Link between cracking mechanisms of trilayer films on flexible substrates and electro-mechanical reliability under biaxial loading

Flexible electronics are a technological innovation that involves the use of flexible polymer substrates as the basis structure for the assembly of electronic circuits.^1–3 Currently, flexible electronic devices have new emerging applications, especially for foldable displays and even in biology for integration on skin.^4,5 Flexible polymeric substrates show the advantages of low cost, light weight, mechanical compliance, and bendability.⁶ Nonetheless, these systems suffer from limited durability, both mechanically and electrically due to the multicracking phenomenon during loading.^7,8

Flexible electronics are generally fabricated from single and multilayers of various thicknesses and materials. Metallic multilayers have been an important field of study for materials scientists for almost three decades with the Cu/Nb system^9–11 being one of the most studied, followed by Cu/Ni,^9,10,12 Cu/W,^13,14 Cu/Cr,¹² Cu/V,¹⁵ and Al/Nb.¹⁵ An advantage of metallic multilayers is the improved yield strength due to the addition of more interfaces to hinder dislocation movement through confined layer slip (CLS) models^16,17 and smaller grain sizes inherent to thin films described by the Hall–Petch theory. For many multilayer applications, the individual layer thicknesses ranged from 1 nm up to 100 nm, and an increased hardness was measured with nanoindentation as the single layer thickness was reduced.^12,15,16,18

In flexible electronics, the most utilized experiment to evaluate single and multilayer film systems is the fragmentation test,^19,20 which is uniaxial straining with the load applied parallel to the interfaces of the film(s) on compliant polymer substrates. For multilayers, such as the Cu/Nb system and others, evaluated with fragmentation testing, brittle fracture at relatively low applied strains (mostly less than 1% strain) was observed rather than an improved strength.^{13,14,21–23} A more detailed look at how ductile/brittle bilayers on polymer substrates behave under uniaxial tension found that normally ductile metal films will perform similar to an adjacent brittle metal film.^24–29 This behavior was observed when the brittle layer is used as an adhesion interlayer or as a protective layer on top of the ductile film (similar to a passivation layer) because cracks form first in the brittle layers. Using finite element (FE) simulations,²⁴  experiments with transparent substrates,^28,30  and selective etching,^31,32  it was found that the cracks that form in the brittle layer act as stress concentration points in the ductile layer at the same or similar position where the cracks are located, regardless of the position of the brittle layer (interlayer versus overlayer). Therefore, it is necessary to further study and understand how individual thin films react under different loading conditions.

Many works have studied the mechanical behavior of multilayers in order to profit from interfaces and mechanical contrasts (ductile/brittle, stiffness) between each layer to improve durability.^26,33 However, deformation mechanisms, the role of interfaces, and layer stacking effects are not fully understood by the scientific community. Especially, understanding the initiation and evolution of cracks at the nanoscale in multilayer systems is still challenging. In this context, the contribution of synchrotron x-ray diffraction (XRD) is essential to study in situ mechanical properties of these complex nanosystems.³⁴ When one film thickness in the multilayer is varied, such as in the work of Polyakov et al.,²² load sharing phenomena was observed in the Cu/Nb system. This study used in situ XRD straining and varied the Cu thickness, while keeping the Nb thickness constant and demonstrated how the multilayer architecture (layer thicknesses and layer order) could be tailored to improve the mechanical behavior of the multilayer. What is also of interest is that in situ XRD straining of multilayers will measure the stresses in all Cu layers and all Nb layers without the ability to separate the different layer positions. Often with in situ XRD experiments, the reflection geometry is used, as will be presented here. In this geometry, it is possible to measure the stress evolution in each layer material separately through the Bragg peak shifts^35,36 if the layers are not repeated and the peaks of the different layers do not overlap. In addition, coupling XRD with electrical resistance measurements is helpful to better understand the deformation mechanisms of the whole multilayer systems.^8, In situ electrical resistance measurements can correlate fracture or deformation events depending on the best electrically load carrying material (materials with lowest resistance). When the electrical response compared to the constant volume approximation theory³⁷ deviates, it is clear when brittle fracture or more ductile deformation occurs during straining. Therefore, only the material or layer with the best conductivity reflects behavior changes due to loading, since it will overshadow behavior changes of the other materials or layers.

The aim of this work is to study the fundamental cracking aspects in trilayer systems composed of three distinct materials under biaxial straining. The specificity of in situ XRD enables following the evolution of lattice strains in the different layers. The chosen trilayer is composed of two brittle materials (Cr, Mo) and one ductile (Cu). Mo is deposited directly on a polyimide (PI) substrate (first layer), Cu is the middle layer, and Cr the top layer [Fig. 1(a)]. The two different film systems will be compared in terms of stress development and electrical response to provide insight into how fracture and deformation of multilayers can be influenced by increasing the ductile layer thickness. The theory is that increasing the middle ductile layer will improve the fracture resistance of multilayers.

The layers have been deposited by magnetron sputter deposition onto 50 μm thick precut PI (Kapton-HN, DuPont) substrates cut in a cruciform shaped similar to Ref. 38. One PI/Mo/Cu/Cr triple layer architecture had a nominal 100 nm thickness for each layer and a second architecture with the same layer order, but with a 500 nm thick Cu layer. Of note is the strong contrast in residual stress in each layer. XRD measurements showed that, for both systems, the Cr top layer is strongly tensile (around 2.5 GPa), Mo is strongly compressive (between −1.5 and −2.0 GPa), and Cu is very slightly tensile (a few 0.1 GPa). Due to the Cr layer having a tensile residual stress, the chosen film architecture is convenient to study crack propagation initiated in the top brittle layer. The objective is to follow the influence of the Cu ductile layer thickness on the multiplication and propagation of cracks through the whole trilayer and the related effect on electrical behavior.

The films were incrementally equibiaxially loaded in situ up to 3.5% strain at the DiffAbs beamline of the SOLEIL synchrotron in combination with digital image correlation (DIC)^39,40 and electrical resistance measurements⁴¹ [Figs. 1(a)–1(d)] similar to Refs. 33 and 36. The initial XRD scans before straining were used to calculate the residual stresses of each layer (sin²ψ method).⁴² For the DIC, a random speckle pattern from spray paint, consisting of crystalline rutile-type TiO₂, on the backside of the sample was used. The diffraction peaks of the stress-free rutile-type TiO₂ were also used as the calibration of the diffraction patterns for the strained metal films.³⁹ Electrical in situ resistance measurements were performed using the Van der Pauw method as described in Ref. 41. Silver paste was used to contact the surface of the sample with thin copper wires connected to the electrometers that were arranged rectangularly far from the borders of the biaxially strained area. The XRD experiments were performed with a beam energy of 9.66 keV (λ = 0.124 nm, spot size 244 × 207 μm², XPAD-S140 detector). The in situ film stresses during the straining experiment were determined with the sin²ψ method, where the stress is calculated from the measured deformation of the crystal lattice using elastic constants.⁴² Eight ψ angles (70, 60, 50, 40, 30, 20, 10, and 0°) and the x-ray elastic constants (i.e., elastic constant that links the x-ray lattice strain to the macroscopic stress acting on the film) of the metal layers were used for Mo{110}, Cu{111}, and Cr{110} [1/2S₂(110)_Mo = 4 × 10⁻¹² Pa⁻¹, (1/2S₂(111)_Cu = 7.9 × 10⁻¹² Pa⁻¹), (1/2S₂(110)_Cr = 4.5 × 10⁻¹² Pa⁻¹)].⁴³ The thin films do not show any strong texture and can be considered as quasi-isotropic, i.e., macroscopically elastically isotropic.⁴² Only one principal direction (one azimuthal angle) instead of two was measured with XRD to increase the density of measured points. The position (2θ) and full width at half maximum (FWHM) of the diffraction peaks were determined using a custom routine with Python 2.7 utilizing a Pearson VII function⁴⁴ and a linear background. The FWHM evolution provides information about the lattice defect density and strain heterogeneities through changes of the peak width and, thus, contributes to the determination of different behavior (domains) in the sample.³³ Following the tensile experiments, all samples were examined with confocal laser scanning microscopy (CLSM, Olympus LEXT 4100), scanning electron microscopy (SEM), and focused ion beam cross-sections (Zeiss Leo 1540).

Biaxial straining of trilayers with 100 and 500 nm of Cu emphasized how the thickness of the middle layer influences the electromechanical behavior, i.e., the internal stress in each layer and the combined electrical resistance. For the first triple layer [Figs. 2(a) and 2(b)], with 100 nm of Cu, two domains of mechanical behavior can be distinguished using the stress data and the FWHM. While the stress evolution is related to the mean lattice strain in each layer, the FWHM evolution is the signature of strain heterogeneities occurring during deformation.³⁵ Domain (i) of Fig. 2(a) illustrates a linear increase in stress in Cr and Mo that characterizes an elastic behavior of both brittle materials and a slightly nonlinear increase in Cu that is due to some plastic deformation in this ductile layer. The electrical resistance remains almost constant in domain (i). At the end of domain (i), the stress value of Cr is about 3.4 GPa while it is −1.0 GPa for Mo and 0.5 GPa in Cu. The domain (ii) of Fig. 2(a) is characterized by the stress decrease in the Cr layer, which is related to the initiation of cracking in this top layer. Domain (ii) corresponds to a slight stress decrease in Cu and a (compressive) stress plateau in Mo, indicating that the cracking initiated in the top Cr layer also induced subsequent fracture of the whole film system. The crack propagation through all three layers can be seen on the electrical resistance curve in Fig. 2(a) (dashed green line), which increases sharply from the beginning of domain (ii). Therefore, in this triple layer, the thickness of the ductile interlayer is too low to prevent direct crack propagation through all three layers. Globally, a slight increase of FWHM is observed in Cr and Cu due to cracking and plasticity/cracking, respectively [see Fig. 2(b)]. A similar FWHM increase is not observed in Mo because the layer remains in a compressive state, rather a slight decrease is observed in domain (ii) which may be due to elastic recovery after cracking and is still under investigation.

The behavior of the triple layer with 500 nm of Cu is more complex [Fig. 2(c)] and domain (i) can be divided into three parts. The domain (i₁) corresponds to the elastic regime in Cr and Mo, and to the elastoplastic regime in Cu. At the end of this domain (i₁), the stress in Cr is almost 3.3 GPa, comparable to the maximum value obtained for the first system, while Mo is still slightly compressive (about −0.2 GPa) and Cu slightly tensile (about 0.6 GPa). Domain (i₂) starts at the stress decrease in the Cr top layer related to crack initiation, at a similar stress level as the first system. In this domain (i₂), it can be seen that Mo stress continues to increase further to 0.3 GPa (tensile), indicating that the bottom brittle layer has not yet reached its fracture stress. At the same time, the stress in Cu decreases, which is believed to be due to strong localized plastic deformation beneath the initiated cracks of the Cr layer (similar to crack blunting³³). This localized plasticity is also seen as the strong increase of the FWHM in domain (i₂) for Cu due to dislocation storage [Fig. 2(d)]. Thus, the first cracks (primary cracks) in the top Cr layer that formed at (i₁) induce stress concentration cites in Cu,²⁴ but not to a sufficient depth to immediately force cracks in the lower Mo film to form. As a consequence, no significant change in electrical resistance can be seen at this stage [Fig. 2(d), green dashed line], indicating that the Cu film is continuous enough to allow current flow. It should be noted here that the stress in Cr strongly decreases in domain (i₂), which generally corresponds to the multiplication of cracks in the Cr layer. The crack multiplication is accompanied by a strong increase in FWHM of the Cr Bragg peak [see Fig. 2(d)].^34,36 Domain (i₃) corresponds to the decreasing stress in the Mo layer that is attributed to the crack initiation in the bottom layer. Even if the measured stress in Mo is low (0.3 GPa), the local value can be much higher because of heterogeneities induced by localized plasticity in Cu (through the interface), then the stress must be high enough to initiate cracks in Mo. The initiation of cracks in the Mo layer occurs where the local stress is higher and are not necessarily vertically aligned with cracks initiated in Cr due to the complex stress field in Cu [created in domain (i₂)] that may induce high heterogeneities in Mo. Moreover, in domain (i₃), the stress in Cr continues to decrease significantly, accompanied by an increase of FWHM and new (secondary) cracks are created only in the Cr layer. A slight increase of electrical resistance from theory is observed in domain (i₃) because through thickness cracks are starting to propagate through the middle Cu layer.

Domain (ii) corresponds to the cracking through all layers. The electrical resistance increases more significantly, but the slope is much lower than for the first system with the 100 nm Cu layer. In this domain, the cracks already present in Cr and Mo layers must find paths through the ductile Cu layer. The stress variations in the three layers are relatively low (slight decrease), as compared to other domains. If the two systems are compared (100 and 500 nm of Cu), it is visible that the stress in the Cu at the end of the test has returned almost to its initial value for the 500 nm film. This is notable due to the strong plastic deformation that the layer undergoes in (i₂) and (i₃) domains, which is less than the case for the other system since the overall cracking is almost instantaneous as soon as the cracks in the Cr are initiated.

The R/R_o response in both systems can be described using what is known from in situ resistance measurements of bilayers under uniaxial straining. For example, the sharp increase of the 100 nm Cu system from the purple solid theory line in Figs. 2(a) and 2(b) qualitatively supports that a high density of long through thickness cracks is present. In the 500 nm Cu system, the slope of the R/R_o increases at a lower rate from the purple theory line [Figs. 2(c) and 2(d)] and indicates that the Cu layer most likely necks between the Cr and Mo films. Necking is known to slightly increase R/R_o of ductile/brittle bilayers, especially as the ductile layer thickness increases.^26,32 At higher applied strains, the slope of the R/R_o increases more and is an indication that more structural damage in the film with the lowest resistivity (highest conductivity) is occurring, in the form of a higher density of through thickness cracks. Additional characterization of the films, presented next, would provide further correlation of the electrical behavior. Compared to Cu/Mo²⁶ and Al/Mo³² bilayers subjected to uniaxial strain, the Cr/Cu/Mo trilayers have a similar response under biaxial loading.

The after straining visualization of the samples was examined with CLSM and SEM. Figures 3(a) and 3(d) show the plan views by CLSM at the same magnification. What is immediately striking is the presence of fragments separated by cracks with strong optical contrast. These cracks are the cracks which propagated through all layers. A first difference is the “wavy” character of the main cracks in the case of Cu 500 nm [Fig. 3(d)]. This character has already been mentioned by Godard et al.⁴⁵ in the case of 600 nm Ni films and attributed to plastic deformation for these thicknesses of several hundreds of nm. Moreover, it can be seen in Fig. 3(d) that the system comprising of 500 nm of Cu shows a network of secondary cracks in the top Cr layer that are much less contrasted. These cracks are attributed to the multiplication of cracks observed only in the Cr top layer in the (i₂) and (i₃) domains [Fig. 2(c)] and do not traverse through the Cu or Mo layers, similar to Putz et al.²⁸ It should be noted that the secondary cracking in the top Cr film would only be observed in the stress data or with images. The electrical resistance may not be able to detect additional cracking in the Cr layer due to the fact that the resistance of the Cu layer would overshadow that of Cr and Mo. SEM images of the 100 nm Cu trilayer [Figs. 3(b) and 3(c)] show a direct and vertical propagation through all layers, in agreement with the interpretations of the stress monitoring in the different layers during deformation [Fig. 2(a)] and the electrical response. In Fig. 3(e), a crack propagating in a tortuous path through the 500 nm Cu layer and in Fig. 3(f) cracks of Cr and Mo join by a very complex path in the 500 nm Cu. The electrical response also supports that necks or transgranular cracks are present in the thicker Cu layer. Moreover, cracks that remain clearly confined in the Cr (secondary cracks) without propagating in the Cu are observed.

Overall, Figs. 3(e) and 3(f) show that there are undoubtedly more channels for electrical conduction in the system with 500 nm of Cu than in that with 100 nm. This is why the changes in electrical resistance shown in Fig. 2 are very different for the two systems and why the magnitudes reached are incomparable (several orders of magnitude as soon as the multicracking phenomena are initiated). These enormous differences are intrinsically due to the deformation mechanisms depending on the architecture of the trilayer system, and which would also be so in more complex multilayer systems. Indeed, the thickness of the Cu layer has an intrinsic influence on its plasticity.⁴⁶ It is known that for layers of several hundred nanometers, Cu (or Au, Al) films are subject to a dislocation-based plasticity with nucleation and motion of few dislocations per grain.⁴⁷ And, a thicker ductile layer is beneficial in developing a large plastic strain field underneath the Cr cracks to help deflect or blunt a propagating crack. Therefore, a crack propagating through the thicker Cu layer will more likely extend at an angle to the load, whereas in the thinner Cu film, the crack propagation is vertical.⁴⁸ Additionally, if large grains are present in the thicker Cu film, cracks could propagate horizontally to connect cracks between the Cr and Mo layers, making the ductile fracture more complex in the 500 nm Cu, as compared to 100 nm Cu trilayer. More globally, previous studies have shown that for ductile layers such as Cu, the 100 nm thickness correspond to a transition between complex (not straight) cracking path related to the in-grain dislocation activity (large thickness and grain size) and vertical cracking path along columnar grain boundaries (small thickness and grain size), either in quasistatic⁴⁹ or fatigue test.⁵⁰ Therefore, it is possible to achieve a higher effective fracture toughness of flexible systems with large ductile layer thicknesses.²⁶ 

To conclude, this study showed that the propagation of a crack in a trilayer system starting from the upper layer can follow more or less direct paths depending on the thickness of a ductile middle layer. These cracking mechanisms have been monitored using in situ XRD and electrical resistance and clearly demonstrate how plastic deformation of the ductile middle layer can make a difference in the electromechanical behavior of flexible or stretchable electronics-dedicated systems. These results are important to better anticipate the nanoscale architecture of thin films to guarantee improved durability and reliability.

SOLEIL is gratefully acknowledged for the beam time allocation (Proposal No. 20210224) as well as the support of D. Thiaudiere. This work was in part supported by the French National Research Agency (ANR, Project No. ANR-20-CE91-0010) and the Austrian Science Fund (FWF, Project No. I 4913-N) within the framework of the project: Nanoarchitected films for unbreakable flexible electronics (NanoFilm). V. L. Terziyska from the Montanuniversität Leoben is also acknowledged for deposition of the samples.

The authors have no conflicts to disclose.

S.A.H. and P.K. have contributed equally to this work.

S. Altaf Husain: Data curation (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Writing – original draft (equal). P. Kreiml: Data curation (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Writing – original draft (equal); Writing – review & editing (equal). P.-O. Renault: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Funding acquisition (equal); Investigation (equal); Methodology (equal); Supervision (equal); Writing – original draft (equal); Writing – review & editing (equal). C. Mitterer: Conceptualization (equal); Data curation (equal); Methodology (equal); Writing – review & editing (equal). M. J. Cordill: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Funding acquisition (equal); Investigation (equal); Methodology (equal); Writing – review & editing (equal). D. Faurie: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Funding acquisition (equal); Investigation (equal); Methodology (equal); Supervision (equal); Writing – original draft (equal); Writing – review & editing (equal).

The data that support the findings of this study are available from the corresponding author upon reasonable request.