Abstract: A substrate warpage determination system comprises at least three first supporting devices and at least three second supporting devices, forming first and second substrate support areas configured to carry a substrate, an actuator configured to move the at least three second supporting devices in a vertical direction, and a controller to drive the actuator. The controller is configured to determine a force exerted by the actuator, compare the determined force exerted by the actuator at the position in a 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.

Abstract: An object handling apparatus for handling a generally planar object, the object handling apparatus including: two support arms, at least one of the two support arms movable relative to another support arm generally in a plane such that the two support arms are operable to grip and hold an object disposed in the plane, wherein each of the support arms includes at least one support pad and at least one aligner, the support pads configured to locally contact a surface of the object and apply a force thereto generally perpendicular to the plane so as to support the object and the at least one aligner configured to locally contact a surface of the object and apply a force thereto generally in the plane so as to grip the object.

Abstract: A substrate warpage determination system comprises at least three first supporting devices and at least three second supporting devices, forming first and second substrate support areas configured to carry a substrate, an actuator configured to move the at least three second supporting devices in a vertical direction, and a controller to drive the actuator. The controller is configured to determine a force exerted by the actuator, compare the determined force exerted by the actuator at the position in a 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.

Abstract: An object handling apparatus for handling a generally planar object, the object handling apparatus including: two support arms, at least one of the two support arms movable relative to another support arm generally in a plane such that the two support arms are operable to grip and hold an object disposed in the plane, wherein each of the support arms includes at least one support pad and at least one aligner, the support pads configured to locally contact a surface of the object and apply a force thereto generally perpendicular to the plane so as to support the object and the at least one aligner configured to locally contact a surface of the object and apply a force thereto generally in the plane so as to grip the object.

Abstract: Methods and apparatuses for determining in-plane distortion (IPD) across a substrate having a plurality of patterned regions. A method includes obtaining intra-region data indicative of a local stress distribution across one of the plurality of patterned regions; determining, based on the intra-region data, inter-region data indicative of a global stress distribution across the substrate; and determining, based on the inter-region data, the IPD across the substrate.

Abstract: A method and control system for determining stress in a substrate. The method includes determining a measured position difference between a measured position of at least one first feature and a measured position of at least one second feature which have been applied on a substrate, and determining local stress in the substrate from the measured position difference.

Abstract: Methods and associated apparatus for reconstructing a free-form geometry of a substrate, the method including: positioning the substrate on a substrate holder configured to retain the substrate under a retaining force that deforms the substrate from its free-form geometry; measuring a height map of the deformed substrate; and reconstructing the free-form geometry of the deformed substrate based on an expected deformation of the substrate by the retaining force and the measured height map.

Abstract: A method and control system for determining stress in a substrate. The method includes determining a measured position difference between a measured position of at least one first feature and a measured position of at least one second feature which have been applied on a substrate, and determining local stress in the substrate from the measured position difference.

Abstract: A method for determining a mechanical property of a layer applied to a substrate and associated control system for controlling a lithographic process. The method includes obtaining measured out-of-plane deformation of the substrate, the out-of-plane deformation including deformation normal to a substrate plane defined by, or parallel to, a substrate surface. The measured out-of-plane deformation is fitted to a second order polynomial in two coordinates associated with the substrate plane and the mechanical property (e.g. anisotropic Young's moduli) of the layer is determined based on characteristics of the fitted second order polynomial. The mechanical property of the layer can be used to calibrate an in-plane distortion model of the substrate for predicting in-plane distortion based on the measured out-of-plane deformation.

Abstract: A substrate table to support a substrate, the substrate table including a main body, burls extending from the main body and having first upper ends that define a support surface to support the substrate, and support pins having second upper ends. The support pins are movable between a retracted position and an extended position. The support pins are arranged to support the substrate in the extended position. The support pins are arranged to be switched to a first stiffness mode and a second stiffness mode. In the first stiffness mode, the support pins have a first stiffness in a direction parallel to the support surface. In the second stiffness mode, the support pins have a second stiffness in the direction parallel to the support surface. The first stiffness is different from the second stiffness.

Abstract: A substrate table to support a substrate, the substrate table including a main body, burls extending from the main body and having first upper ends that define a support surface to support the substrate, and support pins having second upper ends. The support pins are movable between a retracted position and an extended position. The support pins are arranged to support the substrate in the extended position. The support pins are arranged to be switched to a first stiffness mode and a second stiffness mode. In the first stiffness mode, the support pins have a first stiffness in a direction parallel to the support surface. In the second stiffness mode, the support pins have a second stiffness in the direction parallel to the support surface. The first stiffness is different from the second stiffness.