Optimal Decentralized Wavelength Control in Light Sources for Lithography

Pulsed light sources are a critical component of modern lithography, with fine light beam wavelength control paramount for wafer etching accuracy. We study optimal wavelength control by casting it as a decentralized linear quadratic Gaussian (LQG) problem in presence of time-delays. In particular, we consider the multi-optics module (optics and actuators) used for generating the requisite wavelength in light sources as cooperatively interacting systems defined over a directed graph. We show that any measurement and other continuous time-delays can be exactly compensated, and the resulting optimal controller implementation at the individual optics-level outperforms existing wavelength control techniques.