Lithographic apparatus, device manufacturing method, and device manufactured thereby

A lithographic projection apparatus comprising:

• a support structure configured to hold a patterning structure, the patterning structure being configured to pattern a beam of radiation according to a desired pattern;
• a substrate table configured to hold a substrate having an alignment structure;
• and
• an alignment system configured to measure properties of light affected by the alignment structure, to determine a position of the alignment structure relative to the patterning structure based on the measured properties, and to control a relative positioning of the patterning structure and the substrate based on the determined position,
• wherein the alignment system includes a model describing physical properties of the alignment structure, as a function of position, and
• wherein the alignment system is arranged to estimate a value of a parameter of the model that corresponds to at least one of the measured properties and to determine a correction to the determined position based on the estimated value.

A device manufacturing method comprising:

• using a patterning structure to pattern a beam of radiation according to a desired pattern;
• determining a position, relative to the patterning structure, of an alignment structure having spatially periodically variable optical properties, wherein the position is determined during alignment using both positional information from light affected by a substrate having the alignment structure and position-invariant information from the light affected by the substrate;
• determining, based on the position-invariant information, a correction to the determined position of an alignment structure;
• and
• controlling a relative positioning of the patterning structure and the substrate, based on the corrected determined position;
• wherein the alignment structure is selected from among (1) the substrate, (2) another substrate that has been subjected to a processing operation in common with the substrate, and (3) a further substrate that has been subjected to a further processing operation according to the same value of a processing parameter used to subject the substrate to the further processing operation.

A device manufacturing method comprising:

• using a patterning structure to pattern a beam of radiation according to a desired pattern;
• measuring properties of light affected by the alignment structure;
• determining a position of the alignment structure relative to the patterning structure based on the measured properties;
• controlling a relative positioning of the patterning structure and the substrate, based on the determined position;
• wherein said determining the position includes applying a model during alignment that describes physical properties of the alignment structure as a function of the position, estimating a value of a parameter of the model that corresponds to at least one of the measured properties, and determining a correction to the determined position based on the estimated value.