A very large number of articles were written to describe the effect of the substrate in the determination of mechanical properties of thin films [22, 25, 96-105]. Several models were developed to describe the nanoindentation hardness and elastic modulus variation as a function of penetration to film thickness ratio [20, 23, 27, 106-109]. However, this problem continues without a satisfactory solution, and new models are expected to appear in the future. The major difficult factor for modeling the film-substrate behavior under indentation is the complex triaxial stress state in the region constituted by the film, the indenter, and the substrate.
The effect of the substrate in the determination of the hardness of thin films is schematically shown in Figure 8. The elastic zone during indentation is not restricted to the film, but also reaches the substrate. Substrate plastic deformation also occurs for deeper penetrations.
Tsui and Pharr  analyzed the effect of hard substrates on the nanoindentation mechanical property measurement
of soft films. In their work, substrate effects on the measurement of mechanical properties of thin film of aluminum on glass have been studied experimentally by nano-indentation methods. The hardness and elastic modulus of aluminum films with thicknesses of 240, 650, and 1700 nm sputter deposited on glass were systematically characterized as a function of indenter penetration depth using standard nanoindentation methods. They performed scanning electron microscopy and atomic force microscopy of the hardness impressions that revealed that indentation pile up in the aluminum is significantly enhanced by the substrate. It was found the substrate also affects the form of the unloading curve in a manner that has important implications for nanoindentation data analysis procedures. According to the referred article, nanoindentation measurement techniques can overestimate the film hardness and elastic modulus by as much as 100%, depending on the indentation depth, with the largest errors occurring at depths approximately equal to the film thickness. They also verified that indentation pile up in soft aluminum films is significantly enhanced when the films are deposited on hard substrates. In the case where the indentation depth is be about one tenth of the film thickness, the substrate-induced enhancement of pile up is negligible.
Saha and Nix  recently performed a study on the effects of the substrate on the hardness and film modulus using the nanoindentation technique. Different films of Al and W were deposited over substrates like Al, Si, glass, and sapphire. The intrinsic hardness and elastic modulus of the films were analyzed using the relation
where P is the applied load, S is the contact stiffness, H is the hardness, E* is the reduced modulus, and fi is a tip geometrical constant. According to referred authors, for homogeneous materials, P/S2 is constant with depth. Then, plotting P/S2 versus depth may provide useful information about the substrate effect for different combinations of hard film/soft substrate and soft film/hard substrate. The substrate influence is small for soft film over hard substrate. On the other hand, for hard film over soft substrate, the film hardness can be obtained only for total indenter penetrations lower than 10% of the film thickness. Of course, correction of the contact area is needed because pile up will be necessary if the traditional Oliver and Pharr method is used. Considering elastic modulus measurements, the strong effect of the substrate exists because the elastic field presents a longrange character, and special care must be taken in order to extract the actual elastic modulus value for the film material. For a large mismatch between the film and substrate modulus, King's analysis to estimate the film modulus is indicated .
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