The influence of Pt islands on the failure of Pt thin film on a flexible PET substrate

Flexible electronic devices must adapt to compliant polymeric substrates, thus maintaining the mechanical integrity of the multilayer systems is crucial. This study investigates the mechanical failure caused by active islands, focusing on how Pt islands influence the failure mechanism of a thin Pt film on a flexible polyethylene terephthalate (PET) substrate under uniaxial tensile loading. Tensile testing of the Pt film/PET bilayer revealed a failure progression in the Pt blanket film, characterized by crack initiation, elongation and merging, eventually delamination, and buckling, with the increase in tensile strain. Pt islands induced early crack initiation at comparatively low strains due to increased stress near their vertical edges. The impact of island shape and gap on the crack formation in a Pt film was subsequently investigated. The gap between islands, oriented perpendicular to the loading direction, has minimal impact on crack number and density; the presence of Pt islands reduced the stress in the Pt film within the gap, thereby lowering the susceptibility of cracking in these areas. Variations in island shape and gap along loading direction alter the stress profile in the film between islands but did not significantly impact crack density. Crack density is believed to be primarily associated with pre-existing defects, with the formation of cracks serving as a stress relief mechanism that prevents further crack initiation. Our study sheds light on the impact of active islands on blanket film failure and offers practical recommendations to mitigate crack formation, which may contribute to the optimisation of flexible electronics design.


Introduction
Flexible microelectronics is rapidly gaining attention in our daily lives and is poised to become a mainstay of the expanding electronics industry.The advent of strain-accommodating microelectronic systems, capable of bending, stretching, and twisting, integrating multilayered thin film devices onto Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence.Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.flexible polymeric substrates, presents a promising avenue for cost-effective mass production through roll-to-roll processing [1][2][3][4][5].The flexible substrates usually include polyethylene terephthalate (PET) [6], polyimide (PI) [7], and paper [8], which provide a durable, lightweight, and flexible platform for incorporating active electronic components, such as transistors and sensors.Among them, PET is the most common material used due to its excellent combination of mechanical and thermal stability, flexibility, and low cost [6,[9][10][11][12][13].
An archetypical approach for constructing electronic devices on a thin polymer substrate involves attaching metal islands/cells with active elements and sub-circuits upon a blanket inorganic (metallic or dielectric) film supported by a compliant polymer base [14][15][16][17][18].These active islands of various shapes are distributed in an array at predetermined intervals across the substrate.This configuration enhances the electronic circuit's flexibility and resilience, effectively ensuring its functionality against damage during deformation [19][20][21][22].While the polymer substrate and the islands may endure substantial elongation, the thin inorganic blanket film may not [23].The implementation of these islands alters the stress distribution within the supported blanket film, potentially increasing the localised stress level adjacent to these islands and resulting in failure of the thin film [24].The failure of the blanket films, especially in the form of cracking, could compromise the functionality of the device due to a reduction in conductivity [25][26][27][28].
Considerable research has been dedicated to studying the interfacial properties in relation to the failure of blanket films [29][30][31][32].For instance, a submicron Cu film poorly adhered to a compliant PI substrate fracture at tensile strains of 1%-2% while a well-bonded Cu film can sustain strains up to 20% without appreciable cracks [23,24,33].However, there is a lack of research concerning the impact of active islands on the failures in blanket inorganic films.Understanding the potential mechanical failures in these inorganic thin films, particularly in a typical island/thin film/substrate hybrid structure resembling those employed in flexible electronics, is important for guiding device design and improving product durability and reliability.
In this study, a hybrid structure that consists of platinum (Pt) islands, a thin Pt blanket film and a PET substrate was fabricated, mimicking the configuration commonly used in multilayer flexible electronics on a polymer substrate.It should be noted that platinum (Pt) was selected for both the island and blanket film deposition given its widespread use in the fabrication of conductive layers and interconnects in microelectronic [34,35].Compared with Ag or Cu electrodes, which are not stable under heat treatment or long-term exposure in air atmosphere, Pt offers exceptional electrical stability in harsh environments.This is due to its catalytic activity for the reduction of the redox couple, enabling its use as a counter electrode in dyesensitized solar cells [36,37].The inertness, biocompatibility, and excellent electrical properties of Pt have also led to a widespread adoption in biomedical applications, including neural interfaces in implantable devices [38,39].Its excellent conductivity of Pt is essential for electron microscopy.A uniaxial tensile loading was applied to impose strain to the Pt blanket film, and the resultant surface cracking was characterised and analysed.The influence of the Pt islands on the failure of the blanket film under tensile loading was systematically investigated by varying the shape and distribution of the islands.Finite element modelling (FEM) was employed for stress analysis to gain insight into the failure mechanism of the Pt thin film in the presence of the Pt islands.

Material
The 100 µm thick flexible PET film was cut into rectangular strips with dimensions of 80 mm × 10 mm.The strips were subsequently sputter-coated with a 30 nm Pt blanket film using a plasma coater (Q150 T, Quorum). Figure 1(a) displays the PET specimens prior to and after Pt coating, as well as after tensile testing.

Micro-islands fabrication
Pt islands were fabricated using a dual-beam focused ion beam (FIB)-SEM system (FEI Scios Dualbeam, Oregon, USA) operating at an accelerated voltage of 30 kV and a current of 1 nA.The deposition time for each island ranged from 3 to 4 min depending on the island shape.This parameter was optimized to maximise deposition efficiency while minimising ion-beam damage [40,41].A set of 5 islands linearly aligned was fabricated to examine the influence of Pt islands on the cracking behaviour of the thin Pt blanket film.Then, a 3 × 3 array of islands were deposited to study the effect of shape (circular versus square) and gap (varying horizontal (tensile-direction) and vertical distances, denoted as h and v respectively) on the cracking behaviour.Figure 1(b) shows a SEM image of a typical 3 × 3 array of Pt islands on the Pt-coated PET substrate.The square-shape islands had dimensions of 10 µm in edge length and 1 µm in thickness.The circular islands had a diameter of 10 µm and a thickness of 1 µm.

Mechanical test
Tensile testing of the hybrid structure on PET flexible substrates was performed at room temperature using an Instron 5584 Universal tester with a 1 kN load cell in the uniaxial tensile mode at a loading rate of 0.01 mm s −1 .Pre-loading was applied to eliminate errors induced by inappropriate gripping or misalignment.Strain measurement was conducted using an Advanced Video Extensometer (Instron, USA).The gauge length of 30 mm was defined by marking two points on the strip (see figure 1(a)).First, tensile tests were conducted on the bare PET strips to obtain a stress-strain curve to the point of failure.The yield and failure strain of PET were determined to be approximately ε = 2% and 50%, respectively.Subsequently, the PET strips, coated with 30 nm Pt film, underwent progressive tension to determine the failure threshold of the Pt blanket film; the applied maximum strain varied from 2% to 6%.At last, the specimens with different Pt islands configurations on the Pt film/PET bilayer were tested at a maximum strain of 2%.

Characterisation
A laser confocal microscope (LEXT, Olympus) and FIB-SEM dual-beam system were used to analyse the specimen surfaces before and after mechanical loading.The analysis focused on surface cracks, with an emphasis on quantifying crack density.Additionally, the FIB-SEM system was used to obtain crosssectional images of the tested sample and examine the interface between the island and substrate following tensile testing.commercial software ANSYS 22R2.To optimize computational efficiency, the hybrid structure models consist of only three islands aligned either parallel or normal to the tensile direction, with the PET substrate dimension set at 200 µm × 100 µm × 10 µm.Note that the model size is considerably smaller than the tested specimen, but the reduced substrate size is not expected to influence the validity of the model, given the uniaxial nature of the applied loading.The Pt thin film in the model had a thickness of 30 nm, and the islands were accurately scaled to match those on the tested sample.Uniaxial tensile loading was applied to the hybrid structure with one end of the sample fixed, and the load applied to the opposite end.The elastic modulus of PET and Pt used in the model are provided in table 1.The plasticity of PET was defined using a multilinear model based on the experimentally obtained tensile stress-strain curve.The non-linear behaviour of Pt was simulated using a bilinear model with defined properties, including yield strength (240 MPa) and tangent modulus (1.1 GPa) [42].The interfaces were assumed to be fully coherent with no transition zone.

Finite element modelling (FEM)
The regional mesh refinement method was applied in the contact area between the Pt islands and the Pt film to reduce stress singularity.A mesh refinement study was conducted to analyse the influence of mesh element size on the resulting stress values and identify optimal mesh parameters to reduce computational time without compromising the accuracy of the result.The mesh study result is summarised in table 2. As shown, a decrease in element size resulted in an increase in the number of elements.This, in turn, led to a reduction in stress values within the blanket film away from the islands and an increase of stress in the blanket film adjacent to the corner of a square island.The stress variation can be calculated as where σ n and σ n+1 are the corner stresses under mesh schemes n and n + 1.In figure 2(b), the variation of ∆σ with an increasing number of elements is presented.It is observed that, with the number of elements increased from approximately 16.8 k to 300 k, ∆σ decreased rapidly from 61.7% to 20.6%.The convergence of ∆σ occurred at mesh elements count of around 1 FEM analysis was also performed on the Pt film/PET bilayer system to assess the stress in the Pt film under a strain level ranging from 2% to 6%, without the presence of Pt islands.The modelling configurations previously applied to the Pt islands/Pt film/PET hybrid structure were also utilized for the bilayer system, ensuring consistency across simulation.

Mechanical behaviour of the Pt-coated PET substrate
In figure 3(a), a typical stress-strain curve of a PET strip subjected to uniaxial tensile loading to a strain of ε = 50% is presented.Notably, the 30 nm Pt thin film deposited on the PET substrate has a minimal impact on the overall mechanical properties given its thickness is much smaller than that of the PET strip (100 µm).The stress-strain curves of the Ptcoated PET strip closely resemble those of the bare PET strip.As the applied strain gradually increased, the PET strip underwent initial elastic deformation below ε = 2%, transitioning to plastic deformation thereafter.
Figures 3(b)-(f) show the optical images of the Pt blanket film surface after tensile testing at strains from 2% to 6%.As shown, no surface cracks were observed on the Pt film with a tensile strain of 2% applied.However, cracks appeared when the applied strain exceeded 2%.The cracks are longer when tensile strain increased to 3%, as shown in figure 3(c).When the tensile strain reached 5%, the occurrence of film buckling became evident, as indicated by the red arrows in figure 3(e).Upon further increasing the tensile strain to 6%, buckling became more prevalent, as shown in figure 3(f).Figure 4 shows the comparison between the topologies of the Pt film/PET bilayer specimens tested at ε = 4% and 6%.The presence of protrusions indicates Pt film buckling, signifying the occurrence of interfacial delamination.
The crack density ρ c (µm −1 ) on the Pt thin film, defined as the number of cracks per unit length crossing a straight line parallel to the loading direction, was calculated as where N c is the number of cracks, and l is the length of the area of interest, consistently at 130 µm for the Pt film/PET specimens in confocal images.The measurement was repeated 3 times for each specimen.As shown in figures 3(c) and (d), the average ρ c values for specimens tested at strains of 3% and 4% are 0.110 ± 0.004 µm −1 and 0.115 ± 0.009 µm −1 respectively, which are not significantly different (p = 0.733).This suggests that the crack density was nearly at its peak as soon as cracking occurred at a 3% strain.
The stresses in the PET substrate and Pt film, induced by tensile loading on the Pt film/PET bilayer system at various strain levels, were calculated using FEM and are summarised in table 3.As shown, crack initiation occurred when the stress exceeded 221 MPa (ε = 2%).Subsequently, the stress in the Pt film increased from 232 MPa (ε = 3%) to 265 MPa (ε = 6%), while the crack density did not increase significantly.Note that the FEM simulation assumed a bilinear plasticity model for Pt without considering the occurrence of cracking.The formation of cracks will result in stress release in the Pt film, which, in turn, may lead to an overestimation of the stress level when using FEM.Additionally, the properties assigned to Pt in the simulation represent those of bulk material, and variations may exist in the properties of the Pt thin film and islands.Therefore, while the stress values in the Pt film calculated using FEM in table 3 offer valuable guidance and are intended for comparison, they should not be interpreted literally.

The influence of Pt islands on crack formation in Pt film
To investigate the influence of islands on crack formation in the Pt blanket film, a single column of five square Pt islands were deposited on the film.In figure 5(a), the optical image of the specimen before the tensile test shows no presence of cracks on the film.However, cracks can be observed on the Pt film undergone a tensile strain of 2%, as shown in figures 4(b) and (c).Notably, these cracks primarily located in the vicinity of the islands, with no cracks observed in the area without the islands, as evident in the magnified image in figure 5(d).This result indicates that the presence of the islands has led to the formation of localised cracks in the Pt blanket film adjacent to the islands, leading to a lower cracking threshold in this region.

The influence of island shape and gap on crack formation in Pt film
Given that the corners of a rectangular island act as a more effective stress raiser than the perimeter of a circular island, the influence of the island shape on crack formation was also studied.For this purpose, 3 × 3 arrays of Pt islands with square and circular shapes were deposited.The island gaps in the directions parallel (h) and normal (v) to the tensile loading direction were varied to study their influence on the formation and distribution of cracks.Figures 6 and 7 show the SEM images of 5 repeated samples after testing, which were superimposed to visualize the collective crack distribution in the region.Notably, no cracks were observed on the islands, and none extended through the islands.All the cracks in the film were orientated perpendicular to the loading direction, residing in the proximity of the islands.No cracks were oriented along the tensile direction and the minimum cracks were observed in the vertical gaps between the islands.
The numbers of cracks (N c ) in figures 6 and 7 were counted, and crack densities (ρ c ) were calculated using equation (1).The variations in N c are shown in figures 8(a) and (b) for square and circular islands, respectively.It is evident that for both shapes, the value of v has no significant influence on N c .However, an increase in h led to an increased N c .
Figure 9(a) shows the relationship between N c and h for both square and circular islands.Generally, N c increases with the increased gap in the loading direction, although there is no statistically significant difference in N c within the range of 30-50 µm.The N c values for square islands are not significantly different from those of the circular ones, apart from h = 60 µm, which may be an outliner.In contrast, the correlation of N c with h was statistically significant, with a p-value of <0.0001.
Figure 9(b) shows the variation in ρ c with increased h.As shown, the values of ρ c fluctuated around a mean value of 0.65 µm −1 (dotted line), and there is no statistically significant difference in ρ c at different gap h.To provide a benchmark for comparison, the ρ c of the film/PET specimen tested at 3% strain (see figure 3(c)) was added.It is evident that the mean ρ c value of the island/film/PET hybrid structure tested at ε = 2% is lower than the benchmark.

The influence of Pt islands on the interfaces
The FIB cross-sectional milling was employed to characterize the interface and subsurface beneath the Pt islands following the tensile test at ε = 2%.Figure 10(a) shows a SEM image of the cross-section of a Pt island/Pt film/PET structure is presented, and figure 10(b) presents a magnified view of the interface.As shown, no subsurface crack was observed beneath the Pt island, and there were no visible cracks at the interfaces of this three-layer structure.

Failure mechanism of Pt blanket film on PET
The failure of the Pt-coated PET substrate under tensile loading is illustrated in figure 3.As shown in figures 3(c)-(f), the Pt blanket film displayed cracking when the Pt film/PET bilayer was subjected to a strain of 3% or higher.This suggests that cohesive failure, in the form of opening mode cracking, occurred in the Pt blanket film shortly after the onset of plastic deformation in the PET substrate (ε > 2%).The cracks exhibited a consistent alignment perpendicular to the direction of tensile loading.Adhesive failure, in the form of film buckling or delamination, occurred when the applied strain reached 5% (see figure 3(e)) and became pronounced at a strain of 6% (see figure 3(f)).
Figure 11 presents a schematic of the proposed failure mode evolution in the Pt film/PET bilayer system under tensile loading, offering insights into the observed mechanical behaviour shown in figure 3. The bilayer system underwent cracking initially (figure 11  to the observation in figures 3(c)-(e) respectively.Cracks are likely to initiate at the stress raisers in the Pt film due to the inevitable presence of defects, occurring at a threshold strain in the range of 2%-3%, as depicted in figure 11(a) (also see figure 3(c)).Subsequently, these cracks grow vertically in the opening mode, perpendicular to the loading direction, with the increasing tensile strain, as shown in figure 11(b); some of the cracks connected at the extending front, merging into longer cracks (see figure 3(d)).The crack density was influenced by the pre-existing defects in the Pt film [36,37].Once cracks formed, the tensile stress in the Pt film strip isolated by the two cracks significantly reduced, impeding further crack initiation.Consequently, the crack density did not significantly increase as the strain increased from 3% to 6%, as shown in table 3.
Within the strain range of 4%-5%, delamination is believed to initiate at the periphery of the isolated Pt strip, resulting from the cracking of the Pt film, as illustrated in figures 11(c) and (d).This can be ascribed to the increase of shear stress at the interface due to the pronounced elastic-plastic deformation of the PET substrate.It is worth noting that, owing to the development of vertical cracks, the tensile stress in the Pt film strips markedly diminishes and is primarily transferred through the interface due to the continuing elongation of the PET substrate.Some interfacial cracks extend across the width of the Pt strip along the Pt/PET interface, ultimately resulting in buckling (see figures 3(e) and (f)) upon the retraction of the tensile loading, as depicted in figures 11(d) and (f).

The influence of Pt islands on the cracking of Pt film
The effect of the Pt islands on the cracking behaviour of Pt blanket films is demonstrated in figure 5, where cracks are evident in the proximity of the islands while the rest of the    blanket film remains intact with no presence of crack at the strain of 2%.Note that the threshold strain for crack formation in the Pt film was between 2% and 3%, as shown in figures 3(b) and (c).Cracking did not occur in the Pt film at the strain of 2% in the absence of Pt islands.Hence, the presence of Pt islands could induce the formation of cracks in the Pt film at a lower applied strain.
The stress contours derived through FEM analysis for the regions containing those vertically aligned square and circular Pt islands are displayed in figures 12(a) and (b), respectively.It is noteworthy that the introduction of the islands led to increased stresses in the Pt thin film adjacent to the vertical edges of the islands.The stress distribution along the horizontal dotted lines in (a and b) shows that stress levels near the islands exceeded 221 MPa, as illustrated in figures 12(c) and (d).This value corresponds to the stress in the Pt film at ε = 2% in the absence of Pt islands.The stress level in the film along the vertical dotted lines in (a and b) was consistently below 221 MPa, as evident in figures 12(e) and (f), demonstrating a reduction in stress level in between the islands along the vertical direction.This suggests that the presence of islands mitigated the stress in the gap between the islands along the vertical axis.With a critical strain threshold for Pt blanket film cracking identified between 2% and 3%, corresponding to a stress of exceeding 221 MPa (figure 3), cracking was prone to occur in the horizontal inter-island space.However, the presence of Pt islands reduced stress concentration in the interstitial regions in the vertical direction, mitigating the likelihood of cracking in those areas.

The influence of island shape and gap on crack formation in Pt film
The effect of island shape and gap on the Pt film crack formation was studied using the samples with island arrays, with both circular and square shapes, on the Pt blanket film.The vertical (v) and horizontal (h) gaps were varied, and an applied strain of 2% was used for the analysis.The results reveal that, for both shapes, the value of v does not notably influence the number of cracks (N c ), as depicted in figure 8. Conversely, an increase in h correlates with an increased N c .Based on earlier discussion, a reduction in stress level within the Pt film occurs in the vertical space between islands.Stress in this area is consistently below the cracking threshold, suggesting that variation in v would not affect the cracking of Pt film.In contrast, the stress level in the Pt film in the horizontal space between the islands exceeded the cracking threshold of 221 MPa.As a result, the variation in h would influence the number of cracks formed between the islands in these areas.A greater h generally led to an increased N c , as shown in figure 9. Nevertheless, both square and circular islands exhibit similar N c values, except for the outlier at h = 60 µm, suggesting that island shape may not significantly affect N c .Additionally, the crack density (ρ c ) at different h does not exhibit statistically significant differences.It is thus concluded that the increase in h does not significantly change the density of cracks, leading to an inevitable rise in N c as the spacing h between the islands increases.
The FEM stress contours for the hybrid structures with the Pt islands arranged along the tensile direction on the Pt blanket film are shown in figures 13(a)-(c).Given that the island shape has no impact on both N c and ρ c , only square islands with h = 10, 30, and 60 µm are presented.Corresponding stress profiles along the horizontal dotted lines in (a-c) are shown in figures 13(d)-(f).Evidently, the stress in the Pt blanket film between the islands in the horizontal direction exceeds the 221 MPa threshold, increasing the susceptibility of the Pt film to cracking.
In the absence of Pt islands, the Pt blanket film on PET experiences cracking when the applied strain exceeds 2%.The threshold stress is determined to be 221 MPa obtained from the FEM simulation (see table 3).When the stress exceeds 221 MPa, cracks initiate from existing flaws such as microcracks and pores in the Pt film [43][44][45][46].As discussed previously, the crack density is associated with the pre-existing defects in the Pt film, and the formation of cracks impedes further crack generation.Therefore, the horizontal space between the islands has an equal chance of crack formation once the stress exceeds the cracking threshold.It should be noted that although the shape of the island and the variation in h affect the stress profile in the area (see figures 12

Conclusions
This study explores the influence of Pt islands on the failure mechanism of a thin Pt film deposited on a flexible PET substrate under uniaxial tensile loading.The surface cracking of the Pt blanket film under tension was characterized and the impact of the shape and distribution of Pt islands on film cracking was investigated.FEM facilitated the stress analysis to understand the failure mechanism in the presence of Pt islands.The major conclusions of this study are summarised below: • Tensile testing of the Pt film/PET bilayer system revealed that the Pt blanket film initially experienced crack formation, followed by propagation and merging of cracks, ultimately leading to delamination and buckling.• The presence of Pt islands could induce the formation of cracks in the Pt film at relatively low strains, attributed to increased stress in the Pt thin film near the vertical edges of the islands along the tensile loading direction.• The variation in vertical gap between the islands did not affect the crack number and density in the Pt film.The presence of Pt islands diminished the stress in the interstitial regions along the vertical axis, thereby reducing the likelihood of cracking in those areas.• Island shape and horizontal gap variations influenced the stress profile between islands but had no significant impact on crack density.Crack density is primarily associated with pre-existing defects in the Pt film, and the formation of cracks inhibits further crack generation due to stress relief.
In device design, it is crucial to consider that active islands can reduce the cracking threshold of the blanket film.The shape of islands and their gap in the direction normal to tension have minimal influence on cracking behaviour.Nevertheless, the gap in the direction along the tension loading determines the number of cracks but not the overall density.Therefore, it is recommended to increase the number of islands in the nonloading direction while reducing the space in the direction of loading to minimize the total number of cracks.

Figure 2 (
Figure 2(a) shows the three-dimensional (3D) model of Pt islands/Pt film/PET hybrid structure, created using a

Figure 1 .
Figure 1.(a) PET strips in their as-cut, as-deposited and post-tensile test states; (b) SEM image of the FIB-deposited Pt islands on Pt blanket film: h is horizontal (tensile-direction) gap, v is vertical gap.

Figure 2 .
Figure 2. (a) A 3D FEM model of the Pt islands/Pt film/PET hybrid structure; (b) mesh refinement results.

Figure 3 .
Figure 3. (a) A typical stress-strain curve from uniaxial testing of a bare PET strip, and confocal optical images of Pt-coated PET sample after tensile testing at strains of (b) 2%, (c) 3% and (d) 4%.Dotted lines were used to emphasize the fine cracks in (c) and (d) while red arrows in (e) and (f) indicate the occurrence of buckling.Note that it is difficult to identify the fine cracks on the images without magnification, hence dotted lines were used for clarification.Several original images (without dotted lines) are provided in appendix A for reference.

Table 3 .a
FEM-calculated stress values in Pt blanket film, along with experimentally measured crack density, under tension at various strains in the Pt film/PET bilayer system.Derived through FEM simulation.bMeasured experimentally.

Figure 5 .
Figure 5. Confocal optical microscope images illustrating (a) a single column of Pt islands on Pt film before tensile testing, (b) the surface of the specimen after tensile testing at 2% strain, (c) a magnified area in (b) showing cracks on the Pt blanket film in the vicinity of the islands, and (d) a magnified area in (b) away from the islands with no presence of crack on Pt film.Dotted lines were used to emphasize the fine cracks in (c).

Figure 8 .
Figure 8.The relationship between island gaps (v and h) and number of cracks (Nc) for both (a) square and (b) circular islands.

Figure 9 .
Figure 9.The relationship between horizontal (tensile) direction gap h of the Pt islands and (a) number of cracks (Nc) and (b) crack density (ρc) in Pt film.

Figure 10 .
Figure 10.(a) SEM image of a FIB cross-sectioned island after tensile testing at 2% strain, and (b) a magnified view focusing on the interfacial region.

Figure 11 .
Figure 11.Schematic illustrations of the progressive failure process of the Pt blanket film: (a) surface crack formation, (b) surface crack elongation and merging, (c), (d) interfacial delamination and (e), (f) buckling.

Figure 12 .
Figure 12.FEM stress contours in the Pt blanket film at ε = 2% with vertically aligned islands: (a) square and (b) circular-shape islands; arrows indicate tensile direction.Stress levels in the Pt film along the dotted lines in (a) and (b) are shown in (c)-(f).

Table 1 .
Mechanical properties of PET and Pt.
a Data obtained from tensile testing in this study.b Data obtained from Ansys engineering database.

Table 2 .
Element size, total number of elements, values of stress and computation (CP) time.Stress values in the blanket film adjacent to the corners of a square island.million.Additionally, as the element size decreases, the computational time increases exponentially.As shown in table 2, the model utilizing mesh scheme No. 6 with 1209041 elements required approximately 24 h for computation.The computational time required for the model with the next level of mesh scheme exceeded two weeks.Therefore, mesh scheme No. 6 was applied to all the models: 0.75 µm for the substrate, 0.5 µm for the Pt blanket film, and 0.2 µm for the refined contact area.
a Stress values within the blanket film away from the islands.b