Extended axial response range of non-patterned wafer dark-field inspection systems via dual-tailed extended-axial point spread functions

Dark-field imaging systems offer the advantages of non-contact, high sensitivity, and high throughput in non-patterned wafer inspection during semiconductor front-end processes. However, the application of high numerical aperture (NA) objectives with deep ultraviolet (DUV) light sources increases their sensitivity to defocusing caused by micrometer-scale irregularities on wafer surface, leading to false positives and false negatives. In this paper, we propose a family of point spread functions (PSFs), dual-tailed extended-axial PSFs (DTE-PSFs), to enhance the system’s defocus tolerance, improve the signal-to-noise ratio (SNR) under defocused conditions, and extend its axial response range. In this scheme, a custom phase plate, created by optimizing the variance of the PSF intensity gradient across various sampling planes, is placed in the spectral plane of a 4f system integrated behind the objective to manipulate the optical system’s PSF. Experimental results demonstrate that well-designed DTE-PSF can extend the axial response range of the systems by a factor of 2–3 compared to conventional setups, while also offering superior localization performance. The proposed method is efficient, requiring neither post-processing nor additional inspection time, and offers a novel approach to addressing the defocusing issue in dark-field wafer inspection systems.