TW202343156A - Correction method, exposure method, article manufacturing method, program, optical device, and exposure device wherein the correction method includes an obtaining procedure, a determination procedure, and a driving procedure - Google Patents

Abstract

To provide a technology that facilitates accurate correction of imaging errors in optical systems. A correction method that corrects the imaging errors of the optical system that makes the pattern image on the imaged surface by driving multiple mechanisms includes: an obtaining procedure for obtaining, for each of the plurality of mechanisms, an imaging sensitivity matrix indicating a degree of change in the imaging of the optical system with respect to driving of the mechanism; a determination procedure for solving an equation that defines a relationship between a first matrix whose matrix elements are the imaging sensitivity matrices obtained in the obtaining procedure for each of the plurality of mechanisms, a second matrix whose matrix elements are the target driving amount for each of the plurality of mechanisms, and a third matrix formed by the information of the imaging error, thereby determining the aforementioned target driving amount for each of the aforementioned plurality of mechanisms; and a driving procedure for driving each of the plurality of mechanisms in accordance with the target driving amount determined by the determination procedure.

Description

Calibration methods, exposure methods, manufacturing methods of articles, procedures, optical devices and exposure devices

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

The exposure device is a device that, in the lithography process of the manufacturing process of semiconductor devices, flat panel display devices, etc., images the pattern of the master plate through the projection optical system and transfers it to the substrate. As the original plate, for example, a reticle, a mask, etc. can be used. As the substrate, for example, a wafer or a glass plate having a photosensitive material layer (resist layer) provided on the surface can be used.

In exposure devices, requirements for high resolution, high overlay accuracy, and high throughput are increasing year by year. In order to meet these requirements, it is necessary to reduce pattern imaging errors (exposure errors) in optical systems (such as projection optical systems). Therefore, the exposure device is provided with a plurality of correction mechanisms for correcting imaging errors of the optical system. Patent Document 1 describes adjusting an image of a pattern formed on a substrate by the projection optical system by driving the optical elements of the projection optical system, the original plate stage, the substrate stage, and the like. In addition, Patent Document 2 describes correcting imaging errors by deforming an optical element using a plurality of actuators. [Prior technical literature] [Patent Document]

[Patent Document 1] Japanese Patent Application Publication No. 2009-10139 [Patent Document 2] Japanese Patent No. 6730197

[Problem to be solved by the invention]

In order to accurately correct the imaging error of the optical system in the exposure device, it is desired 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 driving amount for each correction mechanism for correcting imaging errors with high accuracy.

Therefore, an object of the present invention is to provide a technology that is useful for accurately correcting the imaging error of an optical system. [Means used to solve problems]

In order to achieve the foregoing object, a correction method as one aspect of the present invention is a correction method that corrects the imaging error of an optical system that images a pattern on an imaged surface by driving a plurality of mechanisms, including: an acquisition program, This is a process for obtaining, for each of the aforementioned plurality of mechanisms, an imaging sensitivity matrix indicating the degree of change in the imaging of the aforementioned optical system with respect to the driving of the mechanism; and a determination program for obtaining, for each of the aforementioned plurality of mechanisms, a determination program for each of the aforementioned plurality of mechanisms. The imaging sensitivity matrix acquired in the acquisition process is a first matrix of matrix elements, a second matrix of matrix elements in which the target drive amounts for each of the plurality of mechanisms are, and a third matrix of the imaging error information. A matrix relational equation is used to determine the target drive amount for each of the plurality of mechanisms; and a driver is a driver that drives each mechanism of the plurality of mechanisms based on the target drive amount determined by the determination program.

Further objects and other aspects of the present invention will become clear from preferred embodiments described below with reference to the drawings. [Invention effect]

According to the present invention, for example, it is possible to provide a technology that is helpful for accurately correcting the imaging error of the optical system.

Hereinafter, embodiments will be described in detail with reference to the drawings. In addition, the following embodiments do not limit the scope of the patent claims of the inventors. Although a plurality of features are described in the embodiments, it is not limited to the case where all of the features are necessary for the invention; in addition, the features may be combined arbitrarily. Furthermore, in the drawings, the same or identical components are denoted by the same reference symbols, and repeated explanations are omitted.

In the following embodiment, an example will be described in which the correction method of the present invention for correcting the imaging error of an optical system that images a pattern on an imaged surface is applied to an exposure device that exposes a substrate. However, it is not Limited to this. The correction method of the present invention can be applied as long as the optical device uses a plurality of mechanisms (correction mechanisms) to correct the imaging error of the optical system that images the pattern on the imaged surface. Optical devices to which the correction method of the present invention can be applied may be provided in other lithography devices, telescopes, microscopes, cameras, laser printers, etc., in addition to the exposure device.

<First Embodiment> The first embodiment of the present invention will be described. FIG. 1(a) is a diagram illustrating a structural example of the exposure device 10 according to this embodiment. The exposure apparatus 10 of this embodiment may include an illumination optical system IL, a projection optical system PO, a reticle stage MS holding the reticle 12 (mask) and moving, a substrate stage WS holding the substrate 18 and moving, and the control unit 11 . The control unit 11 is composed of, for example, a computer (information processing device) including a processor such as a CPU and a memory, and controls the entire exposure device 10 (each part).

The light emitted from the light source (not shown) passes through the slit (not shown) included in the illumination optical system IL, and forms an arc-shaped illumination area long in the Y-axis direction on the original plate 12, for example. The original plate 12 and the substrate 18 are respectively held by the original plate stage MS and the substrate stage WS, and are arranged at optically substantially conjugate positions (positions of the object plane and the 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 the image of the pattern formed on the original plate 12 on the substrate 18 (that is, the pattern of the original plate 12 is imaged on the substrate 18). Then, the master 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 height corresponding to the projection magnification of the projection optical system PO. faster than scanning. Thereby, the pattern formed on the original plate 12 can be transferred to the substrate.

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

However, in the exposure apparatus 10, errors may occur in the position and/or shape of the pattern imaged on the substrate through the projection optical system PO (hereinafter, may be described as an imaging error). Such imaging errors, sometimes also called exposure errors and aberrations, may be caused by vibrations caused by driving the master stage MS and the substrate stage MS, deformation of optical components caused by exposure heat, environmental vibrations, and differences between exposure devices. It is caused by various factors such as differences in accuracy (also called machine differences). Therefore, the exposure device 10 is provided with a plurality of correction mechanisms for correcting the imaging error of the projection optical system PO, and by driving each of the plurality of correction mechanisms, the imaging error of the projection optical system PO is corrected.

In the exposure apparatus 10 of the present embodiment, as a plurality of correction mechanisms that correct the imaging error of the projection optical system PO, for example, among the low-order correction mechanism 13, the high-order correction mechanism 17, the master stage MS, and the substrate stage WS, it is possible to use 2 or more. However, it is not limited to this, 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 is configured to include a lens, a mechanism for driving the lens may be used as a correction mechanism.

Here, a structural example of the low-order correction mechanism 13 and the high-order correction mechanism 17 provided as correction mechanisms in the projection optical system PO will be described. The low-order correction mechanism 13 is a mechanism for correcting part of the low-order components in the imaging error of the projection optical system PO, and can be disposed between the original plate 12 (master stage MS) and the first surface 14a of the plane mirror 14 on the light path between. In addition, the high-order correction mechanism 17 is a mechanism for correcting high-order components in the imaging error of the projection optical system PO, and can be disposed between the second surface 14b of the plane mirror 14 and the substrate 18 (substrate stage WS). On the light path. Depending on its structure, the high-order correction mechanism 17 can correct part of the low-order components in the imaging error of the projection optical system PO. In this embodiment, the low-order component refers to the component of less than the third order in the imaging error, and the high-order component refers to the component of the third order or higher in the imaging error.

FIG. 1( b ) is a diagram illustrating a structural example of the low-level correction mechanism 13 . The low-level correction mechanism 13 includes an optical element 13a having a convex surface and an optical element 13b having a concave surface. The convex surface of the optical element 13a and the concave surface of the optical element 13b are opposed to each other with a gap Gap (air gap). The low-level correction mechanism 13, under the control of the control unit 11, uses a driving unit (not shown) such as an actuator to move the optical element 13a and the optical element 13b along the Z-axis as shown by the arrow in Fig. 1(b) direction (up and down direction) and/or relative movement in the XY plane direction (lateral direction). As a result, 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 illustrating a structural example of the high-level correction mechanism 17 . Figure 2(a) is a view of the high-order correction mechanism 17 when viewed from the optical axis direction (Z-axis direction); Figures 2(b) to (c) are views when viewed from a direction perpendicular to the optical axis direction (X-axis direction) Picture of the high-end correction mechanism at 17 hours. 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. Under the control of the control unit 11, the high-level correction mechanism 17 applies force to the outer periphery of the optical element 17a through each of the plurality of actuators 17b, thereby deforming the effective optical area ER (the area through which light passes) of the optical element 17a. For example, as shown in FIG. 2(c) , each actuator 17b is driven in the arrow direction to deform the effective optical area ER of the optical element 17a. This makes it 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 greater the number of actuators 17b, the greater the order of correctable imaging errors, but it is preferably configured taking into account constraints such as actual configuration space and manufacturing cost.

[Construction of optical device] Hereinafter, a structural example of the optical device 20 will be described. FIG. 3 is a schematic diagram illustrating a structural example of the optical device 20 according to 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 plate 12 on the substrate 18 as the imaged surface, and includes a plurality of correction mechanisms 21 and a control unit 22 (processing unit). In the example of FIG. 3 , correction mechanisms M1 to Mn (n is the number of correction mechanisms 21 ) are provided as a plurality of correction mechanisms 21 .

Each of the plurality of correction mechanisms 21 includes a structure 21a and a driving part 21b. The driving part 21b drives the structure 21a to change the position, posture and/or shape of the structure 21a, thereby changing the projection optical system PO. The mechanism by which imaging performance (imaging characteristics) changes. For example, when the correction mechanism 21 is the low-level correction mechanism 13, the structure 21a is the optical elements 13a to 13b, and the driving part 21b is an actuator that relatively moves the optical elements 13a to 13b. When the correction mechanism 21 is the high-level correction mechanism 17, the structure 21a is the optical element 17a, and the driving part 21b is a plurality of actuators 17b that drives the optical element 17a. In addition, the correction mechanism 21 may also be a mechanism that changes the imaging performance of the projection optical system PO by moving the master stage MS and/or the substrate stage WS parallel or tilting. In this case, the structure 21a of the calibration mechanism 21 is the master table MS and/or the substrate table WS, and the driving part 21b is an actuator that drives the master table MS and/or the substrate table WS.

The control unit 22 is composed of, for example, a computer having a processor such as a CPU and a memory, and controls each correction mechanism 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 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 unit 22c controls the drive of each correction mechanism 21 by giving a drive instruction to each correction mechanism 21 in accordance with the target drive amount determined by the calculation unit 22b.

Here, as shown in FIG. 4 , the integrated sensitivity matrix stored in the storage unit 22 a can be horizontally combined (connected, integration) to generate. The imaging sensitivity matrix represents the degree of change in the imaging of the projection optical system PO with respect to the driving of a correction mechanism 21 (hereinafter, sometimes referred to as the target correction mechanism 21) that is the target of obtaining the imaging sensitivity matrix. The imaging sensitivity matrix can also be understood as a matrix representing changes in the positions of each evaluation point on the substrate 18 (imaged surface).

Hereinafter, the method of generating the imaging sensitivity matrix and the integrated sensitivity matrix, and the method of determining the target drive amount of each correction mechanism 21 required to correct the imaging error of the projection optical system PO will be specifically described.

First, the imaging sensitivity matrix of each correction mechanism 21 will be described. The imaging sensitivity used in this embodiment refers to an evaluation point on the imaged surface (optical area) when one actuator constituting the driving unit 21b of the object correction mechanism 21 is driven with a predetermined driving amount (unit driving amount). The amount of change in imaging performance (such as position). The imaging sensitivity obtained by driving one actuator generally uses a plurality of evaluation points on the imaged surface, so it becomes a vector. Moreover, imaging performance refers to the optical index required for such correction of distortion or focus variation.

By sequentially driving each actuator in the driving part 21b of the object correction mechanism 21 with a predetermined driving amount, an imaging sensitivity vector corresponding to the number of actuators is obtained. Furthermore, the matrix formed by arranging these vectors is the imaging sensitivity matrix. Let the number of evaluation points on the imaged surface be m, let the number of actuators of the k-th correction mechanism 21 be p _k , and let the imaging performance of each evaluation point when driving the i-th actuator be When the variation vector is set to c _i , the imaging sensitivity matrix C _k can be expressed by the following formula (1). The imaging sensitivity matrix of each correction mechanism 21 can be obtained through an analytical model of each correction mechanism 21 or by mounting the correction mechanism 21 on the exposure device 10 and actually measuring the imaging performance of the projection optical system PO.

Next, the integrated sensitivity matrix will be described. The integrated sensitivity matrix of this embodiment combines a plurality of imaging sensitivity matrices respectively obtained for a plurality of correction mechanisms 21 in a horizontal arrangement, and becomes one imaging sensitivity matrix in appearance. If the integrated sensitivity matrix is set to C, it can be expressed as the following equation (2). The dimension of the integrated sensitivity matrix C is "m×r". Where r=(p ₁ +p ₂ +...+p _n ), p ₁ , p ₂ ,...p _n represent the number of actuators respectively provided in the correction mechanisms M1 to Mn. Therefore, r represents the total number of actuators of each correction mechanism. In this way, by horizontally combining the imaging sensitivity matrices of each correction mechanism, an integrated sensitivity matrix can be generated. Generally speaking, the integrated sensitivity matrix does not become a square matrix because the number of evaluation points m is not equal to the total number of actuators r. In addition, the imaging sensitivity matrix may be generated in advance by the calculation unit 22b and stored in the storage unit 22a.

Here, when the master stage MS and/or the substrate stage WS are used 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 is the number of correction degrees of freedom that can be performed on each stage. For example, 2 degrees of freedom for in-plane translation (X-axis direction, Y-axis direction), 3 degrees of freedom for tilt (rotation direction about the X-axis, rotation direction about the Y-axis, rotation direction about the Z-axis), etc. In addition, in the case of correction mechanisms such as the low-order correction mechanism 13 and the high-order correction mechanism 17 that adjust the position and/or attitude of the optical element to correct the imaging error of the projection optical system PO, similarly, the number of actuators, It also 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 unit 22b will be described. To correct the imaging error of the projection optical system PO, it is necessary to prepare in advance information/data (hereinafter, sometimes referred to as imaging error information) indicating the imaging error of the projection optical system PO that should be corrected. The imaging error information represents the imaging error (for example, overlay error) of each evaluation point on the substrate 18 (imaged surface), and can be expressed as a matrix (for example, a vector) having the same number of matrix elements as the number of evaluation points. In addition, the imaging error information may be a matrix having the same number of matrix elements as the matrix elements of the above-mentioned imaging sensitivity matrix. The imaging error information may be based on the results of measuring the overlay error of the substrate patterned by the exposure device 10 using an external inspection device, the results of actually measuring the imaging performance of the projection optical system PO in the exposure device 10 , or may be based on the results of performing generated from the results of exposure simulation. The generated imaging error information can be supplied to the calculation unit 22b of the control unit 22. FIG. 3 shows an example in which the imaging error information is supplied from an external device to the calculation unit 22b, but it may be stored in the storage unit 22a in advance.

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, the integrated sensitivity matrix (the first matrix) is defined, the drive amount matrix (the second matrix) in which the target drive amount of each correction mechanism 21 is a matrix element, and the imaging error matrix (the second matrix) which is composed of the imaging error information are solved. 3 matrix) to determine the target drive amount of each correction mechanism 21. Generally speaking, the drive amount matrix is a vector with the total number of actuators of each drive mechanism r×1, and the imaging error matrix is a vector with the number of evaluation points m×1. This equation can be expressed by the following equation (3) if the integrated sensitivity matrix is set to C, the driving amount matrix is set to D, and the imaging error matrix is set to S.

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

Here, , is the virtual inverse matrix of the unified sensitivity matrix, and the method of solving simultaneous equations based on this virtual inverse matrix is mathematically equivalent to the least squares method. In addition, the driving amount matrix obtained in this way , is obtained as a matrix in which the target drive amounts of each correction mechanism M1 to Mn are arranged as matrix elements, and has the following meaning. That is, based on the characteristics of the virtual inverse matrix, when a longitudinal matrix in which the number of columns m of the integrated sensitivity matrix is greater than the number of rows r is combined, the driving amount matrix is obtained , becomes the least square solution that minimizes equation (5).

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

That is, in order to improve the correction accuracy of the imaging error of the projection optical system PO, it is better to form a vertically long integrated sensitivity matrix than to form a horizontally wide integrated sensitivity matrix. On the other hand, when it is desired to reduce the energy input to the correction mechanism 21 as much as possible, it is better to create a horizontally wide integrated sensitivity matrix rather than a vertically long integrated sensitivity matrix. The method of creating the horizontal integrated sensitivity matrix is basically the same as the method of creating the vertical integrated sensitivity matrix, which is to combine the imaging sensitivity matrices of each correction mechanism horizontally. The characteristic is that the number m of evaluation points is smaller than the number r obtained by adding up the number of actuators (or the number of correction degrees of freedom) of each correction mechanism 21 .

Here, in this embodiment, when creating the integrated sensitivity matrix, each imaging sensitivity matrix is combined laterally, but each imaging sensitivity matrix may be transposed (that is, the columns become the arrangement of evaluation points, and the rows become the actuators). arrangement) and then combined in the longitudinal direction. In this case, the integrated sensitivity matrix needs to be transposed when performing matrix calculations.

[Modification] FIG. 5 is a schematic diagram illustrating 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 that the information stored in the storage unit 22a of the control unit 22 is different. In the optical device 20 of this modification, a plurality of imaging sensitivity matrices respectively obtained for a plurality of correction mechanisms 21 may be stored in the storage unit 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.

[Correction method for imaging errors] Hereinafter, a method of correcting the imaging error of the projection optical system PO will be described. FIG. 6 is a flow chart illustrating a method for correcting imaging errors of the projection optical system PO. Each program in the flowchart shown in FIG. 6 can be executed by the control unit 22 (for example, the calculation unit 22b) of the optical device 20.

In step S11 , the control unit 22 obtains the imaging sensitivity matrix for each correction mechanism of the plurality of correction mechanisms 21 . That is, the control unit 22 obtains a plurality of imaging sensitivity matrices respectively obtained for a plurality of correction mechanisms 21 . The imaging sensitivity matrix, as mentioned above, can be obtained through analytical models or actual measurements. 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 mentioned 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 mentioned above, the imaging error information can be generated based on the measurement results of the overlay error by an external inspection device, actual measurement results in the exposure device 10 , exposure simulation results, etc.

In step S14 , the control unit 22 generates a matrix defining the integrated sensitivity matrix (first matrix) generated in step S12 , the imaging error matrix (third matrix) obtained in step S13 , and a target drive amount indicating the target drive amount of each correction mechanism 21 . Equation of the relationship between the driving amount matrix (second matrix). For example, when the integrated sensitivity matrix is set to C, the driving amount matrix is set to D, and the imaging error matrix is set to S, the control unit 22 can generate the equation: S=CD as shown in the above equation (3). The equation of.

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, an integrated sensitivity matrix using a combined sensitivity matrix (a plurality of combined sensitivity matrices) obtained for each of the plurality of correction mechanisms 21 as a matrix element is used to determine the reduction of the projection optical system PO. Target drive amount of each correction mechanism 21 for imaging error. Thereby, it is possible to perform correction with high accuracy on the entire plurality of correction mechanisms 21 so as to reduce the imaging error of the projection optical system PO.

<Second Embodiment> A second embodiment of the present invention will be described. This embodiment basically succeeds the first embodiment, and is the same as that described in the first embodiment except for the matters mentioned below.

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

First, the physical constraints of the correction mechanism 21 will be described. The physical constraints of the correction mechanism, such as the aforementioned high-order correction mechanism 17 (see FIG. 2 ), require correction of the imaging error of the projection optical system PO by using a plurality of actuators 17 b to deform the optical element 17 a. Consider the correction mechanism (deformation mechanism). In the high-order correction mechanism 17, depending on the driving amount of each actuator 17b for deforming the optical element 17a (for example, the difference between the driving amounts of adjacent actuators 17b), there is a possibility that excessive force is applied to the optical element 17a. The optical element 17a is cracked due to the stress. Therefore, it is necessary to limit the difference Δh in the driving amounts of the plurality of actuators 17b (especially between adjacent actuators 17b) so that the stress generated in the optical element 17a is insufficient to cause damage. Therefore, it is preferable to use the difference Δh in the driving amounts of the plurality of actuators 17b such that the stress generated in the optical element 17a is less than the breaking stress as the constraint condition. For example, assuming that the distance between adjacent actuators 17b is L, the greater Δh/L is, the greater the stress applied to the optical element 17a will be. If it exceeds the breaking stress, cracking will occur. Therefore, the difference Δh of the maximum driving amount in the range where the stress generated by the optical element 17a is insufficient to break the stress based on the interval L of the actuator 17b can be used as a constraint condition. In addition, the correction mechanism to which physical constraints are given is not limited to a correction mechanism (deformation mechanism) that performs deformation driving of an optical element, such as the high-order correction mechanism 17 .

Next, constraints imposed by the system requirements of the projection optical system PO or the exposure device 10 will be described. As a constraint from the system requirements, consider the side effects of driving a plurality of correction mechanisms 21 . For example, in the correction mechanism 21 that adjusts (changes) the position and/or attitude of a structure such as an optical element, a desired imaging error (first imaging error, such as distortion) can be corrected. However, when the correction mechanism 21 is driven to correct a desired imaging error, an imaging error of a different type from the desired imaging error (a second imaging error, such as an astigmatism component) may occur (increase) as a side effect. . Therefore, it is necessary to drive each correction mechanism of the plurality of correction mechanisms 21 so that the second imaging error (astigmatism component) generated as a side effect falls within the allowable range (becomes below the allowable value), and this can be used as a constraint condition . In addition, constraints derived from system requirements are not limited to the above examples.

In this way, when there are physical constraints and constraints from system requirements, the driving quantity matrix is obtained It is better to use constrained optimization techniques. In terms of constrained optimization techniques, they include various types such as obstacle function method, penalty function method, Lagrangian multiplication, sequential quadratic programming method, continuous linear programming method, etc. Although there are problems of being good at/not good at each, as long as Just choose the method appropriate to the problem you're solving. For example, when using the numerical analysis software matlab of The MathWorks Company, you can use the lsqlin function for constrained linear least squares problems. As a physical constraint, let the matrix used to calculate the difference in drive amounts between adjacent actuators be A, and the allowable value of the difference in drive amounts between adjacent actuators be b , then the constraint condition expression is expressed by the following equation (6).

Here, when matrix A is multiplied by drive amount matrix D, the difference in drive amount is obtained. Therefore, the driving quantity matrix obtained by band constraints , can be expressed as the following equation (7) in matlab. In addition, the above example is an example using a function of MATLAB, and it can also be other optimization calculation tools or self-made optimization calculation tools.

<3rd Embodiment> A third embodiment of the present invention will be described. This embodiment is basically inherited from the first embodiment, and is the same as that described in the second embodiment except for the matters mentioned below. In addition, in this embodiment, the second embodiment (that is, optimization with constraints) can also be applied.

In this embodiment, a correction method of the optical device 20 including the low-order correction mechanism 13 and the high-order correction mechanism 17 will be described. FIG. 8 is a schematic diagram illustrating a structural example of the optical device 20 according to this embodiment. In this case, the integrated sensitivity matrix is generated from the imaging sensitivity matrix of the low-order correction mechanism 13 and the sensitivity matrix of the high-order correction mechanism 17 . Generally speaking, low-order imaging errors have a larger error amount (scalar quantity) than high-order imaging errors, and the correction amount of the low-order correction mechanism 13 is larger than that of the high-order correction mechanism 17 . Although the high-level correction mechanism 17 can also correct low-level imaging errors, as explained in the second embodiment, there are physical constraints such as preventing the rupture of the optical element 17a, and it cannot increase the adjacent actuation without limit. The difference between the driving amounts of the devices 17b. Therefore, by setting the constraint condition of the difference in driving amount for the high-order correction mechanism 17 , imaging errors from low-order to high-order can be corrected safely and accurately 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 this 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. In addition, the number of low-order correction mechanisms and high-order correction mechanisms is not limited.

＜Embodiment of manufacturing method of article＞ The method of manufacturing an article according to an embodiment of the present invention is suitable for manufacturing articles such as microdevices such as semiconductor devices and elements having a fine structure. The manufacturing method of an article according to this embodiment includes: a process of forming a latent image pattern (a process of exposing the substrate) using the above-mentioned exposure device on the photosensitive agent applied to the substrate; and the substrate on which the latent image pattern is formed in the above-mentioned process. The process of developing (processing). Furthermore, the manufacturing method includes other well-known procedures (oxidation, film formation, evaporation, doping, planarization, etching, resist stripping, cutting, bonding, packaging, etc.). The method of manufacturing an article according to this embodiment is advantageous in at least one of the performance, quality, productivity, and production cost of the article compared with conventional methods.

<Other Examples> The present invention can also provide a program that implements one or more functions of the above-described embodiments to a system or device via a network or a storage medium, and use one or more processors in a computer of the system or device to convert the program The processing of reading and executing is realized. In addition, it can also be implemented through a circuit (for example, ASIC) that implements more than one function.

The invention is not limited to the above-described embodiments, and various changes and modifications can be made without departing from the spirit and scope of the invention. Therefore, the patent application is drafted to disclose the scope of the invention.

10:Exposure device 11:Control Department 12:Original board 13: Low-level correction mechanism 17:High-end correction mechanism 18:Substrate IL: illumination optical system MS:Original station PO: Projection optical system WS:Substrate table 20:Optical device 21: Correction mechanism 22:Control Department

[Fig. 1] A diagram illustrating a structural example of an exposure device. [Fig. 2] A diagram illustrating a structural example of a high-end correction mechanism. [Fig. 3] A schematic diagram illustrating a configuration example of the optical device according to the first embodiment. [Fig. 4] A schematic diagram for explaining the generation of the integrated sensitivity matrix. [Fig. 5] A schematic diagram illustrating a modification of the optical device according to the first embodiment. [Fig. 6] A flowchart illustrating a method for correcting imaging errors of a projection optical system. [Fig. 7] A diagram for explaining the calculation processing of the calculation unit in the second embodiment. [Fig. 8] A schematic diagram illustrating a modification of the optical device according to the third embodiment.

20:Optical device

21: Correction mechanism

21a:Constructs

21b:Drive Department

22:Control Department

22a: Preservation Department

22b: Calculation Department

22c: Drive instruction part

Claims (13)

A correction method that corrects the imaging error of an optical system that causes a pattern to be imaged on the imaged surface by driving a plurality of mechanisms. Include: Obtaining a program for obtaining, for each of the plurality of mechanisms, an imaging sensitivity matrix indicating a degree of change in the imaging of the optical system with respect to driving of the mechanism; Determining a program that defines a first matrix in which the imaging sensitivity matrix obtained in the acquisition process for each of the plurality of mechanisms is a matrix element, and a target drive amount for each of the plurality of mechanisms is a matrix. An equation of the relationship between the second matrix of elements and the third matrix formed from the information of the aforementioned imaging error, thereby determining the aforementioned target driving amount for each of the aforementioned plurality of mechanisms; and A driver program drives each of the plurality of mechanisms in accordance with the target drive amount determined by the determination program. The correction method of claim 1, wherein the first matrix is obtained by combining matrix elements in the horizontal or vertical direction of the imaging sensitivity matrices obtained in the acquisition process for each of the plurality of mechanisms. The correction method of claim 1, wherein in the determination program, when the first matrix is C, the second matrix is D, and the third matrix is S, the equation formed by S=CD is solved. , thereby determining the target drive amount for each of the plurality of mechanisms. The correction method of claim 1, wherein in the determination program, the equation is solved using a least squares method to determine the target drive amount for each of the plurality of mechanisms. The correction method of Claim 1, wherein in the determination process, the equation is solved in a manner that satisfies a predetermined constraint condition, thereby determining the target drive amount for each of the plurality of mechanisms. Such as the correction method of request item 5, wherein, The aforementioned plurality of mechanisms include a deformation mechanism that uses a plurality of actuators to deform the optical element, The constraint conditions include conditions for limiting differences in driving amounts of the plurality of actuators in the deformation mechanism. The correction method of claim 5, wherein the constraint condition includes driving the second imaging error in a manner such that a second imaging error of a different type from the imaging error falls within an allowable range when the imaging error is corrected. Conditions for each of multiple institutions. The correction method of claim 1, wherein the plurality of mechanisms include at least one mechanism for correcting low-order components of the aforementioned imaging error and at least one mechanism for correcting high-order components of the aforementioned imaging error. An exposure method that includes: A correction program that uses the correction method according to any one of claims 1 to 8 to correct the imaging error of the optical system that images the pattern on the substrate as the imaged surface; and The exposure process is to expose the substrate using the optical system that has corrected the imaging error through the correction process. A method of making an item, including: An exposure procedure, which is to expose the substrate using the exposure method of claim 9; A processing procedure for processing the aforementioned substrate exposed by the aforementioned exposure procedure; and A manufacturing process for manufacturing an article from the above-mentioned substrate processed in the above-mentioned processing process. A program that is stored in a memory medium in order to cause a computer to perform the correction method in any one of claims 1 to 8. an optical device, Has: A plurality of mechanisms that correct the imaging errors of the optical system that causes the pattern to be imaged on the imaged surface; and The Control Department, which controls each of the aforementioned plurality of organizations; The control unit drives each of the plurality of mechanisms using the correction method according to any one of claims 1 to 8 to correct the imaging error. An exposure device for exposing a substrate, Has: An optical system that images the pattern on the aforementioned substrate as the imaged surface; and The optical device of claim 12.

Images