Giorgio Cortelli1, Luca Patruno1, Tobias Cramer2, Beatrice Fraboni2, Stefano de Miranda1. 1. Department of Civil, Chemical, Environmental and Materials Engineering, University of Bologna, Viale del Risorgimento 2, 40136 Bologna, Italy. 2. Department of Physics and Astronomy, University of Bologna, Viale Berti Pichat 6/2, 40127 Bologna, Italy.
Abstract
Stretchable conductors are of crucial relevance for emerging technologies such as wearable electronics, low-invasive bioelectronic implants, or soft actuators for robotics. A critical issue for their development regards the understanding of defect formation and fracture of conducting pathways during stress-strain cycles. Here we present a combination of atomic force microscopy (AFM) methods that provides multichannel images of surface morphology, conductivity, and elastic modulus during sample deformation. To develop the method, we investigate in detail the mechanical interactions between the AFM tip and a stretched, free-standing thin film sample. Our findings reveal the conditions to avoid artifacts related to sample bending modes or resonant excitations. As an example, we analyze strain effects in thin gold films deposited on a soft silicone substrate. Our technique allows one to observe the details of microcrack opening during tensile strain and their impact on local current transport and surface mechanics. We find that although the film fractures into separate fragments, at higher strain a current transport is sustained by a tunneling mechanism. The microscopic observation of local defect formation and their correlation to local conductivity will provide insight into the design of more robust and fatigue resistant stretchable conductors.
Stretchable conductors are of crucial relevance for emerging technologies such as wearable electronics, low-invasive bioelectronic implants, or soft actuators for robotics. A critical issue for their development regards the understanding of defect formation and fracture of conducting pathways during stress-strain cycles. Here we present a combination of atomic force microscopy (AFM) methods that provides multichannel images of surface morphology, conductivity, and elastic modulus during sample deformation. To develop the method, we investigate in detail the mechanical interactions between the AFM tip and a stretched, free-standing thin film sample. Our findings reveal the conditions to avoid artifacts related to sample bending modes or resonant excitations. As an example, we analyze strain effects in thin gold films deposited on a soft silicone substrate. Our technique allows one to observe the details of microcrack opening during tensile strain and their impact on local current transport and surface mechanics. We find that although the film fractures into separate fragments, at higher strain a current transport is sustained by a tunneling mechanism. The microscopic observation of local defect formation and their correlation to local conductivity will provide insight into the design of more robust and fatigue resistant stretchable conductors.
Stretchable
conductive thin films on polymeric substrates are of
pivotal importance for several novel applications such as flexible
and wearable electronics, stretchable bioelectronic implants, microelectromechanical
systems, or soft actuators for robotics.[1−3] In these applications,
the electrical properties of the thin film have to withstand the mechanically
demanding deformations occurring during device operation and wear.[4] A fundamental problem regards the mismatch in
elastic properties between conductive thin film and the dielectric
substrate material. Conductivity relies on rigid metals or conducting
polymers, whereas the substrate is made of soft elastomers to warrant
device compliance. Differences in elastic moduli spanning orders of
magnitude are often the case and lead to the buildup of interfacial
stress during deformation. The consequences are defect formation and
defect evolution as observed in the form of thin film necks, cracks,
fracture, and delamination. Understanding the microscopic mechanism
of defect formation as well as the impact of defects on the electric
properties is of paramount importance to optimize the mechanical wear
resistance as needed in future application scenarios. Despite this
need, microscopy techniques that characterize local morphological,
mechanical, and electric properties of the metal layers in situ during
the deformation process are still missing.[5,6] Only
such multichannel imaging techniques will ultimately enable the correlation
of morphological defects to the electrical response.To date,
several studies demonstrate optical or electron microscopy
techniques combined with mechanical stretching to provide rapid imaging
of the metallic surface during sample deformation.[1−3,7−9] Digital image analysis allows
one to quantify the local strain field and to obtain quantitative
information on the onset of crack formation, the crack length, and
the crack density as a function of the strain.[6,10−12] These are all parameters of central importance to
describe the fracture mechanics of such thin films. The drawback of
optical or electronic imaging techniques comes from the reflection-based
image reconstruction that cannot provide quantitative information
on surface height changes. Accordingly, it is difficult to clearly
distinguish through and part-through surface cracks or necking structures
in tensile strain experiments or to distinguish bulged structures
from delaminated ones. Instead, quantitative morphological information
is provided by atomic force microscopy (AFM) or confocal laser scanning
microscopy. First reports demonstrate the applicability of these microscopy
techniques for in situ experiments combined with macroscopic mechanical
testing and conductivity measurements.[13] Such data is highly needed to establish quantitative models for
predicting the degradation of conductivity as a function of strain.[1,3,4,12,14−16]Despite these
successes, several crucial local properties of the
metal thin film remain experimentally inaccessible, hampering the
development of more precise and realistic mechanical models. This
regards in particular local conductivity, which is notoriously influenced
by the development of the crack pattern. In fact, current models assume
ohmic conductance in the defect-free parts of the metal layer, whereas
through-thickness cracks are considered as completely isolating barriers.[17,18] Relying on these two assumptions, the determination of the conductivity
of the cracked metallic film reduces to the determination of the geometry
of the ohmically conducting pathway connecting through the fractured
film. Once it is known, one can estimate the increase in the effective
path length and its width reduction during the fracture process to
predict the reduction in macroscopic conductivity. So far, no experimental
confirmation has been obtained for these central assumptions. Observations
such as the degradation of conductivity at large strain values already
point to a more complicated role of local conductivity.[17]To address these issues, we report here
an in situ atomic force
microscopy method that provides multichannel images of local surface
morphology, mechanics, and conductivity on strained metal thin films.
The method employs fast repetitive force spectroscopy experiments
combined with a conducting AFM probe. Its application on a free-standing
strained sample is demonstrated, allowing efficient acquisition of
multichannel images at different strain values.Possible artifacts
due to substrate bending or resonant vibration
are analyzed in detail to derive the optimized experimental conditions
for AFM measurements on free-standing samples. As an example, we investigate
the fracture of a thin gold film deposited with an adhesion layer
on silicon elastomer substrates. Similar films have important roles
as stretchable conductor lines in implantable electronics.[19−22] The combination of topographic, micromechanical, and electrical
imaging channels in our microscopy technique allows one to clearly
distinguish different defect types and to understand their effect
on the macroscopic properties. For example, we find that although
the macroscopic conductivity shows linear ohmic conducting behavior,
the local current paths connecting individual fragments behave in
a strongly nonlinear way at increasing strain. The observation points
to the relevance of tunneling based transport processes in microcracked
geometries.
Experimental Section
PDMS/Cr/Au
Preparation
Polydimethylsiloxane (PDMS)
was obtained by mixing cross-linker and Sylgard 184 silicone in a
ratio of 1:8. After intensive stirring, the mixture was degassed to
remove air bubbles. A layer of a few micrometers of polyacrylic acid
(PAA) was spin-coated on the glass substrate before casting PDMS to
decrease the adhesion. After pouring the PDMS mixture, it was allowed
to set for 20 min to spread homogeneously onto the glass. Samples
were then stored for 1 h at 70 °C in an oven. Then the chromium
adhesion layer (5 nm thickness) and gold (18 nm thickness) were deposited
on the glass/PDMS substrates by thermal evaporation (source sample
distance = 25 cm, vacuum pressure = 5.5 × 10–6 mbar). Before clamping the sample in the strain stage, the sample
was manually bent and twisted to precrack the gold surface to avoid
the formation of a single crack cutting all conductive paths. During
release from the glass carrier, the sample is subjected to tensile
strain as well as bending and twisting. Forces leading to these deformations
are applied with a plastic tweezer and are of about 0.5 N. The deformations
cause microcrack formation in the metallic coating. The crack pattern
is similar to observations described in the literature.[20,22−25] The electrical contacts were made with copper tape and a conductive
epoxy silver-based (without the hardener to keep it liquid) to increase
the contact stability during strain variation.
AFM Probe
A Park
System NX10 atomic force microscope
was used in the experiments. The Rocky Mountain Nanotechnology probe
25Pt300B was used to perform fast repetitive force spectroscopy. The
AFM tip used for resonant frequencies investigation was PPP CONTSCR,
while for thickness measurement it was NCHR, with both being from
Nanosensors. Before each experiment, the tip sensitivity and force
constant are calibrated by an indentation on a silicon surface and
thermal tune method. The AFM tips 25Pt300B, PPP CONTSCR, and NCHR
have spring constants equal to 18, 0.2, and 5 N m–1, respectively.
AFM Resonant Frequency Investigation
A loudspeaker
(Visaton K50) was used as a source of acoustic waves and controlled
by a function generator (integrated in the Zurich Instruments MFLI
Lock-in Amplifier). The vibrations of the sample were probed by using
a very soft AFM tip (PPP CONTSCR) in contact with a set point force
of 10 nN. The position sensitive photo detector voltage signal (Va-b) was recorded by using a lock-in
amplifier as a function of the loudspeaker excitation frequency. Since
the impact of a 20 nm thick metal layer on the resonance frequencies
is considered negligible, we performed the experiments on pure PDMS
substrates (2.1 mm thick). The strain stage shown in Figures a and S1 was used to apply different tensile strain values, and
sample oscillation was measured in the frequency range from 10 Hz
to 40 kHz.
Figure 1
Experimental design of multichannel AFM in situ experiments. (a)
Scheme of the experimental setup. The stretcher used to apply tensile
strain to the sample is represented by its clamps. The electrical
circuit permits application of bias between the tip and sample to
measure local currents entering the conducting AFM tip and to measure
also the macroscopic sample conductivity. (b) Optical microscopy image
of the investigated microcracked gold layer. (c) Force–indentation
and current–indentation curves obtained in a single-pixel acquisition.
Blue and red arrows represent the load and unload, respectively.
Experimental design of multichannel AFM in situ experiments. (a)
Scheme of the experimental setup. The stretcher used to apply tensile
strain to the sample is represented by its clamps. The electrical
circuit permits application of bias between the tip and sample to
measure local currents entering the conducting AFM tip and to measure
also the macroscopic sample conductivity. (b) Optical microscopy image
of the investigated microcracked gold layer. (c) Force–indentation
and current–indentation curves obtained in a single-pixel acquisition.
Blue and red arrows represent the load and unload, respectively.
AFM Multichannel Imaging
Height,
stiffness, and current
maps were generated by performing a fast force spectroscopy for each
pixel of the image. Working in contact mode, before fast force spectroscopy,
the approach of the AFM tip to the sample surface is performed. The
approach is concluded when the set point force is reached. To move
from pixel to pixel, the tip is lifted from the substrate. Then the
XY stage is moved to place the new pixel below the tip and a tip approach
is performed before the next force spectroscopy starts. As force spectroscopy
parameters, we set the maximum force to be 500 nN while the speed
of the tip along the Z-axis was 100 μm s–1. We set the lift height as 1 μm, the time for
the pixel-to-pixel motion as 5 ms, and a preapproach time of 100 μs.
These parameters were optimized on PDMS/Cr/Au surfaces, and acquisition
of 128 × 128 pixel images of 40 × 40 μm2 sample area was achieved in ca. 30 min. Current maps were obtained
by applying a potential difference of 100 mV for strain 0% and 10
V for greater strain values, between the sample and the tip. The macroscopic I–V curves were acquired with a
source meter unit (SMU), tuning the voltage between −7 and
7 V, and measuring the current.
Results
Our in situ atomic force microscopy technique is based on the experimental
setup shown in Figure a. This setup provides multichannel acquisitions to map the surface
morphology, micromechanics, and local conductivity as a function of
the strain applied to the sample. A conductive AFM probe is used to
perform simultaneously conductive AFM and force spectroscopy. During
a conductive AFM experiment, a bias voltage is applied between the
AFM probe and the sample to measure the local electrical current (Ilocal) that enters the probe through the contact
area with the thin film. At the same time, the macroscopic current
(Imacro) flowing in the entire sample
is measured with a SMU. Uniaxial tensile strain is applied by a custom-designed
strain stage in which a screw controls the distance between two clamps
that hold the free-standing sample (Figure S1). The dimensions of the sample holder of the strain stage are 2
× 3.5 cm2. The multichannel images are obtained through
fast repetition force spectroscopy. Each pixel of the image corresponds
to force spectroscopy performed with a conductive probe and can thus
provide information on surface height, stiffness, and local current
measured at a threshold force.To test the AFM method, we analyzed
the strain response of a thin
gold film deposited with a chromium adhesion layer on a silicon elastomer
substrate. Such films are considered a prototype of a stretchable
conductor, as during strain a pattern of microcracks evolves, which
absorbs the strain by 3D deformation while maintaining an interconnected
conductive pathway in the gold layer.[25]Figure b shows an
optical microscopy image of such a microcracked film with a gold thickness
of 18 nm and PDMS substrate of 2.1 mm thickness as investigated in
our experiments. A typical measurement curve acquired with force spectroscopy
and conductive AFM on a gold region is shown in Figure c.[26] During the
measurement, the AFM probe is pushed into and retracted from the sample
at constant speed while the force, the current, and the tip position
relative to the surface (indentation) are measured. When the tip contacts
the conductive film, an increase of force and a sudden rise in current
are recorded. During indentation, the current reaches a saturation
value while the force increases linearly. Upon retraction, the force
follows the loading curve as expected for an elastic response. Due
to adhesion, the surface sticks to the tip when it is displaced above
the surface and a negative force is measured while the current remains
stable until the contact is lost during snap off.Since the
images are obtained through fast repetition of the force
spectroscopy experiment, it is crucial to investigate the possible
excitation of resonant oscillations of the free-standing sample that
would interfere with the AFM characterization. To study resonant oscillations,
we used the experimental setup shown in Figure a. Oscillation modes were excited by sound
produced at different frequencies with a speaker connected to a function
generator. The oscillations of the sample were probed with an AFM
tip in contact with the sample. The AFM tip deflection signal was
recorded with a lock-in amplifier and analyzed as a function of frequency. Figure b shows the measured
frequency response of the sample vibrations at different strain. As
expected, an increase in strain corresponds to a shift of the resonance
peak to higher frequencies. To ensure that the AFM measurements are
not affected by the sample’s vibrations, the fast repetitive
acquisitions must operate at frequencies below the first resonance
peak. The resonant frequencies of the sample depend on its dimensions
and the strain applied. Therefore, these parameters define limits
in which the setup can operate.
Figure 2
Investigation of measurement artifacts
in AFM experiments on free-standing
stretched samples. (a) Scheme of the experimental setup to measure
the stretched sample’s resonant frequencies. Oscillation modes
are excited by sound produced at different frequencies. The response
of the sample is measured with AFM in contact mode. (b) Sample oscillation
frequency spectra at different strains. Note that the peak corresponding
to the first mode moves to the right as the strain increases. (c)
Peak frequency, extracted from the data in Figure b, as a function of strain. The red line
corresponds to the analytical model. (d) Power spectral density of
forces between the sample and AFM probe occurring during fast repetitive
force spectroscopy acquisition. Note that tip–sample interactions
occur at frequencies below the first vibration mode of the free-standing
sample, thus excluding possible resonant interactions.
Investigation of measurement artifacts
in AFM experiments on free-standing
stretched samples. (a) Scheme of the experimental setup to measure
the stretched sample’s resonant frequencies. Oscillation modes
are excited by sound produced at different frequencies. The response
of the sample is measured with AFM in contact mode. (b) Sample oscillation
frequency spectra at different strains. Note that the peak corresponding
to the first mode moves to the right as the strain increases. (c)
Peak frequency, extracted from the data in Figure b, as a function of strain. The red line
corresponds to the analytical model. (d) Power spectral density of
forces between the sample and AFM probe occurring during fast repetitive
force spectroscopy acquisition. Note that tip–sample interactions
occur at frequencies below the first vibration mode of the free-standing
sample, thus excluding possible resonant interactions.To understand the dependence of the resonant frequencies
on the
sample dimensions and the strain, we developed a model starting from
the well-known Rayleigh quotient method for vibration analysis and
compared it with the experimental results.[27] The sample is modeled as a prestressed plate clamped at two ends.
Geometrical variations due to large strains and Poisson effects have
been accounted for here. In fact, as the strain increases, the length
increases while the width and thickness decrease. With these considerations,
we obtained the following formula for the first vibrating mode of
a rectangular plate clamped at two ends to which a prestress is applied:where L and h are the length and the thickness
of the sample, respectively, while
ρ is the density, E is the elastic modulus,
ν is the Poisson ratio, and ε is the strain. More details
can be found in the Supporting Information. We then compared the experimental results with the analytical model.
To do so, we considered the dimensions of our sample and the PDMS
material parameters (h = 2.1 mm, L = 19.5 mm, ν = 0.5, ρ = 0.965 g cm–3, E = 2.21 MPa). The elastic modulus of our PDMS
substrate was determined from indentation experiments relying on the
Hertz model for the indentation of a rigid spherical tip into an elastic
half-space.[28] As shown in Figure c, the analytical model agrees
well with the experimental results, even though no fitting parameters
are involved. To exclude the excitation of substrate resonant oscillations,
the force spectroscopy experiments have to be conducted in a frequency
space below the first oscillation peak. Therefore, the repetition
rate of the force spectroscopy has to be much smaller than the first
mode resonant frequency, as all the next modes will have greater frequencies.
In this way, the operation regime is approximately quasi-static and
modal amplification is avoided. The power spectral density of tip–sample
oscillation modes occurring during the approach and retract movement
of the tip is shown in Figure d. The inset displays the related time transient of the tip–sample
force as caused by vertical movements during consecutive fast force
spectroscopy measurements performed in the center of the sample. The
sampling rate during the acquisitions was 1.5 kHz, and the total duration
was around 80 s. The power spectral density demonstrates that significant
frequency components are only below 100 Hz. This is sufficiently lower
than the frequency of the first sample oscillation mode starting at
300 Hz to exclude the excitation of sample oscillatory modes and to
warrant stable AFM measurement conditions.A second possible
artifact during force spectroscopy measurements
on free-standing samples regards global sample deflection. It must
be ensured that the displacement due to bending of the free-standing
sample, δflex, can be neglected with respect to the
local displacement under the tip, δhertz, during
indentation. Combining the expressions for beam deflection with the
Hertz model, the ratio between the deflection and the indentation
is expressed aswhere is the beam cross section inertia and B is the sample
width. Considering our experimental case,
we obtain δflex/δhertz = 0.0008.
For example, considering 500 nN as the maximum, the deflection of
the sample is around 1 nm while the indentation is 1 μm. Therefore,
the bending of the sample is negligible with respect to the indentation.
For this estimation, we neglected the impact of the thin gold layer.
A detailed discussion of eq is provided in the Supporting Information.Knowing the operational limits of our setup, we tested the
in situ
atomic force microscopy method on the stretchable conductor prototype
PDMS/Cr/Au. Figure shows the surface height, stiffness, and current maps for three
different strain values, 0%, 5%, and 10%, respectively. The blue dashed
lines indicate the position of the profile reported at the bottom
of Figure . The straining
direction is indicated by the red arrows. The heights of the morphology
map represent the Z position when the maximum force
value is reached. The stiffness is calculated as the slope of the
force–indentation curve, while the local electrical current
is measured at maximum force. The morphology maps (Z height) and the extracted profiles show that at 0% strain the microcracks
are closed. As the strain increases, the size of the microcracks increases.
As expected, cracks are oriented in a direction normal to the strain.
The maps show that the density of microcracks in the gold thin film
is not strain-dependent: no new cracks are formed during the experiment.
In the morphology maps at 5% and 10% strain, a second effect is present:
the buckling of the gold layer. This is due to the Poisson effect,
i.e., the compression of the sample in the direction orthogonal to
the applied strain.[29] In particular, the
sample transversal strain is expected to be νε and it
is accommodated by the formation of ripples on the sample surfaces,
with crests aligned with the applied strain.
Figure 3
In situ AFM multichannel
acquisition. (a) Morphology, stiffness,
and current maps as a function of strain acquired on the same region
of a microcracked gold film deposited on PDMS elastomer. The strain
direction is represented by the two red arrows on the left. (b) Height,
stiffness, and current profiles extracted from the AFM maps. The dashed
blue lines in (a) indicate the positions of the profiles.
In situ AFM multichannel
acquisition. (a) Morphology, stiffness,
and current maps as a function of strain acquired on the same region
of a microcracked gold film deposited on PDMS elastomer. The strain
direction is represented by the two red arrows on the left. (b) Height,
stiffness, and current profiles extracted from the AFM maps. The dashed
blue lines in (a) indicate the positions of the profiles.The stiffness maps show that the gold film is more compliant
near
the cracks. In fact, the width of the microcracks in the stiffness
maps appears greater than about 1 μm, as measured from the profiles.
It can be conjectured that this effect is caused by the loss of rigidity
of the gold film when it is indented close to the microcracks.[26],[30] Also, note that
the stiffness of the gold film does not vary with strain. This indicates
that the applied strain has two main effects: widen the microcracks
and, through the buckling of the gold layer, create ripples with crests
aligned with the straining direction. From the stiffness maps, we
estimated the elastic moduli of the metal thin film and the polymeric
substrate. Considering the stiffness density distributions shown in
Figure a, one can see the presence of two peaks. The lower stiffness
peak corresponds to the substrate and is therefore the result of the
force spectroscopies performed in the microcracks. As the strain increases,
the part of the image where microcracks are present increases. Therefore,
the peak is more and more evident. On the other hand, the second peak
corresponds to the force spectroscopies made on the regions with the
gold film. Fitting the stiffness density distributions with a sum
of two Gaussians, we estimated the average stiffness values of the
PDMS (dotted lines) and the thin gold film (dashed lines). Given the
mean values, we calculated the elastic modulus of PDMS with the Hertz
model for a spherical rigid indenter in an infinite half-space, obtaining
the following values: E0%PDMS = 2.8 ± 0.5 MPa, E5%PDMS = 2.6
± 0.5 MPa, and E10%PDMS = 2.8 ± 0.2 MPa. To calculate
the elastic modulus of the gold thin film, we used the linear relationship
between force and displacement as predicted by the indentation model
of rigid thin film deposited on a compliant substrate.[26] The values obtained are E0%Au = 92 ±
23 GPa,, E5%Au = 85 ± 27 GPa, and E10%Au = 125
± 43 GPa. The elastic modulus of the gold thin film is found
to be comparable with the bulk value.Current maps shown in Figure were obtained by
applying a potential difference of
100 mV for strain 0% and 10 V for greater strain values, between the
sample and the tip. At 0% strain, the gold film is entirely conductive,
and the presence of the microcracks does not seem to have a major
impact. In this regime the measured current is limited by the tip–sample
contact. At higher strain values instead, there is a drop in the conductivity
of the sample. The measured currents are 3 orders of magnitude lower.
Close observation of the current maps and comparison with the height
maps allows us to identify the two crucial factors that impact the
local current value: First, the height map shows that the microcracks
separate the gold thin film into individual fragments, and on the
current map we see that each fragment is characterized by a constant
current signal. Accordingly, we can conclude that a high conductivity
is preserved within a fragment and the current is limited by how the
fragment is connected to the rest of the film. Second, the map shows
that different fragments are characterized by different current values.
This demonstrates that the current is controlled by the transport
path that links an individual gold fragment to the device contact.
Barriers in the current transport path due to weakly connected fragments
insert resistance that reduces the measured current. The current map
therefore also contains important information on how the current transport
through the microcracked film evolves during strain and highlights
the stochastic nature of the fracture process.To investigate
the current transport onto individual fragments
in more detail, we performed conductive AFM I–V scans at different strain values (Figure b). In the figure, we compare the local conducting
AFM analysis with the overall current flowing through the sample on
a normalized linear scale and logarithmic scale. Both the local AFM
current as well as macroscopic sample current show a significant decrease
with increasing strain. However, they show different shapes as the
strain is increased. The macroscopic I–V curves maintain a linear, ohmic behavior, while the local
current curves show a transition from linear at 0% strain to superlinear
at elevated strains. The observed change in shape suggests that charge
transport at the microscale between the gold fragments occurs by a
field enhanced tunneling effect when strain is applied. Similar measurement
curves have been obtained by studying the tunnel effect in gold nanogap
junctions.[31,32] A quantitative description of
tunneling transport across metal–insulator–metal systems
is provided by the Simmons model.[33] The
model introduces as parameters the insulator width (s), the height of the potential barrier (φ), and the overall
current scale (A), which corresponds to the area
of the two metal regions where charge transport by the tunneling effect
occurs. The model provides a good fit to our data and the obtained
parameter values are reported in Table . The barrier height of 5.4 eV and the gap size of
a few angstroms indicates a dielectric mediated tunneling mechanism
that proceeds through gaps between different gold fragments. Although
the significant strain causes a widening of the cracks in the thin
film, in the direction orthogonal to the strain, fragments remain
closely spaced therefore enabling a tunneling mediated transfer path.
In the macroscopic current measurement, the transition to the superlinear
behavior is not present because a large number of fragments participate
in the transport path. Accordingly, several small cracks have to be
overcome and they all induce small potential steps driving field induced
tunneling. At individual steps, the potential drop remains well below
the tunneling barrier height and a linear response is maintained.
Figure 4
(a) Stiffness histograms obtained from stiffness maps at different
strains. The peak at lower stiffness corresponds to the PDMS, while
the peak at higher stiffness corresponds to Au thin film. The dotted
and dashed lines are Gaussian fits to estimate the average stiffness
of PDMS and Au, respectively. (b) The first graph on the left shows
the macroscopic I–V curve
of the entire metallic thin film at different strains. The graph in
the middle shows the microscopic I–V curve of a single gold region acquired with C-AFM at different
strains. The insets report the same data in a semilogarithmic plot
to show the orders of magnitude. The graph on the right shows the
microscopic I–V curve not
normalized and fitted with the Simmons model describing the tunneling
for a metal–insulator–metal system.
Table 1
Parameters of the Simmons Model Estimated
by Fitting the Local I–V Experimental
Data
strain
S (Å)
φ (eV)
A (Å2)
5%
2.80 ± 0.04
5.7 ± 0.2
0.29 ± 0.01
10%
2.86 ± 0.02
5.4 ± 0.1
0.11 ± 0.01
(a) Stiffness histograms obtained from stiffness maps at different
strains. The peak at lower stiffness corresponds to the PDMS, while
the peak at higher stiffness corresponds to Au thin film. The dotted
and dashed lines are Gaussian fits to estimate the average stiffness
of PDMS and Au, respectively. (b) The first graph on the left shows
the macroscopic I–V curve
of the entire metallic thin film at different strains. The graph in
the middle shows the microscopic I–V curve of a single gold region acquired with C-AFM at different
strains. The insets report the same data in a semilogarithmic plot
to show the orders of magnitude. The graph on the right shows the
microscopic I–V curve not
normalized and fitted with the Simmons model describing the tunneling
for a metal–insulator–metal system.
Discussion and Conclusions
Our work demonstrates an
in situ experimental method to investigate
strain effects in materials and devices for stretchable electronics.
Based on fast repetitive force spectroscopy acquisition with a conductive
AFM probe, the method enables the microscopic investigation of morphological,
mechanical, and electrical properties as a function of strain. The
development became possible through a detailed investigation of possible
artifacts that can occur when dynamic AFM techniques are performed
on a free-standing substrate, only attached at its two ends to the
clamps of a tensile stretcher. By deriving and testing the analytical
equations that describe substrate deflection and resonant vibrations
(eqs and 2), we find the experimental conditions for stable, artifact-free
image acquisition. Disturbing sample deformation modes can be reduced
by using elastic substrates with a sufficiently large thickness to
length ratio and a high elastic modulus or by operating force spectroscopy
at slower approach and retract velocities to avoid excitation of resonant
modes.Once the conditions for stable measurements are met,
our method
provides an unprecedented multichannel imaging technique to correlate
morphological defects generated during tensile strain with the mechanical
and electrical response. As an example, we analyze the tensile deformation
and conductivity changes of a thin gold film deposited with a chromium
adhesion layer on a silicon elastomer substrate (PDMS). With our experimental
setup, we provide unique insight into the mechanisms of charge transport
across gold regions separated by microcracks. For this, the combination
of all three imaging channels is crucial: First, the surface height
mapping allows us to identify gold fragments surrounded by microcracks
and to investigate their morphological evolution during strain. Second,
the micromechanical imaging channel provides quantitative measurements
of the local elastic modulus. It demonstrates that the externally
applied strain is locally absorbed in microcrack widening while gold
fragments do not alter their physical extension and stiffness properties
as increasing strain. Third, the local conducting properties demonstrate
that individual gold fragments remain highly conductive and transport
is crucially determined by cracks separating the conducting fragments.
We note that, for gold on elastomer films, processing conditions such
as gold and adhesion layer thickness as well as pretreatment procedures
have a crucial impact on how the microcrack pattern forms and separates
islands. In the case studied here, we find at lower strains that a
fully conductive, ohmic pathway remains present even though cracks
widen in the direction perpendicular to the strain. Instead, at higher
strains, our detailed analysis of local I–V curves demonstrates the transition from the ohmic regime
into a tunneling dominated regime, where local barriers have to be
overcome by a field enhanced tunneling mechanism. We associate such
barriers to microcracks oriented in the direction parallel to the
strain. Only in this direction, cracks do not open significantly,
thus leaving fragments in close enough proximity to permit tunneling
transfer.In conclusion, our work demonstrates a new in situ
experimental
approach to investigate mechanical and electrical properties and their
correlation at the microscale. It enables one to map properties of
stretched samples as a function of strain and to access experimentally
the local electrical properties. Both are crucial aspects to understand
and predict the properties of stretchable conductors. Based on fast
force spectroscopy measurements, the technique is compatible with
different materials applied for stretchable electronics comprising
hard metallic as well as softer polymeric conductors. We highlight
the value of the method by demonstrating the transition from local
ohmic transport to field enhanced tunneling at increasing tensile
strain in a microcracked gold layer. So far, models of the conductivity
of thin films subjected to strain, assume ohmic transport in the defect-free
parts of the metal layer, whereas through-thickness cracks are considered
as completely isolating barriers.[17,18] However, our
results show that charge transport occurs even if a conducting fragment
is completely surrounded by microcracks due to the tunneling effect,
introducing a conduction mechanism that has not been accounted for
in models.
Authors: Fei Hang; Dun Lu; Russell J Bailey; Ines Jimenez-Palomar; Urszula Stachewicz; Beatriz Cortes-Ballesteros; Martin Davies; Martin Zech; Christoph Bödefeld; Asa H Barber Journal: Nanotechnology Date: 2011-08-16 Impact factor: 3.874