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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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