Relative positioning method for near-field beam spot array with optical microscope image of lithographic patterns using linear regression

A method for simply analyzing the relation between spot positions of near-field beam sources with micrometer pitch is proposed using an optical microscope. Based on the locations of spots in an optical microscopy image of lithographic patterns, the effective relative position is derived using simple linear regression. Numerical analysis is performed to introduce the concept and to evaluate the methodology with random noise. The accuracy and uncertainty of the proposed method are discussed. To confirm the method's feasibility, the experiments are conducted using fabricated probe array, and the experimental and numerical results are compared on the basis of uncertainty. An arbitrary pattern is recorded with respect to relative coordinates obtained based on the effective positions. We suggest a simple strategy for controlling beam spot array locations for pattern design in near-field lithography with less than 5-nm uncertainty.