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1. Introduction to Nanoindentation Process2. Model Description3. Model Validation4. Results and Discussion5. Effect of Substrates6. Conclusion and Future Work
Outline
Displacement Sensor
Force Sensor
Film
Substrate
Indenter
Displacement of Indenter h Ap
plie
d L
oa
d o
n I
nd
en
ter
P
LoadingUnloading
dP/dh
1. Introduction to Nanoindentation Process
100 nm
100 nm
1000 nm
900 nm
Indenter: Diamond
Film: Copper
Substrate: 1. Copper 2. Sapphire 3. Silicon 4. Glass 5. Polymer
2. Model Description-Dimensions and Materials of The Model
3.70
Elastic
Materials
E (GPa)
v (-)
Diamond 1147 0.3
Sapphire 440 0.3
Silicon 172 0.3
Glass 73 0.3
Polymer 30 0.3
Elastic/Plastic
Mateirial
E
(GPa)
V(-) Y
(GPa)
Plastic Constitutive
Copper 130 0.3 1.3 nK
0 0.01 0.02 0.03 0.04 0.050
0.5
1
1.5
2
2.5
3
(-)
(G
Pa
) Elastic Plastic
2. Model Description -Materials Properties
Indenter
Film
Substrate
Element Type: 4-Noded Axisymmetric
Element Size (Edge length):~2 nm (Indentation region)~10 nm (Other region)
Mesh Sensitivity:Refined-mesh model gives similar results.
2. Model Description -Mesh and Element
cA
unloadingcr dh
dP
AE
2/12/11
4
Experimental :
Theoretical:
i
i
s
s
r
Ev
Ev
E22 11
1
rE : Reduced Modulus
sE sv : Film’s E and v
sE sv : Indenter’s E and v
: Indenter and film’s contact area
3. Model Validation-Reduced Modulus (copper substrate)
0 5 10 15 20 25 30
0
2
4
6
8
10
12
14x 104
Displacement of Indenter h (nm)
Ap
plie
d Lo
ad o
n I
nden
ter
P (
nN
)
Simulated P vs. hTheoretical P vs. h
Pa)128.6056(GrESimulated:
Theoretical: Pa)128.2340(GrE
3. Model Validation-Theoretical and Simulated Results (copper substrate)
0 5 10 15 20 25 30 3502468
1012141618
x 104
Displacement of Indenter h (nm)
Fo
rce
on I
nden
ter
P (
nN
)
coppersapphiresiliconglasspolymer
E reducing
Model’s Prediction Experimental Results (W, Nix et al, Acta Materialia, 50, 23, 2002)
5. Effect of Substrates- Load vs. Displacement
0 50 100 150 200 250 300 350 400 450 50060
80
100
120
140
160
180
200
220
Substrate Youngs Modulus Es(GPa)
Re
duce
d Y
oun
gs
Mod
ulus
Er
(GP
a)
coppersappsiliconglasspolymerTheoretical Er
y=-0.00090793*x2
+0.75727*x+46.0508
Model’s Prediction Experimental Results (W, Nix et al, Acta Materialia, 50, 23, 2002)
5. Effect of Substrates- Reduced Modulus
0 100 200 300 400 500 600 700 800 900 1000-12
-10
-8
-6
-4
-2
0
X (nm)
De
flect
ion
of S
ubs
trat
e T
op
Sur
face
(nm
)
coppersappsiliconglasspolymer
5. Effect of Substrates- Deflection of Substrate
1. Nanoindentation process can be simulated using finite element method.
2. The reduced modulus predicted by the finite-element model is very close to analytical results.
3. Stiff substrate tends to overestimate thin film’s modulus, and compliant substrate tends to underestimate thin film’s modulus.
5. Conclusion