Analysis of thin films exhibiting large plastic deformation during nanoindentation: A modified Winkler approach
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rald R. Bourne George S. Ansell Department of Metallurgical and Materials Engineering, Colorado School of Mines, Golden, Colorado 80401, USA (Received 11 February 2015; accepted 1 June 2015)
A novel method for the analysis of the mechanical properties of thin films is presented and uses a modified Winkler (bed of springs) approach to estimate indentation hardness and reduced modulus using nanoindentation data. This method is especially useful in situations where significant plastic deformation occurs in the thin film resulting in pileup of material and a divergence from accepted tip area calculations. The model has been adapted into a MATLAB script and its derivation is presented. A proof of concept study was completed using Au thin films over a range of thickness and deposition methods. Results are compared with traditional nanoindentation analysis methods and validated against the Hall–Petch relationship. It can be seen that this modified Winkler approach accurately predicts material pile-up as well as contact area for films up to 500 nm in thickness.
I. INTRODUCTION
In general, the development and implementation of new materials rely on proper knowledge of the response to external loading. As more advanced materials are developed the response to loading can begin to diverge from simple, accepted evaluation methods. One such situation is the case of thin film materials. The deposition of thin films has been used in a wide range of applications in the electronics, tribology, nuclear, and the biomedical fields, just to name a few.1 One concern with the development of thin films is the characterization of the mechanical properties of the films, this characterization is notoriously difficult as the thickness of the films prevents the use of traditional freestanding testing methodologies. One method that has been successful in characterizing hard and brittle thin film materials has been use of the nanoindentation approach.2 With depth sensing indentation machines, load and displacement are measured, however, an area of residual impression is necessary for the analysis of modulus and hardness. For micrometer and larger scale indentation depths, ideal tip geometry can be assumed and an area function can be generated from simple geometric relationships. For thin films, indentation depths are required to be on the order of the nanometer and in this case, the ideal Contributing Editor: George M. Pharr a) Address all correspondence to this author. e-mail: bboesl@fiu.edu DOI: 10.1557/jmr.2015.171 J. Mater. Res., Vol. 30, No. 13, Jul 14, 2015
area function breaks down and greatly underestimates the residual area. To add to the complexity, the residual impression cannot be imaged or measured optically at this scale, necessitating the use of much costlier electron microscopy techniques. One method to determine residual area, developed by Oliver and Pharr,3 involves creating a series of indents of varying depths on a standard sample of known elastic modulus, typically fused quartz. From the data, a function can be generated to describe the co
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