Multitaper and Multisegment Spectral Estimation of Line-Edge Roughness

摘要

Line-edge roughness (LER) has important impacts on the quality of semiconductor device performance, and power spectrum estimates are useful tools in characterizing it. These estimates are often obtained by taking measurements of many lines and averaging a classical power spectrum estimate from each one. While this approach improves the variance of the estimate there are disadvantages to the collection of many measurements with current microscopy techniques. We propose techniques with widespread application in other fields which simultaneously reduce data requirements and variance of LER power spectrum estimates over current approaches at the price of computational complexity. Multitaper spectral analysis uses an orthogonal collection of data windowing functions or tapers on a set of data to obtain a set of approximately statistically independent spectrum estimates. The Welch overlapped segment averaging spectrum estimate is an earlier approach to reusing data. There are known techniques to calculate error bars for these families of spectrum estimators, and we experiment with random rough lines simulated by Mack's technique based on the Thorsos method.