Assurance device, assurance method, and assurance program

Abstract

To provide an assurance device, an assurance method, and an assurance program capable of properly assuring the shape of a pattern of a photomask.SOLUTION: According to one embodiment, an assurance device includes a processing unit that acquires or calculates a second moment of a pattern of a photomask or a value that varies according to the second moment, acquires or calculates the second moment or the value of the pattern included in the design data of the photomask, and acquires or calculates the second moment or the value of the pattern included in the image data of the photomask. The device further includes a comparison unit that calculates and outputs the difference between the second moment or the value of the pattern included in the design data and the second moment or the value of the pattern included in the image data.SELECTED DRAWING: Figure 8

Description

[Technical Field]

[0001] FIELD Embodiments of the present invention relate to a guarantee device, a guarantee method, and a guarantee program. [Background technology]

[0002] Inverse lithography technology (ILT) has been attracting attention as a way to miniaturize semiconductor device patterns. However, when photomasks for semiconductor device lithography are designed using ILT, the shape of the photomask pattern generally becomes complex. As a result, it becomes difficult to guarantee the shape of the photomask pattern. [Prior art documents] [Patent documents]

[0003] [Patent Document 1] Japanese Patent Application Laid-Open No. 2008-181124 [Patent Document 2] Japanese Patent Application Laid-Open No. 2004-013095 Summary of the Invention [Problem to be solved by the invention]

[0004] A guarantee device, a guarantee method, and a guarantee program are provided that can properly guarantee the shape of a photomask pattern. [Means for solving the problem]

[0005] According to one embodiment, the assurance device includes a processing unit that acquires or calculates a second moment of a pattern of a photomask or a value that varies depending on the second moment, the processing unit acquiring or calculating the second moment or the value of the pattern included in design data of the photomask and acquiring or calculating the second moment or the value of the pattern included in image data of the photomask. The device further includes a comparison unit that calculates and outputs the difference between the second moment or the value of the pattern included in the design data and the second moment or the value of the pattern included in the image data. [Brief explanation of the drawings]

[0006] [Figure 1] 2A to 2C are cross-sectional views illustrating a method for manufacturing the photomask of the first embodiment. [Figure 2] 2A to 2C are cross-sectional views illustrating a method for manufacturing the semiconductor device according to the first embodiment. [Figure 3] 1 is a plan view showing the structure of a photomask and a semiconductor device according to a first embodiment. [Figure 4] 4A to 4C are plan views showing examples of SEM images of mask patterns of a first comparative example, a second comparative example, and the first embodiment. [Figure 5] FIG. 2 is a plan view showing an SEM image of a mask pattern of the first embodiment and the shape of the mask pattern extracted from this SEM image. [Figure 6] FIG. 2 is a plan view for explaining the shape of a mask pattern in the first embodiment. [Figure 7] 4 is a graph for explaining the n-th moment of the first embodiment. [Figure 8] 2 is a block diagram showing the hardware configuration and the functional configuration of the guarantee device of the first embodiment. FIG. [Figure 9] FIG. 10 is a plan view showing the shape of a mask pattern according to a second embodiment. [Figure 10] FIG. 10 is a plan view showing the shape of a mask pattern according to a third embodiment. [Figure 11]FIG. 11 is a plan view showing the shape of a mask pattern in a modified example of the third embodiment. [Figure 12] FIG. 10 is a plan view for explaining design data and correction data of a photomask according to a fourth embodiment. [Figure 13] FIG. 13 is a plan view for explaining an example of a display method according to the fifth embodiment. [Figure 14] FIG. 13 is a plan view for explaining another example of the display method according to the fifth embodiment. DETAILED DESCRIPTION OF THE INVENTION

[0007] DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS Hereinafter, embodiments of the present invention will be described with reference to the drawings. In Figures 1 to 14, the same components are denoted by the same reference numerals, and duplicated descriptions will be omitted.

[0008] (First embodiment) FIG. 1 is a cross-sectional view showing a method for manufacturing a photomask (reticle) 1 according to the first embodiment.

[0009] First, a substrate (mask blank) 11 for a photomask 1 is prepared, a light-shielding layer 12 is formed on the substrate 11, and a resist layer 13 is formed on the light-shielding layer 12 (FIG. 1(a)). Next, an electron beam B for pattern writing is irradiated onto the resist layer 13 (FIG. 1(a)).

[0010] The substrate 11 is a transparent substrate such as a quartz substrate or a glass substrate. The substrate 11 has the function of transmitting light incident on the photomask 1. The light-shielding layer 12 is an opaque layer such as a chromium (Cr) layer. The light-shielding layer 12 has the function of blocking light incident on the photomask 1. The resist layer 13 may be either positive or negative.

[0011] 1(a) shows the X, Y, and Z directions, which intersect with each other. In FIG. 1(a), the X and Y directions are parallel to the surface of the substrate 11 and perpendicular to each other, and the Z direction is perpendicular to the surface of the substrate 11. In this specification, the +Z direction is treated as the upward direction, and the −Z direction is treated as the downward direction. The −Z direction may or may not coincide with the direction of gravity.

[0012] Next, the resist layer 13 is developed (FIG. 1(b)). As a result, a plurality of resist patterns 13a are formed from the resist layer 13. Each resist pattern 13a has, for example, a circular shape in a plan view, and is used to form a mask pattern for a memory hole of a three-dimensional semiconductor memory, as will be described later.

[0013] Next, the light-shielding layer 12 is processed by RIE (Reactive Ion Etching) using the resist layer 13 (FIG. 1(c)). As a result, the resist pattern 13a is transferred to the light-shielding layer 12, and a plurality of light-shielding patterns 12a are formed from the light-shielding layer 12. Each light-shielding pattern 12a has, for example, a circular shape in a plan view, and is used as a mask pattern for forming memory holes in a three-dimensional semiconductor memory. Hereinafter, the light-shielding pattern 12a is also referred to as a "mask pattern 12a." The resist layer 13 is removed after the light-shielding layer 12 is processed.

[0014] In this way, the photomask 1 of this embodiment is manufactured. Thereafter, the mask pattern 12a of the photomask 1 is imaged by a SEM (Scanning Electron Microscope) 101 to obtain image data of the SEM image of the photomask 1 (FIG. 1(d)). How to use this image data will be described later.

[0015] 2A to 2C are cross-sectional views showing a method for manufacturing the semiconductor device 2 of the first embodiment. The semiconductor device 2 is, for example, a three-dimensional semiconductor memory.

[0016] First, a substrate (wafer) 21 for the semiconductor device 2 is prepared, a process layer 22 is formed on the substrate 21, and a resist layer 23 is formed on the process layer 22 (FIG. 2(a)). The substrate 21 is, for example, a semiconductor substrate such as a silicon (Si) substrate. The process layer 22 is, for example, a laminated film including multiple sacrificial layers (e.g., silicon nitride films) and multiple insulating films (e.g., silicon oxide films) alternately. The resist layer 23 may be either positive or negative. In FIG. 2(a), the X and Y directions are parallel to the surface of the substrate 21 and perpendicular to each other, and the Z direction is perpendicular to the surface of the substrate 21.

[0017] Next, the resist layer 23 is exposed to light (FIG. 2(b)). In FIG. 2(b), the above-mentioned photomask 1 is irradiated with light L, and the resist layer 23 is exposed to the light L that has passed through the photomask 1. The light L is, for example, laser light such as argon fluoride laser light.

[0018] Next, the resist layer 23 is developed (FIG. 2(c)). As a result, a plurality of holes H1 corresponding to the mask pattern 12a are formed in the resist layer 23. The remaining portion 23a of the resist layer 23 is the portion of the resist layer 23 other than the holes H1. Each hole H1 has, for example, a circular shape in a plan view, and is used to form memory holes of a three-dimensional semiconductor memory, as will be described later.

[0019] Next, the layer to be processed 22 is processed by RIE using the resist layer 23 (FIG. 2(d)). As a result, the hole H1 is transferred to the layer to be processed 22, and multiple holes H2 are formed in the layer to be processed 22. The remaining portion 22a of the layer to be processed 22 is the portion of the layer to be processed 22 other than the holes H2. Each hole H2 has, for example, a circular shape in a plan view, and is used as a memory hole of a three-dimensional semiconductor memory. Hereinafter, the hole H2 will also be referred to as a "memory hole H2." The resist layer 23 is removed after the layer to be processed 22 is processed.

[0020] In this manner, the semiconductor device 2 of this embodiment is manufactured. The semiconductor device 2 may be a device other than a three-dimensional semiconductor memory, for example, a logic circuit device. Furthermore, the photomask 2 of this embodiment may be used to manufacture a device other than the semiconductor device 2.

[0021] FIG. 3 is a plan view showing the structures of the photomask 1 and the semiconductor device 2 of the first embodiment.

[0022] Fig. 3(a) shows the layout of multiple mask patterns 12a included in the photomask 1. Each mask pattern 12a shown in Fig. 3(a) has a circular shape in a plan view. Fig. 1(c) and Fig. 1(d) show XZ cross sections along line A-A' shown in Fig. 3(a).

[0023] Fig. 3(b) shows the layout of multiple memory holes H2 included in the semiconductor device 2. Each memory hole H2 shown in Fig. 3(b) has a circular shape in a plan view. Fig. 2(d) shows an XZ cross section along line BB' shown in Fig. 3(b).

[0024] Note that the planar shape of the memory hole H2 may not match the planar shape of the mask pattern 12a. For example, when the planar shape of the memory hole H2 is circular, the planar shape of the mask pattern 12a may be a shape other than circular (for example, a square or a shape close to a square). Furthermore, the planar shape of the mask pattern 12a may be a shape designed in consideration of OPC (Optical Proximity Correction).

[0025] FIG. 4 is a plan view showing examples of SEM images of the mask pattern 12a of the first comparative example, the second comparative example, and the first embodiment.

[0026] Fig. 4(a) shows an SEM image of a mask pattern 12a when the photomask 1 of the first comparative example is imaged by an SEM 101. The thick lines shown in Fig. 4(a) represent the edges of the mask pattern 12a. The mask pattern 12a shown in Fig. 4(a) has a planar shape that is close to a square.

[0027] 4(a) further shows a region R called ROI (Region of Interest: measurement target region). In FIG. 4(a), the shape of the ROI is rectangular (oblong), and the ROI overlaps the left edge and the right edge of the mask pattern 12a.

[0028] Mask assurance (pattern assurance) in this comparative example is performed using ROI. Mask assurance refers to determining whether the shape of mask pattern 12a of photomask 1 meets predetermined specifications. For example, if it is determined that the shape of mask pattern 12a to be measured meets predetermined specifications, photomask 1 is determined to be a non-defective product, and photomask 1 is eligible for shipment. On the other hand, if it is determined that the shape of mask pattern 12a to be measured does not meet predetermined specifications, photomask 1 is determined to be a defective product, and photomask 1 is excluded from shipment.

[0029] In the mask assurance of this comparative example, an ROI is set on an SEM image, the positions of the left and right edges of the mask pattern 12a are extracted within the ROI, and the distance between the left and right edges is measured as the dimensions of the mask pattern 12a. In this case, the distance between the left and right edges is measured at multiple locations within the ROI, the average value of the distances at these locations is calculated, and it is determined whether the average value meets the predetermined specifications. Using the average value to perform mask assurance makes it possible to reduce noise in distance measurements. Since the larger the ROI, the more noise can be reduced, it is desirable to set the ROI as large as possible.

[0030] As semiconductor devices become smaller, the mask pattern 12a also becomes smaller. The size (dimension) of the mask pattern 12a may become smaller than 1 μm, for example, to several tens of nanometers. It is preferable to perform the inspection of such a mask pattern 12a using an electron microscope rather than an optical microscope. Therefore, the mask inspection in this comparative example is performed using an SEM image captured by the SEM 101.

[0031] Fig. 4(b) shows an SEM image of the mask pattern 12a when the photomask 1 of the second comparative example is imaged by the SEM 101. The mask pattern 12a shown in Fig. 4(b) has a planar shape close to a parallelogram. This indicates that the mask pattern 12a has become finer from the first comparative example to the second comparative example, and the shape of the mask pattern 12a has become more complex.

[0032] FIG. 4(b) further shows three regions R corresponding to the ROI. Generally, an ROI can only be set between two straight, parallel edges. Therefore, it is more difficult to set an ROI in this comparative example than in the first comparative example. As a result, the ROI in the first comparative example is set to a simple shape using one region R, whereas the ROI in this comparative example is set to a complex shape using three regions R.

[0033] FIG. 4(c) shows an SEM image of the mask pattern 12a when the photomask 1 of the first embodiment is imaged by the SEM 101. The photomask 1 of this embodiment has the mask pattern 12a designed by ILT. In ILT, the shape of the mask pattern 12a for processing the pattern of the resist layer 23 (the pattern of the holes H1) into a desired shape is calculated by solving an inverse problem. ILT has the advantage that it is suitable for miniaturizing the mask pattern 12a. However, when the photomask 1 is designed by ILT, the shape of the mask pattern 12a generally becomes complex.

[0034] The mask pattern 12a shown in FIG. 4(c) has a complex shape that does not have any part that includes two straight, parallel edges. Therefore, in this embodiment, it is nearly impossible to set an ROI. Therefore, the mask qualification in this embodiment is performed using a method other than ROI, as will be described later. The mask qualification method in this embodiment is suitable for a photomask 1 designed by ILT, but can also be applied to other photomasks 1.

[0035] Next, a method for guaranteeing the shape of the mask pattern 12a of the photomask 1 of this embodiment will be described in detail. In this description, reference will be made as appropriate to Figures 5 to 8. The guarantee method of this embodiment is executed, for example, by a guarantee device 201 shown in Figure 8. Details of the guarantee device 201 will be described later.

[0036] The assurance method of this embodiment is performed using design data and image data of the photomask 1. The design data is prepared before manufacturing the photomask 1 and is used when manufacturing the photomask 1 in the steps shown in FIGS. 1(a) to 1(c). On the other hand, the image data is acquired by imaging the photomask 1 with the SEM 101 in the step shown in FIG. 1(d). In this way, image data of the SEM image is acquired.

[0037] FIG. 5 is a plan view showing an SEM image of the mask pattern 12a of the first embodiment and the shape of the mask pattern 12a extracted from this SEM image.

[0038] 5(a), like FIG. 4(c), shows an SEM image of the photomask 1 of this embodiment obtained by capturing the image of the photomask 1 using the SEM 101. Since the photomask 1 of this embodiment was designed using ILT, the mask pattern 12a included in this SEM image has a complex shape. The symbol E in FIG. 5(a) indicates the contour (edge) of the mask pattern 12a.

[0039] The image data of the SEM image includes image data of the mask pattern 12a and image data of the portion of the photomask 1 near the mask pattern 12a. In this embodiment, the contour E of the mask pattern 12a is extracted from the image data of the SEM image. This makes it possible to extract the shape of the mask pattern 12a from the SEM image. Figure 5(b) shows the shape of the mask pattern 12a extracted from the SEM image.

[0040] Similarly, in this embodiment, the contour E of the mask pattern 12a is extracted from the design data of the photomask 1. For example, the contour E of the mask pattern 12a is extracted from design data relating to the shape of the mask pattern 12a or the shape of a portion of the photomask 1 near the mask pattern 12a. This makes it possible to extract the shape of the mask pattern 12a from the design data relating to the shape of the photomask 1.

[0041] The assurance method of this embodiment calculates the second moment of the mask pattern 12a included in the design data of the photomask 1 and the second moment of the mask pattern 12a included in the image data of the photomask 1. In this case, the former second moment (hereinafter also referred to as the "second moment of the design data") is calculated using the contour E extracted from the design data, and the latter second moment (hereinafter also referred to as the "second moment of the image data") is calculated using the contour E extracted from the image data.

[0042] The assurance method of this embodiment performs mask assurance by comparing the second moment of the design data with the second moment of the image data. According to this embodiment, by using the second moment instead of ROI, it becomes possible to ensure the shape of the mask pattern 12a of the photomask 1. For example, even if the shape of the mask pattern 12a is complex, it becomes possible to appropriately ensure the shape of the mask pattern 12a.

[0043] A method for calculating the second moment of image data will be specifically described below. In this embodiment, the second moment of design data is also calculated by the following method.

[0044] Fig. 6 is a plan view for explaining the shape of the mask pattern 12a of the first embodiment. Fig. 6(a) shows the shape of the mask pattern 12a extracted from an SEM image, similar to Fig. 5(b). Fig. 6(a) also shows an area D occupied by the mask pattern 12a and a closed curve C surrounding the area D. The closed curve C corresponds to the above-mentioned contour E. The shape of the area D corresponds to the shape of the mask pattern 12a in plan view (hereinafter also referred to as the "mask shape"). Fig. 6(b) will be described later.

[0045] The mask function m(k x ,k y ) is expressed by equation (1).

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[0046] In the double integral (Fourier transform) of equation (1), x represents the X coordinate shown in FIG. 6(a), y represents the Y coordinate shown in FIG. 6(a), and D represents the area D shown in FIG. 6(a). x and k y represents the wave number, i represents the imaginary unit, and e represents Napier's constant. The mask function m(k x ,k y ) corresponds to the distribution function of diffracted light obtained by irradiating the mask pattern 12a with light. Therefore, the mask function m(k x ,k y ) represents the shape of the image formed on the resist layer 23 by the exposure shown in FIG. 2(b).

[0047] By expanding the exponential function in equation (1) into a series, concretely expressing the second-order terms of the series, and omitting the cross-terms of x and y, the mask function m(k x ,k y ) is transformed into equation (2).

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[0048] where S represents the area of ​​the region D and is given by equation (3). cg and y cg are the X and Y coordinates of the center of gravity of region D, respectively, and are given by equations (4) and (5). x and σ y represent the second moments in the X and Y directions around the center of gravity of region D, respectively, and are given by equations (6) and (7).

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[0049] The above "S" and "x" cg and y cg " "σ x and σ y " correspond to the 0th moment, the 1st moment, and the 2nd moment of the area D (mask pattern 12a), respectively. cg and y cg are also called the first power moment of x and the first power moment of y, respectively, and σ x and σ y are also called the x-squared and y-squared moments, respectively.

[0050] The exponential part of equation (2) is exp{-i(k x x cg +k y y cg )}. This exponent part gives the phase on the Fourier plane and represents the position on the real plane. If the phase on the Fourier plane changes, the position on the real plane will change. As shown in equation (2), the mask function m(k x,k y ) is the exponent part, S, σ x , and σ y In this embodiment, S and x cg , y cg , σ x , and σ y Mask assurance is performed using

[0051] Here, according to Green's theorem, the double integral can be replaced with a line integral (circumference integral) as shown in equation (8).

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[0052] However, P and Q are C 1 6(a) and C represents the closed curve C shown in FIG.

[0053] According to Green's theorem in equation (8), equations (3) to (7) can be transformed into equations (9) to (13), respectively.

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[0054] In this embodiment, the contour E of the mask pattern 12a is extracted from the image data of the mask pattern 12a. This makes it possible to identify the shape of the closed curve C, and as a result, it becomes possible to calculate the contour integrals of the equations (9) to (13) using the identified closed curve C. In this embodiment, S and x calculated by the equations (9) to (13) are cg , ycg , σ x , and σ y Mask assurance is performed using

[0055] In this embodiment, the shape of the extracted contour E is approximated by a polygon having three or more vertices, as shown in FIG. 6(b). In FIG. 6(b), each vertex of the polygon is located on the contour E, and the vertices of the polygon are connected by line segments. According to this embodiment, the shape of the closed curve C is regarded as this polygon, and the contour integrals of equations (9) to (13) are calculated to obtain S, x cg , y cg , σ x , and σ y In this case, by applying curved interpolation such as linear interpolation or Bezier interpolation between the vertices of the polygon, it becomes possible to calculate the contour integral with high accuracy.

[0056] The mask assurance in this embodiment is based on the second moment "σ x " "σ y The second moment is calculated using the above formula (12) and formula (13). However, formula (12) and formula (13) do not use the area "S" and the barycentric coordinate "x cg " "y cg Therefore, when calculating the second moment, the area and the center of gravity coordinates are also calculated using equations (9), (10), and (11).

[0057] In this embodiment, mask assurance is performed using second moments calculated from image data and second moments calculated from design data. The method for calculating second moments from design data is the same as the method for calculating second moments from image data. Therefore, equations (9) to (13) are also used when calculating second moments from design data. In this case, the shape of the closed curve C is identified by extracting the contour E from the design data.

[0058] In this embodiment, the second moment of the design data is compared with the second moment of the image data, and the mask quality is guaranteed using the comparison result of these second moments. For example, the second moment σ of the design data is x and the second moment of the image data σ x The absolute value of the difference between the two is smaller than the threshold, and the second moment σ of the design data is y and the second moment of the image data σ y If the absolute value of the difference between the design data and the second moment σ is smaller than a threshold value, the photomask 1 may be determined to be a non-defective product. x and the second moment of the image data σ x The absolute value of the difference between the two is greater than the threshold, or the second moment σ of the design data is y and the second moment of the image data σ y If the absolute value of the difference between the second-order moments is greater than a threshold, the photomask 1 may be determined to be defective. In this case, the comparison of the second-order moments and the determination of whether the photomask is good or bad may both be performed by the device, or the comparison of the second-order moments may be performed by the device and the determination of whether the photomask is good or bad may be performed by a human.

[0059] As described above, in this embodiment, mask assurance is performed using the second moment instead of ROI. This makes it possible to perform mask assurance even when dealing with a mask pattern 12a for which it is difficult to set an ROI, such as a mask pattern 12a designed by ILT. Note that the mask assurance in this embodiment may be performed using a value that changes depending on the second moment instead of the second moment. An example of such mask assurance will be described later.

[0060] In the following, to facilitate understanding of the nth moment (n is an integer equal to or greater than 0) of the mask pattern 12a of this embodiment, the nth moment of a general function f(x) will be described. Fig. 7 is a graph for explaining the nth moment of the first embodiment.

[0061] The n-th moment of the function f(x) is expressed by equation (14).

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[0062] Substituting 0 for n in equation (14) gives the 0th moment of f(x), as shown in equation (15).

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[0063] In equation (15), the zeroth moment of f(x) is the value s, which represents the area of ​​the drawing between the x-axis and the curve f(x) in the interval [0, t].

[0064] Substituting 1 for n in equation (14) gives the first moment of f(x), as shown in equation (16).

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[0065] In equation (16), the first moment of f(x) is the function of the value s and the value x G The value x G represents the x-coordinate of the center of gravity of the above figure.

[0066] Substituting 2 for n in equation (14) gives the second moment of f(x), as shown in equation (17).

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[0067] In equation (17), the second moment of f(x) is the value I G The value I G represents the extent of the spread of the figure in the x direction.

[0068] FIG. 7(a) shows a figure (rectangle) whose length in the y direction is a and whose length in the x direction is b. FIG. 7(a) also shows the x coordinate of the center of gravity of this figure, "x G In Figure 7(a), the second moment I of this figure is GHowever, according to equation (17), ab 3 This is calculated as / 12.

[0069] Figure 7(b) shows a figure (rectangle) whose length in the x direction is a and whose length in the y direction is b. Figure 7(b) also shows the x coordinate of the center of gravity of this figure, "x G In Figure 7(b), the second moment I of this figure is G However, according to equation (17), ba 3 This is calculated as / 12.

[0070] In Figure 7(a) and Figure 7(b), a is longer than b (a>b). Therefore, the second moment I of the figure shown in Figure 7(b) is G (=ba 3 / 12) is the second moment I of the figure shown in Figure 7(a). G (=ab 3 / 12), which corresponds to the fact that the shape shown in Figure 7(a) has a small spread in the x direction, while the shape shown in Figure 7(b) has a large spread in the x direction.

[0071] FIG. 8 is a block diagram showing the hardware configuration and the functional configuration of the assurance device 201 of the first embodiment.

[0072] Fig. 8(a) shows the hardware configuration of the assurance device 201 of this embodiment. As shown in Fig. 8(a), the assurance device 201 includes an information processing unit 211, a storage unit 212, a display unit 213, an input unit 214, and a communication unit 215. The assurance device 201 is, for example, a computer such as a PC (Personal Computer).

[0073] The information processing unit 211 includes, for example, a CPU (Central Processing Unit), etc. The storage unit 212 includes, for example, a ROM (Read Only Memory), a RAM (Random Access Memory), a HDD (Hard Disk Drive), a memory drive, a memory interface, etc. The memory drive and memory interface are used to insert a recording medium such as a semiconductor memory into the assurance device 201.

[0074] The display unit 213 includes, for example, a liquid crystal display and an indicator. The input unit 214 includes, for example, a keyboard and a mouse. The communication unit 215 includes, for example, a communication interface. The communication interface is used, for example, to connect the assurance device 201 to a communication network via a wired or wireless connection.

[0075] In this embodiment, a guarantee program for mask guarantee is stored, for example, in the ROM or HDD of the storage unit 212. The functional configuration shown in Fig. 8(b), which will be described later, is realized, for example, by executing this guarantee program by the CPU of the information processing unit 211.

[0076] When installing the guarantee program in the guarantee device 201, a computer-readable recording medium on which the guarantee program is recorded may be prepared, and the guarantee program may be installed from this recording medium in the guarantee device 201. On the other hand, the guarantee program may be installed in the guarantee device 201 by downloading it from a network.

[0077] Fig. 8(b) shows the functional configuration of the assurance device 201 of this embodiment. As shown in Fig. 8(b), the assurance device 201 includes an acquisition unit 221, an extraction unit 222, a calculation unit 223, a comparison unit 224, and an output unit 225. The acquisition unit 221, the extraction unit 222, and the calculation unit 223 are examples of processing units.

[0078] The acquisition unit 221 acquires design data and image data of the photomask 1. For example, before the processing of the assurance method of this embodiment is started, a user of the assurance device 201 saves the design data and image data in the HDD of the storage unit 212, and when the processing of the assurance method of this embodiment is started, the acquisition unit 221 acquires the design data and image data from the HDD of the storage unit 212.

[0079] At least one of the design data and image data may be automatically stored in the HDD of the storage unit 212. For example, the image data may be automatically transmitted from the SEM 101 to the assurance device 201 and stored in the HDD of the storage unit 212. Furthermore, the acquisition unit 221 may acquire at least one of the design data and image data from a device outside the assurance device 201 when processing of the assurance method of this embodiment is started. For example, the design data may be acquired from a server device in which the design data is stored. Furthermore, the image data may be acquired from the SEM 101 that acquired the image data by imaging.

[0080] The extraction unit 222 extracts the contour E of the mask pattern 12a from the design data, and also extracts the contour E of the mask pattern 12a from the image data. The contour E extracted from the design data and the image data is used to identify the closed curve C for calculating the above-mentioned contour integral.

[0081] The calculation unit 223 calculates the area S and the center of gravity x of the mask pattern 12a included in the design data based on the design data. cg , y cg , and the second moment σ x , σ y This calculation is performed by calculating the contour integrals of the equations (9) to (13) using the contour E extracted from the design data. The calculation unit 223 further calculates the area S and the barycentric coordinate x of the mask pattern 12a included in the image data based on the image data. cg , y cg , and the second moment σ x , σ yThis calculation is performed by calculating the contour integrals of equations (9) to (13) using the contour E extracted from the image data. The contour integrals for the design data and image data may be calculated using, for example, the polygons described above.

[0082] The comparison unit 224 compares the second moment of the design data with the second moment of the image data. For example, the comparison unit 224 compares the second moment σ of the design data with the second moment σ of the image data. x and the second moment of the image data σ x and the second moment σ of the design data y and the second moment of the image data σ y Compare with.

[0083] The output unit 225 outputs information related to the design data and / or image data. For example, the output unit 225 may output the information by storing the comparison result between the second moment of the design data and the second moment of the image data in a storage device (e.g., HDD of the storage unit 212). The output unit 225 may also output the information by displaying the shape of the contour E extracted from the design data or the shape of the contour E extracted from the image data on a display device (e.g., liquid crystal display of the display unit 213). The storage device and display device may be provided outside the assurance device 201.

[0084] The comparison unit 224 of this embodiment uses the second moment σ of the design data. x and the second moment of the image data σ x (hereinafter referred to as the "first difference") and the second moment σ of the design data y and the second moment of the image data σ yThe comparison unit 224 of this embodiment outputs the calculation results of the first difference and the second difference and stores them in the HDD of the storage unit 212. By checking these calculation results, the user can determine whether the photomask 1 is a good product or a defective product. For example, if the absolute value of the first difference is smaller than a threshold value and the absolute value of the second difference is smaller than a threshold value, the photomask 1 may be determined to be a good product. On the other hand, if the absolute value of the first difference is larger than the threshold value or the absolute value of the second difference is larger than the threshold value, the photomask 1 may be determined to be a defective product.

[0085] The comparison unit 224 may compare the absolute value of the first difference with a threshold value and also compare the absolute value of the second difference with a threshold value, and the output unit 225 may store the comparison results of the absolute value of the first difference with the threshold value and the comparison results of the absolute value of the second difference with the threshold value. The comparison unit 224 may also determine whether the photomask 1 is a good product or a defective product based on these comparison results, and the output unit 225 may store the determination results. In these cases, the user can more easily determine whether the photomask 1 is a good product or a defective product.

[0086] The threshold value may be determined by calculating the change in shape that the mask shape causes to the pattern on the substrate (wafer) 21 by lithography simulation, so that the change in shape of the pattern on the substrate (wafer) 21 falls within a predetermined tolerance, or may be determined so that the value obtained by dividing the absolute value of the difference by the second moment of the design data falls within a few percent. The threshold value may also be determined by a conventional mask assurance method.

[0087] Furthermore, the acquisition unit 221 acquires the second moment σ of the design data instead of the design data. x , σ y For example, the second moment σ may be obtained from the design data by a device outside the assurance device 201. x , σ y Calculate the second moment σ x , σ ymay be stored in the HDD of the storage unit 212. In this case, the acquisition unit 221 may store the second moment σ of the design data. x , σ y is acquired from the HDD of the storage unit 212, and the comparison unit 224 compares this second moment σ x , σ y is used for comparison.

[0088] Similarly, the acquisition unit 221 acquires the second moment σ of the image data instead of the image data. x , σ y For example, a device outside the guarantee device 201 may acquire the second moment σ from the image data. x , σ y Calculate the second moment σ x , σ y may be stored in the HDD of the storage unit 212. In this case, the acquisition unit 221 may store the second moment σ of the image data. x , σ y is acquired from the HDD of the storage unit 212, and the comparison unit 224 compares this second moment σ x , σ y is used for comparison.

[0089] As described above, in this embodiment, mask assurance is performed by comparing the second moment of the design data with the second moment of the image data. Therefore, according to this embodiment, it is possible to appropriately guarantee the shape of the mask pattern 12a of the photomask 1. For example, even if the shape of the mask pattern 12a is complex, it is possible to appropriately guarantee the mask.

[0090] (Second embodiment) FIG. 9 is a plan view showing the shape of a mask pattern 12a of the second embodiment.

[0091] Fig. 9 shows the shape of the mask pattern 12a extracted from the SEM image, similar to Fig. 6(a). Fig. 9 also shows the area D occupied by the mask pattern 12a and the closed curve C (outline E) surrounding the area D, similar to Fig. 6(a).

[0092] In this embodiment, as shown in Fig. 9, a region D' corresponding to the region D is defined. The region D' is defined by the area S of the region D and the coordinates of the center of gravity x cg , y cg It is a rectangular region (rectangular region) having the same area and center of gravity coordinates as those of the region D'. Figure 9 shows the width W, which is the dimension in the X direction of the region D', and the height H, which is the dimension in the Y direction of the region D'. The width W and height H are defined by equations (18) and (19), respectively.

number

number

[0093] However, the coefficient γ in the equations (18) and (19) is defined by the equation (20).

number

[0094] Calculating W·H using equations (18) and (19), W·H=γ 2 σ x σ y If we substitute equation (20) into this equation, we get W·H=S. This means that the area W·H of region D' is equal to the area S of region D.

[0095] The assurance method of this embodiment defines a region R' for the mask pattern 12a included in the design data of the photomask 1, and calculates the width W and height H of this region R'. The assurance method of this embodiment further defines a region R' for the mask pattern 12a included in the image data of the photomask 1, and calculates the width W and height H of this region R'. Hereinafter, the former region R', width W, and height H will also be referred to as the "region R', width W, and height H of the design data," and the latter region R', width W, and height H will also be referred to as the "region R', width W, and height H of the image data." The region R', width W, and height H of the design data are calculated based on the S, x cg , y cg , σx , and σ y The area R', width W, and height H of the image data are defined and calculated using the equations (18) to (20). cg , y cg , σ x , and σ y and are defined and calculated using equations (18) to (20). cg , y cg , σ x , and σ y can be calculated by the guarantee method of the first embodiment.

[0096] The assurance method of this embodiment performs mask assurance by comparing the width W and height H of the design data with the width W and height H of the image data. According to this embodiment, by using the width W and height H instead of the ROI, it is possible to ensure the shape of the mask pattern 12a of the photomask 1. For example, even if the shape of the mask pattern 12a is complex, it is possible to appropriately ensure the shape of the mask pattern 12a. Furthermore, according to this embodiment, the second moment σ, which is generally unfamiliar to users, is used. x , σ y Instead of the above, by using the width W and height H, which are generally familiar to users, it is possible to perform mask assurance that is easy for users to understand. The width W and height H are expressed by the second moment σ x , σ y This is an example of a value that changes depending on

[0097] The guarantee method of this embodiment is executed by, for example, a guarantee device 201 shown in Fig. 8. In this case, a calculation unit 223 calculates the width W and height H of the design data and the width W and height H of the image data, and a comparison unit 224 compares the width W and height H of the design data with the width W and height H of the image data. The comparison unit 224 calculates the second moment σ of the design data as the first difference. x and the second moment of the image data σ x Instead of the difference between the width W of the design data and the width W of the image data, the difference between the width W of the design data and the width W of the image data is calculated, and the second moment σ of the design data is used as the second difference. yand the second moment of the image data σ y Instead of the difference between the height H of the design data and the height H of the image data, the difference between the height H of the design data and the height H of the image data is calculated. The use of the first difference and the second difference in this embodiment is similar to the use of the first difference and the second difference in the first embodiment.

[0098] Alternatively, the acquiring unit 221 may acquire the width W and height H of the design data instead of the design data. In this case, the comparing unit 224 uses the width W and height H for comparison. Similarly, the acquiring unit 221 may acquire the width W and height H of the image data instead of the image data. In this case, the comparing unit 224 uses the width W and height H for comparison.

[0099] As described above, in this embodiment, mask assurance is performed by comparing the width W and height H of the design data with the width W and height H of the image data. Therefore, according to this embodiment, similar to the first embodiment, it is possible to appropriately guarantee the shape of the mask pattern 12a of the photomask 1.

[0100] (Third embodiment) FIG. 10 is a plan view showing the shape of a mask pattern 12a according to the third embodiment.

[0101] FIG. 10(a) shows the shapes of multiple mask patterns 12a extracted from an SEM image. FIG. 10(b) shows a unit U including eight mask patterns 12a aligned roughly along the Y direction. The eight mask patterns 12a in the unit U shown in FIG. 10(b) have different planar shapes. On the other hand, FIG. 10(a) shows a structure in which multiple units U having roughly the same planar shape are periodically arranged along the X direction. When the semiconductor device 2 has a periodic structure, the photomask 1 generally includes multiple mask patterns 12a arranged periodically.

[0102] In this embodiment, the multiple mask patterns 12a shown in FIG. 10(a) are classified into eight groups G1 to G8 based on the planar shape of each mask pattern 12a. Each of the groups G1 to G8 includes two or more mask patterns 12a that are considered to have the same planar shape. The eight mask patterns 12a in each unit U belong to groups G1 to G8, respectively, as shown in FIG. 10(b). In FIG. 10(a), two or more mask patterns 12a belonging to the same group are adjacent to each other in the X direction and have planar shapes that overlap with each other due to translational movement in the X direction. The number of groups may be 1 to 7, or 9 or more.

[0103] Here, it is assumed that mask assurance is performed using first to Nth (N is an integer of 2 or more) mask patterns 12a of the photomask 1. In the first embodiment, for each of the first to Nth mask patterns 12a, the second moment σ of the design data is calculated. x , σ y and the second moment of the image data σ x , σ y For example, the second moment σ of the Kth mask pattern 12a of the design data is compared with x , σ y and the second moment σ of the Kth mask pattern 12a of the image data. x , σ y (K is an integer satisfying 1≦K≦N) to perform mask assurance. Similarly, in the second embodiment, for each of the first to Nth mask patterns 12a, the width W and height H of the design data are compared with the width W and height H of the image data to perform mask assurance. On the other hand, in the third embodiment, the first to Nth mask patterns 12a are classified into groups G1 to G8, and the comparison between the design data and the image data is performed for each group, rather than for each mask pattern 12a.

[0104] The guarantee method of this embodiment classifies a plurality of mask patterns 12a included in the design data of the photomask 1 into groups G1 to G8, and calculates the second moment σ of two or more mask patterns 12a belonging to each group. x , σ yThe guarantee method of this embodiment further classifies the mask patterns 12a included in the image data of the photomask 1 into groups G1 to G8, and calculates the average and variation of the second moment σ of two or more mask patterns 12a belonging to each group. x , σ y Hereinafter, the former mean and variation are also referred to as "mean and variation of the second moment of the design data," and the latter mean and variation are also referred to as "mean and variation of the second moment of the image data." Note that the second moment σ of each mask pattern 12a of the design data and image data is x , σ y can be calculated by the guarantee method of the first embodiment.

[0105] The assurance method of this embodiment performs mask assurance by comparing the average and variance of the second-order moments of the design data with the average and variance of the second-order moments of the image data. According to this embodiment, by using the average and variance of the second-order moments instead of the ROI, it is possible to ensure the shape of the mask pattern 12a of the photomask 1. For example, even if the shape of the mask pattern 12a is complex, it is possible to appropriately ensure the shape of the mask pattern 12a. Furthermore, according to this embodiment, by using the average and variance of the second-order moments of two or more mask patterns 12a instead of the second-order moments of each mask pattern 12a, it is possible to reduce the number of comparisons and to relax the criteria for determining whether a product is good. The average and variance of the second-order moments are examples of values ​​that change depending on the second-order moments.

[0106] The assurance method of this embodiment is executed by, for example, an assurance device 201 shown in Fig. 8. In this case, a calculation unit 223 calculates the average and variance of the second moments of the design data and the average and variance of the second moments of the image data, and a comparison unit 224 compares the average and variance of the second moments of the design data with the average and variance of the second moments of the image data. The comparison unit 224 calculates the second moment σ of the design data as the first difference. xand the second moment σ of the image data x The difference between the mean and the second moment of the design data is calculated as the second difference. y and the second moment σ of the image data y The comparison unit 224 further calculates the difference between the average of the second moment σ of the design data as a third difference. x Variation of the second moment σ of the image data x The difference between the variation of the design data and the actual value is calculated, and the fourth difference is the second moment σ of the design data. y Variation of the second moment σ of the image data y The difference between the average and the variance is calculated. The method of using the first to fourth differences in this embodiment is the same as the method of using the first and second differences in the first embodiment. Note that in this embodiment, instead of using both the average and the variance, it is also possible to use only either the average or the variance.

[0107] Alternatively, the acquiring unit 221 may acquire the average and variation of the second moment of the design data instead of the design data. In this case, the comparing unit 224 uses these averages and variations for comparison. Similarly, the acquiring unit 221 may acquire the average and variation of the second moment of the image data instead of the image data. In this case, the comparing unit 224 uses these averages and variations for comparison.

[0108] FIG. 11 is a plan view showing the shape of a mask pattern 12a according to a modification of the third embodiment.

[0109] FIG. 11(a) shows the shapes of multiple mask patterns 12a extracted from an SEM image. FIG. 11(b) shows one of these mask patterns 12a. The multiple mask patterns 12a shown in FIG. 11(a) have planar shapes that overlap each other due to rotational movement within the XY plane. Note that the rotational movement here may be a combination of rotational movement and translational movement. Furthermore, the multiple mask patterns 12a shown in FIG. 11(a) may be planar figures that overlap each other due to symmetrical movement about an axis (e.g., the X axis or the Y axis) within the XY plane.

[0110] When classifying the multiple mask patterns 12a of the photomask 1 into one or more groups, two or more mask patterns 12a belonging to the same group may have planar shapes that overlap each other due to translational movement, or may have planar shapes that overlap each other due to rotational movement, which makes it possible to classify the mask patterns 12a into groups in a larger number of cases.

[0111] As described above, in this embodiment, mask assurance is performed by comparing the average and variation of the second-order moments of the design data with the average and variation of the second-order moments of the image data. Therefore, according to this embodiment, as in the first and second embodiments, it is possible to appropriately guarantee the shape of the mask pattern 12a of the photomask 1.

[0112] (Fourth embodiment) FIG. 12 is a plan view for explaining the design data and correction data of the photomask 1 of the fourth embodiment.

[0113] 12(a) shows a contour P1 of the mask pattern 12a included in the design data. Specifically, the design data of the photomask 1 includes design data related to the shape of the mask pattern 12a, and the contour P1 indicates the contour of the mask pattern 12a indicated by the design data related to the shape of the mask pattern 12a.

[0114] FIG. 12(a) further shows a contour P2 of the mask pattern 12a included in the correction data obtained by correcting the design data. Generally, the contour P1 of the mask pattern 12a included in the design data does not match the contour of the mask pattern 12a actually formed in the process shown in FIG. 1(c). This is because errors occur during electron beam lithography (FIG. 1(a)), development (FIG. 1(b)), and etching (FIG. 1(c)). Therefore, in this embodiment, mask quality assurance is performed using correction data instead of the design data itself. The correction data in this embodiment is obtained by predicting the effects of electron beam lithography, development, etching, and other processes on the shape of the mask pattern 12a and correcting the design data in consideration of these predictions. Therefore, the contour P2 is closer to the contour of the mask pattern 12a actually formed than the contour P1.

[0115] 12(b) shows an enlarged view of contours P1 and P2. Generally, the corners of contour P1 have a linear shape, while the corners of contour P2 have a rounded shape. This is because the corners of mask pattern 12a are generally designed to have a linear shape when photomask 1 is designed, but are generally formed to have a rounded shape due to errors when photomask 1 is manufactured.

[0116] The process of manufacturing the photomask 1 is called the mask process. An example of a mask process model that predicts the rounding of corners due to the mask process will be described below. The mask process model predicts how the shape of the mask pattern 12a included in the design data will change after the mask process. The correction data in this embodiment is obtained by correcting the design data using the mask process model.

[0117] Generally, the mask process is performed through electron beam lithography, development, etching, etc., and therefore the mask process model is expressed as a convolution integral of the region D and an exponential decay function, as shown in equation (21).

number

[0118] where H(x, y) is a mask shape function and G(x, y) is an exponential decay function. The exponential decay function G(x, y) is given by equation (22).

number

[0119] Here, σ is a constant that characterizes the mask process. For example, when the resolution of the mask process is high, the value of σ becomes small.

[0120] The mask shape function H(x, y) is a function that determines the shape of the mask pattern 12a after the mask process by the contour line of a certain threshold. The double integral in equation (21) can be replaced by a circular integral as shown in equation (23) according to Green's theorem.

number

[0121] The correction data of this embodiment may be applied to any of the first to third embodiments. When the correction data of this embodiment is applied to the second embodiment, the assurance method of this embodiment defines a region R' for the mask pattern 12a included in the correction data of the photomask 1, and calculates the width W and height H of this region R'. The assurance method of this embodiment further defines a region R' for the mask pattern 12a included in the image data of the photomask 1, and calculates the width W and height H of this region R'. The assurance method of this embodiment then performs mask assurance by comparing the width W and height H of the correction data with the width W and height H of the image data.

[0122] The guarantee method of this embodiment is executed by, for example, the guarantee device 201 shown in Fig. 8. In this case, the calculation unit 223 calculates the width W and height H of the corrected data and the width W and height H of the image data, and the comparison unit 224 compares the width W and height H of the corrected data with the width W and height H of the image data. The comparison unit 224 calculates the difference between the width W of the corrected data and the width W of the image data as the first difference, and calculates the difference between the height H of the corrected data and the height H of the image data as the second difference. The use of the first difference and the second difference in this embodiment is similar to the use of the first difference and the second difference in the first embodiment.

[0123] Alternatively, the acquiring unit 221 may acquire the width W and height H of the corrected data instead of the corrected data. In this case, the comparing unit 224 uses the width W and height H for comparison. Similarly, the acquiring unit 221 may acquire the width W and height H of the image data instead of the image data. In this case, the comparing unit 224 uses the width W and height H for comparison.

[0124] According to this embodiment, by using the correction data instead of the design data itself, it is possible to, for example, relax the criteria for determining whether a product is good or not. This is because the mask pattern 12a of the correction data is generally closer to the mask pattern 12a that is actually formed than the mask pattern 12a of the design data, and the difference between the correction data and image data is smaller than the difference between the design data and image data.

[0125] As described above, in this embodiment, mask quality assurance is performed using correction data instead of design data itself. Therefore, according to this embodiment, similar to the first to third embodiments, it is possible to appropriately guarantee the shape of the mask pattern 12a of the photomask 1.

[0126] (Fifth embodiment) 13 is a plan view for explaining an example of a display method according to the fifth embodiment. The display method according to this embodiment is performed, for example, as part of the guarantee method according to any one of the first to fourth embodiments.

[0127] Fig. 13(a), like Fig. 4(c) and Fig. 5(a), shows an SEM image of the photomask 1 of this embodiment obtained by imaging it with the SEM 101. Fig. 13(b), like Fig. 5(b), shows the shape of the mask pattern 12a extracted from the SEM image.

[0128] In this embodiment, the contour E of the mask pattern 12a is extracted from the image data of the photomask 1. Furthermore, a region D' is defined for this mask pattern 12a, and the width W and height H of the region D' are calculated. In the display method of this embodiment, as shown in FIG. 13(c), the mask pattern 12a extracted from the image data and the region D' corresponding to this mask pattern 12a are displayed superimposed on the screen of a display device. This makes it possible to present to the user the results of extracting the mask pattern 12a from the image data and the results of calculating the region D' (width W and height H). At this time, the mask pattern 12a and region D' of this embodiment are displayed so that the center of gravity of the mask pattern 12a and the center of gravity of the region D' overlap.

[0129] FIG. 14 is a plan view for explaining another example of the display method according to the fifth embodiment.

[0130] 14(a) shows the contour P1 of the mask pattern 12a included in the design data of the photomask 1, similar to FIG. 12(a).

[0131] In this embodiment, the contour P1 of the mask pattern 12a is extracted from the design data of the photomask 1. Furthermore, a region P1' is defined for this mask pattern 12a in the same manner as the above-described region D', and the width W and height H of the region P1' are calculated. In the display method of this embodiment, as shown in FIG. 14(b), the mask pattern 12a extracted from the design data and the region P1' corresponding to this mask pattern 12a are displayed superimposed on the screen of a display device. This makes it possible to present to the user the results of extracting the mask pattern 12a from the design data and the calculation results of the region P1' (width W and height H). In this case, the mask pattern 12a and the region P1' of this embodiment are displayed so that the center of gravity of the mask pattern 12a and the center of gravity of the region P1' overlap. The display method of this embodiment may also be performed using correction data instead of the design data itself.

[0132] The display method of this embodiment is performed by, for example, the output unit 225 of the assurance device 201 shown in Fig. 8. In this case, the display device may be the display unit 213 of the assurance device 201, or may be a device outside the assurance device 201. Furthermore, the display method of this embodiment may display the mask pattern 12a and region D' shown in Fig. 13(c) and the mask pattern 12a and region P1' shown in Fig. 14(b) superimposed on the screen of the display device.

[0133] Although several embodiments have been described above, these embodiments are presented only as examples and are not intended to limit the scope of the invention. The novel devices, methods, and programs described herein may be embodied in various other forms. Furthermore, various omissions, substitutions, and modifications may be made to the forms of the devices, methods, and programs described herein without departing from the spirit of the invention. The appended claims and their equivalents are intended to cover such forms and modifications that fall within the scope and spirit of the invention. [Explanation of symbols]

[0134] 1: Photomask, 2: Semiconductor device, 11: substrate, 12: light-shielding layer, 12a: light-shielding pattern (mask pattern), 13: resist layer, 13a: resist pattern, 21: Substrate, 22: Processed layer, 22a: Remaining part, 23: resist layer, 23a: remaining portion, 101: SEM, 201: Assurance device, 211: Information processing unit, 212: storage unit, 213: display unit, 214: input unit, 215: communication unit, 221: Acquisition unit, 222: Extraction unit, 223: Calculation unit, 224: comparison unit, 225: output unit

Claims

1. a processing unit that acquires or calculates a second moment of a pattern of a photomask or a value that changes depending on the second moment, the processing unit acquiring or calculating the second moment or the value of the pattern included in design data of the photomask and acquiring or calculating the second moment or the value of the pattern included in image data of the photomask; a comparison unit that calculates and outputs a difference between the second moment or the value of the pattern included in the design data and the second moment or the value of the pattern included in the image data; A guarantee device comprising:

2. 2. The guarantee device according to claim 1, wherein the processing unit comprises: an acquisition unit that acquires the design data or the image data; and a calculation unit that calculates the second moment or the value based on the design data or the image data.

3. the processing unit further includes an extraction unit that extracts a contour of the pattern from the design data or the image data, The guarantee device according to claim 2 , wherein the calculation unit calculates the second moment or the value by utilizing the contour extracted from the design data or the image data.

4. The guarantee device according to claim 3 , wherein the calculation unit calculates the second moment or the value by approximating the contour with a polygon.

5. The guarantee device according to claim 2 , wherein the calculation unit calculates the second moment or the value using Green's theorem.

6. The guarantee device according to claim 2 , wherein the acquisition unit acquires the image data obtained by capturing an image of the photomask.

7. the processing unit further acquires or calculates an area and a center of gravity of the pattern, and calculates a width and a height of a rectangle having the same area and center of gravity as the area and center of gravity of the pattern based on the area, center of gravity, and second moment of the pattern; 2. The guarantee device according to claim 1, wherein the comparison unit calculates and outputs a difference between the width and height of the rectangle corresponding to the pattern included in the design data and the width and height of the rectangle corresponding to the pattern included in the image data.

8. 8. The apparatus of claim 7, wherein the area of ​​the pattern is a zeroth moment of the pattern and the center of gravity of the pattern is a first moment of the pattern.

9. the processing unit, when the photomask includes a plurality of patterns and the plurality of patterns includes two or more patterns that can be considered to have the same shape, obtains or calculates an average of the second moments of the two or more patterns; 2. The guarantee device according to claim 1, wherein the comparison unit calculates and outputs a difference between the average for the two or more patterns included in the design data and the average for the two or more patterns included in the image data.

10. The processing unit further acquires or calculates variations in the second moments of the two or more patterns; 10. The guarantee device according to claim 9, wherein the comparison unit further calculates and outputs a difference between the variation regarding the two or more patterns included in the design data and the variation regarding the two or more patterns included in the image data.

11. The assurance device according to claim 9 , wherein the two or more patterns have shapes that overlap each other by translational movement, rotational movement, or axisymmetric movement.

12. the processing unit classifies the plurality of patterns into one or more groups based on the shape of each pattern; The assurance device according to claim 9 , wherein the two or more patterns belong to the same group among the one or more groups.

13. 2. The guarantee device according to claim 1, wherein the processing unit acquires or calculates, as the second-order moment or the value of the pattern included in the design data, the second-order moment or the value of the pattern included in corrected data obtained by correcting the design data.

14. The assurance device according to claim 1 , further comprising an output unit that outputs information related to the design data and / or the image data.

15. 15. The guarantee device according to claim 14, wherein the output unit outputs a comparison result between the second moment or the value of the pattern included in the design data and the second moment or the value of the pattern included in the image data.

16. The assurance device according to claim 15 , wherein the output unit outputs the comparison result in a form that is stored in a storage device.

17. 15. The guarantee device according to claim 14, wherein the output unit displays the pattern and / or a rectangle corresponding to the pattern based on the design data, or displays the pattern and / or a rectangle corresponding to the pattern based on the image data.

18. 18. The guarantee device according to claim 17, wherein the output unit displays the pattern and the rectangle displayed based on the design data in an overlapping manner, or displays the pattern and the rectangle displayed based on the image data in an overlapping manner.

19. When acquiring or calculating a second-order moment of a pattern of a photomask or a value that changes depending on the second-order moment, the second-order moment or the value of the pattern included in design data of the photomask is acquired or calculated, and the second-order moment or the value of the pattern included in image data of the photomask is acquired or calculated; calculating and outputting a difference between the second moment or the value of the pattern included in the design data and the second moment or the value of the pattern included in the image data; Warranty methods, including:

20. When acquiring or calculating a second-order moment of a pattern of a photomask or a value that changes depending on the second-order moment, the second-order moment or the value of the pattern included in design data of the photomask is acquired or calculated, and the second-order moment or the value of the pattern included in image data of the photomask is acquired or calculated; calculating and outputting a difference between the second moment or the value of the pattern included in the design data and the second moment or the value of the pattern included in the image data; A guarantee program that causes a computer to execute a guarantee method including the steps of:

Images