Analysis device, analysis method, and program

Abstract

To provide an analysis device, an analysis method, and a program, in which the time to analyze the X-ray scattering intensity distribution is reduced.SOLUTION: An analysis device 100 according to an embodiment includes: an extraction part 110 that extracts, from data expressing a target structure, information about an electron density difference at a different material interface included in the target structure and information about a surface element included in the different material interface; and a calculation part 120 that calculates the area at the different material interface for calculating the scattering intensity distribution of the X-ray delivered to the target structure, on the basis of the information about the electron density difference and the information about the surface element.SELECTED DRAWING: Figure 2

Description

[Technical field]

[0001] The present invention relates to an analysis device, an analysis method, and a program. [Background technology]

[0002] Patent Document 1 discloses a technique for measuring the thickness of each layer in a laminate by applying a phase contrast imaging method using X-rays. [Prior art documents] [Patent documents]

[0003] [Patent Document 1] Patent Publication No. 2022-83881 Summary of the Invention [Problem to be solved by the invention]

[0004] A technique that reduces the time required to analyze the scattering intensity distribution of X-rays is desired.

[0005] The present invention has been made to solve such problems, and has an object to provide an analysis device, an analysis method, and a program that reduce the time required to analyze the scattering intensity distribution of X-rays. [Means for solving the problem]

[0006] An analysis device according to an embodiment includes: an extracting unit that extracts information on an electron density difference at a boundary surface of different materials included in the target structure and information on a surface element included in the boundary surface of different materials from data representing the target structure; a calculation unit that calculates a surface integral at the boundary surface of different materials based on information about the electron density difference and information about the surface elements in order to calculate a scattering intensity distribution of the X-rays irradiated to the target structure; Equipped with.

[0007] An analysis method according to an embodiment includes: extracting information on an electron density difference at a boundary surface of different materials included in the target structure and information on surface elements included in the boundary surface of different materials from data representing the target structure; calculating a surface integral at the boundary surface of different materials for calculating a scattering intensity distribution of the X-rays applied to the target structure based on information about the electron density difference and information about the surface elements; Includes.

[0008] In one embodiment, the program On the computer, extracting information on an electron density difference at a boundary surface of different materials included in the target structure and information on surface elements included in the boundary surface of different materials from data representing the target structure; calculating a surface integral at the boundary surface of different materials for calculating a scattering intensity distribution of the X-rays applied to the target structure based on information about the electron density difference and information about the surface elements; Execute the command. Effect of the Invention

[0009] The present invention can provide an analysis device, an analysis method, and a program that reduce the time required to analyze the scattering intensity distribution of X-rays. [Brief description of the drawings]

[0010] [Figure 1] FIG. 2 is a diagram for explaining scattering vectors when an X-ray is applied to a target structure. [Diagram 2] FIG. 1 is a block diagram showing a configuration of an analysis device according to a first embodiment. [Diagram 3] 1 is a diagram for explaining a boundary surface of different materials included in a target structure; [Figure 4] FIG. 2 is a perspective view showing an example of a target structure. [Diagram 5] FIG. 2 is a diagram for explaining an analysis method according to the first embodiment. [Figure 6] FIG. 1 is a perspective view of a representation of a target structure according to the prior art; [Figure 7] FIG. 1 is a diagram for explaining a verification result of the analysis method according to the first embodiment. [Figure 8] FIG. 2 is a diagram for explaining the effect of the first embodiment. [Figure 9] FIG. 2 is a diagram for explaining the effect of the first embodiment. [Figure 10] FIG. 2 is a diagram for explaining the effect of the first embodiment. [Figure 11] FIG. 2 is a diagram for explaining the effect of the first embodiment. [Figure 12] FIG. 2 is a diagram for explaining the effect of the first embodiment. [Figure 13] FIG. 2 is a diagram for explaining the effect of the first embodiment. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0011] For clarity of explanation, the following description and drawings are omitted and simplified as appropriate. In addition, in each drawing, the same elements are given the same reference numerals, and duplicate explanations are omitted as necessary.

[0012] Consideration leading to the embodiment First, the circumstances by which the present inventor arrived at the invention according to the embodiment will be described. Fig. 1 is a diagram for explaining scattering vectors when a plane wave X-ray is applied to a target structure having periodicity. In the formulas in the following explanation, bold alphabets represent vectors. Since bold alphabets cannot be used in documents, normal formatting is used, and "(bold)" is added immediately after the relevant alphabet.

[0013] The wave vector of the X-ray is denoted as k (boldface), and the wave vector of the scattered wave is k s (boldface). The scattering vector q (boldface) is expressed as k s (boldface)-k(boldface). As shown in equation (1), the scattering intensity distribution I(q(boldface)) is expressed as the square of the three-dimensional Fourier transform equation obtained by solving the Schrödinger equation using the Born approximation.

[0014]

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[0015] When the incident X-ray has a spread represented by the distribution W(k (bold)), the scattering intensity distribution I smear I(q(boldface)) is calculated by the two-dimensional convolution integral of I(q(boldface)) and W(k(boldface)) as shown in equation (2). I smear While (q(bold)) involves a two-dimensional convolution integral, I(q(bold)) involves a three-dimensional integral. Therefore, the time it takes to compute I(q(bold)) is usually about 1 / 100th of that of I(q(bold)). smear This is longer than the time it takes to calculate (q(bold)).

[0016]

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[0017] In general, the above I(q (boldface)) is calculated for a target structure modeled as a combination of primitive shapes such as a rectangular parallelepiped or a cylinder, for which the 3D Fourier transform can be analytically solved. However, structural data obtained by process simulations and topography simulations that reflect physical processes generally cannot be expressed by primitive shapes alone, and must be expressed as a mesh. And since it is not possible to analytically solve the integral (3D Fourier transform) for a structure expressed as a mesh, it is necessary to express the target structure as a sufficiently fine rectangular parallelepiped mesh and perform normal numerical integration or integration using an analytical solution for a rectangular parallelepiped, which poses the problem of long calculation times.

[0018] Therefore, the present disclosure provides an analysis device, an analysis method, and a program that reduce the time required to analyze the scattering intensity distribution when a plane wave X-ray is irradiated onto a complex target structure.

[0019] EMBODIMENT 1 2 is a block diagram showing a configuration of the analysis device 100 according to the first embodiment. The analysis device 100 may be a computer device operated by a processor executing a program stored in a memory. The analysis device 100 may be composed of a plurality of computer devices. In this case, the components or functions constituting the analysis device 100 may be distributed and arranged in the plurality of computer devices. The plurality of computers may be connected via a network or directly connected via a cable or the like. As the processor, a CPU (Central Processing Unit), a GPU (Graphics Processing Unit), an FPGA (field-programmable gate array), or the like may be used.

[0020] Analysis device 100 includes an extraction unit 110, a calculation unit 120, and a storage unit 130. The storage unit 130 is realized by a storage device accessible by the processor.

[0021] The extraction unit 110 extracts information on the electron density difference at the different material boundary surface included in the target structure and information on the surface elements included in the different material boundary surface from the data representing the target structure. The information on the electron density difference represents the difference between the electron density associated with the front side of the different material boundary surface and the electron density associated with the back side of the different material boundary surface. For example, when the surface element is a triangle, the surface element information may include coordinate information of the three vertices of the triangle. Note that the shape of the surface element is not limited to a triangle.

[0022] The calculation unit 120 calculates the surface integral at the boundary surface of different materials for calculating the scattering intensity distribution of the X-rays applied to the target structure based on the information on the electron density difference and the information on the surface elements. The calculation unit 120 may calculate the surface integral for each of the multiple surface elements and calculate the scattering intensity distribution as the sum of the surface integrals.

[0023] The target structure may include a plurality of different material boundary surfaces. When the target structure includes a first different material boundary surface and a second different material boundary surface having the same shape, the extraction unit 110 stores information about the surface elements of the first different material boundary surface in the storage unit 130. When calculating the surface integral of the second different material boundary surface, the calculation unit 120 may read the information about the first different material boundary surface from the storage unit 130 and use the information calculated from the read information as information about the surface elements of the second different material boundary surface.

[0024] Furthermore, the calculation unit 120 may classify surface elements into one of a number of groups according to the orientation of the surface elements (X direction, Y direction, Z direction) and calculate the scattering intensity distribution taking the classification result into account. For example, the calculation unit 120 can efficiently calculate the scattering intensity distribution by arranging information about surface elements classified into the same group in a continuous memory and performing calculations.

[0025] Furthermore, the calculation unit 120 may process the surface integrals of multiple surface elements in parallel. For example, the calculation unit 120 may assign the surface integrals of each of the multiple surface elements to one of multiple processor cores, and execute parallel processing in the multiple processor cores.

[0026] Next, we will explain the reason why the scattering intensity distribution of X-rays can be calculated by the surface integral at the boundary surface of different materials with reference to formulas. The scattering intensity distribution when a plane wave X-ray is applied to a target structure having periodicity is calculated by squaring the three-dimensional Fourier transform equation shown in the above formula (1). The vector field D (boldface) (r (boldface)) that diverges the integrand function included in formula (1) is expressed by formula (3).

[0027]

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[0028] Substituting the divergence of this vector field D(boldface)(r(boldface)) into the integrand in equation (1), by the divergence theorem, the volume integral can be calculated by the surface integral, as shown in equation (4).

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[0029] For example, if a volume element is a tetrahedron composed of four triangular planes (area elements), the volume integral is calculated as the sum of the surface integrals on the four planes. Since volume elements are tiled within the analysis object, two area elements are paired within a structure associated with one material. Area elements that are not paired within a structure are paired with a vacuum, etc. If we look at the sum of the surface integrals on paired area elements with element numbers k and k', the equation for the face is the same but the direction of the area vector is opposite, so equation (5) holds.

[0030]

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[0031] In other words, the surface integrals at the boundary surfaces of the same material cancel each other out, and only the boundary surfaces of different materials contribute to the scattering intensity distribution. In other words, the scattering intensity distribution is calculated by extracting information on the boundary surfaces of different materials represented by curved surface 31 from the unstructured mesh data shown in Fig. 3 and finding the sum of the surface integrals thereon. Meshes with the same hatching correspond to the same material, that is, the same electron density. The scattering intensity distribution of X-rays can be calculated as the sum of the surface integrals on the boundary surfaces of different materials, without performing volume integration on the volume elements included in the unstructured mesh data or surface integration on the volume elements.

[0032] Next, the operation of the analysis device 100 will be described in detail with reference to Figures 4 and 5. With reference to Figure 4, a rectangular parallelepiped hole is opened in the multilayer film 22 on the rectangular parallelepiped substrate 21. The substrate 21 and the multilayer film 22 are stacked in the Z direction. Meshes with the same hatching correspond to the same material, that is, the same electron density.

[0033] First, the extraction unit 110 of the analysis device 100 extracts information about surface elements included in the boundary surface of different materials. FIG. 5 is an explanatory diagram showing an example of information about surface elements extracted by the extraction unit 110. For example, the extraction unit 110 extracts information about surface elements, such as r 0 (bold), r 1 (bold), and r 2 Extract the coordinate information and the electron density difference Δρ shown in (bold). Then, A (bold) = r 1 (bold)-r 0 (boldface) is calculated, and B(boldface) = r 2 (bold)-r 0 (bold), and calculate S(bold) = (A(bold) x B(bold)) / 2.

[0034] The calculation unit 120 of the analysis device 100 calculates the basis vectors of a new coordinate system, indicated by a dotted line fixed to the boundary surface of different materials, based on the extracted information. The basis of the original coordinate system is e x (bold)=(1,0,0),e y (bold)=(0,1,0),e z (bold) = (0,0,1). The base of the new coordinate system is e z ´(bold)=S(bold) / |S(bold)|, e x ´(bold)=A(bold) / |A(bold)|, e y ´(bold)=e z ´(bold)×e x The transformation rule between the original coordinate system and the new coordinate system is expressed by a matrix combining the inner products of these bases. The calculation unit 120 calculates the matrix shown in formula (6) based on the base vectors.

[0035]

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[0036] The surface integral in the new coordinate system fixed to the interface of different materials can be calculated analytically. triangle (q x , q y ), the scattering intensity distribution from one surface element when viewed from the original coordinates is expressed by equation (7).

[0037]

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[0038] The calculation unit 120 can calculate the scattering intensity distribution by calculating the scattering intensity distribution shown in equation (7) for all surface elements, performing conversion based on equation (6), and adding up the conversion results according to equation (8).

[0039]

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[0040] In the conventional technology, the scattering intensity distribution when X-rays are applied to a target structure represented by a rectangular parallelepiped mesh is calculated by adding up the analytical solutions of the scattering intensity distribution when X-rays are applied to one rectangular parallelepiped mesh over the entire target region. In this case, it was necessary to convert the mesh representation of the target structure shown in Fig. 4 to a representation using a rectangular parallelepiped mesh as shown in Fig. 6.

[0041] On the other hand, in the first embodiment, there is no need to convert the mesh data shown in FIG. 4 into the rectangular parallelepiped mesh data shown in FIG. 6, and the scattering intensity distribution can be calculated directly from the mesh data shown in FIG. 4. Furthermore, unless there are an extremely large number of boundaries between different materials, the amount of calculation in the analysis method according to the first embodiment is smaller. In order to compare the conventional technology with the first embodiment, the inventor divided the target structure shown in FIG. 4 into 526 in the X direction, 152 in the Y direction, and 5200 in the Z direction so that the target structure is represented by a rectangular parallelepiped mesh with each side being 1 mm. Then, the inventor divided the X component q of the scattering vector into x The sampling points of [1 / nm] are set to 526, and the Y component q y The number of sampling points of [1 / nm] was set to 152, and the time required to analyze the scattering intensity distribution was measured. When the conventional technology was used, the time required to generate a rectangular parallelepiped mesh was 16425 seconds, and the time required to calculate the scattering distribution intensity was 11147 seconds. When the first embodiment was used, the generation of a rectangular parallelepiped mesh was not necessary, and the time required to calculate the scattering distribution intensity was 5 seconds. Therefore, the analysis speed according to the first embodiment is 5514.4 (=(16425+11147) / 5) times faster than the analysis speed according to the conventional technology.

[0042] In addition, as shown in FIG. 7, the results of calculating the scattering distribution using the conventional technique and the results of calculating the scattering distribution using the first embodiment are consistent. For ease of viewing, the square root of the scattering intensity distribution is plotted for the main part of the scattering vector, and q x =q y = 0 is normalized to be 1. For the entire calculated range, the maximum absolute value of the difference at each point between the calculation results according to embodiment 1 and the calculation results according to the conventional technology is 0.00033304, which is sufficiently small.

[0043] In the first embodiment, the scattering intensity distribution when X-rays are applied to a target structure is calculated using a surface integral rather than a volume integral, which can reduce the required calculation time. In addition, there is no need to convert the mesh data of the target structure into rectangular parallelepiped mesh data.

[0044] Other effects include the following two. In both the conventional method of adding analytical solutions of rectangular parallelepiped meshes over the entire area and the method of adding the results of applying fast Fourier transform in the XY direction in the Z direction, the target structure of the simulation is expressed as a small rectangular parallelepiped, so that surfaces tilted with respect to the reference coordinates and curved surfaces become jagged, which reduces the simulation accuracy. To prevent this, a sufficiently fine rectangular parallelepiped mesh can be used, but in that case, the number of meshes increases and the calculation time becomes enormous. Since the first embodiment does not convert to this rectangular parallelepiped mesh, the accuracy reduction and calculation time increase due to discretization of the target structure as described above do not occur, and the scattering intensity distribution can be obtained from structure data in a form closer to the original. For example, when the scattering intensity distribution of a cylindrical target structure with a radius of 100 nm and a height of 100 nm shown in FIG. 8 is calculated using the conventional technology, the circle is expressed using a rectangular parallelepiped (square) as shown in FIG. 9, and is no longer a strict circle in the XY direction, so the scattering intensity distribution is distorted. In the first embodiment, since it is not necessary to represent a cylinder with a rectangular parallelepiped cell, the first embodiment can obtain a scattering intensity distribution closer to the exact solution than the conventional technology, as shown in FIG.

[0045] In addition, when using fast Fourier transform, it is necessary to use a mesh that is uniform in the XY direction, so even if there is no curved or inclined plane, when converting to a uniform rectangular parallelepiped mesh, the boundary surface of different materials will be shifted from its original position. In the first embodiment, since conversion to a rectangular parallelepiped mesh itself is not performed, such a problem does not occur. For example, when calculating the scattering intensity distribution from a rectangular parallelepiped with each side of 100 nm shown in FIG. 11, as shown in FIG. 12, the position of the boundary surface of different materials will be shifted when the rectangular parallelepiped is expressed by a rectangular parallelepiped mesh. Therefore, when using the conventional technology, the position of the zero point that should appear will be shifted from the exact solution, as shown in FIG. 13. On the other hand, the first embodiment can calculate a scattering intensity distribution that matches the exact solution.

[0046] The present invention is not limited to the above-described embodiment, and can be modified as appropriate without departing from the spirit and scope of the present invention. [Explanation of symbols]

[0047] 100 Analyzer 110 Extraction part 120 Calculation section 130 Storage section 21 Substrate 22 Multilayer film 31 Curved surface

Claims

1. an extracting unit that extracts information on an electron density difference at a boundary surface of different materials included in the target structure and information on a surface element included in the boundary surface of different materials from data representing the target structure; a calculation unit that calculates a surface integral at the boundary surface of different materials based on information about the electron density difference and information about the surface elements, in order to calculate a scattering intensity distribution of the X-rays irradiated on the target structure; An analysis device equipped with:

2. the target structure includes a first dissimilar material interface and a second dissimilar material interface having the same shape; the extraction unit writes information about the surface elements of the first different material boundary surface into a storage device; The calculation unit uses information based on the information on the surface elements of the first different material boundary surface read from the storage device as information on the surface elements of the second different material boundary surface. The analysis device according to claim 1 .

3. The calculation unit classifies the surface elements into one of a plurality of groups according to the orientation of the surface elements, and executes the surface integral taking into account a result of the classification. The analysis device according to claim 1 or 2.

4. The calculation unit assigns an area integral of each of a plurality of surface elements to any of a plurality of processor cores, and executes parallel processing in the plurality of processor cores. The analysis device according to claim 1 or 2.

5. extracting information on an electron density difference at a boundary surface of different materials included in the target structure and information on surface elements included in the boundary surface of different materials from data representing the target structure; calculating a surface integral at the boundary surface of different materials for calculating a scattering intensity distribution of the X-rays irradiated to the target structure based on information about the electron density difference and information about the surface elements; Analysis methods including:

6. On the computer, extracting information on an electron density difference at a boundary surface of different materials included in the target structure and information on surface elements included in the boundary surface of different materials from data representing the target structure; calculating a surface integral at the boundary surface of different materials for calculating a scattering intensity distribution of the X-rays irradiated to the target structure based on information about the electron density difference and information about the surface elements; A program that executes the following.

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