A 27 MHZ TEMPERATURE COMPENSATED MEMS OSCILLATOR
WITH SUB-PPM INSTABILITY
Roozbeh Tabrizian, Mauricio Pardo and Farrokh Ayazi
Georgia Institute of Technology, Atlanta, Georgia, USA
ABSTRACT
MEMS RESONATOR
This paper reports on the design, implementation and
characterization of a low phase-noise 27 MHz MEMS
oscillator with sub-ppm temperature instability based on a
high-Q composite bulk acoustic wave (BAW) resonator.
An array of silicon dioxide (SiO2) pillars has been
uniformly embedded in the body of a piezoelectrically
transduced silicon resonator to compensate its negative
temperature coefficient of frequency (TCF). Using this
technique, an overall frequency drift of 83 ppm is
achieved for the resonator over the temperature range of
20°C to 100°C while resonator Q remains greater than
7,500 in atmospheric pressure. An electronically
compensated oscillator using this resonator exhibits
sub-ppm temperature instability with a consistent phase
noise (PN) behavior over the entire temperature range and
a value of -101dBc/Hz at 1 kHz offset-frequency.
Long-term stability measurement has been carried out for
both temperature-compensated resonator and oscillator in
an environmental chamber to study their stability
over time.
The aluminum-nitride-on-silicon (AlN-on-Si) BAW
resonator with embedded array of SiO2 pillars is
schematically shown in Fig. 1. The AlN thin film
sandwiched between molybdenum (Mo) electrodes is
used for excitation and sensing of the 1st longitudinal
extensional (LE) mode in the resonator via the
piezoelectric transduction; as such, these devices do not
require a DC electric field for operation which makes
them substantially immune to dielectric charging effect
that can cause drift in capacitive Si/SiO2 composite
resonators [6]. Furthermore, small motional resistances
achieved from the large electromechanical coupling of
AlN piezoelectric transduction alleviates the requirement
of high gain for oscillator sustaining circuitry and
therefore reduces power consumption.
INTRODUCTION
Typical silicon resonators exhibit a native TCF of
around 30 ppm/°C, which translates to an overall drift of
~3750 ppm over the temperature range of 40°C to 85°C,
making electronic temperature compensation challenging,
especially where sub–ppm instability is required.
Figure 1: a) Temperature compensated BAW resonator
with embedded array of SiO2 pillars and AlN piezoelectric
transduction; b) AA’ cross section.
Several passive temperature compensation techniques
have been reported for silicon resonators [1-5]. One
approach is based on the addition of a material with
positive temperature coefficient of Young’s modulus
(TCE), such as SiO2, in parallel layers with the stack to
create a composite resonator with reduced overall TCF.
However, due to fabrication limitations, full TCF
compensation using this technique has been limited to
thin substrates and lower frequency resonators [1].
Resonator Design for Temperature Compensation
The temperature sensitivity of the resonance
frequency in BAW resonators is mainly due to the finite
temperature coefficients of the Young’s modulus (TCE(n))
of the resonator material:
=
In this paper, we utilize a compensation technique for
laterally-vibrating silicon BAW resonators using an
embedded array of SiO2 pillars [1]. By uniformly
distributing pillars inside the resonator body, pure bulk
modes can be excited without degradation of resonator
parameters. Being applicable to thick silicon substrates,
this method realizes full compensation of the linear
temperature-induced frequency drift of BAW devices that
exhibit high Q in air with superior power handling.
Therefore, this compensation technique enables the
implementation of reference oscillators with excellent PN
performance across a wide temperature range.
The small residual frequency drift of these resonators,
resulted from the higher-order temperature coefficients,
can be further cancelled out using low power analog
electronic techniques to achieve sub-ppm temperature
instability over the entire temperature range.
978-1-4673-0325-5/12/$31.00 ©2012 IEEE
1+
( )
(1)
Here, ET is the Young’s modulus at the temperature T
(°C). Since TCE(1) of silicon and silicon dioxide have
values of the opposite signs [7], a proper composition of
Si and SiO2 can be used to fully compensate the linear
temperature dependence of the resonance frequency.
For this purpose, an array of SiO2 pillars is embedded
in the silicon body of the resonator. The required amount
for full compensation of TCE(1) has been calculated
through analytical derivations and FEM simulations [1].
The distribution of the SiO2 pillars in the resonator
body has been chosen to be as uniform as possible to
enable the excitation of the LE modes in the BAW
resonator.
Figure 2 shows the displacement and stress field for
the pure 1st LE mode of the composite resonator with
embedded array of SiO2 pillars with uniform distribution.
23
MEMS 2012, Paris, FRANCE, 29 January - 2 February 2012
Fabrication Process
To fabricate the composite resonators, trenches with
slightly tapered sidewalls are first etched into a silicon
wafer for desired depth (i.e. 20um). This is followed by
the conformal deposition of LPCVD TEOS at 850 °C,
partially filling trenches and covering the top surface of
the wafer. The substrate is then annealed at 1050°C for
two hours to densify TEOS and improve surface
roughness. Since a nearly smooth surface is required for
the deposition of Mo electrodes and high-quality AlN, the
top SiO2 layer thinned down by wet etching in HF to
improve surface smoothness. The rest of the fabrication
process is similar to the one reported in [5] with some
minor modifications. Figure 4 shows an SEM picture of a
fabricated temperature-stable 27MHz resonator with
uniformly distributed embedded array of SiO2 pillars.
Figure 2: Simulated 1st LE (a) mode shape and (b) stress
field of AlN-on-Si BAW resonator with embedded array
of SiO2 pillars.
For the 1st LE mode, the resonance frequency can be
calculated from:
(2)
where W is the width (frequency defining dimension) of
the resonator and Eeq and eq are the equivalent Young’s
modulus and density of the composite structure.
Considering (2), the full compensation of the TCE(1) of
silicon using silicon dioxide results in a quadratic
temperature-frequency characteristic for the compensated
resonator due to higher order TCE(n) (n>1).
Since in the temperature range of interest (-40°C to
85°C) the effect of TCE(2) in the frequency drift is much
smaller compared to TCE(1) [7], the composite resonator
shows ~45 reduction in the overall frequency drift in this
range. Furthermore, the resulting parabolic temperaturefrequency characteristic provides a local-zero-TCF
| < ) where the resonance
operation region (|
frequency is insensitive to temperature variations (i.e.
lim
( ) = 0). Figure 2 compares temperature
dependence of the equivalent Young’s modulus of the
composite resonator with silicon and silicon dioxide.
Figure 4: (a) SEM image of AlN-on-Si BAW resonator
with embedded array of SiO2 pillars; (b) close-up view of
SiO2 pillars in the body of the resonator.
Resonator Characterization
Figure 5 shows the frequency response of the
temperature compensated composite resonator.
Figure 3: Qualitative comparison of the temperature
dependency of Young’s modulus for Si, SiO2 and their
composition (not to scale the quantities); equations for Si
and SiO2 extracted from [2] and [7].
Figure 5: Frequency response of the temperature
compensated resonator in Fig. 4; inset shows the spurious
free response in a large frequency span.
24
A Q of 7,600 has been achieved in air with the
insertion loss of ~15 dB. The device shows a spuriousfree frequency response within a 10MHz span around the
resonance frequency.
Figure 6 shows the temperature characteristic of the
device.
maximize the available tuning range, electronic
cancellation of these shunt capacitances is achieved by
using active inductors to resonate out the shunt parasitic
capacitances. For this purpose, high-Q tunable active
inductors are implemented on-chip to provide the specific
value of the emulated inductor required for parasitic
compensation.
Selectable on-chip capacitor-banks in addition to a
phase-shifter have been placed in the feedback loop to
provide required electronic tuning of the resonance
frequency at the operating temperature.
Figure 8 shows the system block diagram for the
compensated MEMS oscillator.
Figure 6: Temperature characteristic of the resonance
frequency and Q of the resonator in Fig. 4; local-TCF is
approximately zero at 40°C.
A frequency drift of 83 ppm has been achieved over
the temperature range of 20°C to 100°C with parabolic
temperature-frequency characteristic.
The composite
temperature-stable resonator has a consistent Q higher
than 7,500 over the entire temperature range.
A long term frequency measurement has been
performed on these devices at an elevated temperature of
100°C in vacuum to investigate the instability of their
resonance frequency over time. A small frequency
variation of 2.4 ppm over a period of 50 days of operation
(Fig. 7) has been observed, which is attributed to the low
accuracy of the temperature control unit of the vacuum
probe station ( 1°C) and finite local TCF of the device at
100°C (~3ppm/°C).
Figure 8: The system block diagram for the 27 MHz
temperature-compensated MEMS oscillator.
A TIA-based sustaining amplifier is used to reduce
the input referred noise [8], and to minimize the loading
of the resonant device. The inverter-based TIA offers
about 100dB gain and embeds the phase-shifter for
tuning.
The switched scheme of the capacitor banks provides
about 60ppm of tuning (in discrete steps of 15ppm/step)
while the TIA phase-shifter provides 60ppm of
continuous tuning with high precision.
Oscillator Characterization
Figure 9 shows the PN performance measured for 6
temperature points.
Figure 7: Steady-state stability measurement for passively
temperature-compensated resonator.
TUNABLE MEMS OSCILLATOR
Oscillator Design
Electronic tuning can be used to further reduce the
thermal drift of the MEMS oscillator. The main challenge
in using circuit techniques for this task is the presence of
large parasitic shunt capacitances in the device, resulted
from large dielectric constant of AlN and extended Mo
pads required for efficient transduction. These shunt
capacitances considerably limit the frequency pulling
range and hence the electronic tuning efficiency. To
Figure 9: Phase noise performance of temperature
compensated oscillator at 6 temperature points showing
consistent behavior over the temperature range.
25
A PN of -101dBc/Hz at 1 kHz offset-frequency with
consistent behavior across the entire temperature range is
measured for the temperature-compensated MEMS
oscillator. This is the lowest reported PN to date for any
temperature compensated MEMS oscillator with sub-ppm
temperature instability.
Figure 10 shows the result of stability measurement
for the oscillator operating in air, which has been carried
out in a chamber with temperature-control accuracy of
0.3°C at 6 different temperature points after applying
required tuning to operate at a constant frequency with an
accuracy of 0.1 Hz (< 4ppb). This accuracy is provided
by fine frequency tuning available from phase shifter and
is limited by the resolution of frequency measurement
setup (Agilent 53181A). Interestingly, the stability result
at 40°C, which corresponds to the local-zero-TCF region
of the resonator, shows a variation of less than 100ppb.
temperature instability level over the entire temperature
range of -20°C to 80°C. Furthermore, the stability result at
40°C, which corresponds to the local-zero-TCF region of
the resonator, shows a variation of less than 100 ppb. A
PN of -101dBc/Hz at 1 kHz offset-frequency with
consistent behavior across the entire temperature range is
measured for the oscillator which is the lowest reported
phase noise to date for any temperature compensated
MEMS oscillator with sub-ppm temperature instability.
ACKNOWLEDGEMENTS
This work has been supported by the Integrated
Device Technology (IDT), Inc. The authors would like to
thank the OEM Group for AlN thin film deposition.
REFERENCES
[1] R. Tabrizian, G. Casinovi and F. Ayazi,
"Temperature-Stable
High-Q
AlN-on-Silicon
Resonators with Embedded Array of Oxide Pillars,"
Solid-State Sensors, Actuators, and Microsystems
Workshop (Hilton Head 2010), June 2010, pp. 100101.
[2] R. Melamud, et al, "Temperature Insensitive
Composite Micromechanical Resonators," Journal of
Microelectromechanical Systems, Vol. 18, No. 6, pp.
1409-1419, 2009.
[3] A.K. Samarao, G. Casinovi, and F. Ayazi, “Passive
TCF
Compensation
in
High
Q
Silicon
Micromechanical Resonators,” IEEE International
Conference on Micro Electro Mechanical Systems
(MEMS 2010), Hong Kong, Jan. 2010, pp. 116-119.
[4] A.K. Samarao and F. Ayazi, “Temperature
Compensation
of
Silicon
Micromechanical
Resonators via Degenerate Doping,” IEEE
International Electron Devices Meeting (IEDM
2009), Baltimore, MD, Dec. 2009, pp. 789-792.
[5] W. Pan and F. Ayazi, “Thin-Film Piezoelectric-onSubstrate Resonators with Q Enhancement and TCF
Reduction,” IEEE International Conference on Micro
Electro Mechanical Systems (MEMS 2010), Hong
Kong, Jan. 2010, pp. 104-107.
[6] G. Bahl et al, “Observation of fixed and mobile
charge in composite MEMS resonators”, Solid-State
Sensors, Actuators, and Microsystems Workshop,
Hilton Head 2008, Hilton Head, SC, USA, pp 102105.
[7] H. J. McSkimin, “Measurement of elastic constants at
low temperatures by means of ultrasonic waves—
Data for silicon and germanium single crystals, and
for fused silica,” J. Appl. Phys., vol. 24, no. 8, pp.
988–997, Aug. 1953.
[8] H.M. Lavasani, W. Pan, F. Ayazi, "An electronically
temperature-compensated 427MHz low phase-noise
AlN-on-Si
micromechanical
reference
oscillator," 2010 IEEE Radio Frequency Integrated
Circuits Symposium (RFIC), pp.329-332, 2010.
Figure 10: Steady-state stability measurement for fullycompensated oscillator after applying active tuning to
operate at f0 0.1 Hz (a) at 6 temperature points; (b) at
40°C.
CONCLUSION
A uniformly distributed array of SiO2 pillars have
been embedded in the silicon body of an AlN-on-Si
resonator to fully compensate the linear term of
temperature dependency of the resonance frequency
without degradation of resonator parameters. A quadratic
temperature characteristic resulted from smaller higher
order temperature coefficients of Young’s modulus shows
an overall drift of 83 ppm over the temperature range of
-20°C to 100°C which is ~45 smaller compared to
uncompensated silicon resonators. An oscillator
implemented using these temperature-compensated
composite resonators employs active tuning mechanisms
to cancel out the residual frequency drift of the MEMS
device to an accuracy of <4ppb, while showing sub-ppm
CONTACT
*R. Tabrizian, tel: +1-404-259-7322; roozbeh@gatech.com
26