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

Abstract

To provide a method for determining an edge position in a SEM image.SOLUTION: An edge position determination method includes: aggregating intensity values in an extension direction of a line in a SEM image of a line-and-space pattern to determine average edge positions; fitting a first intensity profile indicating a distribution of the intensity values along a direction perpendicular to the extension direction in a coordinate indicating each position in the extension direction of the SEM image by using a weight function created to have the largest weight at the average edge positions and a fitting function specified according to the first intensity profile; and determining edge positions in the coordinate from a second intensity profile obtained by the fitting.SELECTED DRAWING: Figure 6

Description

[Technical Field]

[0001] The present disclosure relates to an edge location determination method, an edge location determination device, and an edge analysis method. [Background technology]

[0002] In recent years, semiconductor exposure devices have been required to improve their resolution in response to the miniaturization and high integration of semiconductor integrated circuits. To this end, the wavelength of light emitted from exposure light sources has been shortened. For example, KrF excimer laser devices, which output laser light with a wavelength of approximately 248 nm, and ArF excimer laser devices, which output laser light with a wavelength of approximately 193 nm, are used as gas laser devices for exposure.

[0003] The spectral linewidth of the spontaneously oscillating light from KrF excimer laser devices and ArF excimer laser devices is as wide as 350 to 400 pm. Therefore, if a projection lens is constructed using a material that transmits ultraviolet light, such as KrF and ArF laser light, chromatic aberration may occur. As a result, resolution may decrease. Therefore, it is necessary to narrow the spectral linewidth of the laser light output from the gas laser device to a level where chromatic aberration can be ignored. Therefore, a line narrowing module (LNM) containing a line narrowing element (e.g., an etalon or grating) may be installed inside the laser resonator of the gas laser device to narrow the spectral linewidth. A gas laser device that narrows the spectral linewidth is called a line narrowing gas laser device. [Prior art documents] [Patent documents]

[0004] [Patent Document 1] Summary of JP 2016-217816 A

[0005] An edge position determination method according to one aspect of the present disclosure determines an average edge position by aggregating intensity values ​​in the extension direction of lines in a line-and-space SEM image, fits a first intensity profile showing the distribution of intensity values ​​along a direction perpendicular to the extension direction at coordinates indicating each position in the extension direction of the SEM image using a weighting function that maximizes the weight at the average edge position and a fitting function determined according to the first intensity profile, and determines the edge position at the coordinates from a second intensity profile obtained by fitting.

[0006] An edge position determination device according to one aspect of the present disclosure includes a communication controller that acquires a line-and-space SEM image, and a processor that determines an average edge position by aggregating intensity values ​​in the extension direction of the lines in the SEM image, fits a first intensity profile along a direction perpendicular to the extension direction at coordinates indicating each position in the extension direction of the SEM image using a weighting function that maximizes the weight at the average edge position and a fitting function determined according to the first intensity profile, and determines the edge position at the coordinates from a second intensity profile obtained by fitting.

[0007] An edge analysis method according to one aspect of the present disclosure determines an average edge position by aggregating intensity values ​​in the extension direction of lines in a line-and-space SEM image, fits a first intensity profile along a direction perpendicular to the extension direction at coordinates indicating each position in the extension direction of the SEM image using a weighting function that maximizes the weight at the average edge position and a fitting function determined according to the first intensity profile, determines the edge position at the coordinates from a second intensity profile obtained by fitting, and performs PSD analysis on the edge positions at multiple positions in the extension direction. [Brief explanation of the drawings]

[0008] Some embodiments of the present disclosure will now be described, by way of example only, with reference to the accompanying drawings, in which: [Figure 1]FIG. 1 shows the configuration of an edge position determining device in a comparative example. [Figure 2] FIG. 2 shows a portion of an SEM image containing lines and spaces. [Figure 3] FIG. 3 is a flowchart showing an outline of edge analysis processing in the comparative example. [Figure 4] Figure 4 shows an example of a line and space SEM image. [Figure 5] FIG. 5 shows an example of an intensity profile along the X direction at coordinate i in the Y direction in FIG. [Figure 6] FIG. 6 is a flowchart showing the details of the process of determining a pattern edge from an SEM image in the first embodiment. [Figure 7] FIG. 7 is a flowchart showing the details of the process for determining the average edge position. [Figure 8] FIG. 8 shows an example of an average intensity profile. [Figure 9] FIG. 9 shows an example of a weighting function. [Figure 10] FIG. 10 shows another example of a weighting function. [Figure 11] FIG. 11 shows another example of a weighting function. [Figure 12] FIG. 12 shows a state in which the weighting functions are added in the number equal to the number of average edge positions. [Figure 13] FIG. 13 shows an example of an individual profile. [Figure 14] FIG. 14 shows an example of a weighted individual profile. [Figure 15] FIG. 15 is a flowchart showing the details of the process for determining the edge position. [Figure 16] FIG. 16 shows an example of a smoothed individual profile. [Figure 17] FIG. 17 shows the edge positions included in the array data arranged on the XY plane. [Figure 18] FIG. 18 shows an example of the results of PSD analysis of a pattern edge. [Figure 19]FIG. 19 is a flowchart showing the details of the process of determining a pattern edge from an SEM image in the second embodiment. Embodiment

[0009] <Contents> 1. Comparative Example 2. Issues with the comparative example 3. Selective noise reduction by multiplying the weighting function f(x) 3.1 Process for determining pattern edges from SEM images 3.2 Effect 4. Using the weight function f(x) as the weight for local regression 4.1 Process for determining pattern edges from SEM images 4.2 Effect 5.Other

[0010] Hereinafter, embodiments of the present disclosure will be described in detail with reference to the drawings. The embodiments described below show some examples of the present disclosure and do not limit the content of the present disclosure. Furthermore, not all of the configurations and operations described in each embodiment are necessarily essential as the configurations and operations of the present disclosure. Note that the same components are given the same reference symbols, and redundant explanations will be omitted.

[0011] 1. Comparative Example 1 shows the configuration of an edge position determining device 100 in a comparative example. The comparative example of the present disclosure is a configuration that the applicant recognizes as being known only by the applicant, and is not a publicly known example that the applicant acknowledges.

[0012] The edge position determination apparatus 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 an SEM image of a semiconductor substrate (not shown) captured by the CD-SEM 200 from the CD-SEM 200 or from another external device that stores the SEM image. The SEM image includes a fine line processing pattern called line and space formed by exposure and development of the semiconductor substrate.

[0013] 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 configured or programmed to execute various processes included in the present disclosure. The processor 20 determines the edge positions of the line and space using the SEM image acquired by the communication controller 10. Furthermore, the processor 20 evaluates exposure performance by performing edge analysis using the edge positions.

[0014] Figure 2 shows a portion of an SEM image containing lines and spaces. In an SEM image, the edges that are the boundaries between lines and spaces appear bright, while the line and space portions other than the edges appear dark. LER (line edge roughness) indicates the deviation of the edge from the ideal position, and LWR (line width roughness) indicates the variation in the distance between the edges on both sides of the line. Requirements for LER and LWR in semiconductor lithography are becoming stricter every year. In order to accurately analyze the causative factors of LER and LWR, it is necessary to accurately determine the edge position. In the following explanation, no distinction will be made between LER and LWR, and only LER will be used as a representative term.

[0015] 3 is a flowchart showing an outline of edge analysis processing in the comparative example. Edge analysis is performed as follows.

[0016] In S1, the processor 20 acquires an SEM image of an exposed and developed semiconductor wafer from the communication controller 10. In S2, the processor 20 determines a pattern edge from the SEM image. The pattern edge is provided as array data of a large number of edge positions obtained from the SEM image. In S3, the processor 20 performs PSD (power spectral density) analysis of the pattern edge. PSD analysis is a signal analysis that breaks down a signal into signal strength per unit frequency. PSD analysis of a pattern edge means performing PSD analysis by regarding the LER as a signal, and investigating what spatial frequency components the LER is made up of.

[0017] Figure 4 shows an example of a line and space SEM image. The extension direction of the lines is the Y direction. The direction perpendicular to the extension direction is the X direction. The position in the X direction is represented by x. If the number of pixels in the Y direction of this SEM image is n and the coordinate of an arbitrary position in the Y direction is i, i can take on an integer value between 1 and n.

[0018] 2. Issues with the comparative example FIG. 5 shows an example of an intensity profile along the X direction at coordinate i in the Y direction in FIG. 4. The intensity profile shown in FIG. 5 is designated as individual profile I(i,x). Individual profile I(i,x) corresponds to the first intensity profile in this disclosure. Since edges appear bright in FIG. 4, it is conceivable to determine the edge position by identifying the areas of high intensity in FIG. 5. However, SEM images are very noisy, which poses the following two problems.

[0019] Problem 1: There are multiple pixels with high intensity near the edge position, and it can be difficult to determine which pixel corresponds to the edge position.

[0020] Problem 2: When determining the edge position using a certain intensity value as a threshold, there are cases where a part that is not the true edge position is detected as the edge position, or where the true edge position cannot be detected at all.

[0021] The first method to solve this problem is to detect the edge position after smoothing the noise using a Gaussian filter, etc. However, smoothing the noise may result in the loss of information about high spatial frequency components.

[0022] A second method for solving the problem, as described in Japanese Patent Application Laid-Open No. 2016-217816, involves calculating an integrated luminance profile in the extension direction of the pattern to determine the functional form of a fitting function, and then fitting using individual luminance profiles that have not been integrated and a fitting function having the calculated functional form. However, if the individual luminance profiles contain a lot of noise, it may not be possible to accurately detect the edge position. Furthermore, since the functional form of the fitting function is calculated from an integrated luminance profile, the fitting may be affected by luminance profiles at other positions in the extension direction of the pattern.

[0023] The embodiments described below relate to suppressing the influence of noise in line-and-space SEM images and detecting edge positions with high accuracy.

[0024] 3. Selective noise reduction by multiplying the weighting function f(x) 3.1 Process for determining pattern edges from SEM images Fig. 6 is a flowchart showing details of the process of determining a pattern edge from an SEM image in the first embodiment. The configuration of the edge position determining device 100 in the first embodiment is the same as that described with reference to Fig. 1. The edge analysis process in the first embodiment is the same as that described with reference to Fig. 3. Fig. 6 corresponds to the subroutine of S2 in Fig. 3.

[0025] In S21, the processor 20 determines one or more average edge positions a1, a2, ... from the SEM image. If there are edges on both sides of a line, the number of average edge positions a1, a2, ... included in one SEM image is twice the number of lines.

[0026] 7 is a flowchart showing the details of the process for determining the average edge positions a1, a2, .... Fig. 7 corresponds to the subroutine of S21 in Fig. 6.

[0027] In S211, the processor 20 calculates an average intensity profile ΣI(i,x) / n by averaging the intensity values ​​included in n individual profiles I(i,x) in the Y direction. The average intensity profile ΣI(i,x) / n corresponds to the fourth intensity profile in this disclosure. The average intensity profile ΣI(i,x) / n is obtained by aggregating the individual profiles I(i,x) from i=1 to i=n for each value of x and dividing by n.

[0028] Figure 8 shows an example of the average intensity profile ΣI(i,x) / n. While the individual profile I(i,x) shown in Figure 5 has a large amount of noise, the average intensity profile ΣI(i,x) / n shown in Figure 8 has been averaged in the Y direction and has a small amount of noise.

[0029] 7 again, in S212, the processor 20 determines average edge positions a1, a2, ... from the average intensity profile ΣI(i,x) / n. For example, peak positions may be detected from the average intensity profile ΣI(i,x) / n to determine the average edge positions a1, a2, ..., or the center positions of each range in the average intensity profile ΣI(i,x) / n that is equal to or greater than a threshold may be determined as the average edge positions a1, a2, .... Alternatively, the average intensity profile ΣI(i,x) / n may be smoothed using either the LOWESS (locally weighted scatterplot smoothing) method or the LOESS (locally estimated scatterplot smoothing) method to determine the average edge positions a1, a2, .... The distance between one average edge position and the closest other average edge position is defined as d.

[0030] After S212 in FIG. 7, the processor 20 ends the processing of this flowchart and returns to the processing shown in FIG.

[0031] In S22 of FIG. 6, the processor 20 creates a weighting function f(x) that maximizes the weight at the average edge positions a1, a2, . . .

[0032] 9 to 11 show different examples of the weighting function f(x). In each of FIGS. 9 to 11, the average edge position is a, a constant corresponding to the X-direction magnification of the weighting function f(x) is b, and a section whose distance from the average edge position a is equal to or less than a predetermined value is defined as first section #1. The predetermined value is a value smaller than the interval d, for example, d / 2. In each of FIGS. 9 to 11, the value of the weighting function f(x) at the average edge position a has a peak value of 1.0, and the weighting function f(x) is symmetrical about the average edge position a in first section #1.

[0033] 9, the section where the distance from the average edge position a is greater than a predetermined value is designated as second section #2, and in FIGS. 10 and 11, the section where the distance from the average edge position a is greater than a predetermined value is designated as second section #20. In second sections #2 and #20, the value of weighting function f(x) is less than half the peak value. Furthermore, in each of FIGS. 9 to 11, the value of weighting function f(x) at positions a+d / 2 and ad / 2, where the distance from the average edge position a is half the interval d, is less than half the peak value.

[0034] In FIG. 9, in the section where |(xa) / b| is 1 or less, the weighting function f(x) is (1-|(xa) / b| 3 ) 3 and the weighting function f(x) is 0 in the section where |(xa) / b| is greater than 1. Specifically, FIG. 9 shows the case where b=d / 2. When the section where |(xa) / b| is 1 or less includes the entire first section #1, or when the section where |(xa) / b| is 1 or less coincides with the first section #1, the weighting function f(x) shown in FIG. 9 is a function that, when capturing an increase or decrease based on the average edge position a, becomes smaller as the distance from the average edge position a in the first section #1 increases. In the first section, the absolute value of the derivative of this weighting function f(x) is smallest at the average edge position a, e.g., 0.

[0035] In Figure 9, when the section where |(xa) / b| is greater than 1 includes the entire second section #2, or when the section where |(xa) / b| is greater than 1 coincides with the second section #2, the weighting function f(x) is a constant value in the second section #2 regardless of the distance from the average edge position a, and this constant value is 0.

[0036] In Figure 10, the weighting function f(x) is exp(-((xa) / b) 2 ) is shown in Figure 11. The weighting function f(x) is 1 / (1+((xa) / b) 210 and 11 is a function that, when an increase or decrease is detected with respect to the average edge position a, decreases as the distance from the average edge position a increases in all sections including the first and second sections #1 and #20. The absolute value of the derivative of this weighting function f(x) is minimum at the average edge position a, e.g., 0.

[0037] 12 shows the state in which the weighting function f(x) is added for the number of average edge positions a1, a2, .... The first region #1 of the weighting function f(x) centered on the average edge position a1 and the first region #1 of the weighting function f(x) centered on the average edge position a2 are connected with almost no gaps, but because the value of the weighting function f(x) when the distance from the average edge positions a1 and a2 is half the interval d is less than half the peak value, the weight is reduced between the average edge positions a1 and a2. The weight is also reduced in the second region #2, which is far from both the average edge positions a2 and a3.

[0038] 6 again, in S23, the processor 20 sets the value of the coordinate i in the Y direction to 0. In S24, the processor 20 adds 1 to the value of i to update the value of i.

[0039] In S25, the processor 20 calculates a weighted individual profile I(i,x)f(x) by multiplying the individual profile I(i,x) by a weighting function f(x). Here, the weighting function f(x) used is the same regardless of the position in the Y direction. The weighted individual profile I(i,x)f(x) corresponds to the third intensity profile in this disclosure.

[0040] Fig. 13 shows an example of an individual profile I(i,x), which is a reprint of Fig. 5. Fig. 14 shows an example of a weighted individual profile I(i,x)f(x). Large weights are assigned to parts close to the average edge position a1, a2, ..., while small weights are assigned to parts far from the average edge position a1, a2, ..., thereby reducing noise.

[0041] Referring again to FIG. 6, in S26, the processor 20 determines edge positions e1, e2, . . . from the weighted individual profile I(i,x)f(x).

[0042] 15 is a flowchart showing the details of the process for determining the edge positions e1, e2, .... Fig. 15 corresponds to the subroutine of S26 in Fig. 6.

[0043] In S261, the processor 20 performs local regression on the weighted individual profile I(i,x)f(x) to calculate a smoothed individual profile LOESS(I(i,x)f(x)). The smoothed individual profile LOESS(I(i,x)f(x)) is an example of a second intensity profile in the present disclosure. The local regression process includes a fitting process using a fitting function determined according to the weighted individual profile I(i,x)f(x). Either the LOWESS method or the LOESS method can be used as the fitting method.

[0044] 16 shows an example of a smoothed individual profile LOESS(I(i,x)f(x)), which is smoother than the weighted individual profile I(i,x)f(x) shown in FIG.

[0045] 15 again, in S262, the processor 20 calculates the peak positions of the smoothed individual profile LOESS(I(i,x)f(x)) and sets them as edge positions e1, e2, ... After S262, the processor 20 ends the processing of this flowchart and returns to the processing shown in FIG.

[0046] 6, the processor 20 determines whether the value of the Y-direction coordinate i has reached n. If the value of i has reached n (S27: YES), the processor 20 proceeds to S28. If the value of i has not reached n (S27: NO), the processor 20 returns to S24.

[0047] In S28, the processor 20 generates arrangement data of the pattern edges from n sets of data of the edge positions e1, e2, . . . obtained by repeating S24 to S26 n times.

[0048] 17 shows the edge positions e1, e2, ... included in the array data arranged on the XY plane. After S28 in FIG. 6, the processor 20 ends the processing of this flowchart and returns to the processing shown in FIG.

[0049] Figure 18 shows an example of the results of PSD analysis of a pattern edge. Among the spatial frequency components of LER, components with a spatial frequency of 15 / μm or less are often caused by the light source device, while components with a spatial frequency greater than 15 / μm are often caused by the resist material. PSD analysis can identify the cause of LER and be useful for improving exposure performance.

[0050] 3.2 Effect (1) According to the first embodiment, the edge position determination method first determines average edge positions a1, a2, ... by summing intensity values ​​in the Y direction in a line-and-space SEM image. Next, an individual profile I(i, x) indicating the distribution of intensity values ​​along the X direction perpendicular to the Y direction at coordinate i indicating each position in the Y direction of the SEM image is fitted using a weighting function f(x) that maximizes the weight at the average edge positions a1, a2, ... and a fitting function determined according to the individual profile I(i, x). Next, the edge positions e1, e2, ... at coordinate i are determined from the smoothed individual profile LOESS(I(i, x)f(x)) obtained by fitting.

[0051] This uses a weighting function f(x) that maximizes the weight at the average edge positions a1, a2, ..., thereby preventing loss of intensity value data near the average edge positions a1, a2, ..., and reducing noise in areas away from the average edge positions a1, a2, .... Furthermore, fitting is performed using a fitting function determined according to the individual profile I(i,x), so that the influence of intensity profiles at other coordinates i can be suppressed.

[0052] (2) According to the first embodiment, the weighting function f(x) is a function that becomes smaller as the distance from the average edge position a1, a2, ... increases in the first section #1 where the distance is equal to or less than a predetermined value smaller than the interval d between the average edge position and another closest average edge position.

[0053] According to this, the smaller the distance from the average edge position a1, a2, ..., the more data loss is suppressed, and the greater the distance from the average edge position a1, a2, ..., the more noise can be reduced. Therefore, it becomes more likely that parts that are true edge positions can be determined as edge positions e1, e2, ..., and parts that are not true edge positions can be determined as not being edge positions e1, e2, ....

[0054] (3) According to the first embodiment, in the first section, the absolute value of the derivative of the weighting function is smallest at the average edge positions a1, a2, . . .

[0055] According to this, the rate of decrease is made gentler near the average edge positions a1, a2, ..., so that a certain width of area that is likely to be the true edge position is highly evaluated, thereby reducing the possibility of missing the true edge position.

[0056] (4) According to the first embodiment, the weighting function f(x) is symmetrical with respect to the average edge positions a1, a2, ... in the first section #1 where the distance from the average edge positions a1, a2, ... is equal to or less than a predetermined value.

[0057] According to this, the edge positions e1, e2, . . . can be determined by equally evaluating the intensity values ​​at positions equidistant from the average edge positions a1, a2, .

[0058] (5) According to the first embodiment, the value of the weighting function f(x) is less than half the weight at the average edge position a1, a2, ... in the second sections #2 and #20 where the distance from the average edge position a1, a2, ... is greater than a predetermined value.

[0059] According to this, by setting the weight to less than half of the peak value when the distance from the average edge position a1, a2, ... is greater than a predetermined value, it is possible to prevent noise in areas that are very unlikely to be the true edge position from affecting the determination of the edge positions e1, e2, ...

[0060] (6) According to the first embodiment, the value of the weighting function f(x) is less than half the weight at the average edge position a1, a2, ... when the distance from the average edge position a1, a2, ... is half the interval d.

[0061] According to this, by making the weight between peaks sufficiently small, it is possible to reduce the possibility that parts that are not true edge positions are determined to be edge positions e1, e2, . . . .

[0062] (7) According to the first embodiment, the value of the weighting function f(x) is constant in the second section #2 where the distance from the average edge position a1, a2, . . . is greater than a predetermined value, regardless of the distance.

[0063] According to this, by setting the weight to a constant value when the distance from the average edge position a1, a2, . . . is greater than a predetermined value, the calculation load can be reduced in areas that are very unlikely to be the true edge position.

[0064] (8) According to the first embodiment, the value of the weighting function f(x) is 0 in the second section #2 where the distance from the average edge position a1, a2, . . . is greater than a predetermined value, regardless of the distance.

[0065] According to this, by setting the weight to 0 when the distance from the average edge position a1, a2, . . . is greater than a predetermined value, it is possible to ignore parts that are very unlikely to be the true edge position.

[0066] (9) According to the first embodiment, when the position in the X direction perpendicular to the Y direction is x, the average edge position is a, and b is a constant, the weighting function f(x) is (1-|(xa) / b|) in the range where |(xa) / b| is 1 or less. 3 ) 3 and is 0 in the interval where |(xa) / b| is greater than 1.

[0067] This allows setting a weighting function f(x) in which the weight is maximum at the average edge position a and decreases according to the constant b as the distance from the average edge position a increases. Also, by setting the weight to 0 in the section where |(xa) / b| is greater than 1, it is possible to ignore parts that are very unlikely to be the true edge position.

[0068] (10) According to the first embodiment, when the position in the X direction perpendicular to the Y direction is x, the average edge position is a, and b is a constant, the weighting function f(x) is exp(-((xa) / b) 2 )

[0069] According to this, a Gaussian function in which the weight is maximum at the average edge position a and the weight monotonically decreases according to the constant b as the distance from the average edge position a increases can be set as the weight function f(x).

[0070] (11) According to the first embodiment, when the position in the X direction perpendicular to the Y direction is x, the average edge position is a, and b is a constant, the weighting function f(x) is 1 / (1+((xa) / b) 2 )

[0071] According to this, the weighting function f(x) can be set as a Lorentz function in which the weighting is maximum at the average edge position a and monotonically decreases according to the constant b as the distance from the average edge position a increases.

[0072] (12) According to the first embodiment, an individual profile I(i, x) at a first coordinate indicating a first position in the Y direction and an individual profile I(i, x) at a second coordinate indicating a second position in the Y direction are fitted using the same weighting function f(x).

[0073] According to this, even if the coordinate i in the extension direction of the line is different, the evaluation is performed using the same weighting function f(x), so that the variation in evaluation due to the difference in the coordinate i can be reduced.

[0074] (13) According to the first embodiment, a weighted individual profile I(i, x)f(x) obtained by multiplying the individual profile I(i, x) by a weighting function f(x) is fitted with a fitting function to obtain a smoothed individual profile LOESS(I(i, x)f(x)).

[0075] According to this, by multiplying by the weighting function f(x) before fitting, the calculation load of fitting can be reduced.

[0076] (14) According to the first embodiment, the method of fitting the weighted individual profile I(i,x)f(x) with the fitting function is either the LOWESS method or the LOESS method.

[0077] This allows accurate fitting without the fitting function being restricted to a specific function form.

[0078] (15) According to the first embodiment, the peak positions of the smoothed individual profile LOESS(I(i,x)f(x)) are determined as the edge positions e1, e2, . . .

[0079] This allows the edge positions e1, e2, . . . to be determined accurately.

[0080] (16) According to the first embodiment, the average intensity profile ΣI(i,x) / n obtained by aggregating the intensity values ​​contained in the individual profile I(i,x) in the Y direction is smoothed to determine the average edge positions a1, a2, ...

[0081] According to this, by smoothing the average intensity profile ΣI(i,x) / n, the average edge positions a1, a2, . . . can be accurately determined.

[0082] (17) According to the first embodiment, the method for smoothing the average intensity profile ΣI(i,x) / n is either the LOWESS method or the LOESS method.

[0083] According to this, by using either the LOWESS method or the LOESS method, the average intensity profile ΣI(i,x) / n can be accurately smoothed.

[0084] In other respects, the first embodiment is similar to the comparative example.

[0085] 4. Using the weight function f(x) as the weight for local regression 4.1 Process for determining pattern edges from SEM images Fig. 19 is a flowchart showing details of the process of determining a pattern edge from an SEM image in the second embodiment. The configuration of the edge position determining device 100 in the second embodiment is the same as that described with reference to Fig. 1. The edge analysis process in the second embodiment is the same as that described with reference to Fig. 3. Fig. 19 corresponds to the subroutine of S2 in Fig. 3, and differs from the first embodiment in that it performs the process of S26a instead of S25 and S26 in Fig. 6.

[0086] In S26a, the processor 20 performs local regression on the individual profile I(i,x) using a weighting function f(x) as the weight of the local regression to determine edge positions e1, e2, ... The smoothed individual profile obtained by the weighted local regression in S26a is an example of a second intensity profile in the present disclosure. The local regression process includes a fitting process using a fitting function determined according to the individual profile I(i,x). Either the LOWESS method or the LOESS method can be used as the fitting method. The weighting function f(x) used when fitting the individual profile I(i,x) is the same regardless of the position in the Y direction.

[0087] 4.2 Effect (18) According to the second embodiment, the weighting function f(x) is used as a weight when fitting the individual profile I(i, x) with the fitting function.

[0088] This method can speed up calculations because it is not necessary to multiply the individual profile I(i,x) by the weighting function f(x).

[0089] In other respects, the second embodiment is similar to the first embodiment.

[0090] 5.Other The above description is intended to be illustrative rather than limiting. Thus, it will be apparent to one skilled in the art that modifications can be made to the disclosed embodiments without departing from the scope of the claims. It will also be apparent to one skilled in the art that the disclosed embodiments can be used in combination.

[0091] Terms used throughout this specification and claims should be construed as "open ended" unless expressly stated otherwise. For example, words such as "comprise," "have," "comprise," and "equip" should be construed as meaning "without excluding the presence of elements other than those listed." In addition, the modifier "a" should be construed as meaning "at least one" or "one or more." In addition, the term "at least one of A, B, and C" should be construed as "A," "B," "C," "A+B," "A+C," "B+C," or "A+B+C." Furthermore, it should be construed as including combinations of these with elements other than "A," "B," and "C."

Claims

1. determining an average edge position by summing intensity values ​​in the direction of line extension in the SEM image of the line and space; fitting a first intensity profile indicating a distribution of intensity values ​​along a direction perpendicular to the stretching direction at coordinates indicating each position in the stretching direction of the SEM image using a weighting function that maximizes a weight at the average edge position and a fitting function determined in accordance with the first intensity profile; determining an edge position in the coordinates from the second intensity profile obtained by fitting; Edge location method.

2. 2. The edge location determination method of claim 1, the weighting function is a function that decreases as the distance from the average edge position increases in a first section where the distance is equal to or less than a predetermined value that is smaller than the interval between the average edge position and another closest average edge position; Edge location method.

3. 3. The edge location determination method according to claim 2, further comprising: In the first section, the absolute value of the derivative of the weighting function is minimum at the average edge position. Edge location method.

4. 3. The edge location determination method according to claim 2, further comprising: the weighting function is symmetric about the average edge position in the first interval; Edge location method.

5. 3. The edge location determination method according to claim 2, further comprising: a value of the weighting function is equal to or less than half of the weight at the average edge position in a second section where the distance is greater than the predetermined value; Edge location method.

6. 3. The edge location determination method according to claim 2, further comprising: the value of the weighting function is less than or equal to half the weight at the average edge position when the distance is half the interval; Edge location method.

7. 3. The edge location determination method according to claim 2, further comprising: the value of the weighting function is a constant value regardless of the distance in a second section in which the distance is greater than the predetermined value; Edge location method.

8. 3. The edge location determination method according to claim 2, further comprising: the value of the weighting function is 0 in a second section in which the distance is greater than the predetermined value, regardless of the distance; Edge location method.

9. 2. The edge location determination method of claim 1, When the position in the direction perpendicular to the stretching direction is x, the average edge position is a, and b is a constant, the weighting function is (1-|(x-a) / b|) in the range where |(x-a) / b| is 1 or less. ３ ) ３ and is 0 in the interval where |(x−a) / b| is greater than 1. Edge location method.

10. 2. The edge location determination method of claim 1, When the position in the direction perpendicular to the stretching direction is x, the average edge position is a, and b is a constant, the weighting function is exp(-((x-a) / b) ２ ) Edge location method.

11. 2. The edge location determination method of claim 1, When the position in the direction perpendicular to the stretching direction is x, the average edge position is a, and b is a constant, the weighting function is 1 / (1+((x-a) / b) ２ ) Edge location method.

12. 2. The edge location determination method of claim 1, fitting the first intensity profile at a first coordinate indicating a first position in the stretching direction and the first intensity profile at a second coordinate indicating a second position in the stretching direction using the same weighting function; Edge location method.

13. 2. The edge location determination method of claim 1, obtaining the second intensity profile by fitting a third intensity profile obtained by multiplying the first intensity profile by the weighting function with the fitting function; Edge location method.

14. 2. The edge location determination method of claim 1, The method of fitting with the fitting function is either the LOWESS method or the LOESS method. Edge location method.

15. 2. The edge location determination method of claim 1, determining a peak position of the second intensity profile as the edge position; Edge location method.

16. 2. The edge location determination method of claim 1, determining the average edge position by smoothing a fourth intensity profile obtained by summing the intensity values ​​included in the first intensity profile in the stretching direction; Edge location method.

17. 17. The edge location method of claim 16, further comprising: the fourth method for smoothing the intensity profile is either a LOWESS method or a LOESS method; Edge location method.

18. 2. The edge location determination method of claim 1, using the weighting function as a weight when fitting the first intensity profile with the fitting function; Edge location method.

19. a communication controller for acquiring a line and space SEM image; 1. A processor, comprising: aggregating intensity values ​​in the direction of line extension in the SEM image to determine an average edge position; fitting a first intensity profile along a direction perpendicular to the extension direction at coordinates indicating each position in the extension direction of the SEM image using a weighting function that maximizes a weight at the average edge position and a fitting function that is determined according to the first intensity profile; The edge position in the coordinate system is determined from the second intensity profile obtained by fitting. the processor; An edge location determination device comprising:

20. determining an average edge position by summing intensity values ​​in the direction of line extension in the SEM image of the line and space; fitting a first intensity profile along a direction perpendicular to the extension direction at coordinates indicating each position in the extension direction of the SEM image using a weighting function that maximizes a weight at the average edge position and a fitting function that is determined according to the first intensity profile; determining an edge position at the coordinates from the second intensity profile obtained by fitting; performing a PSD analysis on the edge positions at a plurality of positions in the extension direction; Edge analysis methods.

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