Object positioning in lithography

1. An object positioning system comprising:

an object to be positioned;

a measurement system with one or more sensors configured to measure the position of the object in one or more degrees of freedom relative to a reference, wherein each of the one or more sensors of the measurement system has an associated measurement area on the object of which the position in one or more degrees of freedom relative to the reference is measured and wherein a location of at least one measurement area on the object is dependent on the position of the object in at least one degree of freedom;

an actuator system with one or more actuators configured to position the object;

a control system configured to drive the actuator system in dependency of an output of the measurement system and a set point representing a desired position of the object,

wherein the control system comprises an observer with a dynamic model of the object to estimate an internal dynamic behavior of the object based on an input to the object and the output of the measurement system,

wherein the dynamic model includes a dependency of the location of at least one measurement area on the position of the object in at least one degree of freedom, and

wherein the control system is configured to drive the actuator system in dependency of an output of the observer, and

wherein the control system is configured to compensate the output of the measurement system for the internal dynamic behavior using the estimated internal dynamic behavior.

2. The system according to claim 1 , wherein when the dynamic model of the object is described as a differential equation having a state equation estimating the internal dynamic behavior and an output equation estimating the output of the measurement system based on the estimated internal dynamic behavior, at least one coefficient of the output equation of the differential equation depends on the location of the at least one measurement area that is dependent on the position of the object in the at least one degree of freedom.

3. The system according to claim 1 , wherein the observer comprises a feedback loop configured to generate a correction term for the estimated internal dynamic behavior that can be described as a weighting matrix times a difference between the output of the measurement system and a by the observer estimated output of the measurement system, and wherein the weighting matrix comprises at least one coefficient depending on the location of the at least one measurement area that is dependent on the position of the object in the at least one degree of freedom.

4. The system according to claim 3 , wherein the weighting matrix is selected such that a dynamic behavior of the difference between the output of the measurement system and the estimated output of the measurement system as defined by the observer is less dependent on the location of the at least one measurement area that is dependent on the position of the object in the at least one degree of freedom.

5. The system according to claim 1 , wherein the location of the at least one measurement area that is dependent on the position of the object in the at least one degree of freedom is determined from the set point.

6. The system according to claim 1 , wherein the control system is configured to dampen the internal dynamical behavior using the estimated internal dynamic behavior.

7. The system according to claim 1 , wherein the measurement system comprises more sensors than degrees of freedom that the object is positionable in.

8. The system according to claim 1 , wherein the one or more sensors of the measurement system are interferometers having a radiation source arranged to be stationary relative to the reference, wherein radiation from the radiation source is directed towards the measurement area on the object.

9. The system according to claim 1 , wherein the one or more sensors of the measurement system are encoder type sensors having a sensor head and a grating, and wherein the sensor head is arranged to be stationary relative to the reference and the grating is arranged on the object.

10. The system according to claim 9 , wherein the grating of the measurement system comprises a grating arranged on the top surface of the object and a grating arranged on the bottom surface of the object.

11. A lithographic apparatus comprising an object positioning system according to claim 1 .

12. A lithographic apparatus according to claim 11 , further comprising:

an illumination system configured to condition a radiation beam;

a support constructed to support a patterning device, the patterning device being capable of imparting the radiation with a pattern in its cross-section to form a patterned radiation beam;

a substrate table constructed to hold a substrate; and

a projection system configured to project the patterned radiation beam onto a target portion,

wherein the object is the support or the substrate table.

13. A device manufacturing method wherein use is made of an object positioning system according to claim 1 .

14. A method for positioning an object, the method comprising:

providing a measurement system with one or more sensors configured to measure a position of the object in one or more degrees of freedom relative to a reference, wherein each of the one or more sensors of the measurement system has an associated measurement area on the object of which the position in one or more degrees of freedom relative to the reference is measured, and wherein a location of at least one measurement area on the object is dependent on the position of the object in at least one degree of freedom;

providing an actuator system with one or more actuators configured to position the object;

providing a set point representing a desired position of the object;

providing a dynamic model of the object to estimate an internal dynamic behavior of the object, wherein the dynamic model includes a dependency of the location of at least one measurement area on the position of the object in at least one degree of freedom;

estimating the internal dynamic behavior of the object using the dynamic model by providing to the dynamic model, an input to the object and the by the measurement system measured position of the object;

compensating the output of the measurement system for the internal dynamic behavior using the estimated internal dynamic behavior; and

positioning the object with the actuator system based on the set point and the by the measurement system measured position of the object while taking the internal dynamical behavior into account.

15. The method according to claim 14 , wherein when the dynamic model of the object is described as a differential equation having a state equation estimating the internal dynamic behavior and an output equation estimating the output of the measurement system based on the estimated internal dynamic behavior, at least one coefficient of the output equation of the differential equation depends on the location of the at least one measurement area that is dependent on the position of the object in the at least one degree of freedom.

16. The method according to claim 14 , comprising performing a feedback loop to generate a correction term for the estimated internal dynamic behavior that can be described as a weighting matrix times a difference between the output of the measurement system and an estimated output of the measurement system, and wherein the weighting matrix comprises at least one coefficient depending on the location of the at least one measurement area that is dependent on the position of the object in the at least one degree of freedom.

17. The method according to claim 14 , comprising dampening the internal dynamical behavior using the estimated internal dynamic behavior.

18. The method according to claim 14 , wherein the measurement system comprises more sensors than degrees of freedom that the object is positionable in.

19. A non-transitory computer-readable medium comprising instructions, when executed, configured to cause a computer system to at least:

obtain a measured position of an object using a measurement system, the measurement system having one or more sensors configured to measure the position of the object in one or more degrees of freedom relative to a reference, wherein each of the one or more sensors of the measurement system has an associated measurement area on the object of which the position in one or more degrees of freedom relative to the reference is measured, and wherein a location of at least one measurement area on the object is dependent on the position of the object in at least one degree of freedom;

estimate an internal dynamic behavior of the object using a dynamic model of the object by providing to the dynamic model, an input to the object and the by the measurement system measured position of the object, the dynamic model configured to estimate the internal dynamic behavior of the object and the dynamic model including a dependency of the location of at least one measurement area on the position of the object in at least one degree of freedom;

cause compensation of the output of the measurement system for the internal dynamic behavior using the estimated internal dynamic behavior; and

output information to enable positioning of the object with an actuator system based on a set point representing a desired position of the object and the by the measurement system measured position of the object while taking the internal dynamical behavior into account.

20. The computer-readable medium of claim 19 , wherein the dynamic model of the object is described as a differential equation having a state equation estimating the internal dynamic behavior and an output equation estimating the output of the measurement system based on the estimated internal dynamic behavior, and at least one coefficient of the output equation of the differential equation depends on the location of the at least one measurement area that is dependent on the position of the object in the at least one degree of freedom.