Statistical- and image-noise effects on experimental spectrum of line-edge and line-width roughness

The accuracy of estimated line-edge-roughness and line-widthroughness (LER and LWR) statistics is mostly determined by the noise inherent in experimental power spectral densities (PSDs). One type of noise is statistical noise, a kind of jagged structure, that is caused by the finiteness of a number NL of line segments used in analyses. To keep the estimation error below 5%, the ratio of sampling interval to correlation length should be 0.3 or smaller, and NL needs to be larger than 100 under the condition that the length of line segments is 2000 nm or larger, in compliance with the Semiconductor Equipment and Materials International standard. Another noise type is scanning-electron-microscope image noise. It causes edge-detection errors and induces an additional variation in LER/LWR. This variation raises the minima of PSDs and accordingly enhances the errors. The factor of the error enhancement is suppressed below 1.5 by controlling the ratio of image-noise-induced LER/LWR variance to the true variance below 0.6. This is achieved by averaging image pixels perpendicularly to fine lines, and is free from any appreciable drawbacks. The experimental results agree well with analytical approximations to Monte-Carlo results that are separately obtained. This leads us to obtain more general guidelines for accurate analyses by using the analytical formulas.