Determining the elastic modulus and hardness of an ultra-thin film on a substrate using nanoindentation

Abstract – A data analysis procedure has been developed to estimate the contact area in an elasto-plastic indentation of a thin film bonded to a substrate. The procedure can be used to derive the elastic modulus and hardness of the film from the indentation load, displacement, and contact stiffness data at indentation depths that are a significant fraction of the film thickness. The analysis is based on Yu’s elastic solution for the contact of a rigid conical punch on a layered half-space and uses an approach similar to the Oliver-Pharr method for bulk materials. The methodology is demonstrated for both compliant films on stiff substrates and the reverse combination and shows improved accuracy over previous methods. 

This manuscript has been submitted to JMR.  

"Code.ppt" is the supplementary code for solving elastic indentation oflayered half-space following Yu's approach. This is indeed a .zip file,NOT a .ppt file. The extension is intensionally modified to "cheat" thesystem, as Imechanica does not allow uploading .zip file. To run thecode, one need to first download the file, and change the fileextension back to .zip, and unzip the files into the working folder ofmatlab.

function Y=ElasticConeIndent(alpha, beta, t, E2, v1, v2)

Input
alpha: half angle of the conical punch in degree, NOT radian.
beta: shear modulus ratio of the film to that of the substrate.
t (nm): film thickness
E2: Young's modulus of the substrate
v1: Poisson's ratio of the film
v2: Poisson's ratio of the substrate

Output Y=[h(nm), P(mN), a(nm)]
h(nm): indentation depth
P(mN): indentatio load
a(nm): contact radius

Result is in numerical form, with a/t in the range from 0.1 to 100.