Aperture and illumination optimization of a laser-scanning darkfield defect inspection system based on an observer-independent metric

Detecting sub-100 nm defects on unpatterned wafers presents challenges due to stochastic scattering from surface roughness that masks defect signatures. While conventional threshold-based designed apertures can block unwanted scattering signals, it predominantly rely on empirical approaches lacking a theoretical foundation. This paper introduces a fully theoretical optimization framework for laser-scanning darkfield inspection systems that addresses this limitation. We derive a rigorous, observer-independent signal-to-noise ratio (SNR) metric using a bidirectional reflectance distribution function (BRDF) model, introduce what we believe to be a novel BRDF variance (BRDFV) model to quantify roughness-induced noise from finite illumination areas, and apply a two-stage optimization process to maximize detection sensitivity. Our method significantly reduces the minimum detectable particle radius by up to 60% across diverse noise conditions. This framework is robust, scalable, and extendable to multi-channel systems for advanced classification tasks, offering a pathway toward next-generation wafer inspection tools.