The Exposure-Defocus Forest

Abstract

The exposure-defocus (E-D) forest, a large cluster of E-D trees, is a valuable lithography characterization tool. With the E-D forest, processing parameters are compressed into relevant ones that are significant for manufacturing. It forms a universal quantitative base for comparison of lithographic performance, hence an essential vehicle to analyze and optimize the imaging performance of lithographic systems. This paper shows the physical meaning of the E-D space and the construction of E-D tree and E-D forest from aerial, developed, or etched images either from simulation or from experimental linewidth measurement results. The performance criteria based on E-D trees and optimization in depth of focus, exposure latitude, and E-D window area, are explained. The significance of dealing with an entire E-D forest, instead of single trees, is shown. The difference between linewidth-based and edge-based E-D trees is given. Examples of E-D forest application include: Determining the mutual dependence of depth of focus and exposure latitude; Optimizing the imaging lens numerical aperture and the degree of partial coherence; Determining the resist operation window; Characterizing and reducing optical proximity effects; Evaluating phase shifting masks; Optimizing off-axis illumination; and Comparing the performance of optical and X-ray lithography.