3.155J/6.152J Lecture 13: MEMS Lab Testing
Prof. Martin A. Schmidt
Massachusetts Institute of Technology
10/31/2005
Outline
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Review of the Process and Testing
Mechanics
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„
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Cantilever
Fixed-Fixed Beam
Second-order effects
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Residual stress
Support compliance
References
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Senturia, Microsystems Design, Kluwer
Fall 2005 – M.A. Schmidt
3.155J/6.152J – Lecture 13 – Slide 2
The Process – Lab 1
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Grow 1.0µm of Si-Rich Silicon Nitride (SiNx)
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LPCVD Process (details to follow)
Characterize (UV1280)
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Thickness
Refractive index
Fall 2005 – M.A. Schmidt
3.155J/6.152J – Lecture 13 – Slide 3
The Process – Lab 1
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Pattern Transfer
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Deposit photoresist
Expose on contact aligner
Plasma etch using SF6 chemistry
Strip resist
Fall 2005 – M.A. Schmidt
3.155J/6.152J – Lecture 13 – Slide 4
The Process – Lab 2
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KOH Undercut Etch
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20%, 80C
Fall 2005 – M.A. Schmidt
3.155J/6.152J – Lecture 13 – Slide 5
The Process – Lab 3
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Break the wafer into die
Mount the die on a metal plate
Test using the Hysitron Nanoindenter
F
w
Fall 2005 – M.A. Schmidt
3.155J/6.152J – Lecture 13 – Slide 6
Testing
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Cantilever
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Young’s Modulus
Fixed-Fixed Beams
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Young’s Modulus
Residual Stress
Fall 2005 – M.A. Schmidt
3.155J/6.152J – Lecture 13 – Slide 7
The Mask
Fall 2005 – M.A. Schmidt
3.155J/6.152J – Lecture 13 – Slide 8
The Mask - Cantilevers
Fall 2005 – M.A. Schmidt
3.155J/6.152J – Lecture 13 – Slide 9
The Mask – Fixed-Fixed Beams
Fall 2005 – M.A. Schmidt
3.155J/6.152J – Lecture 13 – Slide 10
Cantilever Data
Force (m icroN ewtons)
F=kx
12
10
8
6
4
2
0
0
100
200
300
400
500
600
Displacement (nanometers)
Fall 2005 – M.A. Schmidt
3.155J/6.152J – Lecture 13 – Slide 11
Force on a Beam
Fall 2005 – M.A. Schmidt
C.V. Thompson – 6.778J
3.155J/6.152J – Lecture 13 – Slide 12
Uniaxial Stress
C.V. Thompson – 6.778J
Fall 2005 – M.A. Schmidt
3.155J/6.152J – Lecture 13 – Slide 13
Material Properties: Elastic/Plastic
Figure removed for copyright reasons.
C.V. Thompson – 6.778J
Fall 2005 – M.A. Schmidt
3.155J/6.152J – Lecture 13 – Slide 14
Material Properties: Brittle
Figure removed for copyright reasons.
C.V. Thompson – 6.778J
Fall 2005 – M.A. Schmidt
3.155J/6.152J – Lecture 13 – Slide 15
Differential Equation of Bending
w(x)
x
dx
ds
z
x
d2w =
M
EI
dx2
θ(x)
dθ
Figure by MIT OCW.
H = thickness
W = width
I=
(
(
1
WH3
12
Reference: Senturia, S.D. Microsystems Design. Norwell, MA: Kluwer Academic Publisher, 2001.
C.V. Thompson – 6.778J
Fall 2005 – M.A. Schmidt
3.155J/6.152J – Lecture 13 – Slide 16
POINT LOAD
F
MR
0
FR
x
L
Figure by MIT OCW.
Deflection of a Cantilever - 2
3L
Ref: Senturia (Kluwer)
C.V. Thompson – 6.778J
Fall 2005 – M.A. Schmidt
3.155J/6.152J – Lecture 13 – Slide 18
Deflection of a Cantilever - 3
W = width
H = thickness
L = length
Ref: Senturia (Kluwer)
C.V. Thompson – 6.778J
Fall 2005 – M.A. Schmidt
3.155J/6.152J – Lecture 13 – Slide 19
Deflection of a Plate - 1
ANTICLASTIC CURVATURE
Given axial strain εx = z
ρ
(
ρ/ν
(
Poission effect leads to transverse
strain εy given by εy=-νεx where ν
is Poisson's ratio (unitless and
about 1/3 for most materials)
ρ
So εy = ν z
ρ
(
(
More important as W
L
(beams approach plates)
Original
cross-section
Figure by MIT OCW.
Fall 2005 – M.A. Schmidt
Ref: Senturia (Kluwer)
C.V. Thompson – 6.778J
3.155J/6.152J – Lecture 13 – Slide 20
Deflection of a Plate - 2
εx =
σ x − νσ y
E
But ε y is
constrained to be zero
⇒ 0 = εy =
σ y − νσ x
E
⇓
⎛ E ⎞
σx = ⎜
ε
2 ⎟ x
1 −2ν4
⎝1
4
3⎠
Replace Modulus(E)
with Plate Modulus
Plate Modulus
Ref: Senturia (Kluwer)
Fall 2005 – M.A. Schmidt
3.155J/6.152J – Lecture 13 – Slide 21
Fixed-Fixed Beam
Load (m icroN ewtons)
1800
1600
1400
1200
1000
800
600
400
200
0
0
500
1000
1500
2000
2500
3000
3500
Displacement (nanometers)
Fall 2005 – M.A. Schmidt
3.155J/6.152J – Lecture 13 – Slide 22
Fixed-Fixed Beam: Large Displacement
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Beam stretches under large displacement
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Becomes ‘stiffer’
Solved by Energy Methods
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c=w
Ref: Senturia (Kluwer)
Fall 2005 – M.A. Schmidt
3.155J/6.152J – Lecture 13 – Slide 23
Residual Axial Stress in Beams
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Residual axial stress in a beam
contributes to it bending stiffness
2ρWP0 = 2σ0WH
σ0 H
⇒ P0 =
Leads to the Euler beam equation
ρ
which is equivalent to a distributed load
d 2w
q0 = P0W = σ0WH 2
dx
Insert as added load into beam equation :
d 4w
EI 4 = q + q0
dx
d 4w
d 2w
EI 4 − σ0WH 2 = q
dx
dx
Ref: Senturia (6.777)
Fall 2005 – M.A. Schmidt
3.155J/6.152J – Lecture 13 – Slide 24
Effect of stress on stiffness
Figure removed for copyright reasons.
Graph found in Senturia, S.D. Microsystems Design. Norwell, MA: Kluwer Academic Publisher, 2001.
Ref: Senturia (6.777)
Fall 2005 – M.A. Schmidt
3.155J/6.152J – Lecture 13 – Slide 25
Effect of Residual Stress
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Not an issue in cantilevers
For a point load, F, in the center of a bridge
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Important when
„
Ref: Senturia (Kluwer)
Fall 2005 – M.A. Schmidt
3.155J/6.152J – Lecture 13 – Slide 26
Compliant Supports
C.V. Thompson – 6.778J
Fall 2005 – M.A. Schmidt
3.155J/6.152J – Lecture 13 – Slide 27
MEMS Lab Report
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Report Young’s Modulus extracted from
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Cantilevers
Fixed-Fixed Beams
Explain differences from ideal theory
Compare to literature values for mechanical
properties
Assess the effects of:
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Residual stress
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Estimate from measurements
Experimental error
Compliant supports
Beam versus Plate
Others….
Fall 2005 – M.A. Schmidt
3.155J/6.152J – Lecture 13 – Slide 28