Heuristics for Truncating the Number of Optical Kernels in Hopkins Image Calculations for Model-Based OPC Treatment

摘要

In the application of model-based optical proximity correction (OPC) to a full chip layout, lithography simulators require fast imaging algorithms to quickly obtain the critical dimensions (CDs) of the printed features. Model accuracy is frequently traded-off for speed in order to shorten the computation time for full chip design. The sum-of-coherent systems approximation represents the current standard for fast image computation. This approximation decomposes the optical system response function in the Hopkins imaging equation into a sum of products of its eigenfunctions, or kernels, via singular value decomposition. The partially-coherent optical imaging system is then represented as a sum of images formed by coherently illuminated optical systems with transfer functions corresponding to the kernels of the optical system response. The eigenvalues usually decay quickly, depending on the properties of the optical system. Current models will typically use the first few dominant kernels since each additional kernel adds to the computational time. However, there is no general guideline that indicates where to cut off the series in order to obtain the necessary accuracy. In this paper, we propose a generally applicable heuristic for choosing the number of kernels. We describe a few heuristics that show how to truncate the number of kernels that are included in a lithography model calibration, resulting in a more efficient model for OPC treatment. The heuristics are based on various eigenvalue measures such as the energy or the degree of coherence and express the CD error as a function of these measures. The heuristics then show the number of kernels needed for a given accuracy.