Fatigue in thin films Lifetime and damage formation.pdf

Materials Science and Engineering A319–321 (2001) 919–923
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Fatigue in thin films: lifetime and damage formation
O. Kraft *, R. Schwaiger, P. Wellner
Max-Planck-lnstitut für Metallforschung and Institut für Metallkunde of the Uniersity, Seestr. 92, 70714 Stuttgart, Germany
Abstract
Two new techniques, developed for studying the fatigue behavior of thin metal films on substrates, are presented: The first
technique involves deposition of Cu films onto elastic polyimide substrates. During cyclic tensile testing of the film–substrate
composite, the film is subjected to tension–compression cycles, since it is plastically deformed, while the substrate undergoes only
elastic deformation. Using this technique, it was found that, for 3 m thick Cu films, the number of cycles to failure follows the
phenomenological Coffin–Manson relationship. For the other technique, thin films, here Ag films with thicknesses ranging from
0.2 to 1.5 m, are deposited onto micromachined SiO 2 cantilever beams. The beams are then deflected with a frequency of 45 Hz
using a nanoindentation system. A detailed investigation of the damage formation in both fatigued Cu and Ag films revealed
surface roughening prior to failure. Extrusions and cracks are formed inside large grains and between small grains, respectively.
© 2001 Elsevier Science B.V. All rights reserved.
Keywords: Polyimide; Fatigue; Thin films; Cu; Ag
1. Introduction
Fatigue of thin film materials has not yet been studied
systematically. Since the mechanical properties of
thin films may be different from those of bulk materials
[1–3], fatigue behavior cannot be extrapolated from
results of bulk studies. For ductile bulk materials, it is
well-known that fatigue crack initiation processes are
often related to the formation of persistent slip bands
[4]. These slip bands, which have a typical width of
several micrometers, lead to extrusions at the sample
surface and stress concentrations, or to strain localization
inside grains, and eventually to crack formation. It
is uncertain, if similar processes can occur in thin film
materials, since the typical size of slip bands in bulk
materials exceeds the thickness and the grain size of
most thin films. Indeed, in the few TEM studies, conducted
so far on fatigued metal foils and thin films, the
formation of dislocation structures was observed to be
suppressed in fine grained Cu foils [5–7].
In fatigue testing of metals, it is common to distinguish
between regimes of high cycle fatigue (HCF) and
low cycle fatigue (LCF). In the former, the stress
* Corresponding author. Tel./fax: +49-711-2095123.
E-mail address: oliver.kraft@po.uni-stuttgart.de (O. Kraft).
amplitude does not exceed the yield strength of the
material and the number N f of cycles to failure is
typically above 10 3 –10 4 . In the LCF regime, the material
is plastically strained in each cycle. Therefore, it is
common to report lifetimes of a material as a function
of the plastic strain range pl using the empirically
established Coffin–Manson relationship [8]:
pl
2 = f(2N f ) c (1)
where f and c are the fatigue ductility coefficient and
exponent, respectively. In the HCF regime, fatigue tests
are usually conducted under stress control and lifetimes
generally obey a similar equation:
a
2 = f(2N f ) b (2)
where a is the applied stress amplitude, f and b are
the fatigue strength coefficient and exponent, respectively.
It was found that Cu foils or films with a
thickness of more than 10 m follow, depending on the
fatigue test conducted, one of these empirical relationships
[5,6,9,10]. However, it is not obvious if the relationships
still hold for films with smaller thickness and
grain size.
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O. Kraft et al. / Materials Science and Engineering A319–321 (2001) 919–923
It is the aim of this paper to elucidate the fatigue
mechanisms in constrained volumes and to determine
fatigue lifetimes under these conditions. We present
two methods, which we developed to study the fatigue
behavior of thin metal films on substrates: The
first technique involves tensile testing of Cu films deposited
onto elastic polyimide substrates. Tensile testing
of these specimen results in tension–compression
cycles in the plastically deformed thin film while the
substrate is elastically deformed only. The second
technique utilizes the cyclic deflection of thin Ag films
deposited onto micromachined SiO 2 cantilever beam
using a nanoindentation system.
2. Experimental
2.1. Tensile testing
For processing of the tensile specimen, shown in
Fig. 1a, the 125 m thick polyimide substrates (Kapton,
Du Pont) were initially cleaned by rinsing with
ethanol and pressurized CO 2 . Then, the sample was
mounted in the deposition system (base pressure of
5×10 −7 mbar) and activated by an oxygen plasma
(O 2 pressure 1×10 −2 mbar, power 100 W, bias
−300 V). Without breaking vacuum, 3 m thick Cu
films were then sputter deposited at a substrate temperature
of 300°C, a rate of 60 nm per min with an
Ar pressure of 2×10 −3 mbar, a power of 150 W
and a bias of −80 V. After deposition, the samples
were annealed in a vacuum furnace (6×10 −6 mbar)
at a temperature of 400°C.
The tensile tests were performed in an electromechanical
tensile tester (Zwicki 1120, Zwick) under
load control. Samples were cyclically loaded between
a minimum load of 2 N to maximum loads in the
range of 15–60 N. Under these conditions, the film is
strained with constant total strain ranges between 0.7
and 2.1% as determined from the crosshead displacement
and monitored as a function of the number of
cycles. It is not possible to determine the film stress
using this configuration because the externally applied
force is predominantly governed by the mechanical
properties of the substrate. However, microtensile
tests on comparable samples using an X-ray diffraction
technique enabled the measurements of stress–
strain behavior during such experiments as
exemplified in Fig. 1b [11]. On loading and unloading,
the film is plastically deformed in tension and in
compression for a total and plastic strain range of 0.5
and 0.15%, respectively.
2.2. Microbeam bending
Fig. 1. Microtensile testing; (a) Sample geometry of the 125 m thick
polyimide foil substrate and the Cu film sputtered in the middle
section of the dog-bone shaped sample. (b) Typical stress-strain
behavior for a Cu film on a polyimide substrate during cyclic loading
as measured by X-ray diffraction (second cycle of 0.7 m thick Cu
film, from [11]). The total applied strain range of the cycle is 0.5%,
whereas the plastic strain range amounts only to about 0.15% as
indicated by the arrow within the hysteresis loop.
The microbeam samples are shown schematically in
Fig. 2a. They consist of a 2.83 m thick SiO 2 layer
and a thinner Ag film. The Ag films, ranging from
0.2 to 1.5 m in thickness, were sputter deposited at
a temperature of about −190°C and annealed at +
100°C. A detailed description of film deposition and
the testing procedure is given in [12]. The testing procedure
is briefly described as follows, the beams are
deflected by a commercial nanoindentation system
(Nano II, MTS Corp.), which applies a cyclic load
P=P mean +P o cos(2t), where P mean is the mean
load, P o the load amplitude and the frequency,
which was chosen to be 45 Hz. In this configuration,
the largest strain occurs at the fixed end of the beam
(as indicated in Fig. 2a). Based on elastic beam bending
theory, this strain can be calculated from the
lever length L and the applied load as:
= P(L−x) (z−q) (3)
IE
where I is the moment of inertia, E the Young’s
modulus of the substrate material, q the position of
the neutral axis, and x and z the coordinates along
the length and the thickness of the beam. The mo-

O. Kraft et al. / Materials Science and Engineering A319–321 (2001) 919–923 921
3. Results
3.1. Tensile testing
The 3 m thick Cu films on the polyimide substrates
had grains which were found to be equiaxed rather than
columnar with a median grain size of 0.8 m. Also, no
distinct texture was observed. As a typical example,
Fig. 3a shows the total strain range as a function of the
number of cycles for a bare substrate and a sample with
aCufilm. The maximum load was 25 N. It can be seen
that the strain range for the sample with the film is
initially smaller because the sample stiffness is higher
due the film. After about 4000 cycles, the strain range
Fig. 2. Microbeam bending; (a) Schematic of the sample and loading
geometry, the beam consists of a 2.83 m thick SiO 2 layer onto which
0.2–1.5 m thick Ag films were sputter deposited. The load P is
induced by a nanoindentation system with a wedge-shaped tip having
a wedge length of 10 m and an opening angle of 90°. The tip
contacts the beam in the dark shaded area, where the Ag film has
been removed by focused ion beam milling. (b) Schematic of the
straining conditions: The load P is cycled with an amplitude of P
around a mean value of P mean . The resulting cyclic strain for the Ag
film at the fixed end of the beam (hatched area in (a)) is also
represented.
ment of inertia and the position of the neutral axis
depend on the thicknesses and the elastic properties of
the beam and film [13]. As a result of the applied cyclic
load, the metal film at the fixed end of the microbeam
is subjected to a cyclic strain as schematically shown in
Fig. 2b. For lifetime studies, the lever length, the mean
load and the load amplitude were varied, resulting in
values for mean and in the range of 0.2–2.3% and
0.2–0.6%, respectively. We report our results as a function
of max = mean +1/2. The film is yielding at such
strains and the corresponding stress range in the experiment
can, therefore, not be calculated. Fig. 2b also
indicates that under the dynamic loading conditions,
the cyclic strain is phase shifted relative to the cyclic
load. This phase shift was measured throughout the
experiment and used to monitor the stiffness of the
beam as a function of the number of cycles as described
elsewhere [12].
All films were investigated by focused ion beam
microscopy (FEI 200) and X-ray diffraction to determine
grain size and texture, respectively. After testing,
fatigue damage was characterized by scanning electron
and focused ion beam microscopy.
Fig. 3. (a) Total strain range for a 3 m thick Cu film on a polyimide
substrate and a bare substrate. Both experiments were conducted
under load control with a maximum load of 25 N and a minimum
load of 2 N. The lifetime was defined as the number of cycles at
which the strain range increased. (b) Number of cycles to failure as a
function of total strain range.

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O. Kraft et al. / Materials Science and Engineering A319–321 (2001) 919–923
3.2. Microbeam bending
The grains in the Ag films on the SiO 2 microbeams
were found to be columnar and had a median grain size
of about 0.9 m independent of the film thickness. The
majority of grains was (111)-oriented with a smaller
fraction of (100)-oriented grains. The latter increased
with increasing film thickness. As an example of a
typical microbeam bending experiment, Fig. 4a shows
the beam stiffness as function of the number of cycles
for a beam with a 0.8 m thick film and a maximum
strain max of 2.2%. Initially, the beam stiffness is nearly
constant. The dramatic decrease in stiffness after approximately
6×10 −5 cycles indicates the onset of
severe damage formation. Similar experiments conducted
on samples with different film thicknesses are
summarized in Fig. 4b. The filled symbols denote the
experiments in which a distinct decrease in beam stiffness
was observed within 3.9×10 6 cycles accompanied
by crack formation. Only films with a thickness of 0.6
m or more suffered from fatigue damage.
3.3. Damage morphology
Typical micrographs of fatigue damage are shown in
Fig. 5. For both Cu and Ag films, the damage morphology
can be described as follows, extrusions (marked as
E) are formed within large grains, whereas intergranular
cracks (C) were found in fine grained regions of the
film. The extrusion height is comparable to the film
thickness. Underneath the extrusions, large voids are
found at the interface between the film and the substrate.
Some more detailed observations of the fatigue
damage in the Ag films are described in [12].
Fig. 4. (a) Stiffness of a microbeam with 0.8 m thick film cycled to
max of 2.2% at a frequency of 45 Hz. The sudden decrease of stiffness
indicates the onset of damage formation. (b) Map for damage formation
as a function of Ag film thickness and maximum strain. Thick
films showed fatigue damage within 3.9×10 6 cycles (filled symbols)
whereas thin films did not show structural features of fatigue (open
symbols). The transition occurs for 0.6 and 0.8 m thick films as
function of maximum strain.
increases, i.e. the sample stiffness decreases. After
10000 cycles, the strain range has reached the level of
the bare substrate indicating that the film is no longer
contributing to the sample stiffness. The number N f of
cycles to failure in these experiments was defined as the
interception of two linear curve fits as demonstrated in
Fig. 3a. In Fig. 3b, this number is plotted versus the
total strain range. As expected, the lifetime decreases
with increasing strain range following a relationship as
given by Eq. (1).
4. Discussion
Two techniques have been developed to study the
fatigue behavior of thin films on substrates. Central to
both methods is the use of an elastic substrate, which
acts as an antagonist to an external mechanical loading.
As a result, films are deformed in tension on loading
and in compression on unloading. Another important
aspect of these experiments is that film fatigue damage
is not catastrophic because the undamaged substrate
maintains some mechanical integrity of the sample.
However, the degradation of the film, i.e. crack formation
and propagation, is manifested as a decrease in
stiffness of the film–substrate composite. Based on this
distinct decrease in stiffness, the lifetime of Cu films on
polyimide substrates was determined as a function of
applied total strain range. It was not possible to determine
the plastic strain range, since the film stress was
not measurable during the experiments. As a result,
Fig. 3b is plotted as the initial total strain range as a

O. Kraft et al. / Materials Science and Engineering A319–321 (2001) 919–923 923
significantly slower or suppressed in thinner films,
which would be qualitatively in agreement with the fact
that the strength of metal films increases with decreasing
film thickness [1,2,14]. However, it is currently not
clear, if the formation of the extrusions is related to the
occurrence of dislocation structures, such as persistent
slip bands, as in bulk materials. More systematic studies,
including TEM investigations, are currently pursued
to obtain a deeper understanding of fatigue
mechanisms in thin films.
5. Summary
Fig. 5. Damage morphology after fatigue testing; (a) Focused ion
beam micrograph of a 3 m thick Cu film on a polyimide substrate,
large extrusions and cracks are marked by E and C, respectively. (b)
SEM micrograph showing the 0.8 Ag film, from the test described in
Fig. 4a, at the fixed end of a microbeam. Large extrusions (marked
by E) are connected by a crack (C).
function of N f . The data follow Eq. (1) with an exponent
of −0.4, which is somewhat higher than typically
observed values of −0.5 to −0.7 for many bulk metal
materials [8]. This is partially accounted for by the use
of the total strain range instead of the plastic strain
range, because the difference between the two is more
important at small strain ranges. As a result of this
consideration, the exponent of −0.4 can be regarded
as an upper bound.
The microbeam bending experiments reveal that the
fatigue behavior changes significantly, when the film
thickness is reduced below 1 m. Fig. 4b shows that
films thinner than 0.6 m did not fatigue within 3.9×
10 6 cycles. The formation of extrusions appears to be
In an attempt to systematically study the fatigue
behavior of thin metal films as a function of film
thickness, grain size, and straining conditions, we have
developed two new methods. Central to both methods
is the use of an elastic substrate, which acts as an
antagonist to an external mechanical loading. First
results can be summarized as follows; fatigue damage
includes the formation of large transgranular extrusions
and intergranular cracks. The crack formation is associated
with a distinct decrease in stiffness of the film–
substrate composite. The lifetime of 3 m thick Cu
films on polyimide substrates follows a Coffin–
Manson-type relationship. No fatigue damage was
found in Ag films with thicknesses below 0.6 m as
tested by dynamic microbeam deflection.
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