Nanoindentation measurement of Young's modulus for compliant layers on stiffer substrates including the effect of Poisson's ratios

Finite element analysis (FEA) is used to investigate the effect of the Poisson's ratios of both the overlayer and the substrate on the nanoindentation of an elastic two-phase system where the elastic overlayer is more compliant than the underlying elastic substrate. A rigid spherical indenter is used as a probe. It is found that nanoindentation results may be expressed analytically using a simple extension of the previously described equation (Clifford and Seah 2006 Nanotechnology 17 5283). This simple function describes the reduced modulus value measured using Oliver and Pharr's method (1992 J. Mater. Res. 7 1564) for any modulus values or Poisson's ratio values of the overlayer and substrate, overlayer thickness or indenter tip radius. This equation and the FEA behind it are tested using experimental published data for the nanoindentation of a silicon dioxide layer on silicon.