Partial state-feedback reduced-order switching predictive models for next-generation optical lithography systems

• To link theory with practice while ensuring efficiency, we propose a reduced- order switching predictive model using partial state feedback. • Reduced order partial-feedback LTI models are derived from large-scale finite-element and computational fluid dynamics models to simplify large-scale systems for computational efficiency. • A region based switching logic is used to addresses the uncertainties. • Global uniform ultimate bounded asymptotic stability is establised through the application of small-gain theorem. • Benefits of proposed methodology is shown via on-product measurement of placement errors and throughput from an actual lithographic scanner system. 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 s 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.