Delamination of Compressed Thin Films
Introduction
Thin-solid films deposited over substrates are presently used in strikingly diverse technological applications. For instance, wear-resistant coatings in metal-cutting tools have attained considerable technological importance and, as such, have been the subject of extensive research. Since its appearance in 1969, the coating of cutting tools has afforded an order-of-magnitude improvement in performance and productivity in the machine tool industry (Quinto, 1988). This is a remarkable feat because the volume of the coating barely amounts to about 1% of the volume of the tool. The coatings are thin films of single elements (e.g., C, B); binary compounds, including metallic (e.g., Ti, Zr, Hf, Ta, and V nitrites, carbides, and borides), covalent (e.g., SiC, B4C), and ionic compounds (e.g., Al2O3, Ti, Th, Zr, and Hf bioxides, Be and Mg oxides); and ternary compounds (e.g., nitrites, in particular Ti1–x Zrx N and Ti1–x Alx N) (Musil et al., 1993, Randhawa et al., 1988). Usual coating thicknesses range from 5–10 μm. Most commercial coatings comprise three layers, e.g., TiC/TiCN/TiN or TiC/Al2O3/TiN, albeit as many as 103 nanometric layers may be utilized. A more recent development concerns the utilization of “gradient coatings,” wherein the composition of the coating varies continuously across its thickness, leading to improved mechanical performance (Holleck et al., 1985, Quinto, 1988, Musil et al., 1993). The most common substrate materials used in metal-cutting tools are steels and silicon.
Some of the films that find application in cutting tools are also of importance in the manufacture of integrated circuits. A case in point is that of TiN (also TaN, Ta, W, V, Cr, Nb) films used as diffusion barriers between silicon substrates and metallic (Al, Au, Ag) conductive layers (Leusink et al., 1993). These barriers are inserted to prevent the diffusion of substrate atoms into the conductive layers, and the attendant degradation of the electrical performance of the latter (Granneman, 1993). A second example involving thin anodic oxide films is provided by the microelectronics industry, where such films are employed as insulating and protective coatings (Stark et al., 1993).
Additional examples of film/substrate systems are afforded by the automotive and optical industries, where glass has been largely replaced by optical polymers. These materials are advantageous from the standpoint of weight and formability. However, optical polymers suffer from a number of shortcomings, including low surface hardness, loss of transparency and mechanical properties when exposed to UV radiation, and severe sensitivity to certain chemicals, including hydrocarbons. The introduction of transparent silicon oxide and silicon nitrite coatings has been instrumental in overcoming these problems. A further example of application of thin films in the manufacture of optical devices is the deposition of oxidic coatings (silicon, tantalum, tungsten, and nickel oxides) on glass. These coatings are employed as high- or low-refractive layers in lenses, filters, and mirrors (Pulker, 1987). In yet another optical application, thin multilayer films made of heavy metals (Zr, W) are used in combination with carbon substrates in reflective components for soft X-ray regions (Aouadi et al., 1992).
Ceramic thermal barrier coatings are extensively used in the aircraft and automobile industries. These coatings increase the operating temperature of engines, which results in improved efficiency and lower cooling requirements for the substrate (Geiger, 1992). For example, partially-stabilized zirconia is deposited on airfoils to reduce the operating temperature of underlying nickel-based superalloy blades (Twigg and Page, 1993, Jordan and Faber, 1993).
Depending on the specific film/substrate pair and on processing and service conditions, thin films may be subjected to very large compressive stresses. Although a certain level of compression in the thin film may be desirable—as in the integrated circuit industry, where small compressive stresses in the order of 0.01–0.05 GPa are deemed beneficial (Granneman, 1993)—large compressive stresses, as are likely to occur in many systems, may lead to failure by a variety of stress relief mechanisms. These include hillock formation (d’Heurle, 1989, Jou and Chung, 1993), peeling by adhesion failure at the film/substrate interface (Chopra, 1969), creep and plastic flow (Chopra, 1969), and buckling-driven delamination (Hutchinson and Suo, 1991).
In this article, we specifically concern ourselves with the buckling-driven delamination mechanism, whereby a portion of the film buckles away from the substrate, thereby forming a blister (also termed buckle or wrinkle). Blisters may grow by interfacial fracture, a process which, under the appropriate conditions, may result in the catastrophic failure of the component. Blisters are often observed to adopt convoluted—even bizarre–shapes and to fold into intricate patterns. A principal objective of this article is to review some recent developments based on the use of direct methods of the calculus of variations which have proven useful for understanding the mechanics of folding of thin films (Ortiz and Gioia, 1994). These developments are reviewed in Section III, which is extracted from the original publication. The remaining sections are devoted to the application of these principles to the problem of predicting the shape of thin-film blisters.
Section snippets
SOURCES OF RESIDUAL STRESSES IN THIN FILMS
When the deposition temperature is greatly in excess of the service temperature, residual thermal stresses inevitably arise as a result of mismatches in the thermal expansion coefficients of film and substrate. In some applications, the temperature differential can be as high as 1000°C, and the attendant stresses and strains in the film of the order of 1 GPa and 1%, respectively (Yelon and Voegeli, 1964, Chopra, 1969, Hutchinson et al., 1992, Jordan and Faber, 1993, Jou and Chung, 1993, Twigg
Folding Patterns as Energy Minimizers
The delamination of compressed thin films has been investigated by a number of researchers (see, e.g., the review of Hutchinson and Suo, 1991). The studies to date have by and large been based on conventional elastic stability theory and interfacial fracture mechanics, and have primarily been concerned with the stability of blisters of simple shapes, such as circular and straight-sided flaws (Hutchinson et al., 1992, Nilsson et al., 1993). However, conventional methods of analysis tend to
Film Morphologies
In the foregoing, we have been primarily concerned with the analytical characterization of the film deflections in the interior and at the boundary of a blister of known shape. In the remainder of this article, we turn to the problem of determining the possible shapes of blisters. We shall assume that a blister adopts such shape as is required to balance the driving force for delamination, on one hand, and the static or kinetic interfacial fracture resistance, on the other. The requisite
Conclusion
The solutions reported in the preceding sections reveal a rich geometrical structure of the telephone-cord morphology which cannot be fully appreciated by a linear configurational stability analysis. In the wake of the cord, regions of slowly varying positive curvature are punctuated by narrow zones of negative curvature, or cusps. While the curvature becomes singular at the vertex of the cusp, the tangent to the boundary remains continuously turning through the singularity and the cusp has a
Acknowledgments
This work has been funded by the National Science Foundation through Brown University’s Materials Research Group on “Micro-Mechanics of Failure Resistant Materials.” We are grateful to Ashraf F. Bastawros of Brown University for making available to us the unpublished micrograph in Figure 8.
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