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Novel Method for Analyzing Crack
Growth in Polymeric Microtensile
Specimens by In Situ Atomic
Force Microscopy
Journal Article
Author(s):
Lang, U.; Suess, T.; Wojtas, N.; Dual, Jürg
Publication date:
2010
Permanent link:
https://doi.org/10.3929/ethz-b-000016956
Rights / license:
In Copyright - Non-Commercial Use Permitted
Originally published in:
Experimental Mechanics 50(4), https://doi.org/10.1007/s11340-009-9240-y
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Experimental Mechanics (2010) 50:463–472
DOI 10.1007/s11340-009-9240-y
Novel Method for Analyzing Crack Growth in Polymeric
Microtensile Specimens by In Situ Atomic Force
Microscopy
U. Lang · T. Süss · N. Wojtas · J. Dual
Received: 22 May 2008 / Accepted: 23 February 2009 / Published online: 27 March 2009
© Society for Experimental Mechanics 2009
Abstract In this paper a micro tensile test which al-
lows the determination and observation of the crack
growth behaviour in thin polymer layers is presented.
The setup consists of micromanipulators and piezo ac-
tuators for straining the sample while an atomic force
microscope (AFM) is used for scanning the crack tip
area with high lateral resolution. The stress in the
specimen is determined by an optical microscope for
observation of the deflection of a force sensing beam.
The material under investigation is an amorphous and
strongly entangled thermoplastic polyimide which can
be patterned photolithographically and is spin cast to
form layers of 3 μm thickness. The results show the
potential of the setup to measure crack length, crack
tip opening and nominal stress. The stress-crack length-
diagram then allows to determine different stages dur-
ing crack growth.
Keywords Polyimide · Tensile testing · In situ · AFM
U. Lang (
B
) · T. Süss · N. Wojtas · J. Dual
Center of Mechanics—Department of Mechanical
and Process Engineering, ETH Zurich, Tannenstr. 3,
8092 Zurich, Switzerland
e-mail: udo.lang@alumni.ethz.ch
Introduction
Crack initiation and growth are key issues when it
comes to the mechanical reliability of microelectronic
devices and microelectromechanical systems (MEMS).
Especially in organic electronics where flexible sub-
strates will play a major role these issues will become of
utmost importance. It is therefore necessary to develop
methods which allow the experimental investigation of
fracture processes in thin organic layers as mechani-
cal failure of devices is usually accompanied by crack
propagation. Since polymers are often amorphous, non
conductive and cannot withstand the electron beam
of electron microscopes for a long time, the approach
herein is therefore based on the use of an AFM to
determine in situ crack propagation during straining
of a polymer specimen. Similar setups have been used
to examine silicon [1–7], thin metal films on polymer
substrates [8–10] and pure polymer samples [11–18].
In contrast to those approaches, in the experiments
presented here, the force measurement is integrated
in the microfabricated samples as presented by Haque
and Saif in [19]. This technique allows to investigate
thin samples with micrometer thickness and to mea-
sure forces in the range of millinewtons. By using an
optical microscope the deformation of a silicon force
sensing beam can be observed and by applying beam
mechanics the force acting on the specimen can be
determined (Fig. 1). The tensile samples in this re-
search are made from the polyimide PI 2723 from HD
Microsystems (Wilmington, DE, USA). Polyimide was
chosen because it is widely used as a passivation layer to
protect microelectronic devices from moisture and cor-
rosion. Additionally, polyimides are often used as stress
buffer layers during packaging of dies [20]. Moreover,
464 Exp Mech (2010) 50:463–472
rigid extension rod
microscope camera
pulling force
PI specimen
distance between silicon frame
and extension rod to be
measured by microscope
AFM
cantilever
Si frame
AFM tip
Si beams
pulling force
notch in PI specimen
force sensing beam
Fig. 1 Principle of the setup: the specimen is strained between
two silicon beams while crack growth is monitored in situ by
an AFM. A photolithographically structured notch results in a
locally well defined crack initiation. The deformation of a force
sensing beam is determined by an optical microscope. The rigid
extension rod is necessary because the actual force sensing beam
is hidden underneath the AFM. The three pin holes in the Si
frame are used for force transmission by small pins from the
external piezo actuators to the specimen
polyimides are promising candidates for flexible sub-
strates in organic electronics [21, 22] and in the MEMS
community as a membrane material [23–25].
Experimental
Specimens
The specimen itself consists of a freestanding 3 μm
polyimide PI 2723 tensile probe and a silicon frame.
They are both shown in Fig. 2 with dimensions. Con-
nected to one of the silicon beams there is an extension
rod which can be considered a rigid body. Based on
this assumption, the deformation of the silicon force
sensing beam is transferred directly to this extension
rod. Therefore the deflection of the beam can be deter-
mined by measuring the distance between the extension
beam and the rigid silicon frame. This is necessary
because the actual force sensing beam is hidden be-
hind the AFM and can therefore not be monitored
directly. The geometry of the PI tensile probe is based
on an international norm on tensile tests of polymers
[26] with an additional single notch on one side. The
fabrication of the specimens is mainly based on the
Bosch deep dry etching process and is explained in
[27] in detail. The polyimide used in these experiments
is PI 2723 as mentioned before. It is photodefinable
and can be applied by spin coating. It is therefore
also very suitable for MEMS applications. Its morphol-
ogy shows a very amorphous structure caused by a
strong entanglement of the chains (Knaus, M, HD Mi-
crosystems Europe, Neu-Isenburg, Germany, personal
communication, October 2008). As its glass transition
temperature is rather high (> 320 °C, [20]) and the tests
are conducted at room temperature, the thermoplast
will be in its glassy state and therefore one can ex-
pect a rather brittle and very limited viscous behaviour
Fig. 2 Dimensions of setup: (a) shows the overall size of the specimen and of the extension rod (in mm), (b) shows the dimensions of
the silicon force sensing beam (in mm) and its orientation on the wafer and (c) shows the dimensions (in μm) of the polyimide specimen
including the notch. The thickness of the silicon (100) wafer is 525 μm. The thickness of the PI specimen is 3 μm
Exp Mech (2010) 50:463–472 465
[28–30]. This behaviour has indeed already been shown
in [31] for polyimide (Kapton) films. As PI 2723 is even
more entangled than Kapton tape (Knaus, M, HD Mi-
crosystems Europe, Neu-Isenburg, Germany, personal
communication, October 2008) one could therefore
assume that viscous effects and the size of the plastic
zone in front of the crack tip will be limited in size.
Atomic Force Microscope
An easyScan AFM (Nanosurf AG, Liestal,
Switzerland) was used in the experiments. Its main
characteristics are a maximum scan range of 100 μm
in x- and y- directions and of 20 μm in z- direction.
In actual experiments the lateral scan range was set
to 60 μm at a sampling rate of 256 which yielded a
resolution in x- and y- direction of 0.23 μm. For such
an area a scan usually takes about 3 minutes. Scans are
typically taken in contact mode and closed loop control
with a load of 11 nN and automatic z-offset adjustment.
The cantilevers were of type Contr-16 (Nanosensors
AG, Neuchâtel, Switzerland) and had a typical tip
diameter of less than 10 nm and a tip height of about
10 - 15 μm.
Detection of Forces
Mechanics of force sensing beam
The principle used herein for measuring forces is based
on the deformation of single crystal silicon double fixed
beams and was first presented by Haque and Saif in
[19]. As shown in Fig. 1 the application of an external
force on the first beam leads to the deformation of
that beam, to the straining of the specimen and to the
deformation of the second force sensing beam.
The calculation of a force causing large deflections
of double fixed beams was first presented by Frisch-Fay
[32] in detail. Here, a brief summary of his explanations
only as far as necessary to understand the train of
thought is given. The main idea is that when such a
beam with two fixed ends undergoes a large deflection,
then also normal forces will develop in axial direction.
It should be emphasized that large deflections in this
context mean that normal forces develop in the beam,
but that the actual deflection in the middle is small
compared to the overall length of the beam. Figure 3
shows a beam which is loaded with a force of 2P
and the corresponding free body diagram. Contrary to
first order theory the equilibrium is derived from the
deflected state. This leads to an additional moment Ny.
2P
P
P
N
M
0
L
f
x
y
N
2L
M
b
Fig. 3 Deformation of double fixed beam under a load of 2P and
corresponding free body diagram
Equilibrium of moments at an arbitrary point x along
the half of the beam therefore is:
M
b
= EI
d
2
y
dx
2
= Ny + M
0
− P(L −x) (1)
where M
b
is the bending moment at position x, E
is Young‘s Modulus of the beam material and I the
moment of inertia of the beam for bending about the
z - axis. The general solution of equation (1)is
y = C
1
cosh tx +C
2
sinh tx + Ax + B (2)
where C
1
and C
2
have to be found from boundary
conditions for a double fixed beam and from beam
symmetry, while A =−P/N, B = (PL − M
0
)/N and
t =
√
(N/EI) can then be found from comparing coef-
ficients in equation (2) and equation (1). Considering
the axial extension of the beam caused by the constant
normal force N (for small slopes) and some additional
calculus yields an equation for N:
N
3
=
A
c
EP
2
2
3
2
−
1
2
tanh
2
u −
3
2
tanh u
u
(3)
with u = tL/2 and A
c
as the cross sectional area of the
beam. Solving equation (3)forP yields
P =
2N
3
A
c
E
3
2
−
1
2
tanh
2
u −
3
2
tanh u
u
−
1
2
. (4)
Using equations (2)and(4) and calculating the value
of y(x) at x = 0 (middle of the beam) leads to
f = 2
2I
A
c
(
u −tanh u
)
·
3
2
−
1
2
tanh
2
u −
3
2
tanh u
u
−
1
2
(5)
466 Exp Mech (2010) 50:463–472
which is the desired relation between P and the deflec-
tion f at the middle of the beam. For f given from
the experiment, equation (5) is numerically solved for
u. P is then obtained from equation (4)usingu =
tL/2 and t =
√
(N/EI). This calculation can be easily
programmed with any numerical computing program
e.g. Mathematica or Matlab. In these experiments a
simple Matlab code was used to calculate P from the
measured deflection f. The maximum stress due to
bending then develops at the fixed ends of the beam
and is given by
σ
max
=
1
3
E
h
L
2
u
2
·
1 +
√
6tanhu
3
2
−
1
2
tanh
2
u −
3
2
tanh u
u
−
1
2
(6)
where h is the height of the beam, in this case 200 μm
(see Fig. 2). Assuming a yield strength of 7 GPa
and a Young‘s modulus of 169 GPa for silicon in
< 110 >direction [33], a theoretical maximum detectable
force P of ≈60 N can be obtained from equation (4).
The optical system (see “Measurement of beam deflec-
tion and crack growth”) permits a resolve limit of about
1 μm which yields with equations (4)and(5) a force
resolution of about 0.0012 N.
Measurement of beam deflection and crack growth
Measuring the actual displacement of the extension rod
during experiments was done by an high magnification
zoom lens (1×–12×) (Navitar Inc., Rochester, USA)
with a 2 megapixel CCD camera (Moticam 2000, Motic
Deutschland GmbH, Wetzlar, Germany) attached to it
(see Fig. 1). For every AFM scan also a image of the
extension rod was taken. The rod displacement was
then determined by carefully measuring the distance
between the rod and the frame using the image analysis
program Motic Images Plus 2.0. This program allows
to determine lateral dimensions with its distance tool.
Before measurements the program was furthermore
calibrated using a distance normal. The actual measure-
ments were then conducted by determining the normal
distance between the easily identifiable corners of the
extension rod and the frame and then calculating the
mean. Motic Images Plus 2.0 was also used to determine
crack length. For this, the AFM scans were carefully
analyzed by determining the distance from the bottom
of the notch to the tip of the crack (see also Section
“Results”).
microscope camera
PCs for control of AFM
and actuators
piezo actuators
micromanipulators
specimen
3 pins for straining
the specimen
Fig. 4 Experimental setup. Two micromanipulators and two
piezo actuators are used. They point pairwise into opposite di-
rections which results in larger maximum displacements. Further-
more the notch area can thus be kept in a central position
Actuation and Control
Figure 4 shows the actual setup. For the experiments
the samples are put on the pins which transfer the
motion generated by the micromanipulators and piezo
actuators (model P-280, 100 μm range, PI GmbH,
Karlsruhe, Germany) to the specimens. The microma-
nipulators are necessary to bring the pins in contact
with the specimen to make sure that the whole range of
the piezo actuators can be used for precisely straining
the specimen. An actual experiment is conducted step-
wise: the specimen is strained for approximately 5 μm
whereat this overall displacement is composed of two
displacements of 2.5 μm pointing in opposite directions.
The region of interest i.e. the notch thus remains in
principle unmoved. Then an AFM scan and a image
of the extension rod are taken. Then the specimen is
strained for an additional 5 μm and again scans and
images are taken and so forth until rupture of the
sample. The whole experiment is therefore controlled
by actuator displacements. During manual actuation it
might happen that the two micromanipulators are not
actuated exactly the same way and thus the crack might
be moved away from the central position of the AFM
scan. This can then be accounted for in the AFM scan
software by readjusting the scan area without adverse
effects on the samples.
![Fig. 6 The different stages during crack propagation. The terms are used according to [46]](/figures/fig-6-the-different-stages-during-crack-propagation-the-jemmh8v3.webp)
