Evaluation method, exposure apparatus, and article manufacturing method

Abstract

To provide technology suitable for performing highly precise measurement of optical characteristics.SOLUTION: An evaluation method for evaluating an optical characteristic of a projection optical system is provided. The evaluation method includes a measurement step of illuminating a test reticle having a test pattern disposed on an object plane of the projection optical system, and measuring an amount of positional deviation of an image of the test pattern formed on an image plane of the projection optical system, and an estimation step of estimating the optical characteristic of the projection optical system based on a result of the measurement, wherein in the estimation step, the optical characteristic is estimated using a polynomial model including a regularization term.SELECTED DRAWING: Figure 2

Description

[Technical Field]

[0001] The present invention relates to an evaluation method, an exposure apparatus, and an article manufacturing method. [Background technology]

[0002] Conventionally, a reticle with a test pattern can be used to measure the optical characteristics (best focus position, astigmatism, field curvature, wavefront aberration, etc.) of the projection optical system of an exposure apparatus. The test pattern is exposed using the reticle, the position of the exposed test pattern image is detected, and the optical characteristics of the projection optical system are determined based on the detection results (for example, Patent Document 1).

[0003] The optical characteristic is, for example, wavefront aberration. Wavefront aberration is a scalar quantity defined within a pupil with two-dimensional coordinates, and can be expressed as a function of two variables, such as W(x, y). Here, x and y are variables representing position coordinates on the pupil, and are normalized so that the distance from the center of the pupil to the edge of the pupil is 1. W represents wavefront aberration. Wavefront aberration is often expressed in units where the exposure wavelength is 1 unit, such as λ (lambda) or mλ (millilambda), which is 1 / 1000 of that. Furthermore, because wavefront aberration is defined within an approximately circular pupil, it is convenient to express it using the Zernike orthogonal function system. The Zernike orthogonal function system has the characteristic of being orthogonal within a unit circle. For example, wavefront aberration can be expressed by the following equation:

[0004]

number

[0005] [Patent Document 1] Patent No. 4343685 Summary of the Invention [Problem to be solved by the invention]

[0006] However, conventional optical characteristic measurement methods have a problem in that it is difficult to obtain measurement data near the pupil edge, which means that it is necessary to estimate the wavefront aberration of the entire pupil without any measurement data near the pupil edge, making it difficult to measure wavefront aberration with high accuracy.

[0007] The present invention provides an advantageous technique for measuring optical properties with high accuracy. [Means for solving the problem]

[0008] According to one aspect of the present invention, there is provided an evaluation method for evaluating the optical characteristics of a projection optical system, comprising: a measurement step of illuminating a test reticle having a test pattern placed on an object plane of the projection optical system and measuring the amount of positional deviation of an image of the test pattern formed on an image plane of the projection optical system; and an estimation step of estimating the optical characteristics of the projection optical system based on the results of the measurement, wherein the estimation step estimates the optical characteristics using a polynomial model including a regularization term. [Effects of the Invention]

[0009] According to the present invention, it is possible to provide an advantageous technique for measuring optical characteristics with high accuracy. [Brief explanation of the drawings]

[0010] [Figure 1] FIG. 1 is a diagram showing the configuration of an exposure apparatus. [Figure 2] FIG. 1 is a diagram showing a configuration for implementing a method for evaluating optical characteristics. [Figure 3] FIG. 1 is a diagram showing the configuration of a test reticle for measuring optical characteristics. [Figure 4] Schematic diagram of a light spot formed on the pupil plane of a projection optical system. [Figure 5] 5A and 5B are schematic diagrams showing image deviation of an image formed on an image plane. [Figure 6] A diagram showing the effect of a polynomial model including a regularization term. [Figure 7] FIG. 1 is a diagram showing an example of the configuration of a neural network. [Figure 8] A diagram showing the effect of neural networks. [Figure 9] 1 is a flowchart of a method for evaluating optical properties. [Figure 10] 1 is a flowchart of a method for evaluating optical properties. [Figure 11] A diagram showing Zernike polynomials. DETAILED DESCRIPTION OF THE INVENTION

[0011] Hereinafter, embodiments will be described in detail with reference to the accompanying drawings. Note that the following embodiments do not limit the scope of the invention claimed. Although multiple features are described in the embodiments, not all of these multiple features are necessarily essential to the invention, and multiple features may be combined arbitrarily. Furthermore, in the accompanying drawings, the same reference numerals are used to designate the same or similar components, and redundant explanations will be omitted.

[0012] First Embodiment An embodiment for evaluating the optical characteristics of a projection optical system in an exposure apparatus will be described below.

[0013] FIG. 1 is a diagram showing the configuration of an exposure apparatus EX. The exposure apparatus EX is a lithography apparatus used in a lithography process, which is a manufacturing process for articles or devices such as semiconductor elements or liquid crystal display elements, and forms a pattern on a substrate W. In this specification and drawings, directions are indicated in an XYZ coordinate system, with the horizontal plane being the XY plane. Generally, the substrate W to be exposed is placed on a substrate stage WS so that its surface is parallel to the horizontal plane (XY plane). Therefore, in the following, the directions perpendicular to each other in a plane along the substrate mounting surface of the substrate stage WS are referred to as the X-axis and Y-axis, and the direction perpendicular to the X-axis and Y-axis is referred to as the Z-axis. In the following, the directions parallel to the X-axis, Y-axis, and Z-axis in the XYZ coordinate system are referred to as the X-direction, Y-direction, and Z-direction, respectively.

[0014] The exposure apparatus EX may be a scanning exposure apparatus (scanner). A scanning exposure apparatus is an exposure apparatus of a type that exposes a pattern formed on the reticle R onto the substrate W while synchronously moving the reticle R and the substrate W in a scanning direction (e.g., the Y direction). However, the present invention is not limited to scanning exposure apparatuses. The exposure apparatus EX may also be an exposure apparatus (stepper) that exposes the pattern of the reticle R onto the substrate W while the reticle R and the substrate W are fixed.

[0015] In this embodiment, the exposure apparatus EX is a step-and-scan scanning exposure apparatus that scans and exposes a substrate W using slit light. The exposure apparatus EX may include an illumination optical system IL, a reticle stage RS that holds a reticle R, a projection optical system 2, a substrate stage WS that holds a substrate W, an imaging unit AS, a detection unit D, a controller MC, and a processor IP. The controller MC may be configured, for example, by a computer (information processing device) having a processor such as a CPU (Central Processing Unit) and a storage unit such as a memory. The controller MC controls the exposure process of the substrate W by controlling each part of the exposure apparatus EX in accordance with a program stored in the storage unit. The program may also include a program for causing the processor to execute each step of a measurement method (evaluation method) described below.

[0016] The illumination optical system IL illuminates a portion of the reticle R with light emitted from a light source (not shown), such as an excimer laser. The reticle R and the substrate W are held by a reticle stage RS and a substrate stage WS, respectively, and are positioned at optically conjugate positions via the projection optical system 2. The reticle R is positioned on the object plane of the projection optical system 2, and the substrate W is positioned on the image plane of the projection optical system 2. The projection optical system 2 has a predetermined projection magnification (for example, 1 / 2 or 1 / 4), and projects the pattern formed on the reticle R onto the substrate.

[0017] The reticle stage RS and the substrate stage WS are configured to be movable in a direction perpendicular to the optical axis of the projection optical system 2, and are scanned relative to each other in synchronization with each other at a speed ratio that corresponds to the projection magnification of the projection optical system 2. This allows the shot area SH to be scanned over the substrate, and the pattern of the reticle R to be transferred to the shot area SH on the substrate. Then, by repeating this scanning exposure sequentially for each of the multiple shot areas on the substrate, the exposure process for one substrate W can be completed.

[0018] The detection unit D includes, for example, a laser interferometer, and detects the position of the substrate stage WS. The laser interferometer included in the detection unit D, for example, irradiates a laser beam toward a reflector M provided on the substrate stage WS, and detects the displacement of the substrate stage WS from a reference position by the laser beam reflected by the reflector M. This allows the detection unit D to obtain the current position of the substrate stage WS based on the displacement. Here, the detection unit D uses a laser interferometer when detecting the position of the substrate stage WS, but this is not limited to this, and an encoder, for example, may also be used.

[0019] The substrate stage WS holds the substrate W via a substrate chuck (not shown) that chucks the substrate W. The substrate stage WS can be driven by a substrate driving mechanism (not shown). The substrate driving mechanism is a positioning mechanism that positions the substrate W. The substrate driving mechanism includes a linear motor or the like, and can move the substrate W held by the substrate stage WS by driving the substrate stage WS in the X direction, Y direction, Z direction, and rotational directions around each axis.

[0020] The imaging unit AS may include an illumination unit (not shown). Light from the illumination unit illuminates the substrate W, and the reflected light enters the imaging unit AS. The imaging unit AS captures the incident light with an imaging element and generates an image signal. The image signal is transferred to the processing unit IP.

[0021] The processing unit IP may perform measurement processing of the mark position using a template matching method or the like based on the image acquired by the imaging unit AS. The processing unit IP may also perform processing to determine the optical characteristics of the projection optical system 2 by measuring the amount of positional deviation of an image of a test pattern obtained using a test reticle (described later) and processing the measurement results. The processing unit IP may be a computer device including a CPU and memory. The processing unit IP and the control unit MC may be configured as separate devices, or the functions of the processing unit IP and the control unit MC may be realized by a single computer device.

[0022] FIG. 2 is a diagram showing a configuration for implementing an optical characteristic evaluation method according to an embodiment. The optical characteristic evaluation according to this embodiment can be performed on an exposure apparatus EX. Evaluating the optical characteristics of the projection optical system on the exposure apparatus is important for apparatus maintenance. The projection optical system unit installed in the exposure apparatus has its optical characteristics measured and adjusted using a measuring instrument such as an interferometer during the unit assembly stage before being installed on the exposure apparatus main body. However, optical characteristics can change due to differences in the way the unit and the main body are held and fastened, as well as differences in the surrounding environment, such as temperature. Furthermore, optical characteristics can change due to environmental changes during transportation between shipping from the factory and installation at the customer's site. Furthermore, optical characteristics can change over time while the system is in use at the customer's site. It is necessary to accurately grasp these changes in optical characteristics and correct them using a correction system as necessary to maintain excellent optical performance of the exposure apparatus. For this reason, it is important to measure the optical characteristics of the projection optical system on the exposure apparatus with high accuracy.

[0023] The optical characteristic measuring method of this embodiment uses a test reticle 1 having a test pattern for measuring optical characteristics, as shown in FIG. 2. A diffuser 11 is disposed on the upper surface of the test reticle 1. A pinhole 12 is formed below the diffuser 11 on the upper surface of the test reticle 1. Aberration measurement marks 13 are also provided on the lower surface of the test reticle 1. For example, multiple aberration measurement marks are provided for each pinhole. The multiple aberration measurement marks are arranged, for example, in a grid pattern so that light emitted from each aberration measurement mark evenly covers the pupil of the projection optical system. As disclosed in Japanese Patent No. 4343685 (Patent Document 1), the aberration measurement marks are designed to suppress high-frequency components of diffracted light.

[0024] The test reticle 1 is illuminated by the illumination optical system IL. The light that illuminates the test reticle 1 passes through a diffuser 11, a pinhole 12, and an aberration measurement mark 13, and then enters the projection optical system 2. The light beam that enters the projection optical system 2 passes through the pupil plane 21 of the projection optical system 2. After being narrowed by the pinhole 12, this light beam passes through the aberration measurement mark 13, which is designed to suppress the high-frequency components of diffracted light, and is therefore narrowed to a fine spot. As a result, this light beam forms a localized spot on the pupil plane 21 of the projection optical system 2. This light beam is bent by the local tilt of the wavefront aberration on the pupil plane, and reaches the image plane 3 of the projection optical system 2.

[0025] A substrate W is placed on the image plane 3 of the projection optical system 2. The substrate W is coated with a photosensitive material such as resist, and an image of the aberration measurement mark 13 is projected and exposed onto it. At this time, the image is exposed at a position shifted from its original position depending on the amount by which the light beam is bent by the wavefront aberration. In other words, the position shift of the image of the aberration measurement mark 13 contains information about the local tilt of the wavefront aberration at the point where the light emitted from that aberration measurement mark 13 intersects with the pupil plane 21. By measuring the position shift of the images of multiple aberration measurement marks 13, information about the local tilt of the wavefront aberration over almost the entire area on the pupil plane can be obtained. The wavefront aberration can be measured by reconstructing the wavefront aberration from this information.

[0026] FIG. 3 shows the detailed configuration of a test reticle 1 having a test pattern for measuring optical characteristics. The illumination light beam is diffused by a diffuser plate 11 disposed above the upper surface of the reticle, passes through a pinhole 12 formed on the upper surface of the reticle, and is incident on an aberration measurement mark 13 formed on the lower surface of the reticle. At this time, the light beam illuminating the aberration measurement mark 13 has an angle corresponding to the diameter of the pinhole. In FIG. 2, this light beam is defined by a lower limit ray 14 (lower marginal ray) and an upper limit ray 15 (upper marginal ray). The aberration measurement mark 13 is designed to suppress high-frequency components of diffracted light. Therefore, the light beam passing through the aberration measurement mark 13 emerges downward from the aberration measurement mark 13 as a thin diffracted light with suppressed high frequencies. In FIG. 3, the light beam passing through the aberration measurement mark 13 is defined by a lower limit ray 16 (lower marginal ray) and an upper limit ray 17 (upper marginal ray). 3, a plurality of aberration measurement marks 13 are formed on the underside of the reticle. In one example, the plurality of aberration measurement marks 13 are arranged in a grid pattern. A thin beam of light is formed at each of the plurality of aberration measurement marks 13 and is emitted downward.

[0027] These light beams enter the projection optical system 2. Figure 4 is a schematic diagram showing the state of the light beams reaching the pupil plane 21 of the projection optical system 2. The relative positional relationship between the pinhole 12 and each of the multiple aberration measurement marks 13 determines the position where the center of each light beam intersects with the pupil plane 21, resulting in the formation of multiple light beam spots on the pupil plane 21 corresponding to the multiple aberration measurement marks 13. In Figure 4, the edge 22 of the pupil plane 21 is determined by the iris diaphragm, lens diameter, etc., and represents the boundary of the area through which light rays can pass. Here, for light beam spots 23, where the entire light beam falls within the pupil plane 21, all of the light beam can pass through the projection optical system 2 and form a normal image on the image plane 3. However, for light beam spots 24a and 24b, where part of the light beam extends beyond the edge 22 of the pupil plane 21, part of the light beam is vignetted by the pupil plane 21, and therefore a normal image is not formed on the image plane 3. This often results in poor image resolution or abnormal line widths, making it impossible to measure image shift. Therefore, it is difficult to obtain image shift data for aberration measurement marks used to measure the pupil periphery. Furthermore, the light rays that emerge from the pupil periphery and reach the image plane form a large angle with the normal to the image plane. For example, in the case of a projection optical system with NA = 0.86, the angle between the marginal ray and the normal to the image plane is 59 degrees. Because the angle between the ray and the normal to the image plane is large, there is a greater possibility that the amount of light required to expose the resist will be insufficient or that the ray will be affected by instability in the resist process, compared to light rays with a small angle. These are also factors that make it difficult to obtain data for the pupil periphery.

[0028] FIG. 5 is a schematic diagram visualizing image shift data of an image formed on the image plane 3. The shift data can be obtained, for example, by exposing and developing a substrate W placed on the image plane 3 and observing the resist pattern with a measuring device outside the exposure tool. Alternatively, the shift data can be obtained by observing the resist latent image on the exposed substrate using a scope (imaging unit AS) of the exposure tool. Since image shift has X- and Y-direction components, in FIG. 5 the image shift is represented by vectors 26. Each vector corresponds to the image shift of each aberration measurement mark 13. Each vector is drawn starting from the position where the light ray emitted from each aberration measurement mark 13 intersects with the pupil plane 21. As mentioned above, image shift data cannot be obtained in the pupil periphery. Therefore, in FIG. 5, there is no data (vector) in the pupil periphery, which is the area outside the circle indicated by the dashed line 25 (e.g., the area 0.88 mm or more away from the pupil center).

[0029] Each vector corresponds to the local gradient of the wavefront aberration at that position. To reconstruct the wavefront aberration from this, for example, we do the following. As mentioned earlier, the wavefront aberration is expressed by Zernike coefficients, for example, terms 2 to 36. Therefore, calculating the wavefront aberration is a matter of calculating the Zernike coefficients using shift data as input.

[0030] The problem is formulated. Let the number of shift data be N. N is equal to twice the number of aberration measurement marks for which image shift is measured (because image shift consists of two components, in the x and y directions). Also, let the number of Zernike coefficients to be determined be M. For example, if wavefront aberration is expressed using Zernike coefficients c2 to c36, then M = 35. Next, define the sensitivity matrix S. The sensitivity matrix S is a matrix with N rows and M columns, and is expressed as follows:

[0031]

number

[0032] Element s in the i-th row and j-th column of the sensitivity matrix S ijis the shift amount of the image of the ith aberration measurement mark when the jth term of the Zernike polynomial exists by unit amount. By calculating the local slope of the Zernike function and multiplying it by λ / NA, each s ij The local gradient can be obtained by differentiating the Zernike function. Alternatively, the gradient of the least-squares plane in a finite range can be obtained as the local gradient. In addition, s can be obtained by a partial coherent imaging simulation that reproduces this measurement method. ij You can also ask for:

[0033] Here, the column vector formed by the measured shift data is defined as B. The column vector B is a column vector with N elements and is expressed as follows:

[0034]

number

[0035] the i-th element b of column vector B i is the measured shift amount of the image of the i-th aberration measurement mark.

[0036] Next, let X be a column vector composed of Zernike coefficients to be found. The column vector X has M elements and is expressed as follows:

[0037]

number

[0038] j-th element x of column vector X j is the j-th Zernike coefficient value.

[0039] Using the above S, B, and X, the problem of finding Zernike coefficients from shift data can be solved as follows: SX=B By solving this equation for X, we can find the Zernike coefficients.

[0040] In the above equation, N is larger than M, so multiple regression or similar methods have traditionally been used to solve the problem. Multiple regression is a method that defines a loss function L using the following equation and finds X that minimizes it (T represents the transpose matrix):

[0041] L=(B-SX) T (B-SX)

[0042] However, when estimating the wavefront aberration of the entire pupil using multiple regression without data on the pupil periphery, the pupil periphery is extrapolated. Extrapolation is the process of using known numerical data to find predicted values ​​outside the range of that data. This extrapolation can result in calculations that are not highly accurate. For example, the measured shift data always contains measurement errors. Solutions obtained by multiple regression exhibit very unstable behavior, with solutions varying significantly depending on how the errors are incorporated. This results in poor measurement reproducibility. Furthermore, wavefront aberration includes not only Zernike terms up to 36, but also higher-order terms, such as terms 37 and above. These higher-order terms affect the Zernike terms up to 36 in the multiple regression solution, resulting in values ​​that differ from the original coefficient values ​​up to 36, making it impossible to determine the correct value.

[0043] These problems exist in conventional methods for measuring wavefront aberration. The present invention addresses these problems by using a machine learning technique. In the first embodiment, a method for estimating optical characteristics using a polynomial model including a regularization term, among the machine learning techniques for determining wavefront aberration, will be described. In this embodiment, the optical characteristics are typically wavefront aberration at the pupil plane 21 of the projection optical system 2.

[0044] The method for calculating the wavefront aberration in this embodiment uses a method that applies a technique called Ridge regression. In this embodiment, a regularization matrix A is introduced. The regularization matrix A is a diagonal matrix with M rows and M columns, and each component α jIn this embodiment, the terms used for fitting the Zernike polynomial are the second to 169th terms. Therefore, M=168.

[0045]

number

[0046] Then, we define the loss function L as follows and find X that minimizes it.

[0047] L=(B-SX) T (B-SX)+X T AX

[0048] Compared to the loss function of multiple regression, the second term X T AX is added. This is a term called a regularization term, and has the effect of preventing the solution from becoming too large (limiting the value of the coefficients). The reason why multiple regression cannot obtain a reasonable solution is that it overfits the data inside the pupil, ignoring the peripheral parts of the pupil where there is no data. Such solutions often have large absolute values ​​for the individual terms in the solution, so it is effective to use a regularization term to prevent the absolute value of each term from becoming too large.

[0049] α, the j-th element of the regularization matrix A j is the regularization parameter for the j-th Zernike coefficient value. j is a so-called hyperparameter that influences the performance of this optimization. j is not determined automatically, so some value must be given externally. j The value of the regularization parameter α is preferably determined based on the characteristics of the wavefront aberration data or adjusted based on past wavefront aberration data. j How to determine is explained below.

[0050] (1) First, during the unit assembly stage, the optical characteristics of the projection optical system are measured using a measuring instrument such as an interferometer, and the projection optical system is adjusted so that each term in the Zernike coefficients of wavefront aberration is sufficiently small. In this state, the unit is temporarily completed. When the completed projection optical system is mounted on the exposure tool, its optical characteristics may change due to differences in the holding and fastening methods between the time of unit assembly and the time of mounting on the exposure tool, as well as differences in the ambient environment, such as temperature. Previous data on the assembly and adjustment of exposure tools has shown that the wavefront aberration components that change at this time are dominated by the low-order components C2 to C9, while terms C10 and above do not change significantly. In other words, terms C10 and above do not change significantly from the small adjusted values ​​at the time of unit completion.

[0051] (2) Furthermore, between the time the exposure tool is shipped from the factory and the time it is installed at the customer's site, the optical characteristics of the projection optical system may change due to environmental changes during transportation. In this case, too, it has been found from previous installation data on exposure tools that the components of the wavefront aberration that change are dominated by the low-order components C2 to C9, and that terms C10 and beyond do not change significantly.

[0052] (3) Furthermore, there is a possibility that the optical characteristics may change over time while the lens is in use at the customer's site. In this case, too, it has been found from the accumulated data on changes over time that the components of the wavefront aberration that change are dominated by the low-order components from C2 to C9, and that the terms from C10 onwards do not change significantly.

[0053] (4) The above items (1) to (3) can be understood as follows: After the projection optical system unit is completed, one of the factors that causes aberration changes is that the individual optical components (lenses, mirrors, etc.) that make up the projection optical system may move slightly within the lens barrel. Aberration changes caused by slight changes in the lens's attitude, such as movement in a direction parallel to the optical axis, movement in a direction perpendicular to the optical axis, or tilt with respect to the optical axis, tend to be relatively low-order aberrations, such as Seidel's third-order aberrations and low-order decentration aberrations. Therefore, it is thought that wavefront aberrations that change mainly involve the relatively low-order C9 term.

[0054] Based on the above findings, the regularization parameter α j For , it is desirable to set small values ​​up to the terms corresponding to C9 and below, and to set somewhat larger values ​​for terms corresponding to C10 and above. This is because the terms C10 and above are adjusted to sufficiently small values ​​during the unit assembly stage and do not change much, so they are likely to remain small even on the exposure tool itself. Therefore, for terms that are known to be somewhat small, it is appropriate to increase the regularization parameter to constrain the solution so that it does not become too large. Conversely, for terms C9 and below, there is a possibility that they will change and become large on the exposure tool, so it is appropriate to reduce the regularization parameter to allow them to take any value freely.

[0055] Reasonable regularization parameter α j In order to find the value of , we repeatedly performed calculations while changing the balance between the terms corresponding to C9 and below and the terms corresponding to C10 and above in various ways, and searched for conditions under which a good solution could be obtained. As a result, for the terms corresponding to C9 and below, the regularization parameter α j = 0, and for terms corresponding to C10 or higher, the regularization parameter α j The inventors have found that it is preferable to set the regularization parameter α to a certain value. j can be determined based on the results of measurements performed in conjunction with at least one of a number of events, including assembly and adjustment of the projection optical system 2, transportation, and the operation period exceeding a predetermined period.

[0056] Figure 6 shows that for a certain exposure equipment unit, the terms corresponding to C9 and below are α j = 0, and for terms corresponding to C10 or more, α jThe RMSE on the vertical axis is the result of calculations carried out while changing . The RMSE on the vertical axis is the value obtained by taking the root mean square of the difference between the Zernike terms calculated from the shift data using the method of this embodiment and the Zernike terms obtained by interferometer measurement during unit assembly, which are considered to be the correct data. However, aberration components that are thought to have changed when the projection optical system is mounted on the exposure apparatus main body have been removed in the calculation. In other words, the smaller the RMSE on the vertical axis, the more accurate the prediction. Conventional multiple regression uses α on the graph. j = 0. α j Although α = 0 is outside the range of the graph, the RMSE at that time is a value that far exceeds 3. j It can be seen that good prediction results can be obtained when the value of α is in the range of 1 to 100. j It can be seen that the RMSE is smallest at around 10, which means that the deviation from the correct data is smallest.

[0057] Based on the above, the flow of the optical property evaluation method according to this embodiment is shown in FIG.

[0058] In S1, a test reticle 1 having a test pattern, which is placed on the object plane of the projection optical system 2, is illuminated, and a substrate W, which is placed on the image plane 3 of the projection optical system 2, is exposed. This creates an exposed substrate (exposed sample).

[0059] In S2, the image shift (amount of positional shift) of the test pattern image formed on the exposure sample (substrate W) is measured. The amount of image shift may be measured using a measuring device outside the exposure tool, or may be measured using the scope (imaging unit AS) of the exposure tool.

[0060] In S3, the optical characteristics of the projection optical system 2 are estimated based on the results of the above measurement. In this embodiment, the wavefront aberration is estimated using a polynomial model. In the measurement step of S2, due to vignetting occurring on the pupil plane 21, some data on the amount of positional deviation of the image formed by light that emerges from the pupil periphery and reaches the image plane 3 is missing. In response to this, in the estimation step of S3, in a state where such missing data has occurred, the wavefront aberration of the entire pupil is estimated using a polynomial model including a regularization term. At this time, a predetermined hyperparameter (regularization parameter) is used. In this embodiment, the regularization parameter α of the terms corresponding to C2 to C9 is j is set to 0, and the regularization parameter α for the terms corresponding to C10 to C169 is j is set to 10 and the Zernike coefficient is calculated using Ridge regression.

[0061] In S4, C2 to C36 of the Zernike coefficients obtained in S3 are output as optical characteristics.

[0062] In this embodiment, the regularization parameter α of the term corresponding to the term of C10 or more is j Although a uniform value of around 10 is considered to be good, it may be set more precisely based on the characteristics of the data. For example, the regularization parameter α j and the regularization parameter α for terms corresponding to C36 and above j and are different values. Furthermore, α for each value of j j may be different values, which may further improve prediction accuracy by matching the regularization parameters to the characteristics of the data.

[0063] In this embodiment, a method using Ridge regression has been described as a method using a polynomial model including a regularization term. However, such a polynomial model is not limited to Ridge regression. Lasso regression (Least Absolute Shrinkage and Selection Operator Regression) may be used instead of Ridge regression. Alternatively, PLS regression (Partial Least Squares Regression) may be used. Alternatively, a combination of these may be used. In other words, the polynomial model may be a regression model using at least one of Ridge regression, Lasso regression, and PLS regression. Alternatively, the polynomial model does not have to be a regression model.

[0064] As described above, in this embodiment, wavefront aberration is predicted from shift data using a polynomial model including a regularization term. This allows for better prediction results than conventional multiple regression. In this case, it is preferable to determine the regularization parameters (hyperparameters) that control the effect of regularization based on the characteristics and trends of the wavefront aberration data of the projection optical system. The wavefront aberration data may be past actual measurement data or data measured by another measuring instrument. By using this method, it is possible to provide a method that can measure optical characteristics with high accuracy even when only partial information about the wavefront aberration is available.

[0065] Second Embodiment In the second embodiment, a method using a multilayer perceptron network, so-called deep learning, among machine learning methods for determining wavefront aberration will be described.

[0066] A wavefront aberration measuring method using deep learning according to the second embodiment will be described with reference to FIG. 7. FIG. 7 is a diagram showing an example of the configuration of a neural network according to this embodiment. Note that FIG. 7 is a schematic representation of a calculation concept and does not represent an actual object. In FIG. 7, the neural network has an input layer 4 and an output layer 6, and further has a hidden layer 5 which is an intermediate layer between the input layer 4 and the output layer 6.

[0067] The input layer 4 receives the aforementioned column vector B. The column vector B is a column vector with N elements composed of measured shift data, and the i-th element b i is the measured shift amount of the image of the i-th aberration measurement mark.

[0068] The output layer 6 outputs the aforementioned column vector X. The column vector X is a column vector with M elements composed of the Zernike coefficients to be calculated, and the j-th element x j is the j-th Zernike coefficient value.

[0069] The hidden layer 5 includes multiple layers, each with numerous nodes. Each node is connected to nodes in the upstream layer and receives the output values ​​from those nodes. Each node is also connected to nodes in the downstream layer and passes the output values ​​to those nodes. Each node uses a nonlinear activation function to determine its output value based on the sum of multiple input values. Commonly used nonlinear functions include the sigmoid function and ReLU (Rectified Linear Unit). ReLU is a function that always outputs 0 when the input value is less than or equal to 0, and the same value as the input value when the input value is greater than 0. Each node has a weight assigned to its connection. The value output by the upstream node is multiplied by the weight assigned to that connection before being input to the downstream node. By adjusting the weight of each connection, the network can be adjusted so that the appropriate wavefront aberration Zernike coefficients are output when shift data is input. These weights are the hyperparameters in this case. These weights cannot be determined within the optimization method and must be provided externally. Learning is performed to determine these weights.

[0070] Supervised learning is required to optimize the weights of each connection in the network. In this embodiment, supervised learning is performed as follows. For example, first wavefront aberration data obtained by measuring wavefront aberration in advance without any missing data on the amount of positional deviation is acquired and used as training data. Learning of the neural network is performed using as input data second wavefront aberration data obtained in a state where data on the amount of positional deviation of an image formed by light that emerges from the peripheral part of the pupil and reaches the image plane is missing. A specific example is shown below.

[0071] When assembling the unit, the wavefront aberration of the projection optical system is measured, for example, by an interferometer external to the exposure tool. Unlike wavefront aberration measurements performed on the exposure tool itself, measurements using an interferometer are not limited by the lack of data in the peripheral areas of the pupil, and complete wavefront aberration data (first wavefront aberration data) can be obtained across the entire pupil. Therefore, first, a large amount of wavefront aberration data is prepared for an optical system of the same type as a projection optical system that has been manufactured in the past.

[0072] Next, a simulation of wavefront aberration measurement on the exposure tool body is performed for the large number of wavefront aberration data thus prepared, and a large number of virtual shift data (second wavefront aberration data) are created. Like the actual shift data, this virtual shift data lacks data on the periphery of the pupil. Note that, since actual shift data has measurement errors, virtual errors equivalent to the measurement errors may also be added to the virtual shift data obtained by simulation.

[0073] Finally, the wavefront aberration data measured by the interferometer and the shift data created from it are used as pairs of training data and input data. By preparing a large number of such pairs, supervised learning is achieved. Backpropagation is an effective method for supervised learning. Nowadays, there are many machine learning libraries available in various programming environments, and by utilizing these, various learning techniques can be used in addition to backpropagation.

[0074] The conditions for the neural network in this embodiment are explained below. There were two hidden layers 5, each with 512 nodes, and the activation function type was ReLU. The layers were fully connected (all nodes were connected to each other). Approximately 9,000 pairs of shifted data and training data were prepared, of which 70% were used for training and 30% for testing. Figure 8 shows the results of predicting wavefront aberration Zernike coefficients from shifted data using a neural network trained in this way. Figure 8 compares the prediction results for one sample of test data using a conventional method with the method using the neural network of this embodiment. Figure 8(A) shows the prediction results using the conventional method (multiple regression). The horizontal axis represents the Zernike term number, and the vertical axis represents the Zernike coefficient value. The dotted line 8 represents the training data, and the solid line 7 represents the prediction results. Figure 8(B) shows the prediction results using the method using the neural network of this embodiment. The dotted line 9 represents the training data, and the solid line 10 represents the prediction results. The closer the predicted result and the training data lines are, the better the prediction. Comparing the two graphs, it can be seen that the neural network method of this embodiment significantly improves the degree of agreement between the predicted result and the training data compared to the conventional multiple regression method. Furthermore, for the approximately 2,700 data points used in the test, the root mean square error of the predicted Zernike coefficient value relative to the training value was calculated for each data point, and the average value was calculated. The conventional method gave a value of 9.18 mλ, while the neural network method of this embodiment gave a significantly smaller value of 1.34 mλ, confirming that the prediction accuracy has improved.

[0075] This means that by having the neural network learn to predict the entire pupil, including the pupil periphery, by considering only the inner information of the wavefront aberration, the neural network has mastered the shape pattern and structure of the wavefront aberration contained in the training data. As a result, it can be understood that it has become possible to successfully predict the entire pupil, including the pupil periphery, using only the inner information of the wavefront aberration. In other words, by using a neural network, it is possible to improve the prediction accuracy of wavefront aberration, thereby providing a method that can measure optical characteristics with high accuracy from shift data that lacks data on the pupil periphery.

[0076] Based on the above, the flow of the optical property evaluation method according to this embodiment is shown in FIG.

[0077] In S11, a test reticle 1 having a test pattern, which is placed on the object plane of the projection optical system 2, is illuminated, and a substrate W, which is placed on the image plane 3 of the projection optical system 2, is exposed. This creates an exposed substrate (exposed sample).

[0078] In S12, the image shift (amount of positional shift) of the image of the test pattern formed on the exposure sample (substrate W) is measured. The amount of image shift may be measured using a measuring device outside the exposure tool, or may be measured using the scope (imaging unit AS) of the exposure tool. In S13, the wavefront aberration is predicted by a neural network using weight information previously acquired through supervised learning.

[0079] The above-described neural network conditions (number of layers, number of nodes, learning method, etc.) are merely examples, and other conditions may be set as long as they are in line with the gist of the present disclosure. In addition, in this embodiment, the wavefront aberration measured by an interferometer during unit assembly and the shift data generated by simulation therefrom are used as input data and training data, respectively. However, training data can also be prepared by other methods. For example, shift data acquired on the exposure apparatus itself can be used as input data, and wavefront aberration data measured by an interferometer during unit assembly can be used as training data. Alternatively, wavefront aberration data acquired on the exposure apparatus itself by a method other than using a test reticle 1 having a test pattern for measuring optical characteristics can be used as training data. For example, aberration data measured by a measurement optical system can be used as training data. In this embodiment, wavefront aberration data from an optical system of the same type as a previously manufactured projection optical system is used as training data. However, even if the projection optical system is not of the same type (same product), if the lens configuration and manufacturing method inside the projection optical system are similar, the wavefront aberration trends will be similar, so wavefront aberration data from another product can also be used as training data.

[0080] <Embodiment of an article manufacturing method> The article manufacturing method according to an embodiment of the present invention is suitable for manufacturing articles such as microdevices, such as semiconductor devices, and elements having microstructures. The article manufacturing method according to this embodiment includes a step of forming a latent image pattern on a photosensitive agent applied to a substrate using the above-described exposure apparatus (a step of exposing the substrate), and a step of developing the substrate on which the latent image pattern has been formed. Furthermore, this manufacturing method includes other well-known steps (oxidation, film formation, vapor deposition, doping, planarization, etching, resist stripping, dicing, bonding, packaging, etc.). The article manufacturing method according to this embodiment is advantageous over conventional methods in at least one of article performance, quality, productivity, and production cost.

[0081] <Other embodiments> The present invention can also be realized by supplying a program that realizes one or more functions of the above-described embodiments to a system or device via a network or a storage medium, and having one or more processors in the computer of the system or device read and execute the program. It can also be realized by a circuit (e.g., ASIC) that realizes one or more functions.

[0082] The disclosure of the present specification includes at least the following techniques. (Item 1) 1. A method for evaluating optical characteristics of a projection optical system, comprising: a measuring step of illuminating a test reticle having a test pattern disposed on an object plane of the projection optical system and measuring a positional deviation of an image of the test pattern formed on an image plane of the projection optical system; an estimation step of estimating optical characteristics of the projection optical system based on the measurement results, In the estimating step, the optical properties are estimated using a polynomial model including a regularization term. An evaluation method characterized by: (Item 2) the optical characteristic is a wavefront aberration on a pupil plane of the projection optical system, The data of the positional deviation amount measured in the measurement step is partially missing due to vignetting occurring on the pupil plane, the estimation step estimates the wavefront aberration of the entire pupil using a polynomial model including the regularization term in a state in which the data loss occurs. 2. The evaluation method according to item 1, (Item 3) 3. The evaluation method according to item 1 or 2, wherein the polynomial model is a regression model using at least one of Ridge regression, Lasso regression, and PLS regression. (Item 4) 4. The evaluation method according to item 3, wherein the polynomial model is a regression model using Ridge regression for Zernike polynomials. (Item 5) The element s in the i-th row and j-th column indicates the amount of positional deviation of the image of the i-th mark constituting the test pattern when the j-th term of the Zernike polynomial exists in a unit amount. ij Let S be the sensitivity matrix of N rows and M columns, including Let B be a column vector with N elements consisting of the measured positional deviations, Let X be a column vector with M elements consisting of the Zernike coefficients to be calculated, The j-th element, α, indicates the regularization parameter for the j-th Zernike coefficient value. j Let A be a diagonal matrix with M rows and M columns, When the transposed matrix is ​​represented by T, The loss function L is L=(B-SX) T (B-SX)+X T AX and determine the Zernike coefficients by finding X that minimizes this. 5. The evaluation method according to item 4. (Item 6) The regularization parameter α j is determined based on the result of measurement by the measurement process performed in conjunction with at least one of a plurality of events including assembly and adjustment of the projection optical system, transportation, and the operation period exceeding a predetermined period. (Item 7) 2. The evaluation method according to item 1, wherein the regularization term is a term that limits the value of a coefficient. (Item 8) 8. The evaluation method according to any one of items 1 to 7, wherein in the measurement step, the test pattern is transferred onto a resist applied to a substrate placed on the image plane to form a latent image, and the amount of misregistration is measured by observing the formed latent image or a resist pattern obtained by developing the latent image. (Item 9) 1. A method for evaluating optical characteristics of a projection optical system, comprising: a measuring step of illuminating a test reticle having a test pattern disposed on an object plane of the projection optical system and measuring a positional deviation of an image of the test pattern formed on an image plane of the projection optical system; an estimation step of estimating optical characteristics of the projection optical system based on the measurement results, In the estimation step, the optical properties are estimated using a neural network. An evaluation method characterized by: (Item 10) the optical characteristic is a wavefront aberration on a pupil plane of the projection optical system, The data of the positional deviation amount measured in the measurement step is partially missing due to vignetting occurring on the pupil plane, the estimation step estimates the wavefront aberration of the entire pupil using the neural network in a state where the data loss occurs; 10. The evaluation method according to item 9, (Item 11) Item 11. The evaluation method according to item 10, wherein the neural network is trained using first wavefront aberration data obtained by measuring the wavefront aberration in advance without any missing data on the amount of positional deviation. (Item 12) Item 12. The evaluation method according to item 11, wherein the neural network is trained using the first wavefront aberration data as training data and the second wavefront aberration data obtained in a state where data on the amount of positional deviation measured in the measurement step is missing as input data. (Item 13) 13. The evaluation method according to item 11 or 12, wherein the first wavefront aberration data is obtained by measuring the wavefront aberration of the projection optical system using an interferometer. (Item 14) Item 13. The evaluation method according to item 12, wherein the second wavefront aberration data is obtained by simulating wavefront aberration measurement of the projection optical system. (Item 15) 15. The evaluation method according to any one of items 9 to 14, wherein in the measurement step, the test pattern is transferred onto a resist applied to a substrate placed on the image plane to form a latent image, and the amount of misregistration is measured by observing the formed latent image or a resist pattern obtained by developing the latent image. (Item 16) 1. An exposure apparatus that projects a pattern of an original onto a substrate using a projection optical system to expose the substrate, a processing unit for determining optical characteristics of the projection optical system by illuminating a test reticle having a test pattern arranged on an object plane of the projection optical system, measuring a positional deviation of an image of the test pattern formed on an image plane of the projection optical system, and processing the measurement results obtained; the processing unit estimates the optical properties using a polynomial model including a regularization term; An exposure apparatus characterized by: (Item 17) 1. An exposure apparatus that projects a pattern of an original onto a substrate using a projection optical system to expose the substrate, a processing unit for determining optical characteristics of the projection optical system by illuminating a test reticle having a test pattern arranged on an object plane of the projection optical system, measuring a positional deviation of an image of the test pattern formed on an image plane of the projection optical system, and processing the measurement results obtained; The processing unit estimates the optical characteristics using a neural network. An exposure apparatus characterized by: (Item 18) Item 16 or 17, exposing a substrate using the exposure apparatus; developing the exposed substrate; and manufacturing an article from the developed substrate.

[0083] 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. Accordingly, the following claims are appended to apprise the public of the scope of the invention. [Explanation of symbols]

[0084] 1: Test reticle, 2: Projection optical system, 3: Image plane, 11: Diffuser, 12: Pinhole, 13: Aberration measurement mark, W: Substrate

Claims

1. 1. A method for evaluating optical characteristics of a projection optical system, comprising: a measuring step of illuminating a test reticle having a test pattern disposed on an object plane of the projection optical system and measuring a positional deviation of an image of the test pattern formed on an image plane of the projection optical system; an estimation step of estimating optical characteristics of the projection optical system based on the measurement results, In the estimating step, the optical properties are estimated using a polynomial model including a regularization term. An evaluation method characterized by:

2. the optical characteristic is a wavefront aberration on a pupil plane of the projection optical system, The data of the positional deviation amount measured in the measurement step is partially missing due to vignetting occurring on the pupil plane, the estimation step estimates the wavefront aberration of the entire pupil using a polynomial model including the regularization term in a state in which the data loss occurs. The evaluation method according to claim 1 .

3. 2. The evaluation method according to claim 1, wherein the polynomial model is a regression model using at least one of Ridge regression, Lasso regression, and PLS regression.

4. 4. The evaluation method according to claim 3, wherein the polynomial model is a regression model using Ridge regression on Zernike polynomials.

5. The element s in the i-th row and j-th column indicates the amount of positional deviation of the image of the i-th mark constituting the test pattern when the j-th term of the Zernike polynomial exists in a unit amount. ｉｊ Let S be a sensitivity matrix of N rows and M columns, including A column vector having N elements constituted by the measured positional deviation amounts is denoted by B, Let X be a column vector with M elements consisting of Zernike coefficients to be calculated, α, the jth element indicating the regularization parameter for the jth Zernike coefficient value ｊ Let A be a diagonal matrix with M rows and M columns, When the transposed matrix is ​​represented by T, The loss function L is L=(B-SX) Ｔ (B-SX)+X Ｔ AX and determine the Zernike coefficients by finding X that minimizes this.

5. The evaluation method according to claim 4.

6. The regularization parameter α ｊ is determined based on a result of a measurement performed in the measurement process in association with at least one of a plurality of events including assembly and adjustment of the projection optical system, transportation, and the operation period exceeding a predetermined period.

7. 2. The evaluation method according to claim 1, wherein the regularization term is a term that limits the value of a coefficient.

8. 8. The evaluation method according to claim 1, wherein the measurement step comprises transferring the test pattern onto a resist applied to a substrate placed on the image plane to form a latent image, and measuring the amount of misalignment by observing the formed latent image or a resist pattern obtained by developing the latent image.

9. 1. A method for evaluating optical characteristics of a projection optical system, comprising: a measuring step of illuminating a test reticle having a test pattern disposed on an object plane of the projection optical system and measuring a positional deviation of an image of the test pattern formed on an image plane of the projection optical system; an estimation step of estimating optical characteristics of the projection optical system based on the measurement results, In the estimation step, the optical properties are estimated using a neural network. An evaluation method characterized by:

10. the optical characteristic is a wavefront aberration on a pupil plane of the projection optical system, The data of the positional deviation amount measured in the measurement step is partially missing due to vignetting occurring on the pupil plane, the estimation step estimates the wavefront aberration of the entire pupil using the neural network in a state where the data loss occurs; 10. The evaluation method according to claim 9.

11. 11. The evaluation method according to claim 10, wherein the neural network is trained using first wavefront aberration data obtained by measuring the wavefront aberration in advance without any missing data on the amount of positional deviation.

12. 12. The evaluation method according to claim 11, wherein the neural network is trained using the first wavefront aberration data as training data and second wavefront aberration data obtained in a state where data on the amount of positional deviation measured in the measurement step is missing as input data.

13. 12. The evaluation method according to claim 11, wherein the first wavefront aberration data is obtained by measuring the wavefront aberration of the projection optical system using an interferometer.

14. 13. The evaluation method according to claim 12, wherein the second wavefront aberration data is obtained by simulating a wavefront aberration measurement of the projection optical system.

15. 15. The evaluation method according to claim 9, wherein the measurement step comprises transferring the test pattern onto a resist applied to a substrate placed on the image plane to form a latent image, and measuring the amount of misalignment by observing the formed latent image or a resist pattern obtained by developing the latent image.

16. 1. An exposure apparatus that projects a pattern of an original onto a substrate using a projection optical system to expose the substrate, a processing unit for determining optical characteristics of the projection optical system by illuminating a test reticle having a test pattern arranged on an object plane of the projection optical system, measuring a positional deviation of an image of the test pattern formed on an image plane of the projection optical system, and processing the measurement results obtained; the processing unit estimates the optical properties using a polynomial model including a regularization term; An exposure apparatus characterized by:

17. 1. An exposure apparatus that projects a pattern of an original onto a substrate using a projection optical system to expose the substrate, a processing unit for determining optical characteristics of the projection optical system by illuminating a test reticle having a test pattern arranged on an object plane of the projection optical system, measuring a positional deviation of an image of the test pattern formed on an image plane of the projection optical system, and processing the measurement results obtained; The processing unit estimates the optical characteristics using a neural network. An exposure apparatus characterized by:

18. exposing a substrate using the exposure apparatus according to claim 16 or 17; developing the exposed substrate; and manufacturing an article from the developed substrate.

Images