In short
- AFM measures the height at every point of an area, so it gives areal roughness parameters (Sa, Sq, Sz) as well as profile parameters (Ra, Rq) along a line.
- A roughness value only means something with its scan size, pixel number, mode, tip and levelling.
- The floor of what can be measured is the instrument’s Z noise — for example Sq = 139.6 pm on SrTiO₃ in closed loop.
Measurement
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.
Definitions
Roughness parameters
| Parameter | Definition | Calculated on |
|---|---|---|
| Ra | Arithmetic mean of the absolute height deviations from the mean line | a profile (line) |
| Rq | Root mean square of the height deviations (RMS roughness of a profile) | a profile (line) |
| Sa | Arithmetic mean of the absolute height deviations from the mean plane | an area (ISO 25178) |
| Sq | Root mean square of the height deviations — RMS roughness of the area | an area (ISO 25178) |
| Sz | Maximum height: highest peak plus deepest valley | an area (ISO 25178) |
| Ssk, Sku | Skewness and kurtosis of the height distribution — peaks vs valleys, sharp vs flat | an area (ISO 25178) |
Good practice
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.
Read more
Related pages
FAQ
Frequently Asked Questions
What is the difference between Ra and Sa?
Ra is the arithmetic mean deviation of a single profile (a line), from the profile standards; Sa is the same quantity calculated over an area, from the areal standard ISO 25178. An AFM image is an area, so Sa and Sq describe it best; Ra and Rq are used when a line profile is analysed.
What is the difference between Sa and Sq?
Sa is the mean of the absolute height deviations from the mean plane; Sq is the root mean square of those deviations (RMS roughness). Sq weights large deviations more, so it is always equal to or larger than Sa.
Why does the measured roughness depend on the scan size?
Roughness exists at every length scale. A small scan does not include long-wavelength waviness, and a large scan with the same number of pixels cannot resolve the finest features. Always report the scan size and pixel number with a roughness value, and compare samples at the same settings.
What is the smallest roughness an AFM can measure?
It is limited by the noise of the instrument in the vertical (Z) direction. As an example, on SrTiO₃ in resonant mode the Nano-Observer measured an RMS roughness Sq of 139.6 pm in closed loop and 157.7 pm in open loop.
Which AFM mode should be used for roughness measurement?
Resonant (tapping) mode for most samples, as it does not drag the tip across the surface; low force on soft samples. Contact mode can be used on hard, robust surfaces. Use a sharp tip, because the tip radius limits the smallest features that can be measured.
Questions about roughness measurement?
Ask the application scientists behind our AFMs and modes — about your samples, probes, set-up or which mode fits your measurement. We answer every message personally.