Kernel-based fast aerial image computation for a large scale design of integrated circuit patterns

Abstract

A method of simulating aerial images of large mask areas obtained during the exposure step of a photo-lithographic process when fabricating a semiconductor integrated circuit silicon wafer is described. The method includes the steps of defining mask patterns to be projected by the exposure system to create images of the mask patterns; determining an appropriate sampling range and sampling interval; generating a characteristic matrix describing the exposure system; inverting the matrix to obtain eigenvalues as well as the eigenvectors (or kernels) representing the decomposition of the exposure system; convolving the mask patterns with these eigenvectors; and weighing the resulting convolution by the eigenvalues to form the aerial images. The method is characterized in that the characteristic matrix is precisely defined by the sampling range and the sampling interval, such that the sampling range is the shortest possible and the sampling interval, the largest possible, without sacrificing accuracy. The method of generating aerial images of patterns having large mask areas provides a speed improvement of several orders of magnitude over conventional approaches.