JP2010156849A - Generation method, method for making original plate, exposure method, method for producing device and program - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a technique for generating data on a pattern of an original plate in order to form the minute pattern, with high accuracy. <P>SOLUTION: The method for generating data on the pattern of the original plate includes: a division step of dividing an effective light source to be formed on a pupil plane of a projection optical system into a plurality of zones; a first decision step of deciding the incident angle of a plane wave entering each of the plurality of divided zones; a first calculation step of calculating the transmitted light distributions to be formed on the pupil plane by electromagnetic field numerical computations, by using a plurality of plane waves entering the plurality of divided zones respectively at the decided incident angles; a second calculation step of calculating approximate aerial images to be formed on the pupil plane of the projection optical system by the plurality of plane waves, on the basis of the plurality of calculated transmitted light distributions; a generation step of summing up a plurality of calculated approximate aerial images to generate an aerial image map; and a second decision step of deciding the pattern of the original plate, on the basis of the aerial image map generated. <P>COPYRIGHT: (C)2010,JPO&INPIT

Description

  The present invention relates to a generation method, an original creation method, an exposure method, a device manufacturing method, and a program.

  An exposure apparatus is used when a semiconductor device such as a semiconductor memory or a logic circuit is manufactured by using a photolithography technique. The exposure apparatus projects a pattern formed on an original plate (mask or reticle) onto a substrate such as a wafer by a projection optical system and transfers the pattern. In recent years, miniaturization of semiconductor devices has progressed, and in an exposure apparatus, it is necessary to form a pattern having a dimension smaller than the exposure wavelength (exposure light wavelength).

  For a pattern having a dimension smaller than the exposure wavelength, the influence of light diffraction appears remarkably, so that the pattern outline (pattern shape) is not formed on the wafer as it is. Specifically, the shape accuracy of the pattern formed on the wafer is greatly deteriorated due to the corners of the pattern being rounded or the length of the pattern being shortened. Therefore, in order to reduce the deterioration of the shape accuracy of the pattern formed on the wafer, a technique for inserting an auxiliary pattern having a dimension that is not resolved with respect to the main pattern that is to be formed (that is, to be resolved) on the wafer. Has been proposed (see Patent Documents 1 to 3).

  Patent Documents 1 and 2 disclose techniques for deriving the insertion position of the auxiliary pattern by numerical calculation. In such a technique, an interference map (hereinafter referred to as “interference map”) is obtained by numerical calculation, and a position (region) that interferes with each other on the mask and a position (region) that cancels interference are derived. . Then, an auxiliary pattern is inserted at a position where interference occurs in the interference map so that the phase of light passing through the main pattern and the phase of light passing through the auxiliary pattern are equal. As a result, the light passing through the main pattern and the light passing through the auxiliary pattern strongly interfere with each other, and the target pattern can be accurately formed on the wafer. Since the mask surface and the wafer surface are in an imaging relationship, the interference map can be regarded as obtaining the amplitude on the image surface. Here, the target pattern is an element existing on the mask and transferred to the wafer. Also, Patent Document 3 discloses a method for obtaining auxiliary pattern information numerically.

  The relationship between the mask pattern and the wafer pattern in the exposure apparatus is a partial coherent imaging relationship. In partial coherent imaging, coherence on the mask surface can be obtained from information on the effective light source, and an aerial image can be calculated from the spectrum distribution (diffracted light distribution) of the mask pattern and the pupil information of the projection optical system. Here, coherence is the degree of interference according to the distance on the mask surface. The effective light source is a Fourier transform of the coherent distribution on the mask surface, and is a light intensity distribution formed on the pupil plane of the projection optical system when there is no mask.

  The coherence of an effective light source can be considered using a mutual transmission coefficient (TCC). TCC is defined by the pupil plane of the projection optical system, and is an overlapping portion of the effective light source, the pupil function of the projection optical system, and the complex conjugate of the pupil function of the projection optical system. In Patent Document 3, the pupil function of the projection optical system and the position of the effective light source are fixed, and only the position of the complex conjugate of the pupil function of the projection optical system is made variable to represent the TCC function two-dimensionally and approximated in the air. An image (hereinafter referred to as “approximate aerial image”) is obtained. Then, by inserting an auxiliary pattern near the peak position other than the target pattern of the approximate aerial image, a mask pattern for accurately forming the target pattern on the wafer can be obtained.

On the other hand, as a method for accurately obtaining light transmitted through a mask, a strict electromagnetic field numerical calculation method (for example, FDTD method or RCWA method) based on a mask well equation is generally known.
JP 2004-221594 A JP 2005-183981 A JP 2008-40470 A

  However, in the prior art, since the distribution of light transmitted through the mask (transmitted light distribution) is approximately obtained, the target pattern is formed on the wafer with sufficient accuracy against the pattern that is rapidly miniaturized. It has become impossible to obtain a mask pattern.

  Therefore, the present invention has been made in view of the above-described problems of the prior art, and an object of the present invention is to provide a technique for generating original pattern data for accurately forming a fine pattern.

  In order to achieve the above object, a generation method according to a first aspect of the present invention includes an illumination optical system that illuminates an original using light from a light source, and a projection optical system that projects a pattern of the original onto a substrate. A pattern generation method for generating pattern data of an original plate used in an exposure apparatus provided with a computer, wherein the pattern data is formed on a pupil plane of the projection optical system when the original plate is not arranged on the object plane of the projection optical system. A dividing step of dividing the effective light source into a plurality of regions, a first determining step of determining an incident angle of a plane wave incident on each of the plurality of regions divided in the dividing step, and the first determining step For each of the plurality of plane waves incident on each of the plurality of regions at the determined incident angle, the light from the light source passes through a pattern arranged on the object plane of the projection optical system. A first calculation step of calculating a transmitted light distribution formed on the pupil plane of the projection optical system by an electromagnetic field numerical calculation based on a Maxwell equation, and a plurality of transmitted light distributions calculated in the first calculation step. Based on each, a second calculation step of calculating an approximate aerial image formed on the image plane of the projection optical system by each of the plurality of plane waves, and a plurality of approximate aerial images calculated in the second calculation step Are added to each other to generate an aerial image map, and based on the aerial image map generated in the generation step, a second determination step is performed to determine the pattern of the original plate.

  According to a second aspect of the present invention, there is provided a generation method in which an original is used in an exposure apparatus including an illumination optical system that illuminates an original using light from a light source and a projection optical system that projects a pattern of the original onto a substrate. A method of generating the pattern data of the above by a computer, wherein the light from the light source passes through the pattern arranged on the object plane of the projection optical system and forms on the pupil plane of the projection optical system Is calculated by an electromagnetic field numerical calculation based on the Maxwell equation, and an approximate aerial image formed on the image plane of the projection optical system based on the transmitted light distribution calculated in the first calculation step. And a determination step of determining a pattern of the original plate based on the approximate aerial image calculated in the second calculation step. And butterflies.

  According to a third aspect of the present invention, there is provided a method for creating an original, which is characterized by creating an original based on data generated by the above-described generation method.

  An exposure method according to a fourth aspect of the present invention includes a step of illuminating an original produced by the above-described original production method, a step of projecting an image of the original pattern onto a substrate via a projection optical system, It is characterized by having.

  A device manufacturing method according to a fifth aspect of the present invention includes a step of exposing a substrate using the exposure method described above, and a step of developing the exposed substrate.

  According to a sixth aspect of the present invention, there is provided a program for an original used in an exposure apparatus including an illumination optical system that illuminates an original using light from a light source and a projection optical system that projects a pattern of the original onto a substrate. A program for causing a computer to execute a generation method for generating pattern data, which is formed on the pupil plane of the projection optical system when the original is not disposed on the object plane of the projection optical system. A dividing step for dividing the effective light source to be divided into a plurality of regions, a first determining step for determining an incident angle of a plane wave incident on each of the plurality of regions divided in the dividing step, and the first determining step The light from the light source is arranged on the object plane of the projection optical system for each of a plurality of plane waves incident on each of the plurality of regions at an incident angle determined in A first calculation step of calculating a transmitted light distribution that passes through the pattern and forms on the pupil plane of the projection optical system by an electromagnetic field numerical calculation based on a Maxwell equation, and a plurality of calculations calculated in the first calculation step Calculated in the second calculation step and the second calculation step for calculating an approximate aerial image that each of the plurality of plane waves forms on the image plane of the projection optical system based on each of the transmitted light distributions of A generation step of adding a plurality of approximate aerial images to generate an aerial image map; and a second determination step of determining a pattern of the original based on the aerial image map generated in the generation step. It is characterized by that.

  According to a seventh aspect of the present invention, there is provided a program for an original used in an exposure apparatus including an illumination optical system that illuminates an original using light from a light source and a projection optical system that projects a pattern of the original onto a substrate. A program for causing a computer to execute a generation method for generating pattern data, wherein the projection optical system allows the light from the light source to pass through a pattern arranged on an object plane of the projection optical system. A transmission light distribution formed on the pupil plane of the projection optical system based on a first calculation step of calculating by electromagnetic field numerical calculation based on Maxwell's equations and the transmission light distribution calculated in the first calculation step. A second calculation step of calculating an approximate aerial image formed on the image plane; and a pattern of the original based on the approximate aerial image calculated in the second calculation step. Characterized in that to execute a determination step of determining a down, a.

  Further objects and other aspects of the present invention will become apparent from the preferred embodiments described below with reference to the accompanying drawings.

  ADVANTAGE OF THE INVENTION According to this invention, the technique which produces | generates the data of the pattern of the original plate which forms a fine pattern accurately can be provided, for example.

  DESCRIPTION OF EXEMPLARY EMBODIMENTS Hereinafter, preferred embodiments of the invention will be described with reference to the accompanying drawings. In addition, in each figure, the same reference number is attached | subjected about the same member and the overlapping description is abbreviate | omitted.

  The present invention generates original pattern data used in the manufacture of various devices such as semiconductor chips such as IC and LSI, display elements such as liquid crystal panels, detection elements such as magnetic heads, imaging elements such as CCDs, and micromechanics. Can be applied when. Here, the micromechanics refers to a technique for creating a micron-scale mechanical system having advanced functions by applying a semiconductor integrated circuit manufacturing technique to the manufacture of a fine structure, or the mechanical system itself. The present invention is suitable for, for example, an effective light source and original plate data used in an exposure apparatus having a projection optical system having a large numerical aperture (NA) or an immersion exposure apparatus that fills a space between the projection optical system and the wafer with a liquid. .

  The concepts disclosed in the present invention can be modeled mathematically. Therefore, it can be implemented as a software function of a computer system. The software function of the computer system includes programming having executable software code, and in this embodiment, a mask pattern that accurately forms a fine pattern can be determined to generate original data. . The software code is executed by the processor of the computer system. During software code operation, the code or associated data record is stored on a computer platform. However, the software code may be stored elsewhere or loaded into a suitable computer system. Thus, the software code can be held on a computer readable recording medium as one or more modules. The present invention can be described in the form of the above-described code, and can function as one or more software products.

  FIG. 1 is a schematic block diagram illustrating a configuration of a processing apparatus 1 that executes a generation method according to one aspect of the present invention. Such a generation method includes data of an original pattern (mask) used in an exposure apparatus including an illumination optical system that illuminates an original (mask) using light from a light source and a projection optical system that projects the original pattern onto a substrate. Data).

  The processing device 1 is configured by, for example, a general-purpose computer, and as illustrated in FIG. 1, a bus wiring 10, a control unit 20, a display unit 30, a storage unit 40, an input unit 50, a medium interface 60, and the like. Have

  The bus wiring 10 connects the control unit 20, the display unit 30, the storage unit 40, the input unit 50, and the medium interface 60 to each other.

  The control unit 20 includes a CPU, GPU, DSP, or microcomputer, and includes a cache memory for temporary storage. The control unit 20 activates and executes the mask data generation program 401 stored in the storage unit 40 based on the activation command of the mask data generation program 401 input from the user via the input unit 50. The control unit 20 uses the data stored in the storage unit 40 to execute calculations related to the generation of mask data.

  The display unit 30 is configured by a display device such as a CRT display or a liquid crystal display, for example. The display unit 30 displays, for example, information related to execution of the mask data generation program 401 (for example, a two-dimensional image 412 of an approximate aerial image and mask data 408 described later).

  The storage unit 40 is configured by, for example, a memory or a hard disk. The storage unit 40 stores a mask data generation program 401 provided from the storage medium 70 connected to the medium interface 60.

  The storage unit 40 includes pattern data 402, effective light source information 403, NA information 404, λ information 405, aberration information 406, and registration information 407 as input information when executing the mask data generation program 401. Remember. The storage unit 40 stores mask data (mask pattern) 408 as output information after the mask data generation program 401 is executed. Further, the storage unit 40 temporarily transmits transmitted light distribution 409, an approximate aerial image 410, an aerial image map 411, a two-dimensional image 412, and deformation pattern data (mainly) as temporarily stored information during execution of the mask data generation program 401. Pattern and auxiliary pattern) 413 are stored.

  The mask data generation program 401 is a program for generating mask data 408 indicating data such as a mask pattern used in an exposure apparatus and a pattern formed by a pattern forming unit of a spatial light modulator (SLM). Here, the pattern is formed by a closed figure, and the pattern of the entire mask is composed of the aggregate.

  The pattern data 402 is data of a layout designed pattern (a resolution pattern formed on a wafer and called a layout pattern or a target pattern) in designing an integrated circuit or the like.

  The effective light source information 403 is a light intensity distribution (effective) formed on the pupil plane of the projection optical system when there is no aberration, birefringence and transmission unevenness in the projection optical system and no mask is arranged on the object plane of the projection optical system. Light source) and polarization information.

  The NA information 404 is information related to the numerical aperture (NA) on the image plane side of the projection optical system.

  The λ information 405 is information regarding the wavelength λ of light (exposure light) emitted from the light source.

  The aberration information 406 is information regarding the aberration of the projection optical system. When the projection optical system has birefringence, a phase shift occurs according to the birefringence. Such phase shift can also be considered as a kind of aberration.

  The resist information 407 is information regarding the resist applied to the wafer.

  The mask data 408 is data indicating a mask pattern which is an actual original generated by executing the mask data generation program 401.

  The transmitted light distribution 409 is generated during execution of the mask data generation program 401, and the light from the light source passes through the mask pattern arranged on the object plane of the projection optical system and is formed on the pupil plane of the projection optical system. The light distribution is shown.

  The approximate aerial image 410 is generated during execution of the mask data generation program 401, and shows an approximate aerial image distribution formed by interference with main diffracted light on the wafer surface.

  The aerial image map 411 is generated during execution of the mask data generation program 401 and is obtained by adding a plurality of approximate aerial images 410. Note that the aerial image map 411 may be the approximate aerial image 410 itself.

  A two-dimensional image 412 is generated during execution of the mask data generation program 401, and is a two-dimensional image when the approximate aerial image 410 is cut with a reference slice value.

  The deformation pattern data 413 is data including a main pattern that is deformed by executing the mask data generation program 401 and an auxiliary pattern that is inserted by executing the mask data generation program 401.

  Note that the pattern data 402, the mask data 408, and the deformation pattern data 413 include the position, size, shape, transmittance, phase information, and the like of the main pattern and the auxiliary pattern. Further, the pattern data 402, the mask data 408, and the deformation pattern data 413 include transmittance and phase information of a region (background) where the main pattern and the auxiliary pattern do not exist.

  The input unit 50 includes, for example, a keyboard and a mouse. The user can input input information of the mask data generation program 401 through the input unit 50.

  The medium interface 60 includes, for example, a flexible disk drive, a CD-ROM drive, a DVD-ROM drive, a USB interface, and the like, and is configured to be connectable to the storage medium 70. The storage medium 70 is a flexible disk, CD-ROM, DVD-ROM, USB memory, or the like, and provides a mask data generation program 401 and other programs executed by the processing device 1.

  Hereinafter, a process in which the control unit 20 of the processing apparatus 1 executes the mask data generation program 401 to generate the mask data 408 will be described with reference to FIG. It is assumed that input information including pattern data 402, effective light source information 403, NA information 404, λ information 405, aberration information 406, and registration information 407 is determined in advance by the user. The user can select the input information stored in the storage unit 40 via the input unit 50, or can directly input the input information.

  In step S202, the control unit 20 determines whether to divide the effective light source into a plurality of regions based on the effective light source information 403. In the present embodiment, when plane waves incident on each point on the effective light source are considered and the incident angles satisfy a certain condition, the effective light source is divided into a plurality of regions. Each point on the effective light source corresponds to a plane wave having a different incident angle on a one-to-one basis. For example, as shown in FIG. 3, the angle (incident angle) formed by the plane wave incident direction vector and the normal of the mask substrate is θ, the projection of the plane wave incident direction vector onto the substrate, and the x-axis (1 on the substrate). The angle (projection angle) formed by two directions) is defined as φ. If there is an incident angle θ exceeding 10 ° with respect to a point on the effective light source, or if there is a difference between the incident angle θ and the projection angle φ exceeding 90 °, the effective light source Is divided into a plurality of regions. However, the condition for dividing the effective light source is not limited to this. On the other hand, the incident angle of the plane wave incident on each point on the effective light source can be regarded as the same at any point on the effective light source (that is, light from any point on the effective light source passes through the mask and forms the same transmitted light distribution). In this case, it is not necessary to divide the effective light source into a plurality of regions. In this way, when it is determined that the effective light source is divided into a plurality of areas, the process proceeds to step S204, and when it is determined that the effective light source is not divided into a plurality of areas, the process proceeds to step S208. Here, FIG. 3 is a diagram schematically showing the relationship between the mask and the plane wave incident on the mask.

  In step S204, the control unit 20 divides the effective light source into a plurality of regions. Specifically, the control unit 20 divides the effective light source into regions where the incident angles of the incident plane waves can be regarded as the same. In other words, in each of the divided regions, the effective light source is divided so that the light from each point on the region can be regarded as forming the same transmitted light distribution through the mask.

  In step S206, the control unit 20 determines the incident angle of the plane wave incident on each of the plurality of regions divided in step S204 (first determination step). As described above, since the effective light source is divided into regions in step S204 where the incident angles of the incident plane waves can be regarded as the same, the incident angles of the plane waves incident on each of the plurality of regions are uniquely determined. Can do.

  In step S208, the control unit 20 calculates a transmitted light distribution 409 formed on the pupil plane of the projection optical system by the light from the light source passing through the mask pattern by electromagnetic field numerical calculation based on the Maxwell equation. Here, when the effective light source is divided into a plurality of regions, the transmitted light distribution is calculated for each of the plurality of plane waves incident on each of the plurality of regions at the incident angle determined in step S206 (first step). 1 calculation step). On the other hand, when the effective light source is not divided into a plurality of regions, one transmitted light distribution is calculated based on the effective light source information 403. Note that when the transmitted light distribution is first calculated by executing the mask data generation program 401, the pattern data 402 is used as a mask pattern. In step S208, since the electromagnetic field numerical calculation based on the Maxwell equation is used, a strict transmitted light distribution can be calculated.

  Here, the reason why the strict transmitted light distribution is calculated in step S208 will be described. Conventionally, as a method for calculating the transmitted light distribution, a method called Kirchhoff approximation is known which gives a step function type distribution with the electric field amplitude immediately after the transmission part being 1 and the electric field amplitude immediately after the light shielding part being 0. However, the transmitted light distribution calculated from the Kirchhoff approximation is an approximate transmitted light distribution, and is different from the strict transmitted light distribution calculated from the electromagnetic field numerical calculation (exact calculation) based on the Maxwell equation. For example, when a plane wave of y-polarized light (linearly polarized light in the y direction) is obliquely incident on the light-shielded isolated line pattern as shown in FIG. 4 from the short direction, it is calculated from each of the Kirchhoff approximation and the exact calculation. The distribution of the electric field (y component) is shown in FIG. In addition, when a y-polarized plane wave is obliquely incident from a short direction to a transmission-type isolated line pattern as shown in FIG. 4, the electric field (y component) calculated from each of Kirchhoff approximation and exact calculation is used. The distribution is shown in FIG. 5 and 6, the vertical axis employs the y-direction electric field amplitude, and the horizontal axis employs the x-direction position. 5 and 6, it can be seen that the electric field calculated from the Kirchhoff approximation is greatly different from the electric field calculated from the exact calculation. Therefore, in the present embodiment, a strict transmitted light distribution is calculated by electromagnetic field numerical calculation (for example, FDTD method or RCWA method) based on Maxwell's equations.

  In step S210, the control unit 20 calculates the approximate aerial image 410 that the transmitted light distribution forms on the image plane of the projection optical system based on the transmitted light distribution calculated in step S208. Here, when the effective light source is divided into a plurality of regions, each of the plurality of plane waves is formed based on each of the plurality of transmitted light distributions formed by each of the plurality of plane waves calculated in step S208. The approximate aerial image to be calculated is calculated (second calculation step). On the other hand, when the effective light source is not divided into a plurality of regions, one approximate aerial image is calculated based on one transmitted light distribution calculated in step S208.

  In step S210, there are two reasons for calculating the approximate aerial image without calculating the exact aerial image. The first reason is that the time for calculating the approximate aerial image is far less than the time for calculating the exact aerial image. The second reason is that the coherence of the pattern is emphasized in the approximate aerial image, and the state of the optical proximity effect is easy to understand.

Various methods for calculating an approximate aerial image have been disclosed in the past. For example, an approximate aerial image can be calculated by modifying the interference map in Patent Document 1. A singular value decomposition is performed on a transmission cross coefficient (TCC), and the i-th eigenvalue is set to λ _i and the i-th eigenfunction is set to Φ _i (f, g). However, (f, g) are the coordinates of the pupil plane of the projection optical system. TCC indicates the coherence of the effective light source (the degree of interference according to the distance on the mask surface). According to Patent Document 1, the interference map e (x, y) is assumed to be a sum of a plurality of eigenfunctions, and can be expressed by the following Expression 1.

  In Equation 1, FT represents a Fourier transform. In general, N ′ is 1.

  In Patent Document 1, the mask pattern is replaced with dots and lines, and the interference map of the entire mask is derived by convolution with the interference map. Therefore, the interference map e (x, y) shows simple coherence.

  However, since the interference map e (x, y) does not consider the mask pattern (outer shape, etc.), when used for calculating the approximate aerial image, the interference map e ′ (x, y taking into account the mask pattern). y) must be derived.

Therefore, TCC is subjected to singular value decomposition, the i-th eigenvalue is λ _i , the i-th eigenfunction is Φ _i (f, g), and the diffracted light distribution of the mask pattern is a (f, g). In this case, an interference map e ′ (x, y) in consideration of the mask pattern can be derived from Equation 2 below. The diffracted light distribution is a Fourier transform of the transmitted light distribution.

  By using the interference map e ′ (x, y) shown in Equation 2, an approximate aerial image can be calculated. Alternatively, the interference map e ′ (x, y) may be an approximate aerial image.

  In step S212, the control unit 20 generates an aerial image map 411. Specifically, when the effective light source is divided into a plurality of regions, the control unit 20 adds a plurality of approximate aerial images formed by each of the plurality of plane waves calculated in step S210 to obtain an aerial image. Generate a map. Therefore, when the effective light source is not divided into a plurality of regions, the approximate aerial image calculated in step S210 becomes an aerial image map as it is.

  In step S214, the control unit 20 determines whether to deform the main pattern. In the present embodiment, it is assumed that whether or not to deform the main pattern is input by the user. However, if the difference between the aerial image map generated in step S212 and the reference aerial image map is within the allowable range, it is determined that the main pattern is not deformed. If the difference is outside the allowable range, the main pattern is determined. You may make it determine with changing. If it is determined that the main pattern is to be deformed, the process proceeds to step S216. If it is determined that the main pattern is not to be deformed, the process proceeds to step S222.

  In step S216, the control unit 20 extracts a two-dimensional image from the aerial image map generated in step S212. Specifically, a reference slice value (Io) is set, and a two-dimensional image at the cross section of the aerial image map is extracted. For example, when the mask pattern is a transmission pattern, a portion where the intensity value of the aerial image map is equal to or greater than a predetermined value (a threshold value that can be arbitrarily set) is extracted as a two-dimensional image. Further, when the mask pattern is a light shielding pattern, a portion where the intensity value of the approximate aerial image is a predetermined value (a threshold value that can be arbitrarily set) or less is extracted as a two-dimensional image.

  In step S218, the control unit 20 deforms the main pattern based on the two-dimensional image extracted in step S216. Specifically, the two-dimensional image extracted in step S216 is compared with the target pattern, and the main pattern is deformed so that the difference between the two-dimensional image and the target pattern is within an allowable range. Here, the parameter (evaluation value) when comparing the two-dimensional image with the target pattern may be a line width, a pattern length, or the like, or a NILS (Normalized Image Log Slope) or intensity peak value. May be. Note that the main pattern deformed in step S218 is the deformation pattern data 413.

  In step S220, the control unit 20 determines whether or not to calculate the approximate aerial image again based on the main pattern deformed in step S218. In the present embodiment, it is assumed that whether or not the approximate aerial image is calculated again is input by the user. If it is determined that the approximate aerial image is calculated again, the process returns to step S208, and the transmitted light distribution is calculated. In this case, the deformation pattern data 413 is used as a mask pattern. If it is determined not to calculate the approximate aerial image again, the process proceeds to step S222.

  In step S222, the control unit 20 inserts an auxiliary pattern into the main pattern (the modified main pattern when step S218 is performed) based on the aerial image map generated in step S214. Specifically, first, the position (auxiliary pattern insertion position) for inserting the auxiliary pattern is extracted from the aerial image map. The auxiliary pattern insertion position has a light intensity peak (maximum value or minimum value) in a region that does not exceed the reference slice value (Io) and does not overlap the main pattern (that is, a region other than the region where the target pattern is projected). This is the peak part. It should be noted that the auxiliary pattern insertion position is actually a portion on the mask corresponding to the peak portion. Then, the size of the auxiliary pattern is determined based on the light intensity of the peak portion, and the auxiliary pattern having such a size is inserted at the auxiliary pattern insertion position. Note that the auxiliary pattern inserted in step S222 is the deformation pattern data 413.

  In step S224, the control unit 20 generates data (deformed pattern data 413) including the main pattern and the auxiliary pattern determined in steps S214 to S222 (second determination step) as mask data 408.

  Thus, in this embodiment, since the mask pattern is determined from the exact transmitted light distribution calculated by the electromagnetic field numerical calculation based on the Maxwell equation, mask data (mask pattern) for forming a fine pattern with high accuracy. Can be generated. In addition, the effective light source is divided into regions where the incident angle of the plane wave incident is the same, and the strict transmitted light distribution is calculated for each of these regions, so that mask data for forming a fine pattern with higher accuracy can be obtained. It is possible to generate.

  The mask data generated by the processing apparatus 1 is given as a GDS file to an electron beam (EB) drawing apparatus, for example, and a mask is created by drawing a pattern such as Cr corresponding to the mask data on the substrate. . Note that the mask pattern to be created may include patterns other than the mask data generated by the above-described mask data creation program.

  Hereinafter, in the first and second embodiments, mask data (mask pattern) generated by executing the mask data generation program will be described in detail. Note that the wavelength of the exposure light is λ, and the numerical aperture on the image side of the projection optical system is NA. Also, let σ be the ratio of the numerical aperture of the illumination light incident on the mask surface from the illumination optical system and the numerical aperture on the object side of the projection optical system.

  In the exposure apparatus, since various values can be set for the wavelength λ of the exposure light and the numerical aperture NA of the projection optical system, it is preferable to normalize the mask pattern size by (λ / NA). For example, when λ is 193 nm and NA is 1.35, the 45 nm pattern becomes 0.31 by the above-described normalization. Such normalization is referred to as k1 conversion.

  The pattern size on the mask surface and the pattern size on the wafer surface differ by the magnification of the projection optical system. However, in the following, in order to simplify the explanation, the size of the pattern on the mask surface and the pattern on the wafer surface are obtained by multiplying the size of the pattern on the mask surface by the magnification (1/4) of the projection optical system. Is made to correspond to 1: 1.

  In the first embodiment, the case where the NA of the projection optical system is 1.35 (corresponding to NA information) and the wavelength of the exposure light is 193 nm (corresponding to λ information) is considered as the exposure apparatus. The projection optical system has no aberration (corresponding to aberration information), does not consider the resist applied to the wafer (corresponding to resist information), and uses water having a refractive index of 1.44 as the immersion liquid.

  The target pattern (pattern data) is an isolated line pattern as shown in FIG. 4 and has a line width of 180 nm and a length of 1800 nm. In FIG. 4, it is assumed that the isolated line pattern is a light-shielding pattern (that is, the transmittance is 0), and the transmittance of a region (background) where such an isolated line pattern does not exist is 1. The phases were all 0 °. Note that the center of gravity of the isolated line pattern is the origin, and the x axis is defined in the short side direction and the y axis is defined in the long side direction.

  As shown in FIG. 7, the effective light source is tangential (tangential direction) polarized quadrupole illumination (corresponding to effective light source information) having a σ (radius) of 0.7 to 0.9 and an opening angle of 30 °. Use. The central value of σ is represented as σ0, and is 0.8 in this embodiment. In FIG. 7, the white circle represents σ = 1, and the four white areas represent the light irradiation unit.

  First, when the approximate aerial image is calculated from the transmitted light distribution obtained by the Kirchhoff approximation (conventional technology) for the isolated line pattern (light-shielding pattern) shown in FIG. 4 and the effective light source shown in FIG. 7, the approximate aerial image shown in FIG. An image is obtained. In FIG. 8, the target pattern is shown by being overlaid with white lines.

  Next, an approximate aerial image calculated by executing the above-described mask data generation program, that is, an approximate aerial image obtained from a transmitted light distribution obtained by numerical calculation (exact calculation) based on the Maxwell equation will be described.

  If it is considered that plane waves having different incident angles are incident on each point of the effective light source, the effective light source shown in FIG. 7 is divided into four regions (effective light sources) as shown in FIGS. Is done. In other words, the incident angle of the plane wave is greatly different between the effective light sources shown in FIGS. However, in the effective light source shown in FIG. 9 to FIG. 12, the incident angle of the plane wave does not greatly differ, and there is no problem even if it approximates one incident angle.

  From the isolated line pattern shown in FIG. 4, y is determined from an angle (θ = 9.9666663 °, φ = 0 °) corresponding to the center point (u = 0.8, v = 0) of the effective light source shown in FIG. When a polarized plane wave is incident, the electric field (transmitted light distribution) calculated from the exact calculation is as shown in FIG. The same applies to the electric field calculated from the strict calculation when a y-polarized plane wave is incident from an angle corresponding to the center point of the effective light source shown in FIGS. Here, FDTD method was used as exact calculation. Regarding the structure of the mask, the refractive index of the substrate (glass substrate) was 1.56, and the thickness, refractive index, and extinction coefficient of the substrate-side light-shielding body were 55 nm, 1.477, and 1.762, respectively. In addition, the thickness, refractive index, and extinction coefficient of the upper light shield were set to 18 nm, 1.965, and 1.204, respectively. Furthermore, the electric field extraction position is set to a distance of 10 nm from the uppermost surface of the light shielding body, and the incident angle is 9.96666763 ° inside the substrate so that it is an arctangent of σ0 × NA / 4 with respect to the normal of the substrate in the air. It was.

  Further, when the approximate aerial image is calculated from the exact transmitted light distribution obtained from the exact calculation and each of the effective light sources shown in FIGS. 9 to 12, the approximate aerial image shown in FIGS. 13 to 16 is obtained. In general, it is necessary to calculate an approximate aerial image in consideration of the transmitted light distribution obtained from exact calculation having three components of x, y, and z.

  Further, by adding the approximate aerial images shown in FIGS. 13 to 16, as shown in FIG. 17, the approximate aerial image (aerial image map) for the effective light source (tangentially polarized quadrupole illumination) shown in FIG. ) Is obtained.

  Then, based on the approximate aerial image shown in FIG. 17, the insertion position of the auxiliary pattern is determined and the auxiliary pattern is inserted. However, it may be difficult to determine the insertion position of the auxiliary pattern directly from the approximate aerial image shown in FIG. In the approximate aerial image shown in FIG. 17, since the difference in value is very small, if the peak position is determined as the insertion position of the auxiliary pattern, the arrangement becomes unstable. In such a case, a Laplacian operation is performed on the approximate aerial image shown in FIG. 17 to obtain a differential approximate aerial image as shown in FIG. When obtaining the peak position, if the target pattern is a line pattern, it is necessary to obtain the peak position in at least two directions, ie, the longitudinal direction and the direction orthogonal thereto.

  When the peak position is determined as the auxiliary pattern insertion position in the differential approximate aerial image shown in FIG. 18, an auxiliary pattern having symmetry with respect to the target pattern can be inserted as shown in FIG. It should be noted that the size of the auxiliary pattern should not be resolved and should be optimal for improving the resolution of the target pattern. Here, all the auxiliary patterns were squares with a side of 20 nm, the transmittance was 0, and the phase was 0 °. In FIG. 19, the auxiliary pattern inserted by applying strict calculation is indicated by a thick line, and the auxiliary pattern inserted by applying Kirchhoff approximation (conventional technology) is indicated by a thin line. The auxiliary pattern was inserted up to the second round surrounding the target pattern. Referring to FIG. 19, the first and second auxiliary patterns surrounding the target pattern are slightly shifted inward when inserted by applying strict calculation.

  Image characteristics are evaluated by calculating aerial images for the mask patterns shown in FIG. 19 (a mask pattern in which an auxiliary pattern is inserted by applying strict calculation and a mask pattern in which an auxiliary pattern is inserted by applying Kirchhoff approximation). The results obtained are shown in FIGS. FIG. 20 shows the CD defocus characteristic at y = 0 (position 1), and FIG. 20 shows the NILS defocus characteristic at y = 0 (position 1). Referring to FIGS. 20 and 21, image characteristics are improved in the mask pattern in which the auxiliary pattern is inserted by applying strict calculation, compared to the mask pattern in which the auxiliary pattern is inserted by applying Kirchhoff approximation. I understand.

  In the second embodiment, as in the first embodiment, as an exposure apparatus, the NA of the projection optical system is 1.35 (corresponding to NA information), and the wavelength of the exposure light is 193 nm (corresponding to λ information). Think about the case. The projection optical system has no aberration (corresponding to aberration information), does not consider the resist applied to the wafer (corresponding to resist information), and uses water having a refractive index of 1.44 as the immersion liquid.

  The target pattern (pattern data) is an isolated line pattern as shown in FIG. 4 and has a line width of 180 nm and a length of 1800 nm. In FIG. 4, it is assumed that the isolated line pattern is a transmissive pattern (that is, the transmittance is 1), and the transmittance of a region (background) where such an isolated line pattern does not exist is 0. The phases were all 0 °.

  As in the first embodiment, the effective light source uses the tangentially polarized quadrupole illumination shown in FIG.

  When the approximate aerial image is calculated from the transmitted light distribution obtained by the Kirchhoff approximation (conventional technology) for the isolated line pattern (transmission pattern) shown in FIG. 4 and the effective light source shown in FIG. 7, the approximate aerial image shown in FIG. can get. In FIG. 22, the target pattern is shown superimposed with a black line.

  From the isolated line pattern shown in FIG. 4, y is determined from an angle (θ = 9.9666663 °, φ = 0 °) corresponding to the center point (u = 0.8, v = 0) of the effective light source shown in FIG. When a polarized plane wave is incident, the electric field (transmitted light distribution) calculated from the exact calculation is as shown in FIG.

  As in the first embodiment, an approximate aerial image is calculated from the exact transmitted light distribution obtained from the exact calculation and each of the effective light sources shown in FIGS. 9 to 12, and the approximate aerial images are added together to obtain FIG. An approximate aerial image (aerial image map) shown in FIG. Also, a differential approximate aerial image as shown in FIG. 24 is obtained by performing a Laplacian operation on the approximate aerial image shown in FIG.

  When the peak position is determined as the auxiliary pattern insertion position in the differential approximate aerial image shown in FIG. 24, an auxiliary pattern having symmetry with respect to the target pattern can be inserted as shown in FIG. Here, all the auxiliary patterns were squares with a side of 20 nm, the transmittance was 1, and the phase was 0 °. In FIG. 25, auxiliary patterns inserted by applying strict calculation are indicated by thick lines, and auxiliary patterns inserted by applying Kirchhoff approximation (prior art) are indicated by thin lines. The auxiliary pattern was inserted up to the second round surrounding the target pattern. Referring to FIG. 25, the difference between the case where the exact calculation is applied and the case where the Kirchhoff approximation is performed is larger than that in the first embodiment.

  Image characteristics are evaluated by calculating aerial images for the mask patterns shown in FIG. 25 (a mask pattern in which an auxiliary pattern is inserted by applying strict calculation and a mask pattern in which an auxiliary pattern is inserted by applying Kirchhoff approximation). The results are shown in FIG. 26 and FIG. FIG. 26 shows the CD defocus characteristic at y = 0 (position 1), and FIG. 27 shows the NILS defocus characteristic at y = 0 (position 1). 26 and 27, the mask pattern in which the auxiliary pattern is inserted by applying strict calculation has improved image characteristics than the mask pattern in which the auxiliary pattern is inserted by applying Kirchhoff approximation. I understand.

  Next, the exposure apparatus 100 will be described with reference to FIG. FIG. 28 is a schematic block diagram showing the configuration of the exposure apparatus 100. Here, as the mask, the mask 130 created based on the mask data generated by executing the above-described mask data generation program is used.

  The exposure apparatus 100 is an immersion exposure apparatus that exposes the pattern of the mask 130 onto the wafer 150 via the liquid LW supplied between the projection optical system 140 and the wafer 150. In this embodiment, the exposure apparatus 100 applies the step-and-scan method, but a step-and-repeat method and other exposure methods can also be applied.

  As shown in FIG. 28, the exposure apparatus 100 includes an illumination optical system 120, a mask stage 135 on which a mask 130 is placed, a projection optical system 140, a wafer stage 155 on which a wafer 150 is placed, and a liquid supply / recovery unit. 160 and a main control system 170. The light source 110 and the illumination optical system 120 constitute an illumination device that illuminates the mask 130 on which a transfer circuit pattern is formed.

The light source 110 uses an excimer laser such as a KrF excimer laser having a wavelength of about 248 nm or an ArF excimer laser having a wavelength of about 193 nm. However, the type and number of the light sources 110 are not limited. For example, an F ₂ laser having a wavelength of about 157 nm can be used as the light source 110.

  The illumination optical system 120 is an optical system that illuminates the mask 130 using light from the light source 110. The illumination optical system 120 can realize various illumination modes such as conventional illumination and modified illumination (for example, quadrupole illumination). In this embodiment, the illumination optical system 120 includes a beam shaping optical system 121, a condensing optical system 122, a polarization controller 123, an optical integrator 124, and an aperture stop 125. Furthermore, the illumination optical system 120 includes a condenser lens 126, a bending mirror 127, a masking blade 128, and an imaging lens 129.

  The beam shaping optical system 121 uses, for example, a beam expander including a plurality of cylindrical lenses. The beam shaping optical system 121 converts the aspect ratio of the cross-sectional shape of the parallel light from the light source 110 into a predetermined value (for example, the cross-sectional shape is changed from a rectangle to a square). In this embodiment, the beam shaping optical system 121 shapes the light from the light source 110 into light having a size and a divergence angle necessary for illuminating the optical integrator 124.

  The condensing optical system 122 includes a plurality of optical elements, and efficiently guides the light shaped by the beam shaping optical system 121 to the optical integrator 124. The condensing optical system 122 includes, for example, a zoom lens system, and adjusts the distribution of the shape and angle of light incident on the optical integrator 124.

  The polarization controller 123 includes, for example, a polarizing element, and is disposed at a position substantially conjugate with the pupil plane 142 of the projection optical system 140. The polarization controller 123 controls the polarization state of a predetermined area of the effective light source formed on the pupil plane 142 of the projection optical system 140.

  The optical integrator 124 has a function of making the illumination light that illuminates the mask 130 uniform, converting the angle distribution of the incident light into a position distribution, and emitting it. The optical integrator 124 uses, for example, a fly-eye lens in which the entrance surface and the exit surface are maintained in a Fourier transform relationship. The fly-eye lens is configured by combining a plurality of rod lenses (that is, micro lens elements). However, the optical integrator 124 is not limited to the fly-eye lens, and may use an optical rod, a diffraction grating, a cylindrical lens array plate arranged so that each set is orthogonal, or the like.

  The aperture stop 125 is disposed at a position immediately after the exit surface of the optical integrator 124 and at a position substantially conjugate with an effective light source formed on the pupil plane 142 of the projection optical system 140. The aperture shape of the aperture stop 125 corresponds to the light intensity distribution (that is, the effective light source shape) of the effective light source formed on the pupil plane 142 of the projection optical system 140. In other words, the aperture stop 125 controls the light intensity distribution of the effective light source. The aperture stop 125 is configured to be switchable according to the illumination mode. The shape of the effective light source may be adjusted by arranging a diffractive optical element (CGH) or a prism on the light source side of the optical integrator 124 without using the aperture stop or in combination.

  The condensing lens 126 condenses the light emitted from the secondary light source formed near the exit surface of the optical integrator 124 and passed through the aperture stop 125, and uniformly illuminates the masking blade 128 via the bending mirror 127. To do.

  The masking blade 128 is disposed at a position substantially conjugate with the mask 130, and includes a plurality of movable light shielding plates. The masking blade 128 forms a substantially rectangular opening corresponding to the effective area of the projection optical system 140. The light that has passed through the masking blade 128 is used as illumination light that illuminates the mask 130.

  The imaging lens 129 images the light that has passed through the opening of the masking blade 128 on the mask 130.

  The mask 130 is manufactured based on the mask data generated by the processing apparatus 1 described above, and has a circuit pattern (main pattern) to be transferred and an auxiliary pattern. The mask 130 is supported and driven by the mask stage 135. Diffracted light emitted from the mask 130 is projected onto the wafer 150 via the projection optical system 140. The mask 130 and the wafer 150 are arranged in an optically conjugate relationship. Since the exposure apparatus 100 is a step-and-scan exposure apparatus, the circuit pattern to be transferred from the mask 130 is transferred to the wafer 150 by synchronously scanning the mask 130 and the wafer 150. If exposure apparatus 100 is a step-and-repeat exposure apparatus, exposure is performed with mask 130 and wafer 150 being stationary.

  The mask stage 135 supports the mask 130 via a mask chuck and is connected to a driving mechanism (not shown). A drive mechanism (not shown) is configured by, for example, a linear motor, and drives the mask stage 135 in the X-axis direction, the Y-axis direction, the X-axis direction, and the rotation direction of each axis. In the plane of the mask 130 or the wafer 150, the scanning direction is the Y axis, the direction perpendicular to the Y axis is the X axis, and the direction perpendicular to the mask 130 or the wafer 150 is the Z axis.

  The projection optical system 140 is an optical system that projects the circuit pattern of the mask 130 onto the wafer 150. The projection optical system 140 can use a refractive system, a catadioptric system, or a reflective system. The final lens (final surface) of the projection optical system 140 is coated to reduce (protect) the influence of the liquid LW supplied from the liquid supply / recovery unit 160.

  The wafer 150 is a substrate onto which the circuit pattern of the mask 130 is projected (transferred). However, the wafer 150 can be replaced with a glass plate or other substrate. A resist is applied to the wafer 150.

  The wafer stage 155 supports the wafer 150 and moves the wafer 150 in the X-axis direction, the Y-axis direction, the Z-axis direction, and the rotation directions of the respective axes using a linear motor, similarly to the mask stage 135.

  The liquid supply / recovery unit 160 has a function of supplying the liquid LW to the space between the final lens (final surface) of the projection optical system 140 and the wafer 150. The liquid supply / recovery unit 160 has a function of recovering the liquid LW supplied to the space between the final lens of the projection optical system 140 and the wafer 150. For the liquid LW, a substance that has a high transmittance with respect to the exposure light, does not attach dirt to the projection optical system 140 (the final lens thereof), and has a good matching with the resist process is selected.

  The main control system 170 has a CPU and a memory, and controls the operation of the exposure apparatus 100. For example, the main control system 170 is electrically connected to the mask stage 135, the wafer stage 155, and the liquid supply / recovery unit 160, and controls synchronous scanning of the mask stage 135 and the wafer stage 155. In addition, the main control system 170 controls supply and recovery of the liquid LW or switching of the stop based on the scanning direction and speed of the wafer stage 155 at the time of exposure.

  In the exposure, the light beam emitted from the light source 110 illuminates the mask 130 by the illumination optical system 120. The light flux that passes through the mask 130 and reflects the circuit pattern is imaged on the wafer 150 by the projection optical system 140 via the liquid LW. As described above, the mask 130 used by the exposure apparatus 100 has improved image characteristics as compared with the mask created by the conventional technique, and can form a fine pattern with high accuracy. Therefore, the exposure apparatus 100 can provide a high-quality device (semiconductor element, LCD element, imaging element (CCD, etc.), thin film magnetic head, etc.) with high throughput and high economic efficiency. Such a device includes a step of exposing a substrate (wafer, glass plate, etc.) coated with a photoresist (photosensitive agent) using the exposure apparatus 100, a step of developing the exposed substrate, and other known steps. , Manufactured by going through.

  As mentioned above, although preferable embodiment of this invention was described, it cannot be overemphasized that this invention is not limited to these embodiment, A various deformation | transformation and change are possible within the range of the summary.

It is a schematic block diagram which shows the structure of the processing apparatus which performs the production | generation method as 1 side of this invention. It is a flowchart for demonstrating the process which the control part of the processing apparatus shown in FIG. 1 performs a mask data generation program, and produces | generates mask data. It is a figure which shows typically the relationship between a mask and the plane wave which injects into a mask. It is a figure which shows the isolated line pattern as an example of the pattern of a mask. FIG. 5 is a diagram showing electric field distributions calculated from Kirchhoff approximation and exact calculation when y-polarized plane waves are obliquely incident from the short direction to the isolated line pattern (light-shielding type) shown in FIG. 4. 4 shows distributions of electric fields (y-components) calculated from Kirchhoff approximation and exact calculation when y-polarized plane waves are obliquely incident from the short direction to the isolated line pattern (transmission type) shown in FIG. FIG. It is a figure which shows an example of an effective light source. It is a figure which shows the approximate aerial image calculated from Kirchhoff approximation (prior art) with respect to the isolated line pattern shown in FIG. 4, and the effective light source shown in FIG. It is a figure which shows one area | region (effective light source) at the time of dividing the effective light source shown in FIG. 7 into four areas. It is a figure which shows one area | region (effective light source) at the time of dividing the effective light source shown in FIG. 7 into four areas. It is a figure which shows one area | region (effective light source) at the time of dividing the effective light source shown in FIG. 7 into four areas. It is a figure which shows one area | region (effective light source) at the time of dividing the effective light source shown in FIG. 7 into four areas. It is a figure which shows the approximate aerial image calculated from the exact transmitted light distribution calculated | required from the electromagnetic field numerical calculation based on a Maxwell equation, and the effective light source shown in FIG. It is a figure which shows the approximate aerial image calculated from the exact transmitted light distribution calculated | required from the electromagnetic field numerical calculation based on a Maxwell equation, and the effective light source shown in FIG. It is a figure which shows the approximate aerial image calculated from the exact transmitted light distribution calculated | required from the electromagnetic field numerical calculation based on a Maxwell equation, and the effective light source shown in FIG. It is a figure which shows the approximate aerial image calculated from the exact transmitted light distribution calculated | required from the electromagnetic field numerical calculation based on a Maxwell equation, and the effective light source shown in FIG. It is a figure which shows the approximate aerial image (aerial image map) which added the approximate aerial image shown in FIG. 13 thru | or FIG. It is a figure which shows the differential approximate aerial image obtained by performing a Laplacian operation to the approximate aerial image shown in FIG. It is a figure which shows the mask pattern containing a target pattern and the auxiliary pattern inserted by applying each of Kirchhoff approximation and exact calculation. It is a figure which shows the result (CD defocus characteristic) which computed the aerial image with respect to the mask pattern shown in FIG. 19, and evaluated the image characteristic. It is a figure which shows the result (NILS defocus characteristic) which calculated the aerial image with respect to the mask pattern shown in FIG. 19, and evaluated the image characteristic. It is a figure which shows the approximate aerial image calculated from Kirchhoff approximation (prior art) with respect to the isolated line pattern shown in FIG. 4, and the effective light source shown in FIG. It is a figure which shows the approximate aerial image (aerial image map) which added together the approximate aerial image calculated from the exact transmitted light distribution calculated | required from exact calculation, and each of the effective light source shown in FIG. 9 thru | or FIG. It is a figure which shows the differential approximate aerial image obtained by performing a Laplacian operation to the approximate aerial image shown in FIG. It is a figure which shows the mask pattern containing a target pattern and the auxiliary pattern inserted by applying each of Kirchhoff approximation and exact calculation. It is a figure which shows the result (CD defocus characteristic) which computed the aerial image with respect to the mask pattern shown in FIG. 25, and evaluated the image characteristic. It is a figure which shows the result (NILS defocus characteristic) which computed the aerial image with respect to the mask pattern shown in FIG. 25, and evaluated the image characteristic. It is a schematic block diagram which shows the structure of exposure apparatus.

Explanation of symbols

DESCRIPTION OF SYMBOLS 1 Processing apparatus 20 Control part 40 Memory | storage part 401 Mask data generation program 402 Pattern data 403 Effective light source information 408 Mask data 409 Transmission light distribution 410 Approximate aerial image 411 Aerial image map 412 Two-dimensional image 413 Deformation pattern data 70 Storage medium 100 Exposure apparatus 110 Light source 120 Illumination optical system 130 Mask 140 Projection optical system 150 Wafer

Claims (9)

A generation method for generating data of a pattern of an original by a computer used in an exposure apparatus that includes an illumination optical system that illuminates the original using light from a light source and a projection optical system that projects the pattern of the original on a substrate. And
A dividing step of dividing the effective light source formed on the pupil plane of the projection optical system into a plurality of regions when the original is not disposed on the object plane of the projection optical system;
A first determining step of determining an incident angle of a plane wave incident on each of the plurality of regions divided in the dividing step;
For each of the plurality of plane waves incident on each of the plurality of regions at the incident angle determined in the first determination step, light from the light source passes through a pattern disposed on the object plane of the projection optical system. A first calculation step of calculating a transmitted light distribution formed on the pupil plane of the projection optical system by an electromagnetic field numerical calculation based on a Maxwell equation;
A second calculating step of calculating an approximate aerial image formed by each of the plurality of plane waves on the image plane of the projection optical system based on each of the plurality of transmitted light distributions calculated in the first calculating step; ,
A generating step of adding a plurality of approximate aerial images calculated in the second calculating step to generate an aerial image map;
A second determining step of determining a pattern of the original based on the aerial image map generated in the generating step;
A generation method characterized by comprising: The pattern of the original plate includes a main pattern and an auxiliary pattern,
The generation method according to claim 1, wherein in the second determination step, the auxiliary pattern is inserted into the main pattern. An extraction step of extracting a two-dimensional image from the aerial image map generated in the generation step;
A deformation step of deforming the main pattern such that a difference between the two-dimensional image extracted in the extraction step and a target pattern to be formed on the substrate is within an allowable range;
The generation method according to claim 2, further comprising: A generation method for generating data of a pattern of an original by a computer used in an exposure apparatus that includes an illumination optical system that illuminates the original using light from a light source and a projection optical system that projects the pattern of the original on a substrate. And
A transmitted light distribution formed on the pupil plane of the projection optical system by passing light from the light source through a pattern disposed on the object plane of the projection optical system is calculated by first calculating an electromagnetic field based on Maxwell's equations A calculation step;
A second calculation step of calculating an approximate aerial image formed on the image plane of the projection optical system based on the transmitted light distribution calculated in the first calculation step;
A determining step for determining a pattern of the original based on the approximate aerial image calculated in the second calculating step;
A generation method characterized by comprising:   5. A method for creating an original plate, wherein the original plate is created based on data generated by the generation method according to claim 1. Illuminating the original produced by the original production method according to claim 5;
Projecting an image of the original pattern onto a substrate via a projection optical system;
An exposure method comprising: Exposing the substrate using the exposure method according to claim 6;
Developing the exposed substrate;
A device manufacturing method characterized by comprising: A generation method for generating original pattern data used in an exposure apparatus including an illumination optical system that illuminates an original using light from a light source and a projection optical system that projects the original pattern onto a substrate is executed on a computer A program for
In the computer,
A dividing step of dividing the effective light source formed on the pupil plane of the projection optical system into a plurality of regions when the original is not disposed on the object plane of the projection optical system;
A first determining step of determining an incident angle of a plane wave incident on each of the plurality of regions divided in the dividing step;
For each of the plurality of plane waves incident on each of the plurality of regions at the incident angle determined in the first determination step, light from the light source passes through a pattern disposed on the object plane of the projection optical system. A first calculation step of calculating a transmitted light distribution formed on the pupil plane of the projection optical system by an electromagnetic field numerical calculation based on a Maxwell equation;
A second calculating step of calculating an approximate aerial image formed by each of the plurality of plane waves on the image plane of the projection optical system based on each of the plurality of transmitted light distributions calculated in the first calculating step; ,
A generating step of adding a plurality of approximate aerial images calculated in the second calculating step to generate an aerial image map;
A second determining step of determining a pattern of the original based on the aerial image map generated in the generating step;
A program characterized by having executed. A generation method for generating original pattern data used in an exposure apparatus including an illumination optical system that illuminates an original using light from a light source and a projection optical system that projects the original pattern onto a substrate is executed on a computer A program for
In the computer,
A transmitted light distribution formed on the pupil plane of the projection optical system by passing light from the light source through a pattern disposed on the object plane of the projection optical system is calculated by electromagnetic field numerical calculation based on Maxwell's equations A calculation step;
A second calculation step of calculating an approximate aerial image formed on the image plane of the projection optical system based on the transmitted light distribution calculated in the first calculation step;
A determining step for determining a pattern of the original based on the approximate aerial image calculated in the second calculating step;
A program characterized by having executed.