF. The overall TCF are worse witha SiN/SiOC Bragg reflector than with a W/SiO2 one. Oncemore, we find a random variation of quality factors.

For the resonator based on a SiN/SiOC acoustic reflec-tor, we investigated the impact of pressure on both TCFand frequency. For temperatures below 0C, decreasingpressure is necessary to prevent condensation inside thechamber, not only on resonators but also on RF probes,calibration substrate, thermal regulator, etc. Thus, newcharacterizations have been performed from +20C upto +125C at atmospheric pressure. Afterwards, for thesame temperature points, previous measures realized at2.10−6 mbar have been superimposed on the atmosphericpressure measurements. As a result, for several resonators,TCF has been slightly improved at about 1 to 2 ppm/C


Fig. 9. Drifts of antiresonance frequencies of various SMR (150 ×150 µm2 for active area) with SiN/SiOC Bragg reflector at2.10−6 mBar and atmospheric pressure.

Fig. 10. Drifts of resonance frequencies of various SMR (150 ×150 µm2 for active area) with SiN/SiOC Bragg reflector at2.10−6 mBar and atmospheric pressure.

at atmospheric pressure. In terms of frequency and as de-picted in Figs. 9 and 10, antiresonance and resonance arealways lower to about 1 to 2 MHz at atmospheric pressure.We think that air pressure increases resonator density thatdecreases resonance and antiresonance frequencies.

In conclusion, to reduce TCF, three methods should bedirectly coupled. First, a few years ago, Lakin et al. [26]demonstrated the ability of SiO2 to compensate resonatorsthermally when inserted into structures. This point isclearly verified in our measures. Therefore, the results letus assume that increasing SiO2 thickness on the top elec-trode should reduce TCF as well. Second, Bragg reflectorswith SiN/SiOC must be obviously changed for W/SiO2.Finally, increasing AlN and reducing Mo thicknesses ismandatory for active stacks of resonators. This is the wayto increase TCF up to zero. We used analytical modelingfor this study.

Fig. 11. AlN thickness with respect to Mo thickness to meet 2.14 GHzat 25C.

VI. Temperature Compensation Study with

Analytical Modeling

Because of the findings mentioned in the conclusion ofthe previous section, we investigated the impact of differ-ent AlN/Mo thickness ratios and a variable SiO2 thick-ness on the top electrode because its positive temperaturecoefficient of stiffness is well known for temperature com-pensation. For modeling, a Bragg reflector is composedof a W/SiO2 multilayer stack. The array of analysis isdefined between 0C and 120C because the thermal ex-pansion coefficient is quasi-constant (i.e., independent oftemperatures between 0C and 120C). A program usingMathcad software (Mathsoft Engineering and Education,Inc., Needham, MA) is developed to adjust automaticallyAlN thickness for keeping a constant antiresonance fre-quency at room temperature (25C) when thicknesses ofMo and SiO2 on the top electrode vary. The first analy-sis involved increasing AlN/Mo thickness ratio while keep-ing a constant antiresonance frequency at room tempera-ture, without taking into account the mass-loading of SiO2.Fig. 11 shows the AlN thickness versus Mo thickness tomeet the targeted antiresonance frequency of 2.14 GHz at25C. The TCF at antiresonance, resonance frequencies,and coupling factor are illustrated in Fig. 12. As a result,TCFa is calculated around room temperature from 0C to120C, and it is not better than −8 ppm/C for very thinelectrodes of 10 nm that would not facilitate AlN growth.The TCFr is lower than TCFa as observed in the experi-ments. Moreover, for such a thin layer of Mo, the couplingfactor strongly decreases. Consequently, these results showthe necessity of including a layer with a positive temper-ature coefficient of stiffness as SiO2, and such a layer ismore efficient because it is close to the active stack.

Thus, Fig. 13 shows the trend of TCF at antireso-nance with respect to the SiO2 mass-loading thickness de-posited on the top electrode for various Mo thicknesses.The thicker the Mo, the thinner AlN and the thicker SiO2


Fig. 12. Simulated TCF at resonance, antiresonance, and couplingfactor at 20C vs. Mo thickness.

Fig. 13. TCF at antiresonance frequency for various SiO2, Mo andconsequently AlN thicknesses designed to keep 2.14 GHz at 25C.

have to be for having full temperature compensation. Atthe same time, Fig. 14 must be kept in mind; the thickerthe SiO2, the smaller the coupling factor. Consequently,thinning Mo to allow the SiO2 to be as thin as possible,while reaching a zero TCFa, should increase the couplingfactor. In turn, it involves also a decrease of the couplingfactor because thicknesses are going far from the optimalAlN/Mo thickness ratio. In general, designers try to opti-mize this last thickness ratio, but regarding temperaturecompensation, optimizing the coupling factor implies tak-ing into account the SiO2/Mo/AlN/Mo stack to reach azero TCFa and maximizing coupling factor. To know theevolution of the maximum of coupling for the two extremetemperatures of the analysis, either 0C or 120C, we plotthe Fig. 15. In this case and for a given SiO2 thickness,we choose the corresponding Mo thickness (and then AlNthickness) that gives the best coupling factor. The maxi-mum coupling factor is then calculated for 0C and 120C.In these two conditions, the corresponding antiresonance

Fig. 14. Coupling factor in respect to Mo thickness for various SiO2thicknesses and for one fixed temperature.

Fig. 15. Maximum of coupling factor with respect to SiO2 thicknessfor the two extreme temperatures of analysis, either 0C or 120C.

frequency is not 2.14 GHz as the temperature is not 25C.As expected, the maximum of coupling factor decreaseswhen SiO2 thickness increases. On this plot, comparisonbetween the two extreme temperatures of the analysis re-veals that the coupling factor slightly decreases when tem-perature increases, that is, in good accordance with mea-sures. Fig. 16 shows the trend of AlN, Mo thicknesses, andmass-loading of SiO2 to obtain 2.14 GHz at room tem-perature. As expected, AlN becomes thinner when Mo isgetting thicker, and the higher the mass-loading of SiO2,the thinner AlN must be for increasing antiresonance fre-quency to keep the targeted 2.14 GHz at 25C.

VII. Results and Discussion

The numerous characterizations of our different SMRtechnologies under variable temperatures reveal the trendfor studying temperature compensation. It demonstrates


Fig. 16. AlN and Mo thicknesses for various SiO2 thicknesses to keep2.14 GHz at 25C.

that SiO2 is profitable in the multilayer stack and in-creasing AlN thickness while reducing Mo thickness al-lows thermal stability to be improved. The modified modelto take into account temperature dependence on stiffness,length, density, piezoelectricity, and dielectric permittivityfits very well with the experiment. Modeling gives layerthicknesses for subsequent resonator design. Therefore, byoptimizing the SiO2/Mo/AlN/Mo stack thickness, it ispossible to minimize the decrease in the coupling factordue to mass-loading of SiO2 on the top electrode. At thesame time, results indicate that reaching a zero TCFa ispossible while keeping realistic layer thicknesses. Never-theless, it must be kept in mind that the given layer thick-nesses are very dependent on the temperature coefficientof stiffness of SiO2 and other materials found in the liter-ature. Furthermore, care must be taken when characteriz-ing structures at variable pressures, especially for temper-atures below 0C, even if a pressure as low as 2.10−6 mBarseems to be having a minor effect on TCF and its frequen-cies. Finally, although we show in this work how resonatorscan be temperature compensated by depositing a SiO2layer on the top electrode, another way to improve ther-mal stability of resonators must be focused on the top SiO2layer of the Bragg reflector. Since this layer is very close tothe piezoelectric layer, increasing its thickness must havea strong impact on TCF.

Acknowledgment

The authors are grateful to Pascal Ancey and GuyParat from STMicroelectronics and CEA-LETI, respec-tively, for providing samples.

References

[1] M.-A. Dubois, J.-F. Carpentier, P. Vincent, C. Billard, G. Parat,C. Muller, P. Ancey, and P. Conty, “Monolithic above-IC res-onator technology for integrated architectures in mobile and

wireless communication,” IEEE J. Solid-State Circuits, vol. 41,pp. 7–16, Jan. 2006.

[2] L. Elbrecht, R. Aigne, C.-I. Lin, and H.-J. Timme, “Integrationof bulk acoustic wave filters: Concepts and trends,” MicrowaveSymposium Digest, 2004 IEEE MTT-S International, vol. 1, pp.395–398, Jun. 2004.

[3] P.-H. Sung, C.-M. Fang, P.-Z. Chang, Y.-C. Chin, and P.-Y.Chen, “The method for integrating FBAR with circuitry onCMOS chip,” presented at Frequency Control Symposium andExposition, 2004, in Proc. 2004 IEEE Int., Aug. 2004, pp. 562–565.

[4] R. Aigner, “MEMS in RF-filter applications: thin film bulk-acoustic-wave technology,” in 13th Int. Conf. Transducers,IEEE Solid-State Sensors, Actuators and Microsystems, Digestof Technical Papers, vol. 1, Jun. 2005, pp. 5–8.

[5] R. Ruby, J. Larson, C. Feng, and S. Fazzio, “The effectof perimeter geometry on FBAR resonator electrical perfor-mance,” IEEE Microwave Symposium Digest, vol. 4, pp. 217–220, Jun. 2005.

[6] A. Volatier, E. Defay, A. N’Hari, J. F. Carpentier, P. Ancey, andB. Dubus, “Design, elaboration and characterization of coupledresonator filters for WCDMA applications,” in Proc. IEEE Ul-trason. Symp., Oct. 2006, pp. 829–832.

[7] J. D. Larson, R. C. Ruby, P. D. Bradley, J. Wen, S.-L. Kok, andA. Chien, “‘Power handling and temperature coefficient studiesin FBAR duplexers for the 1900 MHz PCS band,” in Proc. IEEEUltrason. Symp., Oct. 2000, pp. 869–874.

[8] K. M. Lakin, G. R. Kline, and K. T. McCarron, “High-Qmicrowave acoustic resonators and filters,” IEEE Trans. Mi-crowave Theory Tech., vol. 41, no. 12, pp. 2139–2146, Dec. 1993.

[9] K. Nakamura and H. Kanbara, “Theoretical analysis of a piezo-electric thin film resonator with acoustic quarter wave multi-layers,” in Proc. Int. IEEE Freq. Contr. Symp., May 1998, pp.876–881.

[10] R. S. Naik, J. J. Lutsky, R. Reif, and C. G. Sodini, “Electrome-chanical coupling constant extraction of thin-film piezoelectricmaterials using a bulk acoustic wave resonator,” IEEE Trans.Ultrason., Ferroelect., Freq. Contr., vol. 45, no. 1, pp. 257–263,Jan. 1998.

[11] J. Rosenbaum, Bulk Acoustic Wave Theory and Devices. Nor-wood, MA: Artech House, Inc., 1988.

[12] R. Lanz, “Piezoelectric thin film for bulk acoustic wave resonatorapplications: From processing to microwave filters,” Thesis No.2991, EPFL Laboratory, Lausanne, Switzerland, 2004.

[13] G. F. Iriarte, “AlN thin film electroacoustic devices,” Thesis No.817, Acta Universitatis Upsaliennis, Uppsala, Sweden, 2003.

[14] M. A. Dubois and P. Muralt, “Properties of aluminium nitridethin films for piezoelectric transducers and microwave filters ap-plications,” Appl. Phys. Lett., vol. 74, no. 20, pp. 3032–3034,May 1999.

[15] G. Bu, D. Ciplys, M. Shur, L. J. Schowalter, S. Schujman, andR. Gaska, “Temperature coefficient of SAW frequency in singlecrystal bulk AlN,” Electron. Lett., vol. 39, no. 9, pp. 755–757,May 2003.

[16] M. A. Dubois, “Aluminum nitride and lead zirconate-titanatethin films for ultrasonic applications: Integration, propertiesand devices,” Thesis No. 2086, EPFL Laboratory, Lausanne,Switzerland, 1999.

[17] S. Ohta, K. Nakamura, A. Doi, and Y. Ishida, “Temperaturecharacteristics of solidly mounted piezoelectric thin film res-onators,” in Proc. IEEE Ultrason. Symp., Oct. 2003, pp. 2011–2015.

[18] R. R. Reeber and K. Wang, “High temperature elastic con-stant prediction of some group III-nitrides,” Nitride Semi-conductor, MRS Internet journal, vol. Res. 6, no. 3, 2001,http://nsr.mij.mrs.org/6/3/complete.utf.html.

[19] NIST properties data summaries:http://www.ceramics.nist.gov/srd/summary/SiO2.htm.

[20] F. H. Featherston and J. R. Neighbours, “Elastic constants oftantalum, tungsten and molybdenum,” Physical Review, vol.130, no. 4, pp. 1324–1333, May 1963.

[21] R. Lowrie and A. M. Gonas, “Dynamic elastic properties of poly-cristalline tungsten, 24C–1800C∗,” J. Appl. Phys., vol. 36, no.7, pp. 2189–2192, Jul. 1965.

[22] C. Bourgeois, E. Steinsland, N. Blanc, and N. F. de Rooij, “De-sign of resonators for the determination of the temperature coef-


ficients of elastic constants of monocrystalline silicon,” in Proc.IEEE Int. Freq. Contr. Symp., May 1997, pp. 791–799.

[23] GoodFellow internet website: http://www.goodfellow.com/csp/active/gfMaterials.csp.

[24] S. L. Pinkett, W. D. Hunt, B. P. Barber, and P. L. Gammel, “De-termination of ZnO temperature coefficients using thin film bulkacoustic wave resonators,” IEEE Trans. Ultrason., Ferroelect.,Freq. Contr., vol. 49, no. 11, pp. 1491–1496, Nov. 2002.

[25] S. L. Pinkett and W. D. Hunt, “Temperature characteristics ofZnO-based thin film bulk acoustic wave resonators,” in Proc.IEEE Ultrason. Symp., Oct. 2001, pp. 823–826.

[26] K. M. Lakin, K. T. McCarron, and J. F. McDonald, “Temper-ature compensated bulk acoustic thin film resonators,” in Proc.IEEE Ultrason. Symp., Oct. 2000, pp. 855–858.

Brice Ivira received an M.S. degree in mi-croelectronic engineering from University ofClermont-Ferrand II in 2003 and a Ph.D. de-gree from the Institut National Polytechniquede Grenoble in 2006. For his Ph.D., he workedat the Institute of Microelectronics, Electro-magnetism and Photonics (IMEP) of Greno-ble. His research interest focused on self-heating aspects under high RF power, tem-perature modeling (FEM, analytical 1D), im-pact of harsh environments, and aging. He isnow pursuing a post-doctoral degree in BAW

resonator areas at the CEA-LETI lab of Grenoble. He contributes tothe development of new tunable devices for RF applications.

Philippe Benech received an M.S. degreein microelectronics from University of Mont-pellier in 1987 and a Ph.D. degree in instru-mentation from University Joseph Fourier,France, in 1990. Since 2000, he has been aprofessor at University Joseph Fourier and aresearcher at IMEP. His field of interest is inthe domain of integration of passive compo-nents and function for telecommunications.

Rene-Yves Fillit is a well-known senior pro-fessor on temperature and stress measure-ment. He worked for five years in the fieldof radioastronomy, before joining a researchgroup in material science and mechanical en-gineering at the Ecole N.S. des Mines engi-neering college of Saint-Etienne, France. Witha team of five researchers, he published thefirst detection of a comet at the radio wave-lengths of the OH signal (1665–1667 MHz)reported in the Circular 2607 of the Interna-tional Astronomical Union. He has published

more than 100 papers, with a citation index greater than 300, and heowns several European patents and particularly the X-ray Dosopha-tex device. He is now the scientific manager of a thermomechani-cal and microstructural characterization platform for materials andMEMS. This platform involves four electronic microscopes, five X-raydiffractometers, two XPS-AUGER systems, and a brand-new high-resolution infrared bench.

Fabien Ndagijimana is a professor at Uni-versite Joseph Fourier in Grenoble, France. Hereceived his Ph.D., specializing in microwaveand optoelectronics, in December 1990 fromthe Institut National Polytechnique de Greno-ble (INPG) in France. He then joined thefaculty of Electrical Engineering ENSERGas associate professor, where he teaches mi-crowave techniques and electromagnetic mod-eling. Since September 1997, he has been pro-fessor at the Institut Universitaire de Tech-nologie (IUT) de Grenoble. His research ac-

tivity at IMEP focuses on the characterization and electromagneticmodeling of microwave and high-speed circuits and their integra-tion into silicon/SOI technologies for wireless radiofrequency appli-cations.

Pascal Ancey received an M.S. degree fromINSA, France, in 1990 and a Ph.D. degree inmicroelectronics in 1997 from University Paris7 for his thesis on micro-sensors for humidityand condensation measurement.

In 1991, he joined the IMRA Centre asR&D engineer to develop thermoelectric ma-terials and oscillators. From 1996 to 1999, hebecame responsible for the thermo-mechanicsteam, where he was involved in the develop-ment of sensors and actuators for automotiveapplications in collaboration with Toyota and

Valeo. In 2000, he joined STMicroelectronics, a front-end technologymanufacturing group, where he manages the advanced R&D team,Above IC and Derivatives. He is responsible for the developmentof advanced integrated passive components (high-k decoupling ca-pacitor, high-Q inductor), RF-MEMS (including micro switch, vari-able capacitor, and electromechanical resonator), and BAW devices(including FBAR and SMR architecture, filter and duplexer, andcoupled resonator filter). He is also in charge of the developmentof various integration strategies such as System on Chip (includingabove IC, embedded SOI, and SON platforms for MEMS), and Sys-tem in Package (including wafer scale packaging, 3D packaging, andRF module). He is the coordinator of the European project MAR-TINA related to the development of above IC FBAR resonators andfilters and the technical manager of the two European IntegratedProjects: MIMOSA related to the development of a microsystemsplatform for mobile services and applications and MINAMI, which isrelated to the micro-nano integrated platform for transverse ambientintelligence applications. He also actively participates in EURIMUSfunded projects such as EPADIMD related to the platform for ad-vanced active implantable medical devices, including new RF devicessuch as BAW filters. He has published more than 50 articles in in-ternational journals and conferences, and he is author or co-authorof about 30 international patents.

Guy Parat received an engineering degreein microelectronics in 1990. In 1983, he joinedthe LETI-CEA Grenoble, working for eightyears on II-VI photovoltaic detectors and onsilicon CCD process developments in the InfraRed Laboratory. In 1991, he joined the MicroPackaging team where he developed flip chiptechnology, silicon multi- chip modules, andopto-electrical modules. From 1999 to 2003,he managed projects on passive componentsintegration on silicon and glass substrates forMobile Phones. Since 2003, he has managed a

project on BAW filter developments for RF applications.

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