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.