JP2023162947A - Correction method, exposure method, article manufacturing method, program, optical device, and exposure device - Google Patents

Abstract

To provide a technique advantageous for accurately correcting image errors of an optical system.SOLUTION: A correction method for correcting image errors of an optical system imaging a pattern on an imaged surface by driving a plurality of mechanisms includes: an acquisition step of acquiring an image sensitivity matrix indicating a change degree of an image of the optical system for driving of the mechanisms, for each of the plurality of mechanisms; a determination step of solving an equation defining a relation among a first matrix of defining the image sensitivity matrix acquired by the acquisition step for each of the plurality of mechanisms as a matrix element, a second matrix of defining a target driving amount for each of the plurality of mechanisms as a matrix element, and a third matrix composed of information on the image errors, and thereby determining the target drive amount for each of the plurality of mechanisms; and a driving step of driving each of the plurality of mechanisms according to the target driving amount determined by the determination step.SELECTED DRAWING: Figure 3

Description

The present invention relates to a correction method, an exposure method, an article manufacturing method, a program, an optical device, and an exposure device.

An exposure apparatus is an apparatus that images and transfers a pattern of an original onto a substrate via a projection optical system in a lithography process that is a manufacturing process of semiconductor devices, flat panel display devices, and the like. As the original plate, for example, a reticle or a mask can be used, and as the substrate, for example, a wafer or a glass plate having a layer of photosensitive material (resist layer) provided on the surface can be used.

For exposure equipment, demands for high resolution, high overlay accuracy, and high throughput are increasing year by year, and in order to meet these demands, it is necessary to reduce pattern imaging errors (exposure errors) in optical systems (e.g. projection optical systems). There is a need to. Therefore, the exposure apparatus is provided with a plurality of correction mechanisms for correcting imaging errors of the optical system. Patent Document 1 describes that an image of a pattern formed on a substrate by a projection optical system is adjusted by driving optical elements of the projection optical system, an original stage, a substrate stage, and the like. Further, Patent Document 2 describes that an imaging error is corrected by deforming an optical element using a plurality of actuators.

Japanese Patent Application Publication No. 2009-10139 Patent No. 6730197

In order to accurately correct the imaging error of the optical system in the exposure apparatus, it is desirable to accurately determine the target drive amount for each of the plurality of correction mechanisms. However, Patent Documents 1 and 2 do not describe a method for determining the target drive amount of each correction mechanism for accurately correcting imaging errors.

Therefore, an object of the present invention is to provide an advantageous technique for accurately correcting the imaging error of an optical system.

In order to achieve the above object, a correction method as one aspect of the present invention is a correction method that corrects an imaging error of an optical system that images a pattern on an imaged surface by driving a plurality of mechanisms. an acquisition step of acquiring, for each of the plurality of mechanisms, an imaging sensitivity matrix indicating a degree of change in imaging of the optical system with respect to driving of the mechanism; and an acquisition step of acquiring an imaging sensitivity matrix for each of the plurality of mechanisms, a first matrix whose matrix elements are the imaging sensitivity matrix, a second matrix whose matrix elements are the target drive amounts for each of the plurality of mechanisms, and a third matrix comprising information about the imaging error; a determining step of determining the target driving amount for each of the plurality of mechanisms by solving an equation that defines the relationship; and driving each of the plurality of mechanisms in accordance with the target driving amount determined in the determining step. The method is characterized by including a driving step.

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

According to the present invention, for example, it is possible to provide an advantageous technique for accurately correcting imaging errors in an optical system.

Diagram showing an example of the configuration of an exposure device Diagram showing an example of the configuration of a high-order correction mechanism Schematic diagram showing a configuration example of the optical device of the first embodiment Schematic diagram to explain the generation of integrated sensitivity matrix A schematic diagram showing a modification of the optical device of the first embodiment Flowchart showing a method for correcting imaging errors in the projection optical system Diagram for explaining arithmetic processing in the arithmetic unit of the second embodiment Schematic diagram showing a modification of the optical device of the third embodiment

Hereinafter, embodiments will be described in detail with reference to the accompanying drawings. Note that the following embodiments do not limit the claimed invention. Although a plurality of features are described in the embodiments, not all of these features are essential to the invention, and the plurality of features may be arbitrarily combined. Furthermore, in the accompanying drawings, the same or similar components are designated by the same reference numerals, and redundant description will be omitted.

In the following embodiments, an example will be described in which a correction method according to the present invention, which corrects an imaging error of an optical system that images a pattern on an imaged surface, is applied to an exposure apparatus that exposes a substrate, but is not limited thereto. It's not something you can do. The correction method according to the present invention can be applied to any optical device that uses a plurality of mechanisms (correction mechanisms) to correct an imaging error of an optical system that images a pattern on an image surface. In addition to the exposure apparatus, optical apparatuses to which the correction method according to the present invention can be applied can be provided, for example, in other lithography apparatuses than the exposure apparatus, telescopes, microscopes, cameras, laser printers, and the like.

<First embodiment>
A first embodiment according to the present invention will be described. FIG. 1A is a diagram showing an example of the configuration of an exposure apparatus 10 according to the present embodiment. The exposure apparatus 10 of this embodiment includes an illumination optical system IL, a projection optical system PO, an original stage MS that holds and moves the original 12 (mask), and a substrate stage WS that holds and moves the substrate 18. The controller 11 may include a controller 11. The control unit 11 is configured by a computer (information processing device) including, for example, a processor such as a CPU and a memory, and controls the entire exposure apparatus 10 (each unit).

The light emitted from the light source (not shown) forms, for example, an arcuate illumination area long in the Y-axis direction on the original 12 via a slit (not shown) included in the illumination optical system IL. The original 12 and the substrate 18 are each held by an original stage MS and a substrate stage WS, and are moved to optically approximately conjugate positions (positions of the object plane and image plane of the projection optical system PO) via the projection optical system PO. ). The projection optical system PO has a predetermined projection magnification and projects an image of the pattern formed on the original 12 onto the substrate 18 (that is, images the pattern of the original 12 onto the substrate 18). Then, the original stage MS and the substrate stage WS are moved in a direction parallel to the object plane of the projection optical system PO (for example, the Y-axis direction in FIG. 1(a)) at a speed ratio according to the projection magnification of the projection optical system PO. Let it scan. Thereby, the pattern formed on the original plate 12 can be transferred onto the substrate.

The projection optical system PO may include, for example, a low-order correction mechanism 13, a plane mirror 14, a concave mirror 15, a convex mirror 16, and a high-order correction mechanism 17, as shown in FIG. 1(a). The light emitted from the illumination optical system IL and passed through the original 12 passes through the low-order correction mechanism 13, is reflected by the first surface 14a of the plane mirror 14, and enters the first surface 15a of the concave mirror 15. The light reflected by the first surface 15a of the concave mirror 15 is reflected by the convex mirror 16 and enters the second surface 15b of the concave mirror 15. The light reflected by the second surface 15b of the concave mirror 15 is reflected by the second surface 14b of the plane mirror 14, passes through the high-order correction mechanism 17, and forms an image on the substrate. In the projection optical system PO configured in this way, the reflective surface of the convex mirror 16 serves as an optical pupil.

By the way, in the exposure apparatus 10, an error (hereinafter sometimes referred to as an imaging error) may occur in the position and/or shape of the pattern imaged on the substrate by the projection optical system PO. Such imaging errors are sometimes called exposure errors or aberrations, and are caused by vibrations caused by driving the original stage MS and substrate stage MS, deformation of optical members due to exposure heat, environmental vibrations, and differences in precision between exposure devices ( This can occur due to various factors such as machine differences (also called machine differences). Therefore, the exposure apparatus 10 is provided with a plurality of correction mechanisms for correcting the imaging error of the projection optical system PO, and the imaging error of the projection optical system PO is corrected by driving each of the plurality of correction mechanisms. Ru.

In the exposure apparatus 10 of this embodiment, among the plurality of correction mechanisms for correcting the imaging error of the projection optical system PO, for example, the low-order correction mechanism 13, the high-order correction mechanism 17, the original stage MS, and the substrate stage WS. Two or more may be used. However, the present invention is not limited thereto, and a mechanism other than the above that can correct the imaging error of the projection optical system PO may be used as the correction mechanism. For example, when the projection optical system PO includes a lens, a mechanism for driving the lens may be used as a correction mechanism.

Here, a configuration example of the low-order correction mechanism 13 and the high-order correction mechanism 17 provided in the projection optical system PO as correction mechanisms will be described. The low-order correction mechanism 13 is a mechanism for correcting a part of the low-order components of the imaging error of the projection optical system PO, and is a mechanism for correcting a part of the low-order components of the imaging error of the projection optical system PO. It can be placed on the optical path between the two. Further, the high-order correction mechanism 17 is a mechanism for correcting high-order components of the imaging error of the projection optical system PO, and is a mechanism for correcting high-order components of the imaging error of the projection optical system PO. can be placed on the optical path of. Depending on its configuration, the high-order correction mechanism 17 can also correct some of the low-order components of the imaging error of the projection optical system PO. In this embodiment, the low-order component refers to a component of less than third order in the imaging error, and the high-order component refers to a component of third or higher order in the imaging error.

FIG. 1(b) is a diagram showing an example of the configuration of the low-order correction mechanism 13. The low-order correction mechanism 13 includes an optical element 13a having a convex surface and an optical element 13b having a concave surface, such that the convex surface of the optical element 13a and the concave surface of the optical element 13b face each other with an interval Gap (air gap). It is configured. Under the control of the control unit 11, the low-order correction mechanism 13 moves the optical element 13a and the optical element 13b to Z by a driving unit (not shown) such as an actuator, as shown by the arrow in FIG. 1(b). Relative movement in the axial direction (vertical direction) and/or in the XY plane direction (lateral direction). Thereby, the magnification of the projection optical system PO can be corrected as a low-order component of the imaging error.

FIG. 2 is a diagram showing an example of the configuration of the high-order correction mechanism 17. FIG. 2(a) is a diagram of the high-order correction mechanism 17 viewed from the optical axis direction (Z-axis direction), and FIGS. ) is a view of the higher-order correction mechanism 17. The high-order correction mechanism 17 may include, for example, an optical element 17a configured as a parallel plane plate and a plurality of actuators 17b arranged around the optical element 17a. The high-order correction mechanism 17 applies force to the outer periphery of the optical element 17a using each of the plurality of actuators 17b under the control of the control unit 11, and deforms the effective optical region ER (region through which light passes) of the optical element 17a. . For example, as shown in FIG. 2C, each actuator 17b is driven in the direction of the arrow to deform the effective optical region ER of the optical element 17a. Thereby, it is possible to correct not only the low-order components of the imaging error of the projection optical system PO but also the high-order components. In the high-order correction mechanism 17, the order of correctable imaging errors can be increased as the number of actuators 17b increases, but it is preferable to configure the structure in consideration of constraints such as actual arrangement space and manufacturing cost.

[Configuration of optical device]
An example of the configuration of the optical device 20 will be described below. FIG. 3 is a schematic diagram showing a configuration example of the optical device 20 of this embodiment. The optical device 20 is a device that corrects the imaging error of the projection optical system PO that images the pattern of the original 12 on the substrate 18 as an image-forming surface, and includes a plurality of correction mechanisms 21 and a control unit 22 (processing section). In the example of FIG. 3, as the plurality of correction mechanisms 21, correction mechanisms M1 to Mn (n is the number of correction mechanisms 21) are provided.

Each of the plurality of correction mechanisms 21 includes a structure 21a and a drive section 21b, and the drive section 21b drives the structure 21a to change the position, orientation, and/or shape of the structure 21a, thereby adjusting the projection optical system. This is a mechanism that changes the imaging performance (imaging characteristics) of the system PO. For example, when the correction mechanism 21 is the low-order correction mechanism 13, the structure 21a is the optical elements 13a to 13b, and the drive unit 21b is an actuator that relatively moves the optical elements 13a to 13b. When the correction mechanism 21 is the high-order correction mechanism 17, the structure 21a is the optical element 17a, and the drive section 21b is a plurality of actuators 17b that drive the optical element 17a. Further, the correction mechanism 21 may be a mechanism that changes the imaging performance of the projection optical system PO by translating or tilting the original stage MS and/or the substrate stage WS. In this case, structure 21a of correction mechanism 21 is master stage MS and/or substrate stage WS, and drive unit 21b is an actuator that drives master stage MS and/or substrate stage WS.

The control unit 22 is configured by, for example, a computer having a processor such as a CPU and a memory, and controls each of the plurality of correction mechanisms 21 . In the case of this embodiment, the control unit 22 may include a storage unit 22a (memory), a calculation unit 22b (processor), and a drive instruction unit 22c (driver). The storage unit 22a (storage unit) stores (memorizes) an integrated sensitivity matrix that will be described later. The calculation unit 22b determines (calculates) the target drive amount of each correction mechanism 21 based on the integrated sensitivity matrix stored in the storage unit 22a and the imaging error of the projection optical system PO to be corrected. The drive instruction section 22c controls the drive of each correction mechanism 21 by giving a drive instruction to each correction mechanism 21 according to the target drive amount determined by the calculation section 22b.

Here, as shown in FIG. 4, the integrated sensitivity matrix stored in the storage unit 22a is a matrix that horizontally combines (concatenates, integrates, and ) can be generated by The imaging sensitivity matrix indicates the degree of change in imaging of the projection optical system PO with respect to the drive of one correction mechanism 21 (hereinafter sometimes referred to as the target correction mechanism 21), which is the target for obtaining the imaging sensitivity matrix. It is something. The imaging sensitivity matrix may be understood as a matrix representing changes in the position of each evaluation point on the substrate 18 (imaged surface).

Hereinafter, a method of generating an imaging sensitivity matrix and an integrated sensitivity matrix, and a method of determining a target drive amount of each correction mechanism 21 necessary for correcting an imaging error of the projection optical system PO will be specifically explained.

First, the imaging sensitivity matrix of each correction mechanism 21 will be explained. The imaging sensitivity used in this embodiment refers to the image-forming surface ( refers to the amount of change in imaging performance (eg, position) at an evaluation point in the optical region). Generally, the imaging sensitivity obtained by driving one actuator is a vector because a plurality of evaluation points are used on the imaged surface. Imaging performance refers to optical indicators necessary for correction, such as distortion and focus variation.

By sequentially driving each actuator in the drive unit 21b of the target correction mechanism 21 by a predetermined drive amount, as many imaging sensitivity vectors as there are actuators can be obtained. The imaging sensitivity matrix is a matrix formed by arranging these vectors. The number of evaluation points on the imaging surface is m, the number of actuators of the k-th correction mechanism 21 is p _k , and the vector of change in imaging performance at each evaluation point when driving the i-th actuator is c _i Then, the imaging sensitivity matrix C _k can be expressed by the following equation (1). The imaging sensitivity matrix of each correction mechanism 21 may be obtained from an analytical model of each correction mechanism 21, or may be obtained by mounting the correction mechanism 21 on the exposure apparatus 10 and actually measuring the imaging performance of the projection optical system PO. It's okay.

Next, the integrated sensitivity matrix will be explained. The integrated sensitivity matrix of this embodiment is one in which a plurality of imaging sensitivity matrices respectively acquired for a plurality of correction mechanisms 21 are combined in a horizontally arranged manner to form an apparent single imaging sensitivity matrix. Letting the integrated sensitivity matrix be C, it can be expressed as the following equation (2), and the dimensions of the integrated sensitivity matrix C are "m×r". Here, r=(p ₁ +p ₂ +...+p _n ), and p ₁ , p ₂ , . . . p _n indicate the number of actuators provided in each of the correction mechanisms M1 to Mn. Therefore, r represents the sum of the actuators of each correction mechanism. In this way, by combining the imaging sensitivity matrices of each correction mechanism in the horizontal direction, an integrated sensitivity matrix can be generated. Generally, the integrated sensitivity matrix does not become a square matrix because the number m of evaluation points and the total number r of actuators are not equal. Note that the imaging sensitivity matrix may be generated in advance by the calculation unit 22b and stored in the storage unit 22a.

Here, when using the original stage MS and/or the substrate stage WS as a correction mechanism for correcting the imaging error of the projection optical system PO, the number of actuators is not the number of physical actuators, but the correction must be made at each stage. is the number of degrees of freedom that can be corrected. For example, there are two degrees of freedom for in-plane translation (X-axis direction, Y-axis direction), three degrees of freedom for tilt (rotation direction around the X-axis, rotation direction around the Y-axis, and rotation direction around the Z-axis). Similarly, in the case of a correction mechanism such as the low-order correction mechanism 13 or the high-order correction mechanism 17 that corrects the imaging error of the projection optical system PO by adjusting the position and/or orientation of the optical element, the actuator The number becomes the number of correction degrees of freedom of the correction mechanism.

Next, a method for determining the target drive amount of each correction mechanism 21 in the calculation section 22b will be explained. In order to correct the imaging error of the projection optical system PO, information/data indicating the imaging error of the projection optical system PO to be corrected (hereinafter sometimes referred to as imaging error information) must be prepared in advance. It is necessary to keep it. The imaging error information is information indicating the imaging error (for example, overlay error) of each evaluation point on the substrate 18 (imaged surface), and is a matrix (for example, a vector) having the same number of matrix elements as the number of evaluation points. It can be expressed as Further, the imaging error information may be a matrix having the same number of matrix elements as the matrix elements of the imaging sensitivity matrix described above. The imaging error information may be the result of measuring the overlay error of a substrate on which a pattern is formed by the exposure device 10 using an external inspection device, the result of actually measuring the imaging performance of the projection optical system PO within the exposure device 10, or It can be generated based on the results of simulation. The generated imaging error information may be supplied to the calculation unit 22b of the control unit 22. Although FIG. 3 shows an example in which the imaging error information is supplied from an external device to the calculation section 22b, it may be stored in advance in the storage section 22a.

The calculation unit 22b determines (calculates) the target drive amount of each correction mechanism 21 based on the imaging error information of the projection optical system PO and the integrated sensitivity matrix stored in the storage unit 22a. Specifically, an integrated sensitivity matrix (first matrix), a driving amount matrix (second matrix) whose matrix elements are the target driving amounts of each correction mechanism 21, and a combined error matrix (third matrix) consisting of imaging error information. The target drive amount of each correction mechanism 21 is determined by solving an equation that defines the relationship between Generally, the driving amount matrix is a vector whose total number is r×1, representing the number of actuators of each drive mechanism, and the imaging error matrix is a vector whose total number is m×1, which is the number of evaluation points. The equation can be expressed by the following equation (3), where C is the integrated sensitivity matrix, D is the driving amount matrix, and S is the imaging error matrix.

As described above, since the integrated sensitivity matrix C is not a square matrix, there is no inverse matrix, and the drive amount matrix D cannot be uniquely determined from equation (3). Therefore, the driving amount matrix D can be obtained using a pseudo inverse matrix (or generalized inverse matrix) of the integrated sensitivity matrix C. In this case, the driving amount matrix D is as shown in equation (4).

here,
is a pseudo-inverse matrix of the integrated sensitivity matrix, and solving simultaneous equations using this pseudo-inverse matrix is mathematically equivalent to the method of least squares. Also, the driving amount matrix obtained in this way
is obtained as a matrix in which the target driving amounts of each of the correction mechanisms M1 to Mn are arranged as matrix elements, and has the following meaning. In other words, from the characteristics of the pseudo-inverse matrix, if the integrated sensitivity matrix is a vertical matrix in which the number of rows m is greater than the number of columns r, the driving amount matrix obtained is
becomes the least squares solution that minimizes equation (5).

On the other hand, if the integrated sensitivity matrix is a horizontally long matrix in which the number of rows m is less than the number of columns r, the obtained driving amount matrix
is its norm
becomes the minimum. This means that when driving the actuator of the correction mechanism 21 to correct the imaging error of the projection optical system PO, the energy input to the actuator is minimized.

That is, in order to improve the accuracy of correcting the imaging error of the projection optical system PO, it is better to create a vertically elongated integrated sensitivity matrix than to create a horizontally elongated integrated sensitivity matrix. On the other hand, if it is desired to reduce the energy input to the correction mechanism 21 as much as possible, it is better to create a horizontally elongated integrated sensitivity matrix than to create a vertically elongated integrated sensitivity matrix. The method for creating a horizontally long integrated sensitivity matrix is basically the same as the method for creating a vertically long integrated sensitivity matrix, and the imaging sensitivity matrices of each correction mechanism may be combined in the horizontal direction. However, the feature is that the number m of evaluation points is smaller than the number r, which is the sum of the number of actuators (or the number of correction degrees of freedom) of each correction mechanism 21.

Here, in this embodiment, each imaging sensitivity matrix is combined in the horizontal direction when creating an integrated sensitivity matrix, but each imaging sensitivity matrix is transposed (that is, the rows are a list of evaluation points, and the columns are The actuators may be arranged in a row) and then connected in the vertical direction. In this case, it is necessary to transpose the integrated sensitivity matrix and use it when performing matrix calculations.

[Modified example]
FIG. 5 is a schematic diagram showing a modification of the optical device 20 of this embodiment. The optical device 20 of this modification shown in FIG. 5 differs from the optical device 20 shown in FIG. 3 in the information stored in the storage section 22a of the control section 22. In the optical device 20 of this modification, a plurality of imaging sensitivity matrices obtained for each of the plurality of correction mechanisms 21 can be further stored in the storage section 22a. Then, the calculation unit 22b generates an integrated sensitivity matrix using the plurality of imaging sensitivity matrices stored in the storage unit 22a, and stores the generated integrated sensitivity matrix in the storage unit 22a.

[Imaging error correction method]
Hereinafter, a method of correcting the imaging error of the projection optical system PO will be explained. FIG. 6 is a flowchart showing a method for correcting the imaging error of the projection optical system PO. Each step of the flowchart shown in FIG. 6 can be executed by the control section 22 (for example, the calculation section 22b) of the optical device 20.

In step S11, the control unit 22 obtains an imaging sensitivity matrix for each of the plurality of correction mechanisms 21. That is, the control unit 22 obtains a plurality of imaging sensitivity matrices obtained for the plurality of correction mechanisms 21, respectively. As described above, the imaging sensitivity matrix can be obtained by an analytical model or actual measurement. Next, in step S12, the control unit 22 generates an integrated sensitivity matrix based on the plurality of imaging sensitivity matrices acquired in step S11. As described above, the integrated sensitivity matrix can be generated by arranging and combining a plurality of imaging sensitivity matrices as matrix elements.

In step S13, the control unit 22 acquires information indicating the imaging error of the projection optical system PO to be corrected (imaging error information). As described above, the imaging error information can be generated based on the results of overlay error measurement by an external inspection device, the actual measurement results within the exposure apparatus 10, the results of exposure simulation, and the like.

In step S14, the control unit 22 uses the integrated sensitivity matrix (first matrix) generated in step S12, the imaging error matrix (third matrix) acquired in step S13, and the target drive amount of each correction mechanism 21. An equation is generated that defines the relationship between the drive amount matrix (second matrix) representing the drive amount matrix (second matrix). For example, when the integrated sensitivity matrix is C, the drive amount matrix is D, and the imaging error matrix is S, the control unit 22 generates an equation consisting of S=CD as shown in the above equation (3). be able to.

In step S15, the control unit 22 determines the target drive amount of each correction mechanism 21 by solving the equation generated in step S14. Next, in step S16, the control unit 22 drives each correction mechanism 21 via the drive instruction unit 22c according to the target drive amount of each correction mechanism 21 determined in step S15.

As described above, in this embodiment, the imaging of the projection optical system PO is performed using an integrated sensitivity matrix whose matrix elements are the combined sensitivity matrices (multiple combined sensitivity matrices) obtained for each of the plurality of correction mechanisms 21. A target drive amount of each correction mechanism 21 for reducing errors is determined. Thereby, the plurality of correction mechanisms 21 can collectively perform correction with high accuracy so that the imaging error of the projection optical system PO is reduced.

<Second embodiment>
A second embodiment according to the present invention will be described. This embodiment basically inherits the first embodiment, and is the same as described in the first embodiment except for the matters mentioned below.

FIG. 7 is a diagram for explaining arithmetic processing in the arithmetic unit 22b of this embodiment. As shown in FIG. 7, the calculation unit 22b of this embodiment solves a constrained equation so that a predetermined constraint condition is satisfied, that is, performs constrained optimization when determining the target drive amount of each correction mechanism 21. conduct. Here, the constraint conditions include physical constraints of the correction mechanism 21 and constraints from system requirements of the projection optical system PO or the exposure apparatus 10. Further, the constraint condition may be an equality constraint condition or an inequality constraint condition.

First, the physical constraints of the correction mechanism 21 will be explained. The physical limitation of the correction mechanism is, for example, as in the above-mentioned high-order correction mechanism 17 (see FIG. 2), the imaging error of the projection optical system PO is reduced by deforming the optical element 17a using a plurality of actuators 17b. It is necessary to take this into consideration in the correction mechanism (deformation mechanism) that corrects this. In the high-order correction mechanism 17, depending on the amount of drive of each actuator 17b for deforming the optical element 17a (for example, the difference in the amount of drive between adjacent actuators 17b), excessive stress is applied to the optical element 17a, There is a possibility that the element 17a may be broken. Therefore, it is necessary to limit the difference Δh between the drive amounts of the plurality of actuators 17b (in particular, between adjacent actuators 17b) so that the stress generated in the optical element 17a becomes less than the breaking stress. Therefore, it is preferable that the difference Δh between the driving amounts of the plurality of actuators 17b, which can reduce the stress generated in the optical element 17a to less than the destructive stress, be used as a constraint. For example, if the distance between adjacent actuators 17b is L, the larger Δh/L is, the greater the stress applied to the optical element 17a will be, and if it exceeds the breaking stress, it will break. Therefore, based on the distance L between the actuators 17b, the maximum drive amount difference Δh within a range where the stress generated in the optical element 17a is less than the breaking stress can be used as a constraint. Note that the correction mechanism to which physical constraints are applied is not limited to a correction mechanism (deformation mechanism) that drives the deformation of an optical element, such as the high-order correction mechanism 17.

Next, constraints imposed by system requirements for the projection optical system PO or the exposure apparatus 10 will be explained. As a constraint from the system request, a side effect of driving the plurality of correction mechanisms 21 can be considered. For example, the correction mechanism 21 that adjusts (changes) the position and/or orientation of a structure such as an optical element can correct a desired imaging error (first imaging error, for example, distortion). However, when the correction mechanism 21 is driven so that the desired imaging error is corrected, an imaging error of a type different from the desired imaging error (second imaging error, for example, an astigmatism component) occurs as a side effect ( increase). Therefore, it is necessary to drive each of the plurality of correction mechanisms 21 so that the second imaging error (ast component) that occurs as a side effect falls within the allowable range (below the allowable value), and this is used as a constraint. sell. Note that the constraints from the system requirements are not limited to the above example.

In this way, when physical constraints and constraints from system requirements exist, the driving quantity matrix
It is recommended to apply a constrained optimization method when determining . There are various types of constrained optimization methods, such as barrier function method, penalty function method, Lagrangian undetermined multiplier method, sequential quadratic programming, and continuous linear programming. You just have to choose the appropriate method. For example, when using MathWorks' numerical analysis software matlab, you can use a function called lsqlin for constrained linear least squares problems. Assuming that A is a matrix for calculating the difference in the drive amount between adjacent actuators as a physical constraint condition, and b is the allowable value for the difference in drive amount between the adjacent actuators, the constraint formula is as follows: It is represented by (6).

Here, by multiplying the matrix A by the drive amount matrix D, the difference in drive amounts can be obtained. Therefore, the driving quantity matrix obtained with constraints
can be expressed in matlab as the following equation (7). Note that the above example is an example using matlab functions, and other optimization calculation tools or home-made optimization calculation tools may be used.

<Third embodiment>
A third embodiment according to the present invention will be described. This embodiment basically inherits the first embodiment, and is the same as described in the second embodiment except for the matters mentioned below. Further, in this embodiment, the second embodiment (ie, constrained optimization) may be applied.

In this embodiment, a correction method for the optical device 20 including the above-described low-order correction mechanism 13 and high-order correction mechanism 17 will be described. FIG. 8 is a schematic diagram showing a configuration example of the optical device 20 of this embodiment. In this case, the integrated sensitivity matrix is generated by the imaging sensitivity matrix of the low-order correction mechanism 13 and the sensitivity matrix of the high-order correction mechanism 17. Generally, a low-order imaging error has a larger error amount (scalar amount) than a high-order imaging error, and the correction amount of the low-order correction mechanism 13 is larger than that of the high-order correction mechanism 17. The high-order correction mechanism 17 can also correct low-order imaging errors, but as explained in the second embodiment, there is a physical constraint to prevent cracking of the optical element 17a, and the adjacent actuator It is not possible to increase the difference in the drive amount between the drive units 17b without limit. Therefore, by providing the high-order correction mechanism 17 with a constraint on the drive amount difference, it is possible to safely and accurately correct imaging errors from low-order to high-order in cooperation with the low-order correction mechanism 13. Here, the low-order correction mechanism and the high-order correction mechanism to which the correction method of the present embodiment is applied are not limited to the low-order correction mechanism 13 and the high-order correction mechanism 17 described in the first embodiment. Further, the number of low-order correction mechanisms and high-order correction mechanisms is not limited.

<Embodiment of article manufacturing method>
The article manufacturing method according to the embodiment of the present invention is suitable for manufacturing articles such as micro devices such as semiconductor devices and elements having fine structures. The method for manufacturing an article of the present embodiment includes a step of forming a latent image pattern on a photosensitive agent applied to a substrate using the above-mentioned exposure device (a step of exposing the substrate), and a step of forming a latent image pattern in this step. The method includes a step of developing (processing) the substrate. Additionally, such manufacturing methods include other well-known steps (oxidation, deposition, deposition, doping, planarization, etching, resist stripping, dicing, bonding, packaging, etc.). The method for manufacturing an article according to the present embodiment is advantageous in at least one of the performance, quality, productivity, and production cost of the article compared to conventional methods.

<Other Examples>
The present invention provides a system or device with a program that implements one or more functions of the embodiments described above via a network or a storage medium, and one or more processors in a computer of the system or device reads and executes the program. This can also be achieved by processing. It can also be realized by a circuit (for example, ASIC) that realizes one or more functions.

<Summary of embodiments>
The disclosure of this specification includes the following correction method, exposure method, article manufacturing method, program, optical device, and exposure device.

(Item 1)
A correction method for correcting an imaging error of an optical system that images a pattern on an imaged surface by driving a plurality of mechanisms, the method comprising:
an acquisition step of acquiring, for each of the plurality of mechanisms, an imaging sensitivity matrix indicating a degree of change in imaging of the optical system with respect to driving of the mechanism;
a first matrix whose matrix elements are the imaging sensitivity matrices acquired in the acquisition step for each of the plurality of mechanisms, and a second matrix whose matrix elements are target drive amounts for each of the plurality of mechanisms; a determining step of determining the target drive amount for each of the plurality of mechanisms by solving an equation that defines a relationship between the third matrix consisting of information on the imaging error;
a driving step of driving each of the plurality of mechanisms according to the target driving amount determined in the determining step;
A correction method characterized by comprising:

(Item 2)
Item 1, wherein the first matrix is obtained by horizontally or vertically combining the imaging sensitivity matrices acquired in the acquisition step for each of the plurality of mechanisms as matrix elements. Correction method described.

(Item 3)
In the determining step, the target drive amount is determined for each of the plurality of mechanisms by solving the equation consisting of S=CD, where C is the first matrix, D is the second matrix, and S is the third matrix. The correction method according to item 1 or 2, characterized in that:

(Item 4)
According to any one of items 1 to 3, in the determining step, the target drive amount is determined for each of the plurality of mechanisms by solving the equation using a least squares method. Correction method.

(Item 5)
Any one of items 1 to 4, characterized in that in the determining step, the target drive amount is determined for each of the plurality of mechanisms by solving the equation so that a predetermined constraint condition is satisfied. Correction method described in.

(Item 6)
The plurality of mechanisms include a deformation mechanism that deforms the optical element using a plurality of actuators,
6. The correction method according to item 5, wherein the constraint condition includes a condition for limiting a difference in drive amount of the plurality of actuators in the deformation mechanism.

(Item 7)
The constraint condition is a condition for driving each of the plurality of mechanisms so that when the imaging error is corrected, a second imaging error of a type different from the imaging error falls within an allowable range. The correction method according to item 5 or 6, characterized in that:

(Item 8)
Items 1 to 1, wherein the plurality of mechanisms include at least one mechanism that corrects a low-order component of the imaging error and at least one mechanism that corrects a high-order component of the imaging error. The correction method described in any one item of 7.

(Item 9)
a correction step of correcting an imaging error of an optical system that images a pattern on a substrate as an image-forming surface using the correction method described in any one of items 1 to 8;
an exposure step of exposing the substrate using the optical system in which the imaging error has been corrected by the correction step;
An exposure method characterized by comprising:

(Item 10)
an exposure step of exposing the substrate using the exposure method described in item 9;
a processing step of processing the substrate exposed in the exposure step;
a manufacturing step of manufacturing an article from the substrate processed in the processing step;
A method for manufacturing an article characterized by comprising:

(Item 11)
A program that causes a computer to execute the correction method described in any one of items 1 to 8.

(Item 12)
multiple mechanisms for correcting imaging errors of the optical system that images the pattern on the imaged surface;
a control unit that controls each of the plurality of mechanisms;
Equipped with
An optical device characterized in that the control unit corrects the imaging error by driving each of the plurality of mechanisms using the correction method described in any one of items 1 to 8.

(Item 13)
An exposure device that exposes a substrate,
an optical system that images a pattern on the substrate as an imaged surface;
The optical device according to item 12,
An exposure apparatus comprising:

The invention is not limited to the embodiments described above, and various changes and modifications can be made without departing from the spirit and scope of the invention. Therefore, the following claims are hereby appended to disclose the scope of the invention.

10: Exposure device, 11: Control unit, 12: Original plate, 13: Low-order correction mechanism, 17: High-order correction mechanism, 18: Substrate, IL: Illumination optical system, MS: Original stage, PO: Projection optical system, WS : Substrate stage, 20: Optical device, 21: Correction mechanism, 22: Control unit

Claims (13)

A correction method for correcting an imaging error of an optical system that images a pattern on an imaged surface by driving a plurality of mechanisms, the method comprising:
an acquisition step of acquiring, for each of the plurality of mechanisms, an imaging sensitivity matrix indicating a degree of change in imaging of the optical system with respect to driving of the mechanism;
a first matrix whose matrix elements are the imaging sensitivity matrices acquired in the acquisition step for each of the plurality of mechanisms, and a second matrix whose matrix elements are target drive amounts for each of the plurality of mechanisms; a determining step of determining the target drive amount for each of the plurality of mechanisms by solving an equation that defines a relationship between the third matrix consisting of information on the imaging error;
a driving step of driving each of the plurality of mechanisms according to the target driving amount determined in the determining step;
A correction method characterized by comprising: Claim 1, wherein the first matrix is obtained by combining the imaging sensitivity matrices acquired in the acquisition step for each of the plurality of mechanisms in the horizontal or vertical direction as matrix elements. Correction method described in. In the determining step, the target is determined for each of the plurality of mechanisms by solving the equation consisting of S=CD, where C is the first matrix, D is the second matrix, and S is the third matrix. The correction method according to claim 1, further comprising determining a drive amount. 2. The correction method according to claim 1, wherein in the determining step, the target drive amount is determined for each of the plurality of mechanisms by solving the equation using a least squares method. 2. The correction method according to claim 1, wherein in the determining step, the target drive amount is determined for each of the plurality of mechanisms by solving the equation so that a predetermined constraint condition is satisfied. The plurality of mechanisms include a deformation mechanism that deforms the optical element using a plurality of actuators,
6. The correction method according to claim 5, wherein the constraint condition includes a condition for limiting a difference in drive amount of the plurality of actuators in the deformation mechanism. The constraint condition is a condition for driving each of the plurality of mechanisms so that when the imaging error is corrected, a second imaging error of a type different from the imaging error falls within an allowable range. 6. The correction method according to claim 5, comprising: 2. The plurality of mechanisms include at least one mechanism that corrects a low-order component of the imaging error and at least one mechanism that corrects a high-order component of the imaging error. Correction method described in. A correction step of correcting an imaging error of an optical system that images a pattern on a substrate as an imaged surface using the correction method according to any one of claims 1 to 8;
an exposure step of exposing the substrate using the optical system in which the imaging error has been corrected by the correction step;
An exposure method characterized by comprising: an exposure step of exposing the substrate using the exposure method according to claim 9;
a processing step of processing the substrate exposed in the exposure step;
a manufacturing step of manufacturing an article from the substrate processed in the processing step;
A method for manufacturing an article characterized by comprising: A program for causing a computer to execute the correction method according to any one of claims 1 to 8. multiple mechanisms for correcting imaging errors of the optical system that images the pattern on the imaged surface;
a control unit that controls each of the plurality of mechanisms;
Equipped with
9. An optical device, wherein the control unit corrects the imaging error by driving each of the plurality of mechanisms using the correction method according to claim 1. An exposure device that exposes a substrate,
an optical system that images a pattern on the substrate as an imaged surface;
The optical device according to claim 12;
An exposure apparatus comprising: