E-mail Alert
RSS
| Citation: |
Wang J, Liu J B, Hu S. Source optimization based on adaptive nonlinear particle swarm method in lithography[J].
Opto-Electron Eng, 2021, 48(9): 210167. doi: 10.12086/oee.2021.210167
|
Source optimization based on adaptive nonlinear particle swarm method in lithography
-
Abstract
As an essential resolution enhancement technique, source optimization can improve the quality of advanced lithography. In the field of advanced lithography, the convergence efficiency and optimization ability of the source optimization are very important. Particle swarm optimization (PSO) is a global optimization algorithm. The adaptive control strategy can improve the global search ability of particles, and the nonlinear control strategy can expand the search range of particles. In this paper, a PSO algorithm based on adaptive nonlinear control strategy (ANCS) is proposed to solve the problem of source optimization by transforming it into a multivariable evaluation function. The image optimization simulation is carried out with a brief periodic grating image and an irregular image, and the source shape is optimized by the global iteration property of the proposed method. By using the pattern errors (PEs) as a multivariate merit function, the results of 300 iterations are evaluated, and the PEs of the two kinds of simulation patterns are reduced by 52.2% and 35%, respectively. Compared with the traditional PSO algorithm and genetic algorithm, the proposed method not only improves the imaging quality, but also has higher convergence efficiency. -
-
References
[1] Wong A K K. Resolution Enhancement Techniques in Optical Lithography[M]. Bellingham, Washington: SPIE Press, 2001. [2] Melville D, Rosenbluth A E, Waechter A, et al. Computational lithography. 2011. [3] Liebmann L W. Resolution enhancement techniques in optical lithography: It's not just a mask problem[J]. Proc SPIE, 2001, 4409: 23-32. doi: 10.1117/12.438332 [4] Mack C. Fundamental Principles of Optical Lithography[M]. Chichester, West Sussex: Wiley, 2007. [5] Peng Y, Zhang J Y, Wang Y, et al. High performance source optimization using a gradient-based method in optical lithography[C]//2010 11th International Symposium on Quality Electronic Design, San Jose, CA, USA, 2010: 108-113. [6] Rosenbluth A E, Seong N. Global optimization of the illumination distribution to maximize integrated process window[J]. Proc SPIE, 2006, 6154: 61540H. [7] Ma X, Arce G R. Pixel-based simultaneous source and mask optimization for resolution enhancement in optical lithography[J]. Opt Express, 2009, 17(7): 5783-5793. doi: 10.1364/OE.17.005783 [8] Peng Y, Zhang J Y, Wang Y, et al. Gradient-based source and mask optimization in optical lithography[J]. IEEE Trans Image Process, 2011, 20(10): 2856-2864. doi: 10.1109/TIP.2011.2131668 [9] Jia N N, Lam E Y. Pixelated source mask optimization for process robustness in optical lithography[J]. Opt Express, 2011, 19(20): 19384-19398. doi: 10.1364/OE.19.019384 [10] Li J, Lam E Y. Robust source and mask optimization compensating for mask topography effects in computational lithography[J]. Opt Express, 2014, 22(8): 9471-9485. doi: 10.1364/OE.22.009471 [11] Shen Y J, Peng F, Zhang Z R. Semi-implicit level set formulation for lithographic source and mask optimization[J]. Opt Express, 2019, 27(21): 29659-29668. doi: 10.1364/OE.27.029659 [12] Ma X, Zheng X Q, Arce G R. Fast inverse lithography based on dual-channel model-driven deep learning[J]. Opt Express, 2020, 28(14): 20404-2042. doi: 10.1364/OE.396661 [13] Ma X, Wang Z Q, Lin H J, et al. Optimization of lithography source illumination arrays using diffraction subspaces[J]. Opt Express, 2018, 26(4): 3738-3755. doi: 10.1364/OE.26.003738 [14] Fühner T, Erdmann A, Farkas R, et al. Genetic algorithms to improve mask and illumination geometries in lithographic imaging systems[C]//Applications of Evolutionary Computing, Coimbra, Portugal, 2004: 208-218. [15] Born M, Wolf E. Principles of Optics[M]. Cambridge: Cambridge University Press, 2001. [16] Saleh B E A, Rabbani M. Simulation of partially coherent imagery in the space and frequency domains and by modal expansion[J]. Appl Opt, 1982, 21(15): 2770-2777. doi: 10.1364/AO.21.002770 [17] Zhang Z N, Li S K, Wang X Z, et al. Source mask optimization for extreme-ultraviolet lithography based on thick mask model and social learning particle swarm optimization algorithm[J]. Opt Express, 2021, 29(4): 5448-5465. doi: 10.1364/OE.418242 -
Overview
Overview: With the continuous reduction of critical dimension (CD) of semiconductors, lithography technology has gradually become a key technology in the field of integrated circuit manufacturing. Resolution enhancement technologies (RETs) is to improve the resolution of lithography by modifying the incident angle of the light source and the mask mode under the premise that the wavelength and numerical aperture (NA) remain the same. Due to the influence of experimental conditions, such as temperature, assembly tolerance, and other factors, the aberration is introduced, leading to the deformation of the aerial image. In addition, the optical proximity effect (OPE) will be introduced, if the CD of the pattern is smaller than the illumination wavelength. Therefore, it is very important to solve the above problems to improve the imaging quality and image fidelity. Recently, many researchers have proposed the optimization algorithm based on pixelated representation of illumination source for inverse lithography optimization. This method has not only achieved high modulation and flexibility, but also has great advantages in improving lithography resolution. In this paper, a particle swarm optimization algorithm (PSO) combing with adaptive nonlinear control strategy (ANCS) is proposed to optimize the shape of lithography illumination source based on pixel representation. According to the unique symmetry characteristics of the light source, the light source is characterized by equal separation and dispersion, which can reduce the optimization complexity and improve the iteration efficiency. A simple grating array pattern and a complex and irregular grating array pattern are selected to verify the simulation results, and the pattern errors (PEs) between the photoresist pattern and the ideal pattern are used as the cost function to evaluate the simulation results. The effectiveness of the improved algorithm is verified by simulation of the two grating structures. In order to verify the superiority of ANCS-PSO, it is compared with the traditional particle swarm optimization algorithm and genetic algorithm. The simulation results show that the errors of the two kinds of simulation patterns are reduced by Pattern 01: 52.2%, 41.7%, 37.4%, and Pattern 02: 35 %, 25.3%, 25.3%, respectively, which effectively improves the photoresist image assurance. The comparison of the simulation results of the three algorithms shows that the proposed method not only has higher iteration efficiency, but also has more advantages in improving the quality of lithographic imaging and image fidelity.
-
Access History
Export File
Citation
Wang J, Liu J B, Hu S. Source optimization based on adaptive nonlinear particle swarm method in lithography[J]. Opto-Electron Eng, 2021, 48(9): 210167. doi: 10.12086/oee.2021.210167
Format
Content
DownLoad:
-
Figure 1.
The imaging model of lithography
-
Figure 2.
The representation of source
-
Figure 3.
(a) The annular source shape; (b) The brief array pattern; (c) The irregular pattern
-
Figure 4.
The simulation results of source optimization
-
Figure 5.
The convergence curve of simulation
- Figure .
