Nanoindentation: Depth dependence of silicon hardness studied within contact theory

The behavior of elastic and mechanical properties of silicon submitted to an indentation test is investigated. The study is focused on the behavior of its hardness at the nanoscale. For this aim, we apply a Green-function approach for solving the contact problem of elastic bodies. The anisotropy of the two contacting materials, silicon and a diamond indenter, is taken into account for obtaining the depth dependence of the hardness up to about 90 nm at which the semiconductor-metal phase transition occurs. It is shown that the discrepancy with experimental data can be significantly reduced if one takes into account the anharmonicity of the materials in contact. The anisotropy is represented by the full tensor of second-order elastic constants CIJ and the anharmonicity by the full tensors of higher-order elastic constants C_IJK···. The validity of the theoretical approach was checked by determining the force-depth indentation curve.