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