Indentation Size Effects in Submicron- and Nano-contacts

Contact-induced deformation in micro-electro-mechanical systems (MEMS) and micro-electronic systems often involves contacts between asperities with sizes between the sub-micron and nano-scale regimes. Between these regimes, the asperity sizes can be smaller than the spacings between the defects that carry deformation (dislocations). It is, therefore, difficult to use continuum approaches to model deformation at such fine scales. In this work, nanoindentation techniques were used to investigate contact-induced deformation in single crystal and polycrystalline nickel, gold and silver thin films that are relevant to MEMS and microelectronics. Discrete dislocations models were also used to study the evolution of dislocation substructures and hardness with increasing indent size. We find that the indentation size effect is bi-linear, when the normalized hardness squared (H/H_o)² is plotted against the inverse of the indentor penetration depth (1/h). The bi-linear behavior is attributed to a transition from dislocation source-limited behavior (at the nano-scale where the indent size is less than the dislocation spacing) to well established dislocation structures in the sub-micron regime (where the indent size extends over a number of dislocations in an established dislocation structure). The indentation size dependence of hardness is shown to emerge naturally from discrete dislocation simulations of the indentation experiments.