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In this chapter attention is directed to patterned thin-film structures, where the film material exists as individual lines of various cross-section geometries. Contrary to the case of continuous films in Chap. 3, the deformation field in the line structure is dominated by the edge effect. In addition, the film segment may be entirely surrounded by one or more different materials so a severely confined condition is in place. The most representative example is the metal interconnects in modern integrated circuits. The interconnect structure is composed of several layers of Cu or Al lines embedded within the dielectric material (traditionally silica glass based, SiOx) on top of the Si substrates. They serve as the connection between the functional elements (transistors) and between the transistors and the outside packaging structure. A schematic illustrating a two-level interconnect structure is shown in Fig. 4.1 (see also Fig. 1.4).

In conjunction with the advancement of microelectronics, the art and technology of electronic packaging have progressed rapidly over the last several decades. Packaging protects the semiconductor or other electronic systems from external environment during manufacturing, assembly, shipping, handling and normal operation. It also serves to facilitate power delivery and thermal management (to maintain the device temperature below certain limits). A package is thus a combination of dissimilar materials in close contact, leading to deformation mismatches and internal stress buildup as a result of thermal and mechanical loads [1–7].

One of the simplest types of physical confinement is a thin continuous film (or blanket film) attached to a thick substrate material. Frequently this is a beginning form for creating micro- and nano-scale systems such as the semiconductor devices. Here the focus is on the constraint imposed by the substrate on the thin film. A numerical example is given below as an introductory illustration.