IEEE ELECTRON DEVICE LETTERS, VOL. 29, NO. 4, APRIL 2008 315

A Temperature-Stable Film BulkAcoustic Wave Oscillator

Wei Pang, Member, IEEE, Rich C. Ruby, Senior Member, IEEE, Reed Parker, Philip W. Fisher,Mark A. Unkrich, and John D. Larson, III, Life Fellow, IEEE

Abstract—This letter reports a passively temperature-compensated CMOS oscillator utilizing a film bulk acousticresonator. The resonator exhibiting an f · Q product of 2–4 ×1012 s−1 is composed of molybdenum, aluminum nitride,and a compensation material that has a positive temperaturecoefficient of Young’s modulus. The 604-MHz oscillator consumes5.3 mW from a 3.3-V supply and achieves excellent phasenoise performances of −102, −130, and −149 dBc/Hz at 1,10, and l00 kHz carrier offsets, respectively. The oscillator’stemperature-dependent frequency drift is less than 80 ppm over atemperature range of −35 ◦C to +85 ◦C.

Index Terms—Film bulk acoustic resonator (FBAR), nonlinear-ity, oscillator, phase noise, temperature compensation.

I. INTRODUCTION

THE GENERATION of a precise frequency by means ofa crystal-controlled oscillator can be found in every con-

ceivable electronic product. Much recent work has focused oneliminating the bulky quartz crystal frequency reference usedin clock and frequency generators for wireless and consumerelectronics applications. One of the most formidable challengesin such efforts is achieving the performance of quartz res-onators, particularly a high quality Q factor and a high fre-quency stability over temperature. After 70 years of experience,quartz resonators can be made to have an unloaded Q of> 200 000 at 10–40 MHz and a frequency variation with tem-perature of ±10 ppm over a 120 ◦C range.

Silicon electrostatic MEMS technology has demonstrated13-MHz resonators with Q’s on the order of 130 000 [1].However, due to its −20 ppm/◦C temperature dependence, thepotentially good phase noise of these MEMS oscillators mustbe significantly traded for external temperature compensation[2]. Temperature-compensated silicon resonators have onlydemonstrated Q’s on the order of 4000 for 10-MHz resonators(f · Q product of 4 × 1010) [2], [3]. Attempts at integratingsurface acoustic wave (SAW) quartz devices on chip requirebonding precut quartz blanks onto a processed Si wafer andpatterning interconnects [4].

In this letter, we present the frequency versus tempera-ture characteristics of a low-phase-noise oscillator based on a

Manuscript received November 19, 2007; revised January 10, 2008. Thereview of this letter was arranged by Editor X. Zhou.

The authors are with Avago Technologies, Inc., San Jose, CA 95131 USA(e-mail: pangwei_2001@hotmail.com).

Color versions of one or more of the figures in this letter are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/LED.2008.917116

Fig. 1. Measured fractional frequency change versus temperature of two600-MHz oscillators based on FBARs with different turnover temperatures dueto thickness nonuniformity across the wafer. The standard error in the frequencymeasurement is ±0.01 ppm.

high-Q (e.g., > 1700 at 2.37 GHz) temperature-compensatedfilm bulk acoustic resonator (FBAR). The all-silicon hermeti-cally sealed device exhibits a quadratic temperature behaviorwith a controllable turnover temperature at which the frequencybecomes insensitive to small temperature changes. We shalldescribe and analyze the effect of the compensation material onthe Q factors of an FBAR around series and parallel frequen-cies. The implementation and measurement of the oscillatorwill also be illustrated.

II. RESONATOR DEVICE BEHAVIOR

A Mason model, which is based on a transmission-lineformalism, is used to predict the frequency–temperature (f–T )sensitivity of an FBAR composed of an electrode, aluminumnitride (AlN), and a compensation material. Using the Taylorseries expansion, we can define an expression for the relativechange in frequency and the temperature coefficient as

f(T ) − f(T0)f(T0)

≈∞∑

n=1

N∑m=1

tm

VmTCxm,n × (T − T0)n

N∑m=1

tm

Vm

(1)

where there are N layers in the FBAR stack, tm is the thickness,Vm is the acoustic velocity, and (tm/Vm) × TCxn is calledthe effective nth-order temperature coefficient of material

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316 IEEE ELECTRON DEVICE LETTERS, VOL. 29, NO. 4, APRIL 2008

Fig. 2. Measured frequency drift over temperature of an uncompensated AlN/Mo FBAR with “thin” Mo (left) and “thick” Mo (right). The deviations from linearfitting are used to extract the second term of temperature coefficients of elastic modulus of AlN and Mo films.

properties for each layer. The first-order temperature coeffi-cients of stiffness of sputter-deposited AlN and molybdenum(Mo) films are found to be negative [5]. SiO2 is a well-knownmaterial that can have a positive temperature coefficient ofelastic modulus around room temperature [6]. Equation (1)indicates that the first-order temperature dependence of thefrequency change can be “zeroed out” by introducing SiO2 ofan appropriate thickness.

Fig. 1 is the measured f–T characteristics of two FBAR os-cillators. With the linear terms canceling out, we see a residualquadratic temperature dependence with a turnover temperatureTM ; thus, the frequency change can be simply expressed as

f(T ) − f(TM )f(TM )

≈ β × (T − TM )2. (2)

To determine the source of the quadratic term (β ∼−20 ppb/◦C2), we first characterize the f–T sensitivity foruncompensated FBARs with two extreme AlN/Mo thicknessratios (i.e., 0.73 and 12.3). Fig. 2 shows the measured ∆f/fversus T data and its deviation from linear fitting. The second-order terms for AlN and Mo are found to be about −42.5and +7 ppb/◦C2, respectively. Note that Mo has an oppositesign with AlN, which suggests that the total drift (∼80 ppmin Fig. 1) of the compensated FBAR may be further reducedby increasing the Mo thickness percentage in the stack. Itshould be pointed out that the two curves in Fig. 1 representtwo FBARs across the same wafer with different turnovertemperatures due to thickness nonuniformity across the wafer.Ideally, TM should be set in the middle of a target temperaturerange.

In the experiments, 2000- to 3000-Å-thick oxide layers areintroduced into the acoustic stack. The unloaded Q is calculatedby either a one-port impedance 3-dB bandwidth or the groupdelay method [7]. The latter enables one to analyze the effectof spurious modes on Q and compute Q versus frequencybetween fs and fp. This is particularly advantageous because,in the majority of oscillators, resonators are operated between aseries and a parallel resonance, where its impedance providesthe required circuit inductive reactance. Fig. 3 compares the

Qs and Qp of 1-GHz square-shaped FBARs with and withoutcompensation. The Qs of the compensated FBAR is 30%–50%of the uncompensated one. This can be explained by the sig-nificantly higher acoustic loss of oxide in the acoustic stack.Since the acoustic energy around fs has been shown to be welltrapped in the resonator-defined cavity, the intrinsic acousticloss is the key factor affecting Qs. However, the differencein Qp between compensated and uncompensated resonatorsis much less affected by the inclusion of an oxide film, ascompared to Qs. This implies that there exists some otherloss mechanism, rather than the internal friction loss alone, atfrequencies near fp.

III. OSCILLATOR IMPLEMENTATION

The schematic and small-signal equivalent circuit of theColpitts oscillator is shown in Fig. 4. The transistor M1 withfeedback capacitors C1 and C2 provide the negative resistanceto compensate for the losses from Rm and Ro in the resonator.The circuitry die (∼0.5 mm2) implemented in the Avago0.35-µm CMOS process and FBAR die (∼0.1 mm2) are placedside by side on a laminate. The core oscillator draws 1.6 mAfrom a 3.3-V supply voltage. An Agilent 5052B spectrumanalyzer is used to measure the phase noise. Fig. 5 presents themeasured single-sideband phase noise power spectral density ofa 604-MHz oscillator using a temperature-compensated FBAR.The achieved phase noise is about −101.7 dBc/Hz at a 1-kHzoffset and −158 dBc/Hz at far-from-carrier offsets. The flickernoise onset is between 10 and 20 kHz, and the oscillator’s close-to-carrier noise is a result of the inherent short-term frequencyinstability in the FBAR itself.

IV. CONCLUSION

By introducing a temperature compensation material into theacoustic stack of a resonator, the temperature stability of theFBAR has been improved to a level comparable to quartz (bulkacoustic wave and SAW) resonators. The composite resonatorsshow a quadratic temperature dependence due to the material

PANG et al.: TEMPERATURE-STABLE FILM BULK ACOUSTIC WAVE OSCILLATOR 317

Fig. 3. (a) Comparison of Q factors of 70 000-µm2 FBARs with and without compensation. Note that undesirable spurious resonances (marked by dash circles)occur between fs and fp in an uncompensated FBAR, but they are significantly suppressed in a compensated FBAR due to the lower electromechanical couplingcoefficient (k2

t ). (b) Q factor of a temperature-compensated 10 000-µm2 FBAR at 2.36 GHz.

Fig. 4. Simplified circuit schematic (left) and small-signal equivalent circuit(right) of an FBAR oscillator. The static capacitor Co of the resonator isabsorbed into the active circuit to obtain a deeper insight.

property, which can be further reduced to be in the sub-parts-per-million range with active temperature compensationtechniques [8]. The demonstrated low-phase-noise oscillator

Fig. 5. Phase noise density versus offset frequency plot for the temperature-compensated 604-MHz CMOS oscillator.

is well suitable to high-speed serial data applications such asstandard SATA hard disk drives, developing standard USB3 PCperipherals, and fiber optic transceivers.

318 IEEE ELECTRON DEVICE LETTERS, VOL. 29, NO. 4, APRIL 2008

ACKNOWLEDGMENT

The authors would like to thank J. Choy, S. D. Strathman,and B. Ingram for the fabrication facility and technical help, aswell as K. J. Grannen, D. Lee, C. Feng, L. Callaghan, and theentire FBAR team at Avago.

REFERENCES

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[5] J. D. Larson, III and Y. Oshmyansky, “Measurement of effective kt2, Q,Rp, Rs vs. temperature for Mo/AlN FBAR resonators,” in Proc. IEEE Int.Ultrason. Symp., Oct. 8–11, 2002, pp. 939–943.

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[8] B. P. Otis and J. M. Rabaey, “A 300 µW 1.9-GHz CMOS oscillator uti-lizing micromachined resonators,” IEEE J. Solid State Circuits, vol. 38,no. 7, pp. 1271–1274, Jul. 2003.