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8/7/2019 Main paper presentation
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EngineeringMEMS Resonators with
Low Thermoelastic Damping
Temperature-dependent
internal friction in siliconnanoelectromechanical systems
AdviserProf. Li, Wang Long
SpeakersHwang, Chih-Jay Q26971037
Chen, Po-Wei Q26974093
Li, Wen Rong Q26971061
Nguyen, Huu Nghia Q28977013
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IntroductionIntroduction
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To identify the thermal modes that contribute most to damping,and illustrates how this information may be used to design deviceswith higher quality factors.
We calculate damping in typical micromechanical resonator
structures using Comsol Multiphysics
We compare the results with experimental data reported inliterature for these devices..
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Micromechanical resonators are used in a wide variety of
applications, including inertial sensing, chemical and biological
sensing, acoustic sensing, and microwave transceivers.
The resonators Quality factor(Q), which describes the mechanical
energy damping.
In all applications, it is important to have design control over this
parameter, and in most cases, it is invaluable to minimize the
damping.
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Zener developed general expressions for thermoelastic damping in
vibrating structures, with the specific case study of a beam in its
fundamental flexural mode.
Zener calculated the thermoelastic Q of an isotropic homogenous
resonator to be:
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Zener made in assuming only thermal gradients in one direction
along the beam were significant does not capture the most
important thermal mode, even for a simple beam.
In addition, past efforts to estimate Q without explicitly
calculating the weighting functions have greatly overestimated thedamping behavior of real systems.
We describe a method for using full numerical solutions to
evaluate Q using Zeners approach.
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The imaginary component represents the mechanical vibration
frequency, while the real part provides the rate of decay for an
unforced vibration due to the thermal coupling.
The quality factor of the resonator is defined as
The eigenvalues, i, are complex.
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In some cases, the experimental data appears to have achieved the
thermoelastic limit. For these devices, it is clear that structural
modifications that can engineer a higher thermoelastic limit are
warranted.
In devices where the measured Q value is less than half the
thermoelastic limit, investigation into and minimization of other
damping mechanisms is warranted.
This remarkable correlation between simulation results andexperiments suggests that the flexural beam Q is limited by
thermoelastic damping.
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Experiment
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Resonator Parameters
Resonator Cases
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Results andconclusionResults andconclusion
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We find that the TED Q is two orders higherthan the measured Q.
This suggests that thermoelastic damping, for the fundamental
longitudinal mode, is not a significant contributor to the overall
energy loss in this resonator.
A paddle resonator operating in its torsional resonance wassimulated. The simulated resonant frequency was about 20% lower
than the measured torsional frequency.
The simulated result is consistent with the physical understandingthat torsional deformations produce little or no volumetric expansion
and should therefore have negligible thermoelastic damping.
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Generalized Hookes law for
linear isotropic elastic solids
x = ( ex + ey + ez )+2ex
x = ( ex + ey + ez )+2ey
x = ( ex + ey + ez )+2ez
xy = 2exy
yz = 2eyz
zx = 2ezx
: Lame` constant
: shear modulus
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Thermal strain
T = (T)
: cofficient of thermal expansion
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Force balance
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3-Dequation of motion
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Fouriers law
Entropy
Combine differential fouriers law and entropy
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ReferenceReference
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Amy Duwel, Tob N. Candler, Thomas W. Kenny, and MathewVarghese, Engineering MEMS Resonators With Low
Thermoelastic Damping, Journal of Miroelectromechanical
Systems, Vol. 15, NO. 6, Dec 2006.
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IntroductionIntroduction
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The understanding and control ofcomposition, nanostructure, andinterface properties are important for the development ofnanostructured materials.
High-frequency mechanical resonators presenting high quality
factors are of interest for the development of sensitive forcedetecting devices.
Quality factor of resonant micromechanical devices decreasessteadily with device dimension.
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Defect motion is governed by an activation energy that
will induce Debye relaxation peaks in the temperature
dependence of internal friction.
Debye relaxation is the dielectric relaxation response ofan ideal, non-interacting population of dipoles to an
alternating external electric field. It is usually expressed
in the complex permittivity of a medium as a function of
the field's frequency :
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Fabrication and electrostatic operation of
nanomechanical beams as thin as 30 nm and frequencies
as high as 380 MHz.
Dynamical modeling and characterization ofpaddleoscillators operating in the 110 MHz range.
Reporting the temperature dependent behavior of these
paddle oscillators and observing Debye internal frictionpeaks in the T=160190Krange.
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ExperimentalApproach
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Using electron beam lithography on silicon-on-insulator (SOI)
wafers consisting of a 400-nm-thick oxide buried underneath 200nm of single crystal silicon.
pumped down to the 10-5 Torr range.
The cold finger allows temperature access and control over the T=4300K
range.
The quality factor (Q) is closely approximated from the width of
the resonance peaks using the relation
f0 is the center of the resonance response, and fFWHM is its full
width half maximum.
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Nanofabricated paddle oscillator
d=5.5 mm, w=2 mm, L=2.5 mm, b=175 nm, a=200 nm, h=400 nm
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Identifying two modes of oscillation attributed to theflexural and torsional motion of the supporting beams.
These modes are sufficiently decoupled to allow their
independent excitation by the application of the
appropriate actuation frequency.
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Temperature dependence of the two resonant
frequencies of a metallized device
The frequency steadily
increases as the temperature
decreases to T=80K, at whichpoint an inflection of the slope
is observed. Overall increases
in resonant frequency of6.5%,
and 1.5% are observed at the
lowest temperature for the
flexural and torsional modes.
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Temperature dependence of the internal friction for the two
modes of motion of a metallized and nonmetallized device
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Within the precision of our measurement, all four sets of data
show a peak structure centered at T=160180 K.
The existence of this peak in both metallized and nometallized
devices suggests that the metal overlayer is not responsible for this
loss.
The reduction of the sloped dissipation background in the
nonmetallized device suggests that metal film monotonically
contributes to the total internal friction in that temperature range.
This contribution could possibly peak at much higher temperatures,
as expected from bulk polycrystalline metals.
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A similar peak has been observed at T=135K in larger kilohertz
range microcantilevers, and has been attributed to surface or near-surface related phenomena such as damage or presence of oxide.
The peaks observed in our megahertz-range devices could
potentially be related to similar phenomena, as a shift fromT=120 140K at 210 kHz to T=160 180K at 57 MHz would be
consistent with a Debye relaxation behavior dictated by an
activation energy ofEa=0.25 0.5 eV.
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Results andconclusionResults andconclusion
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The characterization of both modes of motion of these single-stage
paddles consistently suggested a material 50% softer than
expected from bulk silicon.
A temperature dependent frequency shift has been observed.
Low-temperature studies of internal friction at 57 MHz have also
revealed a double peak centered in the T=160 180K range that
would be consistent with the activation energies expected from
near-surface phenomena previously reported in larger devices.
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A thorough understanding of the various extrinsic, intrinsic, and
fundamental processes leading to internal losses at such scales. Itwill enhance the quality of such RF structures.
Previous description allows the development of high-qualityresonators for technological applications, and provide access tofundamental studies of surface effects and mesoscopic internalfriction.
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Select multi-physics modes
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Import object (.sat)
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Import constant
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Subdomain setting Solid, Stress-strain
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boundary setting Solid, Stress-strain
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Subdomain setting Heat Transfer by Conduction
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Boundary setting Heat Transfer by Conduction
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Solver Parameters setting
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Solver
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Calculate Q (Quality factor)
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Quality factor (Q)
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FinalConclu
sionFin
alConclu
sion
Designing the micromechanical resonators we need to calculatequality factor Q that describes the mechanical energy damping andplay an impotant role in the structure.
By using Zener formular (reference 1) and experimence thedependence between temperature, resonant frequency and inertialloss (reference 2) we can easily get Q value and compare the valuebetween calculation and experimence.
The result for the case Torsional 3D we solved with the value
Q = 2e8 simulating by Comsol Multiphysics that is fixed withmeasured value at simulated frequency 4.4 MHz.
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So we can solve the fully coupled thermoelastic dynamcs to obtain
exact expressions for Q in an arbitrary resonator with Comsol
Multiphysic.
With this reason, designing a micromechanical resonator is more
simple by simulating and calculating for exact results.
FinalConclu
sionFin
alConclu
sion
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