Effects of the substrate on the determination of thin film mechanical properties by nanoindentation
Introduction
Determination of the mechanical properties of thin films on substrates by indentation has always been difficult because of the influence of the substrate on the measured properties [1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12]. The indentation response of a thin film on a substrate is a complex function of the elastic and plastic properties of both the film and substrate. The standard methods that are used for extracting properties from the measured load–displacement data were developed primarily for monolithic materials [13]. These same methods are often applied to film/substrate systems for determining film properties without explicit consideration of how the substrate influences the measurements. In order to measure ‘film-only’ properties, a commonly used rule of thumb is to limit the indentation depth to less than 10% of the film thickness [13]. While using this rule is experimentally feasible for films that are greater than about a micrometer in thickness, this approach cannot be used for very thin films. Other methods must be developed for dealing with substrate effects if nanoindentation techniques are to be useful in the mechanical characterization of very thin films. Numerous investigators have used both experimental [14], [15], [16], [17], [18], [19], [20], [21], [22] and theoretical [23], [24], [25], [26], [27], [28], [29] methods to study the problem of extracting ‘true’ film properties from nanoindentation of film/substrate composites.
We have chosen to study a wide range of film/substrate systems, including both soft films on hard substrates and hard films on soft substrates. Specifically, we have studied the indentation properties of aluminum and tungsten films on the following substrates: aluminum, glass, silicon and sapphire. This set of film/substrate systems includes two, Al/glass and W/sapphire, which are nearly elastically homogeneous. For these film/substrate pairs, a measurement of the contact stiffness during indentation, together with knowledge of the elastic modulus of the system, permits a determination of the true contact area and true hardness, irrespective of the effects of pile-up or sink-in around the indenter. Knowledge of the true hardness of the film permits a study of the effects of the elastic modulus mismatch on the nanoindentation properties, using the measured contact stiffness as a function of depth of indentation relative to the film thickness for films on different substrates. The experimental results compare favorably with a modified form of King's model for the effect of elastic modulus mismatch on the nanoindentation properties of thin films on substrates. By conducting experiments on all of these film/substrate pairs we are able to investigate some of the effects that the substrate may have on the determination of mechanical properties of thin films by nanoindentation.
Section snippets
Thin film deposition
Both Al and W were deposited onto the different substrates by sputtering. In the case of Al, the base pressure in the chamber prior to sputtering was 6–10×10−9 Torr and the Ar gas pressure during sputtering was 1.5 mTorr. The sputtering conditions resulted in a deposition rate of 1.6 Å/s. For the W deposition, the base pressure in the system prior to sputtering was 1×10−6 Torr or better and the Ar gas pressure during sputtering was 12 mTorr. The sputtering conditions were 176 W of power with
Aluminum thin films
A series of indentations were made in the Al films with depths ranging from 250 nm to 2500 nm depending on the thickness of the film. The load and stiffness recorded as a function of indentation depth during the experiment were used to calculate the hardness and modulus of the films. Fig. 3 is a plot of the indentation load as a function of indenter displacement to a depth of 1000 nm for the 0.5 μm Al thin films on the four different substrates. The observed load–displacement relations are
Intrinsic film hardness calculated from P/S2 using the constant modulus assumption
The problem with determining the intrinsic hardness of thin films is that the measurement is influenced by the properties of the substrates especially when the film is extremely thin. The hardness measurement of a soft film is enhanced by the hard substrate while the reverse is true for a hard film on a soft substrate. Another problem involves the calculation of the true contact area. Soft films on hard substrates tend to pile-up when indented, while hard films on soft substrates tend to
Modeling the elastic properties of thin films on substrates
The Oliver–Pharr method [13] was developed for monolithic materials. Re-writing Eq. (3), the elastic contact modulus or reduced modulus, Er, is defined aswhere νi and Ei are the Poisson's ratio and elastic modulus, respectively, of the diamond indenter and v and E are the Poisson's ratio and elastic modulus of the material being indented. This equation is applicable to a thin film on a substrate only if the film and substrate have the same elastic properties, i.e. Ef=Es and vf≈
King model
Doerner and Nix [3] developed a model that attempted to account for the influence of the substrate compliance by including a term due to the substrate in the reduced modulus equation. However, the constants that scaled the relative contributions of the film and substrate were determined empirically and were valid only for the particular film on substrate case that they studied.
King [26] modified the solution presented by Doerner and Nix and made it applicable to all film/substrate systems. He
Aluminum films
The Al films were deposited on substrates that either had similar moduli as that of the film (glass and Al) or were stiffer (Si and sapphire). Also, the hardnesses of the Al films were less than those of the substrates. Hence we can assume that the film accommodates all the plastic deformation and the substrate begins to yield only when the indenter is close to the film/substrate interface, as shown earlier. As a result we will also assume that: the hardness calculated for the Al/glass films
Tungsten films
The W films were deposited on substrates that were either more compliant than the film (Al, glass, and Si) or had a similar modulus (sapphire). Also the hardnesses of the W films were greater than the Al and glass substrates, equal to the Si substrate and less than the sapphire substrate. Hence for the case of W on Al and glass, the substrate will begin to yield well before the indenter tip reaches the film/substrate interface, as shown earlier. Because of this, the assumption made in the case
Summary
The objective of this research was to study the effect of substrate properties on the nanoindentation measurement of film properties and to develop methods for extracting the intrinsic film properties from nanoindentation experiments. We tested and analyzed eight different film/substrate systems: Al and W films on aluminum, glass, silicon, and sapphire substrates. By depositing the same film on different substrates we were able to show how the substrate properties affect the measured film
Acknowledgements
Support for this work by the Division of Materials Science, office of Basic Energy Sciences of the United States Department of Energy through grant DE-FG03-89ER45387 is gratefully acknowledged. Vidya Ramaswamy is also acknowledged for her help in depositing the Al films.
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