On the limits of low-numerical-aperture imaging scatterometry

Area of Science:

• Nanophotonics and Metrology
• Optical Characterization Techniques

Background:

• Imaging scatterometry is valuable for nano-grating characterization, but its limitations are not fully understood.
• Key constraints include imaging numerical aperture (NA), required number of unit cells, and analyzable pixel regions.

Purpose of the Study:

• To establish a vectorial image formation (VIF) model for imaging scatterometry.
• To investigate the impact of NA, unit cell count, and illumination spot size on grating reconstruction accuracy.

Main Methods:

• Development of a VIF model integrating finite-difference time-domain (FDTD) and vectorial diffraction theory.
• Simulation of a silicon (Si) grating sample with a finite number of unit cells.

Main Results:

• Accurate grating reconstruction using rigorous coupled-wave analysis (RCWA) requires an upper limit on imaging NA.
• Sufficient unit cells within the illumination spot are necessary for complete zeroth-order diffraction collection.
• Analyzable pixels are limited to regions away from the grating edge due to scattering effects.

Conclusions:

• The study quantifies the relationship between imaging NA, unit cell number, and analyzable region size.
• Higher NA or smaller illumination spot size (smaller D/L ratio) reduces the required unit cells and expands the analyzable area.
• Findings provide critical insights for optimizing imaging scatterometry applications in nano-grating analysis.