  A detailed formulation for the effects of the surface integrity, i.e. surface
topography, surface metallurgy, and surface mechanical properties, on the
mechanics of ultra-thin films is proposed in the framework of linear
elasticity. In this formulation, the ultra-thin film is modeled as a material
bulk covered with two altered layers and two rough surfaces as distinct phases.
Two versions of the proposed formulation are developed. In the first version,
the governing equations are obtained depending on the general form of the
surface topography. In the second version, the governing equations are
reformulated utilizing the average parameters of the surface topography. In the
proposed formulation, measures are incorporated to account for the effects of
the surface topography, i.e. waviness and roughness, surface metallurgy, i.e.
altered layer, and surface excess energy on the mechanics of ultra-thin films.
A case study for the static bending of clamped-clamped ultra-thin films is
analytically solved. A parametric study on the effects of the surface
roughness, waviness, altered layers, and film size on the static bending of
ultra-thin films is presented. In this study, new size-dependent behaviors are
revealed where the mechanics of ultra-thin films can be significantly altered
for the small variations in the surface integrity.
