Substrate warpage determination system

1 . A substrate warpage determination system, comprising:

at least three first supporting devices forming a first substrate support area configured to carry a substrate;

at least three second supporting devices forming a second substrate support area configured to carry the substrate;

an actuator configured to move the at least three second supporting devices in a vertical direction; and

a controller configured to drive the actuator, wherein the controller is configured to:

determine a force exerted by the actuator;

determine a position in the vertical direction of the second substrate support area relative to the first substrate support area; and

drive the actuator to move the at least three second supporting devices from one of:

a lower position, wherein the second substrate support area is below the first substrate support area, as seen in a vertical direction, in order to carry the substrate by the first substrate support area, and

an upper position wherein the second substrate support area is above the first substrate support area, as seen in the vertical direction, in order to carry the substrate by the second substrate support area, to the other one of the lower position and the upper position, and

determine the force exerted by the actuator at the position in the vertical direction of the second substrate support area relative to the first substrate support area, as the at least three second supporting devices move from the one of the lower position and the upper position to the other one of the lower position and the upper position;

compare the determined force exerted by the actuator at the position in the vertical direction of the second substrate support area relative to the first substrate support area to a predetermined force at a predetermined position in the vertical direction of the second substrate support area relative to the first substrate support area, and

determine a warpage of the substrate from the comparison.

2 . The substrate warpage determination system according to claim 1 , wherein the controller is configured to determine the warpage of the substrate from the position in the vertical direction of the second substrate support area relative to the first substrate support area, at which the force exerted by the actuator changes as the at least three second supporting devices move from the one of the lower position and the upper position to the other one of the lower position and the upper position.

3 . The substrate warpage determination system according to claim 2 , wherein the controller is configured to determine the warpage of the substrate from the position in the vertical direction of the second substrate support area relative to the first substrate support area at which the force exerted by the actuator changes to a predetermined fraction of the force exerted by the actuator in the upper position of the at least three second supporting devices.

4 . The substrate warpage determination system of claim 2 , wherein the controller is configured to move the at least three second supporting devices from the one of the lower position and the upper position to the other one of the lower position and the upper position at a constant velocity, and wherein the controller is configured to derive the position of the second substrate support area from the constant velocity and a time elapsed during moving the second substrate support area.

5 . The substrate warpage determination system of claim 1 , wherein the predetermined fraction of the force exerted by the actuator in the upper position of the at least three second supporting devices is between 60% and 90%, more preferably 80%.

6 . The substrate warpage determination system of claim 1 , wherein the one of the lower position and the upper position is the lower position and wherein the other one of the lower position and the upper position is the upper position.

7 . The substrate warpage determination system claim 1 , wherein the at least three first supporting devices are arranged on a first circle extending in the horizontal plane and wherein the at least three second supporting devices are arranged on a second circle extending in the horizontal plane.

8 . The substrate warpage determination system of claim 7 , wherein a diameter of the first circle exceeds a diameter of the second circle.

9 . The substrate warpage determination system of claim 7 , wherein a diameter of the second circle exceeds a diameter of the first circle.

10 . The substrate warpage determination system of claim 7 , wherein the first supporting devices is distributed such that there is one plane of symmetry.

11 . The substrate warpage determination system of claim 7 , wherein the second supporting devices is distributed such that there are three planes of symmetry.

12 . A lithographic apparatus comprising the substrate warpage determination system of claim 1 .

13 . The lithographic apparatus according to claim 12 , further comprising a substrate support configured to hold the substrate and a substrate transfer robot configured to load or unload the substrate, wherein the at least three first supporting devices are comprised in the substrate transfer robot and the at least three second supporting devices are comprised in the substrate support of the lithograpic apparatus.

14 . The lithographic apparatus according to claim 13 , wherein the controller is configured to measure the force exerted by the actuator as the substrate is transferred from the substrate transfer robot to the substrate support or as the substrate is transferred from the substrate support to the substrate transfer robot, and to determine the warpage of the substrate before clamping the substrate on the substrate support.

15 . The lithographic apparatus according to claim 14 , wherein the at least three second supporting devices are e-pins of the substrate support.