Measuring roughness with an AFM An AFM image is a matrix of heights recorded point by point, with sub-nanometre vertical resolution. Roughness parameters are calculated from this height map after levelling: the mean plane (or a low-order polynomial) is subtracted so that sample tilt and scanner bow are not counted as roughness. Compared with optical or stylus profilometry, the AFM resolves much finer lateral features and works on any material, conductive or not, in air, in liquid or under controlled atmosphere — at the price of a smaller field of view. Roughness parameters Ra - Arithmetic mean of the absolute height deviations from the mean line - Calculated on a profile (line) Rq - Root mean square of the height deviations (RMS roughness of a profile) - Calculated on a profile (line) Sa - Arithmetic mean of the absolute height deviations from the mean plane - Calculated on an area (ISO 25178) Sq - Root mean square of the height deviations — RMS roughness of the area - Calculated on an area (ISO 25178) Sz - Maximum height: highest peak plus deepest valley - Calculated on an area (ISO 25178) Ssk, Sku - Skewness and kurtosis of the height distribution — peaks vs valleys, sharp vs flat - Calculated on an area (ISO 25178) Getting a roughness value you can compare - Fix the scan size and pixel number — roughness changes with both; report them with the value. - Level consistently — the same plane or polynomial subtraction on every image. - Use a sharp tip — the tip radius sets the smallest valley the AFM can enter; see the probe selection guide. - Choose the mode for the sample — resonant (tapping) mode for most samples, low force on soft ones, contact mode on hard surfaces. - Measure several areas — one image is one sample of the surface. - Know the noise floor — on very flat surfaces the measured roughness approaches the instrument noise. Figure 1. SrTiO₃, resonant mode, high-resolution topography: open loop (left), RMS roughness Sq = 157.7 pm; closed loop (right), Sq = 139.6 pm. On such flat surfaces the measured roughness reflects the instrument’s Z noise.
