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.
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R. Abermann, Vacuum 41, 1279 (1990). https://doi.org/10.1016/0042-207X(90)93933-A 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.
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E. Chason, Mater. Des. 110, 616 (2016). https://doi.org/10.1016/j.matdes.2016.07.089 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.
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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…