Area evaluation of microscopically rough surfaces

In this article, a novel roughness function is developed which enables the assessment of the area of a microscopically rough surface measured by atomic force microscopy (AFM). A reliable area of a surface with microscopic roughness has proven to be difficult to compute due to the small Vertical and large spatial differences which cause significant round off error in the computation. Instead of the usual procedure of computing the area of a surface directly from the data set, we utilized the fact that surface area increases with roughness. Two roughness parameters, root mean square (rms) and fractal dimension (D-F) yielding vertical and horizontal information, respectively, are employed to provide a reasonably complete description of surface roughness. We show that the area of a microscopically rough surface is exponentially related to D-F and quadratically to rms, and these relationships are the basis of a novel roughness function. This function is shown to be both sensitive to the changes in surface topography, and reliable in providing the area of a surface with microscopic roughness. (C) 1999 American Vacuum Society. [S0734-211X(99)04401-7].