Abstract

Micro-lithographic optical systems require a high modulation at a spatial frequency representing the smallest circuitry detail to be imaged, and also require that this modulation be maintained over a fixed depth of focus representing the longitudinal position error of the photoresist material. This somewhat unusual requirement for micro-lithography optics leads to a rethinking of the basic assumption that higher numerical apertures always lead to better system performance. We observe that for a fixed longitudinal focus error the wave-front error is proportional to the square of the numerical aperture, and for a fixed spatial frequency the 1-D modulation is equal to 1 - (spatial frequency) X (wavelength)/2(numerical aperture). Based on low frequency approximation for the 1-D MTF for defocus, the authors calculate the optimum numerical aperture as a function of both allowable depth of focus and minimum modulation at a fixed spatial frequency. The results are shown to agree with several micro-lithography optical designs. This seemingly trivial application of MTF relationships is not widely appreciated in the micro-lithography community.

© 1992 Optical Society of America