Evaluation method, exposure method, and method for manufacturing an article

1. An evaluation method for evaluating an aberration of a projection optical system in an exposure apparatus, the method comprising:

obtaining a first prediction coefficient which is a prediction coefficient of a first prediction formula which is a prediction formula for an aberration that is symmetrical with respect to an optical axis of the projection optical system, and obtaining a second prediction coefficient which is a prediction coefficient of a second prediction formula which is a prediction formula for an aberration that is asymmetrical with respect to the optical axis of the projection optical system;

determining whether a shape of an illuminated region in an object plane of the projection optical system is symmetrical or asymmetrical with respect to the optical axis; and

evaluating an aberration of the projection optical system using at least one of the first prediction coefficient and the second prediction coefficient, wherein the evaluating comprises:

evaluating the aberration of the projection optical system using the first prediction coefficient in a case where the determining determines that the shape of the illuminated region is symmetrical with respect to the optical axis, and

evaluating the aberration of the projection optical system using the first prediction coefficient and the second prediction coefficient in a case where the determining determines that the shape of the illuminated region is asymmetrical with respect to the optical axis.

2. The evaluation method according to claim 1 , wherein the obtaining comprises:

measuring a focus error and an image shift error in each of a plurality of exposure processes,

obtaining, based on a result of the measuring, time-series data of the symmetrical aberration and the asymmetrical aberration, and

obtaining the first prediction coefficient by fitting the first prediction formula to the time-series data of the symmetrical aberration, and obtaining the second prediction coefficient by fitting the second prediction formula to the time-series data of the asymmetrical aberration.

3. The evaluation method according to claim 2 , wherein the plurality of exposure processes include a plurality of exposure processes for which illuminated regions thereof are respectively different.

4. The evaluation method according to claim 1 , wherein the determining, in a case where a center of gravity of an exposure region is close to the optical axis, determines that the shape of the illuminated region is symmetrical with respect to the optical axis.

5. The evaluation method according to claim 1 , wherein the determining, in a case in which a mask is a multi-layer reticle in which different patterns of layers are respectively formed in a plurality of regions, determines the shape of the illuminated region to be asymmetrical.

6. The evaluation method according to claim 1 , further comprising measuring a focus error and an image shift error between exposure sequences, obtaining data of the symmetrical aberration and the asymmetrical aberration based on a result of the measuring, and based on the obtained data, correcting the first prediction coefficient and the second prediction coefficient.

7. The evaluation method according to claim 1 , wherein the asymmetrical aberration includes at least one of axis deviation, eccentric distortion, one-sided defocusing, on-axis coma aberration, and one-sided defocusing astigmatic aberration.

8. An exposure method performed by an exposure apparatus that projects a pattern formed on a mask onto a substrate via a projection optical system, and exposes the substrate, the method comprising:

evaluating an aberration of the projection optical system by using the evaluation method according to claim 1 ;

adjusting the exposure apparatus based on a result of the evaluation; and

exposing the substrate using the adjusted exposure apparatus.

9. A method for manufacturing an article, comprising:

exposing a substrate in accordance with the exposure method according to claim 8 ; and

developing the exposed substrate,

wherein the article is manufactured from the developed substrate.