APR 10, 2026

A hybrid machine learning framework for systematic optimization of overlay key positions

SPIE Advanced Lithography + Patterning

Authors

Jeng-Hun Suh, Taekwon Jee

Abstract

As semiconductor manufacturing advances into the sub-nanometer era, overlay accuracy control in photolithography has become increasingly critical. While precise overlay measurement is essential, throughput constraints necessitate effective sampling strategies. Conventional key position selection methods, such as heuristic approaches or equidistant placement, depend heavily on engineer experience and lack a systematic optimization framework. Furthermore, the widely used normalized model uncertainty (nMU) metric, though effective for simpler optimization algorithms, does not fully capture actual overlay correction quality when applied with advanced optimizers. We propose a hybrid machine learning framework for systematic overlay key position optimization. The framework integrates a warm-started genetic algorithm (GA) that consistently outperforms both equidistant placement and greedy Cascade in nMU optimization, with particularly strong gains under high-order overlay models where Cascade's greedy approach is most susceptible to local optima. Through evaluation against dense Virtual Fab ground-truth data, we reveal that better nMU does not perfectly correlate with better residual root-mean-square error (RMSE), motivating direct RMSE optimization. To bridge this gap without incurring prohibitive computation cost, a lightweight Ridge regression proxy (r = 0.81) is constructed to predict RMSE from nMU features, reducing per-evaluation cost from 2 s to 0.0018 ms. When used as the GA fitness function, this proxy enables the optimizer to achieve the lowest actual RMSE across all 9 evaluation categories, with up to 30% RMSE reduction compared to equidistant placement at lower key counts. These results demonstrate that domain knowledge-driven hybrid optimization can systematically improve overlay sampling quality, serving as a key enabler for predictive, data-driven process control in advanced semiconductor manufacturing.