Area evaluation of microscopically rough surfaces

Abstract

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 ͑AFM͒. 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 ͑rms͒ 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.

Surface and line-edge roughness in solution and plasma developed negative tone resists: Experiment and simulation

“…Because of its importance in the last few years, several publications discuss the problem of roughness. [1][2][3][4][5][6][7][8][9] Surface roughness ͑SR͒ appears after the spin coating of the photoresist film, while line edge roughness ͑LER͒ appears after the development of the microstructure. However, the two phenomena are closely related.…”

“…In addition, questions related to the measurements needed to characterize roughness, such as rms measurements from atomic force microscopy ͑AFM͒, fractal dimensions, scanning electron microscope ͑SEM͒ measurements, etc. 1,7 should be addressed.…”

Ruthenium films by digital chemical vapor deposition: Selectivity, nanostructure, and work function

“…20 The shoulder and low slope ͑or stretch͒ in the depletion region of the C -V data for the as-deposited sample is indicative of a high interfacial densities of state, which stems from P b0 type of defects and/or roughness. 21,22 These states are significantly reduced upon annealing.…”

Roughness models for particle adhesion

“…Fractals have been employed to characterize surface roughness in much the same way as has the value of the root mean square (RMS) roughness. A number of papers have discussed determining fractal parameters for use in comparing the roughness of two surfaces [27][28][29][30][31]. With the exception of the fractal dimension, D, and the fractal roughness, G, other parameters in Eq.…”