Variational Level-set Formulation for Lithographic Source and Mask Optimization

摘要

This paper addresses the contributing factors in lithographic source and mask optimization,namely,the accuracy of the image formation model and the efficiency of the inverse imaging calculations in the optimization framework.A variational level-set formulation is established to incorporate a distance regularization term and an external energy.The former maintains a signed-distance profile and the latter minimizes the sum of the mismatches between the printed image and the desired one over all locations.Hence the need of reinitialization is eliminated in a principle way securing a stable level-set evolution and accurate computation with a simpler and more efficient numerical implementation.We employ a vector imaging model together with a stratified media model to describe the vector nature of electromagnetic fields propagating in the coupling image formation.Several strategies including computing the convolution operation with Fast Fourier Transform,the electric-field caching technique and the conjugate gradient method are discussed to ease the computation load and improve convergence.