An Improvement of the Doerner-Nix Function for Substrate Effects in Ultrathin Films
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1086-U05-08
An Improvement of the Doerner-Nix Function for Substrate Effects in Ultrathin Films Bo Zhou, and Barton C Prorok Auburn University, Auburn, AL, 36849-5341 ABSTRACT Substrate effects continue to be an important issue in interrogating thin films by nanoindentation. In this study, we examined amorphous thin films of several different materials deposited onto a silicon wafer. These materials span from being considerably softer than the substrate to films significantly harder than the substrate. The thin film Young’s modulus, Ef, was measured with an MTS Nanoindenter XP system and employing the continuous stiffness measurement (CSM). A so-called “flat region,” where the substrate influence was negligible, was observed in the early stage of nearly every CSM modulus-displacement curve for all materials studied. The depth of this region (hcr) was found to vary with the material. Based on the experimental data, we were able to modify the Doerner & Nix function for thin film indentation on a substrate, particularly their parameter alpha (α). The modified function was found to be adept at closely matching all experimental data collected, which spanned both soft films on hard substrates and hard films on soft substrates. INTRODUCTION In the last two decades, instrumented indentation testing has become one of the most important methods for the measurements of bulk and thin film materials mechanical properties [1-15]. As indentation transitioned from micro-scale to the nano-scale regime, new issues arose in interpreting the data. Among them, the influence of the underlying substrate is one of the more important issues. The mechanism of this phenomenon was believed to result from the different manner in which the strain caused by the indent manifests in both the film and substrate. As they are different materials with different crystal structures, microstructures and mechanical properties, the recovered elastic response contains influences from both the film and the substrate. Thus, decoupling the two has been an important area of study in the field. A simple guideline to avoid substrate effects was first recommended by Bückle [2], where for thicker films, if the indent depth is less than 10% of the film thickness, the influence by the substrate can be ignored. However, in films of nanometer scale thickness, limiting the indent depth to 10% of the film results in data reduction errors as the indenter’s geometrical features are comparable in size to the indent depth. Thus, a more precise and universal methods were sought to better determine the true film mechanical properties. In general, the method for determining the Young’s modulus of an indent is to measure the slope of the beginning unloading curve, which is related to the elastic modulus as [3]: π S Er = , (1) 2β A where Er is the reduced modulus, S is the slope and A is the projected area of the contact. The reduced modulus contains both information from the specimen and the indenter tip, thus the specimen modulus is determined as:
1 1 − υ 2 1 − υ i2 = + , (2)
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