Influence of surface stresses on indentation response

Surface stresses lead to an effective change in the elastic constants of thin films and at surfaces. The development of modern scanning probe techniques like contact resonance atomic force microscopy empowers the experimenter to measure at scales where these effects become increasingly relevant. In this paper we employ a computational multiscale approach where we compare density functional theory (DFT) and molecular dynamics simulations as tools to calculate the thin-film/surface elastic behavior for silicon and strontiumtitanate. From the surface elastic constants gained by DFT calculations we develop a continuum finite-element multilayer model to study the impact of surface stresses on indentation experiments. In general the stress field of an indenter and thus the impact of surface stresses on the indentation modulus depends on its contact radius and on its particular shape. We propose an analytical model that describes the behavior of the indentation modulus as a function of the contact radius. We show that this model fits well to simulation results gained for a spherical and a flat punch indenter. Our results demonstrate a surface-stress-induced reduction of the indentation modulus of about 5% for strontiumtitanate and 6% for silicon for a contact radius of [Formula: see text], irrespective of the indenter shape.