Partial State-Feedback Reduced-Order Switching Predictive Models for Next-Generation Optical Lithography Systems

Abstract

This paper presents a partial state-feedback reduced-order switching predictive model designed to support the next-generation lithography roadmap. The proposed approach addresses the trade-off between increasing the number of measurements to improve overlay accuracy and the resulting challenges, including higher measurement noise, reduced throughput and overlay/placement errors under uncertain operating conditions.. By minimizing (die-) placement errors and reducing unnecessary measurements, the method enhances system performance and throughput. This solution employs a streamlined model with adaptive switching logic to manage time-varying uncertainties induced by fluctuating operating conditions. The methodology is implemented on a state-of-the-art lithographic scanner to mitigate the spatial-temporal dynamics of reticle heating, serving as a representative industrial application. Reticle heating, which worsens with increased throughput, introduces spatial-temporal distortions that directly degrade die placement accuracy. Experimental results demonstrate significant improvements: placement errors are reduced by a factor of $2-3$x, and throughput is improved by $0.3$seconds per wafer. Importantly, the method accounts for the fact that increased throughput can exacerbate reticle heating, which directly impacts overlay performance. By actively compensating for these thermomechanical effects, the proposed approach ensures that overlay accuracy is maintained or improved -- even under increased throughput conditions -- highlighting its potential for broader application in advanced lithographic systems, particularly in thermal and vibration control.