Substrate effects on indentation plastic zone development in thin soft films
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A.A. Volinsky Motorola, DigitalDNA Labs, Process and Materials Characterization Lab, Mesa, Arizona 85202
N.R. Moody Materials Reliability Division, Sandia National Labs, Livermore, California 94551-0969
W.W. Gerberich Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, Minnesota 55455 (Received 5 January 2001; accepted 20 August 2001)
Plastic zone evolution in Al–2 wt% Si metal films on silicon and sapphire substrates was studied using nanoindentation and atomic force microscopy (AFM). AFM was used to measure the extent of plastic pileup, which is a measure of the plastic zone radius in the film. It was found that the plastic zone size develops in a self-similar fashion with increasing indenter penetration when normalized by the contact radius, regardless of film hardness or underlying substrate properties. This behavior was used to develop a hardness model that uses the extent of the plastic zone radius to calculate a core region within the indenter contact that is subject to an elevated contact pressure. AFM measurements also indicated that as film thickness decreases, constraint imposed by the indenter and substrate traps the film thereby reducing the pileup volume.
I. INTRODUCTION
The popularity of nanoindentation is due in large part to its ability to probe the mechanical properties of materials in a nondestructive fashion without extensive sample preparation. However, it is often difficult to measure film properties independent of the substrate properties. Several solutions to this problem have been proposed with varying degrees of success, the simplest being the “10% rule,” by which it is proposed that the film properties can be measured for indentation depths less than 10% of the total film thickness. However, this “rule of thumb” has several deficiencies. The rule is too restrictive for soft coatings on hard substrates;1 it may not be restrictive enough for hard coatings on soft substrates; and the shape and size of the plastic zone are sensitive to indenter angle.2,3 In addition, for submicron thick films, it can be experimentally difficult to perform and analyze indents that satisfy this requirement. Other partially empirical approaches have attempted to incorporate the mechanical properties of the substrate 3150
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J. Mater. Res., Vol. 16, No. 11, Nov 2001 Downloaded: 13 Mar 2015
into the hardness measurement through various rules of mixtures.4 –12 These generally express the composite hardness, Hc in the form:13 Hc ⳱ Hs + (Hf − Hs)H ,
(1)
where Hs and Hf are the hardness of the substrate and film, respectively, and H is one of a variety of weighting functions depending upon the particular model. For example, one common approach is to calculate plastic volumes based on the spherical cavity model developed by Hill14 and adapted to the indentation process by Marsh,15 Johnson,16 and Chiang et al.17 However, Ford has suggested that the work of indentation is related to indentation volumes and not plastic volumes.18 In additio
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