Free-standing thin films

1. Measuring the elastic modulus and the residual
stress of free‐standing thin films using
stress 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
1Agilent Technologies, Inc., Nanomechanical Instruments Operations
2Carnegie Mellon, Dept. of Mechanical Engineering and Sandia Natl. Lab
3U i
University of TN, Dept. of Materials Science and Engineering and ORNL
it f TN D t f M t i l S i dE i i d ORNL

2. MOTIVATION AND GOALS
MEMS: mechanical characterization forms the basis to quickly and reliably
simulate complex devices and thus avoids the need to incorporate
simulate complex devices and thus avoids the need to incorporate
extensive prototyping.
Fundamental materials science: controlling the sample geometry and
Fundamental 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 techniques.
fabrication and deposition techniques
Among the challenges: generating reliable data (well understood, robust
experiments that are an accurate reflection of the applied model) and
i t th t t fl ti f th li d d l) d
experimental verification.

3. MOTIVATION AND GOALS
What we’re after:
• The elastic modulus and the residual stress in free‐standing, metallic thin
films
What we set out to accomplish:
1. Simple mathematical model that is easy to implement experimentally
• Uniaxial tension stretching not bending
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 drift
errors associated with thermal drift
4. Experimental verification
• Material selection: Aluminum 5wt% copper

4. PROPOSED MODEL
l
z
P
F1 F2
P
θ θ
h w y
support
post
support
thin film bridge
post P
wedge indenter tip
Δl 2h
ε= = −1
+
⎡ ⎛ 2h ⎞⎤
F P
↑ ∑ Fz = 0 ⇒ F =
l
σ = = Eε + σ r l sin ⎢tan −1⎜ ⎟⎥
2 sinθ
A ⎝ l ⎠⎦
⎣
8 AEh 3 8 Aσ r h 3 4 Aσ r h dP 24 AEh 2 24 Aσ r h 2 4 Aσ r
P= − + S= = − +
3 3 3 3
l dh l
l l l l

5. THE EFFECT OF THERMAL DRIFT
80
100
mple (μN) Δh = dh/dt (time)
80
60
ΔP = dh/dt (time)(Ksprings)
Stiffne (N/m
60
40
Load On Sam
ess
40
20
20
m)
0
length = 150 µm
0 width = 22 µm
thickness = 0.547 µm
-20
-20
0 1000 2000 3000
Displacement (nm)

6. PROPOSED TECHNIQUE
ADVANTAGES: MODEL ASSUMPTIONS:
• minimizes the effect of thermal
minimizes the effect of thermal • center loading
center loading
drift • normal, elastic deformation
• bending moments may be ignored
• improved signal to noise ratio
• rigid support posts
• model is simple to implement
• the film is flat
mathematically
DIMENSIONAL ANALYSIS:
π 2 ⎛σr ⎞
π 4 ⎛t ⎞ π 2 σr
3π 4 π 4 ⎛t ⎞
2 2 2
⎛h⎞
Sl ⎜ ⎟ >>
= ⎜⎟+ ⎜⎟+ ⎜⎟
2 ⎝E⎠
⎝l⎠ 6 ⎝l ⎠ 6 ⎝l ⎠
AE 8 2E

7. EXPERIMENTAL VERIFICATION
• Al 5wt% Cu
• dc‐magnetron sputtered at 175 oC
• length = 150, 300, and 500 µm
• posts are poly Si
• width = 22 µm
• 50 nm TiN protective coating
p g
• thickness 0.547 µm
thickness = 0.547 µm
• wet etchant release with HF
• nominal E = 70 GPa
• selective wet etch of TiN coating
• est. via electrostatic, E = 74.4 GPa ± 2.8,
σ r = 29.9 MPa ± 0.3
=

8. STIFFNESS‐DISPLACEMENT RESPONSE
40
frequency = 20 Hz
35 Loading osc. amp. = 30 nm
Unloading
length = 150 µm
30
tiffness (N/m)
width = 22 µm
25 thickness = 0.571 µm
strain = 0.04%
20
15
estimated by electrostatic
estimated by electrostatic
St
10
techniques:
E = 74.4 GPa ± 3.8%
5
σ r = 29.9 MPa ± 1%
0
-400 0 400 800 1200 1600 2000
Displacement (nm)

9. STIFFNESS‐DISPLACEMENT RESPONSE
40
frequency = 20 Hz
35 Loading osc. amp. = 30 nm
Unloading
length = 150 µm
30
tiffness (N/m)
width = 22 µm
25 thickness = 0.571 µm
Misalignment, strain = 0.04%
20
1.6o
15
estimated by electrostatic
estimated by electrostatic
St
10
techniques:
peak‐to‐peak = E = 74.4 GPa ± 3.8%
5
σ r = 29.9 MPa ± 1%
2 2 ( rms ) = 85 nm
0
-400 0 400 800 1200 1600 2000
Displacement (nm)

10. STIFFNESS‐DISPLACEMENT RESPONSE
40
frequency = 20 Hz
E = 75.3 GPa +/- 1%
35 osc. amp. = 30 nm
σr = 28.7 MPa +/ 0 6%
28 7 +/- 0.6%
length = 150 µm
tiffness (N/m)
30 width = 22 µm
thickness = 0.571 µm
25
strain = 0.04%
20
2
y = 9.628 + 6.662E+12x R = 0.9992
estimated by electrostatic
estimated by electrostatic
15
St
2
techniques:
y = 9.631 + 6.685E+12x R = 0.9992
E = 74.4 GPa ± 3.8%
2
y = 9.651 + 6.74E+12x R = 0.9995
10
σ r = 29.9 MPa ± 1%
2
y = 9.514 + 6.809E+12x R = 0.9994
5
1x10-12 2x10-12 3x10-12 4x10-12 5x10-12
0
Displacement2 (m2)
p (

11. STIFFNESS‐DISPLACEMENT RESPONSE
80
length = 150 μm
70 disp. = 3 μm, 3x
osc. amp. = 40 nm
60
Stiffness (N/m)
length = 300 μm frequency = 45 Hz
50
disp. = 6 μm, 2x
width = 22 µm
width = 22 µm
s
osc. amp. = 60 nm
40
thickness = 0.547 µm
30 strain = 0.08%
length = 500 μm
disp. = 10 μm, 3
S
di 3x
20
osc. amp. = 120 nm
10
0
1.5x10-11 3x10-11 4.5x10-11 6x10-11
0
Displacement2 (m2)

12. EXPERIMENTAL VERIFICATION
GPa)
80
40
Re
sticity (G
70
esidual Stress (MPa)
As expected, the modulus
is independent of length
60
30 and bending behavior
50
Modulus of Elas
Residual stress, on the
other hand, is effected by:
40 20 1. CTE = 23x10‐6/K
E, proposed technique
ΔT = 3 oC
30 E, electrostatic technique
σ = 5.2 MPa
σr , proposed technique
20 2. Bending behavior
10
σr , electrostatic technique
10
0
0
100 200 300 400 500
Bridge Length (μm)
g g (μ )

17. 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 it
Based 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
bending moments and is rigidly mounted – the model is simple to implement
bd d dl dh dl l l
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
~ E matches within 2% of the result obtained by electrostatic actuation,
independent of the observed bending
independent of the observed bending
~ σ r matches within 19.1% of the result obtained by electrostatic actuation,
discrepancy attributed to the CTE (ΔT = 3oC) and/or bending behavior –
dimensional analysis predicted the overestimation