Lifeng Duan

In situ aberration measurement technique based on principal component analysis of aerial image

We propose a novel in situ aberration measurement technique for lithographic projection lens by use of aerial image based on principal component analysis (AMAI-PCA). The aerial image space, principal component space and Zernike space are introduced to create a transformation model between aerial images and Zernike coefficients. First the aberration-induced aerial images of measurement marks are simulated to form an aerial image space with a statistical Box-Behnken design pattern. The aerial image space is then represented by their principal components based on principal component analysis. The principal component coefficients of the aerial images are finally connected with Zernike coefficients by a regression matrix through regression analysis. Therefore in situ aberration measurement can be achieved based on the regression matrix and the principal component coefficients of the detected aerial images. The measurement performance of the proposed AMAI-PCA technique is demonstrated superior compared to that of the conventional TAMIS technique by using a lithographic simulator tool (Prolith). We also tested the actual performance of AMAI-PCA technique on a prototype wafer exposure tool. The testing results show our proposed technique can rapidly measure the aberrations up to high-order Zernike polynomial term with 1σ repeatability of 0.5 nm to 2.3 nm depending on the aberration type and range.

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.

Even aberration measurement of lithographic projection optics based on intensity difference of adjacent peaks in alternating phase-shifting mask image

We propose an in situ technique for measuring an even aberration of lithographic projection optics. By using the Hopkins theory of partially coherent imaging and the thick-mask model, the linear relationship between the intensity difference of adjacent peaks in an alternating phase-shifting mask image and an even aberration is established by equations and verified by numerical results. The sensitivity of measuring the even aberration of lithographic projection optics based on this linear relationship is analyzed, and the measurement mark is designed accordingly. Measurement performance of the present technique is evaluated using the lithographic simulator PROLITH, which shows that the present technique is capable of measuring the even aberration of lithographic projection optics with ultrahigh measurement accuracy.

Translational-symmetry alternating phase shifting mask grating mark used in a linear measurement model of lithographic projection lens aberrations

A linear measurement model of lithographic projection lens aberrations is studied numerically based on the Hopkins theory of partially-coherent imaging and positive resist optical lithography (PROLITH) simulation. In this linearity model, the correlation between the marks structure and its sensitivities to aberrations is analyzed. A method to design a mark with high sensitivity is proved and declared. By use of this method, a translational-symmetry alternating phase shifting mask (Alt-PSM) grating mark is redesigned with all of the even orders, +/-3rd and +/-5th order diffraction light missing. In the evaluation simulation, the measurement accuracies of aberrations prove to be enhanced apparently by use of the redesigned mark instead of the old ones.

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.

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%.

Prediction of lens heating induced aberration via particle filter in optical lithography

In optical lithography, lens heating induced aberrations of a projection lens lead to degradation of imaging quality. In order to accurately compensate for thermal aberrations by integrated manipulators in projection lens, it is crucial to apply an accurate method for thermal aberration prediction. In this paper, an effective and accurate method for thermal aberration prediction is proposed. Double exponential model is simplified in respect of the timing of exposure tools, and particle filter is used to adjust the parameters of the double exponential model. Parameters of the simplified model are updated recursively pursuant to the aberration data measured during the exchange of wafers. The updated model is used to predict thermal aberrations of the lens during the following exposure of wafer. The performance of the algorithm is evaluated by simulation of a projection lens for ArF lithography. Maximum root mean square (RMS) value of perdition error of thermal aberration under annular illumination and dipolar illumination are reduced by 68.3% and 76.1%, respectively. The proposed method is also of well adaptability to different types of aberration measurement error.

The thermal aberration analysis of a lithography projection lens

In optical lithography tools, thermal aberration of a projection lens, which is caused by lens heating, leads to degradation of imaging quality. In addition to in-line feedforward compensation technology [1], the thermal aberration can be reduced by optimizing projection lens design. Thermal aberration analysis of a projection lens benefits the optimization of projection lens design. In this paper, thermal aberration analysis methods using physical model and simplified model are compared. Physical model of lens heating provides accurate thermal aberration analysis, but it is unable to analyze the contribution of an element of the lens to thermal aberration which is significant for thermal optimization[2]. Simplified model supports thermal analysis of an element of a lens[3]. However, only the deformation of lens surface and the variance of refractive index are considered in the simplified model. The thermal aberration analysis, in this paper, shows not only the deformation of lens surface, the variance of refractive index but also the change of optical path should be considered in thermal aberration analysis. On the basis of the analysis, a strategy for optimizing projection lens design is proposed and used to optimize thermal behavior of a lithography projection lens. The RMS value of thermal aberration is reduced by 31.8% in steady state.