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Review Article: Stress in thin films and coatings: Current status, challenges, and

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A. Modeling stress development during polycrystalline thin film growth

1. Nonenergetic deposition conditions

As noted above, there is a large literature quantifying the evolution of stress in numerous systems for many deposition methods and processing conditions. Because of the impact of stress on film performance and failure, there is a strong motivation for trying to understand it in terms of the underlying atomic-level processes occurring during film growth. In this section, we describe recent progress in developing a rate-equation based model to understand the dependence of stress on the temperature, growth rate, and evolving microstructure.

Many different kinetic processes occurring simultaneously during film growth can influence the stress, including deposition, attachment of atoms to terrace ledges, GB formation, and diffusion of atoms on the surface and into the GB. Some of these are shown schematically in Fig. 6. The deposited atoms can have low kinetic energy in nonenergetic processes such as evaporation or electrodeposition. In energetic deposition processes such as MS, the deposited species have much higher thermal kinetic energies that can modify the stress. For example, sputter deposition is commonly used to counteract large tensile stresses that develop in films of refractory materials if nonenergetic deposition is used. The impact of energetic particle bombardment on the intrinsic stress development will be addressed specifically in Secs. , , and .
After adsorption on the surface, the deposited atoms may be mobile if the diffusivity is sufficiently high. These atoms can meet other atoms and form clusters on the surface or diffuse to sinks such as terrace edges or GBs. The film’s microstructure also evolves as the film grows. Starting from a bare substrate, the deposited atoms cluster into islands that are initially not connected, assuming that the film does not wet the substrate. As the thickness increases, the isolated clusters start to intersect and coalesce into a uniform film. This coincides with the formation of GBs between the islands. Ultimately, the film becomes relatively uniform and flat; depending on the material mobility, the grain size may continue to change with the thickness as it grows.126126.
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The measurements of the stress-thickness in Fig. 1(b) show that the film stress goes through different stages corresponding to the evolving microstructure. In the earliest stages, the shallow slope indicates that the incremental stress is small. At a thickness of ∼10 nm, the slope starts to increase, indicating a tensile stress in the layers being deposited. At ∼30 nm, the stress-thickness reaches a maximum and the incremental stress changes from tensile to compressive. After this, the incremental stress remains compressive, and the average stress ultimately becomes compressive.
These different regimes of stress evolution are correlated with the evolution of the film’s microstructure with thickness. The early low-stress stage corresponds to the film consisting of individual islands on the surface. The increasing tensile stress corresponds to the onset of coalescence, where the individual islands start to impinge on each other and form GBs between them. For metal films like Ag, the transition to compressive stress corresponds to the film becoming fully coalesced into a continuous film. This results in the existence of a maximum (tensile peak) in the film force evolution with thickness. Recent findings, based on simultaneously coupling MOSS and surface differential reflectance spectroscopy (SDRS) during deposition of a series of high-mobility metal films, have demonstrated that the onset of film continuity coincides with the tensile peak.127127.
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For materials with lower atomic mobility, the incremental stress may remain tensile and not become compressive, at least under conditions of low-energetic vapor flux.
The evolution of stress with thickness depends on the material and was described as type I or II by Abermann.128128.
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The behavior shown for Ag in Fig. 1 is called type II; this is characterized by the incremental stress changing from tensile to compressive with thickness and relaxing when the growth is interrupted. These materials have relatively high atomic mobility or low melting points, like Al, Ag, or Au. Alternatively, in type I materials, the incremental stress remains tensile with thickness and does not relax when the growth is interrupted. These materials have relatively low atomic mobility or high melting points, such as Mo, Ta, and W.
The different stress behavior depends on the material, but it may also be modified by changing the temperature or growth rate. For instance, evaporated Fe films grown at low temperature show stress-thickness evolution like type I materials, but when the same material is grown at higher temperature, the behavior is like a type II material.35,5835.
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In general, higher growth rates and lower temperatures tend to promote type I behavior, while lower growth rates and higher temperatures promote type II behavior.
The stress depends on the grain size, but its dependence is complicated. Koch et al.129129.
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showed that the smaller grain size can lead to more compressive stress in the growth of a type II material. Similar behavior was found for electrodeposited Ni and Cu films at low growth rates130130.
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where the smaller grain size led to more compressive stress. However, at high growth rates, the smaller grain size led to the stress becoming more tensile. This shows that stress cannot be understood without considering the interaction between the growth rate and the grain size. The model developed below is able to explain this complicated behavior.
There have also been numerous measurements of the stress evolution during relaxation when the growth is interrupted.33,58,13133.
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This relaxation can be reversible if the growth is resumed shortly after the interruption;67,132,13367.
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for longer times, there can also be an irreversible component.134134.
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Measurements of the relaxation dependence on the grain size135135.
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suggest that GBs play a role in relaxation as well as growth stress.
The stress measurements provide guidance about the underlying kinetic processes controlling it. The correspondence between the rise in the tensile stress and the onset of island coalescence suggests that GB formation plays a role. Based on this, Hoffman136136.
R. W. Hoffman, Thin Solid Films 34, 185 (1976). https://doi.org/10.1016/0040-6090(76)90453-3
suggested a mechanism that considers the energy for creating new sections of GB between islands and for elastically deforming the islands. This analysis shows that adjacent islands will…

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