Edge position determination method, edge position determination device, and edge analysis method

Abstract

The invention provides an edge position determination method, an edge position determination device and an edge analysis method. In the edge position determination method, an average edge position is determined by summing up intensity values in the direction of extension of lines and lines in spaced SEM images, and a first intensity distribution is fitted using a weighting function in which the weight at the average edge position is maximum and a fitting function determined from the first intensity distribution, and a second intensity distribution is fitted using a fitting function determined from the second intensity distribution. The first intensity distribution represents a distribution of intensity values along a direction perpendicular to the extension direction at coordinates representing each position in the extension direction of the SEM image, and the edge position at the coordinates is determined on the basis of a second intensity distribution obtained by fitting.

Description

TECHNICAL FIELD

[0001] The present disclosure relates to an edge position determination method, an edge position determination apparatus, and an edge analysis method. BACKGROUND

[0002] In recent years, in a semiconductor exposure apparatus, with miniaturization and high integration of semiconductor integrated circuits, improvement in resolution is required. Therefore, shortening of the wavelength of light emitted from a light source for exposure is being promoted. For example, as a gas laser apparatus for exposure, a KrF excimer laser apparatus which outputs laser light having a wavelength of about 248 nm, and an ArF excimer laser apparatus which outputs laser light having a wavelength of about 193 nm are used.

[0003] The spectral line width of the natural oscillation light of the KrF excimer laser apparatus and the ArF excimer laser apparatus is wide, at 350 to 400 pm. Therefore, if a projection lens is configured of a material which transmits ultraviolet light like KrF and ArF laser light, chromatic aberration sometimes occurs. As a result, the resolution can be reduced. Therefore, it is necessary to narrow the spectral line width of the laser light output from the gas laser apparatus to the extent that chromatic aberration can be ignored. Therefore, in the laser resonator of the gas laser apparatus, in order to narrow the spectral line width, a line narrowing module (LNM) including a line narrowing element (etalon, grating, etc.) is sometimes provided. The gas laser apparatus in which the spectral line width is narrowed is called a line narrowed gas laser apparatus.

[0004] PRIOR ART DOCUMENTS

[0005] PATENT LITERATURE

[0006] Patent Literature 1: Japanese Patent Application Publication No. 2016-217816 SUMMARY

[0007] In an edge position determination method of one aspect of the present disclosure, an average edge position is determined by aggregating intensity values in an extending direction of a line in a SEM image of the line and the space, a first intensity distribution is fitted using a weight function having a largest weight at the average edge position and a fitting function determined based on a first intensity distribution, the first intensity distribution representing a distribution of intensity values along a direction perpendicular to the extending direction at each position of the SEM image representing coordinates of the extending direction, and an edge position at the coordinates is determined based on a second intensity distribution obtained by the fitting.

[0008] An edge location determination apparatus according to one aspect of this disclosure includes: a communication controller that acquires SEM images of lines and intervals; and a processor that sums intensity values ​​along the extension direction of the lines in the SEM image to determine an average edge location, fits a first intensity distribution using a weight function that maximizes the weight at the average edge location and a fitting function determined according to a first intensity distribution, the first intensity distribution being the intensity distribution at coordinates of each location in the SEM image representing the extension direction along a direction perpendicular to the extension direction, and determines the edge location at the coordinates based on a fitted second intensity distribution.

[0009] In one aspect of the edge analysis method disclosed herein, the average edge position is determined by summing the intensity values ​​along the extension direction of the line in the SEM image of the line and the interval. The first intensity distribution is fitted using a weight function with the largest weight at the average edge position and a fitting function determined according to a first intensity distribution, which is the intensity distribution along the direction perpendicular to the extension direction at the coordinates of each position in the SEM image. The edge position at the coordinates is determined according to the fitted second intensity distribution. PSD analysis is performed on the edge positions at multiple positions along the extension direction. Attached Figure Description

[0010] The following description, by way of example only, refers to the accompanying drawings to illustrate several embodiments of this disclosure.

[0011] Figure 1 The edge position in the comparative example determines the structure of the device.

[0012] Figure 2 This represents a portion of an SEM image that includes lines and spacing.

[0013] Figure 3 This is a flowchart illustrating the edge analysis processing in the comparative example.

[0014] Figure 4 An example of a SEM image showing lines and spacing.

[0015] Figure 5 express Figure 4 An example of the intensity distribution along the X direction at coordinate i in the Y direction.

[0016] Figure 6 This is a flowchart illustrating the detailed process of determining the pattern edges based on the SEM image in the first embodiment.

[0017] Figure 7 This is a flowchart showing the details of the process for determining the average edge position.

[0018] Figure 8 Examples representing the average intensity distribution.

[0019] Figure 9 An example of a weight function is shown.

[0020] Figure 10 Another example of a weight function is shown.

[0021] Figure 11 Another example of a weight function is shown.

[0022] Figure 12 A state in which the weight function is summarized in the number of average edge positions is shown.

[0023] Figure 13 An example of a separate distribution is shown.

[0024] Figure 14 An example of a weighted separate distribution is shown.

[0025] Figure 15 is a flowchart showing details of a process of deciding edge positions.

[0026] Figure 16 An example of a smoothed separate distribution is shown.

[0027] Figure 17 A case in which edge positions included in arrangement data are arranged on an XY plane is shown.

[0028] Figure 18 An example of a result of PSD analysis on a pattern edge is shown.

[0029] Figure 19 is a flowchart showing details of a process of deciding a pattern edge from a SEM image in the second embodiment. DETAILED DESCRIPTION

[0030] <CONTENT>

[0031] 1. Comparative Example

[0032] 2. Problems of the Comparative Example

[0033] 3. Method of selectively reducing noise by multiplying a weight function f(x)

[0034] 3.1 Process of deciding a pattern edge from a SEM image

[0035] 3.2 Effects

[0036] 4. Method of using a weight function f(x) as a weight of local regression

[0037] 4.1 Process of deciding a pattern edge from a SEM image

[0038] 4.2 Effects

[0039] 5. Other

[0040] Hereinafter, embodiments of the present disclosure will be described in detail with reference to the accompanying drawings. The embodiments described below represent several examples of the present disclosure, and do not limit the content of the present disclosure. In addition, the structures and actions described in each of the embodiments are not necessarily all essential to the structures and actions of the present disclosure. Furthermore, the same reference symbols are attached to the same constituent elements, and repetitive description is omitted.

[0041] 1. Comparative Example

[0042] Figure 1 The structure of an edge position determination device 100 in a comparative example is shown. The comparative example of the present disclosure is a manner that the applicant recognizes as known only to the applicant, and is not a publicly known example that the applicant himself recognizes.

[0043] The edge position determination device 100 includes a communication controller 10 and a processor 20. The communication controller 10 is connected to an external device such as a CD-SEM (critical dimension scanning electron microscope) 200, and controls communication with the external device. The communication controller 10 acquires a SEM image of a semiconductor substrate not shown, which is captured by the CD-SEM 200, from the CD-SEM 200 or from another external device that holds the SEM image. The SEM image contains a fine line-shaped processed pattern called a line and a space, which is formed by exposure and development of the semiconductor substrate.

[0044] The processor 20 is a processing device including a memory 21 in which a control program is stored and a CPU (central processing unit) 22 that executes the control program. The processor 20 is specially constituted or programmed in order to execute various processes included in the present disclosure. The processor 20 determines the edge positions of the line and the space using the SEM image acquired by the communication controller 10. Further, the processor 20 evaluates the exposure performance by performing edge analysis using the edge positions.

[0045] Figure 2A portion of an SEM image representing a line and a space is shown. In the SEM image, an edge as a boundary of the line and the space appears bright, and a line portion and a space portion other than the edge appear dark. LER (line edge roughness) represents a deviation from an ideal position of the edge, and LWR (line width roughness) represents a deviation of a distance between edges on both sides of the line. The requirements for LER and LWR in semiconductor lithography are becoming stricter year by year. In order to accurately analyze the cause factors of LER and LWR, it is necessary to accurately determine the edge position. In the following description, LER and LWR are not distinguished, and are simply denoted as LER.

[0046] Figure 3 is a flowchart showing an outline of an edge analysis process in a comparative example. The edge analysis is performed as follows.

[0047] In S1, the processor 20 acquires an SEM image of a semiconductor wafer after exposure and development from the communication controller 10. In S2, the processor 20 determines a pattern edge from the SEM image. The pattern edge is given as arrangement data of a plurality of edge positions obtained from the SEM image. In S3, the processor 20 performs PSD (power spectral density) analysis on the pattern edge. PSD analysis refers to signal analysis performed by decomposing a certain signal into the intensity of a signal per unit frequency. PSD analysis of the pattern edge means performing PSD analysis by regarding LER as a signal, and investigating what kind of spatial frequency components LER is composed of.

[0048] Figure 4 An example of an SEM image representing a line and a space is shown. The extending direction of the line is set as the Y direction. The direction perpendicular to the extending direction is set as the X direction. x represents the position in the X direction. When the number of pixels in the Y direction of the SEM image is set as n, and the coordinate of an arbitrary position in the Y direction is set as i, i can take an integer value from 1 to n.

[0049] 2. Problem of the Comparative Example

[0050] Figure 5 An example of an intensity distribution along the X direction at the coordinate i in the Y direction in Figure 4 is shown. The intensity distribution shown in Figure 5 is set as the individual distribution I(i, x). The individual distribution I(i, x) corresponds to the first intensity distribution in the present disclosure. In Figure 4 , the edge appears bright, and thus in order to determine the edge position, it is considered that a portion with high intensity in Figure 5 is set as the edge. However, the SEM image is an image in which noise is very large, and thus there are the following two problems.

[0051] Problem 1: In the vicinity of the edge position, there are multiple pixels with high intensity, and sometimes it is difficult to determine which pixel corresponds to the edge position.

[0052] Problem 2: In the case where a certain intensity value is used as a threshold to determine the edge position, sometimes a part that is not a true edge position is detected as an edge position, or a true edge position cannot be detected.

[0053] As a first method to solve the problem, a method of detecting an edge position after smoothing noise using a Gaussian filter or the like is considered. However, due to the smoothing of noise, information of high spatial frequency components is sometimes lost.

[0054] As a second method to solve the problem, as described in Japanese Patent Application Publication No. 2016-217816, a function form of a fitting function is obtained after obtaining a cumulative luminance distribution in the extension direction of the pattern, and fitting is performed using a separate luminance distribution that is not cumulative and the fitting function having the obtained function form. However, when a lot of noise is included in the separate luminance distribution, sometimes an edge position cannot be accurately detected. In addition, since the function form of the fitting function is obtained from the cumulative luminance distribution, it is possible to be affected by the luminance distribution at other positions in the extension direction of the pattern and perform fitting.

[0055] The embodiment described below relates to suppressing the effect of noise on a SEM image of lines and spaces, and detecting an edge position with high precision.

[0056] 3. Method of selectively reducing noise by multiplying a weight function f(x)

[0057] 3.1 Process of determining a pattern edge from a SEM image

[0058] Figure 6 is a flowchart showing the details of the process of determining a pattern edge from a SEM image in the first embodiment. The structure of the edge position determination device 100 in the first embodiment is the same as that described with reference to Figure 1 the structure described with reference to the first embodiment. The edge analysis process in the first embodiment is the same as the process described with reference to Figure 3 the first embodiment. Figure 6 corresponds to the subroutine of S2 of Figure 3 the first embodiment.

[0059] In S21, the processor 20 determines one or more average edge positions al, a2,... from the SEM image. If there is an edge on both sides of one line, the number of average edge positions al, a2,... included in one SEM image is twice the number of lines.

[0060] Figure 7 is a flowchart showing the details of the process of determining an average edge position al, a2,....Figure 7 corresponding to Figure 6 a subroutine of S21.

[0061] In S211, the processor 20 averages the intensity values included in the n individual distributions I(i, x) in the Y direction, and calculates an average intensity distribution ∑I(i, x) / n. The average intensity distribution ∑I(i, x) / n corresponds to the fourth intensity distribution in the present disclosure. The average intensity distribution ∑I(i, x) / n is obtained by summing the individual distributions I(i, x) for i = 1 to i = n for each value of x and dividing by n.

[0062] Figure 8 An example of the average intensity distribution ∑I(i, x) / n is shown. Figure 5 The noise of the individual distribution I(i, x) shown in (a) is large, and, in contrast to this, Figure 8 The average intensity distribution ∑I(i, x) / n shown in (b) is averaged in the Y direction and the noise is small.

[0063] Referring back to Figure 7 In S212, the processor 20 determines the average edge positions a1, a2,... from the average intensity distribution ∑I(i, x) / n. For example, the average edge positions a1, a2,... can be set as the peak position detected from the average intensity distribution ∑I(i, x) / n, or the center positions of each range above a threshold in the average intensity distribution ∑I(i, x) / n. In addition, the average edge positions a1, a2,... can be determined by smoothing the average intensity distribution ∑I(i, x) / n by any of the LOWESS (locally weighted scatterplot smoothing) method and the LOESS (locally estimated scatterplot smoothing) method. The interval of one average edge position from the nearest average edge position is set to d.

[0064] After S212 of Figure 7 , the processor 20 ends the processing of the present flowchart and returns to the processing shown in Figure 6 .

[0065] In S22 of Figure 6 , the processor 20 creates a weight function f(x) in which the weight is largest at the average edge positions a1, a2,....

[0066] Figures 9-11 Various other examples of the weight function f(x) are shown. In Figures 9-11In each graph, the average edge position is set as 'a', the constant corresponding to the multiplier of the weighting function f(x) in the X direction is set as 'b', and the interval below the average edge position 'a' with a specified value is set as the first interval #1. The specified value is a value smaller than the interval 'd', for example, 'd / 2'. Figures 9-11 In each figure, the value of the weight function f(x) at the average edge position a is the peak value of 1.0. The weight function f(x) is symmetric about the average edge position a in the first interval #1.

[0067] exist Figure 9 In the middle, the intervals whose distance from the average edge position 'a' is greater than a specified value are designated as the second interval #2. Figure 10 and Figure 11 In this context, the intervals where the distance from the average edge position 'a' is greater than a specified value are designated as the second interval #20. Within the second intervals #2 and #20, the value of the weight function f(x) is less than half of the peak value. Furthermore, in... Figures 9-11 In each figure, the weight function f(x) at positions a+d / 2 and ad / 2, which are half the distance from the average edge position a to the interval d, is less than half the peak value.

[0068] exist Figure 9 The diagram shows that in the interval where |(xa) / b| is less than 1, the weight function f(x) is (1-|(xa) / b|). 3 ) 3 The case where the weight function f(x) is 0 in the interval where |(xa) / b| is greater than 1. Specifically, in Figure 9 The example shows the case where b = d / 2. This applies when the interval where |(xa) / b| is less than 1 contains the entire first interval #1, or when the interval where |(xa) / b| is less than 1 coincides with the first interval #1. Figure 9 The weighting function f(x) shown is a function whose value decreases as it is further away from the average edge position a in the first interval #1 when capturing increases and decreases based on the average edge position a. In the first interval, the absolute value of the derivative of the weighting function f(x) is minimum at the average edge position a, for example, it is 0.

[0069] exist Figure 9 In the case where the interval where |(xa) / b| is greater than 1 contains the entire second interval #2, or where the interval where |(xa) / b| is greater than 1 is the same as the second interval #2, the weight function f(x) in the second interval #2 is a fixed value that is independent of the distance from the average edge position a, and this fixed value is 0.

[0070] Figure 10 The diagram shows that the weight function f(x) is exp(-((xa) / b) 2 (The situation is as follows.) Figure 11The case where the weight function f(x) is 1 / (1+((x-a) / b) 2 ) is shown in FIG. 2. Figure 10 and Figure 11 The weight function f(x) shown in FIG. 2 is a function in which the function value is smaller as the distance from the average edge position a is larger in all the intervals including the first interval #1 and the second interval #20 when the increase and decrease is captured with the average edge position a as a reference. The absolute value of the differential of the weight function f(x) is smallest, for example, 0 at the average edge position a.

[0071] Figure 12 The state in which the weight functions f(x) are aggregated in the number of average edge positions a1, a2,... is shown. The first region #1 of the weight function f(x) centered on the average edge position a1 is connected to the first region #1 of the weight function f(x) centered on the average edge position a2 with almost no gap, but the value of the weight function f(x) at the distance that is half the interval d from the average edge positions a1 and a2 is half or less of the peak value, so the weight is reduced in the middle of the average edge positions a1 and a2. In the second region #2 that is far from either of the average edge positions a2 and a3, the weight is reduced.

[0072] Referring again to Figure 6 , in S23, the processor 20 sets the value of the coordinate i in the Y direction to 0. In S24, the processor 20 updates the value of i by adding 1 to the value of i.

[0073] In S25, the processor 20 calculates a weighted individual distribution I(i, x)f(x) by multiplying the individual distribution I(i, x) by the weight function f(x). Here, the weight function f(x) used is the same regardless of the position in the Y direction. The weighted individual distribution I(i, x)f(x) corresponds to the third intensity distribution in the present disclosure.

[0074] Figure 13 An example of the individual distribution I(i, x) is shown, which corresponds to the expression Figure 5 again. Figure 14 An example of the weighted individual distribution I(i, x)f(x) is shown. A large weight is given to the portion close to the average edge positions a1, a2,..., and in contrast, a large weight is not given to the portion far from the average edge positions a1, a2,..., and the noise is reduced.

[0075] Referring again to Figure 6 , in S26, the processor 20 decides the edge positions e1, e2,... from the weighted individual distribution I(i, x)f(x).

[0076] Figure 15 is a flowchart showing the details of the process of deciding the edge positions e1, e2,....Figure 15 corresponds to Figure 6 a subroutine of S26.

[0077] In S261, the processor 20 performs local regression on the weighted individual distribution I(i, x)f(x), and calculates a smoothed individual distribution LOESS(I(i, x)f(x)). The smoothed individual distribution LOESS(I(i, x)f(x)) is an example of the second intensity distribution in the present disclosure. The process of local regression includes a process of fitting using a fitting function determined from the weighted individual distribution I(i, x)f(x). As a method of fitting, any of the LOWESS method and the LOESS method can be used.

[0078] Figure 16 represents an example of the smoothed individual distribution LOESS(I(i, x)f(x)). The smoothed individual distribution I(i, x)f(x) shown in Figure 14 is smoothed.

[0079] Referring back to Figure 15 , in S262, the processor 20 calculates peak positions of the smoothed individual distribution LOESS(I(i, x)f(x)) and sets them as edge positions e1, e2,.... After S262, the processor 20 ends the process of the present flowchart and returns to the process shown in Figure 6 .

[0080] In S27 of Figure 6 , the processor 20 determines whether the value of the coordinate i in the Y direction reaches n. In the case where the value of i reaches n (S27: Yes), the processor 20 causes the process to proceed to S28. In the case where the value of i does not reach n (S27: No), the processor 20 causes the process to return to S24.

[0081] In S28, the processor 20 generates arrangement data of the pattern edges on the basis of n sets of data of the edge positions e1, e2,... obtained by repeating S24 to S26 n times.

[0082] Figure 17 represents a case where the edge positions e1, e2,... included in the arrangement data are arranged on the XY plane. After S28 of Figure 6 , the processor 20 ends the process of the present flowchart and returns to the process shown in Figure 3 .

[0083] Figure 18 represents an example of a result of PSD analysis on the pattern edges. In the spatial frequency components of the LER, components with a spatial frequency of 15 / μm or less are mostly caused by the light source device, and components with a spatial frequency greater than 15 / μm are mostly caused by the resist material. Determining the cause of the LER by PSD analysis can contribute to improvement of the exposure performance.

[0084] 3.2 Action

[0085] (1) According to the first embodiment, the edge position determination method first determines average edge positions al, a2,... by aggregating the intensity values in the Y direction in the SEM images with intervals. Next, using the weight function f(x) having the largest weight at the average edge positions al, a2,... and a fitting function determined from the individual distribution I(i, x) representing the distribution of the intensity values along the X direction perpendicular to the Y direction at the coordinates i of each position of the SEM image, the individual distribution I(i, x) is fitted. Next, the edge positions el, e2,... at the coordinates i are determined from the smoothed individual distribution LOESS(I(i, x)f(x)) obtained by the fitting.

[0086] Thus, since the weight function f(x) having the largest weight at the average edge positions al, a2,... is used, it is possible to suppress the loss of data of the intensity values of the portions close to the average edge positions al, a2,... and to reduce the noise of the portions far from the average edge positions al, a2,.... In addition, since the fitting is performed using the fitting function determined from the individual distribution I(i, x), it is possible to suppress the influence from the intensity distributions at other coordinates i.

[0087] (2) According to the first embodiment, the weight function f(x) is a function in which the function value is smaller as the distance from the average edge position al, a2,... is larger in the first interval #1 in which the distance is equal to or smaller than a prescribed value smaller than the interval d of the average edge position and the nearest average edge position.

[0088] Thus, the smaller the distance from the average edge position al, a2,..., the more it is possible to suppress the loss of data, and the larger the distance from the average edge position al, a2,..., the more it is possible to reduce the noise. Therefore, the possibility that the portions which are the true edge positions are determined as the edge positions el, e2,... and the portions which are not the true edge positions are determined as the edge positions el, e2,... becomes higher.

[0089] (3) According to the first embodiment, in the first interval, the absolute value of the differential of the weight function is the smallest in the average edge positions al, a2,....

[0090] Thus, the decrease is made gentle in the vicinity of the average edge positions al, a2,..., and therefore it is possible to evaluate the portions having a certain degree of width which are the true edge positions with a high possibility highly and to reduce the possibility of overlooking the true edge positions.

[0091] (4) According to the first embodiment, the weight function f(x) is symmetrical about the average edge position a1, a2,... in a first interval #1 in which the distance from the average edge position a1, a2,... is equal to or less than a prescribed value.

[0092] Thus, the intensity values at positions equidistant from the average edge positions a1, a2,... can be equally evaluated to determine the edge positions e1, e2,....

[0093] (5) According to the first embodiment, in a second interval #2 and #20 in which the distance from the average edge position a1, a2,... is greater than a prescribed value, the value of the weight function f(x) is equal to or less than half the weight at the average edge position a1, a2,....

[0094] Thus, by setting the weight in the case where the distance from the average edge position a1, a2,... is greater than a prescribed value to be equal to or less than half the peak value, it is possible to suppress the influence of noise on the determination of the edge positions e1, e2,... in a portion in which the likelihood of being a true edge position is very low.

[0095] (6) According to the first embodiment, in the case where the distance from the average edge position a1, a2,... is equal to half the interval d, the value of the weight function f(x) is equal to or less than half the weight at the average edge position a1, a2,....

[0096] Thus, by sufficiently reducing the weight between peaks, it is possible to reduce the likelihood of determining a portion that is not a true edge position to be an edge position e1, e2,....

[0097] (7) According to the first embodiment, in the second interval #2 in which the distance from the average edge position a1, a2,... is greater than a prescribed value, the value of the weight function f(x) is a fixed value regardless of the above distance.

[0098] Thus, by setting the weight in the case where the distance from the average edge position a1, a2,... is greater than a prescribed value to be a fixed value, it is possible to reduce the computational load in a portion in which the likelihood of being a true edge position is very low.

[0099] (8) According to the first embodiment, in the second interval #2 in which the distance from the average edge position a1, a2,... is greater than a prescribed value, the value of the weight function f(x) is 0 regardless of the above distance.

[0100] Thus, by setting the weight in the case where the distance from the average edge position a1, a2,... is greater than a prescribed value to be 0, it is possible to ignore a portion in which the likelihood of being a true edge position is very low.

[0101] (9) According to the first embodiment, when a position in an X direction perpendicular to the Y direction is set as x, the average edge position is set as a, and b is set as a constant, the weight function f(x) is (1 - |(x-a) / b| for an interval in which |(x-a) / b| is 1 or less, and is 0 for an interval in which |(x-a) / b| is greater than 1. 3 3 3

[0102] Thus, the weight at the average edge position a is maximized, and it is possible to set the weight function f(x) in which the weight decreases according to the constant b as the distance from the average edge position a increases. In addition, by setting the weight to 0 for an interval in which |(x-a) / b| is greater than 1, it is possible to ignore a portion in which the likelihood that it is a true edge position is very low.

[0103] (10) According to the first embodiment, when a position in an X direction perpendicular to the Y direction is set as x, the average edge position is set as a, and b is set as a constant, the weight function f(x) is exp(-((x-a) / b) 2 ) for an interval in which |(x-a) / b| is 1 or less, and is 0 for an interval in which |(x-a) / b| is greater than 1.

[0104] Thus, it is possible to set a Gaussian function in which the weight at the average edge position a is maximized and monotonically decreases according to the constant b as the distance from the average edge position a increases as the weight function f(x).

[0105] (11) According to the first embodiment, when a position in an X direction perpendicular to the Y direction is set as x, the average edge position is set as a, and b is set as a constant, the weight function f(x) is 1 / (1+((x-a) / b) 2 ) for an interval in which |(x-a) / b| is 1 or less, and is 0 for an interval in which |(x-a) / b| is greater than 1.

[0106] Thus, it is possible to set a Lorentz function in which the weight at the average edge position a is maximized and monotonically decreases according to the constant b as the distance from the average edge position a increases as the weight function f(x).

[0107] (12) According to the first embodiment, the individual distribution I(i, x) at a first coordinate indicating a first position in the Y direction and the individual distribution I(i, x) at a second coordinate indicating a second position in the Y direction are fitted using the same weight function f(x) for each other.

[0108] Thus, even if the coordinates i in the extension direction of the line are different, evaluation is performed by the same weight function f(x), and thus it is possible to reduce a deviation in the evaluation caused by a difference in the coordinates i.

[0109] (13) According to the first embodiment, the smoothed individual distribution LOESS(I(i, x)f(x)) is obtained by fitting a weighted individual distribution I(i, x)f(x) obtained by multiplying the individual distribution I(i, x) by the weight function f(x) using the fitting function.​

[0110] Thus, by multiplying the weight function f(x) before fitting, the calculation load of fitting can be reduced.

[0111] (14) According to the first embodiment, the method of fitting the weighted individual distribution I(i, x)f(x) by the fitting function is any of the LOWESS method and the LOESS method.

[0112] Thus, the fitting function is not constrained by a specific function form, and fitting can be accurately performed.

[0113] (15) According to the first embodiment, the peak position of the smoothed individual distribution LOESS(I(i, x)f(x)) is determined as the edge position el, e2,....

[0114] Thus, the edge positions el, e2,.... can be accurately determined.

[0115] (16) According to the first embodiment, the average intensity distribution∑I(i, x) / n obtained by aggregating the intensity values included in the individual distribution I(i, x) in the Y direction is smoothed, and the average edge position al, a2,.... is determined.

[0116] Thus, by smoothing the average intensity distribution∑I(i, x) / n, the average edge positions al, a2,.... can be accurately determined.

[0117] (17) According to the first embodiment, the method of smoothing the average intensity distribution∑I(i, x) / n is any of the LOWESS method and the LOESS method.

[0118] Thus, by using any of the LOWESS method and the LOESS method, the average intensity distribution∑I(i, x) / n can be reliably smoothed.

[0119] As for other aspects, the first embodiment is the same as the comparative example.

[0120] 4. Method of using the weight function f(x) as a weight for local regression

[0121] 4.1 Process of determining the pattern edge from the SEM image

[0122] Figure 19 is a flowchart showing details of the process of determining the pattern edge from the SEM image in the second embodiment. The structure of the edge position determination device 100 in the second embodiment is the same as the structure described with reference to Figure 1 the structure described with reference to Figure 3 the process described with reference to Figure 19 corresponds toFigure 3 the subroutine of S2 of the first embodiment, in place of Figure 6 The second embodiment differs from the first embodiment in that, instead of S25 and S26, S26a is performed.

[0123] In S26a, the processor 20 performs local regression for the individual distribution I(i, x) using the weight function f(x) as the weight of the local regression, and determines the edge positions e1, e2,.... The smoothed individual distribution obtained by the weighted local regression of S26a is an example of the second intensity distribution in the present disclosure. The process of the local regression includes a process of fitting using a fitting function determined from the individual distribution I(i, x). As the method of fitting, any of the LOWESS method and the LOESS method can be used. The weight function f(x) used when fitting the individual distribution I(i, x) is the same regardless of the position in the Y direction.

[0124] 4.2 Effects

[0125] (18) According to the second embodiment, the weight function f(x) is used as the weight when fitting the individual distribution I(i, x) by the fitting function.

[0126] Thus, multiplication of the individual distribution I(i, x) and the weight function f(x) is not required, and it is possible to speed up the calculation.

[0127] As for other aspects, the second embodiment is the same as the first embodiment.

[0128] 5. Other

[0129] The above description is not a limitation but a mere example. Therefore, it is obvious for those skilled in the art that the embodiments of the present disclosure can be changed without departing from the scope of the claims. In addition, it is also obvious for those skilled in the art that the embodiments of the present disclosure can be used in combination.

[0130] Unless otherwise specified, the terms used in the specification and the claims throughout the entire specification should be interpreted as "non-limiting" terms. For example, the terms such as "include", "have", "possess", "is provided with", and the like should be interpreted as "not excluding the existence of the constituent elements other than the recited constituent elements". In addition, the modifier "one" should be interpreted as meaning "at least one" or "one or more than one". In addition, the term "at least one of A, B, and C" should be interpreted as "A", "B", "C", "A+B", "A+C", "B+C", or "A+B+C". Furthermore, it should be interpreted as also including combinations thereof with parts other than "A", "B", and "C".

Claims

1. An edge position determination method, wherein, intensity values in an extending direction of a line in a line and interval SEM image are aggregated to determine an average edge position, using a weight function having a maximum weight at the average edge position and a fitting function determined from a first intensity distribution, the first intensity distribution representing a distribution of the intensity values at coordinates of each position of the SEM image representing the extending direction along a direction perpendicular to the extending direction, the first intensity distribution is fitted, an edge position at the coordinates is determined from a second intensity distribution obtained by the fitting.

2. The edge position determination method according to claim 1, wherein, the weight function is a function having a smaller function value as a distance from the average edge position is larger in a first interval where the distance is below a prescribed value, the prescribed value being smaller than an interval between the average edge position and another nearest average edge position.

3. The edge position determination method according to claim 2, wherein, in the first interval, an absolute value of a differential of the weight function is smallest at the average edge position.

4. The edge position determination method according to claim 2, wherein, the weight function is symmetrical about the average edge position in the first interval.

5. The edge position determination method according to claim 2, wherein, in a second interval where the distance is larger than the prescribed value, a value of the weight function is below half of the weight at the average edge position.

6. The edge position determination method according to claim 2, wherein, in a case where the distance is half of the interval, a value of the weight function is below half of the weight at the average edge position.

7. The edge position determination method according to claim 2, wherein, a value of the weight function is a fixed value irrespective of the distance in a second interval where the distance is larger than the prescribed value.

8. The edge position determination method according to claim 2, wherein, a value of the weight function is 0 irrespective of the distance in a second interval where the distance is larger than the prescribed value.

9. The edge position determination method according to claim 1, wherein, In a case where a position in a direction perpendicular to the extension direction is set as x, the average edge position is set as a, and b is set as a constant, the weight function is (1-|(x-a) / b|) in an interval where |(x-a) / b| is 1 or less, and is 0 in an interval where |(x-a) / b| is greater than 1. 3 ) 3 , 10. The edge position determination method according to claim 1, wherein, When a position in a direction perpendicular to the extension direction is set as x, the average edge position is set as a, and b is set as a constant, the weight function is exp(-((x-a) / b) 2 ).

11. The edge position determination method according to claim 1, wherein, The weight function is 1 / (1+((x-a) / b)) when a position in a direction perpendicular to the extension direction is set as x, the average edge position is set as a, and b is set as a constant. 2 ) 12. The edge position determination method according to claim 1, wherein, the first intensity distribution at a first coordinate representing a first position of the extending direction and the first intensity distribution at a second coordinate representing a second position of the extending direction are fitted using the weight function which is the same as each other.

13. The edge position determination method according to claim 1, wherein, the second intensity distribution is obtained by fitting a third intensity distribution obtained by multiplying the first intensity distribution by the weight function using the fitting function.

14. The edge position determination method according to claim 1, wherein, a method of fitting using the fitting function is any of a LOWESS method and a LOESS method.

15. The edge position determination method according to claim 1, wherein a peak position of the second intensity distribution is determined as the edge position.

16. The edge position determination method according to claim 1, wherein the average edge position is determined by smoothing a fourth intensity distribution, which is obtained by aggregating the intensity values included in the first intensity distribution in the extension direction.

17. The edge position determination method according to claim 16, wherein the method of smoothing the fourth intensity distribution is any of a LOWESS method and a LOESS method.

18. The edge position determination method according to claim 1, wherein the weight function is used as a weight when fitting the first intensity distribution with the fitting function.

19. An edge position determination apparatus comprising: a communication controller that acquires a line-and-space SEM image; and a processor, the processor performs the following processing: determining an average edge position by aggregating intensity values in an extension direction of a line in the SEM image, fitting a first intensity distribution, which is an intensity distribution of the SEM image at a coordinate representing each position of the extension direction in a direction perpendicular to the extension direction, with a fitting function determined from the first intensity distribution using a weight function having a largest weight at the average edge position, determining an edge position at the coordinate from a second intensity distribution obtained by the fitting.

20. An edge analysis method wherein an average edge position is determined by aggregating intensity values in an extension direction of a line in a line-and-space SEM image, a first intensity distribution, which is an intensity distribution of the SEM image at a coordinate representing each position of the extension direction in a direction perpendicular to the extension direction, is fitted with a fitting function determined from the first intensity distribution using a weight function having a largest weight at the average edge position, an edge position at the coordinate is determined from a second intensity distribution obtained by the fitting, PSD analysis is performed on the edge positions at a plurality of positions of the extension direction.

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