ee 247b/me 218: introduction to mems design lecture …ee247b/sp17/lectures/lec11m1... · lecture...
Post on 12-Jun-2018
224 Views
Preview:
TRANSCRIPT
1
EE 247B/ME 218: Introduction to MEMS DesignLecture 11m1: Mechanics of Materials
CTN 2/21/17
Copyright © 2017 Regents of the University of California
EE C245: Introduction to MEMS Design LecM 7 C. Nguyen 9/28/07 21
MEMS Material Properties
EE C245: Introduction to MEMS Design LecM 7 C. Nguyen 9/28/07 22
Material Properties for MEMS
[Mark Spearing, MIT]
√(E/) is acoustic velocity
EE C245: Introduction to MEMS Design LecM 7 C. Nguyen 9/28/07 23
Young’s Modulus Versus Density
[Ashby, Mechanics of Materials,
Pergamon, 1992]
Lines of constant acoustic velocity
EE C245: Introduction to MEMS Design LecM 7 C. Nguyen 9/28/07 24
Yield Strength
• Definition: the stress at which a material experiences significant plastic deformation (defined at 0.2% offset pt.)
• Below the yield point: material deforms elastically returns to its original shape when the applied stress is removed
• Beyond the yield point: some fraction of the deformation is permanent and non-reversible
True Elastic Limit: lowest stress at which dislocations move
Proportionality Limit: point at which curve goes nonlinear
Elastic Limit: stress at which permanent deformation begins
Yield Strength: defined at 0.2% offset pt.
2
EE 247B/ME 218: Introduction to MEMS DesignLecture 11m1: Mechanics of Materials
CTN 2/21/17
Copyright © 2017 Regents of the University of California
EE C245: Introduction to MEMS Design LecM 7 C. Nguyen 9/28/07 25
Yield Strength (cont.)
• Below: typical stress vs. strain curves for brittle (e.g., Si) and ductile (e.g. steel) materials
Stress
Tensile Strength
Fracture
Ductile (Mild Steel)
Brittle (Si)
Proportional Limit
Strain
[Maluf]
(Si @ T=30oC)
(or Si @ T>900oC)
EE C245: Introduction to MEMS Design LecM 7 C. Nguyen 9/28/07 26
Young’s Modulus and Useful Strength
EE C245: Introduction to MEMS Design LecM 7 C. Nguyen 9/28/07 27
Young’s Modulus Versus Strength
[Ashby, Mechanics of Materials,
Pergamon, 1992]
Lines of constant maximum strain
EE C245: Introduction to MEMS Design LecM 7 C. Nguyen 9/28/07 28
Quality Factor (or Q)
3
EE 247B/ME 218: Introduction to MEMS DesignLecture 11m1: Mechanics of Materials
CTN 2/21/17
Copyright © 2017 Regents of the University of California
EE C245: Introduction to MEMS Design LecM 7 C. Nguyen 9/28/07 29
Lr hWr
VPvi
Clamped-Clamped Beam Resonator
Smaller mass higher freq. range and lower series Rx
Smaller mass higher freq. range and lower series Rx(e.g., mr = 10-13 kg)(e.g., mr = 10-13 kg)
Young’s Modulus
Density
Mass
Stiffness
ivoi
203.1
2
1
rr
ro
L
hE
m
kf
Frequency:
Q ~10,000
vi
Resonator Beam
Electrode
VP
C(t)
dt
dCVi Po
Note: If VP = 0V device off
Note: If VP = 0V device off
io
EE C245: Introduction to MEMS Design LecM 7 C. Nguyen 9/28/07 30
Quality Factor (or Q)
•Measure of the frequency selectivity of a tuned circuit
• Definition:
• Example: series LCR circuit
• Example: parallel LCR circuit
dB3CyclePer Lost Energy
CyclePer Energy Total
BW
fQ o
CRR
L
Z
ZQ
o
o
1
Re
Im
LGG
C
Y
YQ
o
o
1
Re
Im
BW-3dB
fo f
EE C245: Introduction to MEMS Design LecM 7 C. Nguyen 9/28/07 31
Selective Low-Loss Filters: Need Q
• In resonator-based filters: high tank Q low insertion loss
• At right: a 0.1% bandwidth, 3-res filter @ 1 GHz (simulated)
heavy insertion loss for resonator Q < 10,000 -40
-35
-30
-25
-20
-15
-10
-5
0
998 999 1000 1001 1002
Frequency [MHz]
Tra
nsm
issi
on
[d
B]
Tank Q30,00020,00010,0005,0004,000
Increasing Insertion
Loss
EE C245: Introduction to MEMS Design LecM 7 C. Nguyen 9/28/07 32
•Main Function: provide a stable output frequency
• Difficulty: superposed noise degrades frequency stability
ivoi
A
Frequency-SelectiveTank
SustainingAmplifier
ov
Ideal Sinusoid:
tofVotov 2sin
Real Sinusoid:
ttoftVotov 2sin
=2/TO
TO
Zero-Crossing Point
Tighter SpectrumTighter Spectrum
Oscillator: Need for High Q
Higher QHigher Q
4
EE 247B/ME 218: Introduction to MEMS DesignLecture 11m1: Mechanics of Materials
CTN 2/21/17
Copyright © 2017 Regents of the University of California
EE C245: Introduction to MEMS Design LecM 7 C. Nguyen 9/28/07 33
• Problem: IC’s cannot achieve Q’s in the thousandstransistors consume too much power to get Qon-chip spiral inductors Q’s no higher than ~10off-chip inductors Q’s in the range of 100’s
•Observation: vibrating mechanical resonances Q > 1,000
• Example: quartz crystal resonators (e.g., in wristwatches)extremely high Q’s ~ 10,000 or higher (Q ~ 106 possible)mechanically vibrates at a distinct frequency in a
thickness-shear mode
Attaining High Q
EE C245: Introduction to MEMS Design LecM 7 C. Nguyen 9/28/07 34
Energy Dissipation and Resonator Q
supportviscousTEDdefects QQQQQ
11111
Anchor LossesAnchor Losses
Material Defect Losses
Material Defect Losses Gas DampingGas Damping
Thermoelastic Damping (TED)Thermoelastic Damping (TED)
Bending CC-Beam
Compression Hot Spot
Tension Cold Spot Heat Flux(TED Loss)
Elastic Wave Radiation(Anchor Loss)
At high frequency, this is our big problem!
At high frequency, this is our big problem!
EE C245: Introduction to MEMS Design LecM 7 C. Nguyen 9/28/07 35
Thermoelastic Damping (TED)
•Occurs when heat moves from compressed parts to tensioned parts heat flux = energy loss
QfT
2
1)()(
pC
TET
4)(
2
222)(
ff
fff
TED
TEDo
22 hC
Kf
pTED
Bending CC-Beam
Compression Hot Spot
Tension Cold Spot Heat Flux(TED Loss)
= thermoelastic damping factor = thermal expansion coefficientT = beam temperatureE = elastic modulus = material densityCp = heat capacity at const. pressureK = thermal conductivityf = beam frequencyh = beam thicknessfTED = characteristic TED frequency
h
EE C245: Introduction to MEMS Design LecM 7 C. Nguyen 9/28/07 36
TED Characteristic Frequency
• Governed byResonator dimensionsMaterial properties
22 hC
Kf
pTED
= material densityCp = heat capacity at const. pressureK = thermal conductivityh = beam thicknessfTED = characteristic TED frequency
Critical Damping F
acto
r,
Relative Frequency, f/fTED
Q
[from Roszhart, Hilton Head 1990]
Peak where Q is minimizedPeak where Q is minimized
5
EE 247B/ME 218: Introduction to MEMS DesignLecture 11m1: Mechanics of Materials
CTN 2/21/17
Copyright © 2017 Regents of the University of California
EE C245: Introduction to MEMS Design LecM 7 C. Nguyen 9/28/07 37
Q vs. Temperature
Quartz Crystal Aluminum Vibrating Resonator
Q ~5,000,000 at 30K
Q ~5,000,000 at 30K
Q ~300,000,000 at 4KQ ~300,000,000 at 4K
Q ~500,000 at 30K
Q ~500,000 at 30K
Q ~1,250,000 at 4KQ ~1,250,000 at 4K
Even aluminum achieves exceptional Q’s at
cryogenic temperatures
Even aluminum achieves exceptional Q’s at
cryogenic temperatures
Mechanism for Q increase with decreasing temperature thought to be linked to less hysteretic motion of material defects
less energy loss per cycle
Mechanism for Q increase with decreasing temperature thought to be linked to less hysteretic motion of material defects
less energy loss per cycle
[from Braginsky, Systems With
Small Dissipation]
EE C245: Introduction to MEMS Design LecM 7 C. Nguyen 9/28/07 38
Output
Input
Input
Output
Support Beams
Wine Glass Disk Resonator
R = 32 m
Anchor
Anchor
Resonator Data
R = 32 m, h = 3 m
d = 80 nm, Vp = 3 V
Resonator Data
R = 32 m, h = 3 m
d = 80 nm, Vp = 3 V
-100
-80
-60
-40
61.325 61.375 61.425
fo = 61.37 MHzQ = 145,780
Frequency [MHz]
Un
matc
hed
Tra
nsm
issio
n [
dB
]
Polysilicon Wine-Glass Disk Resonator
[Y.-W. Lin, Nguyen, JSSC Dec. 04]
Compound Mode (2,1)
EE C245: Introduction to MEMS Design LecM 7 C. Nguyen 9/28/07 39
-100
-98
-96
-94
-92
-90
-88
-86
-84
1507.4 1507.6 1507.8 1508 1508.2
1.51-GHz, Q=11,555 NanocrystallineDiamond Disk Mechanical Resonator
• Impedance-mismatched stem for reduced anchor dissipation
•Operated in the 2nd radial-contour mode
•Q ~11,555 (vacuum); Q ~10,100 (air)
• Below: 20 m diameter disk
PolysiliconElectrode R
Polysilicon Stem(Impedance Mismatched
to Diamond Disk)
GroundPlane
CVD DiamondMechanical Disk
Resonator Frequency [MHz]
Mix
ed
Am
plitu
de [
dB
]
Design/Performance:
R=10m, t=2.2m, d=800Å, VP=7Vfo=1.51 GHz (2nd mode), Q=11,555
fo = 1.51 GHzQ = 11,555 (vac)Q = 10,100 (air)
[Wang, Butler, Nguyen MEMS’04]
Q = 10,100 (air)
EE C245: Introduction to MEMS Design LecM 7 C. Nguyen 9/28/07 40
Disk Resonator Loss Mechanisms
Disk Stem
Nodal Axis
Strain Energy Flow No motion along
the nodal axis, but motion along the finite width
of the stem
No motion along the nodal axis,
but motion along the finite width
of the stem
Stem Height/4 helps
reduce loss, but not perfect
/4 helps reduce loss,
but not perfect
Substrate Loss Thru Anchors
Substrate Loss Thru Anchors
Gas Damping
Gas Damping
Substrate
Hysteretic Motion of
Defect
Hysteretic Motion of
Defect
e-
Electronic Carrier Drift Loss
Electronic Carrier Drift Loss
(Not Dominant in Vacuum)
(Dwarfed By Substrate Loss)
(Dwarfed By Substrate Loss)
(Dominates)
6
EE 247B/ME 218: Introduction to MEMS DesignLecture 11m1: Mechanics of Materials
CTN 2/21/17
Copyright © 2017 Regents of the University of California
EE C245: Introduction to MEMS Design LecM 7 C. Nguyen 9/28/07 41
MEMS Material Property Test Structures
EE C245: Introduction to MEMS Design LecM 7 C. Nguyen 9/28/07 42
Stress Measurement Via Wafer Curvature
• Compressively stressed film bends a wafer into a convex shape
• Tensile stressed film bends a wafer into a concave shape
• Can optically measure the deflection of the wafer before and after the film is deposited
• Determine the radius of curvature R, then apply:
Rt
hE
6
2
= film stress [Pa]E′ = E/(1-) = biaxial elastic modulus [Pa]h = substrate thickness [m]t = film thicknessR = substrate radius of curvature [m]
Si-substrate
Laser
Detector
Mirror
xScan the mirror
x
Slope = 1/R
h
t
R
EE C245: Introduction to MEMS Design LecM 7 C. Nguyen 9/28/07 43
MEMS Stress Test Structure
• Simple Approach: use a clamped-clamped beamCompressive stress causes
bucklingArrays with increasing length
are used to determine the critical buckling load, where
Limitation: Only compressive stress is measurable
2
22
3 L
Ehcritical
E = Young’s modulus [Pa]I = (1/12)Wh3 = moment of inertiaL, W, h indicated in the figure
L
W
h = thickness
EE C245: Introduction to MEMS Design LecM 7 C. Nguyen 9/28/07 44
More Effective Stress Diagnostic
• Single structure measures both compressive and tensile stress
• Expansion or contraction of test beam deflection of pointer
• Vernier movement indicates type and magnitude of stress
Expansion Compression
Contraction Tensile
7
EE 247B/ME 218: Introduction to MEMS DesignLecture 11m1: Mechanics of Materials
CTN 2/21/17
Copyright © 2017 Regents of the University of California
EE C245: Introduction to MEMS Design LecM 7 C. Nguyen 9/28/07 45
Output
Input
Input
Output
Support Beams
Wine Glass Disk Resonator
R = 32 m
Anchor
Anchor
Resonator Data
R = 32 m, h = 3 m
d = 80 nm, Vp = 3 V
Resonator Data
R = 32 m, h = 3 m
d = 80 nm, Vp = 3 V
-100
-80
-60
-40
61.325 61.375 61.425
fo = 61.37 MHzQ = 145,780
Frequency [MHz]
Un
matc
hed
Tra
nsm
issio
n [
dB
]
Q Measurement Using Resonators
[Y.-W. Lin, Nguyen, JSSC Dec. 04]
Compound Mode (2,1)
top related