Effect of white noise on roughness measurements of self-affine fractals

This study formulated and clarified the presentation of the noise-related error terms in the power spectral density (PSD) and height–height correlation function (HHCF) through a roughness analysis of self-affine fractals. Assuming the noise as white noise, this study simulated the PSD and HHCF of the noisy roughness profile in a typical situation: line-edge roughness measurements involved in semiconductor lithography technology. It was found that conventional noise-correction techniques can bias the PSD/HHCF from those of the true roughness profiles because they do not account for the residual noise-induced error. The findings obtained from the roughness analysis and simulation techniques are expected to benefit various applications, such as clarifying the quantitative residual error in specific situations, selecting the optimum analysis method (PSD or HHCF), estimating the required number of averaged profiles (measurements) that yields sufficiently small noise errors, and considering strategies for noise reduction.