A method for correcting image distortion in scanning transmission electron microscope

Abstract

During STEM imaging, the scanning path of the electron probe on the sample is a perfect scanning grid. In the presence of environmental distortion, the fast scanning spacing remains approximately constant. However, the linear and nonlinear offsets between the slow scanning lines may destroy the perfect scanning grid, resulting in linear and nonlinear distortions in the generated image. These distortions become visible as the lattice expands, compresses or shears. The method of correcting STEM image distortion of the present invention is a powerful method for atomic resolution STEM. Compared with traditional methods, the present invention can solve the mismatch problem between the actual 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.

Description

Technical Field

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

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

[0003] During STEM imaging, the electron probe's scan path across the sample follows a perfect scanning grid, consisting of an equidistant grid along both the fast and slow scan directions. The fast scan spacing remains approximately constant in the presence of environmental distortions. However, linear and nonlinear shifts between the slow scan lines disrupt the aforementioned scanning grid. These linear and nonlinear shifts, respectively, produce linear and nonlinear distortions in the resulting image, 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] To correct these distortions in STEM imaging, several methods have been proposed. Currently, mainstream atomic-resolution STEM imaging employs real-time drift correction or the direct summation of spectra from multiple fast dwell times. While these methods offer some improvement, they still introduce artifacts into the measurement when the actual STEM electron probe position does not match the expected position.

[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 achieved through the following technical solution, including the following steps:

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

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

[0011] Step 3. For the nonlinear distortion in step 2, the image with nonlinear distortion is divided into several cross-sections, where each cross-section is regarded as an image with linear distortion, and the distortion value of each image point in the cross-sections is calculated; here, the image is divided into multiple cross-sections according to the crystal structure of the sample in the image with nonlinear distortion.

[0012] Step 4: Based on the coordinates of the image point in the image with linear distortion and the distortion value of the image point, the coordinates of the image point in 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. 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

[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 is made and negative when the compression deformation is made. The relationship between the coordinates of the distorted image pixel and the corresponding original image pixel 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 considered 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 coordinate of the original image point, a j is the shear coefficient of the current intercept surface, with a j =tanθ j , γ j The expansion / compression coefficient of the current intercept surface.

[0029] Furthermore, in 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.

[0030] Furthermore, step 4 twists the distorted image into a parallelogram or a trapezoid based on the calculated coordinates of the original image points.

[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 present invention's method for correcting STEM image distortion is a powerful approach for atomic-resolution STEM. Compared to conventional methods, it can address the mismatch between the true position of the sample and the electron probe in the STEM caused by scanning distortion, thereby correcting 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 Schematic diagram of the distortion value of the expansion distortion along the X-axis;

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

[0037] Figure 5 Flowchart for STEM image distortion correction;

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

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

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

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

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

[0043] Figure 11 This is the SrTiO3 ADF image after correcting 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 described below with reference to 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 follows a perfect scanning grid, including equidistant grids along the fast scanning direction and the slow scanning direction. However, 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 row i and column j 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. The distortion value is as follows: Figure 2 As shown. At this time, the distortion displacement value can be expressed as

[0051] U(i,j)≈ΔX ij =j·d0·tanθ

[0052] Where 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 expansion or compression distortion occurs 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 coordinate of the original image point, 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 controlled 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 subgrid 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 section k is expressed as 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 coordinate of the original image point, a j is the shear coefficient of the current intercept surface, with a j =tanθ j , γ j The expansion / compression coefficient of the current intercept 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 calculates image distortion and shear or expansion / compression coefficients 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. Within each section, the image distortion is corrected for 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 be used to divide the image into sections.

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

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

[0074] Step S2: STEM images were taken using a JEOL JEMARM 200CF scanning transmission electron microscope. 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, dashed lines indicate distortion of the material lattice into diagonal or curved lines. Uncorrected STEM images must first be filtered and their atomic columns located to accurately calculate image distortion values ​​and shear or expansion / compression coefficients. This step can be performed using DigitalMicrograph software.

[0076] For nonlinear distortion images, the material crystal structure and the positioning of the atomic column 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. According to the distortion type, the STEM image lattice is corrected back to the correct crystal structure. The final result is as follows: Figures 9 to 11 shown.

[0077] It is important to note that this method in step S3 does not completely correct the distortion; rather, it maximizes the correction of the deformed lattice back to a slightly distorted one, thereby improving the interpretability of the distorted STEM data. Furthermore, this method requires prior knowledge of the crystal structure, but not detailed lattice parameters.

Claims

1. A method for correcting distortion of a scanning transmission electron microscope image, characterized in that: The following steps are involved: Step 1: Obtain an uncorrected scanning transmission electron microscope image and calculate the distortion value of each image point in the image; the distortion value is the displacement of the image point relative to the corresponding node on the scanning transmission electron microscope scanning grid; Step 2: determining the type of distortion in the image, where 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 several sections, where each section is regarded as an image with linear distortion, and the distortion value of each pixel in the sections is calculated; the image is divided into multiple sections k according to the crystal structure of the sample in the image with nonlinear distortion; the x direction of each section k is regarded as linear distortion, and the shear coefficient of the section k 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 coordinate of the original image point, 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 coordinates of the corresponding original image points is expressed as Step 4: Based on the coordinates of the image point in the image with linear distortion and the distortion value of the image point, the coordinates of the image point in the original image without distortion corresponding to the image point are calculated to complete the correction.

2. The method for correcting the distortion of a scanning transmission electron microscope image 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 the distortion of a scanning transmission electron microscope image according to claim 1, wherein: The linear distortion in step 4 includes linear shear strain and expansion / compression distortion.

4. The method for correcting distortion of a scanning transmission electron microscope image according to claim 3, wherein: 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, and X′ and Y′ as the coordinates of the distorted image point, then 5. The method for correcting distortion of a scanning transmission electron microscope image according to claim 3, wherein: 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 coordinates is:

6. The method for correcting distortion of a scanning transmission electron microscope image according to claim 1, wherein: 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.

7. The method for correcting distortion of a scanning transmission electron microscope image according to claim 1, wherein: Step 4: Based on the calculated coordinates of the original image points, the distorted image is twisted into a parallelogram or a trapezoid.

8. The method for correcting distortion of a scanning transmission electron microscope image according to claim 1, wherein: Before calculating the image distortion value, it is necessary to first filter the uncorrected STEM image and perform atomic column positioning on the image.

Images