Electronic lamination imaging method, device and equipment combining local track and plane wave

Abstract

The invention relates to the technical field of scanning transmission electron microscopy, in particular to an electron lamination imaging method, device and equipment combining a local orbit and a plane wave, and the method comprises the steps: obtaining the actual diffraction intensity generated when an electron beam scans a sample and is located at each scanning position; initializing to-be-optimized parameters of all scanning positions; calculating beam spot functions of all scanning positions and potential function distribution of each layer of the sample; the diffraction intensity is calculated according to the beam spot function and the potential function distribution, the loss value of the loss function is calculated according to the actual diffraction intensity and the calculated diffraction intensity, the to-be-optimized parameters are updated by using the loss value until the loss function is converged, and the advantage of the local orbit in representing high spatial frequency information and the advantage of the plane wave in representing low spatial frequency are combined. And a more accurate sample potential function is obtained. Therefore, the problem that high-precision phase reconstruction is difficult to perform due to the lack of capability of simultaneously and accurately representing high-frequency and low-frequency information in the prior art is solved.

Description

Technical Field

[0001] The present application relates to the field of scanning transmission electron microscopy technology, and in particular to an electron stack imaging method, device and equipment combining local orbits and plane waves. Background Art

[0002] The existing stack imaging method cannot take into account both high and low spatial frequency information, resulting in limited accuracy in reconstructing the charge density distribution and atomic orbitals of the sample, and cannot clearly characterize the spatial distribution of the electronic structure. At the same time, high-precision characterization of the potential function distribution also requires high computational accuracy and efficiency, and existing algorithms are difficult to fit the diffraction signals of the nucleus and inner and outer electrons. Summary of the invention

[0003] The present application provides an electronic stack imaging method, device and equipment combining local orbits and plane waves to solve the problem that the related technology lacks the ability to accurately represent high-frequency and low-frequency information at the same time and is difficult to reconstruct the phase with high precision.

[0004] The first aspect of the present application provides an electron stack imaging method combining local orbits and plane waves, comprising the following steps: obtaining the actual diffraction intensity generated when the electron beam is located at each scanning position when scanning the sample; initializing the parameters to be optimized for all scanning positions, wherein the parameters to be optimized include the local orbit expansion coefficient, the plane wave Fourier coefficient, each order aberration coefficient and the electron beam intensity; calculating the beam spot function of all scanning positions according to the each order aberration coefficient and the electron beam intensity, and calculating the potential function distribution of each layer of the sample according to the local orbit expansion coefficient and the plane wave Fourier coefficient; calculating the diffraction intensity according to the beam spot function and the potential function distribution, calculating the loss value of the loss function according to the actual diffraction intensity and the calculated diffraction intensity, and using the loss value to update the parameters to be optimized until the loss function converges to the target value; and realizing electron stack imaging using the potential function distribution of each layer of the sample after the loss function converges.

[0005] Optionally, the calculation formula of the beam spot function is:

[0006]

[0007] Where i and j are the matrix coordinates of the scanning position; k is the inverse space vector; represents the two-dimensional Fourier transform, χ i,j (k) is the aberration function; A(k) is the aperture function; s i,j is the arithmetic square root of the electron beam intensity at the i,jth scanning position.

[0008] Optionally, the potential function is calculated as:

[0009]

[0010] Among them, r is the real space coordinate; l represents the longitudinal coordinate of the sample potential function distribution; φ i (r) is the basis function of the i-th local orbital; c i,l is the corresponding expansion coefficient; R i,l is the center position of the local orbital; G is the reciprocal space vector, a l,G are the corresponding Fourier coefficients.

[0011] Optionally, the diffraction intensity is calculated according to the beam spot function and the potential function distribution, including: generating an exit wave function according to the beam spot function and the potential function distribution; and using the exit wave function to calculate the diffraction intensity when the electron beam is scanned at each scanning position.

[0012] Optionally, the calculation formula of the output wave function is:

[0013]

[0014] Among them, O l (r) is the sample potential function of the lth layer; is the propagation operator of Fresnel diffraction; P i,j (r) represents the beam spot function at the i,jth scanning position.

[0015] Optionally, the loss function is calculated as:

[0016]

[0017] Where u and v are the coordinates of the diffraction intensity matrix; I i,j Diffraction intensity matrix collected by scanning transmission electron microscopy.

[0018] Optionally, the localized tracks represent high spatial frequency information and the plane waves represent low spatial frequency information.

[0019] The second aspect of the present application provides an electron stack imaging device that combines local orbits and plane waves, including: an acquisition module, used to acquire the actual diffraction intensity generated when the electron beam is located at each scanning position when scanning the sample; an initialization module, used to initialize the parameters to be optimized at all scanning positions, wherein the parameters to be optimized include local orbit expansion coefficients, plane wave Fourier coefficients, aberration coefficients of various orders and electron beam intensity; a calculation module, used to calculate the beam spot function of all scanning positions according to the aberration coefficients of various orders and the electron beam intensity, and calculate the potential function distribution of each layer of the sample according to the local orbit expansion coefficient and the plane wave Fourier coefficient; an update module, used to calculate the diffraction intensity according to the beam spot function and the potential function distribution, calculate the loss value of the loss function according to the actual diffraction intensity and the calculated diffraction intensity, and use the loss value to update the parameters to be optimized until the loss function converges; an imaging module, used to realize electron stack imaging using the potential function distribution of each layer of the sample after the loss function converges.

[0020] The third aspect of the present application provides an electronic device, including: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the electronic stack imaging method combining local orbits and plane waves according to the first aspect.

[0021] The fourth aspect of the present application provides a computer-readable storage medium having a computer program stored thereon, which is executed by a processor to implement the electronic stack imaging method combining local orbits and plane waves according to the first aspect.

[0022] Therefore, this application includes the following beneficial effects:

[0023] The embodiment of the present application first obtains the actual diffraction intensity generated when the electron beam scans the sample at each scanning position, then initializes the parameters to be optimized at all scanning positions, calculates the beam spot function of all scanning positions, and then calculates the potential function distribution of each layer of the sample, calculates the diffraction intensity based on the beam spot function and the potential function distribution, calculates the loss value of the loss function based on the actual diffraction intensity and the calculated diffraction intensity, and uses the loss value to update the parameters to be optimized until the loss function converges. Finally, the potential function distribution of each layer of the sample after the loss function converges is used to realize electron stack imaging, combining the advantages of local orbits in representing high spatial frequency information and the advantages of plane waves in representing low spatial frequencies, and obtaining a more accurate sample potential function. Thus, the problem that the related technology lacks the ability to accurately represent high-frequency and low-frequency information at the same time and is difficult to reconstruct the phase with high precision is solved.

[0024] Additional aspects and advantages of the present application will be given in part in the description below, and in part will become apparent from the description below, or will be learned through the practice of the present application. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] The above and / or additional aspects and advantages of the present application will become apparent and easily understood from the following description of the embodiments in conjunction with the accompanying drawings, in which:

[0026] Figure 1 A flowchart of an electron stack imaging method combining local orbits and plane waves provided according to an embodiment of the present application;

[0027] Figure 2 A calculation flow chart provided according to an embodiment of the present application;

[0028] Figure 3 A schematic diagram of the structure of iron oxide along the [10-1] direction according to an embodiment of the present application;

[0029] Figure 4 A schematic diagram of the phase of a beam spot function obtained by calculation according to an embodiment of the present application;

[0030] Figure 5 A schematic diagram of the beam spot function amplitude obtained by calculation according to an embodiment of the present application;

[0031] Figure 6 A schematic diagram of a local orbital potential function calculated according to an embodiment of the present application;

[0032] Figure 7 is the local orbit expansion coefficient c calculated according to one embodiment of the present application i,l Schematic diagram;

[0033] Figure 8 A schematic diagram of a plane wave potential function obtained by calculation according to an embodiment of the present application;

[0034] Fig. 9 is the plane wave Fourier coefficient a calculated according to one embodiment of the present application l,G Schematic diagram;

[0035] Fig.10 This is an example diagram of an electron stack imaging device combining local orbits and plane waves provided according to an embodiment of the present application;

[0036] Fig.11 It is a schematic diagram of the structure of an electronic device provided according to an embodiment of the present application. DETAILED DESCRIPTION

[0037] The embodiments of the present application are described in detail below, and examples of the embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar elements or elements having the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are intended to be used to explain the present application, and should not be construed as limiting the present application.

[0038] The following describes the electron stack imaging method, device and equipment combining local orbit and plane wave in the embodiment of the present application with reference to the accompanying drawings. In view of the problem that the related technology mentioned in the above background technology lacks the ability to accurately represent high-frequency and low-frequency information at the same time, and it is difficult to reconstruct the phase with high precision, the present application provides an electron stack imaging method combining local orbit and plane wave, in which the actual diffraction intensity generated when the electron beam scans the sample at each scanning position is first obtained, then the parameters to be optimized at all scanning positions are initialized, the beam spot function of all scanning positions is calculated, and then the potential function distribution of each layer of the sample is calculated, the diffraction intensity is calculated according to the beam spot function and the potential function distribution, the loss value of the loss function is calculated according to the actual diffraction intensity and the calculated diffraction intensity, the loss value is used to update the parameters to be optimized until the loss function converges, and finally the potential function distribution of each layer of the sample after the loss function converges is used to realize electron stack imaging, combining the advantages of local orbit in representing high spatial frequency information and the advantages of plane wave in representing low spatial frequency, and obtaining a more accurate sample potential function. Thus, the problem that the related technology lacks the ability to accurately represent high-frequency and low-frequency information at the same time, and it is difficult to reconstruct the phase with high precision is solved.

[0039] Specifically, Figure 1 A schematic flow chart of an electron stack imaging method combining local orbits and plane waves provided in an embodiment of the present application.

[0040] like Figure 1 As shown, the electron stack imaging method combining local orbit and plane wave includes the following steps:

[0041] In step S101, the actual diffraction intensity generated when the electron beam is located at each scanning position when scanning the sample is obtained.

[0042] The actual diffraction intensity is the diffraction pattern formed by electrons scattered from the sample collected when the electron beam scans the surface of the sample, which is specifically manifested as the electron intensity distribution at different positions.

[0043] It can be understood that the embodiments of the present application can use an electron beam to scan the sample and obtain the actual diffraction intensity generated when the electron beam is located at each scanning position when scanning the sample.

[0044] In step S102, the parameters to be optimized of all scanning positions are initialized, wherein the parameters to be optimized include local orbit expansion coefficients, plane wave Fourier coefficients, aberration coefficients of various orders and electron beam intensity.

[0045] Among them, the local orbit refers to the orbital function concentrated near the nucleus or in certain specific areas, which is usually approximated by a set of local basis functions; the plane wave is a simple form of wave, and each point in the diffraction pattern in the embodiment of the present application represents a plane wave; the aberration coefficients of each order involve the aberrations generated in the imaging process and are represented by the aberration function.

[0046] It is understandable that the embodiment of the present application needs to initialize the local orbit expansion coefficients, plane wave Fourier coefficients, aberration coefficients of each order and electron beam intensity of all scanning positions, and use these initialized parameters to be optimized as the basis for subsequent iterative optimization.

[0047] In the embodiment of the present application, the localized tracks represent high spatial frequency information and the plane waves represent low spatial frequency information.

[0048] Among them, high spatial frequency information refers to the characteristics that change rapidly in space, corresponding to the steeply changing areas in the potential function, such as the rapidly changing nuclei and core electron parts in the potential function; low spatial frequency information refers to the characteristics that change slowly in space, such as the relatively smooth and slowly changing valence electron part in the potential function. The high spatial frequency local orbital part captures the high-frequency oscillating potential function characteristics, and the low spatial frequency plane wave part describes the low-frequency smooth potential function characteristics.

[0049] It can be understood that the embodiments of the present application use local orbits to describe the high spatial frequency information in the sample, that is, those parts with steep changes, and use plane waves to represent the low spatial frequency information in the sample, that is, the parts with gentle changes. By combining the information of the two, it is possible to accurately represent both high-frequency and low-frequency information at the same time, and obtain a more complete and accurate description.

[0050] In step S103, the beam spot function of all scanning positions is calculated according to the aberration coefficients of each order and the electron beam intensity, and the potential function distribution of each layer of the sample is calculated according to the local orbital expansion coefficient and the plane wave Fourier coefficient.

[0051] The beam spot function represents the characteristics of the electron beam spot formed at each scanning position when the electron beam passes through the sample. The calculation method will be described in detail below and will not be repeated here.

[0052] It can be understood that the embodiment of the present application first calculates the beam spot function at each position based on the aberration coefficients of each order and the electron beam intensity at each scanning position, and then uses the local orbital expansion coefficient and the plane wave Fourier coefficient to respectively calculate the potential function distribution of each layer of the sample, that is, the local orbit is combined to accurately capture the local rapidly changing atomic nuclei and inner shell electron parts in the sample, and the plane wave is used to represent the relatively smooth and slowly changing valence electron part. Through this method, high-frequency and low-frequency information can be accurately represented at the same time, and the details of the internal structure of the sample and its overall trend can be reconstructed more accurately.

[0053] In the embodiment of the present application, the calculation formula of the beam spot function is:

[0054]

[0055] Where i and j are the matrix coordinates of the scanning position; k is the inverse space vector; represents the two-dimensional Fourier transform, χ i,j (k) is the aberration function; A(k) is the aperture function; s i,j is the arithmetic square root of the electron beam intensity at the i,jth scanning position.

[0056] Specifically, χ i,j (k) is the aberration function, which is expanded as:

[0057]

[0058] Among them, Real{·} represents taking the real part of each element in the matrix, C n,m,i,j is the aberration coefficient C of the i,jth scanning position m,m , that is, the aberration coefficients of each order, R 2 (ω) represents other higher-order expansion terms above the second order in the aberration, where ω is the complex number representation of the reciprocal space vector k, and its value is defined as ω = k u +i·k v , where k u and k v is the inverse space coordinate, represents the conjugate matrix of ω.

[0059] In the embodiment of the present application, the calculation formula of the potential function is:

[0060]

[0061] Among them, r is the real space coordinate; l represents the longitudinal coordinate of the sample potential function distribution; φ i (r) is the basis function of the i-th local orbital; c i,l is the corresponding expansion coefficient; R i,l is the center position of the local orbital; G is the reciprocal space vector, al,G are the corresponding Fourier coefficients.

[0062] It should be noted that the potential function O l (r) is the superposition of the local orbital part and the plane wave part, that is, in, is the local orbital potential function, is the plane wave potential function, corresponding to the above potential function calculation formula,

[0063] In step S104, the diffraction intensity is calculated according to the beam spot function and the potential function distribution, the loss value of the loss function is calculated according to the actual diffraction intensity and the calculated diffraction intensity, and the loss value is used to update the parameter to be optimized until the loss function converges to the target value.

[0064] Among them, the potential function distribution describes the potential distribution inside the sample; the diffraction intensity is calculated based on the beam spot function and the potential function distribution, representing the theoretical diffraction pattern intensity distribution. The calculation method will be described in detail below and will not be repeated here; the loss function is used to quantify the difference between the current diffraction intensity calculated based on the beam spot function and the potential function distribution and the actual diffraction intensity, and optimize the parameters by minimizing the loss value; the target value is set according to actual needs and is not specifically limited here; the method of using the loss value to update the parameters to be optimized until the loss function converges to the target value will be described in detail below and will not be repeated here.

[0065] It can be understood that the embodiment of the present application first uses the beam spot function and the potential function distribution to calculate the diffraction intensity, compares these diffraction intensities with the actual diffraction intensities obtained by actual measurement, and calculates the loss value, which reflects the gap between the prediction and the actual observation. This loss value is used as feedback to adjust the parameters to be optimized to reduce the difference between the theoretical calculation and the actual situation. This process is repeated until the loss function converges, that is, the parameter set that most accurately reflects the actual potential function distribution of the sample is found, thereby achieving high-precision reconstruction of the sample structure.

[0066] In an embodiment of the present application, the diffraction intensity is calculated according to the beam spot function and the potential function distribution, including: generating an exit wave function according to the beam spot function and the potential function distribution; and using the exit wave function to calculate the diffraction intensity when the electron beam is located at each scanning position.

[0067] The generation of the output wave function will be described in detail below and will not be repeated here.

[0068] It can be understood that the embodiment of the present application utilizes the currently estimated beam spot function and potential function distribution to generate an exit wave function, and then uses this exit wave function to calculate the diffraction intensity when the electron beam scans each scanning position of the sample.

[0069] In the embodiment of the present application, the calculation formula of the output wave function is:

[0070]

[0071] Among them, O l (r) is the sample potential function of the lth layer; is the propagation operator of Fresnel diffraction; P i,j (r) represents the beam spot function at the i,jth scanning position.

[0072] In the embodiment of the present application, the calculation formula of the loss function is:

[0073]

[0074] Where u and v are the coordinates of the diffraction intensity matrix; I i,j Diffraction intensity matrix collected by scanning transmission electron microscopy.

[0075] It should be noted that the loss value is used to update the parameters to be optimized until the loss function converges to the target value. First, the loss function needs to be calculated. Regarding the gradient of each parameter to be optimized, for θ t =c i,l ,a l,G ,C n,m,i,j ,s i,j Each parameter to be optimized, where c i,l is the local orbital expansion coefficient, a l,G is the plane wave Fourier coefficient, C n,m,i,j is the aberration coefficient of each order, s i,j is the electron beam intensity, and the target parameter is updated using the calculated gradient: Where α is the learning rate of each parameter, ∈ is the calculation precision, and is the first-order and second-order momentum estimate of the gradient, where β 1 and β 2 are the decay rates of the first-order and second-order momentum estimates, respectively. The various parameters in the update process are optimized using gradient optimization algorithms such as the Adam algorithm, SGD algorithm, and Adagrad algorithm. The specific algorithm is selected according to the actual situation and is not specifically limited here. Finally, the loss function is recalculated using the updated parameters. , repeat the steps of calculating the beam spot function to updating the parameters to be optimized, and iterate repeatedly until the loss function converges to the target value, then the optimized parameter values ​​can be obtained.

[0076] In step S105, electron stack imaging is achieved using the potential function distribution of each layer of the sample after the loss function converges.

[0077] It can be understood that the embodiment of the present application adjusts the parameters to be optimized through iterative optimization so that the loss function gradually converges, so that the predicted diffraction pattern matches the actual diffraction pattern observed in the experiment as accurately as possible. When the loss function converges, it means that the potential function distribution that best reflects the actual situation of the sample is found, and these optimized potential function distributions are used to reconstruct the image of the sample, thereby achieving high-precision electron stack imaging.

[0078] According to the electron stack imaging method combining local orbits and plane waves proposed in the embodiments of the present application, the actual diffraction intensity generated when the electron beam is located at each scanning position when scanning the sample is first obtained, and then the parameters to be optimized at all scanning positions are initialized, the beam spot function of all scanning positions is calculated, and then the potential function distribution of each layer of the sample is calculated, and the diffraction intensity is calculated according to the beam spot function and the potential function distribution. The loss value of the loss function is calculated according to the actual diffraction intensity and the calculated diffraction intensity, and the loss value is used to update the parameters to be optimized until the loss function converges. Finally, the potential function distribution of each layer of the sample after the loss function converges is used to realize electron stack imaging, which combines the advantages of local orbits in representing high spatial frequency information and the advantages of plane waves in representing low spatial frequencies, and obtains a more accurate sample potential function.

[0079] The electron stack imaging method combining local orbit and plane wave is further described below by a specific embodiment. Figure 2 As shown, the following steps are included:

[0080] Step S201, initializing the local orbit expansion coefficients and plane wave Fourier coefficients and waiting for the optimization parameters.

[0081] Step S202: Calculate the beam spot function according to the aberration coefficients of each order and the electron beam intensity.

[0082] Step S203: Calculate the potential function distribution of each layer of the sample according to the local orbital expansion coefficient and the plane wave Fourier coefficient.

[0083] Step S204: Calculate the output wave function according to the beam spot function and the potential function distribution of each layer.

[0084] Step S205: Calculate the diffraction intensity according to the output wave function.

[0085] Step S206, calculating a loss function according to the calculated diffraction intensity and the experimentally collected diffraction intensity, wherein the loss function calculated by the experimentally collected diffraction intensity is obtained by sequentially moving the electron beam to scan each position to obtain a four-dimensional diffraction intensity.

[0086] Step S207, determine whether the loss function converges to the target value, if yes, proceed to step S210, otherwise proceed to step S208.

[0087] Step S208: Calculate the gradient of each parameter to be optimized.

[0088] Step S209, update the parameters to be optimized, and return to step S202.

[0089] Step S210: output the calculated potential functions of each layer.

[0090] In this embodiment, an electron beam is first used to scan point by point at the scanning matrix position of the iron oxide sample, and the four-dimensional diffraction intensity is obtained by moving the electron beam to scan each position in sequence. The convergence half angle used is 25 mrad and the defocus is 10 nm.

[0091] In this example, the projection structure of iron oxide along the [10-1] direction is observed. The schematic diagram of the structure of iron oxide is as follows Figure 3 shown.

[0092] Initialize the local orbital expansion coefficient c i,l , plane wave Fourier coefficient a l,G , each order aberration coefficient C n,m,i,j , electron beam intensity s i,j .

[0093] Based on the aberration coefficients C of each order n,m,i,j , electron beam intensity s i,j Calculate the incident beam spot function P i,j (r):

[0094]

[0095] The phase of the beam spot function is obtained as Figure 4 As shown in Figure 5 shown.

[0096] According to the local orbital expansion coefficient c i,l , plane wave Fourier coefficient a l,G Calculate the potential function distribution of each layer of the sample O l (r):

[0097]

[0098] The average value of the local orbital part in each layer potential function is obtained as follows Figure 6 As shown, the corresponding expansion coefficient c i,l like Figure 7 As shown in the figure, the average value of the plane wave part in the potential function of each layer is obtained as Figure 8 As shown, the corresponding Fourier coefficient a l,G like Fig. 9 shown.

[0099] Next, an electron stack imaging device combining local orbits and plane waves proposed in an embodiment of the present application will be described with reference to the accompanying drawings.

[0100] Fig.10 It is a block diagram of an electron stack imaging device combining local orbits and plane waves according to an embodiment of the present application.

[0101] like Fig.10 As shown, the electronic stack imaging device 10 combining local orbit and plane wave includes: an acquisition module 301 , an initialization module 302 , a calculation module 303 , an update module 304 and an imaging module 305 .

[0102] Among them, the acquisition module 301 is used to obtain the actual diffraction intensity generated when the electron beam is located at each scanning position when scanning the sample; the initialization module 302 is used to initialize the parameters to be optimized at all scanning positions, wherein the parameters to be optimized include the local orbital expansion coefficient, the plane wave Fourier coefficient, the aberration coefficients of each order and the electron beam intensity; the calculation module 303 is used to calculate the beam spot function of all scanning positions according to the aberration coefficients of each order and the electron beam intensity, and calculate the potential function distribution of each layer of the sample according to the local orbital expansion coefficient and the plane wave Fourier coefficient; the update module 304 is used to calculate the diffraction intensity according to the beam spot function and the potential function distribution, calculate the loss value of the loss function according to the actual diffraction intensity and the calculated diffraction intensity, and use the loss value to update the parameters to be optimized until the loss function converges; the imaging module 305 is used to realize electron stack imaging using the potential function distribution of each layer of the sample after the loss function converges.

[0103] In the embodiment of the present application, the calculation formula of the beam spot function is:

[0104]

[0105] Where i and j are the matrix coordinates of the scanning position; k is the inverse space vector; represents the two-dimensional Fourier transform, χ i,j (k) is the aberration function; A(k) is the aperture function; s i,j is the arithmetic square root of the electron beam intensity at the i,jth scanning position.

[0106] In the embodiment of the present application, the calculation formula of the potential function is:

[0107]

[0108] Among them, r is the real space coordinate; l represents the longitudinal coordinate of the sample potential function distribution; φ i (r) is the basis function of the i-th local orbital; c i,l is the corresponding expansion coefficient; Ri,l is the center position of the local orbital; G is the reciprocal space vector, a l,G are the corresponding Fourier coefficients.

[0109] In an embodiment of the present application, the diffraction intensity is calculated based on the beam spot function and the potential function distribution, and the update module 304 is further used to: generate an exit wave function based on the beam spot function and the potential function distribution; and use the exit wave function to calculate the diffraction intensity when the electron beam is scanned at each scanning position.

[0110] In the embodiment of the present application, the calculation formula of the output wave function is:

[0111]

[0112] Among them, O l (r) is the sample potential function of the lth layer; is the propagation operator of Fresnel diffraction; P i,j (r) represents the beam spot function at the i,jth scanning position.

[0113] In the embodiment of the present application, the calculation formula of the loss function is:

[0114]

[0115] Where u and v are the coordinates of the diffraction intensity matrix; I i,j Diffraction intensity matrix collected by scanning transmission electron microscopy.

[0116] In the embodiment of the present application, the localized tracks represent high spatial frequency information and the plane waves represent low spatial frequency information.

[0117] It should be noted that the above explanation of the embodiment of the electron stack imaging method combining local orbits and plane waves is also applicable to the electron stack imaging device combining local orbits and plane waves of this embodiment, and will not be repeated here.

[0118] According to the electron stack imaging device combining local orbit and plane wave proposed in the embodiment of the present application, the actual diffraction intensity generated when the electron beam is located at each scanning position when scanning the sample is obtained, and then the parameters to be optimized at all scanning positions are initialized, the beam spot function of all scanning positions is calculated, and then the potential function distribution of each layer of the sample is calculated, and the diffraction intensity is calculated according to the beam spot function and the potential function distribution. The loss value of the loss function is calculated according to the actual diffraction intensity and the calculated diffraction intensity, and the loss value is used to update the parameters to be optimized until the loss function converges. Finally, the potential function distribution of each layer of the sample after the loss function converges is used to realize electron stack imaging, which combines the advantages of local orbit in representing high spatial frequency information and the advantages of plane waves in representing low spatial frequencies, and obtains a more accurate sample potential function.

[0119] Fig.11 A schematic diagram of the structure of an electronic device provided in an embodiment of the present application. The electronic device may include:

[0120] Memory 401 , processor 402 , and a computer program stored in the memory 401 and executable on the processor 402 .

[0121] When the processor 402 executes the program, the electron stack imaging method combining local orbit and plane wave provided in the above embodiment is implemented.

[0122] Furthermore, the electronic device further comprises:

[0123] The communication interface 403 is used for communication between the memory 401 and the processor 402 .

[0124] The memory 401 is used to store computer programs that can be executed on the processor 402 .

[0125] The memory 401 may include a high-speed RAM (Random Access Memory) memory, and may also include a non-volatile memory, such as at least one disk memory.

[0126] If the memory 401, the processor 402 and the communication interface 403 are implemented independently, the communication interface 403, the memory 401 and the processor 402 can be connected to each other through a bus and communicate with each other. The bus can be an ISA (Industry Standard Architecture) bus, a PCI (Peripheral Component Interconnect) bus or an EISA (Extended Industry Standard Architecture) bus, etc. The bus can be divided into an address bus, a data bus, a control bus, etc. For ease of representation, Fig.11 Only one thick line is used in the diagram, but this does not mean that there is only one bus or only one type of bus.

[0127] Optionally, in a specific implementation, if the memory 401, the processor 402 and the communication interface 403 are integrated on a chip, the memory 401, the processor 402 and the communication interface 403 can communicate with each other through an internal interface.

[0128] The processor 402 may be a CPU (Central Processing Unit), or an ASIC (Application Specific Integrated Circuit), or one or more integrated circuits configured to implement the embodiments of the present application.

[0129] An embodiment of the present application also provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the above-mentioned electron stack imaging method combining local orbits and plane waves.

[0130] In the description of this specification, the description with reference to the terms "one embodiment", "some embodiments", "example", "specific example", or "some examples" etc. means that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present application. In this specification, the schematic representations of the above terms are not necessarily directed to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described may be combined in any one or N embodiments or examples in a suitable manner. In addition, those skilled in the art may combine and combine the different embodiments or examples described in this specification and the features of the different embodiments or examples, without contradiction.

[0131] In addition, the terms "first" and "second" are used for descriptive purposes only and should not be understood as indicating or implying relative importance or implicitly indicating the number of technical features indicated. Therefore, a feature defined as "first" or "second" may explicitly or implicitly include at least one of the features. In the description of this application, "N" means at least two, such as two, three, etc., unless otherwise clearly and specifically defined.

[0132] Any process or method description in a flowchart or otherwise described herein may be understood to represent a module, fragment or portion of code comprising one or N executable instructions for implementing the steps of a custom logical function or process, and the scope of the preferred embodiments of the present application includes alternative implementations in which functions may not be performed in the order shown or discussed, including performing functions in a substantially simultaneous manner or in reverse order depending on the functions involved, which should be understood by technicians in the technical field to which the embodiments of the present application belong.

[0133] It should be understood that the various parts of the present application can be implemented in hardware, software, firmware or a combination thereof. In the above-mentioned embodiments, the steps or methods can be implemented in software or firmware stored in a memory and executed by a suitable instruction execution system. For example, if implemented in hardware, as in another embodiment, it can be implemented by any one of the following technologies known in the art or their combination: a discrete logic circuit having a logic gate circuit for implementing a logic function on a data signal, a dedicated integrated circuit having a suitable combination of logic gate circuits, a programmable gate array, a field programmable gate array, etc.

[0134] A person of ordinary skill in the art may understand that all or part of the steps carried by the method for implementing the above-mentioned embodiment may be completed by instructing related hardware through a program, and the above-mentioned program may be stored in a computer-readable storage medium, which, when executed, includes one of the steps of the method embodiment or a combination thereof.

[0135] Although the embodiments of the present application have been shown and described above, it can be understood that the above embodiments are exemplary and cannot be understood as limitations on the present application. Ordinary technicians in this field can change, modify, replace and modify the above embodiments within the scope of the present application.

Claims

1. An electron stack imaging method combining local orbits and plane waves, characterized in that: The following steps are involved: Obtain the actual diffraction intensity generated when the electron beam is located at each scanning position when scanning the sample; Initializing parameters to be optimized at all scanning positions, wherein the parameters to be optimized include local orbit expansion coefficients, plane wave Fourier coefficients, aberration coefficients of various orders, and electron beam intensity; Calculate the beam spot function of all scanning positions according to the aberration coefficients of each order and the electron beam intensity, and calculate the potential function distribution of each layer of the sample according to the local orbit expansion coefficient and the plane wave Fourier coefficient; Calculating the diffraction intensity according to the beam spot function and the potential function distribution, calculating the loss value of the loss function according to the actual diffraction intensity and the diffraction intensity, and updating the parameter to be optimized by using the loss value until the loss function converges to a target value; The electron stack imaging is realized by utilizing the potential function distribution of each layer of the sample after the loss function converges.

2. The electron stack imaging method combining local orbit and plane wave according to claim 1, characterized in that: The calculation formula of the beam spot function is: Where i and j are the matrix coordinates of the scanning position; k is the inverse space vector; represents the two-dimensional Fourier transform, χ i,j (k) is the aberration function; A(k) is the aperture function; s i,j is the arithmetic square root of the electron beam intensity at the i,jth scanning position.

3. The electron stack imaging method combining local orbit and plane wave according to claim 1, characterized in that: The calculation formula of the potential function is: Among them, r is the real space coordinate; l represents the longitudinal coordinate of the sample potential function distribution; φ i (r) is the basis function of the i-th local orbital; c i,l is the corresponding expansion coefficient; R i,l is the center position of the local orbital; G is the reciprocal space vector, a l,G are the corresponding Fourier coefficients.

4. The electron stack imaging method combining local orbit and plane wave according to claim 1, characterized in that: The calculating the diffraction intensity according to the beam spot function and the potential function distribution comprises: Generate an exit wave function according to the beam spot function and the potential function distribution; The output wave function is used to calculate the diffraction intensity of the electron beam when it is located at each scanning position.

5. The electron stack imaging method combining local orbit and plane wave according to claim 4, characterized in that: The calculation formula of the output wave function is: Among them, O l (r) is the sample potential function of the lth layer; is the propagation operator of Fresnel diffraction; P i,j (r) represents the beam spot function at the i,jth scanning position.

6. The electron stack imaging method combining local orbit and plane wave according to claim 1, characterized in that: The calculation formula of the loss function is: Where u and v are the coordinates of the diffraction intensity matrix; I i,j Diffraction intensity matrix collected by scanning transmission electron microscopy.

7. The electron stack imaging method combining local orbit and plane wave according to claim 1, characterized in that: The localized tracks represent high spatial frequency information and the plane waves represent low spatial frequency information.

8. An electron stack imaging device combining local orbits and plane waves, characterized in that: include: An acquisition module, used for acquiring actual diffraction intensity generated when the electron beam is located at each scanning position when scanning the sample; An initialization module, used for initializing the parameters to be optimized at all scanning positions, wherein the parameters to be optimized include local orbit expansion coefficients, plane wave Fourier coefficients, aberration coefficients of various orders and electron beam intensity; A calculation module, used for calculating the beam spot function of all scanning positions according to the aberration coefficients of each order and the electron beam intensity, and calculating the potential function distribution of each layer of the sample according to the local orbit expansion coefficient and the plane wave Fourier coefficient; An updating module, configured to calculate the diffraction intensity according to the beam spot function and the potential function distribution, calculate the loss value of the loss function according to the actual diffraction intensity and the diffraction intensity, and update the parameter to be optimized by using the loss value until the loss function converges; The imaging module is used to realize electron stack imaging by utilizing the potential function distribution of each layer of the sample after the loss function converges.

9. An electronic device, characterized in that: include: A memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the electron stack imaging method combining local orbits and plane waves as described in any one of claims 1 to 7.

10. A computer-readable storage medium having a computer program or instruction stored thereon, characterized in that: When the computer program or instruction is executed, the electron stack imaging method combining local orbit and plane wave as described in any one of claims 1 to 7 is implemented.

Images