Failure by Simultaneous Grain Growth, Strain Localization, and Interface Debonding in Metal Films on Polymer Substrates

In a previous paper, we have demonstrated that a microcrystalline copper film well bonded to a polymer substrate can be stretched beyond 50% without cracking. The film eventually fails through the co-evolution of necking and debonding from the substrate. Here we report much lower strains to failure (around 10%) for polymer-supported nanocrystalline metal films, whose microstructure is revealed to be unstable under mechanical loading. We find that strain localization and deformation-associated grain growth facilitate each other, resulting in an unstable deformation process. Film/substrate delamination can be found wherever strain localization occurs. We therefore propose that three concomitant mechanisms are responsible for the failure of a plastically deformable but microstructurally unstable thin metal film: strain localization at large grains, deformation-induced grain growth and film debonding from the substrate.


Introduction
Flexible electronics are being developed for diverse applications, such as paper-like displays that can be folded or rolled [1], electronic skins for robots and humans [2], drapeable and conformable electronic textiles [3], and flexible solar cells providing portable and renewable source of energy [4]. In some designs, small islands of stiff functional materials and thin metal interconnects are deposited on a polymer substrate. When the structure is stretched, the stiff islands experience small strains, but the metal interconnects must deform along with the substrate. Such considerations have motivated us to study the behavior of polymer-supported metal films undergoing large deformation.
A polymer-supported metal film behaves differently from a freestanding metal film. When stretched, a freestanding film of a ductile metal ruptures by forming a neck within a narrow region. Although strain within the neck is large, strain elsewhere in the film is small. Recall that the film typically has an extraordinarily large length-to-thickness ratio. Consequently, the net elongation of the freestanding film upon rupture is small, typically less than a few percent [5][6][7][8][9].
For a ductile metal film well bonded to a polymer substrate, finite element simulations have shown that the polymer substrate can retard necking in the metal film, so that the film can elongate infinitely, limited only by rupture of the polymer substrate [10,11]. Experimentally, however, most polymer-supported thin metal films rupture at small elongations (<10%) [12][13][14][15][16][17][18][19], even though elongations as high as 20% have been reported in a few cases [20][21][22]. Our recent experiments, on the other hand, have achieved very large elongations (more than 50%) [23] and have demonstrated that good adhesion between film and substrate is critical to achieving these 6/11/2008 8:53:17 PM 2 large elongations, an observation that is consistent with both theoretical predictions [11] and a previous experimental investigation [18].
Good adhesion is not the only condition needed to achieve large elongation. It is also essential to keep the deformation as uniform as possible. In our previous experiments [23], copper films were sputter-deposited on Kapton substrates and then annealed to allow grains to grow. The thermal treatment stabilized the microstructure of the films and the grain size was normally distributed. In this paper, we focus on the behavior of as-deposited Cu films with an average grain size around 90 nm and a bimodal grain size distribution. Compared to annealed films, these as-deposited films have a much smaller strain-to-failure. The heterogeneous microstructure of these films is detrimental to the overall deformation behavior of the films due to the strong grain-size-dependence of the Cu flow stress [24]. We will show that the early rupture of these films can indeed be attributed to the nonuniform initial microstructure of the films and to the grain growth that occurs in these films during deformation.
Grain growth during deformation has been reported in other nano-crystalline materials. For instance, grain growth has been detected in nano-crystalline Cu during microhardness testing at both cryogenic and room temperatures [25]. In-situ nanoindentation of nano-grained Al films on Si wedges have demonstrated rapid grain boundary migration and coalescence during deformation [26]. Grain growth has also been observed in freestanding nano-crystalline Al films when subjected to uniaxial tension at room temperature [27]. Even though the precise mechanism of deformation-induced grain growth remains under investigation, we are concerned about its consequences. Indeed, we will show that this grain growth coupled with strain 6/11/2008 8:53:17 PM 3 localization and delamination is the cause of early failure in as-deposited Cu films on polymer substrates.
This paper is organized as follows. Section 2 elaborates on the experimental set up and procedures. In Section 3, we first show the remarkable difference in electrical resistance as a function of elongation between annealed and unannealed films. We then explain this difference in terms of microstructure evolution and film fracture. Evidence of grain growth in unannealed films under mechanical loading is provided and its consequences are discussed. Based on our measurements and observations, a failure mechanism involving three concurrent phenomena is proposed. Final conclusions are given in Section 4.

Experimental
The polymer substrates used in this study were 12.7 m thick polyimide foils (Kapton 50HN® by DuPont). The substrates were first ultrasonically cleaned with acetone and methanol.
Then the substrates were covered by a shadow mask with seven 5 x 50 mm rectangular windows to define the coating area. The covered substrates were put inside the chamber of a direct-current (dc) magnetron sputter-deposition system with a base pressure better than 1 x 10 -7 Torr, and were sputter cleaned for 5 minutes using an Ar plasma at a radio-frequency power of 24 W and a pressure of 2 x 10 -2 Torr. Immediately after sputter cleaning, a 1 m Cu layer was deposited onto the substrates through the windows in the shadow mask. The deposition was performed using a 50. 8  vacuum. These annealed specimens were removed from the vacuum chamber after 12 hours to allow them to cool down prior to breaking vacuum. Figure 1 shows FIB (Focused Ion Beam) images of the Cu surface before and after anneal. In general the grain size is much larger after the heat treatment, although a few large grains can also be found in as-deposited specimens.
Additional annealing did not further increase the grain size. This observation is consistent with the theoretical prediction that grain growth in a film is constrained by the thickness of the film [28].
Tensile test specimens with a width of 5 mm were cut from the coated substrates using a razor blade. They were then subjected to uniaxial tension using an Instron 3342 tensile tester. All

Resistance deviation induced by film cracking
We adopt an equation relating the electrical resistance of the intact metal films to its elongation by following the same argument as in our previous paper [23]. Let be the resistance of the metal film, which is stretched to length L and cross-sectional area A. Let , and be the corresponding initial values. Assuming no cracks have formed, the ratio of the resistance of the strained film to the resistance of the unstrained film is Equation (1) implicitly assumes that the electrical resistivity of the films does not change during plastic deformation of the film. Figure 2 plots the normalized resistance R/R 0 as a function of the normalized length L/L 0 for both as-deposited and annealed specimens. The dashed line is the theoretical prediction according to Eq. (1). The resistance of as-deposited films deviates rapidly from the guideline at an elongation of approximately 12%. This sudden departure in the film resistance is caused by the formation and propagation of cracks in the Cu films, as confirmed by post-mortem SEM observations (Fig. 3). Isolated microcracks are observed at low magnification after the specimen is strained by 15% (Fig. 3a). Cracks become interconnected and severe debonding can be observed at an elongation of 40%, as is evident in Fig. 3 The behaviour of annealed specimens is distinctly different. Fig. 2 shows that the resistance of annealed films starts to slowly deviate from the guideline at an elongation of 25%, indicating very little cracking. This observation was confirmed by post-mortem SEM microscopy. Typical micrographs are shown in Fig. 4. Films deformed to 30% (Fig. 4a) and to 50% strain (Fig. 4b) show clear evidence of fracture, although the crack density is much lower than in as-deposited films. Films deformed less than 25%, on the other hand, do not show any evidence of fracture (not shown). The deviation from the theoretical resistance curve is only induced by the formation of cracks in the film and not by an increase in dislocation density as a result of plastic deformation. We know this because very similar Cu films on Kapton substrates, but with a thin Ti or Cr adhesion layer to improve bonding to the substrate, can be plastically deformed to 50% without any appreciable deviation from the theoretical resistance curve [23]. At higher magnification, both intra-and inter-granular cracks can be observed in the annealed films ( Fig.   4c and d). Slip traces are also clearly visible within each grain, indicative of the extensive plastic deformation that occurred in these films. Cross-sectional images of the cracked regions (Fig. 3 in Ref. [23]) reveal that annealed Cu films eventually rupture through co-evolution of necking and debonding from the substrates, in good agreement with finite element simulations [10,11]. While the microstructure of the annealed copper films is stable under mechanical loads, the microstructure of the as-deposited films is not. Evidence of grain growth in the as-deposited films during deformation is presented in Fig. 5, which shows the evolution of the grain structure during deformation. Figure 5 stretched to 10% and 15% strains respectively, also taken six hours after deposition. The only difference between the specimen shown in Fig. 5(b) and those shown in Figs. 5(c) and (d) is that the latter two were plastically deformed. As is evident from the micrographs, there are significant microstructural differences between the specimens: while a few isolated large grains can be observed in undeformed specimen, the deformed films contain many such grains. Grain growth is clearly discontinuous in that a strong bimodal grain size distribution develops. Several mechanisms have been described to explain discontinuous grain growth in nano-crystalline metal films [27]. These include grain growth driven by a reduction in surface energy [29], elastic strain energy [30], or stored deformation energy [31]. A simple energy calculation shows, however, that the driving forces for these mechanisms are smaller than for continuous grain growth.

Unstable
Stress-driven grain growth has also been observed experimentally in nano-crystalline Al films.
At this point, it is not clear whether grain growth in these Cu films is stress or strain driven. In the context of this study, however, the precise mechanism for grain growth is not that important: We will show that grain growth contributes to early strain localization and hence premature failure of the as-deposited films independent of the precise grain growth mechanism.

Simultaneous strain localization and grain growth
To understand the mechanism of rupture in as-deposited films we first review the more straightforward case, i.e., fracture of annealed copper films under uniaxial tension. From a comparison of Figs. 1(a) and (b), it is evident that annealed specimens have a more uniform microstructure than as-deposited films, with a relatively large grain size of 1.5 µm. Moreover, the microstructure of the annealed films remains stable during the deformation, i.e., no grain growth takes place during plastic deformation. Consequently the annealed films deform relatively homogenously until simultaneous delamination and strain localization lead to failure of the films [23].
In contrast, as-deposited specimens have a bimodal grain size distribution: they are mostly nano-crystalline with a few large grains. The nano-crystalline sections of the films have a very high yield strength as a result of the Hall-Petch effect [29]. The large grains, on the other hand, are much easier to plastically deform. Such a microstructure naturally leads to nonuniform deformation. Furthermore, it is evident from Fig. 5 that the number of large grains increases 6/11/2008 8:53:17 PM during plastic deformation. This microstructure leads to deformation behavior that is significantly different from that of annealed films. Figure 6 shows two sets of micrographs taken by SEM and FIB of samples that were stretched by 15 and 30%. The SEM images show the surface topography, while the FIB images show the grain structure of the same areas of the films.
Incipient necks can be observed in the SEM images (Figs. 6a and 6c). The corresponding FIB images in Figs. 6(b) and 6(d), and many others like them, show that these necks are associated with one or more large grains in the film. At 15% strain, the FIB image (Fig. 6b) shows that there are initially many nano-crystalline grains in the necked down area, even though the necks are usually associated with at least one large grain. At 30% strain, however, most of these small grains have disappeared and the areas of strain localization contain mostly large grains. Strain localization and large grains are closely correlated for sufficiently large deformations.
These observations are readily understood as follows. According to the Hall-Petch effect, there is an inverse relationship between the yield strength and the grain size of a polycrystalline material as long as the grain size is above a few tens of nanometers. As a result, the nano-crystalline regions of the films have a much larger yield strength than the large grains, i.e., the large grains can be regarded as soft inclusions embedded in a hard matrix. Under tensile loading, the softer regions will tend to concentrate the deformation. Therefore initial strain localizations are associated with large grains. As these localizations grow they engulf adjacent nano-crystalline regions. As these nano-crystalline regions deform, they undergo grain growth, making it easier for them to plastically deform and thus further localizing deformation. The two 6/11/2008 8:53:17 PM mechanisms, strain localization and grain growth, facilitate each other and lead to ductile film rupture at relatively small overall strains as shown in Figs. 3(c) and (d).

Concomitant debonding
For strain localization to take place and carry on, a third mechanism is requiredfilm/substrate debonding. The argument is the same as in annealed films: debonding makes the film locally freestanding so that necking of the film can be accommodated by a local elongation of the freestanding portion of the film. If there is no strain localization, there is no traction exerted on the interface to initiate debonding; if there is no debonding to release the constraint from the substrate, there is no space for large local deformation in the metal film to take place.
To validate this interpretation, Fig. 7 shows cross-sectional images of unannealed specimens deformed to different elongations. Strain localization and debonding always co-evolve. Figure   7(a) shows a uniform Cu film well bonded to Kapton substrate prior to any deformation. The FIB image confirms that the grains do not have a columnar structure because multiple grains can be found through the film thickness. In Fig. 7(b) at 10% strain, local thinning has taken place along with debonding from the substrate, but few cracks can be found in the specimens. As illustrated in Fig. 7 The failure mode of as-deposited Cu films on polymer substrate is illustrated schematically in Fig. 8. Initially, the as-deposited film is mostly composed of nano-crystalline material with occasional micron-sized grains. Under tensile loading, large grains act as preferential sites for strain localization. Nano-crystalline grains in regions of strain localization start to grow with increasing strain, locally weakening the material and further promoting localization. As strain localization proceeds, tractions are exerted on the film/substrate interface. These tractions cause local delamination of the film, freeing it from the constraint of the underlying substrate. This process, in turn, promotes strain localization. Eventually the film necks down to a knife-edge.
Micro-cracks form in the film and the resistance of the film increases suddenly. In short, the as-deposited Cu films fail through three concurrent mechanisms: strain localization at big grains, deformation-induced grain growth, and debonding from the substrate.

Conclusions
We have conducted a series of experiments on as-deposited and annealed Cu films supported by stretchable polyimide substrates to investigate the failure modes of polycrystalline Cu films under large deformation. Subjected to tensile loading, as-deposited films rupture much earlier than annealed films. This early failure is attributed to the grain structure of the films, which is inhomogeneous and unstable under loading. We demonstrate that the films fail by ductile necking as a result of strain localization at large grains, deformation-associated grain growth, and film debonding from the substrate.   indicates that the size of grains remained unchanged for a film subject no load. A comparison of (b), (c) and (d) indicates that the size of grains markedly increased when the film is pulled by 10% and 15%.