Fast implicit active contour model for inverse lithography.

We combine the ideas from level-set methods in computer vision and inverse imaging to derive a generalized active contour model for inverse lithography problems endowed with a locally implemented semi-implicit difference scheme. We introduce a cognitive analogy to move an initial guess of the interesting pattern contour by image-driven forces to the boundaries of the desired layout pattern. We develop an efficient semi-implicit numerical scheme implemented in the vicinity of the zero level-set and apply additive operator splitting (AOS) with respect to coordinate axes to solve consecutive one-dimensional linear systems of equations with the Thomas method. We demonstrate with simulation results that computation and convergence efficiency are jointly improved with reduced optimization dimensionality and a sufficient large step-size.

Semi-implicit level set formulation for lithographic source and mask optimization.

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.

Efficient optical proximity correction based on semi-implicit additive operator splitting.

Inverse lithography techniques (ILT) have been extensively used by the semiconductor industry to compensate for the inherent image distortions in optical lithography. However, the iterative ILT optimization procedure requires rather prohibitive time steps leading to poor efficiency with explicit time discretization. In this paper, a semi-implicit time discretization scheme is applied, enabling stable computation of mask synthesis with large time steps. Additive operator splittering (AOS) is implemented with respect to coordinate axes, reducing mask synthesis to consecutive one-dimensional updates represented by tridiagonal linear equations, which is solved efficiently by the Thomas algorithm. Simulation results merit the superiority of the proposed semi-implicit approach with improved convergence performance.

Lithographic source and mask optimization with narrow-band level-set method.

Source and mask optimization (SMO) remains a key technique to improve the wafer image printability for technology nodes of 22 nm and beyond, enabling the continuation of the immersion lithography. In this paper, we propose a distance level-set regularized reformulation of the SMO maintaining the desired signed distance property, which secures stable curve evolution and accurate computation with a simpler and more efficient numerical implementation. Consequently, computation load caused by convolution operations and memory requirements of the electric-field caching technique (EFCT) is significantly eased by performing computation only in the narrow band; moreover, the convergence of the updating process is further improved by applying larger Euler time steps of the Courant-Friedrichs-Lewy (CFL) condition with reduced optimization dimensionality. Simulation results of the proposed narrow-band level-set based SMO prove to improve the computation efficiency, memory usage and imaging performance of the full domain methods.

Level-set based mask synthesis with a vector imaging model.

With continuous shrinking of critical dimension (CD) and the application of immersion lithography system to technology nodes 22nm and beyond, the vector nature of electromagnetic fields propagating from mask to wafer plane cannot be ignored, rendering mask synthesis under scalar imaging model inadequate. In this paper, we develop a level-set based optimization framework for mask synthesis with a vector imaging model. The forward model of vector image formation is established, and then the photomask synthesis is addressed as an inverse imaging problem whose variational level-set reformulation is represented by a stable time-dependent model, which is solved by employing conjugate gradient methods of the cost function and readily available finite-difference schemes. Experimental results demonstrate pronounced performance in terms of pattern fidelity and edge placement error, together with notable computation acceleration and better convergence performance.

Hotspot-aware fast source and mask optimization.

Source mask optimization (SMO) is a useful technique for printing the integrated circuit (IC) on a wafer with increasingly smaller feature size. However, complex SMO algorithms generally lead to undesirably long runtime resulting from an optimization of largely identical regions over the whole mask pattern. In this work, a weighted SMO scheme incorporating both an awareness of the hotspots and robustness against process variations is proposed. We show how optimal solutions are reached with fewer iterations by applying various degrees of correction in the corresponding regions. The proposed method includes identifying the hotspots and combining a weight matrix to the cost function for adjustment and control. Simulation results are compared with the mask optimization (under a fixed source) and conventional SMO to illustrate the performance improvement in terms of pattern fidelity, convergence rate and process window size.

Robust level-set-based inverse lithography.

Level-set based inverse lithography technology (ILT) treats photomask design for microlithography as an inverse mathematical problem, interpreted with a time-dependent model, and then solved as a partial differential equation with finite difference schemes. This paper focuses on developing level-set based ILT for partially coherent systems, and upon that an expectation-orient optimization framework weighting the cost function by random process condition variables. These include defocus and aberration to enhance robustness of layout patterns against process variations. Results demonstrating the benefits of defocus-aberration-aware level-set based ILT are presented.

Level-set-based inverse lithography for photomask synthesis.

Inverse lithography technology (ILT) treats photomask design for microlithography as an inverse mathematical problem. We show how the inverse lithography problem can be addressed as an obstacle reconstruction problem or an extended nonlinear image restoration problem, and then solved by a level set time-dependent model with finite difference schemes. We present explicit detailed formulation of the problem together with the first-order temporal and second-order spatial accurate discretization scheme. Experimental results show the superiority of the proposed level set-based ILT over the mainstream gradient methods.

Binary image restoration by positive semidefinite programming.

We report an optimization approach to restore degraded binary images by using positive semidefinite programming when the point spread function (PSF) is known. The approach takes advantage of the combinatorial nature of the problem, considering not only local similarity and spatial context but also the relationship between individual pixel values and the PSF. Numerical experiments confirm the superiority of the approach.