Measurement of the roughness of nano-scale surfaces, both unannealed and with limited anneal, by atomic force microscopy

Abstract

The roughness and bias measured for surfaces scanned by a parabolic atomic-force microscope tip are analyzed computationally for surfaces exhibiting a random, Gaussian population of heights, uncorrelated from pixel to pixel. The fraction of the surface with which the probe is in contact is then analyzed in detail to show the area fraction of the surface that is, in practice, contacted within a defined tolerance. This shows that it is very difficult to measure much of these surfaces for any significant roughness even though the roughness value may sometimes be approximately correct. The surface is then allowed a limited anneal, and the improvement in the validity of the measurement is determined. Annealing removes the very short-range structure and permits more meaningful roughnesses to be determined with a greater fraction of the surface contacted by the probe. This limited anneal may simulate the behaviour of hot atoms that are incident or impacted by energetic ions and that rapidly cool at the surface. Asymmetric, non-Gaussian height distributions are also analyzed, and these generate a significantly different measurement bias that can be more sensitive to the tip radius. The height distribution shapes alter with the tip radius, so accurate estimation of the originating height distribution is not possible. Simple equations are provided to describe the effects.

SIMS of Delta Layers in Organic Materials: Amount of Substance, Secondary Ion Species, Matrix Effects, and Anomalous Structures in Argon Gas Cluster Depth Profiles

“…We match the gradients, and if σ M is 4 nm, we may deduce that σ R is about 2.5 nm and σ 1 about 3 nm, i.e., the long wavelength roughness is slightly smaller than σ 1 . This is what we would expect for the random form of the roughness formed in sputtered surfaces 28 rather than the traditional self-affine fractals of engineered surfaces. 29 As shown in Figures 3 and 8 in the study of mixtures by Seah et al 25 the lower the composition, the greater the intensity enhancement at any given positive Ξ value.…”

“…We match the gradients, and if σ M is 4 nm, we may deduce that σ R is about 2.5 nm and σ 1 about 3 nm, i.e., the long wavelength roughness is slightly smaller than σ 1 . This is what we would expect for the random form of the roughness formed in sputtered surfaces rather than the traditional self-affine fractals of engineered surfaces …”

Systematic Temperature Effects in the Argon Cluster Ion Sputter Depth Profiling of Organic Materials Using Secondary Ion Mass Spectrometry

“…Green et al [13] showed gross amounts of dewetting can occur for Irganox 1010 films less than 5 nm thick after 13 days at room temperature, whereas phenylalanine seemed very stable over longer periods at this thickness [14]. In more recent work, Seah [15] calculates that significant molecular movement by surface diffusion is possible for some organic materials at room temperature. This is, of course, not wanted in most analytical situations.…”

Decomposition of AFM images of ultrasmooth optical surface polished with gas cluster ion beam

“…Nevertheless, under such discretization, physical presence of roughness with higher spatial frequencies can cause distortion of spatial frequencies spectra retrieved from the image, which is so called aliasing. To prevent this, we used AFM cantilevers with tip radius 100 nm serving as a high-frequencies filter [15]. Such a tip radius is quite large for AFM, and we made additional measurements to show that convolution effects do not distort the image in the frequency range of interest.…”