Variational Level-set Formulation for Lithographic Source and Mask Optimization

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.

Adaptive gradient-based source and mask co-optimization with process awareness

We develop a source and mask co-optimization framework incorporating the minimization of edge placement error(EPE)and process variability band(PV Band)into the cost function to compensate simultaneously for the image distortion and the increasingly pronounced lithographic process conditions.Explicit differentiable functions of the EPE and the PV Band are presented,and adaptive gradient methods are applied to break symmetry to escape suboptimal local minima.Dependence on the initial mask conditions is also investigated.Simulation results demonstrate the efficacy of the proposed source and mask optimization approach in pattern fidelity improvement,process robustness enhancement,and almost unaffected performance with random initial masks.