JP5922927B2 - Method for determining position, information processing apparatus, lithography apparatus, and article manufacturing method - Google Patents

Description

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

  In an exposure apparatus for producing a semiconductor, a process of transferring a circuit pattern formed on a reticle (also referred to as a mask or an original) to a substrate such as a wafer or a glass plate coated with a photosensitive material (resist) is performed. In general, for exposure for forming a circuit pattern, it is very important to perform relative alignment between the reticle and the substrate, that is, so-called alignment with high accuracy.

  Conventionally, a plurality of alignment mark images set in advance among alignment marks transferred onto a substrate by exposure together with a circuit pattern are sequentially detected by an alignment optical system to measure the position. Then, the measurement result of these positions is processed to calculate the position of each shot, and the substrate is positioned with respect to the reticle based on the calculation result.

  In recent years, CMP (Chemical Mechanical PolyShing) process technology has been introduced. As a result of applying the CMP process technique to the substrate, the alignment mark becomes asymmetrical, which may deteriorate the alignment accuracy. An alignment measurement error due to such a process technique is called a process factor error, and an asymmetric alignment mark is called an asymmetric mark. Also, the alignment mark becomes an asymmetric mark due to the exposure apparatus factor and the interaction between the process factor and the exposure apparatus factor, which deteriorates the alignment accuracy.

  In order to deal with the alignment measurement error due to the asymmetric mark, in Patent Document 1, the function of the feature extracted from the alignment mark signal and the measurement error is obtained to correct the measurement error. In addition, there is Patent Document 2 as another conventional technique related to the position detection method.

Japanese Patent No. 4227470 JP 2006-108386 A

  The correlation between the feature extracted from the alignment mark signal and the measurement error was calculated under the following simulation conditions. FIG. 12A shows a silicon step mark. The mark has two steps with a total length of 20 μm, a step width of 0.8 μm, and a step interval of 4 μm. The step size d was set to eight types of 70, 110, 150, 180, 220, 260, and 300 nm. At this time, the size of the two steps was the same. Then, the mark is imaged by an alignment optical system having a wavelength of 600 nm, NA: 0.55, and σ: 0.4 to obtain an alignment mark signal. At that time, three types of defocus amounts of 0 and ± 1 μm, two types of aberration amounts of the optical system of 0 and 10 mλ, and three types of telecentricity of 0 and ± 10 mrad were used. Then, an alignment mark signal is prepared in which the combination of the mark step size, defocus amount, aberration, and telecentricity is changed. The alignment mark signal becomes an asymmetric mark signal due to process factors (mark level difference), device factors (defocus amount, aberration, telecentricity), and interaction between process factors and device factors.

  For example, in the method of Patent Document 1, E = 1−a / b is used as the feature amount from the alignment mark signal y (x) as shown in FIG. Here, -1 <E <1, a is the maximum value of the first mark signal, and b is the maximum value of the second mark signal. In FIG. 12C, the measurement results are plotted with the horizontal axis representing the feature amount E and the vertical axis representing the measurement error (nm). As shown in FIG. 12C, the feature quantity E and the measurement error are almost uncorrelated. In the linear approximation, R2 correlation = 0.29. Also, with respect to the method of Patent Document 2, the feature amount from the alignment mark signal was calculated. However, like the method of Patent Document 1, the feature amount and the measurement error were close to no correlation.

  Therefore, an object of the present invention is to provide a technique advantageous for correcting a measurement error, for example.

The present invention relates to a method for obtaining the position of the mark from a detection signal obtained by detecting a mark, wherein the detection signal of the mark along a direction crossing the mark is evaluated at a plurality of evaluation positions in the direction. And a plurality of first evaluation values corresponding to each of the plurality of evaluation positions, wherein the evaluation positions are determined using two windows arranged so as to sandwich the evaluation positions. wherein a first step of determining the first evaluation value indicating the symmetry of the detection signal, based on the first evaluation value of the plurality corresponding to the plurality of evaluation positions in the second to determine the representative positions of the mark And a third step of obtaining a second evaluation value indicating symmetry based on a first evaluation value in each of two regions divided by the representative position with respect to the plurality of first evaluation values, In the fourth step for obtaining the error from the information indicating the relationship between the error of the representative position and the second evaluation value, and the second evaluation value obtained in the third step, and in the second step And a fifth step of obtaining the mark position by correcting the obtained representative position with the error obtained in the fourth step.

  According to the present invention, for example, it is possible to provide a technique advantageous for correcting a measurement error.

It is a figure which shows exposure apparatus and an alignment optical system. It is a figure which shows an alignment mark and an alignment mark signal. It is the figure which showed the flow and ES (x) signal until it calculates the signal of ES (x). It is a figure explaining an example of the method of calculating the representative position of a mark from an alignment mark signal. It is a figure for demonstrating the method for measuring a feature-value. It is a figure which shows the example of the signal of ES (x), and the signal which processed it. It is a figure which shows the relationship between the gravity center position of ES (x) and ES (x), and Skew. It is a figure which shows the procedure which calculates the relational expression of Skew and a measurement error. It is a figure which shows the procedure which correct | amends a measurement error and detects a position. It is a figure which shows the effect of measurement error correction. It is a figure which shows an example of ES (x). It is the schematic which shows the silicon | silicone level | step difference mark, and the graph which shows the relationship between the feature-value and measurement error in a prior art example.

Embodiments of the present invention will be described below with reference to the accompanying drawings. First, a method for calculating a feature quantity correlated with a measurement error will be described in detail. Next, a position measurement method for correcting a measurement error using the calculated feature amount will be described.

Calculation of Feature Quantity Correlated with Measurement Error FIG. 1A is a block diagram of an exposure apparatus. In the present embodiment, an exposure apparatus is used as a lithography apparatus that transfers a pattern to a substrate. However, the present invention can also be applied to a maskless drawing apparatus such as a charged particle beam drawing apparatus or an imprint apparatus. The exposure apparatus 100 transfers a circuit pattern formed on a reticle to the substrate by exposure, for example, by a step-and-scan method or a step-and-repeat method. In the “step and scan method”, the substrate is continuously scanned (scanned) with respect to the reticle to expose the reticle pattern onto the substrate, and after the exposure of one shot is completed, the substrate is stepped to the next exposure This is an exposure method for moving to an area. The “step-and-repeat method” is an exposure method in which the substrate is moved stepwise to the next exposure region for every batch exposure of the substrate.

The exposure apparatus 100 includes a projection optical system 120, a substrate chuck 145, a substrate stage 140, an alignment optical system 150, an alignment signal processing unit 160, and a control unit 170. The alignment optical system 150 constitutes a detector that detects an alignment mark (mark) 180 disposed on the substrate (article) 130 and outputs a detection signal (image signal).
The projection optical system 120 reduces and projects a pattern (circuit pattern or the like) formed on the reticle 110 onto the substrate 130. The substrate chuck 145 holds the substrate 130 on which the base pattern and the alignment mark 180 are formed in the previous process. The movable substrate stage 140 is used to position the substrate 130 at a predetermined position. The alignment optical system 150 measures the position of the alignment mark 180 along the direction crossing the alignment mark 180 (X direction). In FIG. 1A, the illumination optical system that illuminates the reticle 110 with light from the light source and the light source is omitted.

  The control unit 170 includes a CPU and a memory (not shown), and controls the operation of the exposure apparatus 100. The controller 170 is electrically connected to an illumination device (not shown), a reticle stage drive unit (not shown), a substrate stage 140 drive unit, and an alignment signal processing unit 160. The control unit 170 positions the substrate 130 through the driving of the substrate stage 140 based on the position information of the alignment mark 180 from the alignment signal processing unit 160. The alignment signal processing unit 160 and the control unit 170 constitute an information processing apparatus that executes a method for determining the position of the substrate 130 from the detection signal.

  First, the detection principle of the alignment mark 180 will be described. FIG. 1B is an optical path diagram showing the main components of the alignment optical system 150. The illumination light from the alignment light source 151 is reflected by the beam splitter 152, passes through the lens 153, and illuminates the alignment mark 180 on the substrate 130. Light from the alignment mark 180 (reflected light, diffracted light) passes through the lens 153, the beam splitter 152, and the lens 154, is divided by the beam splitter 155, and is received by the CCD sensors 156 and 157, respectively.

  The alignment mark 180 is magnified by an imaging magnification of about 100 times by the lenses 153 and 154 and is imaged on the CCD sensors 156 and 157. The CCD sensors 156 and 157 are used for measuring the displacement of the alignment mark 180 in the X direction and for measuring the displacement of the alignment mark 180 in the Y direction, respectively, and are installed by being rotated 90 degrees with respect to the optical axis. Line sensors may be used as the CCD sensors 156 and 157. In this case, the information is optically integrated by condensing in the vertical direction by a cylindrical lens having power only in the direction perpendicular to the measurement direction. (Averaged) is preferable. Since the measurement principle in the X direction and the Y direction is the same, the position measurement in the X direction will be described.

  The alignment mark 180 is disposed on the scribe line of each shot, and for example, an alignment mark having a shape shown in FIGS. 2A and 2B can be used. Here, FIG. 2A is a plan view of the alignment mark 180A, and FIG. 2B is a cross-sectional view of the alignment mark 180A. In FIG. 2A, the alignment mark 180A includes four mark elements 182A arranged at equal intervals. In practice, a resist is applied on the alignment mark 180A, but the illustration is omitted in FIGS. 2 (a) and 2 (b).

  As shown in FIG. 2A, the alignment mark 180A has four rectangular mark elements 182A of 4 μm in the X direction that is the measurement direction and 20 μm in the Y direction that is the non-measurement direction arranged at a pitch of 20 μm in the X direction. . The cross-sectional structure of the mark element 182A has a concave shape as shown in FIG. Using the alignment mark 180A of FIG. 2A, the image is picked up by the CCD sensor 156 due to the generation of scattered light at the edge portion of a large angle that does not enter the NA of the lenses 153 and 154 and the interference of the scattered light at the edge portion. The obtained image is generally as shown in FIG. The outline of the alignment mark 180A becomes dark. This is an image that is often observed in bright-field images, and can be said to be a feature thereof. Here, FIG. 2C shows a waveform of a mark detection signal when the alignment mark 180A shown in FIG. 2A is optically detected.

  The image of the alignment mark 180 imaged in this way is subjected to alignment signal processing via the alignment signal processing unit 160. Various types of alignment signal processing have been proposed, such as a method for detecting an edge portion of an alignment mark signal (detection signal) and calculating a distance between the edges, and a pattern matching method using normalized correlation. In the prior art, the feature amount is directly calculated from the alignment mark signal in FIG. However, in the present invention, the feature amount is not calculated directly from the alignment mark signal. In the present invention, as shown in FIG. 3A, the alignment mark signal 21 is processed 22 (first step) to determine a first evaluation value, and a feature value (second evaluation value) is determined from the first evaluation value. 23 is determined. In the present embodiment, position measurement is performed using the first evaluation value shown in FIG. However, the present invention is not limited to this, and position measurement may be performed on the alignment mark signal.

  In process 22, the alignment signal processing unit 160 evaluates the waveform of the alignment mark signal 21 at a plurality of evaluation positions in the measurement direction, and determines a first evaluation value indicating the symmetry of the waveform at each evaluation position. The alignment signal processing unit 160 performs evaluation using two windows arranged so as to sandwich the position of interest. The alignment signal processing unit 160 determines the first evaluation value based on the portions in the two windows in the waveform when each evaluation position is the target position. The portions in the two windows are signals in two regions surrounded by two rectangles in the waveform indicating the intensity y (x) of the alignment mark signal 21 in FIG. Note that x is a coordinate indicating the evaluation position. When the alignment mark signal 21 is represented by y (x), the first evaluation value ES (x) is represented by, for example, ES (x) = 1 / S (x). However, S (x) is defined by the equation shown in FIG. That is, an example of ES (x) is represented by the following equation.

  The alignment signal processing unit 160 determines ES (x) for all positions (all x) in the measurement direction of the alignment mark signal 21. FIG. 4B shows an example of the signal represented by ES (x). Note that ES (x) may be obtained by other methods such as a pattern matching method using normalized correlation. The representative position representing the position of the alignment mark is, for example, the barycentric position of the ES (x) graph determined in the process 22. Since the vicinity of the minimum value of S (x) is a discrete signal, it is calculated by complementing subpixels (data between pixels) by function approximation or the like.

  Hereinafter, a method for determining a feature value (second evaluation value) as a basis for mark position measurement will be described with reference to the flowchart of FIG. The program for determining the feature amount is stored in the control unit 170 in FIG. First, in S401, the control unit 170 acquires a signal of the first evaluation value ES (x) at a plurality of evaluation positions (x) determined by the alignment signal processing unit 160. In S402, the control unit 170 determines the skewness Skew of the signal of the first evaluation value ES (x). The skewness Skew constitutes an example of a second evaluation value indicating the symmetry of the first evaluation value at the representative position, which is determined based on the first evaluation value in the two regions divided into two by the representative position of the mark.

The skewness Skew of the signal of the first evaluation value ES (x) is a feature amount in the present embodiment. g is a coordinate indicating the position of the center of gravity in the ES (x) graph. μ ₃ = {Σ (x−g) ³ ES (x)} / ΣES (x), and μ ₂ = {Σ (x−g) ² ES (x)} / ΣES (x). Then, the skewness Skew that is a feature amount is defined as μ ₃ / μ ₂ ^1.5 . The characteristics of the skewness skew will be described with reference to FIG. A of FIG. 5B shows a case where the skewness Skew is a normal distribution, and the skewness Skew = 0 for a distribution that is line-symmetric with respect to the center of gravity of the distribution. A distribution that is not line-symmetric with respect to the center of gravity of the distribution, such as B or C, has a skewness Skew> 0 or a skewness Skew <0.

  The method of determining the feature amount (second evaluation value) built in the control unit 170 of FIG. 1A may be performed according to the procedure of the flowchart of FIG. First, in S4001, the control unit 170 acquires a signal of the first evaluation value. Next, in S4002, the control unit 170 processes the acquired signal. An example of processing signals will be performed later. Finally, in S4003, the control unit 170 determines the skewness Skew of the processed signal.

  An example of a signal subjected to the processing in S4002 is shown. FIG. 6A shows an unprocessed signal and corresponds to FIGS. 3B and 4B. FIG. 6B is an example of a signal obtained by performing a low-pass filter process using a low-pass filter on the signal of FIG. 6 (c) to 6 (e) and (i) are subjected to extraction processing for extracting only a partial region of the signal of FIG. 6 (a). FIG. 6C shows a signal example in which 80% or more of the maximum value of ES (x) in FIG. The lower limit of the range to be zero is not limited to 80%, and may be a value that is larger than the minimum value of ES (x) and smaller than the maximum value of ES (x). FIG. 6D shows a signal example in which 80% or less of the maximum value of ES (x) in FIG. The upper limit of the range to be zero is not limited to 800%, and may be a value smaller than the maximum value of ES (x).

  FIG. 6E shows a signal example in which a range other than 50% or more of the maximum value of ES (x) in FIG. 6A to 90% or less of the maximum value is set to zero. The boundary value defining the range to be zero is not limited to 50% and 90%. FIG. 6F shows a signal example in which 80% or more of the maximum value of ES (x) in FIG. The lower limit of the range to be zero is not limited to 80%, and may be a value that is larger than the minimum value of ES (x) and smaller than the maximum value of ES (x). FIG. 6G shows a signal example in which 80% or less of the maximum value of ES (x) in FIG. The upper limit of the range to be zero is not limited to 80%, and may be a value smaller than the maximum value of ES (x). FIG. 6 (h) is a signal example in which a value other than the range of 50% or more of the maximum value of ES (x) in FIG. 6 (b) to 90% or less of the maximum value is set to zero. The boundary value defining the range to be zero is not limited to 50% and 90%.

  FIG. 6 (i) shows the values of ES (x) other than the region from the position pw1 away from the representative position (x = p) calculated from FIG. 6 (a) to the position pw2 away from the representative position w2. It is an example of a signal set to zero. The representative position x = p is a position that gives the center of gravity position of ES (x) in FIG. 6A or the maximum value or minimum value of ES (x) in FIG. FIG. 6J shows a signal example in which the value of ES (x) other than the region from the position pw1 separated from the representative position calculated from FIG. 6B to the position pw2 separated from the representative position by w2 is zero. It is.

  The signal of ES (x) is processed by performing S4001 and S4002 of FIG. 5C from the alignment mark signal obtained by imaging the alignment mark while fixing the telecentricity, the defocus amount, and the step amount, and changing only the aberration amount. Got a signal. The processed ES (x) signal is shown in FIG. The signal in FIG. 7A is a signal in which the representative position in FIG. 6I is the position having the maximum value of ES (x), and w1 = 17.5 pixels and w2 = 17.5 pixels. FIG. 7B is a graph in which the barycentric position of the processed ES (x) signal is plotted on the horizontal axis and the skewness Skew of each processed ES (x) signal is plotted on the vertical axis. The linear approximation R2 correlation is 0.9999. When the measurement error is y and the skewness (Skew) is x, the relational expression between the measurement error y and the skewness x is y = −97x−16. From this, it is considered that there is a strong correlation between the measurement error and the skewness Skew of the signal obtained by processing the ES (x) signal.

  In the alignment mark signal, a measurement error occurs due to a process factor (mark level difference), a device factor (defocus amount, aberration, telecentricity), and an interaction between the process factor and the device factor. FIG. 7C shows the skewness Skew of the symmetry distribution signal ES (x) obtained by performing the steps S401 and S402 of FIG. The relationship is shown. The signal ES (x) is a signal in which the representative position is a position that gives the maximum value of ES (x) and w1 = w2 = 17.5 pixels in FIG.

Position Measurement Method for Correcting Measurement Error As shown in FIG. 7C, process factors (mark level difference), device factors (defocus amount, aberration, telecentricity), and interaction between process factors and device factors It has been shown that there is a strong correlation between the measurement error due to and the skewness skew of the signal ES (x) of the symmetry distribution. Below, the position determination method of the program built in the control part 170 of Fig.1 (a) is demonstrated using the flowchart of FIG. 8, FIG. FIG. 8 is a procedure for calculating an expression (information) indicating the relationship between the skewness Skew and the measurement error. First, as a database DB, from the alignment mark signal, the skewness Skew determined by the procedure of FIG. 5A or 5C and the processing method of the signal ES (x) used to determine the skewness A set of measurement errors is obtained in advance and stored. There may be a plurality of combinations of skewness, processing method, and measurement error from one alignment mark signal. The processing method is, for example, which of FIG. 6 (a) to FIG. 6 (j) corresponds to. The measurement error is, for example, an overlay error acquired by the overlay inspection apparatus. A combination of the skewness, the processing method, and the measurement error is obtained in advance from each of the N alignment mark signals.

  In S701, the alignment signal processing unit 160 selects a skewness Skew and a measurement error of the same processing method from the DB, and calculates a relational expression between the skewness Skew and the measurement error. The control unit 170 performs S701 for the number of types of processing methods stored in the DB. Finally, the control unit 170 stores the processing method for calculating the skewness in association with the relational expression between the skewness Skew and the measurement error in the DB 2.

  FIG. 9 is a procedure in which the control unit 170 corrects the measurement error and measures the position of the alignment mark. In step S7001, the alignment signal processing unit 160 acquires an alignment mark signal to be measured. In S7002, the alignment signal processing unit 160 obtains a first evaluation value ES (x). The signal of ES (x) is, for example, a signal shown in FIG. In step S7003, the control unit 170 determines the representative position of the mark based on the first evaluation value shown in FIGS. 3B and 4B. In step S7004, the control unit 170 processes the signal ES (x) determined by the alignment signal processing unit 160. For example, processing is performed as shown in FIG. 6B to FIG. 6J. The representative position of the mark may be obtained from an alignment mark signal or a signal obtained by processing ES (x).

  In step S7005, the control unit 170 calculates the skewness Skew of the ES (x) signal processed in step S7004. In step S7006, the control unit 170 acquires a relational expression between the skewness Skew and the measurement error corresponding to the processing method processed in step S7004 from the DB 2 accumulated in advance. In S7007, the control unit 170 calculates the measurement error by substituting the skewness Skew calculated in S7005 into the relational expression between the skewness Skew acquired in S7006 and the measurement error. In step S7008, the control unit 170 determines the corrected mark position by adding the measurement error calculated in step S7007 to the mark representative position determined in step S7003 for correction.

  The effect of the procedure of FIG. 9 was verified. A simulation signal was used as the alignment mark signal. Further, in S7004 of FIG. 9, the signal of ES (x) is a signal processed by the procedure described in FIG. 6 (i). In the processing method of FIG. 6 (i), if the measurement error is y and the skewness (Skew) is x, the relational expression between the measurement error y and the skewness x is as shown in FIG. y = -97x-16. Using this relational expression, the representative position of the mark determined in S7003 was corrected. The effect of the correction is shown in FIG. The measurement error (3σ) 51.75 nm before correction could be reduced to 19.66 nm after correction.

About an example in which the feature amount (second evaluation value) of the alignment mark signal is equal to or greater than the feature amount other than the skewness, the skewness of the ES (x) signal, or the skewness of the processed ES (x) signal. explained. However, the feature amount (second evaluation value) used for calculating the measurement error in the position measurement may not be the skewness of the ES (x) signal. Hereinafter, a case where a feature amount other than the skewness is used will be described.

  In this embodiment, the average value of the slope of ES (x) in one of the two regions divided by the representative position is a, and the average value of the slope of ES (x) in the other region is b. To do. At this time, a value represented by | a | / | b | or (| a |-| b |) / (| a | + | b |) is used as a feature amount (second evaluation value). An example is shown in FIG. Here, as ES (x), a signal not subjected to the processing of FIG. 6A was used. P 'is a representative position. A shows a region on the plus side (X coordinate becomes larger) with respect to the representative position, and B shows a region on the minus side (side where the X coordinate becomes smaller) with respect to the representative position. First, the control unit 170 calculates a differential signal related to x of ES (x). If the average value of the differential signal in region A is a and the average value of the differential signal in region B is b, | a | / | b | or (| a |-| b |) / (| a | + | b |) Was defined as a feature value.

Modification of Lithographic Apparatus In the above-described embodiment, the position of the alignment mark in the exposure apparatus is measured. However, the position measurement according to the present invention can also be applied to a maskless exposure apparatus such as a charged particle beam drawing apparatus or an imprint apparatus having an alignment optical system as illustrated in FIG.

Embodiment of Article Manufacturing Method An article manufacturing method according to an embodiment of the present invention is suitable for manufacturing an article such as a microdevice such as a semiconductor device or an element having a fine structure. The article manufacturing method of the present embodiment includes a step of transferring (forming) a pattern to a substrate (photosensitive agent applied to the substrate) using the above-described lithography apparatus, and processing the substrate to which the pattern has been transferred in such a step. Process. The processing step may include a step of developing the latent image pattern transferred to the substrate. Alternatively, it may include a step of shaping the pattern transferred (formed) on the substrate by the imprint apparatus by etching or the like. Further, the manufacturing method may include other well-known steps (oxidation, film formation, vapor deposition, doping, planarization, etching, resist stripping, dicing, bonding, packaging, and the like). The method for manufacturing an article according to the present embodiment is advantageous in at least one of the performance, quality, productivity, and production cost of the article as compared with the conventional method.

  As mentioned above, although preferable embodiment of this invention was described, it cannot be overemphasized that this invention is not limited to these embodiment, A various deformation | transformation and change are possible within the range of the summary.

Claims (9)

A method for obtaining the position of the mark from a detection signal obtained by detecting the mark,
Evaluating the detection signals of the mark along the direction crossing the mark at a plurality of evaluation positions in the direction, and obtaining a plurality of first evaluation values corresponding to each of the plurality of evaluation positions, Then, using the two windows arranged so as to sandwich each evaluation position, a first step of obtaining the first evaluation value indicating the symmetry of the detection signal at each evaluation position,
A second step of obtaining a representative position of the mark based on the plurality of first evaluation values respectively corresponding to the plurality of evaluation positions;
A third step of obtaining a second evaluation value indicating symmetry based on the first evaluation value in each of two regions divided by the representative position with respect to the plurality of first evaluation values;
A fourth step of obtaining the error from information indicating a relationship between the error of the representative position and the second evaluation value and the second evaluation value obtained in the third step;
A fifth step of determining the position of the mark by correcting the representative position determined in the second step with the error determined in the fourth step;
A method characterized by comprising:   The third step performs at least one of a low-pass filter process for processing the plurality of first evaluation values with a low-pass filter and an extraction process for extracting only a partial region of the plurality of first evaluation values, The method according to claim 1, wherein the second evaluation value is obtained based on data obtained by at least one of processing and extraction processing.   The method according to claim 1, wherein the representative position is a position that gives a center of gravity position, a maximum value, or a minimum value in data for which the representative position is obtained. The coordinate indicating the evaluation position is x, the intensity of the detection signal is y (x), the first evaluation value is ES (x), WC is the coordinate of the central axis of the window, and WW is the window. As the width, ES (x) is

The method according to claim 1, wherein the method is represented by: The coordinate indicating the evaluation position is x, the first evaluation value is ES (x), the coordinate indicating the representative position is g, and μ ₃ = {Σ (x−g) ³ ES (x)} / ΣES (X) and μ ₂ = {Σ (x−g) ² ES (x)} / ΣES (x), and the second evaluation value is expressed by μ ₃ / (μ ₂ ^1.5 ). The method according to any one of claims 1 to 4, characterized in that:   When the average value of the slope of the first evaluation value in one of the two regions is a and the average value of the slope of the first evaluation value in the other region is b, the second evaluation value Is represented by | a | / | b | or (| a |-| b |) / (| a | + | b |). The method described in 1.   An information processing apparatus for obtaining the position of the mark from a mark detection signal, wherein the method according to any one of claims 1 to 6 is executed. A lithographic apparatus for transferring a pattern to a substrate,
A detector that outputs a detection signal obtained by detecting a mark placed on the substrate;
The information processing apparatus according to claim 7, wherein the position of the mark is obtained from a detection signal output from the detector;
A lithographic apparatus comprising: Transferring the pattern to the substrate using the lithographic apparatus according to claim 8;
Processing the substrate to which the pattern has been transferred in the step;
A method for producing an article comprising:

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