Journal of Materials Research


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

Han Lia1 and Joost J. Vlassaka1 c1

a1 School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138


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.

(Received July 31 2008)

(Accepted November 19 2008)

Key Words:

  • Elastic properties;
  • Hardness;
  • Thin film


c1 Address all correspondence to this author. e-mail: