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JOURNAL OF MICROELECTROMECHANICAL SYSTEMS, VOL. 29, NO. 3, JUNE 2020

Thickness-Lamé Thin-Film Piezoelectric-on-Silicon
Resonators
Sarah Shahraini , Student Member, IEEE, Hakhamanesh Mansoorzare , Graduate Student Member, IEEE,
Amirreza Mahigir, Student Member, IEEE, and Reza Abdolvand, Senior Member, IEEE

Abstract— In this paper, Thickness-Lamé (TL) modepiezoelectrically-transduced silicon resonators are studied
and demonstrated. It will be shown that unlike Planar-Laméresonance modes, Thickness-Lamé modes could be efficiently
excited using sputtered polycrystalline piezoelectric films suchas Scandium Aluminum Nitride (ScAlN) due to the constructive
contribution of both d31 and d33 piezoelectric coefficients in the
coupling coefficient. Moreover, it is shown through finite element
analysis and experimental results that the coupling coefficient
improves with the order of the TL harmonic mode excitedin a silicon slab. It is also confirmed that the quality-factor
of TL resonators substantially enhances through utilizationof properly-designed acoustic reflectors (i.e. acoustic isolation
frames) around the tethered resonator block. The temperature
coefficient of frequency is also modeled using finite-element eigenfrequency analysis. It is shown that the turnover temperature of
TL resonators aligned to the [100] plane of a degenerately-dopedn-type silicon substrate varies considerably as the mode shapetransitions from a Thickness-Lamé to a Lateral-Extensionalmode with the gradual increase of wavelength to thickness ratio.
A record Q of 23.2k is measured for a ∼185MHz fundamental
TL resonator in vacuum ( f x Q = 4.3 × 1012 ) while quality
factors of 12.6k ( f x Q = 4.6 × 1012 ) and 6k are also measured
in vacuum for second- and third-harmonic TL resonators
at 326 MHz and 555 MHz respectively. The combination ofhigh turnover temperatures (>80 ◦ C), high quality factor,
and low motional resistance, promises the suitability of suchresonators for extremely-stable oven-controlled oscillator
applications.
[2019-0263]
Index Terms— AlN resonator, coupling efficiency, Lamé mode,
microelectromechanical systems, quality factor optimization,
turnover temperature tuning.

I. I NTRODUCTIONM

ICRO electro-mechanical resonators are at the heartof integrated low-noise oscillators, filters and sensors [1]–[5]. High quality factor (Q) and large coupling
efficiency combined with high thermal stability and power
Manuscript received December 16, 2019; revised January 23, 2020; accepted
February 2, 2020. Date of publication March 12, 2020; date of current
version June 2, 2020. This work was supported in part by the National
Science Foundation (NSF) under Award 1711632. Subject Editor S. Gong.
(Corresponding author: Sarah Shahraini.)
Sarah Shahraini and Amirreza Mahigir are with the Department of Electricaland Computer Engineering, University of Central Florida, Orlando, FL 32816
USA (e-mail: sarah.shahraini@knights.ucf.edu).
Hakhamanesh Mansoorzare is with the Department of Electrical and Computer Engineering, University of Central Florida College of Engineering andComputer Science, Orlando, FL 32816 USA.
Reza Abdolvand is with the Department of Electrical and Computer
Engineering, University of Central Florida, Orlando, FL 32816 USA.
Color versions of one or more of the figures in this article are available
online at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/JMEMS.2020.2972779

handling in small form factors are desired for such applications. Although MEMS resonators offer high quality factor andcoupling efficiency in small size, they generally suffer from
relatively high temperature coefficient of frequency (TCF).
The temperature coefficient of elasticity (TCE) is around−60 ppm/◦ C (TCF∼ −30 ppm/◦ C) for lightly-doped silicon
based MEMS resonators [6], around −50 ppm/◦ C (TCF∼−25 ppm/◦ C) for AlN based resonators [7] and around−140 to −180 ppm/◦C (TCF∼ −70 ppm/◦ C to −90 ppm/◦C)
for Lithium Niobate (LN) resonators [8]. The reported high
TCF for MEMS resonators limits their usage in ultra-stableoscillator applications.
Active and passive temperature compensation methods havebeen studied to reduce the temperature-induced frequency
drift. Degenerate doping of the silicon device layer [9],or incorporation of a material with positive TCE (suchas silicon dioxide) in the form of over-layers [3] or pillars [10] within the resonant structure are amongst the proposed passive temperature compensation methods. However,using an over-layer of oxide adversely impacts both thequality factor (partially due to energy scattering between
layers) and the coupling efficiency while adding to the fabrication complexity. With passive temperature compensationof MEMS resonators, sub-ppm temperature stability remains
out of reach, even though required for many ultra-stable clock
applications.
In active temperature compensation methods on the other
hand, the resonance frequency is actively tuned in real-time
to compensate for the frequency drift caused by the ambient
temperature variations. The most widely studied methods
for active temperature compensation are tuning the termination impedance [11], [12], inducing a variable mechanicalstress [13] and operating the resonator at a constant elevatedtemperature [14] (e.g. oven controlled oscillators). With active
temperature compensation methods sub ppm temperature stability could be achieved over the desired temperature range.
Oven controlled quartz crystal oscillators (OCXO) have been
widely studied in the literature [15] and the same approach
could be used for temperature compensation in MEMS resonators. However, this requires for the resonator turnover
temperature (the temperature at which the TCF changes
polarity) to be greater than the highest nominal operation
range. This is because the TCF is virtually zero at turnover
temperature and therefore the oscillator stability would be
only marginally affected by the temperature control circuitry.
Hence, designing resonators with turnover temperature values

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SHAHRAINI et al.: TL THIN-FILM PIEZOELECTRIC-ON-SILICON RESONATORS

Fig. 1. The simulated stress field in the x and y directions for a pure AlN
planar Lamé mode. In each half vibration cycle, stress field is tensile in one
planar axis and compressive in the other axis (dark blue and dark red indicate
maximum opposing stresses in the center). Therefore, such a planar Lamémode cannot be efficiently excited with thin polycrystalline films laid on topof the resonator body.

above the commercial operation range (80 ◦ C) is critical inrealizing oven-controlled oscillators.
Based on the results reported in literature [6], Lamé modesilicon resonators exhibit the highest turnover temperature
amongst conventional resonance modes for a given silicon
doping concentration.
Although capacitive excitation of planar Lamé modes is frequently reported in silicon resonators at MHz regime [16], [17]but the motional resistance is usually large for these resonators especially at frequencies above 100MHz. Thin-film
piezoelectric-on-substrate (TPoS) platform offers a pathway
to reducing the motional resistance of high-Q silicon-based
resonator. The substrate layer in a TPoS resonator (usually
single crystalline silicon) concurrently enhances the power
handling in these resonators as well [18].
That said, planar Lamé modes, cannot be efficiently actuatedin silicon through piezoelectric transduction. This is becauseof the fact that the sputtered piezoelectric thin-films such as
AlN are isotropic in the plane of the substrate. As illustrated
in Fig. 1, the stress field is the same in magnitude but with
opposite polarities in the X and Y directions for a planar Lamémode and therefore charges cancel out on electrodes that arelaid out across the thin film. In the case of piezoelectric on substrate resonators, since the symmetry would be disrupted withthe presence of the substrate layer (i.e. silicon) planar Lamémodes could be actuated but the coupling efficiency would be
extremely small (<0.0015%) which would drastically increase
the motional resistance of the resonator [19], [20].
An alternative family of Lamé resonators coined as Crosssectional Lamé mode resonators (CLMR) have been recently
demonstrated in thin-film AlN resonators [21], [22] by exciting
Lamé modes in the thickness of the AlN resonator. In CLMRs
both d31 and d33 piezoelectric coefficients constructively contribute in the excitation of a two-dimensional mechanicalvibration (excitation of the Lamé mode in the cross section of
AlN film). As a result, these resonators offer coupling factors
larger than what is achievable in lateral-extensional mode (alsoknown as contour-mode) resonator. A possible limitation ofsuch resonators is that the range of frequencies that could
be achieved is relatively restricted to high frequencies. For
lower-frequency designs the piezoelectric film thickness has

297

to be in the range of 10s of micro-meter and processing sucha thick piezoelectric film (i.e. deposition and etching) is nottrivial if not practically impossible.
In this work we first demonstrate that Thickness-Lamémodes (TLM) could be efficiently excited in silicon withreasonably high Q using a thin-film piezoelectric sputtered
on top of the substrate. Next, we will propose an acoustic
isolation technique to effectively alleviate support loss for
the TLM resonators implemented in the thin-film ScAlN-onsilicon (TPoS) platform. Next, temperature frequency dependency is modeled and studied for TLM TPoS resonators on
a highly-doped n-type silicon layer using COMSOL. Our
simulations confirm that turnover temperature of above 100 ◦ C
is achievable for these resonators at moderately high-doping
concentrations (∼4×1019 /cm3 ). Next, using the COMSOL
model and experimental results, we show that the turnover
temperature is tunable by changing the resonator effective
width to the thickness ratio as the targeted mode transitions
from a Lamé to a quasi Lamé mode and finally converges tolateral-extensional modes. It will also be shown that higher
harmonics of the TLM could be excited in the same silicon
resonator slab. In fact, the coupling factor for the harmonic
TLM resonators increases with the harmonic order.
II. T HICKNESS -L AME M ODE IN TPoS R ESONATORS
Commonly, the d31 piezoelectric coefficient of sputteredpiezoelectric films (e.g. AlN) is utilized to excite lateralextensional (LE) modes in TPoS resonators. For the fundamental LE mode, the width of the resonator is equal to resonancehalf-wavelength. To actuate higher harmonics, interdigitatedelectrode patterns are used. In such patterns the distance
between the centers of two adjacent electrodes (also known
as the finger-pitch (FP)) is equal to the half-wavelength.
As shown in Fig. 2.a, a pure lateral-extensional mode isactuated in a silicon slab when the half-wavelength (λ/2)
 thickness (Th). As λ/2 (i.e. width (W)) decreases andapproaches the thickness of the resonator, mode shapes withproperties between lateral-extensional mode and Lamé mode
emerge in the thickness of the resonator (Fig. 2.b and Fig. 2.c).
Eventually, when λ/2=Th, a pure Thickness-Lamé mode
would be actuated in the resonator slab (Fig. 2.d).
Now, if a thin piezoelectric film sandwiched between two
metal layers is laid out on top of the silicon slab as is
the case in TPoS platform, the d31 and d33 piezoelectriccoefficients of the film, constructively contribute in actuating
the Lamé-mode in the composite structure of (Mo/AlN/Mo/Si).
Caused by the presence of the piezoelectric film and metal
layers, the symmetry of the acoustic medium is perturbed
and therefore technically speaking a pure Lamé-mode can nolonger be excited. Therefore, we refer to these mode shapes as
quasi thickness-lamé modes (QTLM). For QTLM resonators
if the width or the FP is close to the thickness of the resonator,
the resonator would have properties closer to the property of apure Lamé mode resonator. As the FP increases the behaviorof the resonator transitions from Lamé mode to the commonly
excited lateral-extensional mode.
Harmonic QTLM could also be actuated in the thickness,of the TPoS resonator. When the FP is chosen ∼ t icknessnAuthorized licensed use limited to: University of Central Florida. Downloaded on July 23,2020 at 20:49:44 UTC from IEEE Xplore. Restrictions apply.

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Fig. 2. The displacement field for a silicon block resonator with a thicknessof Th=16μm and varying width (i.e. λ/2), where dark blue and dark red colors
identify the minimum and maximum displacement respectfully. For the width
values close to the thickness of the resonator, Lamé mode (d) would substitutelateral extensional mode (a) in the resonator slab. For the width values close to
an integer fraction of the thickness of the resonator, higher harmonic thicknessLamé modes are actuated in the resonator slab (e.g. second harmonic (e) andthird harmonic (f)).

Fig. 4. The stress field in the fundamental a) and third harmonic b) QTLM
resonators. The stress field in the piezoelectric portion of the third harmonicmode is larger and because of that higher coupling efficiencies are expected
for third harmonic QTLM.

TABLE IT HE S IMULATED C OUPLING E FFICIENCIES FOR QTLM AND LEM TP O S
R ESONATORS . A F ULL S TACK OF Mo/ScAlN/Mo/Si I S C ONSIDEREDW ITH THE S AME S ILICON T HICKNESS AS THE FABRICATED R ES ONATORS (0.1 μm Mo/1μm ScAlN/ 0.1μm Mo/ 16μm Si)

Fig. 3. A schematic viewgraph of a quasi-thickness-Lamé mode (QTLM)
TPoS resonator. Electrode patterns are similar to the ones used for lateralextensional mode and the thickness of the silicon slab will enable excitationof the TL mode.

the nth harmonic in the thickness of the resonator is excited.
For example, second and third harmonic QTLM are shown in
Fig. 2.e and Fig. 2.f. Actuating higher order harmonics in the
thickness of the resonator extends the range of frequencies
that could be achieved on the same substrate with QTLM
resonators.
A schematic viewgraph of a QTLM TPoS resonator isshown in Fig. 3. Based on the FP/Th ratio the same structure
enables actuation of the lateral-extensional and the thickness
quasi Lamé modes.
III. Q UASI L AME M ODE TPoS R ESONATOR M ODELING
A. Coupling Efficiency for QTLM TPoS Resonators
As mentioned in the previous section, for the fundamental
QTLM TPoS resonator, the stress field is concentrated in thecenter of resonator stack (mostly in the silicon). Therefore,

the stress concentration in the piezoelectric film is relatively
small and the coupling efficiency is compromised. As higher
order QTLM is actuated in the thickness of the resonator,
the concentration of stress field within the piezoelectric regionof the TPoS resonator increases (Fig. 4) and the coupling
efficiency is expected to improve correspondingly.
A 2D loss-less frequency analysis model in COMSOL isused to study the coupling efficiency of the QTLM TPoS resonators. The resonator stack includes a 16μm silicon coveredby 1μm thick ScAlN (20% Scandium content) sandwiched
between two 100 nm Mo layers. The one port admittanceis simulated using the frequency response analysis and thecoupling efficiency is calculated using modeled series andparallel frequencies. The coupling coefficient for different
harmonics are summarized in Table I. The material property
information for 20% ScAlN is borrowed from [23].
As expected, the coupling efficiency increases for higher
harmonic QTLM TPoS resonators and the QTLM will offer a

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Fig. 5.
The admittance modeled for a second-harmonic QTLM TPoS
resonator with 4 μm silicon topped with 2μm ScAlN.

higher coupling factor than the lateral-extensional mode if the
thickness of the piezoelectric film approaches half wavelengthof the thickness Lamé mode.
A second-harmonic QTLM excited in a 4μm of silicon slab
covered with a 2μm of piezoelectric film (20% ScAlN) is
presented in Fig. 5. The simulated coupling factor is 7.8% for
the second harmonic QTLM TPoS resonator.
B. Support Loss in QTLM TPoS Resonators
The resonator quality factor directly impacts the noise floorof the system in which the resonator is utilized. Therefore,
achieving high quality factors are crucial for many applications
such as oscillators and sensors. Anchor loss, ohmic loss andinterface loss [24] are the main sources of loss in piezoelectricresonators. Although improving the interface loss might bechallenging, these resonators can be designed for minimum
anchor loss [25]–[27].
Since the Lamé mode in the QTLM TPoS resonators isformed on the cross-section of the resonator, there are no
pseudo-nodal points at the sides of the resonator. Consequently, a substantial portion of acoustic energy could beradiated to the substrate through the tethers. By placing
planar acoustic reflectors (etching trenches in the substrate),
the acoustic wave is reflected due to the very large acoustic
mismatch between air and silicon. If these reflectors aredesigned at the proper distance from the tether, the reflectedwave would be constructively interfering with the resonator’s
standing wave [28]–[30].
In this work, we present a novel acoustic isolation frame
to minimize the anchor loss for QTLM. As shown in Fig. 6,
the resonator is carved out of a suspended circular frame. The
radiated acoustic energy through tethers is reflected from theedges of this frame. Based on the size of the isolation frame
the reflected acoustic energy could either improve or degrade
the resonators quality factor. The anchor quality factor is
optimized by optimizing the dimensions of the structure.
A 3D model based on a perfectly matched layer (PML) isdeveloped in COMSOL to study the anchor loss for QTLM
TPoS resonators. The dimension of the acoustic isolation
frame is varied to search for the optimized frame dimensions.
Based on the modeled data, the anchor quality factor is
optimized when the acoustic isolation frame has a diameter

Fig. 6. The PML-based model developed for support loss prediction ina fundamental QTLM TPoS resonator with an acoustic isolation frame.
The resonator and frame dimensions are chosen to resemble the fabricatedresonators.
TABLE II
T HE M ODELED A NCHOR Q UALITY FACTOR FOR THE R ESONATORW ITH A ND W ITHOUT A COUSTIC I SOLATION F RAMEof (2n×FP/2) + 2 × (tether-length). The support quality
factor is improved by an order of magnitude for the optimum
frame dimensions (Table II) for the fundamental QTLM TPoS
resonator with an FP= 17μm ( f resonance ∼185 MHz).
C. Turnover Temperature in QTLM TPoS Resonators
Lamé mode resonators in highly n-type doped silicon are
excellent choices for oven-controlled oscillator applications
for which, the oscillator operates at a constant elevated temperature. If this elevated temperature is close to the turnover
temperature of the resonator, the system would be robust to
the errors of the control system.
For [100] aligned QTLM TPoS resonator, all the resonatorboundaries would be aligned to [100] crystalline plane ofsilicon Fig. 7. Therefore, it is expected that the temperature
behavior of the [100]-aligned QTLM to be similar to planar
Lamé modes fabricated on a 100 silicon substrate previously
reported in [31].
To predict the frequency-shift as a function of the temperature for QTLM TPoS resonators, a 2-D model of thewhole stack of TPoS resonators is developed in COMSOL.
The layer thicknesses in the model reflect the fabricateddevices as follows: top Molybdenum 100 nm, Scandium

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TABLE IIIT HE E LASTIC C ONSTANTS O F P HOSPHORUS -D OPED (n = 6.6 × 1019 cm −3 ) S ILICON AND T HEIR C ORRESPONDINGF IRST AND S ECOND O RDER T EMPERATURE C OEFFICIENTS [6]Fig. 7. On a [100] silicon wafer, the block resonators should be rotated
45 degrees with respect to the wafer flat in order for all faces to be aligned
to [100] crystalline plane, which would be similar to the case for planar Lamémode.

Fig. 8. The modeled TCF curves for resonators with FP 40, 30 and 17 μm.
The turnover temperature shifts toward higher temperature as the FP/ T ratio
approaches unity. The lateral-extensional mode exhibits the lowest turnover
temperatures compared to QTLM resonators.

doped AlN (ScAlN) 1 μm, bottom Molybdenum 100 nm andsilicon 16 μm.
In order to develop TCF curves, stiffness values for silicon,
AlN and Molybdenum and their temperature coefficients wereborrowed from [6](Table III) for phosphorus doped single
crystalline silicon (n=6.6×1019cm−3 ), [32] and [33] for AlN
and Molybdenum respectively. The temperature coefficientof elasticity (TCE) of AlN is assumed to be an adequate
replacement for Scandium doped AlN TCE data.
For single crystalline silicon, the stiffness matrix is calculated for each temperature using Eq.1, Eq.2 and Eq.3:
C11T = C110 + T C 111 × C110 × 10−6 × (T − T0 ) + T C 211

×C110 × 10−9 × (T − T0 )2(1)
C12T = C120 + T C 112 × C120 × 10−6 × (T − T0 ) + T C 212
×C120 × 10−9 × (T − T0 )2
(2)
1
−6
2
C44T = C440 + T C 44 × C440 × 10 × (T − T0 ) + T C 44
×C440 × 10

−9

× (T − T0 )2

(3)

Where C11T , C12T and C44T are the single crystalline silicon
stiffness coefficients at an arbitrary temperature T referenced
to the room temperature and C110 , C120 and C440 are thestiffness coefficient at room temperature (T0 ).
The new stiffness matrix for silicon and stiffness values for
ScAlN and Molybdenum are used to repeat the modal analysis
and to calculate the shifted resonance frequency.

Fig. 9. The turnover temperature of a QTLM TPoS resonator as a functionof FP/Th ratio. Higher turnover temperature is predicted for the resonatorswith FP/Th ratio closer to one. The turnover temperature could be adjusted
lithographically.

The modeled TCF curves for TPoS resonators with FP of
40 μm, 30 μm and 17 μm are shown in Fig. 8. For the quasi
thickness-Lamé mode resonators (FP=17 μm), it was expectedthat the resonator behavior would be similar to the pure Lamémode which is confirmed with our model.
As the finger-pitch to thickness ratio increases thetemperature-frequency behavior of the resonator transitions
from what is known of pure Lamé to what is expected forextensional modes (i.e. the turnover temperature shifts down
(Fig. 9).

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301

Fig. 11. The SEM image of the fundamental QTLM TPoS resonator without
isolation frame (a) and with isolation frame (b).

Fig. 10. The simplified schematic process flow for fabricating QTLM TPoS
resonators.

Therefore, the turnover temperature in QTLM-TPoS resonators can be tuned lithographically by adjusting the FP/Th
ratio. This feature can be used to design resonators with theturnover temperatures slightly above the desired temperature
range for oven controlled oscillator application.
The TCF curves are also modeled for higher harmonics
of QTLM TPoS resonator. For these higher order modes,
the turnover temperatures are predicted to be slightly lower
than the fundamental mode (turnover temperature = 120 ◦ C).
For the temperature range reported in this study, TCE is
negative for both AlN and Molybdenum and positive forhighly doped silicon. For the fundamental thickness-Lamémode the stress filed is mostly concentrated in the centerof the resonator (silicon portion) and as a result the TCF is
dominated by the silicon properties. On the other hand, forhigher harmonic QTLM, a larger portion of the total stress field
is in Mo/ScAlN/Mo compared to the fundamental mode andtherefore the Mo/ScAlN/Mo stack will impact the TCF more
prominently. Hence, lower turnover temperature is predicted
for these higher order modes.
IV. FABRICATION P ROCESSThe QTLM-TPoS resonators are fabricated on a relatively
thick (16 μm) degenerately Arsenic-doped (∼4e19 cm−3 )[100] SOI substrate in a five mask process. The sputtered 20%
Scandium doped AlN film is 1μm thick and is sandwiched
between two 100nm thick layers of Molybdenum.
First, the Mo/ScAlN/Mo stack would be sputtered and the
top metal is dry-etched in an SF6 /O2 plasma to pattern the top
electrodes(Fig. 10.a). Then, the ScAlN is wet etched to create
access to the bottom electrode (Fig. 10.b). An alternatingheated TMAH bath and Sulfuric acid is used for this step. The
ScAlN etch rate of 200 nm/min is achieved with this method.
Then a thin layer of gold is evaporated on the pads to improveohmic contact for probing (Fig. 10.b). The resonator body isthen formed by plasma etching the full stack of material down
to the SOI buried oxide (BOX) layer (Fig. 10.c). Handle layer
silicon is then etched from the backside in a deep-reactive-ionetching tool using Bosch process and the resonator is finallyreleased by wet etching the BOX layer in a buffered oxide
etchant (BOE)(Fig. 10.d).

Fig. 12. The measured frequency response in air for the fundamental QTLM
TPoS resonator with and without acoustic isolation frame (highest measured
Q for both designs). The unloaded quality factor is significantly larger for thedevices with isolation frame.

The scanning electron microscopy (SEM) image of thefundamental QTLM TPoS resonator (FP=17μm) with andwithout isolation frame is shown in Fig. 11.
V. E XPERIMENTAL R ESULTS
The fabricated QTLM TPoS resonators are characterized in atmospheric pressure and partial vacuum using a
ZNB8 network analyzer and a pair of GSG probes (fromFormFactor inc) at ambient temperature. The loaded quality
factors are measured from the transmission frequency response
and the unloaded quality factors are calculated using the
motional resistance of the resonators. The motional resistanceis estimated from the insertion loss at the transmission frequency response peak. One port admittance response is alsomeasured and the coupling coefficients are calculated using
the measured parallel and series resonance frequencies. The
temperature-frequency curves are also measured in a Janiscryogenic vacuum probe station. All the reported plots in thispaper are the raw data collected from the network analyzer
with 50 Ohm termination impedance (no de-embedding is
performed).
TPoS resonators are fabricated on 16 μm thick siliconwith finger pitches ranging from 40 μm (lateral-extensionalmode) to 17 μm (fundamental QTLM), as well as 9 μm (2ndharmonic QTLM) and 6 μm (3rd harmonic QTLM).
The transmission frequency response for the fundamental
QTLM with and without acoustic isolation frame in air isshown in Fig. 12. It is observed that, both quality factor andmotional resistance are improved for the device with isolation
frame. The measured unloaded quality factor of 16.2 k andAuthorized licensed use limited to: University of Central Florida. Downloaded on July 23,2020 at 20:49:44 UTC from IEEE Xplore. Restrictions apply.

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Fig. 13. The measured frequency response of the fundamental QTLM TPoS
resonator in partial vacuum. Unloaded quality factor of 23.2 k is measured at
185 MHz for this resonance mode.
Fig. 15. The measured frequency response for a 3rd-harmonic QTLM TPoS
resonator in air.

Fig. 14. The measured frequency response for a 2nd harmonic QTLM TPoS
resonator in air.

motional resistance of 235 Ohm at 185 MHz for the fundamental QTLM resonator is amongst the best performance
reported for any MEMS resonator at this frequency range(f×Q∼ 3×1012). The measured Q’s are in good agreementwith the trend predicted by our finite element COMSOL model
for anchor quality factor.
As shown in Fig. 13, the transmission frequency response
for the fundamental QTLM TPoS resonator is also measured
in partial vacuum and an unloaded quality factor of ∼23.2 k
is measured for this mode shape in vacuum resulting in an
f×Q∼ 4.3×1012. Such a significant Q enhancement in vacuum(more than 40%) is an indication that the quality factor of theresonator is no longer mostly limited by the anchor loss atestament to efficiency of the acoustic isolation frame.
The measured transmission frequency response for the second (FP=9 μm) and third (FP=6 μm) harmonic QTLM
TPoS resonators are plotted in Fig. 14 and Fig. 15 respectively. We measure unloaded quality factors of 11.1 k and5.5 k at 366 MHz and 555 MHz for the second and third
harmonic QTLM resonator. The measured unloaded quality
factor increased to 12.6 k for the second harmonic QTLM
TPoS resonator (f×Q∼4.6×1012) in vacuum and the Q for
the third-harmonic QTLM improved to 6k in vacuum. The
TCF curves are measured for all three harmonics to confirm
that the measured peaks are indeed quasi Lamé modes.

Fig. 16. The wide spectrum frequency response for a second harmonic
QTLM TPoS resonator. There are no other strong peak close to this mode
which facilitates oscillator applications.

TABLE IV
T HE M EASURED C OUPLING E FFICIENCIES FOR D IFFERENTC LASSES OF TPoS R ESONATOR

A wide spectrum frequency scan is also measured for all
three harmonics. We found that there is no strong spurious
mode close to these quasi Lamé modes. The second harmonic
QTLM spectral response is plotted in Fig. 16. A wide frequency range is deliberately chosen. It is apparent that there
are no other strong modes in the vicinity of the QTLM.
The coupling efficiencies of the resonator are calculated from the measured series and parallel frequencies for
5 different resonators in each class and the highest measured

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TABLE VT HE M EASURED Q UALITY FACTOR FOR THE F UNDAMENTAL QTLM TPoS R ESONATOR C OMPARED TO A
S ELECTED P UBLISHED R ESULTS IN THE S AME F REQUENCY R ANGE

Fig. 17. The measured TCF curves for a lateral-extensional, and two quasi
thickness Lamé mode resonators.

coupling efficiencies are reported in Table IV. As shown inthis table the coupling efficiency improves by actuating higher
harmonic QTLM TPoS resonator. The measured coupling
efficiencies are in good agreement with the finite element
model.
The TCF curves are also measured in vacuum probe station
for Lateral extensional and quasi thickness-Lamé mode TPoS
resonators. As reported in Fig. 17, the TCF is measured for
TPoS resonators with FP=40 μm, FP=30 μm and FP=17 μm
and the measured data are in good agreement with themodeled TCF curves. We measure the turnover temperatureof 45 ◦ C, 80 ◦ C and 150 ◦ C for these devices respectively.
Turnover temperatures reported for QTLM TPoS resonators
are the highest turnover temperatures reported for piezoelectric actuated MEMS resonators without any additional overlayers.
In Table V, the quality factor of the fundamental QTLM
TPoS resonator is compared to several other published resultsfrom resonators in the same range of frequencies. To the bestof our knowledge, the fundamental QTLM TPoS resonator
offers the highest quality factor even compared to highest
reported quality factor for capacitive resonators in this rangeof frequencies.
The best results measured for resonators with FP ranging
from 17 μm to 40 μm are compiled in Table VI. The
measured transmission frequency response for a resonator with
FP=30 μm is shown in Fig.18. As described, in this range

Fig. 18. The measured frequency response for a quasi-thickness Lamé mode
resonator with FP = 30 μm.
TABLE VI
T HE M EASURED R ESONANCE C HARACTERIZATION D ATA C OMPARING
THE LE M ODE TO QTLM R ESONATORS W ITH P ROPERTIEST RANSITIONING F ROM LE TO QTLM FOR A R ANGE OF FP

the resonator mode shape transitions from QTLM to LE.
It is interesting to notice that Q is improved as the device
approaches a true TL mode for the 17 μm finger pitch. Thisis despite the fact that the quality factor is commonly believed
to reduce for higher frequency resonators.
VI. C ONCLUSION
Fundamental and harmonic quasi thickness-Lamémodes (QTLM) are successfully actuated in the thinfilm piezoelectric-on-silicon resonators as the half-wavelength
approaches the thickness of the silicon slab. Anchor quality
factor in these resonators is shown to significantly improve

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304

JOURNAL OF MICROELECTROMECHANICAL SYSTEMS, VOL. 29, NO. 3, JUNE 2020

by designing an acoustic reflector frame. The resonators arefabricated on a 16 μm thick highly Arsenic-doped siliconlayer. A quality factor of 23.2 k (in vacuum) is measured
for a fundamental QTLM TPoS resonator at 185 MHz
with a measured turnover temperature of above 100 ◦ C
which is the highest turnover temperature reported for
piezoelectric resonators without the need for any additional
silicon oxide over-layer. Quality factors of 12.6 k and 6 k arealso measured at 366 MHz and 555 MHz for second- andthird-harmonic QTLM TPoS resonators. Very high measured
quality factor along with low motional resistance and highturnover temperatures presented in these resonators suggest
their suitability for oven-controlled oscillator applications.
ACKNOWLEDGMENT
The authors would like to thank Y. Oshmyansky at
Advanced Modular Systems Inc. for his help with the deposition of ScAlN films.
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SHAHRAINI et al.: TL THIN-FILM PIEZOELECTRIC-ON-SILICON RESONATORS305

Sarah Shahraini (Student Member, IEEE) received
the B.Sc. and M.Sc. degrees in electrical engineeringfrom the K. N. Toosi University of Technology,
Tehran, Iran, in 2010 and 2012, respectively. She
is currently pursuing the Ph.D. degree with the
University of Central Florida, Orlando, FL, USA.
Her research interests lie in the area of microelectromechanical systems with a special focus on design,
fabrication, and characterization of microresonatorsfor stable oscillator, filter, and sensor applications.
Ms. Shahraini was a recipient of the Best Student
Paper Award from the 2018 IEEE International Frequency Control Symposium.

Amirreza Mahigir (Student Member, IEEE)
received the B.Sc. and M.Sc. degrees in electricalengineering from the K. N. Toosi University ofTechnology, Tehran, Iran, in 2009 and 2012, and
the Ph.D. degree from the School of Electrical andComputer Engineering, Louisiana State University,
Baton Rouge, LA, USA, in 2018. He then joined
the University of Central Florida, where he is currently a Post-Doctoral Research Fellow. His researchinterests are in the area of MEMS-base photonic
integrated circuits.

Hakhamanesh Mansoorzare (Graduate Student
Member, IEEE) received the B.S. degree in electricalengineering from the Sharif University of Technology, Tehran, Iran, in 2016. He is currently pursuing
the Ph.D. degree in electrical engineering with the
University of Central Florida, Orlando, FL, USA.
He has been working as a Graduate Research
Assistant with the Dynamic Microsystems Laboratory. His research interests lie in the area of microelectromechanical systems (MEMS) with a special
focus on design, fabrication, and characterization ofpiezoelectric microresonators for radio frequency circuits and sensors.
Mr. Mansoorzare was a recipient of the Best Student Paper Award in
Category 4 from the 2019 Joint Conference of the IEEE International
Frequency Control Symposium and European Frequency and Time Forum andupon entering graduate school, he was awarded the ORC Doctoral Fellowship.

Reza Abdolvand (Senior Member, IEEE) received
the Ph.D. degree from the School of Electrical andComputer Engineering, Georgia Institute of Technology, Atlanta, GA, USA, in 2008.
He was an Assistant Professor with the Schoolof Electrical and Computer Engineering, Oklahoma
State University, Stillwater, OK, USA. In 2014,
he joined the University of Central Florida, Orlando,
FL, USA, where he is currently an Associate Professor and the Director of the Dynamic Microsystems
Laboratory, Department of Electrical Engineeringand Computer Science. He has authored or coauthored two book chaptersand more than 70 peer-reviewed journal and conference articles in his fieldof expertise. He holds 12 U.S. patents. His research interests are in thegeneral area of micro/nanoelectromechanical systems with over 15 yearsof experience in design, fabrication, and characterization of microresonatorswith applications in radio frequency circuits and resonant sensors including
biosensors.
Dr. Abdolvand was a recipient of the National Aeronautics and Space
Administration Patent Application Award in 2009.

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