Abstract: Obtaining a function by convoluting a function representing a light intensity distribution formed by an illumination apparatus on a pupil plane of a projection optical system and a pupil function of the projection optical system. Calculating a Fourier transformed function by Fourier transforming the product of the obtained function and a diffracted light distribution from a pattern on an object plane of the projection optical system. Producing data of the pattern of the mask based on the Fourier transformed function.

Abstract: A storage medium includes a program which causes a computer to execute a method of calculating a light intensity distribution on a pupil plane of an illumination optical system. The method includes: determining an impulse response function of a projection optical system by performing Fourier transform on a pupil function of the projection optical system; setting a length to a second zero point of the impulse response function as a response length, extracting, from elements forming a target pattern, only elements inside am area within radius which is response length, and determining a function indicating the extracted pattern as an image function; and obtaining the light intensity distribution based on the pupil function, the determined impulse response function, and the determined image function.

Abstract: A computer readable medium containing computer-executable instructions which cause a computer to execute processing steps that calculate a light intensity distribution formed on an image plane of a projection optical system. When executed, the medium causes a computer to execute the steps of dividing an effective light source into the plurality of areas, generating, for each of the plurality of areas, a plurality of shifted pupil functions by shifting a pupil function in accordance with a position of each of divided point sources, defining, for each of the plurality of areas, a matrix including the plurality of pupil functions, calculating, for each of the plurality of areas, eigenvalues and eigenfunctions by performing singular value decomposition of the matrix, and calculating, for each of the plurality of areas, the light intensity distribution based on a diffracted light distribution from the mask and the eigenvalues and the eigenfunctions.

Abstract: A two-dimensional transmission cross coefficient is obtained based on a function representing a light intensity distribution formed by an illumination apparatus on a pupil plane of the projection optical system and a pupil function of the projection optical system. Based on the two-dimensional transmission cross coefficient and data of a pattern on an object plane of the projection optical system, an approximate aerial image is calculated by using at least one of plural components of an aerial image on an image plane of the projection optical system. Data of a pattern of an original is produced based on the approximate aerial image.

Abstract: To calculate data of an original, a computer is caused to execute the following steps of converting data regarding an intended pattern to be formed on a substrate into frequency-domain data, calculating a two-dimensional transmission cross coefficient using a function representing an effective light source that an illumination device forms on a pupil plane of a projection optical system when the original is absent on an object plane of the projection optical system and using a pupil function of the projection optical system, calculating a diffracted light distribution from a pattern that is formed on the object plane using both the frequency-domain data and data of at least one component of the calculated two-dimensional transmission cross coefficient, and converting data of the calculated diffracted light distribution into spatial-domain data to determine the data of the original.

Abstract: A measurement method of the present invention is a measurement method for measuring a shape of a target T from an interference pattern generated by interference between a reflected light of the target and a reference spherical surface. The measurement method includes a first measurement step which positions the target T in a first region 30a at a light source side with respect to a focal position 20 of the reference spherical surface to measure the interference pattern, and a second measurement step which positions the target T in a second region 30b opposite to the first region with respect to the focal position 20 of the reference spherical surface to measure the interference pattern.

Abstract: Method for generating data for an original plate used during processing for illuminating the original plate and projecting an image of a pattern onto the original plate onto a substrate via a projection optical system. A two-dimensional transmission cross coefficient is calculated based on a function indicating a distribution of an intensity of light formed on a pupil plane of the projection optical system. An approximate aerial image is calculated based on the calculated two-dimensional transmission cross coefficient and a first pattern on an object plane of the projection optical system. A second pattern is generated having the first pattern on the object place and auxiliary patterns based on the approximate aerial image. The original plate data is generated by repeatedly calculating the approximate aerial image and generating a second pattern that is used as the first pattern on the object plane.

Abstract: The present invention provides a method of determining a structure of an antireflection coating formed on a substrate as an exposure target of an exposure apparatus, the method comprising steps of calculating, an intensity distribution of light diffracted by an original, based on information of an effective light source formed on a pupil plane of a projection optical system, and information of an original pattern, extracting diffracted light having an intensity of not less than a threshold from the intensity distribution calculated in the calculating step, and determining the structure of the antireflection coating, formed on the substrate, such that a reflectance of the antireflection coating falls within a target range when an incident angle of the diffracted light, which has the intensity of not less than the threshold and is extracted in the extracting step, on the antireflection coating formed on the substrate is an input.

Abstract: The present invention provides a calculation method of calculating, by a computer, a light intensity distribution formed on an image plane of a projection optical system, comprising a step of dividing an effective light source formed on a pupil plane of the projection optical system into a plurality of point sources, a step of shifting a pupil function describing a pupil of the projection optical system for each of the plurality of point sources in accordance with positions thereof, thereby generating a plurality of shifted pupil functions, a step of defining a matrix including the plurality of pupil functions, a step of performing singular value decomposition of the matrix, thereby calculating an eigenvalue and an eigenfunction, and a step of calculating the light intensity distribution, based on a distribution of the light diffracted by the pattern of the mask, and the eigenvalue and the eigenfunction.

Abstract: The present invention provides a calculation method of calculating, by a computer, a light intensity distribution formed on an image plane of a projection optical system, comprising a step of dividing an effective light source formed on a pupil plane of the projection optical system into a plurality of point sources, a step of shifting a pupil function describing a pupil of the projection optical system for each of the plurality of point sources in accordance with positions thereof, thereby generating a plurality of shifted pupil functions, a step of defining a matrix including the plurality of pupil functions, a step of performing singular value decomposition of the matrix, thereby calculating an eigenvalue and an eigenfunction, and a step of calculating the light intensity distribution, based on a distribution of the light diffracted by the pattern of the mask, and the eigenvalue and the eigenfunction.

Abstract: A storage medium includes a program which causes a computer to execute a method of calculating a light intensity distribution on a pupil plane of an illumination optical system. The method includes: determining an impulse response function of a projection optical system by performing Fourier transform on a pupil function of the projection optical system; setting a length to a second zero point of the impulse response function as a response length, extracting, from elements forming a target pattern, only elements inside am area within radius which is response length, and determining a function indicating the extracted pattern as an image function; and obtaining the light intensity distribution based on the pupil function, the determined impulse response function, and the determined image function.

Abstract: An apparatus includes a measurement unit and a calculation unit, wherein the calculation unit expresses a measurement error of each measurement as a polynomial including a term that has a coefficient whose value is dependent on setting of the measurement area and a term that has a coefficient whose value is not dependent on the setting of the measurement area, obtains a matrix equation with respect to the coefficients of the polynomial by applying a least-squares method to each of the measurement data items for the overlapping region, assigns data about the terms of the polynomial and each of the measurement data items for the overlapping region to the matrix equation, calculates the coefficients of the polynomial from a singular value decomposition of the matrix equation to which the data has been assigned, and corrects each of the measurement data items for the measurement areas by using the coefficients.

Abstract: A measurement method for measuring a shape of a target using an interference pattern includes the steps of converting a first interference pattern into a first shape of the target (S103 to S105), obtaining a second interference pattern at a position where the target moves in an optical axis direction of the reference surface (S107, S108), unwrapping the second interference pattern after aligning a phase of the first interference pattern with a phase of the second interference pattern (S109), converting the unwrapped second interference pattern into a second shape of the target (S110), determining whether or not the first shape of the target coincides with the second shape (S111), and calculating the shape of the target by adding the integral multiple of a wavelength of the light source to the unwrapped second interference pattern if the first shape does not coincide with the second shape (S112).

Abstract: A computer-readable recording medium recording a mask data generation program which causes a computer to generate data of a mask illuminated by illumination light and used to form a latent image on a photoresist via a projection optical system. The program causes the computer to execute a map generation step of Fourier-transforming a function indicating an effective light source to generate a coherence map expressing a coherence distribution on an object plane of the projection optical system, on which the mask is arranged, an arrangement step of arranging a main pattern at an origin of the coherence map and arranging an auxiliary pattern in a region where a coherence with respect to the origin is not less than a set value, and a data generation step of generating mask data including the main pattern and the auxiliary pattern, which are arranged in the arrangement step.

Abstract: The present invention provides a method of determining a structure of an antireflection coating formed on a substrate as an exposure target of an exposure apparatus, the method comprising steps of calculating, an intensity distribution of light diffracted by an original, based on information of an effective light source formed on a pupil plane of a projection optical system, and information of an original pattern, extracting diffracted light having an intensity of not less than a threshold from the intensity distribution calculated in the calculating step, and determining the structure of the antireflection coating, formed on the substrate, such that a reflectance of the antireflection coating falls within a target range when an incident angle of the diffracted light, which has the intensity of not less than the threshold and is extracted in the extracting step, on the antireflection coating formed on the substrate is an input.

Abstract: An exposure apparatus including an illumination system which illuminates an original, and projection optics which project a pattern of the original illuminated by the illumination system onto a substrate. The apparatus includes an interferometer which forms an interference pattern including aberration information on the projection optics using a polarized light beam emitted from the illumination system, in which the interferometer is a common path interferometer in which two light beams forming interference pattern pass along a path in the projection optics, and a processor which calculates optical characteristics of the projection optics on the basis of the interference pattern formed by the interferometer. The illumination system including a polarization controller which sequentially generates at least three difference polarized light beams with respective polarization states different from each other.

Abstract: A computer readable medium containing computer-executable instructions which cause a computer to execute processing steps that calculate a light intensity distribution formed on an image plane of a projection optical system. When executed, the medium causes a computer to execute the steps of dividing an effective light source into the plurality of areas, generating, for each of the plurality of areas, a plurality of shifted pupil functions by shifting a pupil function in accordance with a position of each of divided point sources, defining, for each of the plurality of areas, a matrix including the plurality of pupil functions, calculating, for each of the plurality of areas, eigenvalues and eigenfunctions by performing singular value decomposition of the matrix, and calculating, for each of the plurality of areas, the light intensity distribution based on a diffracted light distribution from the mask and the eigenvalues and the eigenfunctions.

Abstract: To calculate data of an original, a computer is caused to execute the following steps of converting data regarding an intended pattern to be formed on a substrate into frequency-domain data, calculating a two-dimensional transmission cross coefficient using a function representing an effective light source that an illumination device forms on a pupil plane of a projection optical system when the original is absent on an object plane of the projection optical system and using a pupil function of the projection optical system, calculating a diffracted light distribution from a pattern that is formed on the object plane using both the frequency-domain data and data of at least one component of the calculated two-dimensional transmission cross coefficient, and converting data of the calculated diffracted light distribution into spatial-domain data to determine the data of the original.

Abstract: A computer-readable recording medium recording a mask data generation program, which causes a computer to generate data of a mask illuminated by illumination light and used to form a latent image on a photoresist via a projection optical system.

Abstract: A measurement method of the present invention is a measurement method for measuring a shape of a target T from an interference pattern generated by interference between a reflected light of the target and a reference spherical surface. The measurement method includes a first measurement step which positions the target T in a first region 30a at a light source side with respect to a focal position 20 of the reference spherical surface to measure the interference pattern, and a second measurement step which positions the target T in a second region 30b opposite to the first region with respect to the focal position 20 of the reference spherical surface to measure the interference pattern.