| 摘要 |
Methods, apparatus and computer program products for selfcalibrating two-dimensional metrology stages include using a rigid artifact plate having an NxN array of marks thereon to map each of a two-dimensional array of stage positions (u,v) to a corresponding position in a Cartesian coordinate grid (x,y) to determine the distortion functions Gx(x,y) and Gy(x,y). This mapping function is performed by a series of operations which preferably use an orthogonal Fourier series to decouple determination of a pivoting point and a rotation angle from determination of the distortion functions. These operations include, among other things, determining complete and incomplete non-four-fold rotationally symmetric distortion between the two-dimensional array of stage positions (u,v) and the Cartesian coordinate grid (x,y). Operations are then performed to decouple the determination of the pivoting point and the rotation angle from the determination of the distortion functions Gx(x,y) and Gy(x,y) by determining (i) a two-dimensional translation misalignment error and a rotation misalignment error from the complete and incomplete non-four-fold rotationally symmetric distortion and then determining (ii) complete four-fold rotationally symmetric distortion between the two-dimensional array of stage positions and the Cartesian coordinate grid from, among other things, the two-dimensional translation misalignment error and the rotation misalignment error. These operations provide a highly efficient method of self-calibrating metrology and lithography stages.
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