2D Super-Resolution Metrology Based on Superoscillatory Light

Abstract

Progress in the semiconductor industry relies on the development of increasingly compact devices consisting of complex geometries made from diverse materials. Precise, label-free, and real-time metrology is needed for the characterization and quality control of such structures in both scientific research and industry. However, optical metrology of 2D sub-wavelength structures with nanometer resolution remains a major challenge. Here, a single-shot and label-free optical metrology approach that determines 2D features of nanostructures, is introduced. Accurate experimental measurements with a random statistical error of 18 nm (λ/27) are demonstrated, while simulations suggest that 6 nm (λ/81) may be possible. This is far beyond the diffraction limit that affects conventional metrology. This metrology employs neural network processing of images of the 2D nano-objects interacting with a phase singularity of the incident topologically structured superoscillatory light. A comparison between conventional and topologically structured illuminations shows that the presence of a singularity with a giant phase gradient substantially improves the retrieval of object information in such an optical metrology. This non-invasive nano-metrology opens a range of application opportunities for smart manufacturing processes, quality control, and advanced materials characterization.

Keywords: machine learning; optical metrology; structured light; superoscillatory light; super‐resolution.

Figure 1

2D optical metrology via imaging with topologically structured superoscillatory light and AI analysis. a) The intensity (|E_y |²) and phase (φ(E_y )) profiles of the topologically structured superoscillatory light in the x‐z plane, where phase singularities are indicated by white circles. A measured elliptical aperture, represented by the rectangle, interacts with one phase singularity near the hotspot. b) SEM of a measured sub‐wavelength elliptical hole and the intensity pattern (|E_y |²) of the superoscillatory hotspot in the x‐y plane. c) Flow diagram of the 2D optical metrology, where the superoscillatory light illuminates the measurands (different elliptical holes), and a neural network learns to retrieve the widths and lengths of elliptical apertures from their images.

Figure 2

2D size retrieval of sub‐wavelength elliptical apertures based on experimental topological imaging. a) Image of an elliptical hole with width = 9λ/61 and length = 171λ/244 illuminated by the phase singularity to the left of the hotspot in the superoscillatory field. b,c) Retrieved b) widths (circles) and c) lengths (squares) of elliptical apertures versus their actual sizes, where the ideal cases are marked by diagonal dashed lines.

Figure 3

2D size retrieval of sub‐wavelength elliptical apertures based on simulated topological imaging. a) Simulated image of an elliptical hole (with the same size in Figure 2a) overlapping with a phase singularity of the superoscillatory light. b,c) Retrieved b) widths (circles) and c) lengths (squares) of elliptical apertures versus their actual sizes, where the ideal cases are marked by diagonal dashed lines and the neural network learns and predicts using simulated images.

Figure 4

A comparison of measurement errors under different illumination conditions. a–d) Illumination diagrams of an elliptical hole under the plane wave, tightly‐focused Gaussian, superoscillatory (SO) hotspot, and SO singularity illumination, respectively. e,f) A comparison of measurement errors under such different illumination conditions according to simulations.