Finer grid representation is inevitable to describing mask patterns more accurately in inverse lithography technology
(ILT), thus resulting in large-size mask representation and heavy computational cost. In this work we proposed a fast
convolution method called convolution using basis expansion (CBE) method to resolve computational issues caused by
intensive convolutions. The CBE method process can be elaborated as: 1) Project mask and kernel matrices from fine
grid representation to coarse grid representation under certain basis functions, which is similar to DCT or wavelet
transformations. This matrix formed by the expansion coefficient can be considered as the projection of the original large
matrix on coarse grid; 2) Perform mask and kernel convolutions on coarse grids; 3) the convolution result on fine grids is
restored by interpolation method. The selection of the basis set can be arbitrary. In this paper, we compare the
convolution accuracy and computational cost using 1) linear basis function; 2)discrete cosine basis function; 3) basis
function based on K-L transform for different fine and coarse matrix size ratios n in both 1-D and 2-D conditions. Also,
the quantitative interpolation error of cubic spline interpolation function is discussed. In numerical verification of aerial
image calculation, this new method provides almost the same effectiveness and 10X~20X running speed improvement
comparing to traditional convolution method. The CBE method will show its large effectiveness and efficiency in mask
optimization.
We proposed a new method of generating and optimizing sub-resolution assist features (SRAFs). This method is based
on a newly proposed ILT algorithm-Cost-function-Reduction method (CFRM). CFRM is proved to be much effective
and efficient than gradient-based algorithm and traditional simulated annealing method. We improve CFRM to be an
initial condition independent algorithm (ICIA) by tuning some running parameters. The robustness of ICIA is verified
numerically by six mask patterns and two mask technologies in partial-coherence image model using 100 randomly
generated mask patterns. Results showed that all are converged to similar final mask patterns with less than 3%
differences of the final image edge placement error (EPE). The skeleton of the final mask pattern can be decided by first
tens of iterations. Based on the above properties, an efficient and effective algorithm is proposed to handle SRAFs
placement. This effectiveness method is demonstrated by different patterns using different mask technologies.
The aim of this paper is to explore the use of the Graphic Processing Unit (GPU) for mask design using inverse
lithography technique (ILT). We extend a newly proposed ILT algorithm called cost-function-reduction method (CFRM)
to general partial-coherence image systems. To release heavy computational cost in this algorithm such as intensity
computation, the algorithm is modified for GPU implementation. The scalability of the GPU implementation is
demonstrated using different sizes of matrix in incoherence image system and partial-coherence image system. The total
GPU optimization time for a 25μm×25μm mask in partial-coherence image model is about 8.2 second. About 15X
performance increase have been achieved than that of an algorithm solely implemented on a high-end CPU. The
maximum mask size is limited by GPU card memory.
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