26 June 2003 Theoretical corner rounding analysis and mask writer simulation
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Abstract
We present a derivation of a theoretical corner radius function describing analytically the corner shape and curvature as a function of position on along the feature profile. This function allows us to better describe corner rounding and the process influence (imaging, diffusion, etc.) responsible for corner rounding in mask writing and lithographic imaging. When extracting a corner radius from a feature profile shape, two approaches have been used. The first assumes a single corner radius for the entire profile shape. The profile shape is fit to a single circular function to obtain the corner radius. However because the curvature is not constant the corner radius value thus obtained is contaminated by values not part of the actual corner-even if the profile is data is windowed to contain only points near the corner. The second approach defines the corner radius as equal to the maximum value of the curvature in a region near the corner. This definition is very susceptible to noise in the profile (line edge roughness, etc). A better approach is to fit the profile to a theoretical curvature-verses-position function for a perfect corner imaged using a non-perfect imaging system. This theoretical curvature verses position function can be derived for simple optical imaging systems, chemical diffusion, and Gaussian laser writers. We couple this analysis with simulations of generalized mask writing processes to better understand the nature of corner rounding. The mask writing process is modeled in Fourier space as a convolution with a possibly asymmetric Gaussian kernel. Taking an isocontour of the resulting image corresponding to the desired level of bias gives quick approximate mask shape as might be obtained from a real mask writing device such as a laser writer with an asymmetric intensity profile to its beam.
© (2003) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
Robert L. Jones, Jeffrey D. Byers, "Theoretical corner rounding analysis and mask writer simulation", Proc. SPIE 5040, Optical Microlithography XVI, (26 June 2003); doi: 10.1117/12.485538; https://doi.org/10.1117/12.485538
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