JP2017215481A - Determination method of exposure condition, program, information processing device, exposure device, and article production method - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a method advantageous for exposure of a substrate with a projection optical system having a 4nθ system aberration.SOLUTION: A determination method of determining an exposure condition in an exposure device that exposes a substrate by projecting a pattern of an original plate on the substrate with a projection optical system includes: a setting step of setting a component represented by f(r)*cos(4nθ) and f(r)*sin(4nθ) with (r,θ) as a polar coordinate, n as a natural number and f(r) as a function of r, among a plurality of components of a wave front aberration of the projection optical system; and a determination step of setting an exposure condition such that a focus sensitivity that is a variation of a focus position due to the component is in a target range.SELECTED DRAWING: Figure 4

Description

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

  A display such as a liquid crystal panel or an organic EL panel is manufactured through a lithography process in which a pattern of an original (also referred to as a mask or a reticle) is transferred to a substrate by an exposure apparatus (the substrate is exposed through the pattern). In recent years, there has been a growing demand for higher definition for displays incorporated in smartphones or tablet terminals, and therefore, high resolution is required for exposure apparatuses.

  When the numerical aperture of the projection optical system is NA, the wavelength of the exposure light is λ, and the constant (k1 factor) depending on the exposure process is k1, the resolving power of the exposure apparatus is expressed by the following equation.

(Resolution) = k1 × λ / NA (1)
According to equation (1), in order to improve the resolving power of the exposure apparatus, there are a method of increasing the numerical aperture NA of the projection optical system of the exposure apparatus and a method of shortening the exposure wavelength λ. The numerical aperture of the projection optical system of an exposure apparatus for manufacturing a current display is about 0.08 to 0.10, and the wavelength of exposure light ranges from g-line (wavelength 436 nm) to i-line (wavelength 365 nm) of an ultrahigh pressure mercury lamp. It is a wavelength until. Under these conditions, the resolving power of the exposure apparatus reaches a line width of about 2 μm. Whether increasing the numerical aperture of the projection optical system or shortening the exposure wavelength, it is necessary to suppress the aberration of the projection optical system. As an aberration expression method, an expression using a Zernike polynomial is generally used. The spherical aberration component is expressed in the form of f (r), the coma aberration component is in the form of f (r) · cos θ and f (r) · sin θ, and the astigmatism component is f (r) · cos 2θ and f (r ) · Expressed in the form of sin2θ. Furthermore, there are f (r) · cos 3θ and f (r) · sin 3θ component (aberration of 3θ component), f (r) · cos 4θ and f (r) · sin 4θ component (aberration of 4θ component), and the like. The aberration of the projection optical system is expressed by the linear combination of many components such as these. As is well known, the aberration of the projection optical system affects the shape and size of the pattern transferred to the substrate.

  When the original pattern is actually transferred to the substrate using the exposure apparatus, it is necessary to determine the exposure conditions. The exposure conditions include, for example, an original pattern, illumination conditions, numerical aperture and aberration of the projection optical system, and the exposure conditions such that a predetermined evaluation index such as a process margin becomes an optimum value or a value within a target range. It is determined. Patent Document 1 describes that a mask parameter, an illumination parameter, and an aberration parameter are optimized.

JP 2013-16710 A

  In designing the projection optical system, it is necessary to simultaneously satisfy the constraints on the dimensions of various components of the projection optical system, the overall dimensions of the projection optical system, the processing shape of the optical element, and the like. Even when the projection optical system is designed while considering both the satisfaction of these constraints and the reduction of aberration, there are not a few cases in which aberrations peculiar to the type of the projection optical system remain. Residual aberrations are factors that degrade imaging performance, such as reducing the contrast of an image obtained by projecting an original pattern onto a substrate, or changing the resolution position. In the case of an exposure apparatus for manufacturing a display, the configuration of the projection optical system is often an Offner type or a Dyson type. However, when a projection optical system having a higher NA than before is designed using these projection optical systems, there are various types. Aberrations may remain. Among these aberrations, coma, astigmatism, and distortion can be reduced by using a correction optical element such as a correction plate disposed inside the projection optical system. There is no simple way to adjust the amount of aberration for system aberrations. The aberration of the 4nθ system causes a shift between the focal position of the vertical pattern and the horizontal pattern and the focal position of the oblique pattern, and thus causes a difference in the line width of the pattern depending on the direction. This is not preferable. The aberration of 4nθ system means all or part of aberrations such as 4θ system, 8θ system, and 12θ system.

  An object of the present invention is to provide a method advantageous for exposure of a substrate by a projection optical system having, for example, a 4nθ aberration.

  One aspect of the present invention relates to a determination method for determining an exposure condition in an exposure apparatus that exposes the substrate by projecting an original pattern onto the substrate by a projection optical system, and the determination method includes: Of a plurality of components of wavefront aberration, f (r) · cos (4nθ) and f (r) · sin (4nθ) with polar coordinates, n as a natural number, and f (r) as a function of r A setting step for setting a component to be expressed, and a determination step for determining an exposure condition so that a focus sensitivity, which is a change amount of a focus position due to the component, falls within a target range.

  According to the present invention, for example, a method advantageous for exposure of a substrate by a projection optical system having a 4nθ aberration is provided.

The figure which shows the structure of the exposure apparatus of one Embodiment of this invention. Diagram illustrating the variation of the focus position of the projection optical system with which is one r ⁴ × cos4θ aberration component of 4nθ system (focus sensitivity). The figure which shows the structure of the information processing apparatus of one Embodiment of this invention. The figure which shows the flow of the determination method of the exposure conditions performed by information processing apparatus according to a determination program. The figure which illustrates a defocus characteristic. The figure which illustrates the relationship between a numerical aperture and the variation | change_quantity (focus sensitivity) of a focus position. The figure which illustrates the relationship between a numerical aperture and a focal depth.

  Hereinafter, exemplary embodiments of the present invention will be described with reference to the accompanying drawings.

  FIG. 1 shows the configuration of an exposure apparatus 1 according to one embodiment of the present invention. The exposure apparatus 1 can include an illumination optical system 100, a projection optical system 200, an original plate drive mechanism MD, a substrate drive mechanism SD, a control unit 300, a console 400, and a calculation unit 500. The exposure apparatus 1 exposes the substrate P by illuminating the original M with the illumination optical system 100 and projecting an image of the pattern of the original M onto the substrate P with the projection optical system 200. The exposure apparatus 1 can be configured, for example, as a scanning exposure apparatus that transfers the pattern of the original M onto the substrate P while scanning and driving the original with the original driving mechanism MD and driving the substrate with the substrate driving mechanism SD.

  The illumination optical system 100 can include a light source 101, a wavelength filter 102, an ND filter 103, an optical integrator 104, a condenser lens 105, a beam splitter 106, a light amount detector 107, a masking blade 108, a lens 109, and a reflecting mirror 110. The light source 101 generates light such as ultraviolet light. The light source 101 can include, for example, an ultrahigh pressure mercury lamp or an excimer laser. The light emitted from the light source 101 proceeds in the direction of the arrow. The wavelength filter 102 transmits light in a predetermined wavelength range as exposure light, and blocks other light. The wavelength filter 102 has a function of changing the wavelength of light to be transmitted, whereby the wavelength of exposure light irradiated on the substrate P can be changed. The wavelength of the exposure light may be changed by controlling the light source 101.

  The ND filter 103 adjusts the intensity of exposure light emitted from the light source 101 and transmitted through the wavelength filter 102. The optical integrator 104 equalizes the illuminance distribution of the exposure light that illuminates the original M. The condenser lens 105 condenses the exposure light that has passed through the optical integrator 104. Part of the exposure light transmitted through the condenser lens 105 is split by the beam splitter 106 and enters the light amount detector 107. The light quantity detector 107 is a monitor that confirms that the illuminance of the exposure light that illuminates the original M is within a predetermined range. The masking blade 108 defines the illumination range of the original M. The lens 109 images the illumination range defined by the masking blade 108b on the original M. The reflecting mirror 110 bends the optical axis of the exposure light, and the original M is illuminated by the exposure light from the reflecting mirror 110. The original M is driven in a direction perpendicular to the optical axis by the original driving mechanism MD.

  A pattern is drawn on the pattern surface of the original M, and an image of this pattern is projected onto the substrate P by the projection optical system 200. That is, an image of the pattern of the original M is formed on the substrate P. The projection optical system 200 can be, for example, an Offner projection optical system mainly composed of a concave mirror and a convex mirror, but may be another projection optical system. The projection optical system 200 can include a correction optical element 201, a trapezoidal mirror 202, a concave mirror 203, a convex mirror 204, and an NA stop 205. For example, the correction optical element 201 corrects at least one of coma, astigmatism, and distortion. In FIG. 1, one correction plate is shown as the correction optical element 201, but the same number of correction plates as the number of aberrations to be corrected can be arranged. As a result of correction by the correction optical element 201, the main component of the residual aberration of the projection optical system 200 is a 4nθ component, and the other components can be reduced to a level that can be almost ignored.

  The trapezoidal mirror 202 reflects the exposure light transmitted through the correction optical element 201 toward the concave mirror 203. The exposure light reflected by the concave mirror 203 is reflected by the convex mirror 204 and travels toward the concave mirror 203. An NA stop 205 is disposed in the vicinity of the convex mirror 204, and the numerical aperture of the projection optical system 200 can be changed by changing the diameter of the opening of the NA stop 205 by a driving mechanism (not shown). The exposure light reflected by the convex mirror 204 reaches the substrate P after being reflected by the concave mirror 203 and the trapezoidal mirror 202. The substrate P is driven by the substrate driving mechanism SD in a direction parallel to the optical axis (z-axis direction) and a direction perpendicular to the optical axis. The defocus amount can be changed by moving the substrate in a direction parallel to the optical axis by the substrate driving mechanism SD.

  The control unit 300 controls the overall operation of the exposure apparatus 1. The console 400 is used by an operator to give commands and information to the exposure apparatus 1. The operator can input information such as the numerical aperture of the projection optical system 200, the wavelength of exposure light, and the transmittance of the ND filter 103 to the console 400, for example. Information input to the console 400 is sent to the control unit 300. The control unit 300 can determine the wavelength of the exposure light by controlling the wavelength filter 102, control the transmittance of the ND filter 103 by controlling the ND filter 103, and project by controlling the NA stop 205. The numerical aperture of the optical system 200 is controlled.

  Exposure conditions (for example, the wavelength of exposure light and the numerical aperture of the projection optical system 200) determined by a determination method described later are provided to the control unit 300 through the console 400 or through a communication path (not shown). 300 can execute the exposure of the substrate P according to the exposure conditions. Alternatively, the calculation unit 500 may execute a determination method described later, thereby determine an exposure condition, and perform exposure of the substrate P according to the exposure condition.

Although the wavefront aberration of the projection optical system 200 may have a plurality of components, examples of components that cannot be corrected by the correction optical element 201 include 4nθ-system components. Here, when (r, θ) is a polar coordinate, n is a natural number, and f (r) is a function (wavefront function) of a radial radius r, a component of 4θn system is
f (r) · cos (4nθ) and f (r) · sin (4nθ)
Can be expressed as Among the 4nθ components, particularly n = 1, that is,
f (r) · cos (4θ) and f (r) · sin (4θ)
The component expressed as can cause a line width difference of a pattern formed on the substrate P through exposure.

  The focus position (for example, the best focus position) differs between an aberration-free projection optical system in which no 4nθ system component exists and an actual projection optical system in which a 4nθ system component exists. In other words, the focus position of the actual projection optical system in which the 4nθ system component exists changes with respect to the focus position of the aberration-free projection optical system in which the 4nθ system component does not exist. The amount of change in the focus position of the projection optical system due to the 4nθ system component can vary depending on the exposure conditions (for example, the wavelength of exposure light and the numerical aperture of the projection optical system). Therefore, the amount of change in the focus position of the projection optical system due to the 4nθ system component is referred to as focus sensitivity. For example, an exposure condition in which the amount of change in the focus position of the projection optical system due to a 4nθ system component is small is an exposure condition in which the sensitivity to focus is small and the line width difference caused by the difference in the direction of the pattern to be formed is small. . On the other hand, an exposure condition in which the amount of change in the focus position of the projection optical system due to the 4nθ system component is large is an exposure condition in which the sensitivity to focus is large and the line width difference caused by the difference in the direction of the pattern to be formed is large. .

FIG. 2 illustrates the amount of change in the focus position (focus sensitivity) of the projection optical system having r ⁴ × cos 4θ, which is one of the aberration components of the 4nθ system. In FIG. 4, the horizontal axis represents the k1 factor, which corresponds to k1 in Equation (1). In FIG. 4, the vertical axis indicates the amount of change in focus position (focus sensitivity) for a pattern in a predetermined direction when a component (aberration) of r ⁴ × cos 4θ is given to a projection optical system without aberration. Show. FIG. 4 shows the amount of change in the focus position with respect to six types of exposure conditions configured by combinations of the line widths of the three types of patterns A, B, and C and the two types of exposure wavelengths λa and λb. Has been. Here, the amount of change in the focus position is obtained by changing the numerical aperture NA of the projection optical system. Moreover, the illumination condition which is one of the exposure conditions is annular illumination.

  As can be seen from FIG. 2, there is a condition in which the change amount of the focus position is almost zero in each curve. This is because the 0th-order diffracted light and the 1st-order diffracted light of the exposure light from the original plate are affected by aberrations when they enter the pupil plane of the projection optical system, and the influence that the focus position changes in the light traveling direction, This is a result of canceling out the effect of changing in the opposite direction. In the case of annular illumination, it varies depending on the annular ratio and the magnitude of σ, but there is a condition that the amount of change in the focus position is almost zero when the k1 factor is near 0.35 to 0.45. Even in the case of normal illumination, it is possible to find a condition where the amount of change in the focus position is almost zero. FIG. 2 shows a projection optical system having a 4θ system component (aberration), but there is a condition that the amount of change in the focus position is almost zero for a projection optical system having a 4nθ system component.

  FIG. 3 shows the configuration of an information processing apparatus 600 according to an embodiment of the present invention. The information processing apparatus 600 is configured as an apparatus that determines exposure conditions. In one example, the information processing apparatus 600 is configured to be communicable with the exposure apparatus 1 and can be configured to provide the determined exposure condition to the exposure apparatus 1 by communication. The exposure conditions determined by the information processing apparatus 600 may be provided to the exposure apparatus 1 via an operator. Alternatively, the function of the information processing apparatus 600 may be incorporated in the calculation unit 500.

  The information processing apparatus 600 can be configured by a general purpose or dedicated computer. The information processing apparatus 600 can include a CPU 10, an input unit 20, an output unit 30, a memory 40, a communication unit 50, and a program memory 60. The input unit 20 is a device for inputting information, and may include, for example, a keyboard, a pointing device, a touch panel, a touch pad, a media driver, and the like. The output unit 30 is a device for outputting information, and can include, for example, a display, a printer, a media driver, and the like. A part of the device constituting the input unit 20 and the device constituting the output unit 30 may be common. The memory 40 is a memory that provides a work area for calculation. The communication unit 50 is a device for communicating with the exposure apparatus 1 and / or other external devices, for example. The program memory 60 is a memory that stores the determination program 62. The determination program 62 may be stored in a medium readable by a device such as a computer and provided to the information processing apparatus 600. The information processing apparatus 600 incorporating the determination program 62 or the information processing apparatus 600 that operates according to the determination program 62 constitutes an apparatus that determines the exposure conditions according to the determination program 62. In addition, the information processing apparatus 600 in which the determination program 62 is incorporated or the information processing apparatus 600 that operates according to the determination program 62 executes a determination method that determines the exposure conditions according to the determination program 62.

  FIG. 4 shows a flow of an exposure condition determination method executed by the information processing apparatus 600 according to the determination program 62. In step S301, the information processing apparatus 600 sets a 4nθ system component (aberration component) as the wavefront aberration of the projection optical system 200 based on information input through the input unit 20. Here, among the plurality of wavefront aberration components of the projection optical system 200, the spherical aberration component, the coma aberration component, the astigmatism component, and the like are typically negligible by adjustment of the correction optical element 201. Can be ignored. Therefore, 0 can be set for spherical aberration components, coma aberration components, astigmatism components, and the like. Here, the spherical aberration component is expressed by f (r), the coma aberration component is expressed by f (r) · cos θ and f (r) · sin θ, and the astigmatism component is f (r) · cos 2θ and f ( r) · sin 2θ can be expressed. Of the 4nθ system components, components other than the 4θ system components (components such as the 8θ system and 12θ system) may be negligible. In this case, only the 4θ system component is set among the 4nθ system components. Among the system components, 0 can be set for components other than the 4θ system components. By setting the components other than the 4nθ system to 0, the calculation load can be reduced.

  In step S <b> 302, the information processing apparatus 600 sets initial exposure condition candidates and calculation conditions based on information input through the input unit 20. The initial exposure condition candidate can be given by a combination of initial values of a plurality of parameters relating to exposure. Examples of the plurality of parameters include pattern specifications, the numerical aperture of the projection optical system 200, the wavelength of exposure light, and illumination conditions. The specification of the pattern is information regarding the pattern of the original M, and may include, for example, the line width and arrangement pitch of the line pattern, the dimension of the hole pattern, and the like. When the original M is a phase shift mask, the pattern specification can include the transmittance of the light shielding part and the phase difference formed by the light shielding part and the transmission part. The numerical aperture of the projection optical system 200 is as described above. The wavelength of the exposure light can be adjusted by the wavelength filter 102 and / or the light source 101. The exposure light may be light having a single wavelength or light having a broad wavelength spectrum distribution. When the exposure light is a light having a broad wavelength spectrum distribution, for example, the centroid wavelength may be used, or a weighted integration (weighted average) proportional to the intensity of each individual wavelength after calculation is performed for each individual wavelength. ) May be performed.

  The calculation condition is a condition for designating how to calculate while changing the values of a plurality of parameters constituting the exposure condition candidate in the following steps S303 to S306. In other words, the calculation condition is a condition for designating all exposure conditions to be calculated in steps S303 and S304. The calculation condition can include, for example, a condition for designating how to calculate while changing the numerical aperture of the projection optical system 200.

  In step S <b> 303, the information processing apparatus 600 changes the defocus amount within a range including the best focus position of the projection optical system 200 while changing the characteristics of the image (image characteristics) formed on the surface of the substrate P by the projection optical system 200. ). For example, optical calculation software or a lithography simulator can be used for calculating the image characteristics. The image characteristic may be at least one of, for example, contrast of an optical image formed by the projection optical system 200, NILS (Normalized Image Log-Slope), an optical image CD, a resist CD, and the like. Thereby, a defocus characteristic indicating a relationship between the defocus amount and the image characteristic is obtained. For example, when the defocus characteristic is plotted with the defocus amount as the horizontal axis and the index value indicating the image characteristic as the vertical axis, and the index value is plotted, the curve is an even function curve symmetrical about the defocus amount. Can be expressed as The peak position (position indicating the maximum value or minimum value) of this curve can be defined as the best focus position (defocus amount = 0) of the projection optical system 200 having a 4nθ system component (aberration).

  In step S304, the information processing apparatus 600 calculates a focus position change amount (focus sensitivity) based on the defocus characteristic obtained in step S303. Here, the difference between the best focus position when the projection optical system 200 has no aberration and the best focus position when the projection optical system 200 has a 4nθ system component (aberration) is the amount of change in focus position (focus sensitivity). ).

  In step S305, the information processing apparatus 600 determines whether steps S303 and S304 have been completed for all exposure condition candidates specified by the calculation conditions set in step S302, and branches the process. If steps S303 and S304 have been completed for all parameter values, the information processing apparatus 600 proceeds to step S307, and otherwise proceeds to step S306. In step S306, the information processing apparatus 600 changes the parameter value according to the calculation conditions set in step S302 (for example, changes the parameter value indicating the numerical aperture of the projection optical system), and returns to step S303.

  In step S307, the information processing apparatus 600 determines the plurality of exposure condition candidates based on a plurality of focus sensitivities (amount of change in focus position) obtained for each of the plurality of exposure condition candidates by repeating steps S303 to S306. One of them is determined as an exposure condition. Here, when there is one exposure condition candidate whose focus sensitivity falls within the target range, the information processing apparatus 600 can determine the exposure condition candidate as the exposure condition. On the other hand, when the focus sensitivity falls within the target range with respect to at least two exposure condition candidates among the plurality of exposure condition candidates for which the focus sensitivity is calculated, the information processing apparatus 600 displays the at least two exposure condition candidates. One of the above can be determined as the exposure condition.

  In one example, the information processing apparatus 600 can determine one of the at least two exposure condition candidates as an exposure condition based on a process margin of a pattern formed under the at least two exposure condition candidates. In another example, the information processing apparatus 600 uses one of the at least two exposure condition candidates as the exposure condition based on a depth of focus (DOF) under the at least two exposure condition candidates. Can be determined as In still another example, the information processing apparatus 600 uses one of the at least two exposure condition candidates as an exposure condition based on a MEEF (Mask Error Enhancement Factor) under the at least two exposure condition candidates. Can be determined.

  The information processing apparatus 600 is understood as an information processing apparatus having a setting unit that executes step S301 to set a 4nθ-system component (aberration) and a determination unit that executes steps S302 to S307 to determine an exposure condition. May be. The functions of the setting unit and the determination unit may be provided by hardware configured by a circuit such as an ASIC.

  In the above example, after the focus sensitivity is calculated for a plurality of predetermined exposure condition candidates, the exposure condition that the focus sensitivity falls within the target range is determined. Instead of this method, for example, the focus sensitivity may be calculated while changing the exposure condition candidate, and the exposure condition candidate at the time when the focus sensitivity falls within the target range may be determined as the exposure condition.

  FIG. 5 illustrates the defocus characteristic obtained in step S303. In FIG. 5, the horizontal axis represents the defocus amount, and the vertical axis represents the image characteristics, specifically, the contrast of the optical image formed by the projection optical system 200. In this example, as a plurality of parameters constituting the exposure conditions, a repetitive pattern with a resolution line width of 1.5 μm, a wavelength of exposure light of i rays (365 nm), an illumination condition of annular illumination, and an aperture of the projection optical system 200 The number (NA) was set to 0.08 to 0.12. In this example, for the sake of simplicity, the numerical aperture of the projection optical system 200 is set as an optimization target. In addition, representative 4θ system components (aberration) were set. In FIG. 4, defocus amount = 0 indicates the best focus position in a non-aberration projection optical system, and the defocus amount with the maximum contrast is the amount of change in focus position due to a 4θ system component (aberration) (focus sensitivity). Degree).

  FIG. 6 is a graph plotting the amount of change in focus position (focus sensitivity) in the numerical aperture (NA) = 0.08 to 0.12 obtained from FIG. For example, when the numerical aperture is 0.09, the focus sensitivity is about 1.3 μm. Here, consider a case where the best focus position of the vertical line pattern and the horizontal line pattern changes by +1.3 μm due to the 4θ system component (aberration). In this case, since the best focus position changes by -1.3 μm for these lines and the oblique line in the 45-degree direction, the total difference is 2.6 μm. FIG. 7 is a graph in which the result of calculating a defocus range (depth of focus (DOF)) in which a contrast of 0.5 or more is obtained from the result of FIG. 5 is plotted with the numerical aperture as the horizontal axis. Here, the threshold value of contrast is set to 0.5 in accordance with the criterion that if a contrast of 0.5 or more is obtained, good resolution performance can be obtained. From FIGS. 6 and 7, it is determined that the numerical aperture is 0.10 in the exposure condition that is least susceptible to the change of the focus position due to the 4θ system component (aberration) of the projection optical system and has the largest depth of focus. The

  In this example, the optimum numerical aperture is determined by evaluating the image characteristics while changing the numerical aperture of the projection optical system, but actually, in addition to the numerical aperture, the illumination conditions, the wavelength of the exposure light, and the pitch of the pattern There are various parameters. The influence of the remaining aberration is confirmed while changing the values of these parameters, and an optimum exposure condition is searched. In this case, an enormous amount of time, for example, several days to ten days may be required. However, the optimum exposure condition can be searched by setting the k1 factor to about 0.35 to 0.45, narrowing various parameters to values that are less affected by the 4θ component, and setting the other aberration components to zero. Can be reduced to less than one day.

  In the determination of the exposure condition, it is desirable to search for an exposure condition in which the change amount of the focus position (focus sensitivity) due to the 4nθ system component is substantially 0. The change amount of the focus position is, for example, the focus of the pattern to be exposed. Up to about 20% of the depth can be acceptable. Therefore, the target range of the change amount of the focus position due to the 4nθ system component can be appropriately determined according to the target specification, for example, within 20% of the focal depth.

  The above exposure condition determination method is suitable for manufacturing articles such as semiconductor devices. An article manufacturing method for manufacturing an article such as a semiconductor device may include a preparation process, an exposure process, a development process, and a processing process. In the preparation step, the exposure conditions are determined according to the determination method described above. In the exposure step, the substrate is exposed according to the exposure conditions determined in the preparation step. In the development process, the substrate exposed in the exposure process is developed. In the processing step, the substrate developed in the development step is processed. This treatment can include any of etching, ion implantation, oxidation, and the like.

  The present invention supplies a program that realizes one or more functions of the above-described embodiments to a system or apparatus via a network or a storage medium, and one or more processors in a computer of the system or apparatus read and execute the program This process can be realized. It can also be realized by a circuit (for example, ASIC) that realizes one or more functions.

1: exposure apparatus, 100: illumination optical system, 200: projection optical system, M: original plate, P: substrate, 201: correction optical element, 300: control unit, 400: console, 500, arithmetic unit, 600: information processing apparatus

Claims (17)

A determination method for determining an exposure condition in an exposure apparatus that exposes the substrate by projecting an original pattern onto the substrate by a projection optical system,
Of the plurality of components of the wavefront aberration of the projection optical system, f (r) · cos (4nθ) and f (r) · where (r, θ) is a polar coordinate, n is a natural number, and f (r) is a function of r. a setting step for setting a component expressed by sin (4nθ);
A determining step for determining an exposure condition such that a focus sensitivity that is a change amount of a focus position by the component is within a target range;
A determination method characterized by comprising: In the determining step, the exposure condition is determined so that a focus sensitivity due to a component when n = 1 among the components is within the target range.
The determination method according to claim 1, wherein: In the determining step, the numerical aperture of the projection optical system is determined as the exposure condition.
The determination method according to claim 1 or 2, characterized in that: In the determining step, as the exposure condition, a wavelength of light used for the exposure is determined.
The determination method according to claim 1 or 2, characterized in that: In the determining step, the numerical aperture of the projection optical system and the wavelength of light used for the exposure are determined as the exposure conditions.
The determination method according to claim 1 or 2, characterized in that: In the setting step, components other than the components expressed by f (r) · cos (4nθ) and f (r) · sin (4nθ) among the plurality of components of the wavefront aberration of the projection optical system are set to 0. ,
The determination method according to any one of claims 1 to 5, wherein: The determination step includes
A first step of calculating a defocus characteristic that is a relationship between a defocus amount of the projection optical system and a characteristic of an image formed by the projection optical system for each of a plurality of exposure condition candidates;
A second step of calculating the focus sensitivity based on the defocus characteristic for each of the plurality of exposure condition candidates calculated in the first step;
A third step of determining the exposure condition based on the focus sensitivity for each of the plurality of exposure condition candidates calculated in the second step;
The determination method according to any one of claims 1 to 6, further comprising: In the determining step, when the focus sensitivity calculated for at least two exposure condition candidates among the plurality of exposure condition candidates falls within the target range, a process margin under the at least two exposure condition candidates And determining one of the at least two exposure condition candidates as an exposure condition.
The determination method according to claim 7. In the determining step, when the focus sensitivity calculated for at least two exposure condition candidates among the plurality of exposure condition candidates falls within the target range, the depth of focus under the at least two exposure condition candidates And determining one of the at least two exposure condition candidates as an exposure condition.
The determination method according to claim 7. In the determining step, when the focus sensitivity calculated for at least two exposure condition candidates among the plurality of exposure condition candidates falls within the target range, the substrate under the at least two exposure condition candidates Determining one of the at least two exposure condition candidates as an exposure condition based on illuminance;
The determination method according to claim 7. In the determining step, when the focus sensitivity calculated for at least two exposure condition candidates out of the plurality of exposure condition candidates falls within the target range, the MEEF under the at least two exposure condition candidates ( Based on the Mask Error Enhancement Factor), one of the at least two exposure condition candidates is determined as an exposure condition.
The determination method according to claim 7. The determination step includes
A first step of calculating a defocus characteristic which is a relationship between a defocus amount of the projection optical system and a characteristic of an image formed by the projection optical system;
A second step of calculating the focus sensitivity based on the defocus characteristic calculated in the first step;
A third step of determining the exposure condition based on the focus sensitivity calculated in the second step;
The determination method according to any one of claims 1 to 6, further comprising: The projection optical system is an Offner type projection optical system,
The determination method according to any one of claims 1 to 12, wherein:   A program for causing a computer to execute the determination method according to any one of claims 1 to 13. An information processing apparatus for determining an exposure condition in an exposure apparatus that exposes the substrate by projecting a pattern of an original onto the substrate by a projection optical system,
Of the plurality of components of the wavefront aberration of the projection optical system, f (r) · cos (4nθ) and f (r) · where (r, θ) is a polar coordinate, n is a natural number, and f (r) is a function of r. a setting unit for setting a component expressed by sin (4nθ);
A determining unit that determines an exposure condition such that a focus sensitivity that is a change amount of a focus position due to the component falls within a target range;
An information processing apparatus comprising: An exposure apparatus that exposes the substrate by projecting an original pattern onto the substrate by a projection optical system,
An information processing apparatus according to claim 15;
A control unit for controlling the exposure according to an exposure condition determined by the information processing apparatus;
An exposure apparatus comprising: Determining exposure conditions according to the determination method of any one of claims 1 to 13,
Exposing the substrate according to the exposure conditions determined in the step;
An article manufacturing method comprising:

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