Roughness value calculation device, roughness value calculation method, and program

Abstract

To provide a roughness value calculation device, a roughness value calculation method and a program, capable of quantitatively evaluating roughness of a corner part.SOLUTION: A roughness value calculation device includes: roundness calculation means 21 configured to obtain two approximation straight lines characterizing a corner part from a specific area within a photographic image, and use the two approximation straight lines to calculate a radius and center coordinates of an approximate circle showing roundness of the corner part; roughness measuring range determination means 22 configured to define a start point on one approximation straight line and an end point on the other approximation straight line of the two approximation straight lines, and determine an area between the start point and the end point of the corner part as a measuring range for roughness; distance calculation means 23 configured to use points on an outline of the corner part located within the measuring range as measurement points and calculate, with regard to each measurement point, a distance between the measurement point and a circumference of the approximate circle; and roughness value calculation means 24 configured to calculate a roughness value showing a degree of roughness according to a distribution of distances to the measurement points calculated by the distance calculation means.SELECTED DRAWING: Figure 2

Description

[Technical field]

[0001] The present invention relates to a technique for measuring patterns of semiconductor devices and photomasks and the like used in manufacturing semiconductor devices. [Background technology]

[0002] Semiconductor integrated circuits are becoming finer and more highly integrated to improve performance and productivity, and technological development is underway to form finer patterns with high precision. The pattern dimensions of photomasks used to manufacture semiconductor integrated circuits are often less than 100 nm, and a scanning electron microscope (SEM) specially designed for dimensional measurement is used to measure the dimensions and shapes of specific positions of such fine patterns.

[0003] Furthermore, the quality of manufactured photomasks is checked by inspecting the shape of an image (SEM image) of the photomask photographed by an SEM. That is, the quality of the manufactured photomask is judged based on how rounded the corners of the pattern that should be formed at right angles are in the photographed image such as an SEM image. In this case, the smaller the roundness, the closer the pattern is to the original shape, and therefore the higher the quality of the mask is. A technology for measuring the roundness of such corners has also been proposed (see Patent Document 1). [Prior art documents] [Patent documents]

[0004] [Patent Document 1] Patent No. 4139664 [Patent Document 2] JP 2007-263899 A Summary of the Invention [Problem to be solved by the invention]

[0005] However, the edges of the patterns actually processed on the wafer have roughness (roughness due to minute unevenness, so-called jaggedness) resulting from the process and resist material, and roughness also exists in the corners of the patterns. The larger the roughness, the more it affects the measurement results of the roundness of the corners. Patent Document 2 also describes a method for measuring the roughness of a pattern shape. In Patent Document 2, the pattern to be measured is compared with a reference pattern, and a roughness value is calculated from the difference between the two. However, this method requires a reference pattern that serves as an expected value, and if the alignment between the reference pattern and the measurement target is not accurate, the roughness will be greater than the actual roughness, resulting in a lack of accuracy.

[0006] Therefore, an object of the present invention is to provide a roughness value calculation device, a roughness value calculation measurement method, and a program that are capable of quantitatively evaluating the roughness of corner portions accurately and simply. [Means for solving the problem]

[0007] In order to solve the above problems, the present invention provides a roundness calculation means for calculating two approximation lines that characterize a corner portion from a specific region in a captured image, and calculating a radius and a center coordinate of an approximation circle that represents the roundness of the corner portion using the two approximation lines; a roughness measurement range determining means for determining a starting point on one of the two approximate straight lines and an end point on the other approximate straight line, and determining a roughness measurement range between the starting point and the end point of the corner portion; a distance calculation means for calculating a distance between each of the measurement points on the contour of the corner portion located within the measurement range and the circumference of the approximation circle; a roughness value calculation means for calculating a roughness value indicating a degree of roughness based on the distribution of distances to each of the measurement points calculated by the distance calculation means; The present invention provides a roughness value calculation device having the above-mentioned function.

[0008] Further, the roughness value calculation device according to the present invention comprises: The roughness value may be calculated using a standard deviation σ.

[0009] Further, the roughness value calculation device according to the present invention comprises: The roughness measurement range determining means may determine, as the start point and the end point, points of intersection between a third approximation line calculated when determining the two approximation lines and each of the two approximation lines.

[0010] Further, the roughness value calculation device according to the present invention comprises: The roughness measurement range determination means may obtain a perpendicular line passing through a center of the approximation circle for each of the two approximation lines, and may determine an intersection point between the obtained perpendicular line and one of the approximation lines as the start point, and a point between the obtained perpendicular line and the other approximation line as the end point.

[0011] Further, the roughness value calculation device according to the present invention comprises: The roughness measurement range determination means may determine a predetermined reference axis, and determine that a point on the contour of the corner portion is a measurement point when an angle formed by each point on the contour of the corner portion and a straight line passing through the center of the approximation circle and the reference axis is between an angle formed by a straight line passing through the starting point and the center of the approximation circle and the reference axis and an angle formed by a straight line passing through the end point and the center of the approximation circle and the reference axis.

[0012] The present invention also provides a method for producing a semiconductor device comprising the steps of: The computer Two approximate straight lines that characterize a corner portion are obtained from a specific region in the captured image, and the two approximate straight lines are used to calculate the radius and center coordinates of an approximate circle that represents the roundness of the corner portion; A start point is set on one of the two approximate straight lines, and an end point is set on the other approximate straight line, and a roughness measurement range is determined between the start point and the end point of the corner portion; a measurement point on the contour of the corner portion located within the roughness measurement range is set as a measurement point, and a distance between each measurement point and a circumference of the approximation circle is calculated; calculating a roughness value indicating a degree of roughness based on the distribution of distances to the measurement points calculated by the distance calculation means; A roughness value calculation method is provided.

[0013] The present invention also provides a method for producing a semiconductor device comprising the steps of: Computer, a roundness calculation means for calculating two approximation lines characterizing a corner portion from a specific region in the captured image, and calculating a radius and a center coordinate of an approximation circle representing the roundness of the corner portion using the two approximation lines; a roughness measurement range determining means for determining a starting point on one of the two approximate straight lines and an end point on the other approximate straight line, and determining a roughness measurement range between the starting point and the end point of the corner portion; a distance calculation means for calculating a distance between each of the measurement points on the contour of the corner portion located within the measurement range and the circumference of the approximation circle; a roughness value calculation means for calculating a roughness value indicating a degree of roughness based on the distribution of distances for each of the measurement points calculated by the distance calculation means; The present invention provides a program that functions as a Effect of the Invention

[0014] According to the present invention, it is possible to provide a roughness value calculation device, a roughness value calculation method, and a program capable of quantitatively evaluating the roughness of corner portions. [Brief description of the drawings]

[0015] [Figure 1] 1 is a hardware configuration diagram of a roughness value calculation device according to an embodiment of the present invention. [Diagram 2] 1 is a functional block diagram showing a configuration of a roughness value calculation device according to an embodiment of the present invention; [Diagram 3] 4 is a flowchart showing a processing operation of a roughness value calculation device according to an embodiment of the present invention. [Figure 4] 13 is a diagram showing how an approximation circle is calculated by a roundness calculation means; FIG. [Diagram 5] FIG. 13 is a diagram for explaining how to determine the center coordinates of an approximation circle. [Figure 6] 11A and 11B are diagrams illustrating the relationship between the contour of a corner portion, an approximation circle, and the expected roundness of the contour. [Figure 7] FIG. 13 is a diagram for explaining a method for determining a measurement range. [Figure 8] 11 is a diagram for explaining a method for determining whether or not a point is a measurement point. FIG. [Figure 9] FIG. 13 is a diagram showing the distance between the contour within the measurement range and the circumference of an approximation circle. [Figure 10] FIG. 13 is a diagram showing a modified example of the method for determining the measurement range. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0016] Hereinafter, preferred embodiments of the present invention will be described in detail with reference to the drawings. <1.Device configuration> Fig. 1 is a hardware configuration diagram of a roughness value calculation device 100 according to an embodiment of the present invention. The roughness value calculation device 100 according to this embodiment can be realized by a general-purpose computer, and as shown in Fig. 1, includes a CPU (Central Processing Unit) 1, a RAM (Random Access Memory) 2 which is the main memory of the computer, a large-capacity storage device 3 such as a hard disk, SSD (Solid State Drive), or flash memory for storing programs and data executed by the CPU 1, an instruction input I / F (interface) 4 such as a keyboard or mouse, a data input / output I / F (interface) 5 for data communication with an external device such as a data storage medium, and a display unit 6 which is a display device such as a liquid crystal display, which are connected to each other via a bus.

[0017] In this embodiment, the CPU 1 may be a multi-core CPU. In this case, the CPU 1 has multiple CPU cores and is capable of parallel processing. In the example of FIG. 1, only one RAM 2 is shown, but each CPU core of the CPU 1 is configured to access one RAM 2. Note that there may be multiple CPUs 1. Also, the multi-core CPU may be a CPU that logically has multiple CPU cores.

[0018] Fig. 2 is a functional block diagram showing the configuration of a roughness value calculation device according to this embodiment, in which 10 denotes an image reading means, 20 denotes a calculation processing section, and 30 denotes an output means.

[0019] The image reading means 10 is a means for reading a captured image of a corner portion of a pattern such as a photomask. Specifically, it is realized by connecting a data input device, an external storage medium, and a communication network via the data input / output I / F 5. The captured image of a corner portion of a pattern such as a photomask is usually an SEM image captured by an SEM. The captured image is read into the calculation processing unit 20 via the image reading means 10.

[0020] The calculation processing unit 20 is realized by the CPU 1 reading and executing an operating system (OS) or a dedicated program stored in the storage device 3. The calculation processing unit 20 has a roundness calculation means 21, a roughness measurement range determination means 22, a distance calculation means 23, and a roughness value calculation means 24. In addition to the above-mentioned means, the calculation processing unit 20 can realize various processes such as processes related to a user interface, data input / output, display processing, etc. by the CPU 1 reading and executing a program.

[0021] The roundness calculation means 21 is a means for determining two approximate straight lines that characterize a corner portion from a specific region in a captured image, and calculating the radius and center coordinates of an approximate circle that represents the roundness of the corner portion using the two approximate straight lines. The roughness measurement range determination means 22 is a means for determining a start point on one of the two approximate straight lines, an end point on the other approximate straight line, and determining the area between the start point and the end point of the corner portion as the roughness measurement range.

[0022] The distance calculation means 23 is a means for calculating the distance between each measurement point and the circumference of the approximation circle, with the measurement point being a point on the contour of the corner portion located within the measurement range. The roughness value calculation means 24 is a means for calculating a roughness value indicating the degree of roughness based on the distribution of distances to each measurement point. The roundness calculation means 21, the roughness measurement range determination means 22, the distance calculation means 23, and the roughness value calculation means 24 are included in the arithmetic processing unit 20, and are realized by the CPU 1 executing a dedicated program.

[0023] The output means 30 is a means for graphically outputting the distance distribution of the measurement points calculated by the distance calculation means 23 and the roughness value calculated by the roughness value calculation means 24, and is realized by a display unit 6 such as a printer or a display device via the data input / output I / F 5.

[0024] Each of the constituent means shown in Fig. 2 is actually realized by installing a dedicated program in hardware such as a computer and its peripheral devices, as shown in Fig. 1. That is, the computer executes the contents of each means according to the dedicated program. In this specification, a computer means a device having a calculation processing unit such as a CPU or a GPU and capable of data processing, and includes not only general-purpose computers such as personal computers, but also computers incorporated in various devices such as mobile terminals such as tablets equipped with a CPU, and multi-function mobile phones such as smartphones.

[0025] <2. Processing Operation> The roughness value calculation device in this embodiment photographs a predetermined pattern provided on a photomask or the like, and performs a predetermined process on the photographed image to obtain the roughness value of the corners of the pattern.

[0026] A description will now be given of the roughness value calculation method according to this embodiment, as well as the processing operation of the roughness value calculation device shown in Figures 1 and 2. Figure 3 is a flowchart showing the processing operation of the roughness value calculation device according to this embodiment.

[0027] First, a photographed image of a predetermined pattern such as a photomask is prepared. The photographed image is not particularly limited, but is prepared as a bitmap image with 8 bits per pixel and 256 gradations, for example. In the roughness value calculation device, the image reading means 10 reads the photographed image. Then, the contour in the photographed image is extracted, and the area around the corner of the contour is specified. Here, in order to extract the contour line from the photographed image, a known digital image processing method such as smoothing, edge detection, binarization, thinning, etc. is appropriately used. The area around the corner may be specified by the user directly specifying it via the instruction input I / F 4, and the calculation processing unit 20 may specify it, or the image processing function of the calculation processing unit 20 may be used to regard a predetermined area including a part where the direction of the contour changes significantly as the area around the corner. Also, if the photographed image read by the image reading means 10 is an image in which only the corner portion has already been photographed, it is possible to proceed to a specific roundness calculation without specifying the area in the image.

[0028] Next, the radius and center coordinates of an approximation circle representing the roundness of the corner portion are calculated for the read photographed image (step S10). Specifically, the roundness calculation means 21 calculates the radius and center coordinates of an approximation circle representing the roundness of the corner portion. The roundness of the corner portion can be expressed by the radius of curvature, and the smaller the radius of curvature, the smaller the roundness and the closer it is to an ideal right angle. As described above, in the photomask inspection process, the quality of the manufactured photomask is checked by inspecting the shape of an SEM image, which is an image of the photomask photographed by an electron microscope. At this time, the quality of the manufactured photomask is judged based on how rounded the corner portion of the pattern that should be formed at a right angle is formed in the photographed image such as the SEM image. In this case, the smaller the roundness, the closer it is to the pattern that should be formed, and therefore the mask is judged to be of good quality.

[0029] As a specific method for calculating the roundness of the corner portion, various known methods can be used. In this embodiment, the radius and center coordinates of the approximate arc of the corner portion shape are calculated using the technology described in Japanese Patent No. 4139664. By calculating the radius and center coordinates of the approximate arc of the corner portion shape as an index for quantifying the roundness of the corner portion, it becomes possible to accurately and stably calculate the radius of curvature without being affected by the way the corner range is specified. In addition, there is no need to convert to complicated data such as vector data.

[0030] The process in step S10 will be described in detail. Fig. 4 is a diagram for explaining the calculation of an approximation circle by the roundness calculation means 21. First, as shown in Fig. 4(a), the roundness calculation means 21 extracts a contour (boundary pixel set BS) by smoothing, binarizing, edge detection, and thinning the image data of an image region specified as being near a corner of the mask pattern image. At this time, the coordinate data of each pixel of the boundary pixel set BS is extracted in order to perform a subsequent clustering process.

[0031] Next, using known fuzzy clustering, the boundary pixel set BS shown in Fig. 4(a) is classified into three groups that can be approximated by three straight lines. In this embodiment, the number of classifications is set to three (three straight lines are extracted). As known fuzzy clustering, the method disclosed in Japanese Patent No. 4139664 may be used.

[0032] Next, the roundness calculation means 21 extracts two straight lines that characterize the corner by linearly approximating the boundary pixel set BS. Specifically, the pixel data that constitutes the boundary line of the corner portion is clustered into three groups according to coordinate values ​​in a two-dimensional Euclidean space defined based on the pixel array of the SEM image. Then, each pixel that belongs to each of the three clusters obtained as a result of the clustering is considered as sample data having two variables that represent the coordinates of each pixel, and principal component analysis is performed for each cluster. The first principal component axis of each cluster is found by the principal component analysis, and the first principal component axis is taken as the approximation line that represents that cluster.

[0033] As a result, the three first principal component axes corresponding to the three clusters are obtained as approximate straight lines L1, L2, and L3. The approximate straight lines L1, L2, and L3 can be called the first approximate straight line, the second approximate straight line, and the third approximate straight line, respectively. Since each cluster has a first principal component and a second principal component, the ratio between the two is examined. Then, the one whose ratio is closest to 1 is excluded, and the other two are taken as the two approximate straight lines that characterize the corner.

[0034] The two approximate straight lines L1 and L2 thus obtained are shown in Fig. 4(b). As shown in Fig. 4(b), the straight lines L1 and L2 are straight lines that approximate the straight line portions at both ends of the boundary pixel set BS.

[0035] Next, the area S1 of triangle A1 formed by three approximate straight lines L1, L2, and L3, each of which represents three sets of pixel data obtained as a result of clustering, is calculated. The area S1 of triangle A1 can be calculated using Heron's formula. Figure 4(c) is a diagram showing the approximate straight lines L1, L2, and L3, which are the three first principal component axes corresponding to the above three clusters, and triangle A1.

[0036] On the other hand, as shown in Figure 4(d), the radius r of the circle inscribed in the corner formed by two straight lines and the area S2 of the area (missing area) A2 cut out from the corner by this inscribed circle satisfy the following relationship in [Equation 1]. In [Equation 1], θ is the angle made by the two approximate straight lines L1 and L2. [Equation 1] can be confirmed by a simple area calculation.

[0037]

number

[0038] Therefore, after calculating the area S1 of the triangle A1 formed by the three approximate straight lines L1, L2, and L3, this is substituted into [Equation 1] as S2=S1 to solve for the radius r of the approximate circle, resulting in the following equation as [Equation 2]. By executing the process according to the following [Equation 2], the roundness calculation means 21 can determine the radius r.

[0039]

number

[0040] Once the radius r of the approximation circle is obtained, the center coordinates of the approximation circle are then obtained. FIG. 5 is a diagram for explaining how to determine the center coordinates of the approximation circle. As shown in FIG. 5, a total of four straight lines (indicated with arrows in FIG. 5) are obtained: two straight lines whose distance from the approximation line L1 is r, and two straight lines whose distance from the approximation line L2 is r. Then, of the four intersections where two of the four straight lines intersect, the one closest to the region whose area has been measured is obtained as the center coordinates C. In this way, in step S10, the roundness calculation means 21 calculates the radius r and center coordinates C of the approximation circle as the roundness of the corner portion.

[0041] In this embodiment, the area S1 of the triangle A1 is calculated from the lengths of the three sides of the triangle surrounded by the three straight lines L1, L2, and L3 in step S10 using Heron's formula, but this area S1 is merely an approximation of the area S2 of the missing partial area A2. In contrast, in order to directly calculate the area S2 of the missing partial area A2 shown in FIG. 4(b), the area S2 may be calculated directly by determining the positions of pixels on both straight lines L1 and L2 from the two straight lines L1 and counting up the pixels existing between the pixels on these straight lines and the pixels belonging to the boundary pixel set BS. When calculating the area S2 directly, the number of clusters calculated by the above-mentioned fuzzy clustering may be set to 2 instead of 3, and the two approximate straight lines L1 and L2 may be calculated instead of the approximate straight line L3.

[0042] In step S10, when the radius and center coordinates of the approximation circle expressing the roundness of the corner portion in the photographed image are obtained, the measurement range of the roughness of the corner portion is then determined (step S20). Specifically, the roughness measurement range determination means 22 determines the measurement range of the roughness of the corner portion. First, the idea of ​​determining the roughness measurement range in step S20 will be described. As described above, the approximation circle is obtained as the roundness of the corner portion. Therefore, the difference between the contour of the corner portion and the approximation circle can be considered as the roughness. FIG. 6 is a diagram showing the relationship between the contour of the corner portion, the approximation circle, and the contour excluding the roughness. In FIG. 6, the contour of the corner portion is extracted from the photographed image by thinning processing or the like, the approximation circle is calculated by the roundness calculation means 21 in step S10, and the contour excluding the roughness is a virtual contour without roughness.

[0043] In this embodiment, the measurement range is determined based on two straight lines passing through the center of the approximation circle. If the measurement range is too narrow as shown in FIG. 6(a), some unevenness in the contour of the corner portion is significantly reflected in the roughness value. Conversely, if the measurement range is too wide as shown in FIG. 6(b), the portion far from the arc of the approximation circle is reflected in the roughness value. Therefore, it is important to determine an appropriate measurement range. However, in the method in which the inspector manually determines the roughness measurement range, the value changes depending on how the inspector specifies the range, and it is difficult to set an appropriate measurement range. Therefore, in this embodiment, the measurement range is set as follows.

[0044] FIG. 7 is a diagram for explaining a method of determining the measurement range. In step S20, first, two approximation lines L1 and L2 of the boundary pixel set BS, which are elements for obtaining the approximation circle in step S10, and a line L3, which is a principal component axis in the center of the boundary pixel set BS, are used. The roughness measurement range determination means 22 calculates the intersection point of the approximation line L1 at one end of the boundary pixel set BS and the approximation line L3 at the center of the boundary pixel set BS, and sets the calculated intersection point as the start point P1 of the roughness measurement range. Next, the means 22 calculates the intersection point of the approximation line L2 at the other end of the boundary pixel set BS and the approximation line L3 at the center of the boundary pixel set BS, and sets the calculated intersection point as the end point P2 of the roughness measurement range. That is, as shown in FIG. 7, the intersection points P1 and P2 of the approximation line L3 and the two approximation lines L1 and L2 tangent to the approximation circle are the start point P1 and the end point P2 of the measurement range.

[0045] For convenience, of the intersections P1 and P2, P1 is set as the start point and P2 as the end point, but conversely, P2 may be set as the start point and P1 as the end point. The start point and end point are for convenience in determining the boundary of the measurement range, and therefore differ from the calculation order of each measurement point within the measurement range.

[0046] Next, using the intersection point P1 thus found and the center C of the approximation circle, a straight line LC1 is found that connects the intersection point P1 with the center C of the approximation circle. Similarly, using the intersection point P2 thus found and the center C of the approximation circle, a straight line LC2 is found that connects the intersection point P2 with the center C of the approximation circle. The corner contour sandwiched between the straight lines LC1 and LC2 is defined as the roughness measurement range.

[0047] Once the start point and end point are determined, whether or not a point on the corner contour is a measurement point is determined based on whether or not it is located between the lines LC1 and LC2. Specifically, the roughness measurement range determination means 22 executes the following process to determine whether or not each point on the corner contour is a measurement point.

[0048] Fig. 8 is a diagram for explaining a method of determining whether or not a point is a measurement point. As shown in Fig. 8(a), the coordinates of an arbitrary point Pt on a corner contour are (Xt, Yt), the coordinates of a starting point P1 are (Xp1, Yp1), the coordinates of an end point P2 are (Xp2, Yp2), and the coordinates of a center C of an approximate circle are (Xc, Yc). Then, in order to set the coordinates of the center C to the origin C' (0, 0), the roughness measurement range determination means 22 executes a process according to the following [Equation 3] to offset the coordinates of the point Pt, the starting point P1, and the end point P2 by (Xc, Yc).

[0049] [Number 3] Coordinates of point Pt' = (Xt-Xc, Yt-Yc) Coordinates of starting point P1' = (Xp1-Xc, Yp1-Yc) Coordinates of end point P2' = (Xp2-Xc, Yp2-Yc)

[0050] As a result of executing the process according to [Equation 3], the offset point Pt', start point P1', and start point P2' are obtained. FIG. 8(b) shows the relationship between the offset approximation circle and the coordinate axes. Then, the roughness measurement range determination means 22 determines a predetermined reference axis, and determines that a point on the corner contour is a measurement point when the angle between the reference axis and a straight line passing through each point on the corner contour and the center of the approximation circle is between the angle between the reference axis and the straight line passing through the start point and the center of the approximation circle, and the angle between the reference axis and the straight line passing through the end point and the center of the approximation circle.

[0051] Although any straight line can be used as the reference axis, in this embodiment, the x-axis is used. Therefore, the roughness measurement range determination means 22 determines the angles with the x-axis as the reference axis, that is, the angles θt', θp1', and θp2' (see FIG. 8(b)) between the point Pt', the starting point P1', and the ending point P2' as viewed from the origin C' (0,0), by executing a process according to the following [Equation 4].

[0052] [Number 4] θt'=tan -1 {(Yt-Yc) / (Xt-Xc)} θp1'=tan -1 {(Yp1-Yc) / (Xp1-Xc)} θp2'=tan -1 {(Yp2-Yc) / (Xp2-Xc)}

[0053] If the angle θt' between point Pt' and the x-axis obtained by executing the process according to the above [Equation 4] is between the angle θp1' between the start point P1' and the x-axis and the angle θp2' between the end point P2' and the x-axis, then the point Pt on the corner contour is determined to be a measurement point within the measurement range between the lines LC1 and LC2. Therefore, it may be θp1'≦θt'≦θp2' or it may be θp2'≦θt'≦θp1'. In this way, all measurement points on the corner contour that are within the measurement range are identified.

[0054] Next, the distance between each measurement point included in the obtained measurement range and the circumference of the approximation circle is calculated (step S30). FIG. 9 is a diagram showing the distance between the contour in the measurement range and the circumference of the approximation circle. As in FIG. 6, FIG. 9 shows the contour excluding the corner contour, the approximation circle, and the roughness. The part indicated by the arrows facing each other in FIG. 9 is the distance between the measurement point on the contour to be obtained and the circumference of the approximation circle. There are N (N is an integer equal to or greater than 1) measurement points on the contour included in the measurement range, and the distance calculation means 23 calculates the distance between each measurement point and the circumference. Specifically, the distance calculation means 23 executes a process according to the following [Equation 5] to calculate the distance dn between each measurement point (Xtn, Ytn) (n=1, 2, 3, . . . N: N is a positive integer) and the circumference of the approximation circle.

[0055] [Number 5] distance dn=sqrt{(Xtn-Xc) 2 +(Ytn-Yc) 2}-r

[0056] In [Equation 5], sqrt means the square root in {}. Therefore, sqrt{} indicates the distance between each measurement point (Xtn, Ytn) and the center of the approximation circle (Xc, Yc). Also, r indicates the radius of the approximation circle.

[0057] When there are N measurement points within the measurement range, the process according to the above [Equation 5] is executed for all N measurement points (n=1, 2, 3,...N), thereby obtaining the distances from the circumference for the N measurement points. By using n as a data number, the distances from the circumference of the approximation circle for measurement points with data numbers 1 to N can be obtained. The distribution of the measurement points and the distances indicates the roughness of the corner contour. Note that, in this embodiment, the distance is calculated by using one pixel of the captured image as one measurement point, but the distance may be calculated in sub-pixel units that are finer than a pixel.

[0058] Next, a roughness value is calculated using the calculated distance between each measurement point and the circumference of the approximation circle (step S40). Specifically, the roughness value calculation means 24 calculates the standard deviation σ of the distance between each measurement point and the circumference, or 3σ, which is three times the standard deviation, as the roughness value. By calculating the roughness value in this manner, the roughness value calculation means 24 quantifies the roughness of the corner portion. Note that, although the standard deviation σ or 3σ is used in this embodiment, the standard deviation σ may be multiplied by another number, and any index may be used as long as it can represent roughness.

[0059] Once the roughness value is calculated in step S40, the output means 30 outputs the calculated roughness value (step S50). The output by the output means 30 can be performed in various forms, such as display output or print output. In addition to the roughness value, or instead of the roughness value, other calculation results may be output. For example, the distribution of the distance between the measurement points expressing the roughness and the circumference of the approximation circle may be output in a table format or a graph. In addition, as shown in FIG. 7 and FIG. 9, the approximation circle may be output graphically together with the outlines of the corners.

[0060] By carrying out the above-mentioned processing, it becomes possible to obtain a roughness value based on an accurate range in the contour. In this embodiment, a reference pattern that serves as an expected value is not required in measuring the roughness value of the corner portion of a pattern of a photomask or wafer. Therefore, it is not necessary to align the reference pattern with the measurement target, and the inspector does not need to specify the range to be measured. This makes it possible to measure the roughness value simply and with high accuracy.

[0061] <3. Modifications> In the above embodiment, in step S20, the intersections of the two approximate straight lines L1 and L2 at both ends of the corner and the straight line L3, which is the principal component axis at the center of the corner, are calculated as the roughness measurement range. However, the measurement range may be calculated by a method other than that described in the above embodiment. Next, a modified example of the roughness measurement range calculation process in step S20 will be described.

[0062] 10 is a diagram showing a modified example of the method for determining the measurement range. In the modified example, the roughness measurement range determination means 22 first obtains a normal vector of an approximate straight line L1 passing through the center point C of the approximate circle to obtain a perpendicular line (straight line LC1) passing through the center point C of the approximate circle, and sets the intersection of the straight line LC1 and the approximate straight line L1 as the start point P1 of the roughness measurement range.

[0063] Similarly, the roughness measurement range determination means 22 obtains a perpendicular line (straight line LC2) passing through the center point C of the approximate circle by calculating the normal vector of the approximate straight line L2 passing through the center point C of the approximate circle, and determines the intersection of the straight line LC2 and the approximate straight line L2 as the end point P2 of the roughness measurement range.

[0064] After the start point P1 and the end point P2 are determined, the area between the straight lines LC1 and LC2 passing through the start point P1 is set as the measurement range, and the processes shown in steps S30 and S40 are executed as shown in the above embodiment to determine the roughness value.

[0065] Although the preferred embodiment of the present invention has been described above, the present invention is not limited to the above embodiment and various modifications are possible. For example, in the above embodiment, the roughness value is calculated for the corner portion of the pattern of the photomask or wafer, but the roughness value may be calculated for any object as long as it is an object for which a roughness value needs to be obtained. [Explanation of symbols]

[0066] 1...CPU(Central Processing Unit) 2...RAM(Random Access Memory) 3...Storage device 4. Command input I / F 5. Data input / output interface 6...Display section 10. Image reading means 20. Processing unit 21. Roundness calculation method 22. Roughness measurement range determination means 23. Distance calculation means 24. Roughness value calculation means 30. Output means 100 Roughness value calculation device

Claims

1. a roundness calculation means for calculating two approximation lines that characterize a corner portion from a specific region in a captured image, and calculating a radius and a center coordinate of an approximation circle that represents the roundness of the corner portion using the two approximation lines; a roughness measurement range determining means for determining a starting point on one of the two approximate straight lines and an end point on the other approximate straight line, and determining an area between the starting point and the end point of the corner portion as a roughness measurement range; a distance calculation means for calculating a distance between each of the measurement points on the contour of the corner portion located within the measurement range and the circumference of the approximation circle; a roughness value calculation means for calculating a roughness value based on the distribution of distances to each of the measurement points calculated by the distance calculation means; having The roundness calculation means clustering pixel data of the captured image constituting the boundary line of the corner portion into three groups according to coordinate values ​​in a two-dimensional Euclidean space defined based on the pixel array of the captured image, treating each pixel data belonging to each of the three clusters obtained as a result of the clustering as sample data having two variables representing the coordinates of each pixel, performing principal component analysis for each of the three clusters, determining a first principal component axis of each cluster by the principal component analysis, and setting the first principal component axis of each cluster as an approximate straight line representing each cluster, and determining the two approximate straight lines by excluding, from the approximate straight lines of each of the three clusters, an approximate straight line in which a ratio between the first principal component and the second principal component of each cluster is closest to 1; The roughness measurement range determining means includes: the approximate straight line excluded when the roundness calculation means calculates the two approximate straight lines; and The intersection points with the two approximate straight lines are defined as the start point and the end point, Roughness value calculation device.

2. The roughness value calculation device according to claim 1 , wherein a value using a standard deviation σ is calculated as the roughness value.

3. The computer a first principal component axis of each of the three clusters is determined by the principal component analysis, and the first principal component axis of each of the three clusters is set as an approximation line representing each of the clusters; two approximation lines characterizing the corner portion are obtained by excluding an approximation line having a ratio of the first principal component to the second principal component of each of the three clusters that is closest to 1 from the approximation lines of each of the three clusters; and a radius and a center coordinate of an approximation circle representing the roundness of the corner portion are calculated using the two approximation lines. determining a starting point and an end point of intersection of the two approximate straight lines with the approximate straight lines excluded when determining the two approximate straight lines, and determining a measurement range between the starting point and the end point; points on the contour of the corner portion located within the measurement range are set as measurement points, and a distance between each measurement point and the circumference of the approximation circle is calculated; A roughness value calculation method, comprising: calculating a roughness value indicating a degree of roughness based on the distribution of the calculated distances to each of the measurement points.

4. Computer, a roundness calculation means for clustering pixel data of the captured image constituting a boundary line of a corner portion from a specific region in the captured image into three groups according to coordinate values ​​in a two-dimensional Euclidean space defined on the basis of a pixel array of the captured image, performing principal component analysis for each of the three clusters using each pixel data belonging to each of the three clusters obtained as a result of the clustering as sample data having two variables representing the coordinates of each pixel, determining a first principal component axis of each cluster by the principal component analysis, setting the first principal component axis of each cluster as an approximation straight line representing each cluster, determining two approximation straight lines characterizing the corner portion by excluding an approximation straight line for which a ratio between the first principal component and the second principal component of each cluster is closest to 1 from among the approximation straight lines of each of the three clusters, and calculating a radius and a center coordinate of an approximation circle representing the roundness of the corner portion using the two approximation straight lines; a roughness measurement range determining means for determining a roughness measurement range between a corner portion and the start point and an end point of each of the two approximate straight lines, the start point being determined on one of the two approximate straight lines and the end point being determined on the other approximate straight line, the roughness measurement range being determined by a roughness measurement range determining means for determining a roughness measurement range between the start point and the ... a distance calculation means for calculating a distance between each of the measurement points on the contour of the corner portion located within the measurement range and the circumference of the approximation circle; a roughness value calculation means for calculating a roughness value indicating a degree of roughness based on the distribution of distances for each of the measurement points calculated by the distance calculation means; A program that functions as a

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