Issues in Line Edge and Linewidth Roughness Metrology

In semiconductor electronics applications, line edge and linewidth roughness are generally measured using a root mean square (RMS) metric. The true value of RMS roughness depends upon the length of edge or line that is measured and the chosen sampling interval. Additionally, the true value is obscured by a number of measurement errors: Different finite‐length sections of line have randomly differing roughnesses, producing a sampling error, the expected magnitude of which depends upon the length of line that is sampled and details of its roughness power spectrum. Noise in the microscope images from which roughness is computed results in both a random measurement error and a non‐random measurement bias. These issues and proposed solutions in the literature are reviewed. It is also suggested that there may be a plausible role for non‐RMS metrics, for example estimation of the likelihood of width or edge position extremes based upon direct measurements of the roughness amplitude density function.