Simulation of Non-uniformities in Sources and Optics in Projection Printing

Abstract

The aerial image simulation program SPLAT has been generalized to explore the effects of multi­element source designs and possible problems from residual mirror reflectivity variations versus pupil position on image quality in projection x-ray lithography. To model wavefront attenuation, an optical transmission with apopdization (OTA) factor is introduced, which modifies the magnitude of the pupil function versus ray angle. The OTA is expanded in a Taylor series in polar coordinates. A radial OTA variation of 1- 0.25ρ2 which falls from 1.0 at the center of the lens to 0.75 at the lens edge, required small features to be oversized approximately by 8% to obtain the same image quality. To allow for irregularly shaped sources with non-uniform intensities, the source is represented over a square grid composed of many pixels. The source is defined using geometric primitives that can be assigned arbitrary intensity weights. Typical multiple element sources of the type proposed for EUV projection printing shows that the orientation of the feature with respect to the source has about a 5% effect. The generalization of the source non-uniformity modeling in SPLAT is also applicable to illumination studies in optical projection printing.