Optimization of lithography source illumination arrays using diffraction subspaces

An efficient and robust lithography illumination optimization (ILO) approach is developed based on subspace compressive sensing (CS) and an l_p-norm reconstruction algorithm. Instead of optimizing the source pattern over all its degrees of freedom, the proposed method only optimizes the source pixels in a subspace. The subspace includes the source pixels inducing interference between di erent di raction orders of the mask pattern. The ILO is then formulated as an l_p-norm (0 < p < 1) inverse reconstruction problem under the sparse representation of the source pattern. The subspace CS method benefits from having a significantly smaller number of optimization variables, thus e ectively improving the computation speed. In addition, an l_p-norm reconstruction algorithm is used, which is more robust than l₁-norm reconstruction algorithms. Based on the simulations at 45nm and 14nm technology nodes, the proposed methods prove to improve the computational e ciency, robustness and imaging performance of current ILO methods based on adaptive CS.