Method of obtaining array of plurality of regions on substrate, exposure method, exposure apparatus, method of manufacturing article, non-transitory computer-readable storage medium, and information processing apparatus

An exposure apparatus for exposing a substrate via an original, comprising:

• a processing unit configured to obtain an array of a plurality of regions on a substrate;
• and
• a stage configured to position the substrate based on the array obtained by the processing unit,
• wherein the processing unit
• obtains position measurement data by measuring a mark assigned to each sample region among the plurality of regions on the substrate, and
• estimates a position of each non-measurement region excluding the sample region among the plurality of regions by using a regression model used to estimate the array from the position measurement data, and
• determines, for each non-measurement region, a standard deviation of a distribution of the position of the non-measurement region estimated from the regression model, and
• if the standard deviation for a non-measurement region exceeds a threshold, obtains position measurement data by measuring a mark assigned to the non-measurement region, and obtaining the array from (i) the position measurement data of the sample region, and (ii) the position measurement data obtained for the non-measurement region for which the standard deviation exceeds the threshold, and
• the regression model is a nonparametric regression model.

A non-transitory computer-readable storage medium storing a program configured to cause a computer to execute a method of obtaining an array of a plurality of regions on a substrate, the program causing the computer to execute

• obtaining position measurement data by measuring a mark assigned to each sample region among the plurality of regions on the substrate, and
• estimating a position of each non-measurement region excluding the sample region among the plurality of regions by using a regression model used to estimate the array from the position measurement data,
• wherein the regression model is a nonparametric regression model
• determining, for each non-measurement region, a standard deviation of a distribution of the position of the non-measurement region estimated from the regression model;
• and
• if the standard deviation for a non-measurement region exceeds a threshold, obtaining position measurement data by measuring a mark assigned to the non-measurement region, and obtaining the array from (i) the position measurement data of the sample region, and (ii) the position measurement data obtained for the non-measurement region for which the standard deviation exceeds the threshold.

An information processing apparatus, wherein

• the apparatus is configured to
• obtain position measurement data obtained by measuring a mark assigned to a sample region among a plurality of regions on a substrate,
• estimate a position of a non-measurement region excluding the sample region among the plurality of regions by using a regression model used to estimate an array of the plurality of regions from the position measurement data,
• determines, for each non-measurement region, a standard deviation of a distribution of the position of the non-measurement region estimated from the regression model, and
• if the standard deviation for a non-measurement region exceeds a threshold, obtains position measurement data by measuring a mark assigned to the non-measurement region, and obtaining the array from (i) the position measurement data of the sample region, and (ii) the position measurement data obtained for the non-measurement region for which the standard deviation exceeds the threshold, and
• provide a user interface configured to display information regarding the position of the non-measurement region estimated from the regression model, and
• the regression model is a nonparametric regression model.