In-situ force microscopy to investigate fracture in stretchable electronics: insights on local surface mechanics and conductivity

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 novel atomic force microscopy (AFM) method 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 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 novel insight to design more robust and fatigue resistant stretchable conductors.


Introduction
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][2][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 build-up of interfacial stress during deformation. The consequence 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][2][3][7][8][9] Digital image analysis allows then 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][11][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 or confocal laser scanning microscopy. First reports demonstrate the applicability of these microscopy techniques in insitu 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][15][16] Despite these successes, several crucial local properties of the metal thin film remain experimentally not accessible, 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 on these central assumptions. Observations such as the degradation of conductivity at large strain values point already 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][20][21][22] The combination of topographic, micromechanical and electrical imaging channels in our microscopy technique allows 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 non-linear way at increasing strain. The observation points to the relevance of tunneling based transport processes in microcracked geometries.

Result
Our in-situ atomic force microscopy technique is based on the experimental setup shown in Figure 1a. This setup provides multichannel acquisitions to map the surface morphology, micro-mechanics, 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 ( ) that enters the probe through the contact area with the thin film. At the same time, the macroscopic current ( ) 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 multichannel images are obtained through fast repetition force spectroscopy. Each pixel of the image corresponds to a 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 (PDMS). Such films are considered a prototype of a stretchable conductors, as during strain a pattern of microcracks evolves, that absorbs the strain by 3D deformation while maintaining an inter-connected conductive pathway in the gold layer. [23] Figure 1b shows an optical microscopy image of such a microcracked film with a gold thickness of 18nm and PDMS substrate of 2.1mm 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 1c. [24] 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.  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.
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. [25] The sample is modeled as a pre-stressed plate clamped at two ends. Geometrical variations due to large strains and Poisson effect have been accounted for. 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 pre-stress is applied: where and ℎ are the length and the thickness of the sample, respectively, while is the density, is the elastic modulus, is the Poisson's ratio and 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 ). 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. [26] As shown in Figure   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 2b, as a function of strain. The red line corresponds to the analytical model. d) Power Spectral Density of forces between 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 freestanding sample thus excluding possible resonant interactions.
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 3 shows the surface height, stiffness, and current maps for three different strain values, 0%, 5%, 10% respectively.
The blue dashed lines indicate the position of the profile reported at the bottom ofFigure 3. 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 map at strain 10% 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 that in which the strain is applied. [27] 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. [24,28] Also, note that the stiffness of the gold film does not vary with strain. This indicates that the effect of strain on the single gold region is mainly to increase the distance to other regions, i.e. widen the microcracks.   Figure 3 were obtained by applying a potential difference of 100 mV for strain 0% and 10V for greater strain values, between the sample and the tip. At the same time, we apply a voltage difference of 7V between the two ends of the freestanding film to monitor its macroscopic conductivity and to induce a lateral contrast in the current maps. 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 from linear at 0% strain to superlinear at elevated strains. The observed shape suggests that charge transport at the microscale between the gold fragments occurs by a field enhanced tunneling effect. Similar measurement curves have been obtained by studying the tunnel effect in gold nanogap junctions. [29,30] A quantitative description of tunneling transport across metalinsulator-metal systems is provided by the Simmons model. [31] The model introduces as parameters the insulator width ( ), the height of the potential barrier ( ), and the overall current scale ( ), 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

Conclusions and Discussion
Our work demonstrates a novel in-situ experimental method to investigate strain effects in materials and devices for stretchable electronics. Based on fast repetitive force spectroscopy acquisitions 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 (Equation 1 and Equation 2), we find the experimental conditions for stable, artifact-free image acquisitions. Disturbing sample deformation modes can be reduced by using elastic substrates with a sufficiently large thickness to length ratio, 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 silicon elastomer substrates (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 to identify gold fragments surrounded by microcracks and to investigate their morphological evolution during strain. Second, the micromechanical imaging channel provides quantitative measures on the local elastic modulus. It demonstrates that the externally applied strain is locally absorbed in micro-crack 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, the 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 IV-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 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 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. 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 on 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. 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 the fast force spectroscopy the approach of AFM tip to the sample surface is performed. The approach is concluded when the setpoint 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 500nN, while the speed of the tip along the Z-axis was 100 µ −1 . We set the lift height to be 1µ , the time for the pixel-to-pixel motion to be 5ms, and a pre-approach time of 100 µ . These parameters were optimized on PDMS/Cr/Au surfaces and an acquisition of a 128x128 pixels images of 40x40 µ 2 sample area is achieved in ca. 30 minutes. Current maps were obtained by applying a potential difference of 100 mV for strain 0% and 10V for greater strain values, between the sample and the tip. The macroscopic I-V curves were acquired with a SMU, tuning the voltage between -7 V and 7 V, and measuring the current. The multichannel images of the in-situ AFM experimental method proposed in this work are obtained through fast repetition of the force spectroscopy experiment. Therefore, it is crucial to investigate the possible excitation of resonant oscillations of the free-standing sample that would interfere with the AFM acquisitions. A picture of the strain stage is shown in Figure S1a, while a picture of the experimental setup showing the free-standing configuration, is reported in Figure S1b. To understand the dependence of the resonant frequencies on the sample geometry 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. [25] The sample is modeled as a pre-stressed rectangular plate clamped at two ends. Geometrical variations due to

PDMS/Cr/Au preparation
where and ℎ are the length and the thickness of the sample, respectively, while is the density, is the elastic modulus, is the Poisson's ratio and is the strain.
We then investigated the impact on force-indentation curves of the bending of the sample. In fact, considering the force applied from the AFM tip as a concentrated force, it must be ensured that the bending of the free-standing sample can be neglected with respect to the indentation of the tip inside the sample. To get an estimate of the bending at the center of the sample, we assumed the plate to behave like a beam clamped on both ends. The stiffness of the beam is then given by the formula: