The power spectral density (PSD) is a powerful mathematical tool for characterizing roughness as a function of frequency (or length scale). It is widely used for characterizing surface roughness and edge roughness, and in the semiconductor industry it is used to understand line-edge roughness (LER) and linewidth roughness (LWR). In this tutorial, the definition, measurement, and use of the PSD will be described for LER/LWR characterization. Sources of errors (biases, both systematic and random) will be discussed as well as their mitigation. Finally, interpretation of the shape of the PSD and its meaning in the context of patterning will be briefly addressed.
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