Aberration measurement based on principal component analysis of aerial images of optimized marks

We propose an aberration measurement technique based on principal component analysis of aerial images of optimized marks (AMAI-OM). Zernike aberrations are retrieved using a linear relationship between the aerial image and Zernike coefficients. The linear relationship is composed of the principal components (PCs) and regression matrix. A centering process is introduced to compensate position offsets of the measured aerial image. A new test mark is designed in order to improve the centering accuracy and theoretical accuracy of aberration measurement together. The new test marks are composed of three spaces with different widths, and their parameters are optimized by using an accuracy evaluation function. The offsets of the measured aerial image are compensated in the centering process and the adjusted PC coefficients are obtained. Then the Zernike coefficients are calculated according to these PC coefficients using a least square method. The simulations using the lithography simulators PROLITH and Dr.LiTHO validate the accuracy of our method. Compared with the previous aberration measurement technique based on principal component analysis of aerial image (AMAI-PCA), the measurement accuracy of Zernike aberrations under the real measurement condition of the aerial image is improved by about 50%.