Methodology for evaluating the information distribution in small angle scattering from periodic nanostructures

Optimizing the extraction of information from x-ray measurements while minimizing exposure time is an important area of research in a variety of fields. The semiconductor industry is reaching a point where the traditional optical metrologies need to be augmented in order to better resolve the critical dimensions of structures with feature sizes below 10 nm. Critical dimension small angle x-ray scattering (CDSAXS) is one measurement technique that is capable of characterizing detailed features of periodic nanostructures. As currently implemented, the measurement utilizes the combined scattering from up to 60 different angles. Reducing the number of angles would dramatically improve the feasibility of CDSAXS for implementation in a fabrication setting, but currently there are no clear guidelines as to which angles provide the most information to minimize the uncertainty in the shape of the target structure while maximizing the throughput. In order to develop guidelines for optimizing the angle selection, simulation studies were conducted on a wide variety of structures with subsets of the full angular range to identify which angles minimized the overall shape uncertainty. Analyzing sets of two angle pairs (including all combinations between 0 deg and 60 deg) provides guidance on which angles best constrain the samples. For select samples, higher numbers of angles were included to explore the impact of additional information on the model uncertainty. In general, low angles (<3 deg) best contributed to minimizing the line-width uncertainty, while higher angles near high curvature regions of the scattering profile best constrained the height of the structure. The minimum uncertainty was generally achieved with combinations of the two. This simulation approach can be used to minimize the number of angles measured on real samples and significantly reduce the measurement time.