Appraising the Extensibility of Optics-Based Metrology for Emerging Materials

Abstract

Over the last decade, our group at the National Institute of Standards and Technology (NIST) has explored novel ways to overcome the perceived limitations of applying optical scattering and imaging in the characterization of small silicon features. As a result, we were able to both qualitatively and quantitatively characterize features that are well-below the resolution limit, namely small groupings of well-ordered, periodic nanoscale features. This was achieved by specifying a limited number of parameters to describe these structures and comparing the measurements to extensive electromagnetic simulations with varying parameters. Such imaging simulations, which have yielded quantitative measurements of features less than λ/30 in size, require a priori knowledge of the nominal geometry, number of features, and optical constants of these materials; quantitative information from another tool set can augment such optical parametric fitting through “hybrid metrology,” pioneered by our group at NIST. In the next decade, as the nanoelectronics industry further expands its palette of key emerging materials, it is critical to accurately establish their optical properties. Similar challenges exist for other optics-based, deep-subwavelength measurements, e.g., thickness determination via ellipsometry and parametric fitting via scatterometry. Specifically, the model-based metrology often employed for optics-based methods is challenged by the anisotropy and eventual thickness dependence of the dielectric tensor for two-dimensional materials and ultrathin films. Proper characterization of this tensor empirically or computationally will grow in importance as dimensions continue to decrease. The required steps, known limitations, and potential benefits of atomistic density-functional theory (DFT) simulations are discussed with respect to determining the macroscopic optical response due to feature dimensions only a few atoms in width.