Nanoscale roughness and bias in step height measurements by atomic force microscopy

Abstract

The roughness of a surface exhibiting a Gaussian distribution of heights is analysed, computationally, for scans using two- and three-dimensional probes with flat and spherical tips with various tip widths and radii. These simulate aspects of roughness and surface measurement as observed at the nanoscale with atomic force microscopes. In the Gaussian population of heights, the data points are uncorrelated and at a lateral displacement interval of δ. These initial data points may then be linked by a straight line or by a plane to make a continuum surface. Scanning this surface with a hemispherical probe shows that whilst there is significant distortion (dilation) in the measured profile, the measured root mean square roughness is only slowly reduced as a function of the increasing tip radius. However, the mean measured height of the surface increases significantly with the tip radius in a manner that biases step height measurements for films that are rougher than their respective substrates and vice versa. The calculations show universal curves for this bias as a function of the tip size. The step height bias is important and this is contrasted with results for surfaces exhibiting defined surface waveforms. The bias needs to be included in step height measurements as a correction or as an added uncertainty.

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

“…The surface analyzed here is based on the surface used previously [3]. Briefly, this surface consists of a grid of points at spacing δ, in which the heights at each point are uncorrelated, and with a Gaussian population of heights with a standard deviation, σ.…”

“…However, it is not clear how close the result is to the required measurement. Some issues were dealt with in detail in an earlier study [3], upon which the present work builds.…”

“…Had the former been the case, although the roughness would be reduced, the mean height of the surface would be correctly maintained, whereas in reality, both the roughness and the mean height are affected. Some of these issues are discussed in detail in the earlier work [3] for surfaces exhibiting Gaussian uncorrelated height distributions. A surface with a Gaussian height distribution but with the variations only occurring over long spatial wavelengths could be measured with great accuracy, and it is only as the wavelength of these effects approaches or falls below the radius of the mechanical probe tip, that major errors may accumulate.…”

“…We shall also calculate the mean height of the surface, since this is important for measuring film thicknesses in which the deposited film has a different roughness from that of the substrate. This aspect is largely covered in the earlier study [3]. In that study, both flat-and ball-ended probes were used, but here we shall use a paraboloid probe with a tip generated by rotation of a parabolic profile, since this gives results that may be scaled with the original roughness.…”

Spectral Analysis of Irregular Roughness Artifacts Measured by Atomic Force Microscopy and Laser Scanning Microscopy

“…Even with high imaging resolution, quantitative evaluation of surface roughness at the nanoscale level remains very challenging. The specimen under inspection may have arbitrary structures, and the geometric interaction between the sensing probe and the sample could be excessively intricate for all of these different techniques (Hanlon et al, 2001; Chen & Huang, 2004; Kang et al, 2012; Seah, 2013). To ascertain the correctness of surface areal roughness measurements, reference structures with their topography and statistical quantities precisely controlled are required (Nemoto et al, 2009; Uchidate et al, 2011; Baršić et al, 2012; Liu et al, 2012; Chen et al, 2013; Luo et al, 2013).…”