How levelling and scan line corrections ruin roughness measurement and how to prevent it

Abstract

Surface roughness plays an important role in various fields of nanoscience and nanotechnology. However, the present practices in roughness measurements, typically based on some Atomic Force Microscopy measurements for nanometric roughness or optical or mechanical profilometry for larger scale roughness significantly bias the results. Such biased values are present in nearly all the papers dealing with surface parameters, in the areas of nanotechnology, thin films or material science. Surface roughness, most typically root mean square value of irregularities Sq is often used parameter that is used to control the technologies or to link the surface properties with other material functionality. The error in estimated values depends on the ratio between scan size and roughness correlation length and on the way how the data are processed and can easily be larger than 10% without us noting anything suspicious. Here we present a survey of how large is the problem, detailed analysis of its nature and suggest methods to predict the error in roughness measurements and possibly to correct them. We also present a guidance for choosing suitable scan area during the measurement.

Synthetic Data in Quantitative Scanning Probe Microscopy

“…The underestimation is of course worse for shorter lengths L. However, it is clear that even for quite long scan lines (compared to the correlation length T), the roughness can be considerably underestimated, especially for higher polynomial degrees. A procedure for choosing a suitable scan range to prevent this problem already during the measurement is provided in Reference [141]. meas to true value σ 2 depending on the ratio of profile length L and correlation length T. The bias is plotted for Gaussian and exponential autocorrelation and several common levelling types-subtraction of a few low-degree polynomials and the median.…”

“…The basic case is the adjustment of value distribution to a prescribed one ( coerce ). It has been used for the creation of tunable random roughness for simulations [ 141 ], but also in the production of physical roughness standards [ 142 ]—in this case iteratively to ensure the produced standard conforms to the design. More complex iterative procedures can generate textures with multiple prescribed statistical parameters [ 143 ].…”

“…An example of use of synthetic data for estimation of systematic errors in SPM data processing is the study of levelling-induced bias in roughness measurements [ 29 , 141 ]. Levelling is done as a pre-processing step in nearly all SPM measurements in many variations, from simple row mean value alignment up to polynomial background removal.…”

“…However, it is clear that even for quite long scan lines (compared to the correlation length T ), the roughness can be considerably underestimated, especially for higher polynomial degrees. A procedure for choosing a suitable scan range to prevent this problem already during the measurement is provided in Reference [ 141 ].…”

“…It was found that while humans are good at recognising defects (and marking them for exclusion from the processing), giving them more direct control over the levelling is questionable. The popular 3-point levelling method did not fare particularly well and humans also tended to over-correct random variations (although all levelling methods are guilty of this, even without user input [ 29 , 141 , 146 ]).…”