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524 IEEE TransacTIons on UlTrasonIcs, FErroElEcTrIcs, and FrEqUEncy conTrol, vol. 57, no. 3, March 2010

Abstract—In this paper, the temperature compensation of AlN Lamb wave resonators using edge-type reflectors is theo-retically studied and experimentally demonstrated. By adding a compensating layer of SiO2 with an appropriate thickness, a Lamb wave resonator based on a stack of AlN and SiO2 lay-ers can achieve a zero first-order temperature coefficient of frequency (TCF). Using a composite membrane consisting of 1 μm AlN and 0.83 μm SiO2, a Lamb wave resonator operating at 711 MHz exhibits a first-order TCF of −0.31 ppm/°C and a second-order TCF of −22.3 ppb/°C2 at room temperature. The temperature-dependent fractional frequency variation is less than 250 ppm over a wide temperature range from −55°C to 125°C. This temperature-compensated AlN Lamb wave res-onator is promising for future applications including thermally stable oscillators, filters, and sensors.

I. Introduction

Frequency references with low phase noise and drift are important components for navigation systems,

wireless communication systems, and signal processing ap-plications. as is well known, crystal oscillators (Xos) and temperature-compensated crystal oscillators (TcXos) based on aT-cut quartz dominate this market because aT-cut quartz has outstanding temperature performance and long-term stability. however, there are some draw-backs and fabrication limitations for quartz-based reso-nators related to down-scaling for future applications. In addition, the material properties of quartz limit the inte-gration of frequency references and complementary metal-oxide semiconductor (cMos) circuits on a single chip.

Therefore, in recent years aln thin film technology has attracted many microelectromechanical systems (MEMs) researchers because it can provide a high acoustic phase velocity, small temperature-frequency drifts, low motional resistances, and cMos-compatibility. Many recent rF MEMs studies focus on novel aln-based resonators and filters, such as thin film plate acoustic resonators (FPar) [1], contour-mode resonators [2], [3], layered saW filters [4], and lamb wave resonators [5]–[7]. lamb wave resona-tors based on aT-cut quartz substrate [8], linbo3 thin film [9], and Zno thin film [10] have also been studied.

among these various approaches, lamb wave resonators based on aln thin films are more promising for higher frequency (up to several gigahertz) applications [11] than traditional saW resonators, because aln has a higher acoustic velocity than other piezoelectric materials. The lowest symmetric mode (s0 mode) lamb wave in aln thin film has an acoustic velocity approaching 10 000 m/s, which is much higher than the saW velocity of around 4000 m/s in linbo3 crystal or liTao3 crystal, and the s0 mode lamb wave velocity of around 6000 m/s in linbo3 thin film [9]. Furthermore, compared with other symmet-ric and antisymmetric modes of lamb waves in aln thin film, the s0 mode exhibits a low dispersive characteristic which is beneficial because it improves the fabrication tol-erance to thickness variations of the aln layer [12].

however, similar to thin film bulk acoustic resonators (FBar) and solidly mounted resonators (sMr) using aln thin films, the uncompensated lamb wave resonator also has a first-order TcF of −20 to −30 ppm/°c [12]–[14]. This level of temperature stability is unsuitable for any fre-quency reference application. The temperature-dependent frequency variation mainly results from material softening of these composite structures when the temperature in-creases. The thermal compensation technique of adding a compensating layer of silicon dioxide has been widely ap-plied to different kinds of piezoelectric resonators [12]–[18] and silicon-based electrostatic MEMs resonators [19].

recently, we have theoretically studied the tem-perature compensation of lamb wave resonators using aln/sio2 layered membranes [12]. In this present work, we report the experimental studies on the temperature compensation of aln lamb wave resonators using this technique. specifically, we study the temperature-compen-sated aln lamb wave resonators using edge-type reflec-tors. as shown in Fig. 1, the lamb wave resonator consists of one interdigital transducer (IdT) and two suspended free edges (edge-type reflectors) on the aln/sio2 compos-ite membranes. lamb waves are excited by the interdigital transducer and reflected by the free edges at both sides so that the resonance forms inside this cavity. By designing the correct ratio of the thicknesses of the aln and sio2 layers, a lamb wave resonator using edge-type reflectors with a nearly zero first-order TcF and a resonance fre-quency of 711 Mhz is experimentally demonstrated. The temperature-compensated lamb wave resonator exhibits a quadratic frequency-temperature behavior with a turnover temperature at which the frequency has a very small sen-sitivity to temperature changes.

Temperature-Compensated Aluminum Nitride Lamb Wave Resonators

chih-Ming lin, Student Member, IEEE, Ting-Ta yen, Student Member, IEEE, yun-Ju lai, Student Member, IEEE, Valery V. Felmetsger, Matthew a. hopcroft, Member, IEEE,

Jan h. Kuypers, Member, IEEE, and albert P. Pisano, Member, IEEE

Manuscript received May 20, 2009; accepted december 21, 2009. c.-M. lin, T.-T. yen, y.-J. lai, M. a. hopcroft, and a. P. Pisano are

with the department of Mechanical Engineering, University of califor-nia, Berkeley, ca (e-mail: gimmylin@berkeley.edu).

c.-M. lin, T.-T. yen, y.-J. lai, M. a. hopcroft, J. h. Kuypers, and a. P. Pisano are with the Berkeley sensor and actuator center, Univer-sity of california, Berkeley, ca.

V. V. Felmetsger is with Tegal corporation, san Jose, ca.digital object Identifier 10.1109/TUFFc.2010.1443

II. lamb Waves in aln/sio2 composite Membranes

In this study, we discuss two different configurations of aln lamb wave resonators using sio2 as the compen-sating material as shown in Fig. 2. configuration a rep-resents the aln/sio2 composite membranes with a non-metalized (open-circuited) interface and configuration B represents the aln/sio2 composite membranes with a metalized (short-circuited) interface. The (002) plane of aln thin film is parallel to the sio2 surface and lamb wave propagates in the plane normal to the c-axis of the aln thin film. In this paper, the dispersive characteristics of the aln/sio2 composite membranes are studied by us-ing alder’s approach [20]. The intrinsic electromechanical coupling coefficient k2 is theoretically calculated by the following approximation equation,

kv v

v2

2 2

2»

-o m

o

, (1)

where vo is the phase velocity for a non-metalized interface and vm is the phase velocity for a metalized interface. For more exact simulations, the Green’s function method can be adopted to calculate the electromechanical coupling co-efficient in the piezoelectric membrane [10], [21], [22]. In this study, all the material constants used in the theoreti-cal simulations are taken from the literature [16].

as illustrated in Fig. 3, the dispersive characteristics of the phase velocities and electromechanical coupling co-efficients are obtained for a normalized aln thicknesses haln/λ of 0.091. For the simulation, the IdT on the surface of the aln thin film is ignored and the bottom electrode at the interface between the layers is assumed to be infinitely thin. The solid lines and the dashed lines represent the s0 mode lamb wave dispersion of the phase velocity and electromechanical coupling, respectively. The lines with-out dots represent configuration a, and the lines with dots represent configuration B. From this figure, configurations a and B exhibit almost the same velocity dispersion, but configuration B exhibits a higher electromechanical cou-

pling dispersion than configuration a. clearly, the met-alized interface between the layers enhances the electro-mechanical coupling coefficient. This phenomenon is very similar to lamb waves propagating in aln thin films [7] and Zno thin films [10] with a metalized bottom surface. In the same manner, the metalized interface enhances the electromechanical coupling of the aln/sio2 layered mem-branes. This can be understood by considering an electric field applied between two electrodes with a pitch of λ/2 on an aln plate which has a thickness of 0.091 λ and an elec-trically grounded bottom surface. In this case, the electric field strength through the aln plate is much higher than the electric field strength between the electrodes, enhanc-ing the electromechanical coupling. hence, in this present work, the TcF behavior of configuration B was studied because the higher electromechanical coupling coefficient is more promising for future applications.

525lin et al.: temperature-compensated aln lamb wave resonators

Fig. 1. The illustration of the temperature-compensated aluminum ni-tride (aln) lamb wave resonator using a compensating layer of silicon dioxide (sio2).

Fig. 2. The cross-sectional view of 2 fundamental configurations for zero first-order temperature coefficient of frequency aln lamb wave resona-tors using one layer of sio2. configuration a represents the aln/sio2 composite membranes with a non-metalized (open-circuited) interface and configuration B represents the aln/sio2 composite membranes with a metalized (short-circuited) interface.

Fig. 3. lowest symmetric mode (s0 mode) lamb wave dispersion of phase velocity and electromechanical coupling in the composite aln/sio2 membranes.

as illustrated in Fig. 4, an effective thermal expansion coefficient for estimating the elongation along the lamb wave propagation direction is required for computing the TcF of the composite structures. The effective thermal expansion for an arbitrary stack of layers is computed from the thermal expansion of the neutral plane in the stack [12]. The effective thermal expansion coefficient αeff for a stack of i layers is then given as

aa

eff = =

=

å

å

E t

E t

i i ii

n

i ii

n1

1

, (2)

where Ei is the young’s modulus of ith layer, ti is the thickness of ith layer, and αi is the thermal expansion coefficient of ith layer.

The temperature-dependent stiffness coefficients Cij(T) and temperature-dependent density ρ(T) can be defined as

Cij(T) = Cij(T0)(1 + TCijΔT) (3) ρ(T) = ρ(T0)[1 − (αxeff + αyeff + αz)ΔT], (4)

where T0 refers to the reference temperature of material constants; ΔT is a relative temperature change; TCij re-fers to the relative temperature dependence of the stiffness value Cij; αxeff and αyeff are the effective thermal expan-sion coefficients along the x and y directions, respectively, which are assumed to be identical in this work; and αz is the thermal expansion coefficient along the z direction. It should be noted that (4) for thermal expansion of the composite structure is used in the density expression of each layer. Thus, the TcF for the lamb wave resonator can be written as

TCFLWR xeff=¶¶

-1v

vT

a (5)

where the first term refers to the temperature dependence of lamb wave velocity which is computed using all the temperature dependent parameters (Cij(T), ρ(T)) for ΔT equal to 10°c, v is the lamb wave velocity of the resona-tor material, and αxeff corresponds to the effective thermal expansion coefficient along the wave propagation direction (x direction) in this case.

The TcF of lamb wave resonators with configuration B is theoretically simulated and analyzed. Because only the first-order temperature coefficients are published in the literature [16], all modeling only includes the first-order effects on TcF in this study. The first-order TcF of the lamb wave resonator on the aln/sio2 layered mem-branes is computed based on the temperature-dependent material properties given in the literature [16] and the elec-trode mass loading effect is neglected [12]. on the aln/sio2 composite structures, the first-order TcF of lamb wave resonators with different normalized aln thicknesses haln/λ of 0.05, 0.091, 0.1, 0.15, and 0.2 are depicted in Fig. 5. The analysis shows that the first-order TcF of lamb waves on the aln/sio2 composite membranes has a dispersive character. In other words, the first-order TcF is a function of the relative sio2 thicknesses for different aln thicknesses [12]–[14].

III. Fabrication Process

a five-mask microfabrication process has been used to fabricate the temperature-compensated lamb wave reso-nators. First, a low-stress nitride (lsn) layer for electrical isolation was deposited on the (100) silicon wafer, and then a low temperature oxide (lTo) layer for temperature compensation was deposited on top of the lsn layer. The 150-nm-thick al bottom electrode layer, with an X-ray diffraction (Xrd) full width at half maximum (FWhM) value of 3.35°, was deposited by sputtering and the bot-tom electrodes were patterned by a wet etching process. The molybdenum (Mo) etching stop layer was then de-posited and patterned by a lift-off process. a highly c-axis (002) oriented aln film with a FWhM value of 1.77° was

526 IEEE TransacTIons on UlTrasonIcs, FErroElEcTrIcs, and FrEqUEncy conTrol, vol. 57, no. 3, March 2010

Fig. 4. The effective thermal expansion experienced at the neutral plane is used for estimating the effective elongation in propagation direction.

Fig. 5. The dispersive characteristics of the first-order temperature coef-ficient of frequency (TcF) of lamb wave resonators on the aln/sio2 composite membranes with a metalized (short-circuited) interface and an infinitely thin bottom electrode.

deposited by ac reactive sputtering using an Endeavor-aT sputtering tool from Tegal corporation (Petaluma, ca). The electrical contact vias through the 1-µm-thick aln layer were wet etched, and the 150-nm-thick al top electrode layer was then deposited on the aln layer. The al top electrodes were patterned using a cl2-based reac-tive ion etching (rIE) process. Prior to the dry etching of the aln thin film, a layer of lTo was deposited at 400°c, patterned, and then used as a hard mask. a cF4-based rIE process was used to remove the remaining lTo hard mask and simultaneously pattern the lTo thermal com-pensation layer after the aln layer was patterned by the cl2-based rIE process. Finally, the aln resonators were released by a XeF2-based isotropic dry etching of silicon, and the lsn layer beneath the composite aln/sio2 struc-tures of the aln resonator was also etched by XeF2 dur-ing the release process. Fig. 6 shows a scanning electron micrograph (sEM) of a lamb wave resonator fabricated using the processes described above. Fig. 7 shows an sEM cross-section image of a lamb wave resonator on the com-posite aln/sio2 membrane. as shown in Fig. 7, the com-posite membrane with 1 µm aln and 0.83 µm sio2 was used for all of the temperature-compensated lamb wave resonators in this study.

IV. Experimental results and discussion

The temperature-compensated lamb wave resona-tors were tested in a vacuum probe system (PMc150, suss MicroTec Inc., Waterbury center, VT) that al-lows probing of chuck-mounted wafers while they are cooled via liquid helium and heated by electric heating elements (on the chuck). a feedback-controlled heating unit can provide precise control of the chuck tempera-ture during measurement. s11 parameters for the reso-nators were extracted using an agilent E5071B network

analyzer (agilent Technologies Inc., santa clara, ca). To determine the TcF of the resonators, resonators were measured in the temperature range from −55 to 125°c. The temperature was varied in 5°c steps with 10 min of temperature stabilization time before each measurement, and the s11 parameters for the resonator were measured five times at each 5°c step. Before the measurements were taken, the devices were tempera-ture-cycled over the full temperature range five times to eliminate observed hysteresis [14]. The quality factor Qs of the resonator was extracted from the admittance plot by measuring the 3 dB bandwidth [2], and the six equivalent circuit parameters were determined by fit-ting to the measured results with the modified Butter-worth-Van dyke (MBVd) equivalent circuit model [23]. In addition, the effective coupling coefficient kt

2 of the measured devices is defined as

kff

fft

s

p

s

p

21

2 2=

æ

èççç

ö

ø÷÷÷÷

é

ëêê

ù

ûúú

-p p

tan , (6)

where fs and fp are the resonance frequency and the anti-resonance frequency, respectively.

Two resonator designs were compared in this study, and their parameters are given in Table I. The design 1 resonator has a resonance frequency, fs, of 460 Mhz, a motional resistance, Rm, of 107 Ω, an effective coupling coefficient, kt

2, of 0.33%, and a quality factor, Qs, of 1532. as shown in Fig. 8(a) and (b), the design 2 resonator exhibits a resonance frequency, fs, of 711 Mhz, a motional resistance, Rm, of 150 Ω, an effective coupling coefficient, kt

2, of 0.56%, and a quality factor, Qs, of 980. It should also be noted that there is no spurious mode over a 1 Ghz frequency range, which is excellent for oscillator and filter applications.

527lin et al.: temperature-compensated aln lamb wave resonators

Fig. 6. The scanning electron micrograph of the fabricated lamb wave resonator using edge-type reflectors (design 2).

Fig. 7. The scanning electron micrograph cross-sectional image of the lamb wave resonator on the composite membrane consisting of 1 µm aln and 0.83 µm sio2.

From Table I, the wavelength of the design 2 resonator was 11.04 µm, and the measured resonance frequency is 711 Mhz, so the measured lamb wave phase velocity is roughly equal to 7850 m/s. This measured value is close to the theoretical s0 mode phase velocity, 8435 m/s, for haln/λ of 0.091, and hsio2/λ of 0.075 as shown in Fig. 3. If the 150-nm-thick al bottom electrode (hal/λ = 0.0136) were taken into account in the simulation, the theoreti-cal phase velocity would be reduced to 8142 m/s. The mismatch between theoretical and experimental s0 mode lamb wave velocities might be caused from the neglect of IdT in the simulation. Furthermore, we observe that the effective coupling coefficient kt

2 of design 2 resonator is 0.56%, which is less than the theoretical value of about 2.2% as shown in Fig. 3. The electromechanical coupling coefficient is originally given for an idealized simple struc-ture composed of uniform thin film materials. In fact, the real devices are more complex: the influence of the elec-trode arrangement, the electrode thickness, and the aln film quality are not considered in the theoretical calcula-tion. In general, the intrinsic electromechanical coupling calculated by using (1) overestimates the effective electro-mechanical coupling excited by the interdigital transducer [24]. In addition, as shown in Fig. 8(b), a large electrical capacitance C0 of 488.9 fF is observed from the MBVd equivalent circuit. This electrical capacitance, resulting from the resonator static capacitance of 372.8 fF and an external parasitic capacitance of 116.1 fF, also reduces the effective coupling coefficient kt

2. Furthermore, in this study, the aln thin film has the FWhM value of 1.77° which indicates less than the perfect thin film quality. The combination of these phenomena is suspected to cause the mismatch between the intrinsic and effective electrome-chanical coupling coefficients.

Fig. 9 shows the plot of measured fractional frequency variation for the two design resonators in Table I over a wide temperature range from −55 to 125°c. It should be noted that the total fractional frequency variation of the design 2 resonator is less than 250 ppm over the tem-perature range and the first-order TcF of the design 2 resonator is almost cancelled out. Moreover, the tempera-ture-dependent fractional frequency variation of these two lamb wave resonators shows a quadratic function of tem-perature. as pointed out in Fig. 5, the first-order TcF is dispersive with the relative aln thickness as well as the

relative sio2 thickness. That is to say, the thickness ratio of the aln and sio2 layers determines the first-order TcF of the whole stacked structure.

In Fig. 10, a quadratic polynomial is adopted to fit the experimental results for the design 1 resonator, which shows a first-order TcF of −7.61 ppm/°c as well as a second-order TcF of −15.7 ppb/°c2 at room tempera-ture. The first-order TcF of the design 1 resonator is only reduced to −7.61 ppm/°c because the thickness ratio of aln and sio2 layers is not correct for the zero first-order TcF compensation at its room temperature resonance frequency, 460 Mhz. as a result, although the TcF of the design 1 resonator includes a combination of first-order, second-order, and even higher-order terms, clearly

528 IEEE TransacTIons on UlTrasonIcs, FErroElEcTrIcs, and FrEqUEncy conTrol, vol. 57, no. 3, March 2010

TaBlE I. dimensions of lamb Wave resonators in This study.

design 1 design 2

Top electrode number 13 13aperture 125 µm 155 µmElectrode width 4.44 µm 2.76 µmWavelength, λ 17.76 µm 11.04 µmMetallization ratio 0.5 0.5Top electrode thickness, hIdT 150 nm (al) 150 nm (al)Bottom electrode thickness, hal 150 nm (al) 150 nm (al)aln layer thickness, haln 1 µm 1 µmsio2 layer thickness, hsio2 0.83 µm 0.83 µm

Fig. 8. (a) Measured broadband frequency spectrum of the nearly zero first-order temperature coefficient of frequency lamb wave resonator (design 2) at room temperature. (b) close-up view of the frequency spectrum of the design 2 resonator and the modified Butterworth-Van dyke (MBVd) equivalent circuit model fitting which is used for extract-ing the 6 equivalent circuit parameters.

the residual first-order TcF dominates its temperature-dependent fractional frequency variation.

In contrast, with a proper combination of aln and sio2 layers, the first-order TcF of the design 2 resonator is almost zero at room temperature, so that the second-order term dominates its characteristic of temperature-dependent fractional frequency variation. The experimen-tal result shows a first-order TcF of −0.31 ppm/°c and a second-order TcF of −22.3 ppb/°c2 as depicted in Fig. 11. The fractional frequency variation of the resonator ex-hibits a temperature-dependent quadratic function with a turnover temperature TM of 18.05°c. If room temperature (25°c) is used as the reference temperature, the fractional frequency variation can be expressed as

f T f

fT T

( ) ( )( )

. ( ) . ( ) .

-

= - ´ ´ - - ´ ´ -- -

2525

0 31 10 25 22 3 10 256 9 2

(7)

The turnover temperature TM can also be used as the reference temperature and then the fractional frequency variation can be expressed as

f T f T

f TT T

( ) ( )( )

. ( ) ,-

= - ´ ´ --M

MM21 5 10 9 2 (8)

where a second-order TcF of −21.5 ppb°/c2 was found at the turnover temperature TM.

In the case of the design 2 resonator, the excellent temperature compensation was achieved by using 0.83 µm sio2 (hsio2/λ = 0.075) and 1 µm aln (haln/λ = 0.091) layers, and the first-order TcF is successfully reduced to −0.31 ppm/°c at room temperature. however, we observe

that the experimental results do not show good agreement with the theoretical predictions in Fig. 5. The difference between the experimental and theoretical results is likely caused by the assumption of infinitely thin bottom elec-trodes and the neglect of the IdT effect in the simulation. as shown in Fig. 12, the dashed line represents the theo-retical first-order TcF of the design 2 resonator when the interface is metalized and the al bottom electrode is as-sumed to be infinitely thin; in contrast, the solid line rep-resents the theoretical TcF when the interface is metal-ized and the al bottom electrode is 150 nm thick, and the gray dot represents the experimental result. as is known, the al electrode has a larger thermal expansion coefficient

529lin et al.: temperature-compensated aln lamb wave resonators

Fig. 9. The plot of measured fractional frequency variation versus tem-perature of 2 thermally compensated aln/sio2 lamb wave resonators with different resonance frequencies.

Fig. 10. Measured fractional frequency variation versus temperature of the thermally compensated aln/sio2 lamb wave resonator (design 1). The deviation from linearity is used to extract the second-order tempera-ture coefficient of frequency.

Fig. 11. Measured fractional frequency variation versus temperature of the thermally compensated aln/sio2 lamb wave resonator (design 2). a turnover temperature was found at 18.05°c for this temperature-com-pensated lamb wave resonator.

than aln and sio2, and its thickness is comparable to the thicknesses of the aln and sio2 layers; accordingly, the theoretical first-order TcF of the design 2 resonator decreases from 9.62 ppm/°c to −11.2 ppm/°c when the 150 nm al bottom electrode is taken into account in the simulation. as we can see from Fig. 12, the experimental result lies between these two extremes.

There are several sources of uncertainty in the simu-lation. First, the accuracy of the first-order TcF pre-diction relies heavily on the accuracy of the material property data, in particular, the temperature coeffi-cients of elasticity. at least three different sets of the temperature coefficients of material elasticity for the aln thin film have been published and compared [25]. The layer of lTo is used as the thermal compensating material in our experiments but the material properties of bulk fused silica are used in the simulation because of the lack of reliable material data for the lTo thin film. Furthermore, all of the thin films have residual stresses of several hundred megapascals after deposi-tion, which can affect the first-order TcF variation to a great extent [25]. Finally, although the two resona-tors were fabricated on the same wafer, the thin film depositions (aln, al, and sio2) were not ideally uni-form across the wafer and the uncertainties in the film thicknesses influence the accuracy of the predicted TcF [26]. In this study, the non-uniformity of the al film thickness was about 3%, the non-uniformity of the aln film was about 1%, and the non-uniformity of sio2 film was about 6%. The worst cases for the uncertainties in the simulated first-order TcF (−11.2 ppm/°c) caused by the film non-uniformity are −15.8% and +14.2%, respectively. despite all of these sources of uncertainty, we are encouraged that our experimental results fall

within the range of performance predicted by our model and it is a useful tool for designing zero-TcF lamb wave resonators. In the future, more accurate tempera-ture coefficients of material elasticity as well as residual stresses in thin films are needed to be introduced to the theoretical simulation for a better theoretical prediction of TcF.

V. conclusion

In this paper, we have designed, fabricated, and experi-mentally demonstrated that an aln lamb wave resonator using edge-type reflectors can achieve a nearly zero first-order TcF by adding a layer of sio2 with an appropriate thickness. a temperature-compensated lamb wave reso-nator operating at 711 Mhz exhibits a first-order TcF of −0.31 ppm/°c, a second-order TcF of −22.3 ppb/°c2, a motional resistance, Rm, of 150 Ω, an effective coupling coefficient, kt

2, of 0.56%, and a quality factor, Qs, of 980 at room temperature, 25°c. This temperature-compensated lamb wave resonator also shows a second-order TcF of −21.5 ppb/°c2 at the turnover temperature, 18.05°c. The lamb wave resonator utilizing the lowest symmetric mode on the aln/sio2 composite membranes achieves a high acoustic velocity, approaching 7850 m/s, even though the sio2 layer reduces the overall acoustic velocity in the com-posite membranes. In addition, compared with the lamb wave resonator using grating reflectors, the edge-type reflector design can efficiently reduce the resonator size without sacrificing the quality factor. The temperature-compensated lamb wave resonator using edge-type reflec-tors, with its low motional resistance, small size, potential for cMos integration, and now good temperature stabil-ity, is a very promising technology for advanced rF oscil-lators and filters.

acknowledgments

The authors would like to acknowledge the help with al and aln deposition from dr. s. Tanner at Tegal cor-poration and the help on suss MicroTec PMc150 probe system setup provided by Professor c. T.-c. nguyen’s re-search group at the University of california at Berkeley.

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530 IEEE TransacTIons on UlTrasonIcs, FErroElEcTrIcs, and FrEqUEncy conTrol, vol. 57, no. 3, March 2010

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Chih-Ming Lin (s’08) received the B.s. degree in civil engineering and the M.s. degree in applied mechanics from the national Taiwan University, Taipei, Taiwan, in 2001 and 2003, respectively. he is currently working toward his Ph.d. degree in mechanical engineering at the University of cali-fornia at Berkeley.

From 2004 to 2005, he was a MEMs r&d engineer at the Benq corporation, hsinchu, Tai-wan, where he was involved in the development of integrated cMos-MEMs microfluid injecting

technology for inkjet print heads. since Fall 2007, he has been a graduate student researcher at the Berkeley sensor and actuator center (Bsac). his current research interests include acoustic wave devices, piezoelectric rF n/MEMs resonators and filters, and cMos compatible n/MEMs technologies.

Ten-Ta Yen (s’09) received his double B.s. de-grees in power mechanical engineering and electri-cal engineering, both from the national Tsing hua University, hsinchu, Taiwan, in 2004. he is cur-rently working toward his Ph.d. degree, with Prof. albert P. Pisano, in the department of Mechani-cal Engineering, University of california, Berke-ley, ca. his research interests include rF MEMs and nanotechnology. yen has been a student mem-ber of IEEE since 2009.

Yun-Ju Lai (s’09) received the B.s. degree in mechanical engineering from the national Taiwan University, Taipei, Taiwan, in 2006 and the M.s. degree from the University of california at Berke-ley (UcB) in 2008, where she is currently working toward her Ph.d. in mechanical engineering.

she is a Graduate student researcher with the Berkeley sensor and actuator center, UcB. her research interests include MEMs-based rF devices, inertial sensors, and silicon carbide (sic) MEMs for harsh environments.

Valery V. Felmetsger received his Ph.d. degree in material science and engineering from the Insti-tute of high-current Electronics, Tomsk, russia. his work includes serving as a head of the labora-tory of vacuum and ion-plasma technologies at Metal-ceramics Instrumentation, ryazan, russia, and a chief technology officer at sputtered Films Inc., santa Barbara, ca. currently he is a PVd process development manager at Tegal corpora-tion, san Jose, ca.

Matthew A. Hopcroft received the B.sc. de-gree in computer engineering from The George Washington University, in 1998, the M.Phil. de-gree from the Engineering department, cam-bridge University, in 2002, and the Ph.d. in me-chanical engineering from stanford University in 2007. he is currently a research specialist affili-ated with the Berkeley Micromechanical analysis and design group and the Berkeley sensor and actuator center at the University of california at Berkeley. his research interests include MEMs

material property measurements, microscale and portable power sys-tems, and micromechanical resonators.

531lin et al.: temperature-compensated aln lamb wave resonators

Jan H. Kuypers received the dipl.-Ing. degree from the department of Microsystem Technology IMTEK at the University of Freiburg, Germany, in 2004, and the Ph.d. degree in nanomechanics from Tohoku University, Japan, in 2007. he then worked as a research specialist at the Berkeley sensor and actuator center (Bsac) at the Uni-versity of california at Berkeley. In 2008, he joined the MEMs oscillator company sand 9, Inc., in Boston. he has been working on the evaluation of mechanical properties of MEMs thin films, depo-

sition of aluminum nitride thin films, FBar, sMr, modeling of saW and lamb wave devices, temperature-compensated resonators, wireless saW sensors, MEMs based saW devices, and wafer level packaging. he is the author of the K-model, a higher-order Green’s function-based sim-ulation model for saW and lamb wave devices. he was awarded the best student Paper at the IEEE Ultrasonics symposium 2007. he is member of the IEEE, Ultrasonics, Ferroelectrics, and Frequency control (UFFc) society and the Microwave Theory and Techniques society. since 2007, he has been a member of the technical program committee of the UFFc. his current research efforts are dedicated towards the development of high-performance MEMs oscillators for wireless communications.

Albert (“Al”) P. Pisano received his B.s., M.s., and Ph.d. degrees in mechanical engineer-ing from columbia University in the city of new york in 1976, 1977, and 1981, respectively. Profes-sor Pisano is a director of the Berkeley sensor & actuator center (Bsac) and currently serves as Professor and chair of the department of Me-chanical Engineering at the University of califor-nia at Berkeley. he was elected to the national academy of Engineering in 2001 and elected to Fellow status of the asME in 2004. In 2008, he

was named among the “100 notable People” by the Medical devices and diagnostic Industry (Md&dI) Magazine. Professor Pisano is the co-in-ventor of more than 20 patents in MEMs and has authored or co-au-thored more than 200 archival publications. since 1983 he has graduated over 35 Ph.d. and 65 M.s. students.

532 IEEE TransacTIons on UlTrasonIcs, FErroElEcTrIcs, and FrEqUEncy conTrol, vol. 57, no. 3, March 2010