Pupil Optimization of Incoherent Imaging Systems for Improved CD Linearity

摘要

The CD linearity error rather than other light beam characteristics, such as optical resolution, is only important for microlithography. Optimization of CD linearity can be achieved by proper design of optical system. The method of variations is used here for direct solution of the problem to get the optimal design, the best possible pupil function of final lens in particular. The resulting optimal design depends from the allowed CD linearity error threshold only. In particular, this theory shows that an i-line mask writer should be capable of writing sub-0.25 micron lines and spaces with less than 20 nm CD linearity error (for λ = 413nm and NA=0.86). The optimization method can be used in different models of light propagation, vectorial Debye model is used here in particular. The method is computationally simple since it turns out to be an eigenvalue problem for linear system of equation. Various light polarizations can be utilized. The method is also applicable for partially coherent imaging systems.