Methods and apparatus for simulating interaction of radiation with structures, metrology methods and apparatus, device manufacturing method

A processing apparatus for use in a metrology apparatus in determining parameters of a structure, the structure formed using a lithographic process of a lithographic system and comprising a plurality of sub-structures, the apparatus comprising:

• a processor configured to:
• define a structure model to represent the structure in a two- or three-dimensional model space;
• use the structure model to simulate interaction of radiation with the structure;
• and
• repeat using the structure model while varying parameters of the structure model,
• wherein for using the structure model, the processor is configured to divide the structure model into a series of slices along at least a first dimension of the model space,
• wherein, by the dividing, a sloping face of at least one sub-structure is approximated by a series of steps along at least a second dimension of the model space,
• wherein the processor is further configured to maintain a number of the series of steps approximating the sloping face constant between repeats of using the structure model while a number of the series of slices varies,
• wherein at least one series of steps comprises two or more steps of different extents in the first dimension, the extents of the steps remaining in constant ratio to one another while varying in extent between repeats of using the structure model, and
• wherein the determined parameters are configured to be used for controlling the lithographic system.

A metrology apparatus for use in determining parameters of a structure, the metrology apparatus comprising:

• an irradiation system configured to generate a beam of radiation;
• a substrate support operable with the irradiation system for irradiating the structure including a plurality of sub-structures, the structure formed using a lithographic process of a lithographic system on the substrate with the beam of radiation;
• a detection system configured to detect radiation after interaction with the structure;
• and
• a processing apparatus for use in determining the parameters of the structure comprising:
• a processor configured to:
• define a structure model to represent the structure in a two- or three-dimensional model space;
• use the structure model to simulate interaction of radiation with the structure;
• repeat using the structure model while varying parameters of the structure model,
• wherein for using the structure model, the processor is configured to divide the structure model into a series of slices along at least a first dimension of the model space, and
• wherein, by the dividing, a sloping face of at least one sub-structure is approximated by a series of steps along at least a second dimension of the model space, and
• maintain a number of the series of steps approximating the sloping face constant between repeats of using the structure model while a number of the series of slices varies three or more times,
• wherein the structure model defines:
• a first sub-structure whose extent in the first dimension depends on a first parameter, the first sub-structure having a first sloping face approximated by a first series of steps in the second dimension, a number of steps in the first series of steps being constant between the repeats of using the structure model, and
• a second sub-structure whose extent in the first dimension depends on a second parameter, the second sub-structure having a second sloping face approximated by a second series of steps in the second dimension, a number of steps in the second series of steps being constant between the repeats of using the structure model,
• wherein the dividing the structure model into the series of slices that are continuous across the first and second sub-structures comprises introducing a cut in the second sub-structure to match a step in the first sub-structure without introducing a step in the approximated second sloping face, and
• wherein the determined parameters are configured to be used for controlling the lithographic system.

A device manufacturing method comprising:

• transferring a pattern from a patterning device onto a substrate using a lithographic process of a lithographic system, the pattern defining at least one structure including a plurality of sub-structures;
• measuring, using a metrology apparatus, one or more properties of the structure to determine a value for one or more parameters of the lithographic process;
• and
• applying a correction in subsequent operations of the lithographic process in accordance with the measured one or more properties,
• wherein the measuring the one or more properties of the structure includes determining a property by a method comprising:
• defining a structure model to represent the structure in a two- or three-dimensional model space;
• using the structure model to simulate interaction of radiation with the structure;
• and
• repeating using the structure model while varying parameters of the structure model,
• wherein for using the structure model, dividing the structure model into a series of slices along at least a first dimension of the model space,
• wherein, by the dividing, a sloping face of at least one sub-structure is approximated by a series of steps along at least a second dimension of the model space,
• wherein a number of the series of steps approximating the sloping face is maintained constant between repeats of using the structure model while a number of slices varies,
• wherein the structure model defines:
• a first sub-structure whose extent in the first dimension depends on a first parameter, the first sub-structure having a first sloping face approximated by a first series of steps in the second dimension, a number of steps in the first series of steps being constant between the repeats of using the structure model, and
• a second sub-structure whose extent in the first dimension depends on a second parameter, the second sub-structure having a second sloping face approximated by a second series of steps in the second dimension, a number of steps in the second series of steps being constant between the repeats of using the structure model, and
• wherein the dividing the structure model into the series of slices that are continuous across the first and second sub-structures comprises introducing a cut in the second sub-structure to match a step in the first sub-structure without introducing a step in the approximated second sloping face.

A lithographic system comprising:

• an illumination system configured to condition a radiation beam;
• a support configured to support a patterning device, the patterning device capable of imparting the radiation beam with a pattern in its cross section to form a patterned radiation beam;
• a substrate table constructed to hold a substrate;
• a projection system configured to project the patterned radiation beam onto a target portion of the substrate;
• and
• a metrology apparatus for use in determining parameters of a structure, the metrology apparatus comprising:
• an irradiation system configured to generate a beam of radiation;
• a substrate support operable with the irradiation system for irradiating the structure including a plurality of sub-structures, the structure formed on the substrate with radiation;
• a detection system configured to detect radiation alter interaction with the structure;
• and
• a processing apparatus for use in determining parameters of the structure comprising:
• a processor configured to:
• define a structure model to represent the structure in a two- or three-dimensional model space;
• use the structure model to simulate interaction of radiation with the structure;
• repeat using the structure model while varying parameters of the structure model,
• wherein for using the structure model, the processor is configured to divide the structure model into a series of slices along at least a first dimension of the model space, and
• wherein, by the dividing, a sloping face of at least one sub-structure is approximated by a series of steps along at least a second dimension of the model space, and
• maintain a number of steps approximating the sloping face constant between repeats of using the structure model while a number of slices varies three or more times,
• wherein the structure model defines:
• a first sub-structure whose extent in the first dimension depends on a first parameter, the first sub-structure having a first sloping face approximated by a first series of steps in the second dimension, a number of steps in the first series of steps being constant between the repeats of using the structure model, and
• a second sub-structure whose extent in the first dimension depends on a second parameter, the second sub-structure having a second sloping face approximated by a second series of steps in the second dimension, a number of steps in the second series of steps being constant between the repeats of using the structure model,
• wherein the dividing the structure model into the series of slices that are continuous across the first and second sub-structures comprises introducing a cut in the second sub-structure to match a step in the first sub-structure without introducing a step in the approximated second sloping face.

A non-transitory tangible computer program product comprising machine readable instructions for causing a processor to perform a method of metrology in a metrology apparatus for determining parameters of a structure on a substrate, the structure formed using a lithographic process of a lithographic system and comprising a plurality of sub-structures, the method comprising:

• defining a structure model to represent the structure in a two- or three-dimensional model space;
• using the structure model to simulate interaction of radiation with the structure;
• and
• repeating using the structure model while varying parameters of the structure model,
• wherein for using the structure model, dividing the structure model into a series of slices along at least a first dimension of the model space,
• wherein, by the dividing, a sloping face of at least one sub-structure is approximated by a series of steps along at least a second dimension of the model space,
• wherein a number of the series of steps approximating the sloping face is maintained constant between repeats of using the structure model while a number of the series of slices varies,
• wherein at least one series of steps comprises two or more steps of different extents in the first dimension, the extents of the steps remaining in constant ratio during repeating using the structure model, and
• wherein the determined parameters are configured to be used for controlling the lithographic system.