Positioning apparatus, exposure apparatus, and device manufacturing method

1. An apparatus comprising:

a tabletop having a plane;

a plurality of actuators configured to be driven in a direction perpendicular to the plane to move the tabletop; and

a control unit configured to measure a frequency response of the tabletop and, when a peak is detected at a resonance frequency of elastic vibration of the tabletop, adjust a thrust distribution ratio for the plurality of actuators to reduce the peak.

2. The apparatus according to claim 1 , wherein at least one actuator is arranged at each antinode portion of the elastic vibration generated on the tabletop in each of a plurality of areas formed by nodes of the elastic vibration.

3. The apparatus according to claim 2 , wherein the control unit decreases the thrust distribution ratio for an actuator arranged in an area out of the plurality of areas, where the tabletop moves in phase with a displacement of the elastic vibration; and increases the thrust distribution ratio for an actuator arranged in an area out of the plurality of areas, where the tabletop moves in reverse phase with the displacement.

4. The apparatus according to claim 2 , wherein the plurality of areas are four areas separated by the nodes generated on the tabletop, the nodes extending in first and second directions and intersecting with each other.

5. The apparatus according to claim 4 , wherein the elastic vibration generated on the tabletop is one of torsional vibration and bending vibration.

6. The apparatus according to claim 4 , wherein the control unit vibrates target positions on the tabletop in a direction perpendicular to the plane; and

increases the thrust distribution ratio for one pair of the actuators arranged in two diagonal areas out of the four areas, and decreases the thrust distribution ratio for the other pair of the actuators arranged in another two diagonal areas out of the four areas.

7. The apparatus according to claim 4 , wherein the control unit vibrates target positions on the tabletop in a direction around an axis extending in the first direction; and increases the thrust distribution ratio for one pair of the actuators arranged in one side, and decreases the thrust distribution ratio for the other pair of the actuators arranged in the other side, the two sides being separated by an axis extending in the second direction.

8. The apparatus according to claim 4 , wherein the control unit vibrates target positions on the tabletop in a direction around an axis extending in the second direction; and increases the thrust distribution ratio for one pair of the actuators arranged in one side and decreases the thrust distribution ratio for the other pair of the actuators arranged in the other side, the two sides being separated by an axis extending in the first direction.

9. The apparatus according to claim 8 , wherein the control unit obtains the thrust distribution ratio for the actuators used in positioning the tabletop in a direction perpendicular to the plane, in a direction around the axis extending in the first direction, and in the direction around the axis extending in the second direction; and then obtains the thrust distribution ratio corresponding to a drive command for each direction to avoid interference between movements of the tabletop in the direction perpendicular to the plane, in the direction around the axis extending in the first direction, and in the direction around the axis extending in the second direction.

10. The apparatus according to claim 1 , wherein the tabletop has an approximately square shape.

11. An exposure apparatus including the apparatus according to claim 1 .

12. A method, in an apparatus comprising a tabletop having a plane, and a plurality of actuators configured to be driven in a direction perpendicular to the plane to move the tabletop, for adjusting a thrust distribution ratio for the plurality of actuators, the method comprising:

measuring a frequency response of the tabletop;

confirming whether a peak is detected at a resonance frequency of elastic vibration of the tabletop in a measurement; and

adjusting, when the peak is detected, the thrust distribution ratio to reduce the peak.

13. The method according to claim 12 , further comprising arranging at least one actuator at each antinode portion of the elastic vibration generated on the tabletop in each of a plurality of areas formed by nodes of the elastic vibration.

14. The method according to claim 13 , further comprising:

decreasing the thrust distribution ratio for an actuator arranged in an area out of the plurality of areas, where the tabletop moves in phase with a displacement of the elastic vibration; and

increasing the thrust distribution ratio for an actuator arranged in an area out of the plurality of areas, where the tabletop moves in reverse phase with the displacement.

15. The method according to claim 13 , wherein the plurality of areas are four areas separated by the nodes generated on the tabletop, the nodes extending in first and second directions and intersecting with each other.

16. The method according to claim 15 , wherein the elastic vibration generated on the tabletop is one of torsional vibration and bending vibration.

17. The method according to claim 15 , further comprises:

vibrating target positions on the tabletop in a direction perpendicular to the plane; and

increasing the thrust distribution ratio for one pair of the actuators arranged in two diagonal areas out of the four areas, and decreasing the thrust distribution ratio for the other pair of the actuators arranged in another two diagonal areas out of the four areas.

18. The method according to claim 15 , further comprises:

vibrating target positions on the tabletop in a direction around an axis extending in the first direction; and

increasing the thrust distribution ratio for one pair of the actuators arranged in one side, and decreasing the thrust distribution ratio for the other pair of the actuators arranged in the other side, the two sides being separated by an axis extending in the second direction.

19. The method according to claim 15 , further comprises:

vibrating target positions on the tabletop in a direction around an axis extending in the second direction; and

increasing the thrust distribution ratio for one pair of the actuators arranged in one side and decreasing the thrust distribution ratio for the other pair of the actuators arranged in the other side, the two sides being separated by an axis extending in the first direction.

20. A device manufacturing method comprising:

exposing a substrate to light by using the exposure apparatus according to claim 13 ; and

developing the substrate exposed to light.