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: 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: 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 lithographic process includes clamping a substrate onto a substrate support, measuring positions across the clamped substrate, and applying a pattern to the clamped substrate using the positions measured. A correction is applied to the positioning of the applied pattern in localized regions of the substrate, based on recognition of a warp-induced characteristic in the positions measured across the substrate. The correction may be generated by inferring one or more shape characteristics of the warped substrate using the measured positions and other information. Based on the one or more inferred shape characteristics, a clamping model is applied to simulate deformation of the warped substrate in response to clamping. A correction is calculated based on the simulated deformation.

Abstract: A lithographic process includes clamping a substrate onto a substrate support, measuring positions across the clamped substrate, and applying a pattern to the clamped substrate using the positions measured. A correction is applied to the positioning of the applied pattern in localized regions of the substrate, based on recognition of a warp-induced characteristic in the positions measured across the substrate. The correction may be generated by inferring one or more shape characteristics of the warped substrate using the measured positions and other information. Based on the one or more inferred shape characteristics, a clamping model is applied to simulate deformation of the warped substrate in response to clamping. A correction is calculated based on the simulated deformation.

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.