Generating method, creating method, exposure method, and storage medium

A method of generating, by a computer, data on patterns of a plurality of originals for use in multiple exposure, in which a single-layer pattern is formed on a substrate by exposing the substrate a plurality of times, in an exposure apparatus including an illumination optical system which illuminates an original with light from a light source, and a projection optical system which projects a pattern of the original onto a substrate, the method comprising:

• a first step of Fourier-transforming a temporary target pattern corresponding to a pattern to be formed on the substrate so as to generate a map on a rectangular coordinate system which represents a distribution of diffracted lights from a plurality of pattern elements of the temporary target pattern by a spatial frequency in a plane perpendicular to an optical axis of the projection optical system;
• a second step of specifying a 1st-order diffracted light on the map generated in the first step, the 1st-order diffracted light being located in a first direction of the rectangular coordinate system outside a circle that is centered around an origin of the rectangular coordinate system and is twice as large as a pupil radius of the projection optical system;
• a third step of generating a virtual map by inserting a virtual diffracted light having an amplitude obtained by multiplying an amplitude of the 1st-order diffracted light by a constant at a position defined by shifting the 1st-order diffracted light specified in the second step in a direction opposite to the first direction by ½ a frequency of the 1st-order diffracted light and in a second direction perpendicular to the first direction by ±½ a pitch of the 1st-order diffracted light in the second direction on the map generated in the first step, and determining an effective source corresponding to the virtual map;
• a fourth step of postulating a pupil filter which forms a transmittance distribution, according to which the pupil filter transmits light from a region with an intensity value larger than a predetermined value in the effective source determined in the third step, on a pupil plane of the projection optical system;
• a fifth step of calculating an intensity distribution formed on an image plane of the projection optical system by, out of diffracted lights included in the virtual map generated in the third step, the light having passed through the pupil filter assumed in the fourth step,
• a sixth step of specifying a peak position where an intensity has a peak in the intensity distribution calculated in the fifth step;
• a seventh step of extracting a first pattern element which includes the peak position, specified in the sixth step, from the plurality of pattern elements when the temporary target pattern is projected onto the image plane of the projection optical system;
• and
• an eighth step of generating data on a pattern including the first pattern element extracted in the seventh step as data on a pattern of one original of the plurality of originals,
• wherein a cycle including the first step to the eighth step is repeated using a pattern including a second pattern element obtained by excluding the first pattern element from the plurality of pattern elements as a new temporary target pattern, and the repetition is ended in a round of the cycle, in which the number of second pattern elements becomes zero.

A storage medium storing, in a computer-readable form, a program for generating, by a computer, data on patterns of a plurality of originals for use in multiple exposure, in which a single-layer pattern is formed on a substrate by exposing the substrate a plurality of times, in an exposure apparatus including an illumination optical system which illuminates an original with light from a light source, and a projection optical system which projects a pattern of the original onto a substrate, the program causing the computer to execute:

• a first step of generating a map by sequentially defining as a pattern element of interest a plurality of pattern elements which form a temporary target pattern corresponding to a pattern to be formed on the substrate, and mapping positions of pattern elements other than the pattern element of interest relative to the pattern element of interest using a position of the pattern element of interest as an origin;
• a second step of selecting pattern elements with a periodicity from the map generated in the first step, and determining an effective source corresponding to an array pattern of the selected pattern elements among a plurality of predetermined effective sources;
• a third step of postulating a pupil filter which forms a transmittance distribution, according to which the pupil filter transmits light from a region with an intensity value larger than a predetermined value in the effective source determined in the second step, on a pupil plane of the projection optical system;
• a fourth step of calculating an intensity distribution formed on an image plane of the projection optical system by the light having passed through a temporary target pattern, placed on an object plane of the projection optical system, and the pupil filter, assumed in the third step, when the effective source determined in the second step illuminates the temporary target pattern;
• a fifth step of specifying a peak position where an intensity has a peak in the intensity distribution calculated in the fourth step;
• a sixth step of extracting a first pattern element which includes the peak position, specified in the fifth step, from the plurality of pattern elements when the temporary target pattern is projected onto the image plane of the projection optical system;
• and
• a seventh step of generating data on a pattern including the first pattern element extracted in the sixth step as data on a pattern of one original of the plurality of originals,
• wherein a cycle including the first step to the seventh step is repeated using a pattern including a second pattern element obtained by excluding the first pattern element from the plurality of pattern elements as a new temporary target pattern, and the repetition is ended in a round of the cycle, in which the number of second pattern elements becomes zero.

A storage medium storing, in a computer-readable form, a program for generating, by a computer, data on patterns of a plurality of originals for use in multiple exposure, in which a single-layer pattern is formed on a substrate by exposing the substrate a plurality of times, in an exposure apparatus including an illumination optical system which illuminates an original with light from a light source, and a projection optical system which projects a pattern of the original onto a substrate, the program causing the computer to execute:

• a first step of Fourier-transforming a temporary target pattern corresponding to a pattern to be formed on the substrate so as to generate a map on a rectangular coordinate system which represents a distribution of diffracted lights from a plurality of pattern elements of the temporary target pattern by a spatial frequency in a plane perpendicular to an optical axis of the projection optical system;
• a second step of specifying a 1st-order diffracted light on the map generated in the first step, the 1st-order diffracted light being located in a first direction of the rectangular coordinate system outside a circle that is centered around an origin of the rectangular coordinate system and is twice as large as a pupil radius of the projection optical system;
• a third step of generating a virtual map by inserting a virtual diffracted light having an amplitude obtained by multiplying an amplitude of the 1st-order diffracted light by a constant at a position defined by shifting the 1st-order diffracted light specified in the second step in the first direction by ½ a frequency of the 1st-order diffracted light and in a second direction perpendicular to the first direction by ±½ a pitch of the 1st-order diffracted light in the second direction, and determining an effective source corresponding to the virtual map;
• a fourth step of postulating a pupil filter which forms a transmittance distribution, according to which the pupil filter transmits light from a region with an intensity value larger than a predetermined value in the effective source determined in the third step, on a pupil plane of the projection optical system;
• a fifth step of calculating an intensity distribution formed on an image plane of the projection optical system by, out of diffracted lights included in the virtual map generated in the third step, the light having passed through the pupil filter assumed in the fourth step,
• a sixth step of specifying a peak position where an intensity has a peak in the intensity distribution calculated in the fifth step;
• a seventh step of extracting a first pattern element which includes the peak position, specified in the sixth step, from the plurality of pattern elements when the temporary target pattern is projected onto the image plane of the projection optical system;
• and
• an eighth step of generating data on a pattern including the first pattern element extracted in the seventh step as data on a pattern of one original of the plurality of originals,
• wherein a cycle including the first step to the eighth step is repeated using a pattern including a second pattern element obtained by excluding the first pattern element from the plurality of pattern elements as a new temporary target pattern, and the repetition is ended in a round of the cycle, in which the number of second pattern elements becomes zero.