Displacement correction apparatus, exposure system, exposure method and a computer program product

1. A displacement correction apparatus comprising:

a curvature information storage unit configured to store curvature information of a reticle;

a first insertion module configured to insert coefficients into a curved surface approximating polynomial of the reticle based on the curvature information;

a first displacement information calculation module configured to calculate displacement generated in the reticle being fixed on a reticle stage of an exposure apparatus based on the curved surface approximating polynomial of the reticle; and

a correction information calculation unit configured to calculate correction information correcting a projection lens of the exposure apparatus based on the displacement.

2. A displacement correction apparatus, comprising:

a curvature information storage unit configured to store curvature information of a reticle;

a displacement information calculation unit configured to calculate displacement generated in the reticle being fixed on a reticle stage of an exposure apparatus based on the curvature information;

a coefficient calculation module configured to calculate coefficients of a displacement correction polynomial correcting a projection lens of the exposure apparatus based on the displacement; and

a correction information calculation module configured to calculate correction information correcting the projection lens based on the coefficients of the displacement correction polynomial.

3. A displacement correction apparatus, comprising:

a curvature information storage unit configured to store a first height measured between a surface of a reticle and a first reference plane set for the reticle and a position coordinate on a surface of the reticle at which the first height is measured;

a height calculation module configured to calculate a third height by subtracting a second height measured between a surface of a reticle stage of an exposure apparatus and a second reference plane set for the reticle stage from the first height;

a second insertion module configured to insert coefficients into a curved surface approximating polynomial of the reticle by considering the flatness of the reticle stage, using the third height and a position coordinate on the surface of the reticle stage at which the first and second heights are measured;

a second displacement information calculation module configured to calculate displacement generated in the reticle being fixed on the reticle stage, using a curved surface approximating polynomial of the reticle taking the flatness of the reticle stage into consideration; and

a correction information calculation unit configured to calculate correction information correcting a projection lens of the exposure apparatus based on the displacement.

4. An exposure system, comprising:

an exposure apparatus; and

a displacement correction apparatus, comprising

a curvature information storage unit configured to store curvature information of a reticle,

a first insertion module configured to insert coefficients into a curved surface approximating polynomial of the reticle based on the curvature information,

a first displacement information calculation module configured to calculate displacement generated in the reticle being fixed on a reticle stage of an exposure apparatus based on the curved surface approximating polynomial of the reticle; and

a correction information calculation unit configured to calculate correction information correcting a projection lens of the exposure apparatus based on the displacement.

5. An exposure system, comprising:

an exposure apparatus; and

a displacement correction apparatus, comprising

a curvature information storage unit configured to store curvature information of a reticle;

a displacement information calculation unit configured to calculate displacement generated in the reticle being fixed on a reticle stage of an exposure apparatus based on the curvature information;

a coefficient calculation module configured to calculate coefficients of a displacement correction polynomial correcting a projection lens of the exposure apparatus based on the displacement; and

a correction information calculation module configured to calculate correction information correcting the projection lens based on the coefficients of the displacement correction polynomial.

6. An exposure system, comprising:

an exposure apparatus; and

a displacement correction apparatus comprising:

a curvature information storage unit configured to store information of a first height measured between a surface of a reticle and a first reference plane and a position coordinate on a surface of the reticle at which the first height is measured;

a height calculation module configured to calculate a third height, subtracting a second height measured between a surface of a reticle stage of an exposure apparatus and a second reference plane set for the reticle stage from the first height;

a second insertion module configured to insert coefficients into a curved surface approximating polynomial of the reticle by considering the flatness of the reticle stage, using the third height and a position coordinate on the surface of the reticle stage at which the first and second heights are measured;

a second displacement information calculation module configured to calculate displacement generated in the reticle being fixed on the reticle stage, using a curved surface approximating polynomial of the reticle taking the flatness of the reticle stage into consideration; and

a correction information calculation unit configured to calculate correction information correcting a projection lens of the exposure apparatus based on the displacement.

7. An exposure method, comprising:

measuring curvature information of a reticle;

inserting coefficients into a curved surface approximating polynomial of the reticle based on the curvature information;

calculating a displacement generated in the reticle being fixed on a reticle stage of an exposure apparatus based on the curved surface approximating polynomial of the reticle;

calculating correction information correcting projection lens of the exposure apparatus, using the displacement;

correcting the projection lens by using the correction information; and

exposing the reticle fixed on the reticle stage to a wafer, using the projection lens corrected.

8. An exposure method, comprising:

measuring a first height between a surface of a reticle and a first reference plane set for the reticle and a position coordinate on a surface of the reticle at which the first height is measured;

calculating a third height by subtracting a second height measured from a surface of a reticle stage of an exposure apparatus and a second reference plane set for the reticle stage from the first height;

inserting coefficients into a curved surface approximating polynomial of the reticle by considering the flatness of the reticle stage, using the third height and a position coordinate on the surface of the reticle stage measured at which the first and second heights are measured;

calculating displacement generated in a changed shape of the reticle being fixed on the reticle stage, using a curved surface approximating polynomial of the reticle taking the flatness of the reticle stage into consideration;

calculating correction information correcting projection lens of the exposure apparatus, using the displacement;

correcting the projection lens by using the correction information; and

exposing the reticle fixed on the reticle stage to a wafer, using the projection lens corrected.

9. A computer program product, embedded in a computer readable medium, for executing an application on a displacement correction apparatus, the computer program product comprising:

instructions for reading curvature information of a reticle from a curvature information storage unit;

instructions for inserting coefficients into a curved surface approximating polynomial of the reticle based on the curvature information;

instructions for calculating displacement generated in the reticle being fixed on a reticle stage of an exposure apparatus based on the curved surface approximating polynomial of the reticle;

instructions for calculating correction information correcting a projection lens of the exposure apparatus, using the displacement; and

instructions for storing the correction information in a correction information storage unit.