Piezoelectric Aluminum Nitride Vibrating Contour-Mode MEMS Resonators

TLDR: In this article, a new class of rectangular plate and ring-shaped contour-mode piezoelectric aluminum nitride radio-frequency microelectromechanical system resonators that span a frequency range from 19 to 656 MHz showing high quality factors in air (Qmax=4300 at 229.9 MHz), low motional resistance (ranging from 50 to 700 Omega), and center frequencies that are lithographically defined.

Abstract: This paper reports theoretical analysis and experimental results on a new class of rectangular plate and ring-shaped contour-mode piezoelectric aluminum nitride radio-frequency microelectromechanical systems resonators that span a frequency range from 19 to 656 MHz showing high-quality factors in air (Qmax=4300 at 229.9 MHz), low motional resistance (ranging from 50 to 700 Omega), and center frequencies that are lithographically defined. These resonators achieve the lowest value of motional resistance ever reported for contour-mode resonators and combine it with high Q factors, therefore enabling the fabrication of arrays of high-performance microresonators with different frequencies on a single chip. Uncompensated temperature coefficients of frequency of approximately -25 ppm/degC were also recorded for these resonators. Initial discussions on mass loading mechanisms induced by metal electrodes and energy loss phenomenon are provided

Figures

Fig. 4. Mode shapes analysis performed in ANSYS for a 20 m wide and 90 m inner radius circular ring and a 20 m wide and 180 m inner length squareshaped ring. Nondeformed shape is represented by dashed lines. Electrodes were not included in this simulation.

TABLE II EXPERIMENTAL DATA FOR THE TEMPERATURE COEFFICIENT OF FREQUENCY (TCF) OF THE CONTOUR-MODE AlN RESONATORS PRESENTED IN THIS PAPER

Fig. 5. Shift f =f versus Pt thickness for a 2- m-thick AlN film. For a 200-nm-thick Pt electrode, the frequency shift is approximately 700 ppm/nm. Results are based on (12).

Fig. 8. SEM of a one-port 200 50 m AlN rectangular plate.

Fig. 6. Schematic view of the process flow used to fabricate AlN piezoelectric resonators. (a) Low stress nitride deposition by LPCVD, followed by Pt patterning by liftoff and AlN sputter deposition; (b) open via access to bottom Pt electrode through AlN; (c) deposition of top Al electrode and patterning by dry etch in Cl -based chemistry. AlN is wet etched by hot H PO (160 C); (d) Cl -based dry etching of AlN resonant devices and dry release in XeF .

Fig. 7. Effect of sidewall sloping (as shown in inset) on the fundamental frequency of an unelectroded, 20- m-wide circular ring resonator as the one shown in Fig. 9(a).

Full text

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1406 JOURNAL OF MICROELECTROMECHANICAL SYSTEMS, VOL. 15, NO. 6, DECEMBER 2006
Piezoelectric Aluminum Nitride Vibrating
Contour-Mode MEMS Resonators
Gianluca Piazza, Member, IEEE, Philip J. Stephanou, Member, IEEE, and Albert P. (Al)Pisano
Abstract—This paper reports theoretical analysis and experi-
mental results on a new class of rectangular plate and ring-shaped
contour-mode piezoelectric aluminum nitride radio-frequency
microelectromechanical systems resonators that span a frequency
range from 19 to 656 MHz showing high-quality factors in air
(
Q
max
=4300
at 229.9 MHz), low motional resistance (ranging
from 50 to 700

), and center frequencies that are lithographically
defined. These resonators achieve the lowest value of motional re-
sistance ever reported for contour-mode resonators and combine
it with high Q factors, therefore enabling the fabrication of arrays
of high-performance microresonators with different frequencies
on a single chip. Uncompensated temperature coefficients of
frequency of approximately
25 ppm C were also recorded for
these resonators. Initial discussions on mass loading mechanisms
induced by metal electrodes and energy loss phenomenon are
provided. [2006-0019]
Index Terms—Aluminum nitride, contour-mode resonators, mi-
croelectromechanical systems (MEMS) resonators, piezoelectric
resonators, radio-frequency (RF) MEMS.
I. INTRODUCTION
T
HE demand of consumer electronics for radio-frequency
(RF) filters and frequency reference elements has focused
attention on the reduction of size, power consumption, and price
and pushed current research interests towards the manufacturing
of a single-chip integrated RF solution. Vibrating contour-mode
microelectromechanical system (MEMS) resonators constitute
a very promising technology for ultimately realizing this vision.
Several electrostatically transduced micromechanical
resonators have been demonstrated in the very-high- and
ultra-high-frequency spectra [1]–[4]; despite their sheer high
Q on the order of 10 000, they exhibit large values of motional
resistance (hundreds of k
), which ultimately complicates
the interfacing of these electrostatic devices to 50
RF sys-
tems. The low electromechanical coupling coefficient of the
surface-based electrostatic transduction mechanism cannot be
sufficiently improved without introducing ultrasmall air gaps
(less than 20 nm) in the fabrication process. Furthermore, recent
efforts [5]–[8] trying to act on geometrical parameters, such as
the effective actuation area, in order to reduce the equivalent
Manuscript received February 13, 2006; revised July 8, 2006. This work
was supported by CSAC-DARPA under Grant NBCH1020005. Subject Editor
S. Lucyszyn.
G. Piazza is with the Department of Electrical and Systems Engineering, Uni-
versity of Pennsylvania, Philadelphia, PA 19104 USA.
P. J. Stephanou and A. P. Pisano are with the Department of Mechanical
Engineering, University of California, Berkeley, CA 94720 USA.
Color versions of Figs. 1–4, 6, 7, 12, 14, and 15 are available online at http://
ieeexplore.ieee.org.
Digital Object Identifier 10.1109/JMEMS.2006.886012
motional resistance have not shown very significant improve-
ments. Recently proposed “internal” electrostatic transduction
[9], [10] represents a potential method for reducing the mo-
tional resistance of these resonators, but it is still an unproven
technology and suffers from the need of large bias voltages
that ultimately limit the reliability of ultrathin layers of high-K
dielectrics and intrinsic large capacitance values that mask the
resonator response at high frequencies.
Piezoelectric materials such as aluminum nitride or quartz
inherently offer order of magnitude larger electromechanical
coupling coefficients. Body forces produced by thin piezo-
electric elements have been successfully exploited in surface
acoustic wave (SAW) devices [11], film bulk acoustic wave
resonators (FBARs) [12], and shear-mode quartz resonators
[13], achieving gigahertz frequencies and demonstrating high
Q factors. Despite being a proven technology, SAW devices do
not scale well to RF applications due to the resulting need for
submicrometer lithography and decreasing power handling ca-
pabilities. Moreover, FBARs and shear-mode quartz resonators
do not permit economical manufacturing of a single-chip RF
module because multiple frequencyselective arrays of piezo-
electric resonators cannot be easily fabricated on the same
substrate since film thickness determines the frequency.
This paper introduces a new class of aluminum nitride piezo-
electric resonators that have their fundamental frequency de-
fined by in-plane dimensions, which are prescribed at the com-
puter-aided design (CAD) layout level. For this reason the de-
vices are called contour-mode resonators. The use of contour
modes (with frequencies determined by in-plane dimensions
and not film thickness as for FBARs or shear quartz resonators)
permits the batch fabrication of arrays of piezoelectric microres-
onators with different frequencies on a single chip. These de-
vices, realized in the shape of plates or rings, uniquely combine
multiple frequencies with the ability to interface directly with
50
systems (by means of a low motional resistance generally
varying between 50 and 700
) and achieve high quality fac-
tors (as high as 4300 at 230 MHz) in air. The next sections will
focus on the electromechanical analysis of these resonators, the
techniques used for their fabrication, and their electrical perfor-
mance and offer discussions on the temperature dependence and
mass sensitivity of their center frequency and energy loss mech-
anisms.
II. D
ESIGN OF RECTANGULAR PLATE RESONATORS
Fig. 1 shows a schematic diagram of an AlN contour-mode
resonators shaped as a rectangular plate. The resonator is made
out of an AlN body sandwiched between a bottom Pt electrode
and a top Al electrode. A vertical electric field applied across
the film thickness induces in plane dilation of the structure
1057-7157/$20.00 © 2006 IEEE

PIAZZA et al.: PIEZOELECTRIC ALUMINUM NITRIDE VIBRATING CONTOUR-MODE MEMS RESONATORS 1407
Fig. 1. Schematic representation of one-port AlN contour-mode rectangular
plate resonator.
through the coefficient and excites the resonator either
in length-extensional or width-extensional mode shapes, de-
pending on whether the structure vibrates primarily across its
length or width and the excitation frequency. The equivalent
electromechanical model of the resonator is derived. First
frequency equation and mode shapes are given, and then the
equivalent parameters are computed using an energy method
based on Mason’s derivation [14]. As will be shown, the
analysis of the most important mode shapes for the rectangular
plate can be simplified to the one-dimensional case of a bar
vibrating across either its length or width.
The problem of in-plane vibrations of plates has been solved
in many different ways in the past [15], [16]. It is very com-
plicated to obtain exact closed-form solutions; an approximate
solution that gives the frequency equation and mode shape is re-
ported in [14]
(1)
where
(2)
and
(3)
where
(4)
and
is the width of the resonator, its length, the mode
number, and
and the in-plane Poisson’s ratio and equiva-
lent Young’s modulus of AlN. An equivalent Young’s modulus
was introduced for AlN. This is justified by the in-plane sym-
metry of highly
-axis oriented AlN films as in the case of this
paper.
and are the coordinate of the system with parallel
to the length and
parallel to the width of the plate; and
represent the displacement, respectively, in the and direc-
tions.
Several modes of vibrations can be found in the rectangular
plate either by changing the mode number
or by exchanging
the dimension of length with width (and therefore looking at
width-extensional mode shapes). Only few (Fig. 2) of these
modes of vibration can be electrically detected [15]. Their
detection depends on both the strength of the electromechanical
coupling associated with the particular mode and the quality
factor of the mechanical structure. Intuitively, just those mode
shapes that undergo a net area change over the whole electroded
surface generate a net motional current and can be detected
electrically. Analytically, the electromechanical coupling
takes this effect into account and can be approximately com-
puted as
(5)
where
is the total charge stored on one electrode,
the maximum displacements the structure undergoes at the lo-
cation for which the equivalent parameters are computed,
the piezoelectric coefficient, and the displacement, re-
spectively, in the
and directions, and is the electroded
area of the resonator. The rest of the symbols were defined
in (1)–(4). This value applies for the length-extensional mode
shown in Fig. 2(a). The same result approximately applies to
the width-extensional mode shown in Fig. 2(b), if
is substi-
tuted for
. It is difficult to compute an analytical expression
for the electromechanical coupling of all the modes without re-
sorting to advanced analysis techniques [15]. The values pro-
vided are those associated with the two fundamental modes that
offer practical applications for the resonator and that were ex-
perimentally detected.
The equivalent mass of the resonator can be computed in the
following way:
(6)
where
is the thickness of the plate. Equation (6) applies
to both the fundamental length and width-extensional mode
shapes. It is therefore possible to compute the electromechan-
ical parameters that describe a one-port rectangular plate
vibrating in a length-extensional mode [14]
(7)

1408 JOURNAL OF MICROELECTROMECHANICAL SYSTEMS, VOL. 15, NO. 6, DECEMBER 2006
Fig. 2. Fundamental mode shapes detected in AlN contour-mode rectangular plate resonators. The (a) length-extensional mode and (b) width extension
al mode
are the two most important modes of practical interest. These modes of vibrations are characterized by large strain of the same sign and therefore by lo
w motional
resistance.
Fig. 3. AlN ring-shaped contour-mode micromechanical resonators: (a) one-port circular ring and (b) one-port square-shaped ring.
where is the resonant frequency of the device; , , and
represent, in accordance with the Butterworth Van Dyke
model, the motional components of the resonator, respectively,
resistance, capacitance, and inductance;
is the static parallel
capacitance of the device; and
is the relative dielectric con-
stant of AlN in the z direction. The same values apply for the
width-extensional mode of Fig. 2(b) if
is exchanged with
and vice versa.
In conclusion, the equivalent electromechanical parameters
of a rectangular plate vibrating either in a length or width ex-
tensional contour mode shape were derived. The in-plane di-
mension of the plate (either length or width) set the resonant
frequency. In principle, the designer could act on the second
dimension (width for length-extensional mode and length for
width-extensional mode) to independently set the motional re-
sistance. As was shown in [5], a certain aspect ratio between
length and width of the resonator (generally not larger than
one-tenth) needs to be preserved, in order to maintain the de-
sired mode shape and avoid excitation of spurious responses.
In fact, large aspect ratios tend to make the structure very com-
pliant and susceptible to flexural vibrations.
III. D
ESIGN OF RING-SHAPED RESONATORS
Fig. 3 shows two implementations of ring-shaped contour-
mode AlN microresonators. An AlN elastic body shaped in the
form of a ring (circular or square shaped, but could be gener-
alized to any number of sides) is sandwiched between Al and
Pt electrodes. An electric field applied across the thickness of
the film tends to dilate the structure and makes it vibrate in a
breathing mode across its width. As will be shown, the funda-
mental dimension that sets the center frequency of the microres-
onator is the width of the ring. These resonators are one-port de-
vices in which the whole top surface is electroded. This topology
guarantees that maximum energy is coupled into the desired
mode, minimal motional resistance is obtained, and undesired
modes are minimized. A general theory to derive the frequency
and mode shape of the ring is presented. The equivalent param-
eters will be computed only for the approximate case in which
the average perimeter of the ring is much larger than its width,
which is the case that was experimentally verified.
According to [17], the frequency equation of a circular ring
vibrating in a pure radial-extensional mode shape is given by
(8)
where
(9)
and
is the outer radius of the ring, the inner radius
of the ring,
the Poisson’s ratio of AlN, its mass density,

Frequently asked questions

Q1. What have the authors contributed in "Piezoelectric aluminum nitride vibrating contour-mode mems resonators" ?

This paper reports theoretical analysis and experimental results on a new class of rectangular plate and ring-shaped contour-mode piezoelectric aluminum nitride radio-frequency microelectromechanical systems resonators that span a frequency range from 19 to 656 MHz showing high-quality factors in air ( Qmax = 4300 at 229. 9 MHz ), low motional resistance ( ranging from 50 to 700 Ω ), and center frequencies that are lithographically defined. These resonators achieve the lowest value of motional resistance ever reported for contour-mode resonators and combine it with high Q factors, therefore enabling the fabrication of arrays of high-performance microresonators with different frequencies on a single chip. 

Q2. Why is the Q of a resonator not the dominant loss mechanism?

Because the structure undergoes very small displacement and very small strain gradients by moving only in its plane, thermoelastic damping is not the dominant loss mechanism. 

Q3. What is the effect of air damping on the resonator?

It is believed that the effect of air damping will decrease at higher frequencies because the resonator displacement diminishes with frequency. 

Q4. What causes spurious vibrations in proximity of the fundamental mode?

The authors presume that the presence of 90 corners causes distortion in the width extensional mode shape of the square-shaped ring and induces spurious vibrations in proximity of the fundamental mode. 

Q5. What is the center frequency of the piezoelectric resonators?

The center frequency of these piezoelectric resonators is set by lithographic techniques (and not film thickness as for FBARs or shear quartz resonators), therefore truly enabling the fabrication of arrays of microresonators with different frequencies on a single chip. 

Q6. What is the effect of the anchor stiffness on theresonator frequency?

In any case, the influence of the anchor stiffness on theresonator frequency is a second-order effect and can be considered negligible to a first degree of approximation. 

Q7. What are the significant sources of energy loss in a resonator?

The following are among the most significant sources of energy loss that have been identified:• thermoelastic dissipation ; • anchor losses ; • air damping ; • electrical loading due to electrode resistivity ; • intrinsic material losses either in the AlN film or inthe metal electrodes. 

Q8. What is the effect of the loading on the thickness of the wafer?

Despite this loading effect, the manufacturing tolerances on thickness variation are less stringent than that reported for FBAR (thickness mode resonators), for which less than 0.1% uniformity across the wafer is demanded. 

Q9. What is the effect of the release process on the support length and stiffness of the t?

The undercut produced by the release process affects the support length and stiffness, making it difficult to establish whether the tethers are effectively behaving as quarter-wave reflectors. 

Q10. What is the reason why the resonators are spurious?

Although these devices were able to reach a frequency as high as 475.3 MHz with respectable Q of 1600 and approximately 130 , these resonators show several spurious modes which cannot be suppressed even when notched supports are used. 

Q11. What is the effect of mass loading on the center frequency of the microstructure?

To a first degree of approximation, the effect of mass loading on the center frequency of the microstructure is dominated by the Pt electrode, and Al (generally thinner than Pt because of its higher conductivity) can be neglected. 

Q12. How can you find the modes of vibration in the rectangular plate?

Several modes of vibrations can be found in the rectangular plate either by changing the mode number or by exchanging the dimension of length with width (and therefore looking at width-extensional mode shapes). 

Q13. What is the effect of a single anchor on the quality factor of the device?

It can be intuitively anticipated that the use of a single anchor improves the quality factor of the device and the use of notched solutions (see Fig. 9) reduces the appearance of spurious mode shapes. 

Q14. Why does the TCF of AlN have a single anchor?

This is because either the AlN structures have a single anchor or the modes of vibration have an equivalent stiffness at the anchoring location that is much larger than the stiffness of the anchor itself; therefore any deformation at the clamping location is negligible. 

Q15. How was the frequency response of the resonators measured?

Given the low impedance values shown by the resonators, it was possible to directly measure the frequency response of the resonators. 

Q16. How can the authors compute the effect of mass loading on the center frequency due to Pt?

The effect of mass loading on the center frequency due to Pt can be computed in the following way [18]:(12)where is the unloaded center frequency, is the equivalent Young’s modulus, and is the cross-sectional area perpendicular to the main direction of propagation of the elastic wave in the piezoelectric body. 

Q17. How much does the impact of Pt thickness on the center frequency of the resonator?

It is clear that the impact of Pt thickness on the resonator center frequency is significant (Al has an impact about one-tenth of Pt). 

Q18. What is the effect of the sidewall sloping on the resonator frequency?

According to these considerations, it can be extrapolated that the effect of the sidewall sloping is going to have a more significant impact on higher frequency devices, for which the difference between the top and bottom sides approaches the fundamental wavelength of the resonator.