Effect of Surface Layer on Young’s Modulus of Ultrathin Nanofilms: A Theoretical Model

The existing discrepancy between theoretical models and experimental results in describing the elastic properties of ultra-thin nanofilms (less than 10 nm) is primarily attributed to the oversight of the surface layer thickness impact. To address this, a new model incorporating a surface layer with thickness is proposed in this article. Utilizing a layered model, the Young’s modulus of nanofilms approaches that of bulk materials as the film thickness becomes infinitely large, equating to the Young’s modulus of the bulk material in both layered and unlayered models. The dimensional unit of the surface elastic coefficient in the layered model differs from that of the unlayered model, approximately by the thickness of the film. Numerically, the former is more than double the latter. Predictions using the layered model for ultra-thin films comprising only two surface layers reveal a hardening effect in materials such as Si, Ge, InAs, and GaAs. The increase in Young’s modulus for these materials is 20.81%, 95.28%, 79.03%, and 84.04%, respectively, compared to their bulk counterparts. Moreover, a continuous increase in the Young’s modulus is observed as the thickness further decreases.