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 mesh data expressing a target structure, parameters with a primitive structure formed of a plurality of meshes associated with the same electron density, in which the analysis solution of the scattering intensity distribution of the X-ray delivered to the primitive structure can be calculated on the basis of the parameter; and a calculation part 120 that calculates the scattering intensity distribution of the X-ray delivered to the target structure, on the basis of the parameters.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 measurement technique using transmission small-angle X-ray scattering technology. [Prior art documents] [Patent documents]

[0003] [Patent Document 1] JP 2023-12913 A 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 extraction unit that extracts parameters of a primitive structure composed of a plurality of meshes associated with the same electron density from mesh data representing a target structure, the extraction unit being capable of calculating an analytical solution of a scattering intensity distribution of X-rays irradiated to the primitive structure based on the parameters; A calculation unit that calculates a scattering intensity distribution of X-rays irradiated on the target structure based on the parameters; Equipped with.

[0007] An analysis method according to an embodiment includes: A step-a of extracting parameters of a primitive structure composed of a plurality of meshes corresponding to the same electron density from mesh data representing a target structure, wherein an analytical solution of a scattering intensity distribution of X-rays irradiated to the primitive structure can be calculated based on the parameters; a step b of calculating a scattering intensity distribution of X-rays irradiated on the target structure based on the parameters; Includes.

[0008] In one embodiment, the program On the computer, A process (a) for extracting parameters of a primitive structure composed of a plurality of meshes corresponding to the same electron density from mesh data representing a target structure, the process (a) being capable of calculating an analytical solution of a scattering intensity distribution of X-rays irradiated to the primitive structure based on the parameters; A process-b of calculating a scattering intensity distribution of X-rays irradiated on the target structure based on the parameters; 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] FIG. 1 is a diagram for explaining an example of a target structure. [Figure 4] FIG. 13 is a diagram for explaining a state after a plurality of meshes are fused. [Diagram 5] FIG. 2 is a perspective view showing an example of a target structure. [Figure 6]FIG. 1 is a diagram for explaining a verification result of the analysis method according to 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 In this case, the scattering intensity distribution I(q(bold)) is expressed as the square of the three-dimensional Fourier transform equation obtained by solving the Schrödinger equation using the Born approximation, as shown in equation (1).

[0014]

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[0015] If the incident X-ray has a spread represented by the distribution W(k (bold)), the scattered 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 smearWhile (q(bold)) is a two-dimensional convolution integral, I(q(bold)) is a three-dimensional Fourier transform. Therefore, the time it takes to compute I(q(bold)) is usually about 1 / 2 the time it takes to compute I(q(bold)). smear This is longer than the time it takes to calculate (q(bold)).

[0016]

number

[0017] In general, 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 the above-mentioned primitive shapes alone, and must be expressed by a mesh.

[0018] It is known that the analytical solution for the scattering intensity distribution of X-rays irradiated on a rectangular parallelepiped mesh can be calculated, and the scattering intensity distribution of X-rays irradiated on a target structure can be obtained by adding up the above analytical solution over the entire area. Equation (3) expresses the scattering intensity distribution of X-rays irradiated on a target structure represented by a rectangular parallelepiped mesh. The Z direction represents the incidence direction of the X-rays.

[0019]

number

[0020] Therefore, when the number of meshes expressing the target structure is large, there is a problem that it takes a long time to analyze the scattering intensity distribution of X-rays. Therefore, the present disclosure realizes 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 applied to a complex structure expressed by a mesh.

[0021] 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.

[0022] 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.

[0023] The extraction unit 110 extracts parameters of a primitive structure composed of multiple meshes associated with the same electron density, i.e., the same material, from the mesh data expressing the target structure. A primitive structure is a structure for which an analytical solution of the scattering intensity distribution of X-rays applied to the structure can be calculated, such as a rectangular parallelepiped or a cylinder.

[0024] For example, if the primitive structure is a cuboid, the parameters include the dimensions of the cuboid in the X, Y, and Z directions. The parameters may include the center coordinates of the cuboid. For example, if the primitive structure is a cylinder, the parameters include the radius, height, etc. The parameters may include the position coordinates of the center of the cylinder.

[0025] The calculation unit 120 calculates the scattering intensity distribution of the X-rays applied to the target structure based on the parameters calculated by the extraction unit 110. For example, when the target structure includes a plurality of primitive structures, the calculation unit 120 may calculate an analytical solution based on the parameters for each of the plurality of primitive structures and calculate the scattering intensity distribution as the sum of the analytical solutions.

[0026] The above-mentioned formula (3) is derived on the assumption that the target structure is represented by a three-dimensional array of rectangular parallelepiped meshes. However, since the scattering intensity distribution is calculated as the sum of the results of analytically solving the Fourier transform for each mesh, as long as the target structure is accurately represented, the target structure does not need to be represented as a three-dimensional array. In addition, the size of the rectangular parallelepiped mesh does not need to be small. Therefore, the calculation unit calculates the scattering intensity distribution using formula (4).

[0027]

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[0028] Furthermore, the calculation unit 120 may calculate the scattering intensity distribution based on an electron density (called a reference electron density) associated with more primitive structures than other electron densities. That is, the calculation unit 120 performs a process of subtracting the reference electron density from the electron density associated with each primitive structure, and calculates the scattering intensity distribution according to formula (5).

[0029]

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[0030] Reference electron density ρ ref If is associated with many meshes, then ρ l -ρ ref Since becomes zero, calculations for many meshes are unnecessary. ref The number of primitive structures associated with the reference electron density ρ may be greater than the number of primitive structures associated with any other electron density. The reference electron density may be set before the processing of the extraction unit 110. In this case, the reference electron density ρ refThe number of meshes associated with the reference electron density ρ may be greater than the number of meshes associated with any other electron density. ref may be set for each partial structure included in the target structure. ref may be set by the user.

[0031] When the target structure includes a plurality of partial structures whose electron densities are the same, the calculation unit 120 may calculate an analytical solution by using parameters extracted for the other partial structures. In detail, when the target structure includes a first partial structure and a second partial structure whose electron densities are the same, the extraction unit 110 writes parameters of a primitive structure included in the first partial structure to the storage unit 130. Then, the calculation unit 120 calculates an analytical solution by using the parameters read from the storage unit 130 as parameters of a primitive structure included in the second partial structure. The calculation unit 120 may also assign a process of calculating an analytical solution for each of the plurality of primitive structures to one of a plurality of processor cores, and execute parallel processing with the plurality of processor cores.

[0032] Next, the operation of the analysis device 100 will be specifically described with reference to Fig. 3 and Fig. 4. Fig. 3 shows a target structure represented by a rectangular parallelepiped mesh. For simplicity, the target structure is represented in two dimensions. Meshes with the same hatching correspond to the same material, that is, the same electron density. There are 13 meshes in the horizontal direction and 9 meshes in the vertical direction. Therefore, the target structure is represented by 117 meshes.

[0033] The extraction unit 110 of the analysis device 100 first fuses meshes that have the same electron density and are adjacent in the horizontal direction. Next, the extraction unit 110 fuses meshes that have the same electron density, match in position and size in the horizontal direction, and are adjacent in the vertical direction. This generates a rectangular parallelepiped made up of multiple meshes that have the same electron density. Of course, the extraction unit 110 may fuse meshes that are adjacent in the horizontal direction after fusing meshes that are adjacent in the vertical direction.

[0034] 4 shows the state after the meshes have been fused by the extraction unit 110. The target structure is represented by 17 meshes numbered 0 to 16. The extraction unit 110 then extracts parameters from the 17 rectangular parallelepipeds. Next, the calculation unit 120 of the analysis device 100 calculates the scattering intensity distribution based on the extracted parameters. Specifically, the calculation unit 120 calculates the scattering intensity distribution as the sum of analytical solutions based on the parameters of the meshes.

[0035] Furthermore, the calculation unit of the analysis device 100 may calculate the scattering intensity distribution using equation (5) with the electron densities corresponding to the meshes No. 0, No. 1, No. 3, No. 4, No. 6, No. 7, No. 9, No. 10, No. 12, No. 13, No. 15, and No. 16 as the reference electron densities.

[0036] The target structure represented by 117 (=13*9) meshes in Fig. 3 is represented by 17 meshes in Fig. 4. This increases the calculation speed by 117 / 17=6.9 times. In addition, when the calculation unit 120 calculates the scattering intensity distribution based on the reference electron density, the number of meshes that need to be calculated becomes 5, so the calculation speed increases by 117 / 5=23 times.

[0037] The present inventors have studied the calculation of the scattering intensity distribution when X-rays are applied to a three-dimensional target structure shown in FIG. 5. In FIG. 5, the mesh is shown coarser than that of the structure actually used in the study. A rectangular parallelepiped hole is opened in a multilayer film 22 on a rectangular parallelepiped substrate 21. The substrate 21 and the multilayer film 22 are stacked in the Z direction. Cells with the same hatching correspond to the same material, i.e., the same electron density.

[0038] First, the inventor fused meshes that are associated with the same electron density and are adjacent in the Z direction. Next, the inventor fused meshes that are associated with the same electron density and are adjacent in the X direction. Next, the inventor fused meshes that are associated with the same electron density and are adjacent in the Y direction. Next, the inventor generated list information that lists information on the fused meshes. The list information indicates, for example, the central coordinates of each mesh after fusion, the length of each side of the mesh, and the electron density associated with the mesh. For example, the length of each side of the mesh corresponds to the above-mentioned parameters. Next, the inventor defined the electron density that is associated with the largest number of meshes as the reference electron density ρ ref The scattering intensity distribution was calculated using equation (5). The order of the directions in which the meshes are fused may be changed. This order may be determined by the user or may be determined inside the analysis device 100. In addition, the reference electron density ρ ref may be determined prior to fusing the meshes.

[0039] In FIG. 5, the mesh is shown coarser than it actually is, but the target structure is divided into 526 in the X direction, 152 in the Y direction, and 5200 in the Z direction. x [1 / nm] and Y component q y The sampling points of [1 / nm] were set to 526 and 152, respectively. When the conventional technology was used, that is, when the layers with matching electron density patterns were not merged and formula (3) was used, the calculation time of the scattering intensity distribution was 11147 seconds. On the other hand, when the layers with matching electron densities were merged and the reference electron density was appropriately set, the calculation time of the scattering intensity distribution was 1 second. Therefore, even when the 6 seconds required for preprocessing including the mesh merging and the setting of the reference electron density are taken into consideration, the calculation speed is 1592.4 times faster according to the first embodiment.

[0040] As shown in FIG. 6, the results of calculating the scattering intensity distribution using the conventional technique are consistent with the results of calculating the scattering intensity distribution using the first embodiment. 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 The scattering intensity at e = 0 is normalized to be 1. The maximum absolute value of the difference at each point between the calculation results according to the first embodiment and the calculation results according to the conventional technology for the entire calculated area is 1.0*e -13 and is small enough.

[0041] In the first embodiment, the calculation time can be reduced by using parameters of a primitive structure obtained by fusing a plurality of meshes. In addition, the calculation time can be further reduced by using a reference electron density.

[0042] 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]

[0043] 100 Analyzer 110 Extraction part 120 Calculation section 130 Storage section 21 Substrate 22 Multilayer film

Claims

1. an extraction unit that extracts parameters of a primitive structure composed of a plurality of meshes associated with the same electron density from mesh data representing a target structure, the extraction unit being capable of calculating an analytical solution of a scattering intensity distribution of X-rays irradiated to the primitive structure based on the parameters; A calculation unit that calculates a scattering intensity distribution of X-rays irradiated on the target structure based on the parameters; An analysis device comprising:

2. the target structure includes a first partial structure and a second partial structure whose electron density patterns match each other; The extraction unit writes the parameters of the primitive structure included in the first partial structure to a storage device; The calculation unit uses the parameters read from the storage device as the parameters of the primitive structure included in the second partial structure. The analysis device of claim 1 further comprising:

3. the target structure includes a plurality of primitive structures; The calculation unit assigns a process of calculating the analytical solution for each of the plurality of primitive structures to one of a plurality of processor cores, and executes parallel processing among the plurality of processor cores. The analysis device according to claim 1 or 2.

4. The calculation unit calculates the scattering intensity distribution based on a reference electron density, The reference electron density is associated with a larger number of primitive structures than other electron densities, or the reference electron density is associated with a larger number of meshes than other electron densities.

3. The analysis device according to claim 1 or 2.

5. The number of primitive structures associated with the reference electron density is greater than the number of primitive structures associated with any other electron density, or the number of meshes associated with the reference electron density is greater than the number of meshes associated with any other electron density. The analysis device according to claim 4.

6. A step-a of extracting parameters of a primitive structure composed of a plurality of meshes corresponding to the same electron density from mesh data representing a target structure, the step-a being capable of calculating a scattering intensity distribution of X-rays irradiated to the primitive structure based on the parameters; a step b of calculating a scattering intensity distribution of X-rays irradiated on the target structure based on the parameters; Analysis methods including:

7. On the computer, A process-a for extracting parameters of a primitive structure composed of a plurality of meshes corresponding to the same electron density from mesh data representing a target structure, the process-a being capable of calculating an analytical solution of a scattering intensity distribution of X-rays irradiated to the primitive structure based on the parameters; A process-b of calculating a scattering intensity distribution of X-rays irradiated on the target structure based on the parameters; A program that executes the following.

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