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Elastic Modulus And Residual Stress Of Thin Films
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Transcript of Elastic Modulus And Residual Stress Of Thin Films
Measuring the elastic modulus and the residual stress of free‐standing thin films usingstress of free‐standing thin films using
nanoindentation techniques
E. G. Herbert1, W. C. Oliver1, M. P. De Boer2, G. M. Pharr3,B. Peters1, and A. Lumsdaine1
1 Agilent Technologies, Inc., Nanomechanical Instruments Operations2 Carnegie Mellon, Dept. of Mechanical Engineering and Sandia Natl. Lab3 U i it f TN D t f M t i l S i d E i i d ORNL3 University of TN, Dept. of Materials Science and Engineering and ORNL
MOTIVATION AND GOALS
MEMS: mechanical characterization forms the basis to quickly and reliably simulate complex devices and thus avoids the need to incorporatesimulate complex devices and thus avoids the need to incorporate extensive prototyping.
Fundamental materials science: controlling the sample geometry andFundamental materials science: controlling the sample geometry and dimensions allows enhances our capability to systematically explore structure‐property relationships linked to microstructure, film thickness, fabrication and deposition techniquesfabrication, and deposition techniques.
Among the challenges: generating reliable data (well understood, robust i t th t t fl ti f th li d d l) dexperiments that are an accurate reflection of the applied model) and
experimental verification.
MOTIVATION AND GOALS
What we’re after:• The elastic modulus and the residual stress in free‐standing, metallic thin filmsfilms
What we set out to accomplish:
1. Simple mathematical model that is easy to implement experimentally•Uniaxial tension stretching not bending•Uniaxial tension, stretching not bending
2. Controlling the sample geometry, consistent with assumptions of the model•Dimensional analysis identifies limitations of the model
3. Robust experiment• Stiffness‐displacement, NOT load‐displacement – minimize measurement errors associated with thermal drifterrors associated with thermal drift
4. Experimental verification•Material selection: Aluminum 5wt% copper
l
PROPOSED MODELl
P
P z F1 F2
support postsupport
h w P
θ y
θ
support post thin film bridge
wedge indenter tip
P
2Δ hl
∑ =⇒=↑+
θsin20 PFFz
12tansin
21
−
⎥⎦
⎤⎢⎣
⎡⎟⎠⎞
⎜⎝⎛
=Δ
=−
lhl
hllε
rEAF σεσ +==
lhA
lhA
lAEhP rr σσ 488
3
3
3
3
+−=l
Al
hAlAEh
dhdPS rr σσ 42424
3
2
3
2
+−==lll llldh
THE EFFECT OF THERMAL DRIFT
80
100
60
80
N) Δh = dh/dt (time)
6040
60m
ple
(μ StiffneΔP = dh/dt (time)(Ksprings)
20
4020
On
Sam ess (N/m
0 0
Load
m)
length = 150 µmwidth = 22 µmthickness = 0.547 µm
-20 -200 1000 2000 3000
Displacement (nm)Displacement (nm)
PROPOSED TECHNIQUE
ADVANTAGES:•minimizes the effect of thermal
MODEL ASSUMPTIONS:• center loading•minimizes the effect of thermal
drift
• improved signal to noise ratio
• center loading
• normal, elastic deformation
• bending moments may be ignored
•model is simple to implement
mathematically
• rigid support posts
• the film is flat
DIMENSIONAL ANALYSIS:
Elt
lh
AESl rσπππ
2683 22424
+⎟⎠⎞
⎜⎝⎛+⎟
⎠⎞
⎜⎝⎛= ⎟
⎠
⎞⎜⎝
⎛E
rσπ2
2 24
6⎟⎠⎞
⎜⎝⎛
ltπ>>
EXPERIMENTAL VERIFICATION• Al 5wt% Cu• length = 150, 300, and 500 µm• width = 22 µm• thickness = 0.547 µm
• dc‐magnetron sputtered at 175 oC• posts are poly Si• 50 nm TiN protective coatingthickness 0.547 µm
• nominal E = 70 GPa• est. via electrostatic, E = 74.4 GPa ± 2.8,
= = 29.9 MPa ± 0.3
p g• wet etchant release with HF• selective wet etch of TiN coating
rσ
STIFFNESS‐DISPLACEMENT RESPONSE
35
40
Loadingfrequency = 20 Hzosc. amp. = 30 nm
25
30 Unloading
(N/m
) length = 150 µmwidth = 22 µmthickness = 0.571 µm
10
15
20
tiffn
ess strain = 0.04%
estimated by electrostatic
0
5
10St
estimated by electrostatictechniques:E = 74.4 GPa ± 3.8%
= 29.9 MPa ± 1%rσ0
-400 0 400 800 1200 1600 2000Displacement (nm)
STIFFNESS‐DISPLACEMENT RESPONSE
35
40
Loadingfrequency = 20 Hzosc. amp. = 30 nm
25
30 Unloading
(N/m
) length = 150 µmwidth = 22 µmthickness = 0.571 µm
10
15
20
tiffn
ess strain = 0.04%
estimated by electrostatic
Misalignment,1.6o
0
5
10St
estimated by electrostatictechniques:E = 74.4 GPa ± 3.8%
= 29.9 MPa ± 1%rσpeak‐to‐peak =
nm 85)(22 =rms0
-400 0 400 800 1200 1600 2000Displacement (nm)
STIFFNESS‐DISPLACEMENT RESPONSE
35
40
E = 75.3 GPa +/- 1%
σ = 28 7 MPa +/ 0 6%
frequency = 20 Hzosc. amp. = 30 nm
25
30
(N/m
) σr = 28.7 MPa +/- 0.6%
length = 150 µmwidth = 22 µmthickness = 0.571 µm
15
20y = 9.628 + 6.662E+12x R2= 0.9992 tiffn
ess strain = 0.04%
estimated by electrostatic
10
15y = 9.631 + 6.685E+12x R2= 0.9992
y = 9.651 + 6.74E+12x R2= 0.9995
y = 9.514 + 6.809E+12x R2= 0.9994
St estimated by electrostatictechniques:E = 74.4 GPa ± 3.8%
= 29.9 MPa ± 1%rσ
50 1x10-12 2x10-12 3x10-12 4x10-12 5x10-12
Displacement2 (m2)p ( )
STIFFNESS‐DISPLACEMENT RESPONSE
70
80length = 150 μmdisp. = 3 μm, 3xosc. amp. = 40 nm
50
60
s (N
/m)
length = 300 μmdisp. = 6 μm, 2x
60
frequency = 45 Hz
width = 22 µm
30
40
Stiff
ness osc. amp. = 60 nm
length = 500 μmdi 10 3
width = 22 µmthickness = 0.547 µm
strain = 0.08%
10
20S disp. = 10 μm, 3xosc. amp. = 120 nm
00 1.5x10-11 3x10-11 4.5x10-11 6x10-11
Displacement2 (m2)
EXPERIMENTAL VERIFICATION
70
8040
GPa
)
Re
50
60
70
30
stic
ity (G
esidual
As expected, the modulus is independent of length and bending behavior
30
40
50
20E, proposed technique
E, electrostatic techniqueof E
las Stress
Residual stress, on the other hand, is effected by:1. CTE = 23x10‐6/K
ΔT = 3 oC
10
20 10
E, electrostatic technique
σr , proposed technique
σr , electrostatic technique
odul
us (M
Pa)
= 5.2 MPa2. Bending behavior
σ
0 0100 200 300 400 500
M
Bridge Length (μm)g g (μ )
CLOSING REMARKS• We have proposed a simple model to measure the elastic modulus and residual stress of free‐standing metallic thin films
~ Based on the relationship between stiffness and displacement because itBased on the relationship between stiffness and displacement because it minimizes the effects of thermal drift
~ Model assumes normal, elastic deformation of a flat film that does not support b d d dl d h d l l lbending moments and is rigidly mounted – the model is simple to implement mathematically and dimensional analysis identifies the appropriate limits
• Experimental verification of the proposed technique was provided by measuring the elastic modulus and residual stress of four Al/5wt% Cu free‐standing films
~ Ematches within 2% of the result obtained by electrostatic actuation, independent of the observed bendingindependent of the observed bending
~ matches within 19.1% of the result obtained by electrostatic actuation, discrepancy attributed to the CTE (ΔT = 3oC) and/or bending behavior –
rσ
dimensional analysis predicted the overestimation