Modeling and optimization of lens heating effect for lithographic projector

In optical lithography tools, thermal aberration of a projection lens, which is caused by lens heating effect, leads to degradation of imaging quality. In addition to in-line feedforward compensation technology, thermal aberration can be reduced by optimizing optical design of a projector. Thermal aberration analysis of a projection lens benefits the optimization of optical design. A model of lens heating effect for a lithographic projector is introduced, which is capable of evaluating the synthetical thermal aberration of a projector as well as analyzing the contribution of an individual optical element. Simulation results by the introduced model show that not only the deformation of lens surface, the variance of refractive index but also the change of optical path, which depends on optical design, should be considered in thermal aberration analysis. The contributions of optical elements at different locations of the projector are also analyzed. Based on the model and the simulation results, an optimization method is proposed. A projector for i-line lithography is optimized by the proposed method. Main aberrations Z5, Z9, and Z17 are reduced by about 40%. The image quality of the lithographic projector in steady state is also improved.