A Fast Convolution Method and Its Application in Photomask Synthesis for Wafer Contour Fidelity Using Linear Basis Expansions

Abstract

A new method called CLBE (convolution using linear basis expansion) is proposed to perform fast convolution operation. One convolution operation on fine grids is approximated by a few convolutions on coarse grids based on linear basis expansions. The method is effective for lithography optimization since optical kernels are usually smooth enough to be approximated well by a small number of basis functions. One-dimensional and two-dimensional convolutions are used to numerically demonstrate this method. CLBE is applied in mask optimization and results show that 10X running speed improvement can be achieved without accuracy loss.