Electron beam tomography device, electron beam tomography method, and program therefor

Abstract

To provide an electron beam tomography device that reconstructs a three-dimensional structure of a sample on the basis of electron beam diffraction images acquired from a sample, an electron beam tomography method, and a program therefor.SOLUTION: An electron beam tomography device according to the present invention comprises: a transmission electron microscope that holds a sample in a rotatable manner and emits an electron beam while operating it; a two-dimensional detector that detects an electron beam diffraction graphic group; and an analysis device that reconstructs the three-dimensional structure of the sample using the electron beam diffraction graphic group. The analysis device includes: a data storage unit that stores the electron beam diffraction graphic group; a multivariate analysis unit that performs non-negative value matrix factorization by the element number of 2 or more for the electron beam diffraction graphic group and acquires decomposed electron beam diffraction graphics and corresponding intensity images; a grouping unit that groups the decomposed electron beam diffraction graphics and corresponding intensity images by the element number of 2 or more; and a reconstruction unit that reconstructs the three-dimensional structure of the sample on the basis of the intensity images grouped by the element number of 2 or more.SELECTED DRAWING: Figure 1

Description

Technical Field

[0001] The present invention relates to an electron beam tomography apparatus, an electron beam tomography method, and a program thereof.

Background Art

[0002] By using a scanning transmission electron microscope (STEM), an electron beam probe narrowed by a focusing lens is scanned on a sample, and an image can be obtained by detecting transmitted electrons at each point. In STEM, there is a technique of using an annular dark field (ADF) detector arranged under the sample in synchronization with the scanning of the electron beam probe on the sample, obtaining an intensity image according to the density of the sample, and reconstructing the three-dimensional structure of the sample.

[0003] FIG. 9 is a schematic diagram for reconstructing the three-dimensional structure of a sample in the case of using STEM according to the prior art.

[0004] For example, as shown in FIG. 9, when the sample 900 contains substances indicated by the parts B and C in the base material A and the base material A and the part B have the same composition, even if the sample 900 is reconstructed using STEM, it is difficult to separate the base material A and the part B.

[0005] Angle θ 0 When an electron beam is scanned in the direction of the arrow on the sample 900-0 rotated by, the electrons transmitted through the sample 900-0 are detected by the ADF detector. At this time, the intensity data from the detector is also stored together with the scanning position information of the electron beam. Such intensity data and the scanning position information of the electron beam are used to obtain an intensity image 910-0. However, since the base material A and the part B have the same composition, the intensity data is the same, and there is no difference between the base material A and the part B in the intensity image either. In the intensity image 910-0, the area of the part B is shown by a dotted line for clarity, but it should be noted that actually no difference can be seen.

[0006] Similarly, for the angle θ 1When an electron beam is scanned in the direction of the arrow on the sample 900-1 rotated by [[angle]], the electrons transmitted through the sample 900-1 are detected by the ADF detector, and an intensity image 910-1 is obtained. Here too, since the base material A and the part B have the same composition, the intensity data are the same, and there is no difference between the base material A and the part B in the intensity image 910-1 either.

[0007] In this way, as the angle is rotated, the angle θ n When an electron beam is scanned in the direction of the arrow on the sample 900-n rotated by [[angle]], the electrons transmitted through the sample 900-n are detected by the ADF detector, and an intensity image 910-n is obtained. Here too, since the base material A and the part B have the same composition, the intensity data are the same, and there is no difference between the base material A and the part B in the intensity image 910-n either.

[0008] In this way, the three-dimensional structure 920 reconstructed using the intensity images 910-0, 910-1, ···, 910-n obtained by rotating the sample 900 cannot distinguish between the base material A and the part B. Therefore, when the structures are different but the compositions are the same, it was not possible to distinguish and reconstruct the base material A and the part B of the sample 900. Therefore, the development of a method that can reconstruct the sample with higher accuracy is desired.

[0009] On the other hand, as a method of recording the electron diffraction pattern corresponding to each pixel and analyzing the sample, the 4D-STEM method is known. In the 4D-STEM method, the electron diffraction pattern corresponding to the scanning position is recorded by a two-dimensional detector placed under the sample, and any one electron diffraction pattern of the sample can be analyzed by post-processing, or various STEM images such as scattering absorption intensity, diffraction intensity, and phase intensity can be reproduced. However, there is no technique for reconstructing the three-dimensional structure of a sample using the 4D-STEM method.

[0010] Recently, 4D-STEM data analysis using multivariate analysis has been performed (see, for example, Non-Patent Document 1). Non-Patent Document 1 reports that by applying non-negative matrix factorization (NMF) to 4D-STEM data, the main electron diffraction patterns and the regions that generate them can be separated and visualized. However, even in Non-Patent Document 1, it was not possible to reconstruct the three-dimensional structure of the sample.

Prior Art Documents

Non-Patent Documents

[0011]

Non-Patent Document 1

Summary of the Invention

Problems to be Solved by the Invention

[0012] From the above, an object of the present invention is to provide an electron beam tomography apparatus, an electron beam tomography method, and a program thereof for reconstructing the three-dimensional structure of a sample based on an electron diffraction pattern obtained from the sample.

Means for Solving the Problems

[0013] An electron tomography method for reconstructing a three-dimensional structure of a sample based on an electron diffraction pattern obtained from the sample according to the present invention includes a step of irradiating the sample while scanning an electron beam from a plurality of angles to obtain a group of electron diffraction patterns, wherein the group of electron diffraction patterns consists of a plurality of electron diffraction patterns each having information on an angle and a scanning position; a step of performing non-negative matrix factorization (NMF) on the group of electron diffraction patterns with two or more numbers of elements to create the set of electron diffraction patterns and the corresponding intensity image set with the two or more numbers of elements; a step of grouping the set of electron diffraction patterns and the corresponding intensity image set among the plurality of angles; and a step of reconstructing the three-dimensional structure of the sample based on the grouped intensity image set, thereby solving the above problems. In the grouping step, the set of electron diffraction patterns at adjacent angles among the plurality of angles may be grouped using a cross-correlation function. In the reconstructing step, the three-dimensional structure of the sample may be reconstructed for each of the two or more numbers of elements. The steps of performing the non-negative matrix factorization, the grouping step, and the reconstructing step may be repeated by increasing the two or more numbers of elements by one. An electron tomography apparatus for reconstructing a three-dimensional structure of a sample based on an electron diffraction image obtained from the sample according to the present invention includes a transmission electron microscope that rotatably holds the sample and irradiates the sample while scanning an electron beam from a plurality of angles, a two-dimensional detector that detects an electron diffraction pattern of the sample, and an analysis apparatus that reconstructs the three-dimensional structure of the sample using an electron diffraction pattern group including a plurality of electron diffraction patterns each having information on an angle and a scanning position. The analysis apparatus further includes a data storage unit that stores the electron diffraction pattern group, a multivariate analysis unit that performs non-negative matrix factorization (NMF) on the electron diffraction pattern group with two or more numbers of elements to create a set of electron diffraction patterns with the two or more numbers of elements and a corresponding intensity image set, a grouping unit that groups the set of electron diffraction patterns and the corresponding intensity image set between the plurality of angles, and a reconstruction unit that reconstructs the three-dimensional structure of the sample based on the grouped intensity image set, thereby solving the above problems. The grouping unit may group the set of electron diffraction patterns for adjacent angles among the plurality of angles using a cross-correlation function. The reconstruction unit may reconstruct the three-dimensional structure of the sample for each of the two or more numbers of elements. An electron tomography program used in an electron tomography apparatus for reconstructing a three-dimensional structure of a sample based on an electron diffraction image obtained from the sample according to the present invention, wherein the electron tomography apparatus includes a transmission electron microscope that rotatably holds the sample and irradiates the sample while scanning an electron beam from a plurality of angles, a two-dimensional detector that detects an electron diffraction pattern of the sample, and an analysis apparatus that reconstructs the three-dimensional structure of the sample using a group of electron diffraction patterns each having information on an angle and a scanning position, and causes a computer to realize a function of storing the group of electron diffraction patterns, a multivariate analysis function of performing non-negative matrix factorization (NMF) on the group of electron diffraction patterns with two or more numbers of elements to create the electron diffraction pattern sets with two or more numbers of elements and corresponding intensity image sets, a function of grouping the electron diffraction pattern sets and the corresponding intensity image sets among the plurality of angles, and a function of reconstructing the three-dimensional structure of the sample based on the grouped intensity image sets, thereby solving the above problems. The grouping function may group the electron diffraction pattern sets for adjacent angles among the plurality of angles using a cross-correlation function. The reconstructing function may reconstruct the three-dimensional structure of the sample for each of the two or more numbers of elements.

Advantages of the Invention

[0014] An electron tomography method for reconstructing a three-dimensional structure of a sample based on an electron diffraction pattern obtained from the sample according to the present invention creates an electron diffraction pattern set with two or more numbers of elements and a corresponding intensity image set by performing non-negative matrix factorization (NMF) on electron diffraction patterns irradiated with an electron beam from a plurality of angles. The electron diffraction pattern sets and intensity image sets created according to the number of elements are grouped among the measured angles, enabling highly accurate classification. By using the intensity image sets grouped in this way, even if the sample contains substances with different structures but the same composition, the three-dimensional structure of the sample can be accurately reconstructed.

[0015] An electron tomography apparatus for reconstructing the three-dimensional structure of a sample based on an electron diffraction pattern obtained from the sample of the present invention includes a multivariate analysis unit that performs non-negative matrix factorization (NMF) on a group of electron diffraction patterns from a data storage unit, thereby creating a set of electron diffraction patterns having two or more numbers of elements and a corresponding set of intensity images. The set of electron diffraction patterns and the set of intensity images created according to the number of elements in this way are grouped by a grouping unit, enabling highly accurate element classification. Since the reconstruction unit uses the set of intensity images grouped in this way, even if the sample contains substances with different structures but the same composition, the three-dimensional structure of the sample can be accurately reconstructed.

[0016] A program used in an electron tomography apparatus for reconstructing the three-dimensional structure of a sample based on an electron diffraction image obtained from the sample of the present invention creates a set of electron diffraction patterns having two or more numbers of elements and a corresponding set of intensity images by means of a multivariate analysis function that performs non-negative matrix factorization (NMF) on electron diffraction patterns irradiated with an electron beam from a plurality of angles. The set of electron diffraction patterns and the set of intensity images created according to the number of elements in this way are grouped between the angles measured by a grouping function, enabling highly accurate element classification. Since the reconstruction function uses the set of intensity images grouped in this way, even if the sample contains substances with different structures but the same composition, the three-dimensional structure of the sample can be accurately reconstructed.

Brief Description of the Drawings

[0017]

Figure 1

Figure 2

Figure 3

Figure 4

Figure 5

Figure 6

Figure 7

Figure 8

Figure 9

Mode for Carrying Out the Invention

[0018] Hereinafter, embodiments of the present invention will be described with reference to the drawings. In addition, the same elements are denoted by the same numbers, and the description thereof will be omitted. An electron beam tomography method of the present invention, an electron beam tomography apparatus for carrying out the same, and its program will be described.

[0019] FIG. 1 is a flowchart showing steps of an electron beam tomography method for reconstructing the three-dimensional structure of a sample based on an electron beam diffraction pattern obtained from the sample of the present invention. FIG. 2 is a schematic diagram of an exemplary sample. FIG. 3 is a diagram schematically showing step S110 of FIG. 1. FIG. 4 is a diagram schematically showing step S120 of FIG. 1. FIG. 5 is a schematic diagram of NMF in step S120 of FIG. 1. FIG. 6 is a diagram schematically showing step S130 of FIG. 1. FIG. 7 is a diagram schematically showing step S140 of FIG. 1.

[0020] FIG. 2(A) is a schematic diagram of an exemplary sample S applicable to the electron beam tomography method of the present invention. Here, the sample S contains substances indicated by parts B and C in the base material A. The base material A and part B have the same composition but different crystal structures, and the base material A and part C have different compositions. FIG. 2(B) shows a two-dimensional image of the sample S in FIG. 2(A) viewed from a certain direction. The whole is the base material A, the area indicated by a circle is part B, and the area indicated by a rectangle is part C. The arrow in FIG. 2(B) indicates the scanning direction of the electron beam irradiation.

[0021] A sample S preferably applicable to the electron beam tomography method of the present invention has different parts such as crystal structures although having the same composition as shown in FIG. 2. That is, the electron beam tomography method of the present invention can be applied to a sample having non-uniform parts derived from crystal structures or the like even if the compositions are the same, which are difficult to discriminate by general tomography methods. For example, parts having different crystal structures even if the compositions are the same may be single crystals, polycrystals, or amorphous.

[0022] The electron beam tomography method of the present invention includes the following steps. Step S110: Irradiate the sample while scanning the electron beam from a plurality of angles to obtain a group of electron beam diffraction patterns. Here, the group of electron beam diffraction patterns consists of a plurality of electron beam diffraction patterns each having information on the angle and the scanning position. Step S120: Perform non-negative matrix factorization (NMF) on the group of electron beam diffraction patterns with two or more numbers of elements to create a set of electron beam diffraction patterns with two or more numbers of elements and a corresponding set of intensity images. Step S130: Group the set of electron beam diffraction patterns and the corresponding set of intensity images among a plurality of angles. Step S140: Reconstruct the three-dimensional structure of the sample based on the grouped set of intensity images.

[0023] By performing non - negative matrix factorization (NMF) on an electron diffraction pattern group irradiated with an electron beam from multiple angles, an electron diffraction pattern set corresponding to two or more numbers of elements and a corresponding intensity image set are created. The electron diffraction pattern set and intensity image set created in this way according to the number of elements are grouped between the measured angles, enabling highly accurate element separation. By using the intensity image set grouped in this way, even if the sample contains substances with different structures but the same composition, the three - dimensional structure of the sample can be accurately reconstructed.

[0024] Each step will be described in detail with reference to the drawings. As shown in FIG. 3, in step S110, an electron beam is scanned and irradiated on the sample S from multiple angles to obtain an electron diffraction pattern group. For example, by placing the sample on a sample holder and rotating the sample holder, the angle of the electron beam irradiated on the sample S can be changed. In FIG. 3, the state of changing the angle θ formed between the sample holder and the horizontal direction of the paper surface is shown. From the left figure to the right figure, the angle θ formed is increasing in the order of θ 0 <θ 1 <θ n It can be seen. By rotating the sample holder in this way, the irradiation direction of the electron beam on the sample S changes, and the electron diffraction patterns of each cell of a1~an, b1~bn are obtained.

[0025] In FIG. 3, the electron diffraction pattern obtained at θ 0 is (θ 0 ,a1), (θ 0 ,a2), ···, (θ 0 ,an), (θ 0 ,b1), (θ 0 ,b2), ···, (θ 0 ,bn), ···. Similarly, the electron diffraction pattern obtained at the angle θ 1 is (θ 1 ,a1), (θ 1 ,a2), ···, (θ 1 ,an), (θ 1 ,b1), (θ 1 ,b2), ···, (θ1 , bn), ···, and the included angle is θ n The electron diffraction pattern obtained at is (θ n , a1), (θ n , a2), ···, (θ n , an), (θ n , b1), (θ n , b2), ···, (θ n , bn), ···. In this way, an electron diffraction pattern group composed of a plurality of electron diffraction patterns each having information on the angle and the scanning position is obtained.

[0026] In step S110, illustratively, the sample holder is rotated so that the included angle θ between the sample holder and the horizontal direction in the plane of the paper is an angle greater than 0° and less than or equal to 10° in absolute value, and this is performed until the total of the included angles θ is greater than 0° and less than or equal to 180° in absolute value. Note that, from the viewpoints of the amount of data to be acquired and simplicity, the sample holder is rotated so that the included angle θ between the sample holder and the horizontal direction in the plane of the paper is an angle greater than or equal to 2° and less than or equal to 6° in absolute value, and this is performed until the total of the included angles θ is greater than or equal to 30° and less than or equal to 60° in absolute value. Thereby, the three-dimensional structure of the sample S can be reconstructed with high precision. More preferably, the sample holder is rotated so that the included angle θ between the sample holder and the horizontal direction in the plane of the paper is an angle greater than or equal to 3° and less than or equal to 5° in absolute value, and this is performed until the total of the included angles θ is greater than or equal to 50° and less than or equal to 60° in absolute value. Thereby, since an intensity image with a sufficient amount of data can be obtained, the three-dimensional structure of the sample S can be reconstructed with higher precision.

[0027] In step S120, as shown in FIG. 4, the included angle θ 0 The electron diffraction pattern (θ 0 , a1), (θ 0 , a2), ···, (θ 0 , an), (θ 0 , b1), (θ 0 , b2), ···, (θ 0, bn), ··· are subjected to nonnegative matrix factorization (NMF) with two or more number of elements (here, the number of elements is 3), and a set 410-0 of images corresponding to electron diffraction patterns with two or more number of elements (here, the number of elements is 3) (hereinafter simply referred to as electron diffraction patterns) and a set 420-0 of images corresponding to intensity images corresponding thereto (hereinafter simply referred to as intensity images) are created. By performing NMF, a group (set) of electron diffraction patterns having similar characteristics is newly created.

[0028] According to FIG. 4, the created electron diffraction pattern set 410-0 is based on electron diffraction patterns (θ 0 , a1), (θ 0 , a2), ···, (θ 0 , an), (θ 0 , b1), (θ 0 , b2), ···, (θ 0 , bn), ···, and a new electron diffraction pattern set is created so that the specified number of elements is 3. Here, the electron diffraction pattern set 410-0 includes an electron diffraction pattern 410-01 decomposed into the first element, an electron diffraction pattern 410-02 decomposed into the second element, and an electron diffraction pattern 410-03 decomposed into the third element. The intensity image set 420-0 includes an intensity image 420-01 corresponding to the electron diffraction pattern 410-01 decomposed into the first element, an intensity image 420-02 corresponding to the electron diffraction pattern 410-02 decomposed into the second element, and an intensity image 420-03 corresponding to the electron diffraction pattern 410-03 decomposed into the third element. Since the electron diffraction pattern group acquired in step S110 naturally has intensity data, the intensity image set is automatically created corresponding to the electron diffraction pattern set.

[0029] As shown in FIG. 4, for all of the angles θ 1 from θ n , NMF is performed respectively to create electron diffraction pattern sets 410-1, ···, 410-n and corresponding intensity image sets 420-1, ···, 420-n.

[0030] Similarly, the electron diffraction pattern set 410-1 includes an electron diffraction pattern 410-11 decomposed into a first element, an electron diffraction pattern 410-12 decomposed into a second element, and an electron diffraction pattern 410-13 decomposed into a third element. The intensity image set 420-1 includes an intensity image 420-11 corresponding to the electron diffraction pattern 410-11 decomposed into the first element, an intensity image 420-12 corresponding to the electron diffraction pattern 410-12 decomposed into the second element, and an intensity image 420-13 corresponding to the electron diffraction pattern 410-13 decomposed into the third element.

[0031] The electron diffraction pattern set 410-n includes an electron diffraction pattern 410-n1 decomposed into a first element, an electron diffraction pattern 410-n2 decomposed into a second element, and an electron diffraction pattern 410-n3 decomposed into a third element. The intensity image set 420-n includes an intensity image 420-n1 corresponding to the electron diffraction pattern 410-n1 decomposed into the first element, an intensity image 420-n2 corresponding to the electron diffraction pattern 410-n2 decomposed into the second element, and an intensity image 420-n3 corresponding to the electron diffraction pattern 410-n3 decomposed into the third element.

[0032] Thus, by performing NMF in step S120, an electron diffraction pattern set including electron diffraction patterns with a specified number of elements (here, 3) and a corresponding intensity image set are created for each measured angle.

[0033] Here, referring to FIG. 5, non-negative matrix factorization (NMF) will be described. NMF is a method of decomposing a given non-negative matrix into two non-negative matrices (a basis matrix and a coefficient matrix), and is applied to dimensionality reduction and feature extraction of data. The electron diffraction pattern group obtained in step S110 is represented by a matrix. For example, in FIG. 5, the electron diffraction pattern group at the angle θ 0 consists of electron diffraction patterns (θ 0 , a 0 ) to electron diffraction patterns (θ 0 , N n) are shown. These are represented by matrix 510 and decomposed by NMF into a basis matrix 520 having information on diffraction patterns with a specified number of elements (the number of elements is 3 in FIG. 5) and a coefficient matrix 530 having information on intensity images.

[0034] For example, by rearranging the columns or rows of the basis matrix 520, the electron beam diffraction pattern 410-01 decomposed into the first element, the electron beam diffraction pattern 410-02 decomposed into the second element, and the electron beam diffraction pattern 410-03 decomposed into the third element can be obtained. Similarly, by rearranging the rows or columns of the coefficient matrix, the intensity image 420-01 corresponding to the electron beam diffraction pattern 410-01 decomposed into the first element, the intensity image 420-02 corresponding to the electron beam diffraction pattern 410-02 decomposed into the second element, and the intensity image 420-03 corresponding to the electron beam diffraction pattern 410-03 decomposed into the third element can be obtained.

[0035] Therefore, the electron beam diffraction pattern 410-01 decomposed into the first element in the electron beam diffraction pattern set 410-0 and the electron beam diffraction pattern 410-11 decomposed into the first element in the electron beam diffraction pattern set 410-1, or the electron beam diffraction pattern 410-01 decomposed into the first element in the electron beam diffraction pattern set 410-0 and the electron beam diffraction pattern 410-n1 decomposed into the first element in the electron beam diffraction pattern set 410-n are not necessarily similar to each other. That is, it should be noted that in step S120, it is only decomposed into the specified number of elements within the electron beam diffraction pattern obtained for a predetermined angle.

[0036] In step S120, the number of two or more elements is an integer and is determined by the sample. For example, in the case of the sample S having the base material A, the part B, and the part C shown in FIG. 2, the number of two or more elements can be specified as 3, but it may be arbitrarily set by the user.

[0037] In step S130, each of the electron diffraction patterns decomposed into the elements of the electron diffraction pattern set 410-0 created in step S120 is associated with each of the electron diffraction patterns decomposed into the elements of the other electron diffraction pattern sets 410-1 to 410-n, and the associated electron diffraction patterns are grouped.

[0038] In FIG. 6, the electron diffraction pattern 410-01 decomposed into the first element of the electron diffraction pattern set 410-0 is associated with the electron diffraction pattern 410-11 decomposed into the first element of the electron diffraction pattern set 410-1 and the electron diffraction pattern 410-n2 decomposed into the second element of the electron diffraction pattern set 410-n, and it is shown that they are grouped as the first element. According to the grouping of the electron diffraction patterns, the intensity image 420-01 is grouped with the intensity images 420-11 and 420-n2. Here, it is assumed that the grouped first element has the characteristics of the base material A.

[0039] Similarly, the electron diffraction pattern 410-02 decomposed into the second element of the electron diffraction pattern set 410-0 is associated with the electron diffraction pattern 410-13 decomposed into the third element of the electron diffraction pattern set 410-1 and the electron diffraction pattern 410-n1 decomposed into the first element of the electron diffraction pattern set 410-n, and it is shown that they are grouped as the second element. According to the grouping of the electron diffraction patterns, the intensity image 420-02 is grouped with the intensity images 420-13 and 420-n1. It is assumed that the grouped second element has the characteristics of the part B.

[0040] Similarly, the electron diffraction pattern 410-03 decomposed into the third element of the electron diffraction pattern set 410-0 is associated with the electron diffraction pattern 410-12 decomposed into the second element of the electron diffraction pattern set 410-1 and the electron diffraction pattern 410-n3 decomposed into the third element of the electron diffraction pattern set 410-n, and it is shown that they are grouped as the third element. According to the grouping of the electron diffraction patterns, the intensity image 420-03 is grouped with the intensity image 420-12 and the intensity image 420-n3. The grouped third element is assumed to have the characteristics of site C.

[0041] By grouping the electron diffraction patterns having the same characteristics and the corresponding intensity images over the entire range of angles measured in this way, accurate classification can be achieved.

[0042] In step S130, for grouping, the electron diffraction pattern sets at adjacent angles may use the cross-correlation function. Specifically, it is examined using the cross-correlation function whether the electron diffraction pattern 410-01 decomposed into the first element of the electron diffraction pattern set 410-0 can be grouped with the electron diffraction pattern 410-11 decomposed into the first element of the electron diffraction pattern set 410-1 at an adjacent angle. When it is determined that they are cross-correlated, the electron diffraction patterns 410-01 and 410-11 are grouped, and the cross-correlation for the electron diffraction pattern 410-01 ends. When it is determined that they are not cross-correlated, it is examined using the cross-correlation function whether the electron diffraction pattern 410-01 can be grouped with the electron diffraction pattern 410-12 decomposed into the second element. In this way, it is performed until the electron diffraction pattern 410-01 is grouped with any of the electron diffraction patterns 410-11 to 410-13. Similarly, it is sequentially performed for the electron diffraction patterns 410-02 and 410-03.

[0043] Since cross-correlation is commonly used in image processing, those skilled in the art will understand that by using the cross-correlation function, the degree of match between the selected electron diffraction patterns can be numerically determined. A predetermined value may be set in advance, and if it is equal to or greater than that value, it may be determined that they match. The predetermined value can be set appropriately by the user. For example, the difference in the cross-correlation coefficient may be set to 10%.

[0044] Next, when the grouping of the electron diffraction pattern set 410-0 and the electron diffraction pattern set 410-1 is completed, grouping is performed between the electron diffraction pattern 410-01 and an electron diffraction pattern set (not shown) at an adjacent angle.

[0045] In step S140, the reconstruction can be performed using a well-known technique such as the cross-correlation function. As shown in FIG. 7, the reconstruction may be performed based on the intensity image set for each of two or more numbers of elements. For example, the reconstructed image 610 is a reconstructed image of the base material A based on the intensity image set grouped by the first element, the reconstructed image 620 is a reconstructed image of the part B based on the intensity image set grouped by the second element, and the reconstructed image 630 is a reconstructed image of the part C based on the intensity image set grouped by the third element. Thus, even when the base material A and the part B have the same composition but different crystal structures, the three-dimensional structure of the sample S can be reconstructed with high precision.

[0046] In step S120, the number of elements is specified as 2, for example, and steps S130 and S140 described above are performed. The reconstructed image in step S140 is compared with the original image. If the error is large, return to step S120 again, increase the number of elements by 1, and repeat until the error between the reconstructed image (for example, the number of elements is 3) and the reconstructed image before the increase in the number of elements (for example, the number of elements is 2) becomes small. Note that the error is determined by the least squares error. For example, if the least squares error does not significantly (10% or less) decrease before and after increasing the number of elements, it may be considered that a sufficient number of elements has been obtained and the process ends there.

[0047] Next, an electron beam tomography apparatus of the present invention, which is preferable for implementing the electron beam tomography method of the present invention shown in FIG. 1, will be described. FIG. 8 is a schematic diagram showing the electron beam tomography apparatus of the present invention.

[0048] An electron beam tomography apparatus 800 that reconstructs the three-dimensional structure of a sample based on an electron beam diffraction image obtained from the sample of the present invention includes a transmission electron microscope 810 that rotatably holds the sample S and irradiates the sample S with electron beams from a plurality of angles, a two-dimensional detector 820 that detects the electron beam diffraction pattern of the sample S, and an analysis apparatus 830 that reconstructs the three-dimensional structure of the sample S using a group of electron beam diffraction patterns each having information on the angle and the scanning position.

[0049] The analysis apparatus 830 further includes a data storage unit 831 that stores a group of electron beam diffraction patterns of the sample S, a multivariate analysis unit 832 that performs non-negative matrix factorization (NMF) on the group of electron beam diffraction patterns with two or more element numbers to create a set of electron beam diffraction patterns with two or more element numbers and a corresponding intensity image set, a grouping unit 833 that groups the set of electron beam diffraction patterns and the corresponding intensity image set among a plurality of angles, and a reconstruction unit 834 that reconstructs the three-dimensional structure of the sample S based on the grouped intensity image set.

[0050] The electron beam tomography apparatus of the present invention includes a multivariate analysis unit 832 that performs non-negative matrix factorization (NMF) on the group of electron beam diffraction patterns from the data storage unit 831, thereby creating a set of electron beam diffraction patterns with two or more element numbers and a corresponding intensity image set. The set of electron beam diffraction patterns and the intensity image set created according to the number of elements in this way are grouped by the grouping unit 833, enabling highly accurate element classification. Since the reconstruction unit 834 uses the intensity image set grouped in this way, even if the sample contains substances with different structures but the same composition, the three-dimensional structure of the sample can be accurately reconstructed.

[0051] Each component will be described in detail. The transmission electron microscope 810 may be a known transmission electron microscope, and there is no particular limitation. For example, in an exemplary transmission electron microscope 810, a sample S is attached to a rotatable sample holder 811, and the angle θ formed between the sample holder 811 and the horizontal direction in the plane of the paper can be arbitrarily rotated. The transmission electron microscope 810 includes, for example, an electron source 812, a condenser lens 813, an objective lens 815, a scan coil 816, a projection lens 817, a diaphragm 818, and a detector 819, which are housed in a housing (not shown) whose interior can be depressurized. The transmission electron microscope 810 in FIG. 8 is an example and is not limited to this configuration.

[0052] The electron source 812 of the transmission electron microscope 810 emits an electron beam EB, which is converged to a single point on the surface of the sample S by a lens system such as a condenser lens 813 and an objective lens 815. Further, the electron beam EB is adjusted such that the focal length of the projection lens 817 and the like, and is taken into the detector 819 and further into a two-dimensional detector 820. The electron beam EB is shaped by the diaphragm 818 so that its cross-sectional shape is circular.

[0053] Since the transmission electron microscope 810 is provided with a scan coil 816, the electron beam EB can scan the surface of the sample S, and thereby, the two-dimensional detector 820 detects an electron diffraction pattern having information on various angles and scan positions.

[0054] The data storage unit 831 may be a memory that stores an electron diffraction pattern group (FIG. 3) composed of a plurality of electron diffraction patterns each having information on an angle and a scan position.

[0055] As described with reference to FIGS. 4 and 5, the multivariate analysis unit 832 reads out the electron diffraction pattern group from the data storage unit 831, performs non-negative matrix factorization (NMF) on the electron diffraction pattern group with two or more number of elements, and creates an electron diffraction pattern set and a corresponding intensity image set with two or more number of elements. The number of two or more elements may be arbitrarily set by the user, or may be preset to 2 or 3 as an initial value.

[0056] As described with reference to FIG. 6, the grouping unit 833 groups an electron diffraction pattern set and a corresponding intensity image set among a plurality of angles. Preferably, for adjacent angles among the plurality of angles, the electron diffraction pattern sets are grouped using a cross-correlation function. The grouping unit 833 uses the cross-correlation function to determine that the degree of coincidence between the selected electron diffraction patterns is coincident if it is equal to or greater than a predetermined value, and determines that they do not coincide if it is less than the predetermined value, calculates the degree of coincidence with another electron diffraction pattern, and may repeat until it is determined that they coincide. For example, the predetermined value may be such that the difference in the cross-correlation coefficient is 10%.

[0057] The reconstruction unit 834 performs reconstruction by a well-known technique such as a tomography reconstruction method using the intensity image set grouped in this way. As described with reference to FIG. 7, the reconstruction unit 834 can perform reconstruction for each of two or more element numbers based on the intensity image set.

[0058] Note that the data storage unit 831, the multivariate analysis unit 832, the grouping unit 833, and the reconstruction unit 834 can cooperate with each other and repeat the analysis until a three-dimensional structure of the sample S with high accuracy is obtained. For example, in the multivariate analysis unit 832, as two or more element numbers, for example, 2 is specified, the grouping unit 833 performs grouping, the reconstruction unit 834 performs reconstruction of the sample S, calculates the error between the reconstructed image and the original image, and if the error is large, the multivariate analysis unit 832 increases the element number by 1 and performs the analysis of the grouping unit 833 and the reconstruction unit 834 again, and repeats while increasing the element number by 1 until the error between the reconstructed image (for example, element number 3) and the reconstructed image before the increase in the element number (for example, element number 2) becomes 10% or less. This enables three-dimensional reconstruction of the sample S with high accuracy. Here, the least square error may be adopted for determining the error of the image.

[0059] The analysis device 830 may further include an input terminal (not shown). Thereby, the user can set two or more numbers of elements or arbitrarily set the degree of coincidence between images.

[0060] The electron beam tomography device 800 may further include a display device 840. The display device 840 displays the analysis result of the analysis device 830. When the analysis device 830 does not include an input terminal, the display device 840 may display a user interface and input user input to the analysis device 830. Such a display device 840 is a display device or a projector device.

[0061] The analysis device 830 is not limited as long as it exhibits the above-described functions, but is preferably a computer device including at least a memory, a central processing unit (CPU), a hard disk drive (HDD), a drive device, and a communication control unit. Specifically, an operating system (OS) and an application program (electron beam tomography program) for performing the processes shown in FIG. 1 are stored in the HDD, executed by the CPU, and read from the HDD into the memory. The CPU controls the operations of the drive device, the communication control unit, or the display device 840 according to the content of the application program.

[0062] The electron beam tomography program will be described. The CPU of the computer device executes the electron beam tomography program, receives the data of the electron beam diffraction pattern group detected by the communication control unit, and stores it in the data storage unit 831 (storage function; step S110 (FIG. 1)). Next, the stored data of the electron beam diffraction pattern group is read out, and non-negative matrix factorization (NMF) is performed on the electron beam diffraction pattern group with two or more numbers of elements to create an electron beam diffraction pattern set and a corresponding intensity image set with two or more numbers of elements (multivariate analysis function; step S120 (FIG. 1)).

[0063] Next, the created set of electron diffraction patterns and the corresponding set of intensity images are grouped among a plurality of angles (grouping function; step S130 (FIG. 1)). The grouping function may group the set of electron diffraction patterns for adjacent angles among the plurality of angles using a cross-correlation function. Based on the set of intensity images grouped in this way, the three-dimensional structure of the sample is reconstructed (reconstruction function; step S140 (FIG. 1)). The reconstruction function may reconstruct the three-dimensional structure of the sample for each of two or more numbers of elements. Here too, since steps S110 to S140 are as described above, the description is omitted.

[0064] Although the above application program (electron tomography program) has been described as being stored in an HDD, it may be stored and distributed in a recording medium such as a computer-readable removable disk, or distributed through a network line such as the Internet or a communication control unit and installed in a computer. Note that this recording medium is not a temporary medium such as a carrier wave that does not have a physical form.

Industrial Applicability

[0065] According to the present invention, even if the sample contains substances having different structures but the same composition, these can be distinguished and the three-dimensional structure of the sample can be accurately reconstructed, enabling highly accurate analysis.

Explanation of Signs

[0066] 800 Electron tomography apparatus 810 Transmission electron microscope 811 Sample holder 812 Electron source 813 Condenser lens 815 Objective lens 816 Scan coil 817 Projection lens 818 Aperture 819 Detector 820 Two-dimensional detector 830 Analysis device 831 Data storage unit 832 Multivariate analysis unit 833 Grouping unit 834 Reconstruction unit

Claims

1. 1. An electron tomography method for reconstructing a three-dimensional structure of a sample based on an electron diffraction pattern obtained from the sample, comprising: a step of irradiating the sample with an electron beam from a plurality of angles while scanning the sample, and acquiring a group of electron beam diffraction patterns, the group of electron beam diffraction patterns being made up of a plurality of electron beam diffraction patterns each having information on an angle and a scanning position; performing non-negative matrix factorization (NMF) on the group of electron beam diffraction patterns with an element count of 2 or more to generate an electron beam diffraction pattern set with the element count of 2 or more and a corresponding intensity image set; grouping the set of electron beam diffraction patterns and corresponding set of intensity images between the plurality of angles; reconstructing a three-dimensional structure of the sample based on the grouped intensity image sets; The method includes:

2. The method according to claim 1 , wherein the grouping step groups the sets of electron beam diffraction patterns of adjacent angles among the plurality of angles using a cross-correlation function.

3. The method according to claim 1 or 2, wherein the reconstructing step reconstructs a three-dimensional structure of the sample for each of the two or more numbers of elements.

4. The method according to any one of claims 1 to 3, wherein the step of performing the non-negative matrix factorization, the step of grouping, and the step of reconstructing are repeated by increasing the number of elements of the two or more elements by one.

5. 1. An electron tomography apparatus for reconstructing a three-dimensional structure of a sample based on an electron diffraction image obtained from the sample, comprising: a transmission electron microscope that rotatably holds the sample and irradiates the sample with an electron beam from a plurality of angles while scanning the sample; a two-dimensional detector for detecting an electron beam diffraction pattern of the sample; an analysis device that reconstructs a three-dimensional structure of the sample using a group of electron beam diffraction patterns each of which has information on an angle and a scanning position; Equipped with The analysis device includes: A data storage unit for storing the group of electron beam diffraction patterns; a multivariate analysis unit that performs nonnegative matrix factorization (NMF) on the group of electron beam diffraction patterns with two or more elements to create an electron beam diffraction pattern set with two or more elements and a corresponding intensity image set; a grouping unit that groups the set of electron beam diffraction patterns and the corresponding set of intensity images between the plurality of angles; a reconstruction unit that reconstructs a three-dimensional structure of the sample based on the grouped intensity image sets; The electron beam tomography apparatus further comprises:

6. The electron beam tomography apparatus according to claim 5 , wherein the grouping section groups the sets of electron beam diffraction patterns for adjacent angles among the plurality of angles using a cross-correlation function.

7. The electron beam tomography apparatus according to claim 5 , wherein the reconstruction unit reconstructs a three-dimensional structure of the sample for each of the two or more numbers of elements.

8. 1. An electron tomography program for use in an electron tomography apparatus that reconstructs a three-dimensional structure of a sample based on an electron diffraction image obtained from the sample, comprising: The electron beam tomography apparatus comprises: a transmission electron microscope that rotatably holds the sample and irradiates the sample with an electron beam from a plurality of angles while scanning the sample; a two-dimensional detector for detecting an electron beam diffraction pattern of the sample; an analysis device that reconstructs a three-dimensional structure of the sample using a group of electron beam diffraction patterns each of which has information on an angle and a scanning position; Equipped with A function of storing the group of electron beam diffraction patterns; a multivariate analysis function for performing non-negative matrix factorization (NMF) on the group of electron beam diffraction patterns with two or more elements to generate a set of electron beam diffraction patterns with two or more elements and a corresponding intensity image set; a function of grouping the set of electron beam diffraction patterns and the corresponding set of intensity images between the plurality of angles; a function of reconstructing a three-dimensional structure of the sample based on the grouped intensity image sets; A program that enables a computer to achieve this.

9. 9. The program according to claim 8, wherein the grouping function groups the set of electron beam diffraction patterns for adjacent angles among the plurality of angles using a cross-correlation function.

10. The program according to claim 8 or 9, wherein the function of reconstructing reconstructs a three-dimensional structure of the sample for each of the two or more numbers of elements.

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