Pixelated source mask optimization for process robustness in optical lithography

Optical lithography has enabled the printing of progressively smaller circuit patterns over the years. However, as the feature size shrinks, the lithographic process variation becomes more pronounced. Source-mask optimization (SMO) is a current technology allowing a co-design of the source and the mask for higher resolution imaging. In this paper, we develop a pixelated SMO using inverse imaging, and incorporate the statistical variations explicitly in an optimization framework. Simulation results demonstrate its efficacy in process robustness enhancement. © 2011 Optical Society of America.published_or_final_versio

Cascadic multigrid algorithm for robust inverse mask synthesis in optical lithography

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Robust source and mask optimization compensating for mask topography effects in computational lithography

Mask topography effects need to be taken into consideration for a more accurate solution of source mask optimization (SMO) in advanced optical lithography. However, rigorous 3D mask models generally involve intensive computation and conventional SMO fails to manipulate the mask-induced undesired phase errors that degrade the usable depth of focus (uDOF) and process yield. In this work, an optimization approach incorporating pupil wavefront aberrations into SMO procedure is developed as an alternative to maximize the uDOF. We first design the pupil wavefront function by adding primary and secondary spherical aberrations through the coefficients of the Zernike polynomials, and then apply the conjugate gradient method to achieve an optimal source-mask pair under the condition of aberrated pupil. We also use a statistical model to determine the Zernike coefficients for the phase control and adjustment. Rigorous simulations of thick masks show that this approach provides compensation for mask topography effects by improving the pattern fidelity and increasing uDOF.published_or_final_versio

Level-set-based inverse lithography for mask synthesis using the conjugate gradient and an optimal time step

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Using Machine-Learning to Optimize phase contrast in a Low-Cost Cellphone Microscope

Cellphones equipped with high-quality cameras and powerful CPUs as well as GPUs are widespread. This opens new prospects to use such existing computational and imaging resources to perform medical diagnosis in developing countries at a very low cost. Many relevant samples, like biological cells or waterborn parasites, are almost fully transparent. As they do not exhibit absorption, but alter the light's phase only, they are almost invisible in brightfield microscopy. Expensive equipment and procedures for microscopic contrasting or sample staining often are not available. By applying machine-learning techniques, such as a convolutional neural network (CNN), it is possible to learn a relationship between samples to be examined and its optimal light source shapes, in order to increase e.g. phase contrast, from a given dataset to enable real-time applications. For the experimental setup, we developed a 3D-printed smartphone microscope for less than 100 \$ using off-the-shelf components only such as a low-cost video projector. The fully automated system assures true Koehler illumination with an LCD as the condenser aperture and a reversed smartphone lens as the microscope objective. We show that the effect of a varied light source shape, using the pre-trained CNN, does not only improve the phase contrast, but also the impression of an improvement in optical resolution without adding any special optics, as demonstrated by measurements

Using Machine-Learning to Optimize phase contrast in a Low-Cost Cellphone Microscope

Cellphones equipped with high-quality cameras and powerful CPUs as well as GPUs are widespread. This opens new prospects to use such existing computational and imaging resources to perform medical diagnosis in developing countries at a very low cost. Many relevant samples, like biological cells or waterborn parasites, are almost fully transparent. As they do not exhibit absorption, but alter the light's phase only, they are almost invisible in brightfield microscopy. Expensive equipment and procedures for microscopic contrasting or sample staining often are not available. By applying machine-learning techniques, such as a convolutional neural network (CNN), it is possible to learn a relationship between samples to be examined and its optimal light source shapes, in order to increase e.g. phase contrast, from a given dataset to enable real-time applications. For the experimental setup, we developed a 3D-printed smartphone microscope for less than 100 \$ using off-the-shelf components only such as a low-cost video projector. The fully automated system assures true Koehler illumination with an LCD as the condenser aperture and a reversed smartphone lens as the microscope objective. We show that the effect of a varied light source shape, using the pre-trained CNN, does not only improve the phase contrast, but also the impression of an improvement in optical resolution without adding any special optics, as demonstrated by measurements

Line search based inverse lithography technique for mask design

Following moore\u27s law, microelectronic fabrication techniques have been developed to fabricate deep-submicron devices. Device feature size on wafer turns to be much smaller than the illumination source of nowadays widely used lithography equipments, which is 193 nm wavelength of UV(ultraviolet) light. Diffraction effects can not be avoided when transfer patterns from masks to wafers in the process of lithography because of the extremely small size of features. So the patterns transferred from masks to wafers surface are distorted very much, and it causes many problems, such as poly line end shortening or bridging which result in leakage or short circuit. The industry has been investigating various alternatives, such as EUV(extreme ultra-violet) illumination source. However, the next generation of illumination source, EUV with a wavelength of about 13.5 nm, still has a long way to be put into practice. As a result, Resolution Enhancement Technology (RET) has been increasingly relied uponto minimize image distortions. In advanced process nodes, pixelated mask becomes essential for RET to achieve an acceptable resolution. In this thesis, we investigate the problem of pixelated binary mask design in a partially coherent imaging system. Similar to previous approaches, the mask design problem is formulated as a nonlinear program and is solved by gradient based search. Our contributions are four novel techniques to achieve significantly better image quality than state-of-the-art technology. First, to transform the original bound-constrained formulation to an unconstrained optimization problem, we propose a new non-cyclic transformation of mask variables to replace the well-known cyclic one. As our transformation is monotonic, it enables a better control in flipping pixels. Second, based on this new transformation, we propose a highly efficient line search based heuristic technique to solve the resulting unconstrained optimization problem. Third, we introduce a jump technique. As gradient based search techniques will get trapped at a local minimum, we introduce a new technique named jump in order to jump out of the local minimum and continue the search. It increases the chance to achieve a better result. Fourth, to simplify the optimization, instead of using widely used discretization regularization penalty technique, we directly round the optimized gray mask into binary mask for pattern error evaluation. Experiment results show that the results of state-of-the-art algorithm implemented by Ma and Arce [5] are 8:55% to 358:8% higher than ours