The traditional Denavit–Hatenberg method is a relatively mature method for modeling the kinematics of robots. However, it has an obvious drawback, in that the parameters of the Denavit–Hatenberg model are discontinuous, resulting in singularity when the adjacent joint axes are parallel or close to parallel. As a result, this model is not suitable for kinematic calibration. In this article, to avoid the problem of singularity, the product of exponentials method based on screw theory is employed for kinematics modeling. In addition, the inverse kinematics of the 6R robot manipulator is solved by adopting analytical, geometric, and algebraic methods combined with the Paden–Kahan subproblem as well as matrix theory. Moreover, the kinematic parameters of the Denavit–Hatenberg and the product of exponentials-based models are analyzed, and the singularity of the two models is illustrated. Finally, eight solutions of inverse kinematics are obtained, and the correctness and high level of accuracy of the algorithm proposed in this article are verified. This algorithm provides a reference for the inverse kinematics of robots with three adjacent parallel joints.

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The critical dimension (CD), roughness, and sensitivity are extremely significant indicators for evaluating the imaging performance of photoresists in extreme ultraviolet lithography. As the CD gradually shrinks, tighter indicator control is required for high fidelity imaging. However, current research primarily focuses on the optimization of one indicator of one-dimensional line patterns, and little attention has been paid to two-dimensional patterns. Here, we report an image quality optimization method of two-dimensional contact holes. This method takes horizontal and vertical contact widths, contact edge roughness, and sensitivity as evaluation indicators, and uses machine learning to establish the corresponding relationship between process parameters and each indicator. Then, the simulated annealing algorithm is applied to search for the optimal process parameters, and finally, a set of process parameters with optimum image quality is obtained. Rigorous imaging results of lithography demonstrate that this method has very high optimization accuracy and can improve the overall performance of the device, dramatically accelerating the development of the lithography process.

The line edge roughness (LER) is one of the most critical indicators of photoresist imaging performance, and its measurement using a reliable method is of great significance for lithography. However, most studies only investigate photoresist resolution and sensitivity because LER measurements require an expensive and not widely available critical dimension scanning electron microscopy (SEM) technology; thus, the imaging performance of photoresist has not been adequately evaluated. Here, we report an image processing software developed for offline calculation of LER that can analyze lithographic patterns with resolutions up to ∼15 nm. This software can effectively process all graphic files obtained from commonly used SEM machines by utilizing the adjustable double threshold. To realize the effective detection of high-resolution patterns in advanced lithography, we used SEM images generated from extreme ultraviolet and electron beam lithography to develop and validate the software's graphic recognition algorithm. This image processing software can process typical SEM images and produce reliable LER in an efficient and user-friendly manner, constituting a powerful tool for promoting the development of high-performance photoresist materials.

Resolution, line edge/width roughness, and sensitivity (RLS) are critical indicators for evaluating the imaging performance of resists. As the technology node gradually shrinks, stricter indicator control is required for high-resolution imaging. However, current research can improve only part of the RLS indicators of resists for line patterns, and it is difficult to improve the overall imaging performance of resists in extreme ultraviolet lithography. Here, we report a lithographic process optimization system of line patterns, where RLS models are first established by adopting a machine learning method, and then these models are optimized using a simulated annealing algorithm. Finally, the process parameter combination with optimal imaging quality of line patterns can be obtained. This system can control resist RLS indicators, and it exhibits high optimization accuracy, which facilitates the reduction of process optimization time and cost and accelerates the development of the lithography process.