Analyses of imaging performance degradation caused by birefringence residual in lens materials

Influences of birefringence residual in lens materials of projection optics used for microlithography are investigated based on partially coherent imaging formula that has been modified to incorporate the change of polarization states in lens elements. Birefringent properties are represented by two- dimensional functions with respect to magnitude and fast-axis direction, and they are determined using random numbers to reproduce actual distributions in such materials as calcium fluoride. By repeating calculations using lens data created with different sets of random numbers, the degree of imaging performance degradation is analyzed statistically in terms of the magnitude of birefringence in each lens element, the number of lens element composing a projection lens, and the randomness of fast-axis distributions. It is found that the image contrast for a five-bar line/space pattern decreases squarely proportional to the magnitude, whereas the value decreases linearly proportional to the element number. The influence of randomness is understood in relation to image formations through random phase media.

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