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