Miniaturized fracture experiments to determine the toughness of individual films in a multilayer system
Graphical abstract
Introduction
It is commonly known that the reliability of thin film systems in terms of the fracture behaviour is highly influenced by the mechanical properties of the films such as flow strength, Young’s modulus, strength of the film–substrate interface, as well as the residual stress distribution in the film. When considering multilayer thin film systems, the situation gets more complicated as the combination of various materials increases, for example, the number of interfaces that can potentially fail. Moreover, the stacking sequence plays an important role as well [1], as it critically influences the residual stresses that develop. Additionally, it is worth mentioning that in small dimensions, especially for thin films, the above mentioned properties can differ significantly from their bulk values due to size effects that emerge from reduction of the grain size as well as the dimensional limitations of the reduced film thickness [2], [3]. Therefore, as macroscale material data is not applicable anymore, miniaturized tests have to be applied to study the fracture behaviour at the small length scale [4], [5], [6], and for the material combination used in state of the art and future devices.
An established technique to determine the fracture toughness of (brittle) films is for example indentation [7], [8], but with this method it is challenging to probe a single film, rather than measuring an apparent fracture toughness of the whole film–substrate composite. Therefore, it is more appropriate to determine single film properties by using more advanced small scale testing techniques such as pillar splitting [9], clamped cantilever bending, double cantilever bending, or single cantilever bending experiments [4], [5], [10]. Fracture experiments on bulk materials or single material thin films [6], [11], [12] using micro cantilevers have already been performed [10], [13], [14], [15], but, up to now, not much attention has been paid to multilayer thin film systems [16], [17]. However, with the ongoing miniaturization in microelectronics, the implementation of multilayer thin films rather than single films became more and more important, in terms of mechanical and electrical functionality.
In metallic film systems, the fracture mechanical treatment is governed by the size of the plastic zone in front of the crack tip. To apply linear elastic fracture mechanics (LEFM), the plastic zone size has to be significantly smaller than the sample size and the crack length, with being the critical stress intensity for mode I fracture and the yield strength of the material. It can be expected that for ductile thin films will even reach the sample size, thereby requiring application of elastic–plastic fracture mechanics (E-PFM) and the -integral to determine the crack driving forces [18], [19]. To be able to determine correct data needed for the calculations, such as crack length and correct dimensions, in-situ experiments are preferably applied as demonstrated in [4], [6], [20].
It is known that a material inhomogeneity, such as an interface in a multi-layered system, can influence the crack growth drastically [21]. For instance, if a crack approaches an interface with a stiff/compliant transition () or a hard/soft transition (), the crack extension is promoted, as the crack driving force is amplified. This is the so-called anti-shielding effect. On the other hand, a compliant/stiff interface () or a soft/hard interface () causes a shielding effect, which retards the crack when approaching the interface, as the effective crack driving force is lowered. As long as the plastic zone around the crack tip does not touch the interface, which is the case for small loads, the influence of the Young’s modulus is most significant. As the load is increased and the plastic zone extends into the next layer, the impact of the change in yield strength gains more importance. A third contribution to the effective crack driving force comes from the influence of the hardening parameter, but as this influence is negligible compared to that of Young’s modulus and yield strength, it is not discussed here. In conclusion, the fracture resistance can be highly improved by engineering the layered structure based on the knowledge of Young’s modulus, the material flow behaviour and tailored residual stresses [22], [23], [24].
In this work, the fracture behaviour of copper (Cu) and tungsten (W) multi-layer thin film systems that are subjected to residual stresses with pronounced gradients [25] is investigated under mode I loading. Therefore, we perform a combination of miniaturized fracture experiments in-situ in the scanning electron microscope (SEM) accompanied by finite elements (FE) simulations in order to assess the validity of different fracture mechanical concepts when applied to such complex small scale systems.
Section snippets
Experimental
In the current paper two different stacking configurations of alternating Cu and W layers, namely Cu–W–Cu on Si and W–Cu–W on Si (100), were investigated. The Cu and W films were prepared via physical vapour deposition with a thickness of approx. 500 nm per layer. The grains are almost globular with a grain size ranging from 60 to 70 nm. For a detailed description of the deposition conditions and the material characterization, the reader is referred to a previous work [25].
As already
Finite element simulations
An FE study using ABAQUS (Simulia, Dassault Systems Simulia Austria GmbH) was performed to calculate the -integral for different crack lengths of both layered systems, intended to determine the fracture toughness of the W and the Cu films.
To this purpose, a two dimensional micro cantilever (see Fig. 3) was modelled according to the geometries used in the experiments (Table 1) and the materials properties listed in Table 2.
The yield and hardening behaviour for the W and the Cu layer were
Fracture experiments on W–Cu–W
First the two samples W–Cu–W S1 and S2 without a notch were tested to estimate the fracture stress. The corresponding force–displacement data of S1 is depicted in Fig. 6 and a supplementary online video is available for this test (see Appendix C). The top W layer fractures in the first test cycle T1 and the crack stops at the interface W/Cu. The stiffness of the beam decreases due to the crack extension, which is shown by the fact that the slope of the unloading segment is significantly smaller
Discussion
Up to now, the fracture toughness for such miniaturized samples was most often calculated using LEFM to determine critical -values. The rational for this was of course that for rather low toughness materials the plastic zone is reasonably small compared to the sample size [10], [11], [12], [39], [40]. However, in the presented multilayer samples, additionally the change in elastic properties across the interfaces and the residual stress distribution have to be taken into account. Furthermore,
Conclusion and outlook
In this study we performed miniaturized fracture experiments on Cu–W–Cu and W–Cu–W trilayers on a Si (100) substrate in-situ in the SEM. Subsequently, the resulting mechanical data was used as input data for the FE simulation taking into account the elastic–plastic material behaviour and the residual stresses. With this analysis we could demonstrate the influence of a stressed layered structure on the crack driving forces. Within the current approach we are able to determine valid fracture
Acknowledgements
Financial support by the Austrian Federal Government (in particular from the Bundesministerium für Verkehr, Innovation und Technologie and the Bundesministerium für Wissenschaft, Forschung und Wirtschaft) represented by Österreichische Forschungsförderungsgesellschaft mbH and the Styrian and the Tyrolean Provincial Government, represented by Steirische Wirtschaftsförderungsgesellschaft mbH and Standortagentur Tirol, within the framework of the COMET Funding Programme is gratefully acknowledged
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2021, Thin Solid FilmsCitation Excerpt :If the determined fracture toughness value lies above the corresponding KE-limit(aeff,ry-limit)-value, it is invalid. In this is the case, the J-integral shall be used instead of the stress intensity K as a valid fracture mechanics parameter, and the fracture toughness of the film material shall be measured by the critical J-integral, Jc, which requires the usage of numerical simulations for bimaterial specimens, see [6,19]. Note that an additional material inhomogeneity effect can appear, if the crack tip plastic zone reaches the interface and the materials on either side of the interface exhibit different yield stresses [35,36].
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2020, Materials and DesignCitation Excerpt :All these methods have shown to deliver consistent results [8,28,35–37]. Even fracture properties of thin films in layered systems were successfully characterized [38]. However, no experimentally validated experimental setup exists for mode II and mode III fracture toughness measurements on the microscale at present.