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

High-fidelity source mask optimization for suppressing line-end shortening

Source mask optimization (SMO) is a widely used computational lithography technique for compensating lithographic distortion. However, line-end shortening is still a key factor that cannot be easily corrected and affects the image fidelity of lithography at advanced nodes. This paper proposes a source mask optimization method that suppresses line-end shortening and improves lithography fidelity. An adaptive hybrid weight method is employed to increase the weights of the line end during the optimization, which adaptively updates the weights in each iteration according to the edge placement error (EPE). A cost function containing a penalty term based on the normalized image log slope (NILS) is established to ensure the fidelity of the overall feature when paying more attention to the line-end region. The scope of this penalty term is regulated by widening and extending the split contour to further reduce the line-end shortening. Simulation results show that the proposed method can effectively suppress the line-end shortening and improve the lithography fidelity compared with the traditional SMO method.

Memory efficient constrained optimization of scanning-beam lithography

This article describes a memory efficient method for solving large-scale optimization problems that arise when planning scanning-beam lithography processes. These processes require the identification of an exposure pattern that minimizes the difference between a desired and predicted output image, subject to constraints. The number of free variables is equal to the number of pixels, which can be on the order of millions or billions in practical applications. The proposed method splits the problem domain into a number of smaller overlapping subdomains with constrained boundary conditions, which are then solved sequentially using a constrained gradient search method (L-BFGS-B). Computational time is reduced by exploiting natural sparsity in the problem and employing the fast Fourier transform for efficient gradient calculation. When it comes to the trade-off between memory usage and computational time we can make a different trade-off compared to previous methods, where the required memory is reduced by approximately the number of subdomains at the cost of more computations. In an example problem with 30 million variables, the proposed method reduces memory requirements by 67% but increases computation time by 27%. Variations of the proposed method are expected to find applications in the planning of processes such as scanning laser lithography, scanning electron beam lithography, and focused ion beam deposition, for example.

Exposure latitude aware source and mask optimization for extreme ultraviolet lithography

Extreme ultraviolet (EUV) lithography is a new generation of integrated circuit manufacturing technology with great development prospects. EUV lithography has more significant demand for high exposure latitude (EL) due to greater requirements for the stability of the light source. Source and mask optimization (SMO) technology is widely used to compensate for imaging distortion. In this paper, we propose an EL-aware SMO (ELASMO) method that uses a low-resist threshold sensitivity (LRS) penalty function to improve the EL in EUV lithography. Compared to conventional SMO, the proposed ELASMO method can significantly enhance the aerial image contrast, improve the EL, and enlarge the process window while ensuring high imaging fidelity.

Efficient informatics-based source and mask optimization for optical lithography

Source and mask optimization (SMO) is a widely used computational lithography technology that greatly improves the image fidelity of lithography systems. This paper develops an efficient informatics-based SMO (EISMO) method to improve the image fidelity of lithography systems. First, a communication channel model is established to depict the mechanism of information transmission in the SMO framework, where the source is obtained from the gradient-based SMO algorithm. The manufacturing-aware mask distribution is then optimized to achieve the best mutual information, and the theoretical lower bound of lithography patterning error is obtained. Subsequently, an efficient informatics-based method is proposed to refine the mask optimization result in SMO, further reducing the lithography patterning error. It is shown that the proposed EISMO method is computationally efficient and can achieve superior imaging performance over the conventional SMO method.

Fast heuristic-based source mask optimization for EUV lithography using dual edge evolution and partial sampling

Extreme ultraviolet (EUV) lithography is essential in the advanced technology nodes. Source mask optimization (SMO) for EUV lithography, especially the heuristic-based SMO, is one of the vital resolution enhancement techniques (RET). In this paper, a fast SMO method for EUV based on dual edge evolution and partial sampling strategies is proposed to improve the optimization efficiency and speed of the heuristic algorithm. In the source optimization (SO) stage, the position and intensity of the source points are optimized in turn. Using the sparsity of the optimized source, a partial sampling encoding method is applied to decrease the variables' dimension in optimization. In the mask optimization (MO) stage, the main features (MF) and the sub-resolution assistant features (SRAF) are optimized in turn. A dual edge evolution strategy is used in the MF optimization and the partial sampling encoding method is used in SRAF optimization. Besides, the imaging qualities at different focal planes are improved by SRAF optimization. The optimization efficiency is greatly improved by the dimensionality reduction strategies. Simulations are carried out with various target patterns. Results show the superiority of the proposed method over the previous method, especially for large complex patterns.

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.

Source mask optimization using the covariance matrix adaptation evolution strategy

Source mask optimization (SMO) is one of the indispensable resolution enhancement techniques to guarantee the image fidelity and process robustness for the 2Xnm technology node and beyond. The optimization capacity and convergence efficiency of SMO are important, especially for full-chip SMO. An SMO method using the covariance matrix adaptation evolution strategy (CMA-ES), together with a new source representation method, is proposed in this paper. Based on the forward vector imaging formulation, the encoding and decoding methods of the source and the mask, and the constructed merit function, the source and the mask are optimized using the CMA-ES algorithm. The solution search space and the search step size are adaptively updated during the optimization procedure. Considering the sparsity of the optimal source, the source is represented by a set of ideal point sources with unit intensity and adjustable positions. The advantageous spatial frequency components of the source for imaging performance improvement are identified through the aggregation of the point sources. Simulations and comparisons verify the superior optimization capacity and convergence efficiency of the proposed method.

Vectorial pupil optimization to compensate polarization distortion in immersion lithography system

Polarization distortion innately exists in hyper numerical aperture immersion lithography system. Polarization distortion, mainly including polarization aberration (PA) of lithography projection optics and thick mask induced polarization distortion, would seriously impact on lithography imaging quality. Some computational lithography technologies, such as robust optical proximity correction and robust source and mask optimization, have been introduced and developed to reduce the impact of polarization distortion on lithography imaging. In this paper, we innovate a vectorial pupil optimization (VPO) method to further extend degrees of freedom for pupil optimization and compensate polarization distortion for immersion lithography system. An analytical relationship between lithography imaging and active vectorial pupil, and the gradient-based algorithm is adopted to effectively solve VPO. Extensive simulations demonstrate the VPO method simultaneously compensate the PA of projection optics and the thick mask induced polarization distortion sufficiently. Based on PA-aware source mask optimization, the VPO method can further reduce the impact of polarization distortion on lithography imaging. Compared to current pupil wavefront optimization, the proposed VPO effectively reduces the pattern error by 37.2%, which demonstrates the VPO method can improve lithography pattern fidelity.

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.

Multi-objective lithographic source mask optimization to reduce the uneven impact of polarization aberration at full exposure field

Source and mask optimization (SMO) technology based on vectorial image model is indispensable in immersion lithography process at advanced technology node. Many kinds of algorithms have achieved successes in aspect of fast and robust SMO without accounting polarization aberration (PA). However, because the PA arising from immersion projection optics unevenly impacts on imaging performance, the conventional SMO would not be applicable in real lithography system. In this paper, we first investigate the serious impact of PA on SMO in details. The SMO accounting the assigned PA of one field point is not applicable to other field points, where the pattern fidelity is fiercely worse and the pattern error (PAE) is nearly doubled. Then, we innovate a MOSMO method to reduce the uneven impact of PA on lithography imaging at full exposure field. Compared to the assigned PA aware SMO, the proposed MOSMO reduces the standard deviation of PAE distribution by 53.3% and enlarges the maximum exposure latitude from 4% to 6.7%, which demonstrates the MOSMO is very significant to balance imaging quality and improve process robustness at full exposure field.

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.