A simulation study for evaluating and improving the accuracy of surface roughness measured by atomic force microscopy

The quantitative and precise evaluation of the accuracy of surface roughness measurements by atomic force microscopy (AFM) has not been satisfactorily accomplished because of the difficulty in formulating the measurements affected by tip-sample dilation in an analytical approach. In this study, we explore the possibility of generalizing and formulating, from simulation results, the effect of tip-sample dilation on measurements of surface roughness on Gaussian rough surfaces. By introducing the normalized tip width w(N), defined as the ratio of the effective width of a tip to the correlation length of the surface, approximately generalized formulas that describe well the relationships between the normalized root-mean-square roughness S-qN and w(N) and between the normalized correlation length S-alN and w(N) were derived. Moreover, we found that applying the erosion algorithm to AFM images of Gaussian rough surfaces does not lead to better roughness measurements and the result is related to the effect of tip-sample dilation on the skewness of AFM images. Furthermore, we presented simple but effective estimation formulas for Gaussian rough surfaces that make use of image skewness to quickly estimate the true roughness within an error of less than 10%. This study will be helpful for achieving accurate roughness measurements by using AFM.