Patent ID: 8773153

Claim:
A method of correcting an overlay, comprising: setting a reference map having information relating to predetermined positions of a substrate; measuring an overlay value at each of the predetermined positions to obtain a plurality of overlay measurement values; applying the plurality of overlay measurement values to a polar coordinate function to calculate a correlation coefficient of the polar coordinate function, wherein parameters of the polar coordinate function include coordinate values of the predetermined positions; applying the correlation coefficient to the polar coordinate function with each corresponding coordinate value in substantially the reference map being a parameter to calculate an overlay correction value for the corresponding coordinate value; and generating a correction map such that corresponding positions of the reference map are corrected with corresponding overlay correction values, wherein the polar coordinate function comprises a Zernike polynomial including a plurality of terms of 1, R cos θ, R sin θ, and (2R 2 −1) and the product of the Zernike polynomial and the correlation coefficient including at least C 0 , and wherein the C 0 corresponds to an offset deformation value of the plurality of overlay measurement values, R corresponds to a radial component, and θ corresponds to an azimuth angle component.