Jishuo Yang

Experimental study of the free spectral range (FSR) in FPI with a small plate gap

In this paper we investigate the variation of free spectral range (FSR) for the Fabry-Perot interferometer (FPI) consisting of mirrors with phase shift dispersion. The reflection phase shift on a mirror has been calculated employing the Transfer-Matrix Method and the values of FSR have been calculated under the condition of normal incidence of light beam. Fabry-Perot (FP) cavities have been fabricated employing bulk micromachining technology, and silicon wafers coated with multiplayer dielectric films were used as mirrors. FSR of these FP cavities have been experimentally measured. The experimental data match the calculated results very well. The conclusion is that FSR shortening effect must be taken into account for the FPIs with a small plate gap, as the finesse and the tunable range of tunable FPI can be affected by the shortening effect greatly.

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.

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%.

A defocus measurement method for an in situ aberration measurement method using a phase-shift ring mask

An in situ aberration measurement method using a two dimensional (2D) phase-shift ring mask has been proposed for lithographic projection lenses, which is more accurate and faster than AMAI-PCA method. The defocus of the aerial image of the 2D measurement mask is the main source of the measurement error of this method. In this paper, a defocus measurement method for the aberration measurement method is proposed, in which the residual of the principal component analysis process is used as the criterion. After the defocus is accurately measured, the most suitable linear relationship model, which plays a very important role in the aberration measurement method, can be determined. Simulations with the lithography simulator Dr. LiTHO demonstrated that the accuracy of the defocus measurement method is approximately 1nm. The aberration measurement method can detect 12 Zernike aberrations (Z5~Z16) with maximum systematic error of approximately 1mλ, when the suitable linear relationship model is used.

CDU prediction based on in-situ image measurements

Control of CD uniformity is a key aspect of IC manufacturing. Ability to accurately predict wafer-measured CD prior to exposure is critical to CDU control. In this paper we present a method to calculate a predicted CD value based on in-situ measurements, and estimate CD uniformity across the field of an exposure tool. This method is based on direct measurements of aerial image using a sensor built into the wafer stage of SMEE SSA600-series exposure scanners. Using this sensor to measure image of several features at 9 points across the exposure field, we compare predicted CD and ADI CD obtained using a standard wafer process and CD-SEM.

In situ aberration measurement technique based on quadratic Zernike model

A novel technique (AMAI-Quad) for aberration extraction of lithographic projection based on quadratic relationship model between aerial-image intensity distribution and Zernike coefficients is proposed. Zernike coefficients in this case represent the imaging quality of lithographic projection lens in a semiconductor wafer exposure scanner. The proposed method uses principal component analysis and multivariate linear regression analysis for model generation. This quadratic model is then used to extract Zernike coefficients by nonlinear least-squares. Compared with earlier techniques, based on a linear relationship between Zernike coefficients and aerial images, proposed by Duan, the new method can extend the types of aberrations measured. The application of AMAI-Quad to computed images of lithography simulators PROLITH and Dr.LiTHO for randomly varied wavefront aberrations within a range of 50mλ demonstrated an accuracy improvement of 30%.