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16 July 2002 Linear alignment correction algorithm for deep-submicron lithography
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A new algorithm for correcting misalignment between layers is introduced which is capable of compensating for interdependencies and arbitrary conventions of correctable factors. In this approach, optimal corrections are determined from solving a set of linear equations that exactly negate the effect of the observed misalignment. A series of calibration runs were performed by measuring the effect of a balanced set of forced input corrections on the resulting alignment in order to determine elements of a transformation matrix. This technique was able to calculate the average corrections required to reverse the input offsets within an average of 10nm for translation and 0.1ppm for magnification and rotation offsets. Estimated standard deviations between calculated and input offsets were smaller for y parameters than x, presumably because of better stage reproducibility in the vertical direction. The transformation matrix for Canon EX4 steppers highlighted that chip rotation is affected by inputting corrections to x axis wafer rotation. Calibration wafers with alignment sites that simulated wafer rotations of +/- 0.8585ppm were fabricated. These wafers verified that chip rotation occurs for EX4 steppers as a consequence of automated adjustment for x wafer rotation. The observed responses from these calibration wafers agreed within nanometers of the relevant element of the transformation matrix for that stepper family.
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David H. Ziger and Pierre Leroux "Linear alignment correction algorithm for deep-submicron lithography", Proc. SPIE 4689, Metrology, Inspection, and Process Control for Microlithography XVI, (16 July 2002);

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