Size-Dependent Elastic Properties of Nanofilms: Exponentially Decreased Surface Elasticity Model

In this work, we propose a continuum theoretical model to describe the surface-modulated and size-dependent elastic properties of nanofilms. The influence of surface Young’s modulus (surface biaxial modulus) decreases with increasing the distance from the film surface. The decrease law is assumed as exponential in this work. In core-surface and core-shell models, an imaginary interface between the surface area and bulk-like inner core appears. Since the influence of surface elasticity decreases with the distance from the surface layer continually, the interface is non-existent and non-physical. The present theoretical model eliminates the interface and is proved to be a veritable continuum theory. There is no concept of “bulk-like core area” and “surface area” in current theory. The existence of surface Young’s modulus decrease introduces second and third surface modifications. When the influence of surface Young’s modulus decreases rapidly, i.e. the decrease factor α → ∞, the influence of surface Young’s modulus only works near the surface. And then, the current theory will degenerate into a core-surface one. The current theory is used to describe the size-dependent biaxial modulus of Si, diamond, Au and Cu nanofilms. The theoretical prediction gives good agreement with simulated results of these nanofilms. The present study in this paper is envisaged to provide useful insights for the design and application of nanofilm-based devices.