Demystifying the measurement of periodic structures

TL;DR

This paper evaluates various methods for measuring the period of nanostructured gratings using extensive simulations, providing practical guidance on selecting optimal techniques for accurate metrological assessments.

Contribution

It offers a comprehensive comparison of direct and Fourier space methods for periodic structure measurement, including analysis of defects and measurement conditions.

Findings

Fourier-based methods generally outperform direct measurement techniques.

Defects and measurement noise significantly impact measurement accuracy.

Practical recommendations improve the reliability of periodic structure evaluations.

Abstract

Periodic structures are often found in various areas of nanoscience and nanotechnology with many of them being used for metrological purposes either to calibrate instruments, or forming the basis of measuring devices such as encoders. Evaluating the period of one or two-dimensional periodic structures from topography measurements, e.g. performed using scanning probe microscopy (SPM) methods, can be achieved using different methodologies with many grating evaluation methods having been proposed in the past and applied to a handful of examples. The optimum methodology for determining the grating pitch is not immediately obvious. This paper reports the results of extensive large-scale simulations and analysis to evaluate the performance of both direct and Fourier space data processing methods. Many thousands of simulations have been performed on a variety of different gratings under different measurement conditions and including the simulation of defects encountered in real life situations. The paper concludes with a summary of the merits and disadvantages of the methods together with practical recommendations for the measurements of periodic structures and for developing algorithms for processing them.