Open AccessSemi-implicit level set formulation for lithographic source and mask optimization
Author(s) -
Yongming Shen,
Fei Peng,
Zhenrong Zhang
Publication year - 2019
Publication title -
optics express
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.394
H-Index - 271
ISSN - 1094-4087
DOI - 10.1364/oe.27.029659
Subject(s) - convergence (economics) , stability (learning theory) , discretization , computer science , operator (biology) , set (abstract data type) , tridiagonal matrix , mathematics , algorithm , mathematical optimization , eigenvalues and eigenvectors , physics , mathematical analysis , biochemistry , chemistry , repressor , quantum mechanics , machine learning , transcription factor , economics , gene , programming language , economic growth
The convergence of lithographic source and mask optimization (SMO) has been plagued by the prohibitive time-step dictated by the stability of the explicit Euler-forward scheme in the gradient-based optimization procedure. As a remedy, we solve the distance level-set regularized reformulation of the SMO by discretizing the stability-relevant terms in an implicit manner and apply operator splitting to separately update source and mask patterns in coordinate dimensions by solving the tridiagonal systems of linear equations using the Thomas method, combining stability and simplicity. Simulation results merit the superiority of the proposed SMO approach with improved convergence by overcoming the stability constraints of the Courant-Friedrichs-Lewy (CFL) condition.