Journal of Micro/Nanolithography, MEMS, and MOEMSSystematic errors in the measurement of power spectral density
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Measurement of the power spectral density (PSD) of a rough surface or a feature involves large random and systematic errors. While random errors can be reduced by averaging together many PSDs, systematic errors can be reduced only by carefully studying and understanding the sources of these systematic biases. Using both analytical expressions and numerical simulations for the measurement of the PSD of line-edge roughness, four sources of systematic errors are evaluated: aliasing, leakage, averaging, and image noise. Exact and approximate expressions for each of these terms are derived over a range of roughness exponents, allowing a measured PSD to be corrected for its systematic biases. In the absence of image noise, the smallest measurement bias is obtained when appropriate data windowing is used and when the sampling distance is set to twice the measurement signal width. Uncorrected PSD measurements are likely to systematically bias each of the PSD parameters, with the roughness exponent especially susceptible to bias.