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JOURNAL OF MICROELECTROMECHANICAL SYSTEMS

1

Near-Carrier Phase Noise Suppression at
Turnover Temperature in a Thin-Film
Piezoelectric-on-Silicon Oscillator
Yasaman Majd , Student Member, IEEE, Sarah Shahraini , Member, IEEE,
Garett Goodale, Student Member, IEEE, Heather Hofstee, Graduate Student Member, IEEE,
Hossein Miri Lavasani, Senior Member, IEEE, and Reza Abdolvand , Senior Member, IEEE
Abstract— In this paper, the near-carrier enhancementof phase-noise (PN) at turnover temperature (T t o) in aquasi-thickness-Lamé (QTL) mode thin-film piezoelectric-onsilicon (TPoS) oscillator is reported for the first time. QTL-TPoS
resonators fabricated on degenerately-doped n-type silicon offera T t o greater than 80◦ C and are suitable for implementationof highly-stable ovenized oscillators. In this work, a ∼123MHzQTL-TPoS resonator is heated up to T t o (∼90◦ C) by injecting
current through the silicon body of the resonator. It is experimentally observed that at turnover temperature, the phase-noise slope
close to the carrier frequency ( f < 100Hz ) decreases substantially in contrast to the expected trends. A ∼10dB improvementin phase noise at 10Hz offset and a ∼25dB improvement at 1Hz
offset is recorded when the oscillator is operating at T t o compared
to room temperature.
[2020-0206]
Index Terms— Turnover temperature, phase noise, temperature fluctuation, thickness-Lamé mode.

I. I NTRODUCTIONSTABLE timing devices lie at the heart of most digital
circuits and communications systems. Such oscillators areoften required to demonstrate extreme frequency accuracy aswell as excellent temperature stability (ppm levels or better).
Oven-controlled resonators are widely used to compensate
for the temperature dependence of frequency in resonators
for applications where extreme temperature stability is essential [1], [2]. In recent years, micro-electro-mechanical resonators have offered a new window of opportunity to achieve
low power consumption in micro-oven-controlled oscillators as
an alternative to the legacy quartz-based OCXO due to theirsmall size, and silicon-based fabrication process [2]. The minimum requirement for enabling a highly stable oven-controlled
oscillator is a resonator that exhibits a local zero temperature
coefficient of frequency (i.e. turnover temperature) outside thenominal operating temperature range of the device.

Manuscript received May 16, 2020; accepted June 9, 2020. This work was
supported in part by NSF award #1711632. Subject Editor M. Rais-Zadeh.
(Corresponding author: Yasaman Majd.)
Yasaman Majd, Sarah Shahraini, Garett Goodale, Heather Hofstee, and Reza
Abdolvand are with the Department of Electrical and Computer Engineering, University of Central Florida, Orlando, FL 32816-2368 USA (e-mail:majd92@knights.ucf.edu).
Hossein Miri Lavasani is with the Department of Electrical, Computer, andSystems Engineering, Case Western Reserve University, Cleveland, OH 44106
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.2020.3004317

Several solutions have been proposed to enable suchturnover points in silicon-based resonators [3], [4]. Our group
recently reported a new family of TPOS resonators, which
operate based on the excitation of quasi thickness-Lamé modes
with reasonably high Q and high turnover temperature without
the need for extremely high doping concentrations or any
additional embedded silicon oxide layer [5].
Despite the outstanding progress made in developmentof MEMS-based oscillators, the phase noise performanceof MEMS-based oscillators, does not match those typicallyoffered by quartz oscillators. Specifically, this disparity ismore noticeable in the close-to-carrier noise region. In communication systems with narrow channel spacing, close-tocarrier phase noise is particularly important and constrains theallowable channel spacing [6]. It is postulated that when theresonator size scales down to the nanometer range, there arefundamental thermomechanical mechanisms that dominate thenoise performance of the oscillators assembled based on suchresonators [7]. In this work, we examine whether thermallyinduced fluctuations of frequency could also be responsible forrelatively poor near-carrier performance of oscillators assembled based on micro-scale resonators. In particular, we investigate the effect of operation at turnover temperature on the nearcarrier phase noise of quasi thickness-Lamé mode oscillatorsand postulate that the observed improved performance could
be a result of the reduced thermally-induced fluctuation of
frequency.
II. P HASE N OISE : BACKGROUND AND T HEORY
Phase noise and frequency variations are closely related
to each other, and the term phase noise could be used todescribe random frequency fluctuations of a signal. Several
models have been proposed to predict the phase-noise behaviorof oscillators [8], [9]. The Leeson model is one such model
developed to estimate the behavior of phase noise in anelectrical oscillator [8]. From this linear model, the phase noiseof an oscillator can be defined as: f 1/ f 3
f0 2
2F K T) (1 +)]} (1)[1 + (
L( f ) = 10 log{
Psig
2Q f
| f |
where  f is the offset frequency, f 0 is the oscillation frequency,  f 1/ f 3 is the corner frequency for the flicker noise,k B is the Boltzman constant, T is the temperature, F is noise
factor of the amplifier, and Psig is the power of carrier signal.

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JOURNAL OF MICROELECTROMECHANICAL SYSTEMS

Fig. 1.

The phase-noise spectrum of a typical feedback oscillator.

Since MEMS oscillators contain both electrical and mechanical components, both noise sources should be considered toallow for a comprehensive study of phase noise. Different
regions in the phase noise plot of a general oscillator are
depicted in Fig. 1 [10]. Possible sources for the typical slopeof phase noise in each region are also highlighted in thisfigure. It should be mentioned that all of these different regions
will not necessarily be observed in all oscillators. The firstregion closest to the carrier is the 1/(f4 ) region which istypically attributed to the random frequency fluctuations of theresonant tank. In micromechanical oscillators, this region has
been attributed to adsorption–desorption noise [11], Brownie
noise [11], [12], defect motion or temperature fluctuation ofa resonator [7], [13]. The temperature-induced fluctuations offrequency is assumed to dominate the close-to-career noise as
the resonator dimensions scale down to nanoscale [7], [13].
However, the theoretical limits of temperature fluctuations
resulted from the theory developed in such work won’t predictthe levels of noise typically measured in microscale resonators,
including those presented in this work (this will be shown laterin section IV).
In the present work, we propose investigating the nearcarrier phase noise of a micro-scale oscillator at varying
temperatures, from room temperature to the turnover temperature and beyond. A correlation between the phase noise
and the effective temperature coefficient of frequency (TCF),
if observed, would suggest that the effect of thermally-induced
frequency fluctuations is significant in mechanical resonatorseven at the micro-scale.
With this objective in mind, the characterization of theresonator and oscillator design is briefly discussed first. Then,the effect of resonator’s temperature on near-carrier phasenoise is recorded and it is shown that, in fact the phase noise atturnover temperature reaches a minimum. Similar suppressionof phase noise at the turnover temperature has been reported
by other groups [14].
III. R ESONATOR C HARACTERIZATIONAND O SCILLATOR D ESIGN
The device utilized in this work is a quasi thicknessLamé mode thin-film piezoelectric-on-silicon resonator [5]fabricated on a 16 um degenerately n-type doped [100] SOI

Fig. 2.
The schematic of the quasi thickness-Lamé TPoS (QTL-TPoS)
resonator highlighting the pads for injection of a DC current through silicon
body to efficiently heat the resonator.

Fig. 3. The simulated turnover temperature of a QTL TPoS resonator as afunction of finger pitch to stack thickness ratio [5].

substrate. The piezoelectric film is a 1μm Sc0.2 Al0.8 N layer
sandwiched between two 100 nm Molybdenum layers (provided by Advanced Modular Systems Inc.) overlaid on thesilicon device layer (Fig. 2). The resonator finger pitch (FP),which is the distance between two adjacent top electrodes,
is relatively close to the thickness (t) of these resonators,
and consequently, the pure lateral-extensional mode would
transition to a QTL mode with the advantage of increased
turnover temperature [5].
As shown in Fig. 3, the turnover temperature in QTL
resonators could be designed between the turnover temperatureof a pure lateral extensional mode and a pure thickness-Lamémode.
The scanning electron micrograph (SEM) of the QTL-TPoS
resonator used in this work is presented in Fig. 4 for which
FP = 25μm.
In the silicon contact area (marked in Figure 4), all the
top stack layers are etched down to the silicon device layer
to facilitate injection of a DC current through the silicon
body of the resonator to control the resonator temperature.
A 20 nm AlN seed layer under the bottom metal provides
for the electrical isolation of the AC and DC signals in theresonator. The frequency response of the QTL TPoS resonatorand the simulated resonance mode shape are shown in Fig 5.
An unloaded Q of ∼5 k is measured for this resonator at
123 MHz.

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MAJD et al.: NEAR-CARRIER PHASE NOISE SUPPRESSION AT TURNOVER TEMPERATURE

3

Fig. 4. The scanning electron micrograph of the QTL-TPoS resonator withisolated contact to silicon body for injecting current to heat up the resonator.
Fig. 6. Schematic of the oscillator circuit and the measured output waveform.

Fig. 5. Frequency response of the QTL-TPoS resonator and the stress-profile
profile of the mode-shape.

Due to the low motional impedance of this resonator(∼120), a single high-frequency bipolar junction transistor(BJT) could provide sufficient gain as a sustaining amplifier inthe oscillator feedback loop (Fig. 6). The BJT utilized here is
AT-41486, an NPN bipolar transistor that offers excellent highfrequency performance in terms of gain and noise figure withthe gain bandwidth product of 8 GHz. This transistor is biased
at 2 V with a 2mA bias current. Such a single-transistor
oscillator promotes lower circuit noise due to the reduced
number of components.
In order to connect the oscillator to the 50  terminationof a phase noise analyzer, a buffer stage is required. Here, a
THS4211 IC is utilized as the buffer which offers a wideband
frequency operation. The measured oscillation frequency ofthe circuit is ∼123 MHz with a 1.5 V peak to peak amplitude(The waveform of the oscillator is shown in the inset of Fig. 6).
To characterize the frequency vs temperature behavior of theresonator, the resonator is placed in a vacuum chamber andthe resonator is heated as the pressure is kept at 0.01 Torr.
As seen in Fig. 7, the Tt o is ∼90◦C and the room temperature
TCF is ∼10ppm/◦C.
IV. A NALYSIS OF R ESULTS
As discussed in section II, thermally-induced frequency
fluctuations are postulated to significantly impact the nearcarrier phase noise of an oscillator as the dimensions ofFig. 7. The frequency vs. temperature plot exhibiting a turnover temperature
at ∼90◦ C.

the mechanical resonator approaches the nanoscale regime.
At such small scales, the thermal heat capacity of the resonatoris reduced to a level that random transfer of heat energy
in and out of the resonator will generate appreciable levelsof temperature fluctuation in the resonator. Such temperaturefluctuations in return affect the density and elastic modulusof the resonator which leads to a change in the resonancefrequency [7], [13].
A simple equivalent electrical circuit that captures thethermal diffusion of a structure such as a resonator is shownin Fig. 8 (It is assumed that the resonator is in thermal
equilibrium).
In this figure, the current source (P) models the noise
source, which behaves as a white frequency noise. C and G
represent the heat capacity and the thermal conductivity of theresonator. G is dependent on the dimension of the resonatorand the suspension tethers and can be formulated to include
both radiation and conduction for the systems in which theresonator is operating in vacuum [7]. However, it could beshown that for the resonator and the tether dimensions of ouroscillator (shown in Table I) and considering the excellent
thermal conductivity of silicon (1.5 watt/cm.K) the effect ofradiation could be neglected.
Using the model in Fig. 8, the resulting voltage across
C and G represent the temperature fluctuation T and thedifferential equation describing the heat transfer of the

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JOURNAL OF MICROELECTROMECHANICAL SYSTEMS

Fig. 8. Equivalent electrical circuit for the thermal diffusion of an resonator.
TABLE IT HE D IMENSION OF THE R ESONATOR AND T ETHERS
Fig. 9. The printed circuit board of a custom-made micro-controlled based
temperature controlling circuit.

resonator is written as:d(T )+ GT = P(t)(2)
Cdt
It could be shown that the spectral density of noise due tothe temperature fluctuation resulted from solving this differential equation is [7]:ST ( f ) =4k B T 2 B/G
1 + 4π 2 f 2 C 2 /G 2

(3)

where k B = 1.38 × 10−23 W· sec/K is the Boltzmann’sconstant and T is the resonator’s temperature. The spectral
density of temperature-induced fractional frequency noise isthen calculated from:S y ( f ) = αt2 ST ( f )(4)in which αt denotes TCF of the resonator. Therefore, thethermally-induced root mean square (RMS) fluctuation of frequency is calculated from RMS of (4) multiplied by the center
frequency, and finally the phase noise due to temperaturefluctuation can be calculated as follows:L( f ) = 0.5 ∗

f02
Sy ( f )f2(5)

where f 0 is the carrier frequency and f is the offset frequency
from the carrier.
It is clearly observed from this analysis that if the nearcarrier noise of the oscillator is dominated by the temperaturefluctuation of the resonator, the phase noise could be improvedby reducing αt and it should reach a minimum at turnover temperature where TCF is theoretically zero. Moreover, from (3),we can conclude that at higher offset frequencies, the nonzero
heat capacitance acts as a filter and the amount of spectral
density of temperature fluctuations would be small at higher
frequency from the carrier. As a result, we expect the noise

power spectral density due to the temperature fluctuations
to reduce at higher offset frequencies from the carrier, andthe other noise sources to dominate the behavior of phasenoise.
To investigate whether the resonator temperature fluctuations are significant in our oscillator, and to evaluate theaccuracy of this presented model, we proceed to measure thephase noise at different temperatures.
After placing the oscillator in the vacuum chamber, the resonator is gradually heated while the pressure is kept constant.
A current (Iheat er ) is passed through the resonator by acustom-designed current controller circuit shown in Fig. 9.
This circuit is capable of monitoring the resonator temperature
and automatically keeping the resonator temperature at the
turnover temperature, but this feature of the circuit hasn’t beenutilized for this work.
Current (Iheat er ) is then passed through the resonator until
the frequency is maximized (i.e. Tresonat or = Tt o ). The
variations of frequency versus Iheat er . is shown in Fig. 10 andthe turnover temperature appears to be reached for
Iheat er = 80mA.
Phase noise plots are then measured at different currents
and the results for Iheat er = 0-80mA at 20mA intervals areoverlapped in Fig. 11 while the near-carrier portion of thephase noise is highlighted. It is observed that the slope ofphase noise is significantly reduced at offset frequency lessthan 100Hz which is in contrast to the typical phase noise
behavior that demonstrate steeper slope at close-to-carrier
offset. Overall, more than 8dB and 20dB enhancement are
observed in phase noise at10 Hz and 1Hz respectively when
the resonator is operating at around Tt o relative to the room
temperature operation.
In order to validate that the observed improvement ofphase noise is not directly related to the rising temperature
as opposed to correlating with the TCF, the phase noise wasmeasured for currents above 80mA as well. The phase-noise
values at 10Hz offset from the carries are plotted as a functionof Iheat er in Fig. 12. By examining the data, it can be concluded that close-to-carrier phase noise enhances by increasing
the temperature up to Tt o , and the phase noise deteriorates
beyond that. Hence, it is concluded that the thermally-induced
frequency fluctuations are not a negligible source of noise

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MAJD et al.: NEAR-CARRIER PHASE NOISE SUPPRESSION AT TURNOVER TEMPERATURE

Fig. 10. The variation of center frequency versus the current injected throughthe silicon body of the resonator.

5

Fig. 12. Measured phase noise @10Hz carrier offset for different amountof current injected in the resonator.
TABLE II
T HE C OMPARISON OF THE T HERMALLY-I NDUCED F LUCTUATIONS BASEDON THE M EASURED D ATA AND M ODELS D ESCRIBED IN [7]TABLE IIIT HE C OMPARISON OF P HASE N OISE P ERFORMANCE FOR A S ELECTED
G ROUP OF MEMS-BASED O SCILLATOR R EPORTED IN L ITERATURE
Fig. 11. The measured phase noise at different levels of injected current
through the resonator.

for the oscillator in this region, as the effect of this noise
source is measurably suppressed by operation at turnover
temperature.
By extracting the near-carrier phase noise values at room
temperature from Fig. 11 and substituting in (4) (Phase noise@ 1 Hz = −0.1 dBc/Hz), the equivalent RMS value ofthermally-induced fluctuation of frequency can be estimatedand is calculated to be ∼1 Hz @ 1Hz (note: αt is ∼10 ppm
at room temperature derived from Fig. 7).
To compare the thermally-induced fluctuations based on
the measurements with the values predicted by the model
presented in [7] and [13], the thermally-induced fluctuationof frequency is calculated using the resonator and the tether
dimensions are calculated equations (3) and (4).
The comparison between the data extracted from the measurement and the theoretical prediction is shown in table 2 for
1 Hz and 10 Hz carrier offset at room temperature. As evident
from this Table, there exist a large difference between the values extracted from the theoretical model and the hypothetical
thermally-induced fluctuations extracted based on measured
data. As a result, the theories presented before [7], [13], forpredicting the effects of temperature fluctuations on phasenoise appear to not capture the effect of thermally-induced
noise accurately.

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JOURNAL OF MICROELECTROMECHANICAL SYSTEMS

Nevertheless, by examining the data, we can conclude thattemperature fluctuation is appearing to be one of the dominantsources of noise at near-carrier offset frequencies. However,
the exact mechanism through which this source affects thenoise is not fully understood through the existing models.
Finally, to compare the phase noise results reported herewith prior published results, the performance summary ofseveral state-of-the-art MEMS-based oscillators are shown in
Table 3. Since each oscillator in this list is designed for adifferent frequency, the phase noise values are normalized to
10 MHz for ease of comparison.
V. C ONCLUSION
The near-carrier phase noise behavior of a 123MHz quasithickness-Lamé thin-film piezoelectric-on-silicon oscillator
was studied for variable resonator temperature. It was observedthat the close-to-carrier phase noise improves at turnover
temperature, and specifically, the slope of phase noise plot
decreased for the smaller offset frequencies which is incontrast to the expected trends predicting steeper slope. Thisobservation suggests that the effect of temperature fluctuationsin this region is significant. It is believed that the enhancement of the near-carrier phase noise is a result of minimal
frequency variations at turnover temperature. However, it was
illustrated that existing theories do not predict the significanceof temperature fluctuations at near-carrier phase noise formicro-scale silicon resonators such as those studied here andfurther theoretical studies are warranted.
ACKNOWLEDGMENT
The authors would like to thank Yury Oshmyansky andSergey Mishin from Advanced Modular Systems Inc., forproviding the ScAlN films.
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Yasaman Majd (Student Member, IEEE) received
the B.S. degree in electrical and electronics engineering from the Ferdowsi University of Mashhad,
Mashhad, Iran, in 2014, and the M.S. degree in electrical and electronics engineering from the Shahrood
University of Technology, Shahroud, Iran, in 2017.
She is currently pursuing the Ph.D. degree with the
University of Central Florida, Orlando, FL, USA.
From 2018 to 2019, she was a Visiting Researcher
with the Department of Electrical Engineering, West
Virginia University. Her research interests include
ultrastable MEMS oscillators and RFIC design.

Sarah Shahraini (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, and
the Ph.D. degree from the School of Electricaland Computer Engineering, University of Central
Florida, FL, USA, in 2019.
She joined Intel after her graduation, where she
is currently working as a Research Scientist. Her
research interests include microelectromechanicalsystems with a special focus on design, fabrication,and characterization of microresonators for stable oscillator, filter, and sensor
applications. She was a recipient of the Best Student Paper Award at the2018 IEEE International Frequency Control Symposium.

Garett Goodale (Student Member, IEEE) received
the B.S. degree in electrical and computer engineering from the University of Central Florida,
in May 2020. He is currently pursuing the master’s
degree in electrical engineering.
From 2017 to 2018, he worked as a Student Internat the Advanced Manufacturing Technologies Group,
Lockheed Martin. In Summer 2019, he interned
at Sandia National Laboratories in the Robotics
Division before joining the Dynamic Microsystem
Laboratory, UCF, as an Undergraduate Research
Assistant. His research interests include ultrastable ovenized MEMS oscillators and low-power MEMS sensors.

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MAJD et al.: NEAR-CARRIER PHASE NOISE SUPPRESSION AT TURNOVER TEMPERATURE

Heather Hofstee (Graduate Student Member, IEEE)
received the bachelor’s degree in electrical engineering from the University of Central Florida, Orlando,
FL, USA, in 2019. She is currently a Manufacturing
Process Engineer with Texas Instruments, Dallas,
TX, USA.

Hossein Miri Lavasani (Senior Member, IEEE)
received the B.S. degree in electrical engineeringfrom the Sharif University of Technology, Tehran,Iran, the M.S. degree from Arizona State University,
Tempe, and the Ph.D. degree from the Georgia
Institute of Technology, Atlanta, in 2001, 2003, and2010, respectively. From 2003 to 2004, he was an IC
Design Engineer with the Medtronic Microelectronics Center, Phoenix, working on the development oflogic and mixed-signal circuits for microcontroller
units used in pacemakers. From 2010 to 2019,he was with Broadcom Corporation (formerly Avago Technologies Inc.)and Qualcomm, where he worked on high-speed analog circuits for fiber
optic transceivers and multimode radio transceiver circuits for connectivity
applications. Since 2019, he has been an Assistant Professor with Case Western Reserve University, conducting research on high-speed analog andlow-power smart RF circuits for the IoT applications and interface circuits for
microsystems.

7

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 articles and conference papers in his
field of expertise. He also holds 12 U.S. patents. His research interests include
the general 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. He was a recipient of the National Aeronautics and Space
Administration Patent Application Award in 2009.

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