CN108931890B - Determining method, exposure method, information processing apparatus, medium, and manufacturing method - Google Patents
Determining method, exposure method, information processing apparatus, medium, and manufacturing method Download PDFInfo
- Publication number
- CN108931890B CN108931890B CN201810491571.8A CN201810491571A CN108931890B CN 108931890 B CN108931890 B CN 108931890B CN 201810491571 A CN201810491571 A CN 201810491571A CN 108931890 B CN108931890 B CN 108931890B
- Authority
- CN
- China
- Prior art keywords
- coefficient
- evaluation value
- exposure
- optical system
- projection optical
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Active
Links
- 238000000034 method Methods 0.000 title claims abstract description 51
- 238000004519 manufacturing process Methods 0.000 title claims abstract description 15
- 230000010365 information processing Effects 0.000 title claims abstract description 13
- 230000003287 optical effect Effects 0.000 claims abstract description 166
- 239000000758 substrate Substances 0.000 claims abstract description 82
- 238000003384 imaging method Methods 0.000 claims description 111
- 238000011156 evaluation Methods 0.000 claims description 87
- 230000004075 alteration Effects 0.000 claims description 57
- 230000014509 gene expression Effects 0.000 claims description 30
- 238000005259 measurement Methods 0.000 claims description 19
- 239000003795 chemical substances by application Substances 0.000 claims description 13
- 238000003860 storage Methods 0.000 claims description 8
- 238000012546 transfer Methods 0.000 claims description 8
- 238000012545 processing Methods 0.000 claims description 5
- 201000009310 astigmatism Diseases 0.000 claims description 3
- 238000012937 correction Methods 0.000 description 82
- 238000005286 illumination Methods 0.000 description 15
- 238000010586 diagram Methods 0.000 description 11
- 238000001816 cooling Methods 0.000 description 10
- 230000008859 change Effects 0.000 description 9
- 238000001514 detection method Methods 0.000 description 7
- 238000009826 distribution Methods 0.000 description 7
- 230000008569 process Effects 0.000 description 5
- 230000006870 function Effects 0.000 description 4
- 210000001747 pupil Anatomy 0.000 description 4
- 239000004065 semiconductor Substances 0.000 description 3
- 238000005530 etching Methods 0.000 description 2
- 229920002120 photoresistant polymer Polymers 0.000 description 2
- 206010010071 Coma Diseases 0.000 description 1
- 238000013459 approach Methods 0.000 description 1
- 230000015572 biosynthetic process Effects 0.000 description 1
- 230000000903 blocking effect Effects 0.000 description 1
- 238000006243 chemical reaction Methods 0.000 description 1
- 238000007796 conventional method Methods 0.000 description 1
- 238000011161 development Methods 0.000 description 1
- 239000011521 glass Substances 0.000 description 1
- 230000006872 improvement Effects 0.000 description 1
- 238000005468 ion implantation Methods 0.000 description 1
- 239000004973 liquid crystal related substance Substances 0.000 description 1
- 238000001459 lithography Methods 0.000 description 1
- 238000012423 maintenance Methods 0.000 description 1
- 238000012986 modification Methods 0.000 description 1
- 230000004048 modification Effects 0.000 description 1
- 238000012544 monitoring process Methods 0.000 description 1
- 230000003647 oxidation Effects 0.000 description 1
- 238000007254 oxidation reaction Methods 0.000 description 1
- 230000009467 reduction Effects 0.000 description 1
- 238000007493 shaping process Methods 0.000 description 1
- 238000004904 shortening Methods 0.000 description 1
- 230000003595 spectral effect Effects 0.000 description 1
- 230000006641 stabilisation Effects 0.000 description 1
- 238000011105 stabilization Methods 0.000 description 1
- 230000002123 temporal effect Effects 0.000 description 1
- 238000007740 vapor deposition Methods 0.000 description 1
Images
Classifications
-
- G—PHYSICS
- G03—PHOTOGRAPHY; CINEMATOGRAPHY; ANALOGOUS TECHNIQUES USING WAVES OTHER THAN OPTICAL WAVES; ELECTROGRAPHY; HOLOGRAPHY
- G03F—PHOTOMECHANICAL PRODUCTION OF TEXTURED OR PATTERNED SURFACES, e.g. FOR PRINTING, FOR PROCESSING OF SEMICONDUCTOR DEVICES; MATERIALS THEREFOR; ORIGINALS THEREFOR; APPARATUS SPECIALLY ADAPTED THEREFOR
- G03F7/00—Photomechanical, e.g. photolithographic, production of textured or patterned surfaces, e.g. printing surfaces; Materials therefor, e.g. comprising photoresists; Apparatus specially adapted therefor
- G03F7/70—Microphotolithographic exposure; Apparatus therefor
- G03F7/70483—Information management; Active and passive control; Testing; Wafer monitoring, e.g. pattern monitoring
- G03F7/7055—Exposure light control in all parts of the microlithographic apparatus, e.g. pulse length control or light interruption
-
- G—PHYSICS
- G03—PHOTOGRAPHY; CINEMATOGRAPHY; ANALOGOUS TECHNIQUES USING WAVES OTHER THAN OPTICAL WAVES; ELECTROGRAPHY; HOLOGRAPHY
- G03F—PHOTOMECHANICAL PRODUCTION OF TEXTURED OR PATTERNED SURFACES, e.g. FOR PRINTING, FOR PROCESSING OF SEMICONDUCTOR DEVICES; MATERIALS THEREFOR; ORIGINALS THEREFOR; APPARATUS SPECIALLY ADAPTED THEREFOR
- G03F7/00—Photomechanical, e.g. photolithographic, production of textured or patterned surfaces, e.g. printing surfaces; Materials therefor, e.g. comprising photoresists; Apparatus specially adapted therefor
- G03F7/70—Microphotolithographic exposure; Apparatus therefor
- G03F7/70483—Information management; Active and passive control; Testing; Wafer monitoring, e.g. pattern monitoring
- G03F7/70491—Information management, e.g. software; Active and passive control, e.g. details of controlling exposure processes or exposure tool monitoring processes
- G03F7/705—Modelling or simulating from physical phenomena up to complete wafer processes or whole workflow in wafer productions
-
- G—PHYSICS
- G03—PHOTOGRAPHY; CINEMATOGRAPHY; ANALOGOUS TECHNIQUES USING WAVES OTHER THAN OPTICAL WAVES; ELECTROGRAPHY; HOLOGRAPHY
- G03F—PHOTOMECHANICAL PRODUCTION OF TEXTURED OR PATTERNED SURFACES, e.g. FOR PRINTING, FOR PROCESSING OF SEMICONDUCTOR DEVICES; MATERIALS THEREFOR; ORIGINALS THEREFOR; APPARATUS SPECIALLY ADAPTED THEREFOR
- G03F7/00—Photomechanical, e.g. photolithographic, production of textured or patterned surfaces, e.g. printing surfaces; Materials therefor, e.g. comprising photoresists; Apparatus specially adapted therefor
- G03F7/20—Exposure; Apparatus therefor
-
- G—PHYSICS
- G03—PHOTOGRAPHY; CINEMATOGRAPHY; ANALOGOUS TECHNIQUES USING WAVES OTHER THAN OPTICAL WAVES; ELECTROGRAPHY; HOLOGRAPHY
- G03F—PHOTOMECHANICAL PRODUCTION OF TEXTURED OR PATTERNED SURFACES, e.g. FOR PRINTING, FOR PROCESSING OF SEMICONDUCTOR DEVICES; MATERIALS THEREFOR; ORIGINALS THEREFOR; APPARATUS SPECIALLY ADAPTED THEREFOR
- G03F7/00—Photomechanical, e.g. photolithographic, production of textured or patterned surfaces, e.g. printing surfaces; Materials therefor, e.g. comprising photoresists; Apparatus specially adapted therefor
- G03F7/70—Microphotolithographic exposure; Apparatus therefor
- G03F7/70216—Mask projection systems
-
- G—PHYSICS
- G03—PHOTOGRAPHY; CINEMATOGRAPHY; ANALOGOUS TECHNIQUES USING WAVES OTHER THAN OPTICAL WAVES; ELECTROGRAPHY; HOLOGRAPHY
- G03F—PHOTOMECHANICAL PRODUCTION OF TEXTURED OR PATTERNED SURFACES, e.g. FOR PRINTING, FOR PROCESSING OF SEMICONDUCTOR DEVICES; MATERIALS THEREFOR; ORIGINALS THEREFOR; APPARATUS SPECIALLY ADAPTED THEREFOR
- G03F7/00—Photomechanical, e.g. photolithographic, production of textured or patterned surfaces, e.g. printing surfaces; Materials therefor, e.g. comprising photoresists; Apparatus specially adapted therefor
- G03F7/70—Microphotolithographic exposure; Apparatus therefor
- G03F7/70216—Mask projection systems
- G03F7/70258—Projection system adjustments, e.g. adjustments during exposure or alignment during assembly of projection system
-
- G—PHYSICS
- G03—PHOTOGRAPHY; CINEMATOGRAPHY; ANALOGOUS TECHNIQUES USING WAVES OTHER THAN OPTICAL WAVES; ELECTROGRAPHY; HOLOGRAPHY
- G03F—PHOTOMECHANICAL PRODUCTION OF TEXTURED OR PATTERNED SURFACES, e.g. FOR PRINTING, FOR PROCESSING OF SEMICONDUCTOR DEVICES; MATERIALS THEREFOR; ORIGINALS THEREFOR; APPARATUS SPECIALLY ADAPTED THEREFOR
- G03F7/00—Photomechanical, e.g. photolithographic, production of textured or patterned surfaces, e.g. printing surfaces; Materials therefor, e.g. comprising photoresists; Apparatus specially adapted therefor
- G03F7/70—Microphotolithographic exposure; Apparatus therefor
- G03F7/70483—Information management; Active and passive control; Testing; Wafer monitoring, e.g. pattern monitoring
- G03F7/70491—Information management, e.g. software; Active and passive control, e.g. details of controlling exposure processes or exposure tool monitoring processes
- G03F7/70508—Data handling in all parts of the microlithographic apparatus, e.g. handling pattern data for addressable masks or data transfer to or from different components within the exposure apparatus
-
- G—PHYSICS
- G03—PHOTOGRAPHY; CINEMATOGRAPHY; ANALOGOUS TECHNIQUES USING WAVES OTHER THAN OPTICAL WAVES; ELECTROGRAPHY; HOLOGRAPHY
- G03F—PHOTOMECHANICAL PRODUCTION OF TEXTURED OR PATTERNED SURFACES, e.g. FOR PRINTING, FOR PROCESSING OF SEMICONDUCTOR DEVICES; MATERIALS THEREFOR; ORIGINALS THEREFOR; APPARATUS SPECIALLY ADAPTED THEREFOR
- G03F7/00—Photomechanical, e.g. photolithographic, production of textured or patterned surfaces, e.g. printing surfaces; Materials therefor, e.g. comprising photoresists; Apparatus specially adapted therefor
- G03F7/70—Microphotolithographic exposure; Apparatus therefor
- G03F7/70483—Information management; Active and passive control; Testing; Wafer monitoring, e.g. pattern monitoring
- G03F7/70605—Workpiece metrology
- G03F7/706835—Metrology information management or control
- G03F7/706839—Modelling, e.g. modelling scattering or solving inverse problems
Landscapes
- Physics & Mathematics (AREA)
- General Physics & Mathematics (AREA)
- Exposure And Positioning Against Photoresist Photosensitive Materials (AREA)
- Exposure Of Semiconductors, Excluding Electron Or Ion Beam Exposure (AREA)
Abstract
The invention relates to a determination method, an exposure method, an information processing apparatus, a medium, and a manufacturing method. A method for determining a coefficient indicating a saturation value of an image forming characteristic used in a model equation indicating a variation in the image forming characteristic of a projection optical system in an exposure apparatus for transferring a pattern of a mask to a substrate via the projection optical system.
Description
Technical Field
The invention relates to a determination method, an exposure method, an information processing apparatus, a storage medium, and a method for manufacturing an article.
Background
In the manufacture of fine semiconductor devices such as LSIs and ultra-LSIs, an exposure apparatus is used which projects (reduces) a pattern of a mask (reticle) onto a substrate coated with a resist (photosensitive agent) and transfers the pattern. As the mounting density of semiconductor devices increases, further miniaturization of patterns is required, and with the progress of resist processes, the resolution of exposure apparatuses has been improved. As techniques for improving the resolution of the exposure apparatus, there are shortening of the wavelength of the exposure light and increasing of the Numerical Aperture (NA) of the projection optical system. However, when the resolution is improved in this way, the focal depth of the projection optical system becomes shallow, and therefore, it is important to improve the focal length accuracy in aligning the surface of the substrate with the image plane (focal plane) of the projection optical system.
As one of the important performances of the exposure apparatus, overlay accuracy of each pattern transferred onto the substrate through a plurality of steps is known. The imaging characteristics (focal length, magnification, distortion aberration, astigmatism, wavefront aberration, and the like) of the projection optical system are important elements that affect the overlay accuracy. In recent years, there is a strong trend toward miniaturization of patterns used in ultra LSI, and accordingly, there is an increasing demand for improvement in overlay accuracy.
In the exposure apparatus, when exposure is repeated, the projection optical system absorbs and heats a part of the energy of the exposure light, and then dissipates heat, thereby causing variation in the imaging characteristics of the projection optical system (thermal aberration, exposure aberration). Such a variation in the imaging characteristics of the projection optical system is a factor of reducing the overlay accuracy. Therefore, a technique for compensating for a variation in imaging characteristics of the projection optical system caused by irradiation of the projection optical system with the exposure light is proposed in japanese patent publication No. 63-16725 and japanese patent No. 2828226.
For example, Japanese patent publication No. 63-16725 discloses the following technique: the amount of variation of the imaging characteristic of the projection optical system is calculated using a model formula in which the exposure amount, the exposure time, the non-exposure time, and the like are variables, and the imaging characteristic of the projection optical system is corrected (adjusted) based on the calculation result. The above model equation has a correction coefficient specific to the projection optical system for each imaging characteristic, and the correction coefficient changes depending on the light source distribution formed on the pupil plane of the projection optical system. Therefore, japanese patent No. 2828226 proposes a technique capable of correcting the variation in the imaging characteristics well even if the light source distribution formed on the pupil plane of the projection optical system varies. In japanese patent No. 2828226, correction coefficients corresponding to respective light source distributions formed on the pupil plane of the projection optical system are stored, and when the light source distribution is changed, the correction coefficients corresponding to the light source distributions are read to calculate the amount of change in the imaging characteristics of the projection optical system.
In the related art, in order to predict the variation of the imaging characteristic of the projection optical system during exposure, the imaging characteristic of the projection optical system is measured a plurality of times during exposure, and a correction coefficient is obtained from the measurement result. When exposure is performed under the same exposure condition (illumination pattern, mask, etc.) after the correction coefficient is obtained, the imaging characteristics of the projection optical system are not measured during exposure, and the correction coefficient is used to predict the variation of the projection optical system.
However, when the imaging characteristics of the projection optical system are measured a plurality of times during exposure, if the influence of exposure aberration due to exposure immediately before that remains in the projection optical system, a correction coefficient including an error is obtained. Therefore, before the correction coefficient is found, that is, before the imaging characteristics of the projection optical system are measured a plurality of times during exposure, it is necessary to secure a sufficient cooling (standby) time for eliminating the influence of the exposure aberration, resulting in a decrease in productivity.
Disclosure of Invention
The present invention provides a method for determining a coefficient indicating a saturation value of an imaging characteristic used in a model equation indicating a variation in the imaging characteristic of a projection optical system.
A determining method according to an aspect of the present invention is a determining method for determining a coefficient indicating a saturation value of an image forming characteristic used in a model equation indicating a variation in the image forming characteristic of a projection optical system in an exposure apparatus for transferring a pattern of a mask to a substrate via the projection optical system, the determining method including: a 1 st step of obtaining a 1 st coefficient indicating a saturation value of the imaging characteristic from a plurality of measurement values obtained by measuring the imaging characteristic a plurality of times and a predicted value of the imaging characteristic at the start of exposure of the substrate obtained from the model equation; a 2 nd step of determining whether or not a difference between the 1 st coefficient and a 2 nd coefficient indicating a saturation value of the imaging characteristic used in the model equation stored in the exposure apparatus falls within an allowable range; a 3 rd step of updating the coefficient so that the 1 st coefficient is used in the model equation when the difference falls within the allowable range; and a 4 th step of comparing a 1 st evaluation value of the 1 st coefficient obtained from the predicted value and a 2 nd evaluation value of the 2 nd coefficient obtained from the predicted value of the imaging characteristic obtained from the model expression when the 2 nd coefficient is obtained, if the difference does not converge on the allowable range, updating the coefficient with the 1 st coefficient as a tentative coefficient if the 1 st evaluation value is smaller than the 2 nd evaluation value, and not updating the coefficient if the 1 st evaluation value is equal to or greater than the 2 nd evaluation value.
An exposure method according to another aspect of the present invention is an exposure method for exposing a substrate using an exposure apparatus that transfers a pattern of a mask to the substrate via a projection optical system, the exposure method including: a determination step of determining a coefficient indicating a saturation value of the imaging characteristic used in a model equation indicating a variation in the imaging characteristic of the projection optical system; and an exposure step of adjusting the imaging characteristics of the projection optical system or changing the position of the substrate based on a variation in the imaging characteristics of the projection optical system obtained from the model equation in which the coefficient is determined, and exposing the substrate, the determination step including: a 1 st step of obtaining a 1 st coefficient indicating a saturation value of the imaging characteristic from a plurality of measurement values obtained by measuring the imaging characteristic a plurality of times and a predicted value of the imaging characteristic at the start of exposure of the substrate obtained from the model equation; a 2 nd step of determining whether or not a difference between the 1 st coefficient and a 2 nd coefficient indicating a saturation value of the imaging characteristic used in the model equation stored in the exposure apparatus falls within an allowable range; a 3 rd step of updating the coefficient so that the 1 st coefficient is used in the model equation when the difference falls within the allowable range; and a 4 th step of comparing a 1 st evaluation value of the 1 st coefficient obtained from the predicted value and a 2 nd evaluation value of the 2 nd coefficient obtained from the predicted value of the imaging characteristic obtained from the model expression when the 2 nd coefficient is obtained, if the difference does not converge on the allowable range, updating the coefficient with the 1 st coefficient as a tentative coefficient if the 1 st evaluation value is smaller than the 2 nd evaluation value, and not updating the coefficient if the 1 st evaluation value is equal to or greater than the 2 nd evaluation value.
An information processing apparatus according to still another aspect of the present invention is an information processing apparatus for determining a coefficient indicating a saturation value of an imaging characteristic used in a model equation indicating a variation in the imaging characteristic of a projection optical system in an exposure apparatus for transferring a pattern of a mask to a substrate via the projection optical system, wherein a 1 st coefficient indicating the saturation value of the imaging characteristic is obtained from a plurality of measurement values obtained by measuring the imaging characteristic a plurality of times and a predicted value of the imaging characteristic at the start of exposure of the substrate obtained from the model equation, it is determined whether or not a difference between the 1 st coefficient and a 2 nd coefficient indicating the saturation value of the imaging characteristic used in the model equation stored in the exposure apparatus converges to an allowable range, and when the difference converges to the allowable range, the coefficient is updated so that the 1 st coefficient is used in the model equation, when the difference does not converge on the allowable range, a 1 st evaluation value of the 1 st coefficient obtained from the predicted value and a 2 nd evaluation value of the 2 nd coefficient obtained from the predicted value of the imaging characteristic obtained from the model expression when the 2 nd coefficient is obtained are compared, and if the 1 st evaluation value is smaller than the 2 nd evaluation value, the coefficient is updated with the 1 st coefficient as a tentative coefficient, and if the 1 st evaluation value is equal to or greater than the 2 nd evaluation value, the coefficient is not updated.
A storage medium according to still another aspect of the present invention is a storage medium storing a program for causing an information processing apparatus to execute a determination method of determining a coefficient indicating a saturation value of an image forming characteristic used in a model equation indicating a variation in the image forming characteristic of a projection optical system in an exposure apparatus that transfers a pattern of a mask to a substrate via the projection optical system, the program causing the information processing apparatus to execute: a 1 st step of obtaining a 1 st coefficient indicating a saturation value of the imaging characteristic from a plurality of measurement values obtained by measuring the imaging characteristic a plurality of times and a predicted value of the imaging characteristic at the start of exposure of the substrate obtained from the model equation; a 2 nd step of determining whether or not a difference between the 1 st coefficient and a 2 nd coefficient indicating a saturation value of the imaging characteristic used in the model equation stored in the exposure apparatus falls within an allowable range; a 3 rd step of updating the coefficient so that the 1 st coefficient is used in the model equation when the difference falls within the allowable range; and a 4 th step of comparing a 1 st evaluation value of the 1 st coefficient obtained from the predicted value and a 2 nd evaluation value of the 2 nd coefficient obtained from the predicted value of the imaging characteristic obtained from the model expression when the 2 nd coefficient is obtained, if the difference does not converge on the allowable range, updating the coefficient with the 1 st coefficient as a tentative coefficient if the 1 st evaluation value is smaller than the 2 nd evaluation value, and not updating the coefficient if the 1 st evaluation value is equal to or greater than the 2 nd evaluation value.
A method for manufacturing an article according to still another aspect of the present invention includes: a determination step of determining a coefficient indicating a saturation value of an imaging characteristic used in a model equation indicating a variation of the imaging characteristic of a projection optical system that projects a pattern of a mask onto a substrate; an exposure step of adjusting the imaging characteristics of the projection optical system or changing the position of the substrate based on the variation of the imaging characteristics of the projection optical system obtained from the model equation in which the coefficient is determined, and exposing the photosensitive agent of the substrate; developing the exposed substrate with a photosensitive agent to form a pattern of the photosensitive agent; and forming a pattern on the substrate based on the developed pattern of the photosensitive agent, and processing the substrate on which the pattern is formed to manufacture an article, wherein the determining step includes: a 1 st step of obtaining a 1 st coefficient indicating a saturation value of the imaging characteristic from a plurality of measurement values obtained by measuring the imaging characteristic a plurality of times and a predicted value of the imaging characteristic at the start of exposure of the substrate obtained from the model equation; a 2 nd step of determining whether or not a difference between the 1 st coefficient and a 2 nd coefficient indicating a saturation value of the imaging characteristic used in the model equation stored in the exposure apparatus falls within an allowable range; a 3 rd step of updating the coefficient so that the 1 st coefficient is used in the model equation when the difference falls within the allowable range; and a 4 th step of comparing a 1 st evaluation value of the 1 st coefficient obtained from the predicted value and a 2 nd evaluation value of the 2 nd coefficient obtained from the predicted value of the imaging characteristic obtained from the model expression when the 2 nd coefficient is obtained, if the difference does not converge on the allowable range, updating the coefficient with the 1 st coefficient as a tentative coefficient if the 1 st evaluation value is smaller than the 2 nd evaluation value, and not updating the coefficient if the 1 st evaluation value is equal to or greater than the 2 nd evaluation value.
Other objects and other aspects of the present invention will become more apparent from the following description of preferred embodiments with reference to the accompanying drawings.
Drawings
Fig. 1 is a schematic diagram showing the configuration of an exposure apparatus.
Fig. 2 is a diagram illustrating an example of variation in aberration of the projection optical system.
Fig. 3 is a diagram illustrating an example of variation in aberration of the projection optical system.
Fig. 4 is a diagram illustrating an example of variation in aberration of the projection optical system.
Fig. 5A and 5B are diagrams for explaining the reason why the correction coefficient cannot be accurately obtained.
Fig. 6 is a flowchart for explaining a determination method according to an aspect of the present invention.
Fig. 7 is a diagram illustrating an example of a predicted value of the imaging characteristic (focal length) of the projection optical system.
Fig. 8A and 8B are diagrams for explaining the weighting coefficients.
Detailed Description
Preferred embodiments of the present invention will be described below with reference to the accompanying drawings. In the drawings, the same components are denoted by the same reference numerals, and redundant description thereof will be omitted.
Fig. 1 is a schematic diagram showing the configuration of an exposure apparatus 1. The exposure apparatus 1 is a lithography apparatus that exposes a substrate, specifically, transfers a pattern of a mask (reticle) to the substrate via a projection optical system by a step-and-scan method. However, the exposure apparatus 1 can also apply a step and repeat method and other exposure methods.
The exposure apparatus 1 includes an illumination optical system 104 that illuminates a mask 109 with light from a light source unit 101, a projection optical system 110, and a substrate mounting table 116 that holds and moves a substrate 115. The exposure apparatus 1 further includes an opening drive unit 112, a lens drive unit 113, a laser interferometer 118, a projection optical system 121, a detection optical system 122, and a measurement unit 123. Further, the exposure apparatus 1 includes a light source control unit 102, an illumination control unit 108, a projection control unit 114, a stage control unit 120, and a main control unit 125.
The light source section 101 includes, for example, a pulse light source in which a gas such as KrF or ArF is sealed, and emits light in a far ultraviolet region having a wavelength of about 248 nm. The light source unit 101 further includes a narrowing module, a monitor module, a shutter, and the like. The narrowing module includes a front mirror constituting a resonator, a diffraction grating and a prism for narrowing a wavelength (exposure wavelength), and the like, and the monitor module includes a beam splitter and a detector for monitoring wavelength stability and a spectral width.
The light source control unit 102 controls the gas exchange operation in the light source unit 101, the wavelength stabilization operation of the light emitted from the light source unit 101, the discharge application voltage in the light source unit 101, and the like. In the present embodiment, the light source control unit 102 controls the light source unit 101 under the control of the main control unit 125, instead of controlling the light source unit 101 individually.
The light emitted from the light source unit 101 enters the illumination optical system 104. The light incident on the illumination optical system 104 is shaped into a predetermined beam shape by a beam shaping optical system (not shown) and enters an optical integrator (not shown). The optical integrator forms a large number of 2-order light sources in order to illuminate the mask 109 with a uniform illuminance distribution.
The aperture stop 105 included in the illumination optical system 104 has a substantially circular opening. The illumination control unit 108 controls each unit of the illumination optical system 104 under the control of the main control unit 125 so that the diameter of the opening of the aperture stop 105 and the Numerical Aperture (NA) of the illumination optical system 104 become predetermined values. Since the value of the ratio of the numerical aperture of the illumination optical system 104 to the Numerical Aperture (NA) of the projection optical system 110 is a coherence factor (σ value), the illumination control unit 108 can adjust (set) the σ value by controlling the diameter of the aperture stop 105.
A half mirror 106 for reflecting (extracting) a part of light illuminating the mask 109 is disposed on an optical path of the illumination optical system 104. On the optical path of the light reflected by the half mirror 106, a photosensor 107 for ultraviolet light is disposed. The photosensor 107 generates an output corresponding to the intensity of light (i.e., exposure energy) illuminating the mask 109. The output of the photosensor 107 is converted into exposure energy per 1 pulse by an integrating circuit (not shown) that integrates light emission per pulse of the light source unit 101, and is input to the main control unit 125 via the illumination control unit 108.
The mask 109 is a master having a pattern (circuit pattern) to be transferred onto the substrate 115, and is held on a mask stage (not shown). The mask stage holds the mask 109 and moves in the three-dimensional direction (the optical axis direction of the projection optical system 110 and the plane orthogonal to the optical axis) by a linear motor or the like, for example. Since the exposure apparatus 1 employs a step-and-scan method, the pattern of the mask 109 is transferred to the substrate 115 by scanning the mask 109 and the substrate 115.
The projection optical system 110 includes a plurality of optical elements (lenses, etc.), and projects the pattern of the mask 109 onto (the imaging region of) the substrate 115 by reducing the pattern with a predetermined reduction magnification β (for example, β 1/4).
An aperture stop 111 having a substantially circular opening is disposed on a pupil plane of the projection optical system 110 (fourier transform plane with respect to the mask 109). The aperture driving unit 112 includes a motor and the like, and drives the aperture stop 111 so that the diameter of the opening of the aperture stop 111 becomes a predetermined value. The lens driving unit 113 drives optical elements constituting the projection optical system 110, in the present embodiment, a part of a lens (for example, a field lens) in the optical axis direction of the projection optical system 110 by using air pressure, a piezoelectric element, or the like. The projection control unit 114 controls the aperture driving unit 112 and the lens driving unit 113 under the control of the main control unit 125. In the present embodiment, by driving the lenses constituting the projection optical system 110, variations in various aberrations of the projection optical system 110 are reduced, and the magnification (projection magnification) is maintained well, thereby reducing distortion errors.
The substrate 115 is a substrate on which a pattern of the mask 109 is projected (transferred). A photoresist (a photosensitive agent) is coated on the substrate 115. The substrate 115 includes a wafer, a glass plate, or other substrate.
The substrate mounting table 116 holds the substrate 115 and moves in a three-dimensional direction (the optical axis direction of the projection optical system 110 and a plane orthogonal to the optical axis) by a linear motor or the like, for example. The distance to the movable mirror 117 fixed to the substrate mounting table 116 is measured by the laser interferometer 118, and the position of the substrate mounting table 116 in a plane orthogonal to the optical axis of the projection optical system 110 is detected. The stage controller 120 controls the position of the substrate mounting table 116 (for example, moves the substrate mounting table 116 to a predetermined position) based on the measurement result of the laser interferometer 118 under the control of the main controller 125.
The light projecting optical system 121 and the detection optical system 122 constitute a focal length detection system that detects the position of the substrate 115 in the optical axis direction of the projection optical system 110 (i.e., the height of the surface of the substrate 115). The light projection optical system 121 projects light (non-exposure light) that does not receive light from the photoresist applied to the substrate 115 and condenses the light at each position on the substrate 115. The light reflected at each position of the substrate 115 is incident on the detection optical system 122. In the detection optical system 122, a plurality of light receiving elements for position detection are arranged corresponding to light reflected at each position of the substrate 115. Specifically, the plurality of light receiving elements are arranged such that the light receiving surface of each light receiving element and the reflection point on the substrate 115 are substantially conjugate with each other with the imaging optical system interposed therebetween. Therefore, the positional deviation of the substrate 115 in the optical axis direction of the projection optical system 110 is detected as the positional deviation of light incident on each light receiving element arranged in the detection optical system 122.
The measurement unit 123 is disposed on the image plane side of the projection optical system 110, and in the present embodiment, is the substrate mounting table 116. The measurement unit 123 detects light passing through the projection optical system 110 and measures the imaging characteristics of the projection optical system 110. The measurement unit 123 includes, for example, a light blocking plate having a pinhole through which light from the projection optical system 110 passes, and a photoelectric conversion element that detects light passing through the pinhole.
The main control unit 125 is a computer (information processing apparatus) including a CPU, a memory, and the like, and controls the entire exposure apparatus 1 (each unit of the exposure apparatus 1) via the light source control unit 102, the illumination control unit 108, the projection control unit 114, the stage control unit 120, and the like. In the present embodiment, the main control unit 125 may also have a function of determining a correction coefficient used in a model equation indicating a variation in the imaging characteristics of the projection optical system 110, as described below.
Here, a model equation indicating a variation in imaging performance of the projection optical system 110 due to the irradiation of the exposure light and a correction coefficient for compensating for a variation in imaging characteristics for each exposure condition, which is used to quantify the model equation, will be described. In the present embodiment, the imaging characteristics of the projection optical system 110 include at least 1 of a focal length, a magnification, a distortion aberration, astigmatism, spherical aberration, coma aberration, and wavefront aberration. In addition, wavefront aberrations, as widely known in the art, can be expressed as terms resulting from expanding the wavefront shape with Zernike polynomials. In addition, they are also sometimes collectively referred to as "aberrations".
Fig. 2 is a diagram illustrating an example of a change (temporal change) in aberration of the projection optical system 110. In fig. 2, the abscissa represents time t, and the ordinate represents the aberration amount F at a certain image height of the projection optical system 110. Δ F represents the amount of aberration variation of the projection optical system 110, and the amount of aberration variation Δ F has a different value for each image height. Further, F0 represents an initial (i.e., before exposure) aberration amount of the projection optical system 110.
Referring to fig. 2, after the exposure is started at time t0, the aberration fluctuates with the passage of time, and becomes stable at time t1 to be a constant aberration amount (maximum fluctuation amount) F1. At time t1 and later, even if light (exposure light) is incident on the projection optical system 110, the thermal energy absorbed by the projection optical system 110 and the thermal energy released from the projection optical system 110 reach an equilibrium state, so the amount of aberration does not change from F1. After the exposure is completed at time t2, the aberration returns to the initial state with the passage of time, and becomes the initial aberration amount F0 at time t 3.
The time constant TS1 shown in fig. 2 is a time constant of the heat transfer characteristic of the projection optical system 110. These time constants are values inherent to the projection optical system 110, and are different values for each aberration. Therefore, for example, at the time of maintenance of the exposure apparatus 1, a time constant is acquired for each projection optical system 110 and for each aberration of the projection optical system 110.
The maximum aberration fluctuation amount F1 shown in fig. 2 is expressed by the following equation (1) using the aberration fluctuation amount K per unit light amount (unit exposure energy) and the actual exposure energy Q determined based on parameters such as exposure time, exposure amount, scanning speed, exposure area information, and the like.
F1＝K×Q…(1)
Let the aberration amount at a certain time be Δ Fk. In this case, the state of exposure isIn this state, the aberration amount Δ F after the lapse of time Δ t from a certain point in timek+1This is approximated by the following equation (2) using the maximum fluctuation amount F1 and the time constant TS 1. Similarly, in a state where exposure is not performed, the aberration amount Δ F after the lapse of time Δ t from a certain point in timek+1Is approximated by the following formula (3).
ΔFk+1＝ΔFk+F1×(1-exp(-Δt/TS1))…(2)
ΔFk+1＝ΔFk×exp(-Δt/TS1)…(3)
The fluctuation of the aberration of the projection optical system 110 shown in fig. 2 (the curve shown in fig. 2) was modeled using the equations (1), (2), and (3). However, the expressions (1), (2), and (3) are examples of the present embodiment, and may be modeled using other expressions.
The model expressions indicating the variation in aberration of the projection optical system 110 include an exposure model expression represented by expression (2) and a non-exposure model expression represented by expression (3). The exposure model expression indicates a variation in aberration of the projection optical system 110 during irradiation of the projection optical system 110 with exposure light, that is, a variation in aberration of the projection optical system 110 during exposure. The non-exposure model expression indicates a variation in aberration of the projection optical system 110 in a state where irradiation of the exposure light to the projection optical system 110 is stopped, that is, a variation in aberration of the projection optical system 110 after the end of exposure.
The maximum fluctuation amount F1 used in expression (2) represents a saturation value of the aberration of the projection optical system 110, and is a correction coefficient described later. The correction coefficient may be obtained for each aberration of the projection optical system 110, and may be predicted by using a plurality of model equations having different time constants.
Here, the correction coefficient is predicted using model expressions of a plurality of different time constants TS1, TS2, and TS 3. Regarding model expressions of the plurality of time constants TS1, TS2, and TS3, predicted values of aberrations of the projection optical system 110 at a certain time are F _ TS1, F _ TS2, and F _ TS 3. In this case, the predicted value of the aberration of the projection optical system 110 is the sum of the predicted values for each model equation (F _ TS1+ F _ TS2+ F _ TS 3). Here, the aberration of the projection optical system 110 is predicted by using 3 models, but the present invention is not limited thereto.
When the exposure conditions are changed, the energy density distribution of light (exposure light) entering the projection optical system 110 changes, and therefore the amount of aberration variation and the image height dependency of the projection optical system 110 change. Therefore, the correction coefficient must be obtained for each exposure condition. Here, the exposure conditions include, for example, the shape of the effective light source, the pattern of the mask 109, and the illumination region for illuminating the mask 109.
Consider a case where correction coefficients are obtained for different exposure conditions, for example, the 1 st exposure condition and the 2 nd exposure condition. In this case, in order to obtain the correction coefficient with high accuracy, for example, as shown in fig. 3, a sufficient cooling (standby) time may be secured until the influence of the residual aberration under different exposure conditions disappears. However, since the cooling time is set, productivity is lowered. Fig. 3 is a diagram illustrating an example of variation in aberration of the projection optical system 110. In fig. 3, the abscissa represents time, and the ordinate represents aberration (aberration amount) of the projection optical system 110. Fig. 3 shows a variation in aberration of the projection optical system 110 when the substrate 115 is exposed under the 1 st exposure condition, and a variation in aberration of the projection optical system 110 when the substrate 115 is exposed under the 2 nd exposure condition.
In addition, the expressions (1) to (3) are also established between different exposure conditions. Therefore, for example, as shown in fig. 4, if the correction coefficient in the task immediately before the 1 st exposure condition is accurately obtained, the correction coefficient under each exposure condition can be accurately obtained even if the cooling time is omitted. However, when there is an error in the correction coefficient in the job immediately before the 1 st exposure condition, as shown in fig. 4, when the cooling time is omitted, the correction coefficient under each exposure condition cannot be accurately obtained. Fig. 4 is a diagram illustrating an example of variation in aberration of the projection optical system 110. In fig. 4, the abscissa represents time, and the ordinate represents aberration (aberration amount) of the projection optical system 110. Fig. 4 shows the variation of the aberration of the projection optical system 110 when the substrate 115 is exposed under the 1 st exposure condition, the 2 nd exposure condition, and the 3 rd exposure condition, respectively.
Here, the reason why the correction coefficient under a certain exposure condition cannot be accurately obtained when there is an error in the correction coefficient in the task immediately before the certain exposure condition will be described. For easy understanding, first, a case where there is no error in the correction coefficient in the immediately preceding task is explained.
Here, for example, the imaging characteristics, specifically, the focal length of the projection optical system 110 is measured a plurality of times in 1 lot of exposure, and the exposure time of 1 lot is set to 400 seconds. The time constant TS1 is set to 200 seconds as 1 type. A predicted value of the focal length of the projection optical system 110 generated in the task immediately before the start of exposure (t is 0) is set to 15 nm. Regarding the above predicted values, since the predicted values are predicted using the expressions (1) to (3), if there is no error in the correction coefficients, there is no error in the predicted values at the start of exposure. Fig. 5A shows the measurement values when the focal length of the projection optical system 110 is actually measured at the start of exposure.
When the predicted value at a certain time after exposure is Δ F2 and the predicted value at the next time after exposure is Δ F3, the following equations are obtained using equations (2) and (3) (that is, using the exposure model equation and the non-exposure model equation separately).
ΔF2＝ΔF1+F1×(1-exp(-Δt/TS1))
ΔF3＝ΔF2×(1-exp(-Δt/TS1))
The correction coefficient (maximum fluctuation amount F1) is obtained by fitting a plurality of measured values obtained by measuring the focal length of the projection optical system 110 a plurality of times, with Δ F1 being substituted by 15 nm. In this case, the correction coefficient becomes 100 nm.
Next, a case where there is an error in the correction coefficient in the immediately preceding task, that is, a case where there is an error (prediction error) in the predicted value at the start of exposure is considered. Here, when the prediction error is 15nm, as shown in fig. 5A, the predicted value at the start of exposure (t is 0) is 30 nm. Since the fluctuation amount between the measured values does not change even if there is an error in the predicted value, the correction coefficient is determined for the predicted value using the solid line curve in fig. 5A. In this case, Δ F1 substituted for the above formula is 30nm, so the correction coefficient is 115 nm.
For such different correction coefficients, equation (2) when Δ F1 is 0 is shown in fig. 5B. As can be seen from fig. 5B, when there is a prediction error, the correction coefficient including the error is obtained, and therefore, a curve having a large change from the true correction coefficient is obtained. In this way, when there is a prediction error, the error correction coefficient is obtained as a result.
Therefore, in the present embodiment, a method of determining a correction coefficient used in a model equation representing a variation in imaging characteristics of the projection optical system 110 is proposed, in which the accuracy of the correction coefficient is improved in stages while the cooling time is shortened.
Fig. 6 is a flowchart for explaining a method of determining a correction coefficient used in a model equation indicating a variation in imaging characteristics of the projection optical system 110 in the present embodiment. The determination method described above can be executed by the main control unit 125, or can be executed by an information processing device external to the exposure apparatus 1.
In S1, a correction coefficient (2 nd coefficient) corresponding to the exposure condition of the exposure performed by the exposure apparatus 1 is acquired. The correction coefficient is stored in advance in the exposure apparatus 1 (the memory of the main control unit 125, the storage device of the exposure apparatus 1).
In S2, a predicted value of the imaging characteristic of the projection optical system 110 at the start of exposure is obtained. The predicted value corresponds to a residual of a variation in the imaging characteristic of the projection optical system 110 in the exposure before the present exposure (exposure performed from the present time). If the cooling time is sufficiently set from the end of the previous exposure, the predicted value of the imaging characteristic of the projection optical system 110 at the start of the exposure, which is acquired in S2, approaches zero. However, in the present embodiment, since the cooling time is shortened, the predicted value of the imaging characteristic of the projection optical system 110 at the start of exposure acquired in S2 is not zero.
In S3, exposure is started. In S4, the imaging characteristics of the projection optical system 110 are measured a plurality of times and a plurality of measurement values are obtained while the exposure apparatus 1 is performing exposure of the substrate 115. For example, as described above, the imaging characteristics of the projection optical system 110 are measured by the measurement section 123 a plurality of times between 1 lot of exposure (for example, at the time of replacement of the substrate 115).
In S5, a correction coefficient (1 st coefficient) is determined from the predicted value of the imaging characteristic of the projection optical system 110 at the start of exposure acquired in S2 and the plurality of measured values acquired in S4 using equations (1) to (3) (1 st step).
At S6, it is determined whether or not the correction coefficient obtained at S5 is to be updated to the final correction coefficient used in the model equation. Specifically, it is determined whether or not the absolute value of the difference between the correction coefficient obtained in S1 (the 2 nd coefficient stored in advance in the exposure apparatus 1) and the correction coefficient obtained in S5 (the 1 st coefficient) falls within the allowable range (the 2 nd step). The allowable range is stored in the exposure apparatus 1 in advance. If the absolute value of the difference between the correction coefficient obtained in S1 and the correction coefficient obtained in S5 falls within the allowable range, the process proceeds to S7. If the absolute value of the difference between the correction coefficient obtained in S1 and the correction coefficient obtained in S5 does not fall within the allowable range, the process proceeds to S8.
In S7, the correction coefficient (the 2 nd coefficient) stored in the exposure apparatus 1 is updated so that the correction coefficient (the 1 st coefficient) obtained in S5 is set in the exposure apparatus 1, that is, the correction coefficient obtained in S5 is used in the model equation (the 3 rd step). Thus, when exposure is performed under the same exposure condition, the imaging characteristics of the projection optical system 110 can be predicted using the correction coefficient obtained in S5 and exposure can be performed simultaneously without measuring the imaging characteristics of the projection optical system 110 a plurality of times (S4). Therefore, it is not necessary to measure the imaging characteristics of the projection optical system 110 a plurality of times in 1 lot of exposures, so a decrease in throughput can be suppressed.
At S8, the 1 st evaluation value of the correction coefficient (1 st coefficient) obtained from the predicted value obtained at S2 is compared with the 2 nd evaluation value of the correction coefficient (2 nd coefficient) obtained from the predicted value obtained from the model expression when the correction coefficient obtained at S1 is obtained. In the present embodiment, it is determined whether the 1 st evaluation value is smaller than the 2 nd evaluation value or whether the 1 st evaluation value is equal to or larger than the 2 nd evaluation value. The 2 nd evaluation value is stored in the exposure apparatus 1 in advance in association with the correction coefficient (2 nd coefficient) acquired in S1.
The 1 st evaluation value and the 2 nd evaluation value, more specifically, the evaluation value indicating the reliability of the correction coefficient are obtained from the predicted value Δ F1 at the time of the start of exposure obtained when the correction coefficient obtained in S1 is obtained, and the predicted value Δ F1 obtained in S2. Specifically, the evaluation value V is expressed by an absolute value of a linear sum of a weight coefficient and a predicted value Δ F1 set for each of a plurality of time constants, as shown in the following expression (4).
V ═ Δ F1_ TS1 × weight _ TS1+ Δ F1_ TS2 × weight _ TS2 Δ F1_ TS3 × weight _ TS3| … (4)
The predicted value Δ F1 is predicted from the change in the imaging characteristics of the projection optical system 110 under the previous exposure conditions using equation (3), and therefore the predicted value is obtained for each time constant. The predicted values are Δ F1_ TS1, Δ F1_ TS2, and Δ F1_ TS 3. Here, the time constants are assumed to be 3. The weight _ TS1, the weight _ TS2, and the weight _ TS3 are weight coefficients preset for the exposure apparatus 1 for each time constant.
Here, a case where there is an error (prediction error) in the predicted value Δ F1 is considered. The predicted value Δ F1 is predicted using equation (3) in the immediately preceding task. Fig. 7 shows a case where there is a prediction error in the predicted value Δ F1 and a case where there is no prediction error in the predicted value Δ F1. In fig. 7, the vertical axis represents the focal length of the projection optical system 110, and the horizontal axis represents time. According to the characteristic of expression (3), the prediction error amount a depends on the prediction value B in the case where there is a prediction error, and as the prediction value B becomes smaller, the prediction error amount a also becomes smaller. By setting a sufficient cooling time, the predicted value B can be made as close to zero as possible. Accordingly, the prediction error amount a is also close to zero, and if a correction coefficient is obtained from this state, the correction coefficient does not include an error.
The weight coefficient in expression (4) is described. If there is an error in a component with a long time constant and if there is an error in a component with a short time constant, the influence on the variation of the imaging characteristics of the projection optical systems 110 in 1 lot differs depending on the magnitude of the time constant used in the model equation.
When there is an error in the predicted value at the start of exposure, the correction coefficient obtained from the predicted value also includes an error. As shown in fig. 8A and 8B, the long time constant is set to 200 seconds, and the short time constant is set to 5000 seconds. In fig. 8A and 8B, the vertical axis represents the focal length of the projection optical system 110, and the horizontal axis represents the time. The true correction coefficient was set to 100nm both for long and short time constants, and the error of the correction coefficient was set to 50nm both for long and short time constants. As can be seen from fig. 8A and 8B, the prediction error amount in 1 lot has a greater influence with a short time constant.
Therefore, it is necessary to set the weight coefficient according to the magnitude of the time constant as described above. The evaluation value V corresponds to the degree of influence of the prediction error in the predetermined exposure period, based on the correction coefficient (correction coefficient including the error) obtained in S5, taking into account the influence of the time constant. Therefore, as the value becomes larger, an error is more likely to occur, and therefore, it can be determined that the reliability of the correction coefficient is low.
Returning to fig. 6, in S8, if the 1 st evaluation value is smaller than the 2 nd evaluation value, the process proceeds to S9. In this case, the correction coefficient (1 st coefficient) obtained in S5 has higher reliability than the correction coefficient (2 nd coefficient) stored in the exposure apparatus 1. Therefore, in S9, the correction coefficient used in the model equation, that is, the correction coefficient stored in the exposure apparatus 1 is updated with the correction coefficient obtained in S5 as a provisional coefficient (step 4). However, the correction coefficient obtained in S5 does not satisfy the condition in S6, and is therefore a tentative correction coefficient. Therefore, when the exposure is performed under the same exposure condition, the exposure is performed using the correction coefficient updated in S9 or the correction coefficient acquired in S1. In addition, in S9, along with the update of the correction coefficient, the evaluation value is also updated to the evaluation value (1 st evaluation value) of the correction coefficient (1 st coefficient) obtained in S5.
When the 1 st evaluation value is equal to or greater than the 2 nd evaluation value in S8, the process proceeds to S1 (step 4) without updating the correction coefficients used in the model expression.
As described above, in the present embodiment, the cooling time is shortened, but the accuracy of the correction coefficient can be improved efficiently by using the correction coefficient with high reliability. In the exposure, the variation of the imaging characteristic of the projection optical system 110 is predicted based on the model equation (determination step) in which the correction coefficient is determined in this way. Then, the imaging characteristics of the projection optical system 110 are adjusted and the position of the substrate 115 is changed by the aperture driving unit 112 and the lens driving unit 113 in accordance with the change in the imaging characteristics of the projection optical system 110, and the substrate 115 is exposed (exposure step). Such an exposure method also constitutes an aspect of the present invention.
The method of manufacturing an article according to the embodiment of the present invention is suitable for manufacturing an article such as a device (a semiconductor element, a magnetic storage medium, a liquid crystal display element, or the like). The manufacturing method includes a step of exposing the substrate coated with the photosensitive agent by using the exposure apparatus 1 (the exposure method), and a step of developing the exposed photosensitive agent. Further, an etching step, an ion implantation step, and the like are performed on the substrate using the developed pattern of the photosensitive agent as a mask, thereby forming a circuit pattern on the substrate. These steps of exposure, development, etching, and the like are repeated to form a circuit pattern including a plurality of layers on the substrate. In the subsequent steps, the substrate on which the circuit pattern is formed is cut, and the steps of mounting, bonding, and inspecting the chip are performed. The above-mentioned manufacturing method may include other known steps (oxidation, film formation, vapor deposition, doping, planarization, resist stripping, and the like). The method of manufacturing an article according to the present embodiment is more advantageous than conventional methods in at least 1 of the performance, quality, productivity, and production cost of the article.
The present invention can also be realized by supplying a program that realizes 1 or more functions of the above-described embodiments to a system or an apparatus via a network or a storage medium, and performing processing in which 1 or more processors in a computer of the system or the apparatus read and execute the program. Further, the present invention can be realized by a circuit (for example, ASIC) that realizes 1 or more functions.
OTHER EMBODIMENTS
The embodiments of the present invention can also be realized by a method in which software (programs) that perform the functions of the above-described embodiments are supplied to a system or an apparatus through a network or various storage media, and a computer or a Central Processing Unit (CPU), a Micro Processing Unit (MPU) of the system or the apparatus reads out and executes the methods of the programs.
While the preferred embodiments of the present invention have been described above, it is a matter of course that the present invention is not limited to these embodiments, and various modifications and changes can be made within the scope of the gist thereof.
Claims (10)
1. A method for determining a coefficient indicating a maximum variation amount of an image forming characteristic used in a model equation indicating a variation in the image forming characteristic of a projection optical system in an exposure apparatus for transferring a pattern of a mask to a substrate via the projection optical system, the method comprising:
a 1 st step of obtaining a 1 st coefficient indicating a maximum variation of the imaging characteristics from a plurality of measurement values obtained by measuring the imaging characteristics a plurality of times and a predicted value of the imaging characteristics at the start of exposure of the substrate obtained from the model equation;
a 2 nd step of determining whether or not a difference between the 1 st coefficient and a 2 nd coefficient indicating a maximum variation amount of the imaging characteristic used in the model equation stored in the exposure apparatus falls within an allowable range;
a 3 rd step of updating the coefficient so that the 1 st coefficient is used in the model equation when the difference falls within the allowable range; and
and a 4 th step of comparing a 1 st evaluation value of the 1 st coefficient obtained from the predicted value and a 2 nd evaluation value of the 2 nd coefficient obtained from the predicted value of the imaging characteristic obtained from the model expression when the 2 nd coefficient is obtained, if the difference does not converge on the allowable range, updating the coefficient with the 1 st coefficient as a tentative coefficient if the 1 st evaluation value is smaller than the 2 nd evaluation value, and not updating the coefficient if the 1 st evaluation value is equal to or greater than the 2 nd evaluation value.
2. The method of claim 1,
the model equation includes a plurality of time constants,
the 1 st evaluation value and the 2 nd evaluation value each include an absolute value of a linear sum of the weight coefficient and the predicted value set for each of the plurality of time constants.
3. The decision method according to claim 1 or 2,
the 2 nd evaluation value is stored in the exposure device.
4. The method of claim 3,
in the 4 th step, if the 1 st evaluation value is smaller than the 2 nd evaluation value, the 2 nd evaluation value is updated with the 1 st evaluation value as a provisional evaluation value.
5. The method of claim 1,
the model equations include an exposure model equation representing a variation in the imaging characteristic during exposure of the substrate by the exposure device and a non-exposure model equation representing a variation in the imaging characteristic after the exposure of the substrate is completed by the exposure device,
in the step 1, the predicted value is obtained using the non-exposure model equation.
6. The method of claim 1,
the imaging characteristics include at least 1 of a focal length, a magnification, a distortion aberration, an astigmatism, and a wavefront aberration.
7. An exposure method for exposing a substrate using an exposure apparatus that transfers a pattern of a mask to the substrate via a projection optical system, comprising:
a determination step of determining a coefficient indicating a maximum variation amount of the imaging characteristic used in a model equation indicating a variation of the imaging characteristic of the projection optical system; and
an exposure step of exposing the substrate by adjusting the imaging characteristics of the projection optical system or changing the position of the substrate based on the variation of the imaging characteristics of the projection optical system obtained from the model equation in which the coefficients are determined,
the determining step includes:
a 1 st step of obtaining a 1 st coefficient indicating a maximum variation of the imaging characteristics from a plurality of measurement values obtained by measuring the imaging characteristics a plurality of times and a predicted value of the imaging characteristics at the start of exposure of the substrate obtained from the model equation;
a 2 nd step of determining whether or not a difference between the 1 st coefficient and a 2 nd coefficient indicating a maximum variation amount of the imaging characteristic used in the model equation stored in the exposure apparatus falls within an allowable range;
a 3 rd step of updating the coefficient so that the 1 st coefficient is used in the model equation when the difference falls within the allowable range; and
and a 4 th step of comparing a 1 st evaluation value of the 1 st coefficient obtained from the predicted value and a 2 nd evaluation value of the 2 nd coefficient obtained from the predicted value of the imaging characteristic obtained from the model expression when the 2 nd coefficient is obtained, if the difference does not converge on the allowable range, updating the coefficient with the 1 st coefficient as a tentative coefficient if the 1 st evaluation value is smaller than the 2 nd evaluation value, and not updating the coefficient if the 1 st evaluation value is equal to or greater than the 2 nd evaluation value.
8. An information processing apparatus for determining a coefficient indicating a maximum variation amount of an image forming characteristic used in a model equation indicating a variation in the image forming characteristic of a projection optical system in an exposure apparatus for transferring a pattern of a mask to a substrate via the projection optical system,
determining a 1 st coefficient indicating a maximum variation of the imaging characteristic from a plurality of measurement values obtained by measuring the imaging characteristic a plurality of times and a predicted value of the imaging characteristic at the start of exposure of the substrate obtained from the model equation,
determining whether or not a difference between the 1 st coefficient and a 2 nd coefficient indicating a maximum variation amount of the imaging characteristic used in the model equation stored in the exposure apparatus converges on an allowable range,
updating the coefficient in such a manner that the 1 st coefficient is used in the model expression when the difference converges on the allowable range,
when the difference does not converge on the allowable range, a 1 st evaluation value of the 1 st coefficient obtained from the predicted value and a 2 nd evaluation value of the 2 nd coefficient obtained from the predicted value of the imaging characteristic obtained from the model expression when the 2 nd coefficient is obtained are compared, and if the 1 st evaluation value is smaller than the 2 nd evaluation value, the coefficient is updated with the 1 st coefficient as a tentative coefficient, and if the 1 st evaluation value is equal to or greater than the 2 nd evaluation value, the coefficient is not updated.
9. A storage medium storing a program for causing an information processing apparatus to execute a determination method of determining a coefficient indicating a maximum variation amount of an image forming characteristic used in a model equation indicating a variation of the image forming characteristic of a projection optical system in an exposure apparatus that transfers a pattern of a mask to a substrate via the projection optical system, the determination method being characterized in that,
the program causes the information processing apparatus to execute:
a 1 st step of obtaining a 1 st coefficient indicating a maximum variation of the imaging characteristics from a plurality of measurement values obtained by measuring the imaging characteristics a plurality of times and a predicted value of the imaging characteristics at the start of exposure of the substrate obtained from the model equation;
a 2 nd step of determining whether or not a difference between the 1 st coefficient and a 2 nd coefficient indicating a maximum variation amount of the imaging characteristic used in the model equation stored in the exposure apparatus falls within an allowable range;
a 3 rd step of updating the coefficient so that the 1 st coefficient is used in the model equation when the difference falls within the allowable range; and
and a 4 th step of comparing a 1 st evaluation value of the 1 st coefficient obtained from the predicted value and a 2 nd evaluation value of the 2 nd coefficient obtained from the predicted value of the imaging characteristic obtained from the model expression when the 2 nd coefficient is obtained, if the difference does not converge on the allowable range, updating the coefficient with the 1 st coefficient as a tentative coefficient if the 1 st evaluation value is smaller than the 2 nd evaluation value, and not updating the coefficient if the 1 st evaluation value is equal to or greater than the 2 nd evaluation value.
10. A method for manufacturing an article, comprising:
a determination step of determining, in an exposure apparatus that transfers a pattern of a mask to a substrate via a projection optical system, a coefficient indicating a maximum variation amount of an image forming characteristic used in a model equation indicating a variation of the image forming characteristic of the projection optical system;
an exposure step of adjusting the imaging characteristics of the projection optical system or changing the position of the substrate based on the variation of the imaging characteristics of the projection optical system obtained from the model equation in which the coefficient is determined, and exposing the photosensitive agent of the substrate;
developing the exposed substrate with a photosensitive agent to form a pattern of the photosensitive agent; and
forming a pattern on the substrate based on the developed pattern of the photosensitive agent, and processing the substrate on which the pattern is formed to manufacture an article,
the determining step includes:
a 1 st step of obtaining a 1 st coefficient indicating a maximum variation of the imaging characteristics from a plurality of measurement values obtained by measuring the imaging characteristics a plurality of times and a predicted value of the imaging characteristics at the start of exposure of the substrate obtained from the model equation;
a 2 nd step of determining whether or not a difference between the 1 st coefficient and a 2 nd coefficient indicating a maximum variation amount of the imaging characteristic used in the model equation stored in the exposure apparatus falls within an allowable range;
a 3 rd step of updating the coefficient so that the 1 st coefficient is used in the model equation when the difference falls within the allowable range; and
and a 4 th step of comparing a 1 st evaluation value of the 1 st coefficient obtained from the predicted value and a 2 nd evaluation value of the 2 nd coefficient obtained from the predicted value of the imaging characteristic obtained from the model expression when the 2 nd coefficient is obtained, if the difference does not converge on the allowable range, updating the coefficient with the 1 st coefficient as a tentative coefficient if the 1 st evaluation value is smaller than the 2 nd evaluation value, and not updating the coefficient if the 1 st evaluation value is equal to or greater than the 2 nd evaluation value.
Applications Claiming Priority (2)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| JP2017104943A JP6554141B2 (en) | 2017-05-26 | 2017-05-26 | Determination method, exposure method, information processing apparatus, program, and article manufacturing method |
| JP2017-104943 | 2017-05-26 |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN108931890A CN108931890A (en) | 2018-12-04 |
| CN108931890B true CN108931890B (en) | 2021-05-04 |
Family
ID=64449165
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201810491571.8A Active CN108931890B (en) | 2017-05-26 | 2018-05-22 | Determining method, exposure method, information processing apparatus, medium, and manufacturing method |
Country Status (3)
| Country | Link |
|---|---|
| JP (1) | JP6554141B2 (en) |
| KR (1) | KR102300753B1 (en) |
| CN (1) | CN108931890B (en) |
Families Citing this family (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JP7213757B2 (en) * | 2019-05-31 | 2023-01-27 | キヤノン株式会社 | Exposure apparatus and article manufacturing method |
| JP6924235B2 (en) * | 2019-09-19 | 2021-08-25 | キヤノン株式会社 | Exposure method, exposure equipment, article manufacturing method, and semiconductor device manufacturing method |
| CN114937089A (en) * | 2022-04-25 | 2022-08-23 | 广州极飞科技股份有限公司 | Sensor parameter online calibration method, device, equipment and storage medium |
| CN115227269B (en) * | 2022-06-09 | 2025-07-15 | 奕瑞电子科技集团股份有限公司 | Control method and device for exposure gate of high voltage generator |
| JP7297136B1 (en) | 2022-10-13 | 2023-06-23 | キヤノン株式会社 | Exposure Apparatus, Exposure Apparatus Control Method, Information Processing Apparatus, Information Processing Method, and Article Manufacturing Method |
| JP2024171856A (en) | 2023-05-30 | 2024-12-12 | キヤノン株式会社 | Exposure apparatus, exposure method, and article manufacturing method |
Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN102866589A (en) * | 2011-07-05 | 2013-01-09 | 佳能株式会社 | Determination method and information processing apparatus |
| US20130342819A1 (en) * | 2012-06-22 | 2013-12-26 | Canon Kabushiki Kaisha | Exposure apparatus, exposure method, and method of manufacturing article |
| US20150049315A1 (en) * | 2013-08-13 | 2015-02-19 | Canon Kabushiki Kaisha | Exposure apparatus and method of manufacturing device |
| CN106444291A (en) * | 2015-08-10 | 2017-02-22 | 佳能株式会社 | Evaluation method, exposure apparatus, exposure method, and method of manufacturing article |
Family Cites Families (9)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JP3395280B2 (en) * | 1993-09-21 | 2003-04-07 | 株式会社ニコン | Projection exposure apparatus and method |
| JP2828226B2 (en) | 1995-10-30 | 1998-11-25 | 株式会社ニコン | Projection exposure apparatus and method |
| JP2003059807A (en) * | 2001-08-20 | 2003-02-28 | Nikon Corp | Method of exposure and aligner, and method for manufacturing device |
| JP2004079831A (en) * | 2002-08-20 | 2004-03-11 | Nikon Corp | Exposure method and aligner, and method for manufacturing device |
| KR20050121728A (en) * | 2003-04-16 | 2005-12-27 | 가부시키가이샤 니콘 | Pattern decision method and system, mask manufacturing method, focusing performance adjusting method, exposure method and device, program, and information recording medium |
| JP5264116B2 (en) * | 2007-07-26 | 2013-08-14 | キヤノン株式会社 | Imaging characteristic variation prediction method, exposure apparatus, and device manufacturing method |
| JP2013115348A (en) * | 2011-11-30 | 2013-06-10 | Canon Inc | Calculation method of variation in imaging characteristics of projection optical system, exposure device and manufacturing method of device |
| JP2014143306A (en) * | 2013-01-24 | 2014-08-07 | Canon Inc | Exposure method, exposure device, method of manufacturing device using the same |
| JP6613074B2 (en) * | 2015-08-20 | 2019-11-27 | キヤノン株式会社 | Determination method, exposure apparatus, program, and article manufacturing method |
-
2017
- 2017-05-26 JP JP2017104943A patent/JP6554141B2/en active Active
-
2018
- 2018-04-18 KR KR1020180044750A patent/KR102300753B1/en active Active
- 2018-05-22 CN CN201810491571.8A patent/CN108931890B/en active Active
Patent Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN102866589A (en) * | 2011-07-05 | 2013-01-09 | 佳能株式会社 | Determination method and information processing apparatus |
| US20130342819A1 (en) * | 2012-06-22 | 2013-12-26 | Canon Kabushiki Kaisha | Exposure apparatus, exposure method, and method of manufacturing article |
| US20150049315A1 (en) * | 2013-08-13 | 2015-02-19 | Canon Kabushiki Kaisha | Exposure apparatus and method of manufacturing device |
| CN106444291A (en) * | 2015-08-10 | 2017-02-22 | 佳能株式会社 | Evaluation method, exposure apparatus, exposure method, and method of manufacturing article |
Also Published As
| Publication number | Publication date |
|---|---|
| JP6554141B2 (en) | 2019-07-31 |
| KR20180129625A (en) | 2018-12-05 |
| KR102300753B1 (en) | 2021-09-10 |
| CN108931890A (en) | 2018-12-04 |
| JP2018200390A (en) | 2018-12-20 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN108931890B (en) | Determining method, exposure method, information processing apparatus, medium, and manufacturing method | |
| TWI395072B (en) | Imaging characteristics fluctuation predicting method, exposure apparatus, and device manufacturing method | |
| JP6039932B2 (en) | Exposure apparatus, exposure method, and article manufacturing method | |
| JP6422307B2 (en) | Exposure method, exposure apparatus, and article manufacturing method | |
| JP6381188B2 (en) | Exposure apparatus and device manufacturing method | |
| US9513564B2 (en) | Exposure method, exposure apparatus, and device manufacturing method | |
| US9116444B2 (en) | Method of calculating amount of fluctuation of imaging characteristic of projection optical system, exposure apparatus, and method of fabricating device | |
| US10394134B2 (en) | Exposure method, exposure apparatus, and method of manufacturing article | |
| JP5094517B2 (en) | Exposure apparatus, measurement method, stabilization method, and device manufacturing method | |
| JP2018132569A (en) | Evaluation method of change in image-forming property of projection optical system by exposure heat, exposure apparatus, and device manufacturing method | |
| JP2001244182A (en) | Method of measuring variations in image formation characteristics of projection optical system due to exposure heat and aligner | |
| JP7547185B2 (en) | Information processing apparatus, exposure apparatus, and method for manufacturing an article. | |
| KR101039288B1 (en) | Exposure apparatus, measuring method, stabilization method, and device manufacturing method | |
| JP2006019561A (en) | Exposure method |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |