Method for correcting image distortion of scanning transmission electron microscope

Abstract

In the STEM imaging process, the scanning path of an electron probe on a sample is a perfect scanning grid, under the condition that environment distortion exists, the rapid scanning interval is kept approximately constant, however, linear and non-linear deviation between slow scanning rows may damage the perfect scanning grid, and linear and non-linear distortion is generated in a generated image. These distortions may become visible as the lattice expands, compresses or shears. The method for correcting the STEM image distortion is a powerful method for atomic resolution of the STEM. Compared with the traditional method, the method can solve the problem of mismatching between the real position of the sample and the position of the electronic probe in the STEM caused by scanning distortion, and corrects the distortion of the STEM image.

Description

Technical Field

[0001] The invention relates to the field of scanning transmission electron microscope characterization, and in particular to a method for correcting the distortion of a scanning transmission electron microscope image. Background Art

[0002] Scanning transmission electron microscopy (STEM) focuses the electron beam into an atomic-scale beam spot and uses electromagnetic coils to control the electron beam to scan point by point on the sample surface. At each electron probe position, imaging signals, analytical signals or diffraction patterns can be obtained simultaneously.

[0003] During STEM imaging, the scanning path of the electron probe on the sample is a perfect scanning grid, including an equidistant grid along the fast scan direction and the slow scan direction. In the presence of environmental distortion, the fast scan spacing remains approximately constant, however, the linear and nonlinear offsets between the slow scan lines will destroy the aforementioned scanning grid. These linear and nonlinear offsets produce linear and nonlinear distortions in the generated image, respectively, which become visible as the lattice expands, compresses or shears.

[0004] When acquiring high-quality images, spectra or diffraction images, a single electron probe needs to stay at the sampling position longer. The longer pixel exposure time further exacerbates the problem of linear and nonlinear distortion in STEM imaging, reduces the atomic resolution of the image, and limits the reliability of the results.

[0005] In order to correct these distortions in STEM imaging, some methods have been proposed in the related field. The current mainstream atomic resolution STEM imaging uses real-time drift correction or directly sums the spectra of multiple fast dwell times. These methods have improved the distortion problem, but when the actual STEM electron probe position does not match the expected position, artifacts will still be introduced into the measurement.

[0006] In order to further optimize the image distortion problem, a new distorted image correction method is urgently needed. Summary of the invention

[0007] In view of the problems existing in the prior art, the present invention provides a method for correcting linear distortion and nonlinear distortion of atomic resolution STEM images.

[0008] The present invention is implemented by the following technical solution, comprising the following steps:

[0009] Step 1, obtaining an uncorrected scanning transmission electron microscope image, and calculating the distortion value of each image point of the image; the distortion value is the displacement of the image point relative to the corresponding node on the scanning grid of the scanning transmission electron microscope;

[0010] Step 2: determining the type of distortion of the image, wherein the distortion type includes linear distortion and nonlinear distortion;

[0011] Step 3. With respect to the nonlinear distortion in step 2, the image with nonlinear distortion is divided into a plurality of cross-sections, wherein each cross-section is regarded as an image with linear distortion, and the distortion value of each image point in the plurality of cross-sections is calculated. Here, the image is divided into a plurality of cross-sections according to the crystal structure of the sample in the image with nonlinear distortion.

[0012] Step 4: According to the coordinates of the image point of the image with linear distortion and the distortion value of the image point, the coordinates of the image point of the original image without distortion corresponding to the image point are calculated to complete the correction.

[0013] Furthermore, the scanning direction of the scanning transmission electron microscope includes a fast scanning direction and a slow scanning direction. Assume that the fast scanning direction is the x direction and the slow scanning direction is the y direction. For the image point corresponding to the node of row i and column j of the scanning grid, ΔX ij Indicates the distortion value of the image point along the x direction, ΔY ij represents the distortion value of the image point along the y direction, then the distortion value of the image point can be expressed as

[0014] U(i,j)=ΔX ij +ΔY ij .

[0015] Furthermore, the linear distortion in step 4 includes linear shear strain and expansion / compression distortion.

[0016] Furthermore, linear shear distortion occurs in the slow scanning direction, and its distortion value can be expressed as

[0017] U(i,j)≈ΔX ij =j·d0·tanθ

[0018] Where d0 is the unit grid spacing, tanθ is the shear coefficient, which is denoted as a in the following formula; define X and Y as the coordinates of the original image point, and X′ and Y′ as the coordinates of the distorted image point, then

[0019]

[0020] Furthermore, the distortion value of expansion / compression distortion is

[0021] U(i,j)≈ΔX ij +ΔY ij =i·d0·γ x +i·d0·γ y

[0022] Among them, γ x and γy is the expansion / compression coefficient along the x-direction and y-direction. The coefficient is positive when the expansion deformation occurs and negative when the compression deformation occurs. The relationship between the coordinates of the distorted image point and the corresponding original image point is:

[0023]

[0024] Furthermore, the image with nonlinear distortion is divided into multiple cut planes k, and the x direction of each cut plane is regarded as linear distortion, and the shear coefficient is tanθ j ; The y direction has the same distortion value d j , j k represents the value of j·d0 in each cut surface k, then the distortion value at row i and column j on the cut surface is expressed as

[0025]

[0026] The relationship between the coordinates of the distorted image points on each cut surface and the coordinates of the corresponding original image points is expressed as

[0027]

[0028] X j ′、Y j ′ is the coordinate of the distorted image point, X j , Y j is the original image point coordinate, a j is the shear coefficient of the current intercept surface, with a j =tanθ j , γ j It is the expansion / compression coefficient of the current interception surface.

[0029] Furthermore, the method for determining whether the image has linear distortion in step 2 is to check whether the shear coefficient of the entire uncorrected scanning transmission electron microscope image is constant and whether the expansion / compression ratio is linearly related. If so, linear distortion exists; otherwise, nonlinear distortion exists.

[0030] Furthermore, in step 4, the distorted image is twisted into a parallelogram or a trapezoid according to the calculated coordinates of the original image pixels.

[0031] Furthermore, before calculating the image distortion value, it is necessary to first filter the uncorrected STEM image and perform atomic column positioning on the image.

[0032] The method for correcting STEM image distortion of the present invention is a powerful method for atomic resolution STEM. Compared with the traditional method, the present invention can solve the mismatch problem between the real position of the sample in STEM and the position of the electron probe caused by scanning distortion, and correct the distortion in the STEM image. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Figure 1 Schematic diagram of different types of STEM images;

[0034] Figure 2 Schematic diagram of distortion value of shear distortion;

[0035] Figure 3 It is a schematic diagram of the distortion value of the expansion distortion along the X-axis direction;

[0036] Figure 4 Schematic diagram of distortion value of nonlinear distortion;

[0037] Figure 5 This is the flow chart of STEM image distortion correction;

[0038] Figure 6 ADF image of La2CuO4 with shear distortion;

[0039] Figure 7 ADF image of La2CuO4 with expansion distortion;

[0040] Figure 8 It is the nonlinearly distorted SrTiO3 ADF image;

[0041] Fig. 9 This is the ADF image of La2CuO4 after correcting the linear shear distortion;

[0042] Fig.10 This is the La2CuO4 ADF image after correcting the linear expansion distortion;

[0043] Fig.11 This is the SrTiO3 ADF image after correcting the nonlinear distortion.

[0044] against Figure 1 , where (a) is the scanning path of the electron probe in STEM mode, (b) is the scanning path with shear distortion, (c) is the scanning path with expansion distortion, and (d) is the scanning path with nonlinear distortion. DETAILED DESCRIPTION

[0045] The present invention will be further explained below in conjunction with the accompanying drawings and specific embodiments. It should be understood that the following specific embodiments are only used to illustrate the present invention and are not used to limit the scope of the present invention.

[0046] During STEM imaging, the scanning path of the electron probe on the sample is a perfect scanning grid, including equidistant grids along the fast scanning direction and the slow scanning direction, but in the presence of environmental distortion, the fast scanning spacing remains approximately constant, however, linear and nonlinear offsets between slow scanning lines may destroy the perfect scanning grid.

[0047] Therefore, these linear and nonlinear shifts produce linear and nonlinear distortions in the resulting image, respectively. These distortions become visible as the lattice expands, compresses, or shears. Linear and nonlinear distortions are classified by checking whether the shear and expansion / compression ratios are constant or linear across the image, e.g. Figure 1 shown.

[0048] Considering the displacement between the distorted image and the ideal image, the distortion value is defined as the displacement of all nodes between the distorted image and the ideal grid. The distortion value will have x and y components corresponding to the displacement along the x-axis (fast scanning direction) and y-axis (slow scanning direction), respectively. U(i, j) represents the displacement value of the node at the i-row and j-column of the scanning grid, that is,

[0049] U(i,j)=ΔX ij +ΔY ij .

[0050] For linear shear strain, the scanning grid in the fast scanning direction remains basically unchanged, while the scanning grid in the slow scanning direction is distorted, and its distortion value is as follows: Figure 2 At this time, the distortion displacement value can be expressed as

[0051] U(i,j)≈ΔX ij =j·d0·tanθ

[0052] Among them, tanθ is the shear coefficient, denoted as a in the following formula; d0 is the unit grid spacing.

[0053] Define X', Y' as the coordinates of the distorted image, X, Y as the initial image coordinates, then

[0054]

[0055] For expansion or compression distortion, the scanning grid spacing value changes, as shown in the schematic diagram. Figure 3 As shown, this displacement value can be expressed as

[0056] U(i,j)≈ΔX ij =i·d0·γ x .

[0057] If there is expansion or compression distortion along the Y axis, use γ x and γ yRepresents the expansion / compression coefficient along the x-axis and y-axis. The coefficient is positive when the deformation is expanded and negative when the deformation is compressed.

[0058] U(i,j)≈ΔX ij +ΔY ij =i·d0·γ x +i·d0·γ y .

[0059] At this time, the coordinates of the distorted image can be expressed as

[0060]

[0061] Where X j ′,Y j ′ is the coordinate of the distorted image point, X j , Y j is the original image point coordinate, a j is the shear coefficient of the current intercept surface, with a j =tanθ j , γ j is the expansion / compression coefficient of the current cut surface. Figure 3 In the figure, the expansion deformation is mainly along the x-axis direction, so γ y ≈0.

[0062] For nonlinear distortion, a row of grids is divided into multiple subgrids, each of which is a cut surface. In each cut surface k, the x displacement can be regarded as linear distortion, and the y displacement can be reduced by making each cut surface have the same y value, i.e., d j The size is simply corrected. j is the shear coefficient of sub-grid k, and ΔX ij Indicates that the linear shear distortion value in the x direction at the node in the i-th row and j-th column is

[0063] ΔX ij =j·d0·tanθ j .

[0064] The value of j·d0 in each cut surface k is expressed by j k Indicates that Figure 4 As shown, the nonlinear displacement can be expressed as:

[0065]

[0066] The distortion of each cut surface is corrected, and the coordinates of the distorted image on each cut surface can be expressed as:

[0067]

[0068] Where X j ′,Y j′ is the coordinate of the distorted image point, X j , Y j is the original image point coordinate, a j is the shear coefficient of the current intercept surface, with a j =tanθ j , γ j It is the expansion / compression coefficient of the current interception surface.

[0069] The correction of linear or nonlinear distortion of the above STEM images will be implemented based on Digital Micrograph software. The specific process is as follows: Figure 5 As shown in the flow chart.

[0070] The process first requires calculating the image distortion and shear coefficient or expansion / compression coefficient from the acquired ADF image. For linear distortion, the image is corrected by twisting it into a parallelogram or trapezoid. For nonlinear image distortion, the STEM image and SI data are divided into subsections, corresponding to each unit cell. In each cross-section, the image distortion can be corrected with reference to the linear distortion. Each segment of the image is divided based on the position of the center of the selected atomic column.

[0071] In order to improve the accuracy of atomic column centering, it is usually necessary to filter the input ADF image. After locating the center of the atomic column, each selected atomic center will become the boundary of the slice and is used to divide the image into sections.

[0072] This embodiment takes La2CuO4 and SrTiO3 thin film materials as examples to correct linear and nonlinear distorted STEM images respectively.

[0073] Step S1: Thin films were deposited on LaSrAlO4 and NdGaO3 substrates by laser pulse deposition, respectively. Standard procedures were used for TEM sample preparation, including mechanical grinding, tripod polishing, argon ion beam milling, and plasma cleaning.

[0074] Step S2: STEM was taken using a JEOL JEMARM 200CF scanning transmission electron microscope to obtain uncorrected STEM images. The operating voltage was 200 KV, the convergence half angle was 20.4 mrad, and the probe size was The acquisition process can be equipped with an EDX detector and an electron energy loss spectrometer to synchronously acquire SI signals.

[0075] Step S3: The uncorrected STEM spectra of La2CuO4 and SrTiO3 are as follows: Figures 6 to 8As shown, the dotted line indicates that the material lattice is distorted into an oblique line or curve. The uncorrected STEM image must be filtered first, and then the atomic column is positioned to calculate the accurate image distortion value and shear coefficient or expansion / compression coefficient. This step can be implemented based on DigitalMicrograph software.

[0076] For nonlinear distortion images, the material crystal structure and the positioned atomic columns can be divided into multiple cross-sections. Each cross section can be approximately regarded as a linear distortion, and the corresponding shear coefficient or expansion / compression coefficient can be calculated. The STEM image lattice is corrected back to the correct crystal structure according to the distortion type. The final result is as follows: Figures 9 to 11 shown.

[0077] It should be noted that the method used in step S3 above does not completely correct the distortion. Instead, it maximally corrects the deformed lattice back to a slightly distorted lattice, thereby improving the interpretability of the distorted STEM data. At the same time, this method requires prior knowledge of the crystal structure, but does not require detailed lattice parameters.

Claims

1. A method for correcting the distortion of a scanning transmission electron microscope image, characterized in that: The following steps are involved: Step 1, obtaining an uncorrected scanning transmission electron microscope image, and calculating the distortion value of each image point of the image; the distortion value is the displacement of the image point relative to the corresponding node on the scanning grid of the scanning transmission electron microscope; Step 2: determining the type of distortion of the image, wherein the distortion type includes linear distortion and nonlinear distortion; Step 3: for the nonlinear distortion in step 2, the image with nonlinear distortion is divided into a plurality of cut surfaces, wherein each cut surface is regarded as an image with linear distortion, and the distortion value of each image point in the plurality of cut surfaces is calculated; Step 4: According to the coordinates of the image point of the image with linear distortion and the distortion value of the image point, the coordinates of the image point of the original image without distortion corresponding to the image point are calculated to complete the correction.

2. The method for correcting image distortion according to claim 1, characterized in that: The scanning direction of the scanning transmission electron microscope includes a fast scanning direction and a slow scanning direction. Let the fast scanning direction be the x direction and the slow scanning direction be the y direction. For the image point corresponding to the node of row i and column j of the scanning grid, ΔX ij Indicates the distortion value of the image point along the x direction, ΔY ij represents the distortion value of the image point along the y direction, then the distortion value of the image point can be expressed as U(i,j)=ΔX ij +ΔY ij 。 3. The method for correcting image distortion according to claim 1, characterized in that: The linear distortion in step 4 includes linear shear strain and expansion / compression distortion.

4. The method for correcting image distortion according to claim 3, characterized in that: Linear shear distortion occurs in the slow scanning direction, and its distortion value can be expressed as U(i,j)≈ΔX ij =j·d0·tanθ Where d0 is the unit grid spacing, tanθ is the shear coefficient, which is denoted as a in the following formula; define X and Y as the coordinates of the original image point, X ′ , Y ′ is the coordinate of the distorted image point, then 5. The method for correcting image distortion according to claim 3, characterized in that: The distortion value of expansion / compression distortion is U(i,j)≈ΔX ij +ΔY ij =i·d0·γ x +i·d0·γ y Among them, γ x and γ y is the expansion / compression coefficient along the x-direction and y-direction. The coefficient is positive when the expansion deformation occurs and negative when the compression deformation occurs. The relationship between the coordinates of the distorted image point and the corresponding original image point is:

6. The method for correcting image distortion according to claim 1, characterized in that: Step 3 divides the image into a plurality of cut surfaces k according to the crystal structure of the sample in the image with nonlinear distortion.

7. The method for correcting image distortion according to claim 6, characterized in that: The x-direction of each intercept surface k is considered to be linearly distorted, and the shear coefficient of the intercept surface is tanθ j ; The y direction has the same distortion value d j ;j k represents the value of j·d0 in k, then the distortion value at row i and column j on the cut surface k is expressed as Define X′ j , Y′ j is the coordinate of the distorted image point, X j , Y j is the original image point coordinate, a j is the shear coefficient of the current intercept surface, a j =tanθ j , γ j is the expansion / compression coefficient of the current cut surface, then the relationship between the coordinates of the distorted image points on each cut surface and the corresponding original image points is expressed as 8. The method for correcting image distortion according to claim 1, characterized in that: Step 2: The method for determining whether the image has linear distortion is to check whether the shear coefficient of the entire uncorrected scanning transmission electron microscope image is constant and whether the expansion / compression ratio is linearly related. If so, linear distortion exists; otherwise, nonlinear distortion exists.

9. The method for correcting image distortion according to claim 1, characterized in that: Step 4: According to the calculated coordinates of the original image pixels, the distorted image is twisted into a parallelogram or a trapezoid.

10. The method for correcting image distortion according to claim 1, characterized in that: Before calculating the image distortion value, the uncorrected STEM image needs to be filtered and the atomic columns of the image need to be located.

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