Inverting pupil illumination from resist-based measurements

Computational models used in process and proximity compensation require accurate description of the pupil illumination function of the lithography projector. Traditional top-hat approximation for pupil illumination function is no longer sufficient to meet stringent CD control requirements of low-k1 applications. The pupil illumination profile can change across the exposure field, contributing to across-field linewidth variation. We present a measurement of the pupil illumination based on exposing pinhole patterns on a wafer at different dose and defocus settings, and processing SEM images of patterns printed in photoresist. The fundamental principle of the method is Abbe's formulation of image formation: the intensity-image formed in resist is an incoherent, linear superposition of images each one of which is formed by illuminating the photomask by a single plane-wave. A single plane-wave that is incident on the photomask maps to a single point in the Fourier-transform aperture of the illuminator. The pupil-fill of the illuminator is obtained from SEM images by a model-based method consisting of these steps: First, resist edges in the SEM images are detected by an edge detection algorithm based on Perona-Malik diffusion. Coordinates of the points on the resist edge are obtained with respect to a reference ruler. The image intensity at any resist edge is equal to the dose-to-clear. This provides an equation for the image intensity at each point on the edge of a pinhole image. Multiple values of dose and defocus, and multiple points on each resist edge provide a large system of equations. The result of the inversion for a 193nm 0.75 NA stepper with sigma=0.55/0.85 annular illumination at five exposure field locations is presented. The CD difference between the nominal top-hat illumination and the inverted illumination was up to 1.8 nm for 1:1 line and space features ranging from 100nm to 300nm. Variation of the illumination along the long-dimension of the slit of the scanner caused 0.6 nm of CD variation for the same 1:1 dense lines.