KR20220082731A - Information processing apparatus, exposure apparatus, and method of manufacturing article - Google Patents

Abstract

In order to provide an information processing apparatus capable of efficiently predicting temporal changes in imaging characteristics of a projection optical system installed in an exposure apparatus, an information processing apparatus according to the present invention uses a learning model acquired by machine learning to provide an exposure apparatus An information processing device for predicting temporal changes in imaging characteristics of a projection optical system installed in It is characterized in that it is created by classifying about anisotropy in a cross section parallel to the scanning direction.

Description

Information processing apparatus, exposure apparatus, and manufacturing method of an article TECHNICAL FIELD

The present invention relates to an information processing apparatus, an exposure apparatus, and a method for manufacturing an article.

Conventionally, in the projection optical system provided in the exposure apparatus, it is calculated|required to correct the fluctuation|variation of the imaging characteristic accompanying the absorption of exposure energy.

It is also known that variations in the imaging characteristics of the projection optical system depend on changes in the density distribution of exposure energy in the projection optical system depending on exposure conditions such as the type of circuit pattern formed on the original plate and the effective light source distribution of the illumination light. .

Japanese Patent Laid-Open No. 2009-32875 discloses a method of performing correction by calculating correction coefficients of a predictive model for predicting temporal changes in imaging characteristics of a projection optical system according to such differences in exposure conditions.

In recent years, in exposure apparatuses, the density distribution of exposure energy in the projection optical system is also changed in various ways as the original plate is frequently exchanged with the increase in the type of the original plate on which the circuit pattern of the semiconductor device is formed due to the diversification of products such as semiconductor devices. it is known to do

In addition, in order to cope with such a situation, when it is attempted to calculate the correction coefficient of the predictive model for each of a vast number of exposure conditions using the method disclosed in Japanese Unexamined Patent Application Publication No. 2009-32875, a huge amount of time is required. throw it away

Accordingly, an object of the present invention is to provide an information processing apparatus capable of efficiently predicting temporal changes in imaging characteristics of a projection optical system installed in an exposure apparatus.

An information processing apparatus according to the present invention is an information processing apparatus for predicting temporal changes in imaging characteristics of a projection optical system installed in an exposure apparatus using a learning model acquired by machine learning, wherein input data of the learning model includes: It is characterized in that it is created by classifying at least one of the effective light source distribution in the device and the pattern drawn on the original plate with respect to anisotropy in a cross section parallel to the scanning direction and the non-scan direction.

1 is a schematic diagram of an exposure apparatus including an information processing apparatus according to a first embodiment;
Fig. 2 is a diagram showing an example of temporal change in imaging characteristics of a projection optical system according to exposure;
Fig. 3A is a diagram showing an example of a circuit pattern drawn on a reticle;
Fig. 3B is a diagram showing an example of a circuit pattern drawn on a reticle;
Fig. 4A is a diagram showing an example of an effective light source distribution formed by an illumination optical system;
Fig. 4B is a diagram showing an example of an effective light source distribution formed by an illumination optical system;
Fig. 4C is a diagram showing an example of an effective light source distribution formed by an illumination optical system;
Fig. 4D is a diagram showing an example of an effective light source distribution formed by an illumination optical system;
Fig. 5A is a diagram showing characteristics of density distribution of exposure energy in a projection optical system by X dipole illumination;
Fig. 5B is a diagram showing characteristics of density distribution of exposure energy in a projection optical system by X dipole illumination;
Fig. 5C is a diagram showing characteristics of density distribution of exposure energy in a projection optical system by X dipole illumination;
Fig. 5D is a diagram showing characteristics of density distribution of exposure energy in a projection optical system by X dipole illumination;
Fig. 6A is a diagram showing characteristics of density distribution of exposure energy in a projection optical system by Y dipole illumination;
Fig. 6B is a diagram showing characteristics of density distribution of exposure energy in a projection optical system by Y dipole illumination;
Fig. 6C is a diagram showing characteristics of density distribution of exposure energy in a projection optical system by Y dipole illumination;
Fig. 6D is a diagram showing characteristics of density distribution of exposure energy in a projection optical system by Y dipole illumination;
Fig. 7 is a flowchart of processing performed in the information processing apparatus according to the first embodiment;
Fig. 8A is a schematic diagram showing a state in which a correlation degree is calculated in the information processing apparatus according to the first embodiment;
Fig. 8B is a schematic diagram showing a state in which a correlation degree is calculated in the information processing apparatus according to the first embodiment;
Fig. 8C is a schematic diagram showing how the correlation diagram is calculated in the information processing apparatus according to the first embodiment;
Fig. 9 is a block diagram of an exposure processing system in which an information processing apparatus according to a second embodiment is installed;

Hereinafter, an information processing apparatus according to the present embodiment will be described in detail with reference to the accompanying drawings. At this time, in order to make this embodiment easy to understand, the drawing shown below may be drawn with the scale different from the actual thing.

In the following description, it is assumed that the imaging characteristics include at least one of magnification, focus, distortion, astigmatism, spherical aberration, coma, and wavefront aberration. Here, the wavefront aberration is expressed as each term developed by the Zernike polynomial of the wavefront shape.

Hereinafter, the above-described imaging characteristics may be collectively referred to as aberration.

In the following, the direction perpendicular to the substrate mounting surface of the substrate stage is the optical axis direction (Z direction), and the direction in which the substrate placed on the substrate mounting surface is scanned is the scanning direction (Y direction), parallel to the substrate mounting surface. In the plane, a direction perpendicular to the scanning direction is referred to as a non-scan direction (X direction).

[First embodiment]

Conventionally, in the manufacturing process of semiconductor elements, such as LSI and super-LSI, the exposure apparatus which performs baking formation by projecting and exposing the circuit pattern drawn on the reticle (mask) on the board|substrate (wafer) coated with the photosensitive agent is used.

It is known that, in such an exposure apparatus, optical characteristics such as refractive index change in temperature due to heat generated when a part of the energy of exposure light is absorbed in the projection optical system with repetition of projection exposure.

And if exposure light is continuously irradiated to the projection optical system for a long time, the imaging characteristics of the projection optical system will fluctuate, resulting in a non-negligible amount of deviation in the line width resolution of circuit patterns and alignment precision for accurately superimposing patterns over multiple processes. There are concerns.

Therefore, a method has been proposed for correcting the fluctuation of the imaging characteristic according to the energy of the exposure light irradiated to the projection optical system.

For example, such fluctuations in imaging characteristics (aberrations) are predicted using a predictive model using exposure amount, exposure time, non-exposure time, etc. as variables, and based on the prediction result, the field lens of the substrate stage or projection optical system An exposure apparatus that corrects by moving is known.

Then, by predicting each of the aberrations included in the imaging characteristics of the projection optical system, for example, variations in magnification, focus, distortion, astigmatism, and wavefront aberration using a predictive model, variations in the respective imaging characteristics can be corrected.

Also, conventionally, there has been known a method of changing the correction coefficient of a predictive model using the result of directly measuring the amount of change in the imaging characteristic when the amount of variation in the imaging characteristic of the projection optical system is different from the prediction.

In addition, when a plurality of reticles with different circuit patterns are used, deviations in the predicted values of the amount of change in the imaging characteristics of the projection optical system due to the difference in the circuit patterns are corrected by using the correction coefficient of the predictive model obtained for each reticle. Methods of prediction are known.

Also known is a method of performing correction by calculating a correction coefficient of a predictive model for predicting variations in imaging characteristics of a projection optical system according to exposure conditions such as the type of circuit pattern formed on the reticle and effective light source distribution of illumination light.

In the lithography process included in the manufacturing process of a semiconductor device etc., it is calculated|required to control the fluctuation amount of the imaging characteristic by exposure energy in a projection optical system within an allowable range.

In recent years, as the number of reticles on which circuit patterns of semiconductor devices are formed increases along with the diversification of products such as semiconductor devices, exposure is performed while frequently exchanging the reticles for each product lot in a lithography process.

For this reason, the operator of the exposure apparatus creates control parameters for setting exposure conditions in the exposure apparatus according to the type of the reticle.

Such control parameters include, for example, a reticle ID for identifying a reticle, an illumination mode ID for identifying a setting of an illumination light, an exposure area to which the exposure light is irradiated in the projection optical system, an exposure amount, and the like.

In the method of using the predictive model for predicting the fluctuation of the imaging characteristic of the projection optical system shown above, it is necessary to calculate the correction coefficient for each exposure condition.

Therefore, it takes an enormous amount of time to acquire the correction coefficients for each of the recently diversified reticles using such a conventional method.

Accordingly, in the present embodiment, an object of the present embodiment is to provide an information processing apparatus capable of efficiently predicting variations in the imaging characteristics of the projection optical system for each exposure condition by adopting a configuration as shown below.

Fig. 1 shows a schematic diagram of an exposure apparatus 1 including an information processing apparatus 20 according to a first embodiment.

The exposure apparatus 1 is a lithographic apparatus that exposes a substrate such that a pattern formed on an original plate (reticle, mask) is transferred to a substrate (wafer) by a step-and-scan method.

The exposure apparatus 1 includes an information processing apparatus 20, a laser light source 101, a laser light source control apparatus 102, a main control apparatus 103, an illumination optical system 104, and an illumination optical system control apparatus according to the present embodiment. (108) is provided.

In addition, the exposure apparatus 1 includes a projection optical system 114 , a wafer stage 116 , a wafer stage controller 120 , a reticle stage 123 , a reticle stage controller 124 , and a projection optical system controller 129 . is equipped with

In the laser light source 101, for example, a gas such as KrF is sealed, and a laser beam having a wavelength of 248 nm, for example, is emitted from a far-extra-far region.

And the control of the gas exchange operation|movement in the laser light source 101, the control for wavelength stabilization, control of the discharge application voltage, etc. are performed by the laser light source control apparatus 102. FIG.

The main control apparatus 103 is connected to the exposure apparatus 1 by an interface cable, and generates a command to control the exposure apparatus 1 as a whole.

The illumination optical system 104 guides the beam emitted from the laser light source 101 to the reticle 113 mounted on the reticle stage 123 .

Specifically, the beam emitted from the laser light source 101 passes through the beam shaping optical system 126 and is shaped into a predetermined shape (circular shape, annular shape, quadrupole shape, dipole shape, etc.), and an integrator lens A secondary light source is formed by incident on (105).

And the light flux from the secondary light source is directed by the condenser lens 107 having a function of changing the illuminance distribution of the reticle 113, whereby the variable slit 110 is Kohler illuminated.

The variable slit 110 has a mechanism for changing the opening width, and by controlling the opening width, the intensity distribution (illuminance distribution) of the slit-shaped light (exposure light) in the non-scanning direction is equalized.

An aperture stop 106 having a substantially circular opening is provided between the integrator lens 105 and the condenser lens 107 .

Then, when the illumination optical system controller 108 controls the diameter of the opening of the aperture stop 106 , the numerical aperture NA of the illumination optical system 104 can be set to a desired value.

In addition, since the ratio of the numerical aperture of the illumination optical system 104 to the numerical aperture of the projection optical system 114 is the coherence factor (σ value), the illumination optical system controller 108 controls the aperture stop ( 106), it becomes possible to set the σ value.

A half mirror 111 is disposed on the optical path of the illumination optical system 104 , specifically, between the condenser lens 107 and the variable slit 110 , and a part of the exposure light illuminating the reticle 113 is reflected by the half mirror 111 . ) is reflected by

A photo sensor 109 is disposed on the optical path of the reflected light from the half mirror 111 , and an output corresponding to the intensity (exposure energy) of the exposure light is generated by the photo sensor 109 .

Then, the output of the photosensor 109 is converted into exposure energy per pulse by an integrating circuit (not shown) that integrates for every pulse emission of the laser light source 101, and passes through the illumination optical system controller 108 to the main control device. (103) is input.

A circuit pattern of a semiconductor element for baking is formed in the reticle 113 , and the reticle 113 is illuminated by the illumination optical system 104 .

A variable blade 112 composed of a light blocking member movable in the two-dimensional direction, that is, in the AY plane perpendicular to the optical axis direction, is installed between the variable slit 110 and the reticle stage 123, and the pattern of the reticle 113 is The irradiation area of the surface is arbitrarily set.

The projection optical system 114 guides the exposure light that has passed through the reticle 113 to the wafer 115 placed on the wafer stage 116, so that the reticle is placed on one shot area on the wafer 115 coated with photoresist. (113) It is arranged so that the above pattern is projected onto the image.

When a portion of the pattern on the reticle 113 is reduced and exposed on the wafer 115 at a reduced magnification β (for example, 1/4), the reticle stage 123 and the wafer stage 116 are exposed to a slit-shaped light. Scanning is performed in opposite directions to the scanning direction at the same speed ratio as the reduction magnification β.

Then, by repeating multi-pulse exposure by pulse emission from the laser light source 101 , the pattern formed on the entire surface of the reticle 113 can be transferred to the shot region on the wafer 115 .

The projection optical system 114 is provided with a field lens 127 . The field lens 127 is held by the barrel 130, and the barrel 130, that is, the field lens 127, can be moved in the optical axis direction by a driving mechanism 128 composed of pneumatic pressure or a piezoelectric element. .

Then, the projection optical system controller 129 controls the position of the field lens 127 on the optical axis, thereby suppressing a decrease in the aberration of the projection optical system 114 while improving the projection magnification and reducing the distortion error. are doing

The wafer stage 116 can move in the optical axis direction (Z direction) of the projection optical system 114 and the X and Y directions orthogonal to each other in a plane perpendicular to the Z direction while holding the wafer 115 .

The laser interferometer 118 can measure the position in the XY plane of the wafer stage 116 by measuring the distance between it and the moving mirror 117 fixed to the wafer stage 116 .

The wafer stage controller 120 controls the driving mechanism 119 such as a motor based on the position of the wafer stage 116 measured by the laser interferometer 118 to control the wafer stage 116 in the XY plane. move to a predetermined position in

In the exposure apparatus 1, the reticle 113 and the wafer 115 are positioned so as to have a predetermined positional relationship with each other.

Then, each control for scan exposure is performed by the laser light source controller 102 , the wafer stage controller 120 , and the reticle stage controller 124 based on the synchronization signal from the main controller 103 .

Accordingly, the circuit pattern formed on the entire surface of the reticle 113 is transferred to the chip region of the wafer 115 .

Then, after moving the wafer 115 by a predetermined amount in the XY plane by the wafer stage 116 based on the step-and-scan method, the pattern formed on the reticle 113 is transferred to another chip area of the wafer 115 . Similarly, the operation of projection exposure is sequentially performed.

The information processing apparatus 20 according to the present embodiment is a computer as information processing means, and according to the exposure conditions in the exposure apparatus 1 , the learning capable of efficiently predicting the fluctuation of the imaging characteristics of the projection optical system 114 . can run the program.

In the exposure apparatus 1, the information processing apparatus 20 is configured to transmit and receive data related to the exposure apparatus 1 via the main control apparatus 103 connected by an interface cable.

And the information processing apparatus 20 can control the amount of variation of the imaging characteristic of the projection optical system 114 for each exposure condition of the exposure apparatus 1 within an allowable range.

Next, a predictive model of temporal change of the imaging characteristic of the projection optical system 114 used in the information processing apparatus 20 according to the present embodiment will be described.

Fig. 2 shows an example of the temporal change of the imaging characteristic at a predetermined image height of the projection optical system 114, that is, the amount of aberration (aberration amount) F generated by exposure by the exposure apparatus 1 .

At this time, examples of the aberration referred to herein include magnification, focus, distortion, astigmatism, spherical aberration, coma, wavefront aberration, and the like.

Further, at time t ₀ , it is assumed that the aberration amount F is the initial aberration amount F ₀ , and the difference between the aberration amount F and the initial aberration amount F ₀ , that is, FF ₀ , is defined as the aberration variation amount ΔF, and in general, the aberration variation amount ΔF is the upper limit. Each takes a different value.

As shown in Fig. 2, when the exposure operation is started when the exposure light emitted from the laser light source 101 passes through the projection optical system 114 at time t ₀ , the projection optical system 114 absorbs thermal energy from the exposure light. Accordingly, the aberration amount F fluctuates as time t passes.

Then, at time t ₁ when a predetermined time has elapsed from time t ₀ , the amount of aberration F reaches the amount of aberration in the maximum fluctuation (hereinafter referred to as a maximum amount of fluctuation aberration) F _m .

Thereafter, even when the exposure light passes through the projection optical system 114, the thermal energy absorbed by the projection optical system 114 and the thermal energy emitted by the projection optical system 114 reach equilibrium with each other, so the aberration amount F is It hardly changes from the maximum fluctuation amount F _m .

Then, when the exposure operation is stopped at time t ₂ , the thermal energy absorbed by the projection optical system 114 is released, so that the aberration amount F fluctuates so as to approach the initial aberration amount F ₀ again as time t elapses, and the time At t ₃ , the aberration amount F reaches the initial aberration amount F ₀ .

Here, when the amount of aberration at a predetermined time is F _k , the amount of aberration F _k+1 after exposure operation for the time Δt is the following using the maximum amount of variation F _m and the time constant T _h It is approximated as in Equation (1).

F _k+1 =F _m -(F _m -F _k )×exp(-Δt/T _h ) … (One)

Similarly, when the amount of aberration at a predetermined time is F _k , the amount of aberration F _k+1 after not performing the exposure operation for only the time Δt is obtained by using the initial amount of aberration F _o and the time constant T _c , and using the following formula (2) is approximated.

F _k+1 =F ₀ -(F _o -F _k )×exp(-Δt/T _c ) … (2)

The time constants T _h and T _c in each of the formulas (1) and (2) are equivalent to the time constant on the heat transfer characteristic of the projection optical system 114 and are values unique to the projection optical system 114, and furthermore, Different values depending on the type.

That is, in order to accurately predict the amount of change in the imaging characteristic of the projection optical system 114 depending on the exposure energy, that is, the amount of aberration change ΔF, it is necessary to measure for each projection optical system 114 and measure for each aberration to obtain an appropriate value. have.

In addition, for the maximum amount of variation F _m , using the parameter Q for determining the amount of aberration variation K per unit light amount (unit exposure energy) and the exposure energy incident on the projection optical system 114, can be calculated.

F _m =K×Q … (3)

At this time, the parameter Q is determined from conditions, such as exposure time, exposure amount, scanning speed, and exposure area|region information.

And as shown in Fig. 2, by modeling the temporal change of the aberration amount F of the projection optical system 114 into a curve 201 by a function shown in the above-mentioned equations (1) to (3) (hereinafter, "prediction model") ), the time change of the aberration amount F according to the exposure energy can be predicted.

From the above, in order to accurately predict the temporal change of the imaging characteristic of the projection optical system 114, it is necessary to appropriately determine the amount of aberration variation K per unit exposure energy for each exposure condition.

This is due to the following reasons. That is, the light (diffracted light) diffracted according to the effective light source distribution formed by the illumination optical system 104 and the circuit pattern of the reticle 113 changes according to the exposure conditions at the time of exposure. Moreover, the irradiation area of the pattern surface of the reticle 113 controlled by the variable blade 112 changes according to the exposure conditions at the time of exposure.

This is because, as a result, the energy density distribution of the exposure light incident on the projection optical system 114 changes, so the magnitude of the aberration variation ΔF of the projection optical system 114 and its image height dependence change.

At this time, the image height dependence here means that the amount of variation of the imaging characteristic (aberration) in the non-scan direction (X direction) and the scanning direction (Y direction) on the imaging plane of the projection optical system 114, that is, the amount of aberration variation ΔF, is different from each other. it means

As described above, in the information processing apparatus 20 according to the present embodiment, the predictive model expressed by the equations (1) and (2) is calculated for the temporal change of the imaging characteristic of the projection optical system 114 according to the exposure energy. is used to calculate correction factors such as F _m , F ₀ , T _h and T _c .

And in the information processing apparatus 20 according to the present embodiment, in order to appropriately and efficiently predict the correction coefficient of the predictive model according to the combination of exposure conditions of the product lot to be diversified in the lithography process, machine learning is used to estimate characterized by performing

Specifically, input data is created by modeling and quantitatively classifying the characteristics of the density distribution of exposure energy in the projection optical system 114 .

Next, the teacher data is created by actually measuring the temporal change of the imaging characteristic (aberration) of the projection optical system 114 at the time of exposure and calculating the correction coefficient of the predictive model.

Moreover, in a product lot, machine learning is performed by repeatedly creating the learning data comprised from input data and teacher data, ie, a learning model is created.

Then, by acquiring output data indicating the correction coefficient of the predictive model according to the actual exposure conditions from the created learning model, the temporal change of the imaging characteristic of the projection optical system 114 at the time of exposure can be predicted appropriately and efficiently.

Next, a method for quantitatively classifying the characteristics of the density distribution of exposure energy in the projection optical system 114 from the writing information of the circuit pattern formed on the reticle 113 will be described.

3A and 3B show an example of a circuit pattern drawn on the reticle 113 .

Specifically, by actually measuring the circuit pattern drawn on the reticle 113 or referring to design data, the pitch (interval) of the line and space (hereinafter referred to as L&S) and the line width ratio of the vertical and horizontal lines (HV ratio) ) to find

Here, the pitch of L&S is a factor that determines the diffraction angle of the diffracted light by the circuit pattern, and the HV ratio is a factor that determines the directivity of the diffracted light.

In the example shown in Fig. 3A, a vertically long vertical L&S pattern (hereinafter, sometimes referred to as a vertical pattern) 301 and a horizontally long horizontal L&S pattern (hereinafter referred to as a horizontal pattern) are cases There is) (303) is shown.

At this time, here, the longitudinal direction is the scanning direction (Y direction), and the horizontal direction is the non-scan direction (X direction).

In the vertical pattern 301, L&S are arranged along the horizontal direction so that the interval between adjacent wirings is the pitch 302.

Then, the pitch 302 and the areas V1, V2, V3, V4 and V5 of each vertical wiring are calculated from the writing information of the vertical pattern 301 .

In the horizontal pattern 303, L&S are arranged along the vertical direction so that the interval between adjacent wirings is the pitch 304.

Then, the pitch 304 and the areas H1, H2, H3, H4, and H5 of each horizontal wiring are calculated from the writing information of the horizontal pattern 303 .

In Fig. 3B, a rectangle 305 is displayed in the reticle 113 to indicate an exposure area to which the exposure light is actually irradiated.

The area to which the exposure light is actually irradiated in the vertical pattern 301 is inside the rectangle defined by the sides 306 and 307 of the rectangle 305, and is the sum of the areas of each vertical wiring included in the exposure area. , that is, the total area V is obtained from the areas V1 to V5.

Similarly, in the horizontal pattern 303 , the area to which the exposure light is actually irradiated is inside the rectangle defined by the sides 306 and 308 of the rectangle 305 , and is the sum of the areas of each horizontal wiring included in the exposure area. , that is, the total area H is obtained from the areas H1 to H5.

Then, in order to quantify the directivity of the diffracted light by the circuit pattern drawn on the reticle 113, the ratio between the horizontal wiring and the vertical wiring, that is, the HV ratio, is quantified using the following equation (4).

HV ratio = H/(H+V) … (4)

And in the information processing apparatus 20 according to this embodiment, diffraction by the circuit pattern formed in the reticle 113 based on the above-described L&S pitch and HV ratio using the table shown in Table 1 below. Classify the directivity of light.

For example, in a circuit pattern, when the pitch of the vertical pattern 301 and the horizontal pattern 303 is 600 nm, respectively, it is classified as "500 nm or more and less than 700 nm".

Moreover, in a circuit pattern, when the HV ratio of the vertical pattern 301 and the horizontal pattern 303 is 60 %, it is classified as "50% or more and less than 75%".

Next, a method for quantitatively classifying the characteristics of the density distribution of exposure energy in the projection optical system 114 from the effective light source distribution formed by the illumination optical system 104 will be described.

Specifically, the XY intensity ratio of the illumination light is obtained by actually measuring the light intensity in the effective light source distribution formed by the illumination optical system 104 .

That is, as shown in Fig. 1, through the beam shaping optical system 126 of the illumination optical system 104, the illumination light shaped into a predetermined shape (circular shape, annular shape, quadrupole shape, dipole shape, etc.) Measurement is performed using an effective light source measuring device 135 disposed on the wafer stage 116 . Thereby, the effective light source distribution of the illumination light can be acquired.

FIG. 4A is a diagram showing a mode in which an effective light source distribution is acquired by the effective light source measuring device 135. As shown in FIG.

As shown in Fig. 4A, on the imaging plane 402 of the effective light source distribution 401 in the projection optical system 114, a micro pinhole 403 having a diameter of several tens of mu m is arranged.

Then, the illumination light passing through the projection optical system 114 passes through the very small pinhole 403, and then has a light intensity distribution equivalent to the effective light source distribution 401, that is, in the effective light source distribution 404, the effective light source measuring device 135 has The light receiving unit 405 is irradiated.

The light receiving unit 405 is, for example, a two-dimensional CCD sensor in which CCD pixels are arranged in a 512x512 grid, and an output by photoelectric conversion is performed according to the brightness and darkness of the irradiated illumination light, so that the effective light source distribution 404 of the illumination light can be measured.

Fig. 4B is a plan view of the two-dimensional CCD sensor 405, and shows a state in which the effective light source distribution 404 of the annular illuminating light is irradiated.

Here, the light intensity measured by the CCD pixel (micro point light source) arranged at the positions X and Y is denoted by A(X, Y), and when A(X, Y) = 0, the corresponding CCD pixel It is assumed that no illumination light is irradiated to the

In addition, the light-receiving area of the two-dimensional CCD sensor 405 is divided into four diagonals of a 45 degree direction, a 135 degree direction, a 225 degree direction, and a 315 degree direction with respect to the optical axis.

Then, each region sandwiched by adjacent diagonal lines, that is, the X-direction right region 407 , the Y-direction upper region 408 , the X-direction left region 409 , and the Y-direction lower region 410 (hereinafter, respectively, the XR region) 407, YU region 408, XL region 409, and YD region 410) are defined.

In addition, the integrated values of the light intensities measured by the CCD pixels included in the XR, YU, XL, and _YD regions defined in this way are defined as L _XR , L _YU , L _XL and LYD , respectively.

And the XY intensity ratio in the effective light source distribution of the illumination light acquired by the two-dimensional CCD sensor 405 is calculated|required from Formula (5) shown below.

XY intensity ratio=(L _XL +L _XR )/(L _YU +L _YD +L _XL +L _XR ) … (5)

In the effective light source distribution 404 of the annular illumination light, L _XR , L _YU , L _XL , and _LYD are approximately equal to each other, so that the XY intensity ratio is close to 50%.

Fig. 4C shows a state in which the two-dimensional CCD sensor 405 is irradiated with illumination light (hereinafter referred to as X dipole illumination) having a dipole shape, that is, an effective light source distribution 412 in the X direction.

Fig. 4D shows a state in which the two-dimensional CCD sensor 405 is irradiated with an illumination light having a dipole shape, that is, an effective light source distribution 413 (hereinafter referred to as Y dipole illumination) in the Y direction.

In this case, the XY intensity ratio actually measured in the effective light source distribution 412 by X dipole illumination becomes a value close to 100% from Equation (5).

On the other hand, in the effective light source distribution 413 by Y dipole illumination, the XY intensity ratio actually measured becomes a value close to 0% from Equation (5).

And in the information processing apparatus 20 which concerns on this embodiment, the characteristic of the effective light source distribution of illumination light is quantitatively classified based on the XY intensity ratio mentioned above using the table shown in Table 2 below.

For example, when the XY intensity ratio is measured to be 55% in the effective light source distribution 404 of the annular illumination light, it is classified as "50% or more and less than 60%".

In addition, when the XY intensity ratio is measured to be 98% in the effective light source distribution 412 of the X dipole illumination, it is classified as "90% or more and 100% or less".

In addition, when the XY intensity ratio is measured to be 1% in the effective light source distribution 413 of Y dipole illumination, it is classified as "0% or more and less than 10%".

Next, the exposure conditions in the information processing apparatus 20 according to the present embodiment, the characteristics of the density distribution of the exposure energy in the projection optical system 114 , and the imaging characteristics of the projection optical system 114 , specifically the magnification Describe the relationship between the fluctuations of

5A and 5B schematically show an effective light source distribution 501 of illumination light and a circuit pattern 502 formed on the reticle 113 as examples of exposure conditions, respectively.

As shown in Fig. 5A, the effective light source distribution 501 is an effective light source distribution of X dipole illumination, and has a characteristic that the light intensity is strong in the X direction, that is, the XY intensity ratio is close to 100%.

Further, as shown in Fig. 5B, in the circuit pattern 502, the vertical L&S pattern is larger than the horizontal L&S pattern, that is, the HV ratio is less than 50%, and the diffracted light has a directivity to be scattered in the X direction.

FIG. 5C shows a state in which illumination light is irradiated on the pupil plane 503 of the projection optical system 114 .

Specifically, the 0th-order light 504 symmetrical in the X-direction is irradiated with the illumination light having the effective light source distribution 501 sandwiched between the YZ cross section parallel to the Y-direction including the optical axis AX of the projection optical system 114 . do.

In the vicinity of the 0th-order light 504 , the diffracted lights 505 and 506 generated by diffracting the illumination light by the vertical L&S pattern included in the circuit pattern 502 are irradiated.

Here, the light amount of the 0th-order light 504 is typically larger than that of the diffracted lights 505 and 506 .

And when exposure is continuously performed based on the density distribution of exposure energy in the projection optical system 114 formed from the effective light source distribution 501 and the circuit pattern 502, the 0th-order light 504, the diffracted light 505 and 506 are In the area to be irradiated, a large amount of heat is absorbed, thereby increasing the temperature.

Accordingly, the lens included in the projection optical system 114 is thermally deformed, that is, thermally expanded along the X direction.

FIG. 5D shows a chip region in which projection exposure is performed on the wafer 115 .

As described above, the lens included in the projection optical system 114 is thermally deformed along the X direction, so that, as shown in Fig. 5D, projection is made in the area 508 where the magnification error occurs in the X direction with respect to the designed chip area 507. exposure is performed.

That is, when the density of exposure energy increases in the X direction compared to the Y direction, the magnification fluctuation also becomes large in the X direction compared to the Y direction, and a direction difference (anisotropy) occurs in the magnification fluctuation.

6A and 6B schematically show an effective light source distribution 701 of illumination light and a circuit pattern 702 formed on the reticle 113 as other examples of exposure conditions, respectively.

As shown in Fig. 6A, the effective light source distribution 701 is an effective light source distribution of Y dipole illumination, and has a characteristic that the light intensity in the Y direction is strong, that is, the XY intensity ratio is close to 0%.

Further, as shown in Fig. 6B, in the circuit pattern 702, the horizontal L&S pattern is larger than the vertical L&S pattern, that is, the HV ratio is larger than 50%, and the diffracted light has a directivity to be scattered in the Y direction.

FIG. 6C shows a state in which illumination light is irradiated on the pupil plane 503 of the projection optical system 114 .

Specifically, the 0th-order light 704 symmetrical in the Y-direction is irradiated with the illumination light having the effective light source distribution 701 sandwiched between the XZ cross section parallel to the X-direction including the optical axis AX of the projection optical system 114 . do.

Then, in the vicinity of the 0th-order light 704 , the diffracted lights 705 and 706 generated by diffracting the illumination light by the horizontal L&S pattern included in the circuit pattern 702 are irradiated.

Here, typically, the light amount of the 0th-order light 704 is larger than that of the diffracted light 705 and 706 .

And when exposure is continuously performed based on the density distribution of exposure energy in the projection optical system 114 formed from the effective light source distribution 701 and the circuit pattern 702, the 0th-order light 704, the diffracted light 705 and 706 are In the area to be irradiated, a large amount of heat is absorbed, thereby increasing the temperature.

Accordingly, the lens included in the projection optical system 114 is thermally deformed, that is, thermally expanded along the Y direction.

FIG. 6D shows a chip region to be projected exposed on the wafer 115 .

As described above, the lens included in the projection optical system 114 is thermally deformed along the Y direction, so that, as shown in Fig. 6D, the designed chip area 707 is projected in the area 708 where the magnification error occurs in the Y direction. exposure is performed.

That is, when the density of exposure energy increases in the Y direction compared to the X direction, the magnification fluctuation also increases in the Y direction compared to the X direction, and a direction difference occurs in the magnification fluctuation.

As described above, in the information processing apparatus 20 according to the present embodiment, the XY intensity ratio is calculated and classified in the effective light source distribution formed by the illumination optical system 104 .

Further, in the circuit pattern 702 formed on the reticle 113, the L&S pitch and HV ratio are calculated and classified.

Then, input data is created by quantitatively classifying the characteristics of the density distribution of exposure energy from exposure conditions including the classified XY intensity ratio, L&S pitch, and HV ratio.

In other words, in the information processing apparatus 20 according to the present embodiment, input data is created by classifying exposure conditions in the exposure apparatus 1 with respect to anisotropy in a cross section parallel to the scanning direction and the non-scan direction. .

Next, by performing exposure under the above exposure conditions in the exposure apparatus 1, the temporal change of the imaging characteristic (aberration) of the projection optical system 114 is actually measured, and teacher data is created by calculating the correction coefficient of the predictive model. do.

Then, the learning data composed of the input data and the teacher data are repeatedly created, that is, the correlation between the characteristic amount of the density distribution of the exposure energy and the correction coefficient is repeatedly learned to create a learning model.

Accordingly, by acquiring output data representing the correction coefficient of the predictive model according to the actual exposure condition from the created learning model, the temporal change of the imaging characteristic of the projection optical system 114 at the time of exposure can be appropriately and efficiently predicted. .

Next, the processing actually performed in the information processing apparatus 20 according to the present embodiment will be described.

7 is a flowchart of processing performed in the information processing apparatus 20 according to the present embodiment.

First, in step S1, the feature amount of the effective light source distribution formed by the illumination optical system 104 is calculated.

For example, consider the case where the X dipole illumination shown in Fig. 5A is irradiated. At this time, the effective light source measuring device 135 measures the light intensity distribution equivalent to the effective light source distribution of the X dipole illumination, indicating that the light intensity is strong in the X direction (non-scan direction), for example, the XY intensity ratio is 98% calculated as being

Next, in step S2, the feature amount of the circuit pattern formed on the reticle 113 is calculated.

For example, consider a case in which the circuit pattern shown in Fig. 5B is formed on the reticle 113. As shown in Figs.

At this time, by measuring the circuit pattern formed on the reticle 113 by a reticle line width measuring device (not shown), for example, the L&S pitch is calculated to be 600 nm. In addition, it is calculated that the circuit pattern contains many vertical L&S patterns, for example, the HV ratio is 85%.

Accordingly, it can be seen that the circuit pattern formed on the reticle 113 has a directivity for generating diffracted light along the horizontal direction (X direction).

And in step S3, input data is created by classifying the feature amount of the density distribution of the exposure energy in the projection optical system 114 from the feature amount computed in steps S1 and S2.

An example of a table used when creating input data in step S3 is shown in Table 3 below.

From the table shown in Table 3, the XY intensity ratio = 98% calculated in step S1 is classified as "90% or more and 100% or less", and the L&S pitch = 600 nm calculated in step S2 is "500 nm or more and less than 700 nm" classified as

In addition, HV ratio = 85% calculated in step S2 is classified into "75% or more and 100% or less".

In this way, input data is created by classifying the feature amount of the density distribution of the exposure energy in the projection optical system 114 .

At this time, steps S1 to S3 shown above are referred to as input data creation process 801 .

Next, in step S4, a correction coefficient appropriate to the exposure conditions, that is, corresponding to the input data created in step S3 is estimated. Specifically, it is determined whether a correction coefficient is already included in the learning model.

When the learning model does not include a correction coefficient (No in step S4), the flow advances to step S5, and a correction coefficient of a preset design condition, that is, an initial value of the correction coefficient is selected.

On the other hand, when a correction coefficient is included in the learning model (Yes of step S4), it transfers to step S6, and a correction coefficient with the highest correlation with respect to the input data is selected (the correlation will be described later).

At this time, steps S4 to S6 shown above are referred to as a correction coefficient estimation step 802 .

Fig. 8A shows a predictive model 601 using the correction coefficients M _m , M ₀ , T _h and T _c of the design conditions selected in step S5.

At this time, in Fig. 8A, the magnification M is shown as the imaging characteristic of the projection optical system 114, that is, in the formulas (1) and (2), F _m and F ₀ are replaced with M _m and M ₀ , respectively.

As shown in FIG. 8A , the initial value of the magnification M, that is, the initial magnification is M ₀ , and the exposure light emitted from the laser light source 101 passes through the projection optical system 114 at time t ₀ to start the exposure operation. , then the magnification M represents the time change.

And after the magnification M reaches the maximum variable magnification M _m at time t ₁ , the magnification M hardly changes from the maximum variable magnification M _m .

Then, when the exposure operation is stopped at time t ₂ , the magnification M fluctuates so as to approach the initial magnification M ₀ again while the time t passes, and reaches the initial magnification M ₀ at the time t ₃ .

Note that, in the predictive model 601 , a direction difference does not occur with respect to the temporal change of the magnification M of the projection optical system 114 .

Next, in step S7, the temporal change of the magnification M of the projection optical system 114 is actually measured during exposure processing of the product lot under the exposure conditions shown in FIGS. 5A and 5B.

Fig. 8B shows an example of time change of the magnification M measured in step S7.

Specifically, the temporal changes M _X1 to M _X10 of the magnification M measured at the predetermined X coordinate of the projection optical system 114 and the temporal changes M _Y1 to M _Y10 of the magnification M measured at the predetermined Y coordinate are displayed. has been

Next, in step S8, the correction coefficient of the predictive model represented by Formula (1) and Formula (2) with respect to the data measured in step S7 is computed.

Specifically, with respect to the temporal change M _X1 to MX7 (exposure characteristics) of the magnification M in the X direction from time t ₀ to t ₁ , by fitting the predictive model represented by Formula (1). The correction factors M _X and T _hX are calculated. Then, the time change M _X8 to M _X10 (non-exposure characteristic) of the magnification M in the X direction from time t ₂ to time t ₃ by fitting with the predictive model represented by the formula (2), the correction coefficient M Calculate ₀ and T _cX .

Similarly, with respect to the temporal change M _Y1 to M _Y7 (exposure characteristics) of the magnification M in the Y direction from time t ₀ to time t ₁ , the correction coefficient M _Y by fitting with the predictive model represented by Equation (1). and T _hY . Then, the temporal change M _Y8 to M _Y10 (non-exposure characteristic) of the magnification M in the Y direction from time t ₂ to time t ₃ is fitted with the predictive model represented by Equation (2), whereby the correction coefficient M Calculate ₀ and T _cY .

The predictive models obtained in this way are respectively indicated as predictive models 602 and 603 in Fig. 8B.

In addition, examples of the correction coefficients M _X , M _Y , T _hX , T _hY , T _cX and T _cY calculated in the above step S8 are shown in Table 4 below.

At this time, here, for each of the maximum variation magnifications M _X and M _Y , the ratio of the deviation to the initial magnification M ₀ , that is, (M _X -M ₀ /M ₀ and (M _Y -M ₀ /M ₀ ) is expressed. are doing

In this way, from the table shown in Table 4, teacher data corresponding to the input data shown in Table 3 can be obtained.

At this time, steps S7 and S8 shown above will be referred to as a teacher data creation process 803 .

Next, in step S9, the correlation between the feature amount of the density distribution of exposure energy in the projection optical system 114 as input data and the correction coefficient as the teacher data and output data is calculated from the prediction error in the prediction model. do.

Fig. 8C is a schematic diagram showing the manner in which the above-described correlation is calculated in step S9.

Specifically, in Fig. 8C, a plurality of measurement points obtained by measuring the temporal change of the magnification M of the projection optical system 114 under a predetermined exposure condition and a predictive model 604 using a predetermined correction coefficient are displayed. .

Here, in step S9, the value with the largest error with the prediction model 604 (difference with respect to the measurement point most distant from the prediction model) among the acquired plurality of measurement points is set as the prediction error D, and the prediction error D is predicted. Record as the correlation of model 604 .

That is, in the above example, for the plurality of measurement points measured in step S7, the prediction error D is calculated from each of the prediction model 601 selected in step S5 and the prediction models 602 and 603 obtained in step S8, Record as a correlation diagram.

At this time, for example, the correlation degree calculated in each of the prediction models 602 and 603, that is, the value of the prediction error D is shown in Table 4.

Here, with respect to the correlation, that is, the prediction error D, the ratio of the deviation to the magnification M _calc calculated from the prediction model of the magnification M _meas at the measurement point when the prediction error D is calculated, that is, (M _meas -M _calc ) It is represented by /M _calc .

This makes it possible to quantitatively learn from the input data according to the exposure conditions illustrated in Table 3, the teacher data illustrated in Table 4, and the degree of correlation.

At this time, step S9 shown above is called a learning process 804.

Then, when the exposure processing is performed under the same exposure conditions in the next and subsequent times, the correction coefficient can be estimated based on the correlation data obtained up to this time.

Further, in step S10, it is determined whether or not a product lot is to be produced repeatedly under the same exposure conditions.

And when production is performed (Yes of step S10), it returns to step S4, and when not producing (No of step S10), a process is complete|finished.

Returning to step S4, the correction coefficient estimation step 802 is executed again. That is, the correction coefficient of the predictive model is estimated in step S4.

At this time, the correction coefficient learned in step S9 until the last time is included in the learning model (Yes of step S4).

Therefore, after moving to step S6, the correction coefficient with the smallest prediction error D, ie, the highest correlation, is selected from the correction coefficients accumulated in the learning model in step S6.

And by shifting to step S7 - S10, learning is repeatedly performed until the production of the product lot under the same exposure conditions is complete|finished.

In this way, during the exposure process of the product lot, the time change of the magnification M of the projection optical system 114 for each exposure condition is repeatedly machine-learned and the correction coefficient is accumulated, so that the magnification M changes with time in the X direction and the Y direction. , it is possible to increase the estimation accuracy of the correction coefficient.

Then, in the exposure apparatus 1, when correcting the magnification, distortion, astigmatism, spherical aberration, coma, and wavefront aberration of the projection optical system 114 based on the estimated correction coefficient, the field lens 127 is moved over time. move

In addition, when correcting the focus of the projection optical system 114 based on the estimated correction coefficient, the position of the wafer stage 116 in the optical axis direction is changed with time.

As described above, in the information processing apparatus 20 according to the present embodiment, the exposure conditions in the exposure apparatus are input data, and the correction coefficient of the predictive model for predicting the temporal change of the imaging characteristics of the projection optical system 114 is set to the teacher data. I am creating a learning model with

And even if the number of exposure conditions increases, such as an increase in the type of original plate, by acquiring output data providing a correction coefficient of the predictive model from the created learning model, it is possible to efficiently predict the temporal change of the imaging characteristic of the projection optical system.

In addition, although the time change of the magnification M was demonstrated as a fluctuation|variation in the imaging characteristic of the projection optical system 114 above, it is not limited to this. For example, the information processing apparatus 20 according to the present embodiment can be applied to focus, distortion, astigmatism, spherical aberration, coma, wavefront aberration, and the like as imaging characteristics of the projection optical system 114 .

Moreover, although the characteristic amount of the density distribution of exposure energy by X dipole illumination shown in FIG. 5A - FIG. 5D was demonstrated above, it is not limited to this. For example, the information processing apparatus 20 according to the present embodiment can also be applied to the characteristic amount of the density distribution of exposure energy by Y dipole illumination shown in Figs. 6A to 6D.

[Second embodiment]

Fig. 9 shows a block diagram of an exposure processing system 1000 in which an information processing apparatus 220 according to the second embodiment is installed.

An information processing apparatus 20 according to the first embodiment is a so-called stand-alone type apparatus connected to the main control apparatus 103 by an interface cable in the exposure apparatus 1 as shown in FIG.

On the other hand, as shown in FIG. 9 , the information processing apparatus 220 according to the present embodiment includes a plurality of exposure apparatuses 1001 and 1002 via a network cable 1003 in the exposure processing system 1000 . It is a so-called online type of device that is connected to the device.

9, the information processing device 220 according to the present embodiment is also connected to a reticle pattern measuring device 1005 for measuring the circuit pattern of the reticle 113 via a network cable 1003. .

That is, the information processing apparatus 220 according to the present embodiment is a computer as an information processing means, and can perform machine learning regarding the correction coefficient of the predictive model based on the learning data in each of the plurality of exposure apparatuses.

Specifically, input data is created from the data of the effective light source distribution measured in each exposure apparatus and the data of the circuit pattern measured by the reticle pattern measuring device 1005 .

Then, teacher data is created by calculating a correction coefficient of the predictive model from the measured values of the imaging characteristics of the projection optical system 114 obtained in each exposure apparatus, and correlation data between the input data and the teacher data is calculated and accumulated. .

In this way, by storing the correlation data for each exposure condition learned for a plurality of exposure apparatuses in the storage device 30 and creating a learning model, it becomes possible to further increase the estimation accuracy of the correction coefficient.

As described above, in the information processing apparatus 220 according to the present embodiment, the exposure conditions in the exposure apparatus are input data, and the correction coefficient of the predictive model for predicting the temporal change of the imaging characteristics of the projection optical system 114 is set to the teacher data. I am creating a learning model with

And even if the number of exposure conditions increases, such as an increase in the kind of original plate, the output data which provides the correction coefficient of a predictive model can be acquired from the created learning model.

Furthermore, in the information processing apparatus 220 according to the present embodiment, by creating a learning model using the learning data in the plurality of exposure apparatuses, the temporal change of the imaging characteristic of the projection optical system can be predicted more efficiently.

According to the present invention, it is possible to provide an information processing apparatus capable of efficiently predicting temporal changes in imaging characteristics of a projection optical system installed in an exposure apparatus.

[Production method]

Next, a method of manufacturing an article using the exposure apparatus provided with the information processing apparatus according to any one of the first and second embodiments will be described.

Articles are semiconductor devices, display devices, color filters, optical components, MEMS, and the like.

For example, a semiconductor device is manufactured by passing through a post process including a front process for making a circuit pattern on a wafer, and a manufacturing process for making the circuit chip made in the front process complete as a product.

The pre-process includes an exposure process of exposing a wafer coated with a photosensitive agent using an exposure apparatus equipped with an information processing apparatus according to any one of the first and second embodiments, and a developing process of developing the photosensitive agent.

Then, an etching process, an ion implantation process, etc. are performed using the pattern of the developed photosensitizer as a mask, and a circuit pattern is formed on the wafer.

A circuit pattern composed of a plurality of layers is formed on the wafer by repeating these steps of exposure, development, and etching.

In the post-process, dicing is performed on the wafer on which the circuit pattern is formed, and the chip mounting, bonding, and inspection processes are performed.

A display device is manufactured by passing through the process of forming a transparent electrode. The step of forming the transparent electrode is a step of applying a photosensitive agent on a glass wafer on which a transparent conductive film is deposited, and the photosensitive agent is applied using an exposure apparatus equipped with an information processing device according to any one of the first and second embodiments. and exposing a glass wafer. Moreover, the process of forming a transparent electrode includes the process of developing the exposed photosensitizer.

According to the method for manufacturing an article according to the present embodiment, it is possible to manufacture an article of higher quality and higher productivity than before.

As mentioned above, although preferred embodiment was described, it is not limited to these embodiment, Various deformation|transformation and change are possible within the scope of the summary.

In addition, although the information processing apparatus according to this embodiment has been described above, the information processing method shown above, a program for implementing the method, and a computer-readable recording medium on which the program is recorded are also within the scope of this embodiment. included in

Claims (11)

An information processing apparatus for predicting temporal changes in imaging characteristics of a projection optical system installed in an exposure apparatus using a learning model acquired by machine learning, comprising:
The input data of the learning model is created by classifying at least one of the effective light source distribution in the exposure apparatus and the pattern drawn on the original plate with respect to anisotropy in a cross section parallel to the scanning direction and the non-scan direction. information processing device.
The method of claim 1,
The teacher data of the learning model is created by calculating a correction coefficient by measuring the temporal change of the imaging characteristic of the projection optical system and fitting it to a predictive model.
The method of claim 1,
and the imaging characteristic includes at least one of magnification, focus, distortion, astigmatism, spherical aberration, coma, and wavefront aberration.
The method of claim 1,
The information processing device,
creating input data by classifying at least one of the effective light source distribution in the exposure apparatus and the pattern drawn on the original plate with respect to anisotropy in a cross section parallel to the scanning direction and the non-scan direction;
Teacher data is created by measuring the temporal change of the imaging characteristic of the projection optical system and calculating a correction coefficient by fitting it to a predictive model;
and creating the learning model by performing learning by calculating a correlation between the measured temporal change of the imaging characteristic and each of the teacher data and the output data for estimating the correction coefficient.
5. The method of claim 4,
and the information processing device calculates, as the correlation degree, a prediction error of a measurement point most distant from the prediction model among measurement points of the imaging characteristic.
5. The method of claim 4,
The information processing apparatus generates the learning model by performing the learning for a plurality of the exposure apparatuses.
According to claim 1,
The information processing apparatus is characterized in that the information processing apparatus predicts the temporal change of the imaging characteristics of the projection optical system provided in each of a plurality of the exposure apparatuses using the learning model.
An exposure apparatus for exposing the substrate so as to transfer a pattern drawn on the original plate to the substrate,
An exposure apparatus comprising the information processing apparatus according to any one of claims 1 to 7.
A step of exposing the substrate using the exposure apparatus according to claim 8;
developing the exposed substrate;
and manufacturing the article from the developed substrate.
An information processing method comprising the step of estimating temporal change in imaging characteristics of a projection optical system installed in an exposure apparatus using a learning model acquired by machine learning.
A computer-readable recording medium on which a program for causing a computer to process information is recorded,
A computer-readable recording medium having a program recorded thereon, characterized in that the computer executes a step of predicting the temporal change of the imaging characteristics of the projection optical system installed in the exposure apparatus using a learning model acquired by machine learning.

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