Guanyong Yan

Practical application of aerial image by principal component analysis to measure wavefront aberration of lithographic lens

In this paper, we propose a new method that can extract aber- rations using aerial image measurements and present its experimental results on lithographic tools. Based on physical simulation and statistical analysis, a linear regression matrix is obtained establishing a connection between principal component coefficients of specific aerial images and Zernike coefficients. In the application phase, the aberrations of the pro- jection lens are solved via the use of this regression matrix. An engineering model is established based on an extension of theoretical model that incorporates all the significant systematic errors. The performance of the engineering model as applied on a 0.75 NA ArF scanner is reported. In the experiment, measurement marks oriented in orthogonal directions are used and aerial images at 9 field points are measured. To verify the repeatability of this technique, every point is measured 20 times. By input- ting the aerial images into the engineering model, Zernike coefficients are solved and the results are analyzed. The wafer exposures were performed to evaluate the results of aberration correction.

High-order aberration measurement technique based on a quadratic Zernike model with optimized source

Abstract. In this paper, we propose an aberration metrology (AM) of a lithographic projection lens based on aerial images (AI) by using a quadratic relationship model (Quad) between the aerial-image intensity distribution and the Zernike coefficients. The proposed method (AMAI-Quad) uses principal component analysis and multiple linear regression analyses for model generation. The quadratic model is, then, used to extract Zernike coefficients by a nonlinear least-squares minimizing technique. The best linear constrain condition is estimated by optimizing the illumination settings. Compared with earlier techniques, based on a linear relationship between Zernike coefficients and AIs, the new method can extend the orders of Zernike coefficients measured. The application of AMAI-Quad to AIs, computed by lithography simulators PROLITH and Dr.LiTHO, demonstrated an extension of measurement range to 90mλ and an enhancement of measurement accuracy by more than 30 percent.

Aberration measurement technique based on an analytical linear model of a through-focus aerial image

We propose an in situ aberration measurement technique based on an analytical linear model of through-focus aerial images. The aberrations are retrieved from aerial images of six isolated space patterns, which have the same width but different orientations. The imaging formulas of the space patterns are investigated and simplified, and then an analytical linear relationship between the aerial image intensity distributions and the Zernike coefficients is established. The linear relationship is composed of linear fitting matrices and rotation matrices, which can be calculated numerically in advance and utilized to retrieve Zernike coefficients. Numerical simulations using the lithography simulators PROLITH and Dr.LiTHO demonstrate that the proposed method can measure wavefront aberrations up to Z(37). Experiments on a real lithography tool confirm that our method can monitor lens aberration offset with an accuracy of 0.7 nm.

Analytical analysis of the impact of polarization aberration of projection lens on lithographic imaging

Abstract. In high-numerical aperture (NA) and hyper-NA lithography systems, the polarization aberration of the projection lens leads to imaging degradations. Typically, commercial simulators, which usually entail relatively higher computing cost and lack sufficient theoretical support, are used to explore the relationship. Analytical analysis of the impact of polarization aberration of the projection lens on the aerial image is performed. In the analysis process, an alternating phase-shift mask is used, and different components of the linear polarized illumination light vector are considered. The analytical expressions of image placement error (IPE) and best focus shift (BFS) caused by polarization aberration are derived from the intensity of the aerial image. The linear relationships between IPE and odd Pauli-Zernike polarization aberrations as well as that between BFS and even Pauli-Zernike polarization aberrations are established. Moreover, the polarization aberration sensitivities are given and compared when different components of the linear polarized illumination light vector are adopted. All derived expressions match simulation results well and can be used to understand more fully the detrimental impact of polarization aberration on lithographic imaging. The accuracy of the linear relationships is assessed by the least square method.

Fast rigorous model for mask spectrum simulation and analysis of mask shadowing effects in EUV lithography

A fast rigorous model is developed for the simulation of mask diffraction spectrum in EUV lithography. It combines a modified thin mask model and an equivalent layer method and provides an analytical expression of the diffraction spectrum of mask. Based on this model, we propose a theoretical analysis of the mask shadowing effect. Mathematical expressions for the best mask (object space) focus position and for the required correction of mask pattern size are derived. When the mask focus is positioned in the equivalent plane of the multilayer, the amount of pattern shift is reduced. When the mask pattern size is corrected using the derived formula, taking a space pattern with the target CD of 22 nm as an example, the imaging CD bias between different oriented features is below 0.3 nm.

In situ aberration measurement method using a phase-shift ring mask

Abstract. An in situ aberration measurement method using a phase-shift ring mask is proposed for a lithographic projection lens whose numerical aperture is below 0.8. In this method, two-dimensional phase-shift rings are designed as the measurement mask. A linear relationship model between the intensity distribution of the lateral aerial image and the aberrations is built by principal component analysis and multivariate linear regression analyses. Compared with the principal component analysis of the aerial images (AMAI-PCA) method, in which a binary mask and through-focus aerial images are used for aberration extraction, the aerial images of the phase-shift ring mask contain more useful information, providing the possibility to eliminate the crosstalk between different kinds of aberrations. Therefore, the accuracy of the aberration measurement is improved. Simulations with the lithography simulator Dr.LiTHO showed that the accuracy is improved by 15% and five more Zernike aberrations can be measured compared with the standard AMAI-PCA. Moreover, the proposed method requires less measured aerial images and is faster than the AMAI-PCA.

Fast model for mask spectrum simulation and analysis of mask shadowing effects in extreme ultraviolet lithography

Abstract. A fast model is developed for the simulation of the mask diffraction spectrum in extreme ultraviolet lithography. It combines a modified thin mask model and an equivalent layer method and provides an analytical expression of the diffraction spectrum of the mask. Based on this model, we perform a theoretical analysis of the mask shadowing effect. Mathematical expressions for the best mask (object space) focus position and for the required correction of the mask pattern size are derived. When the mask focus is positioned in the equivalent plane of the multilayer, the amount of pattern shift is reduced. When the mask pattern size is corrected using the derived formula, taking a space pattern with a target critical dimension (CD) of 22 nm as an example, the imaging CD bias between different oriented features is below 0.3 nm.

In situ aberration measurement technique based on an aerial image with an optimized source

Abstract. An in situ aberration measurement technique based on an aerial image with an optimized source is proposed. A linear relationship between the aerial image and Zernike coefficients is established by the principal components and regression matrices, which are obtained in a modeling process through principal component analysis (PCA) and regression analysis. The linear relationship is used to extract Zernike aberrations from the measured aerial image in a retrieval process. The characteristics of regression matrix are analyzed, and the retrieval process of Zernike coefficients is optimized. An evaluation function for the measurement accuracy of Zernike aberrations is proposed, and then a fast procedure to optimize the illumination source is designed. Parameters of the illumination source are optimized according to the evaluation function and applied in our method. The simulators Dr.LiTHO and PROLITH are used to validate the method. Compared to the previous aberration measurement technique based on principal component analysis of an aerial image (AMAI-PCA), the number terms of Zernike coefficients that can be measured are increased from 7 to 27, and the measurement accuracy of Zernike aberrations is improved by more than 20%.

In situ aberration measurement technique based on aerial image with optimized source

An in-situ aberration measurement technique based on aerial image with optimized source is proposed. A linear relationship between aerial image and Zernike coefficients is established by principle component analysis and regression analysis. The linear relationship is used to extract aberrations. The impacts of the source on regression matrix character and the Zernike aberrations measurement accuracy are analyzed. An evaluation function for the aberrations measurement accuracy is introduced to optimize the source. Parameters of the source are optimized by the evaluation function using the simulators Dr.LiTHO and PROLITH. Then the optimized source parameters are adopted in our method. Compared with the previous aberration measurement technique based on principal component analysis of aerial image (AMAI-PCA), the number terms of Zernike coefficients that can be measured are increased from 7 to 27, and the Zernike aberrations measurement accuracy is improved by more than 20%.

Pixelated source optimization for optical lithography via particle swarm optimization

Abstract. Source optimization is one of the key techniques for achieving higher resolution without increasing the complexity of mask design. An efficient source optimization approach is proposed on the basis of particle swarm optimization. The pixelated sources are encoded into particles, which are evaluated by using the pattern error as the fitness function. Afterward, the optimization is implemented by updating the velocities and positions of these particles. This approach is demonstrated using three mask patterns, including a periodic array of contact holes, a vertical line/space design, and a complicated pattern. The pattern errors are reduced by 69.6%, 51.5%, and 40.3%, respectively. Compared with the source optimization approach via genetic algorithm, the proposed approach leads to faster convergence while improving the image quality at the same time. Compared with the source optimization approach via gradient descent method, the proposed approach does not need the calculation of gradients, and it has a strong adaptation to various lithographic models, fitness functions, and resist models. The robustness of the proposed approach to initial sources is also verified.