Electron layer imaging method, device and equipment combining localized orbit and plane wave

Abstract

The application relates to the field of scanning transmission electron microscopy, in particular to an electron superposition imaging method, device and equipment combining a localized orbit and a plane wave, the method comprising the following steps: obtaining actual diffraction intensity generated when an electron beam scans a sample at each scanning position; initializing to-be-optimized parameters of all scanning positions; calculating a beam spot function of all scanning positions and a potential function distribution of each layer of the sample; calculating diffraction intensity according to the beam spot function and the potential function distribution, calculating a loss value of a loss function according to the actual diffraction intensity and the calculated diffraction intensity, updating the to-be-optimized parameters by using the loss value until the loss function converges, and combining the advantages of the localized orbit in representing high spatial frequency information and the advantages of the plane wave in representing low spatial frequency, so that a more accurate sample potential function is obtained. Therefore, the problems that related technologies lack the ability of simultaneously accurately representing high-frequency and low-frequency information and are difficult to perform high-precision reconstruction of a phase are solved.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of scanning transmission electron microscopy, in particular to an electron laminography method combining localized orbitals and plane waves, an electron laminography device and an electron laminography equipment. BACKGROUND

[0002] The existing laminography method cannot consider both high spatial frequency and low spatial frequency information, resulting in limited reconstruction accuracy of the charge density distribution of the sample and the atomic orbital, and the spatial distribution of the electronic structure cannot be clearly characterized. At the same time, high-precision characterization of the potential function distribution also requires high calculation accuracy and efficiency, and the existing algorithm is difficult to fit the diffraction signals of atomic nuclei and inner and outer electrons. SUMMARY

[0003] The present application provides an electron laminography method combining localized orbitals and plane waves, an electron laminography device and an electron laminography equipment to solve the problem that the related art lacks the ability to accurately represent both high-frequency and low-frequency information simultaneously and is difficult to perform high-precision reconstruction of the phase.

[0004] The first aspect of the present application provides an electron laminography method combining localized orbitals and plane waves, comprising the following steps: obtaining actual diffraction intensity generated when an electron beam scans a sample at each scanning position; initializing to-be-optimized parameters of all scanning positions, wherein the to-be-optimized parameters include localized orbital expansion coefficients, plane wave Fourier coefficients, aberration coefficients of each order, and electron beam intensity; calculating beam spot functions of all scanning positions according to the aberration coefficients of each order and the electron beam intensity, and calculating potential function distributions of each layer of the sample according to the localized orbital expansion coefficients and the plane wave Fourier coefficients; calculating diffraction intensity according to the beam spot function and the potential function distribution, calculating a loss value of a loss function according to the actual diffraction intensity and the calculated diffraction intensity, updating the to-be-optimized parameters using the loss value until the loss function converges to a target value; and realizing electron laminography using the potential function distributions of each layer of the sample after the loss function converges.

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

[0006]

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

[0008] Optionally, the calculation formula of the potential function is:

[0009]

[0010] where r is the real space coordinate; l represents the longitudinal coordinate of the sample potential function distribution; φ i (r) is the base 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 inverse space vector, a l,G is the corresponding Fourier coefficient.

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

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

[0013]

[0014] where O l (r) is the sample potential function of the l-th layer; is the propagation operator of Fresnel diffraction; P i,j (r) represents the beam spot function of the i, j-th scanning position.

[0015] Optionally, the calculation formula of the loss function is:

[0016]

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

[0018] Optionally, the local orbital represents high spatial frequency information and the plane wave represents low spatial frequency information.

[0019] The second aspect embodiment of the present application provides an electron laminography imaging device combining local orbitals and plane waves, comprising: an acquisition module configured to acquire actual diffraction intensity generated when an electron beam scans a sample at each scanning position; an initialization module configured to initialize to-be-optimized parameters of all scanning positions, wherein the to-be-optimized parameters comprise local orbital expansion coefficients, plane wave Fourier coefficients, aberration coefficients of each order, and electron beam intensity; a calculation module configured to calculate beam spot functions of all scanning positions according to the aberration coefficients of each order and the electron beam intensity, and calculate potential function distributions of each layer of the sample according to the local orbital expansion coefficients and the plane wave Fourier coefficients; an update module configured to calculate diffraction intensity according to the beam spot functions and the potential function distributions, calculate a loss value of a loss function according to the actual diffraction intensity and the calculated diffraction intensity, and update the to-be-optimized parameters by using the loss value until the loss function converges; and an imaging module configured to realize electron laminography imaging by using the potential function distributions of each layer of the sample after the loss function converges.

[0020] The third aspect of the present application provides an electronic device, comprising a memory, a processor and a computer program stored in the memory and executable on the processor, and the processor executes the program to implement the electron tomography imaging method combining local orbitals and plane waves of the first aspect.

[0021] The fourth aspect of the present application provides a computer readable storage medium, which stores a computer program executable by a processor to implement the electron tomography imaging method combining local orbitals and plane waves of the first aspect.

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

[0023] The embodiment of the present application first acquires the actual diffraction intensity generated when the electron beam scans the sample at each scanning position, then initializes the to-be-optimized parameters of all scanning positions, calculates the beam spot function of all scanning positions, calculates the potential function distribution of each layer of the sample, calculates the diffraction intensity according to the beam spot function and the potential function distribution, calculates the loss value of the loss function according to the actual diffraction intensity and the calculated diffraction intensity, updates the to-be-optimized parameters using the loss value until the loss function converges, and finally realizes electron tomography imaging using the potential function distribution of each layer of the sample after the loss function converges, which combines the advantages of local orbitals in representing high spatial frequency information and the advantages of plane waves in representing low spatial frequency, and obtains a more accurate sample potential function. Therefore, the problem that related technologies lack the ability to accurately represent high frequency and low frequency information at the same time and are difficult to perform high-precision reconstruction of the phase is solved.

[0024] Additional aspects and advantages of the present application will be made apparent by the following description and the accompanying drawings. BRIEF DESCRIPTION OF DRAWINGS

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

[0026] Figure 1 A flowchart of the electron tomography imaging method combining local orbitals and plane waves provided according to an embodiment of the present application is shown in FIG. 1;

[0027] Figure 2 A calculation flowchart provided according to an embodiment of the present application is shown in FIG. 2;

[0028] Figure 3 A structural diagram of iron oxide along the [10-1] direction provided according to an embodiment of the present application is shown in FIG. 3;

[0029] Figure 4 A diagram of the calculated beam spot function phase provided according to an embodiment of the present application is shown in FIG. 4;

[0030] Figure 5 A calculated beam spot function amplitude plot provided according to an embodiment of the present application;

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

[0032] Figure 7 A calculated local orbital expansion coefficient c provided according to an embodiment of the present application i,l A plot;

[0033] Figure 8 A calculated plane wave potential function plot provided according to an embodiment of the present application;

[0034] Figure 9 A calculated plane wave Fourier coefficient a provided according to an embodiment of the present application l,G A plot;

[0035] Figure 10 An example diagram of an electron laminography device incorporating local orbitals and plane waves provided according to an embodiment of the present application;

[0036] Figure 11 A structural diagram of an electronic device provided according to an embodiment of the present application. DETAILED DESCRIPTION

[0037] Embodiments of the present application are described in detail below with reference to the attached drawing figures, wherein the same or like reference numerals are used throughout the drawings to refer to the same or like elements or elements with the same or similar functionality. The embodiments described below are illustrative examples of the present application meant to be used in explaining the present application and are not to be construed as limiting the present application.

[0038] The electronic laminography imaging method, device and equipment combining local orbitals and plane waves are described below with reference to the accompanying drawings. In view of the problem that the related art lacks the ability to accurately represent high-frequency and low-frequency information at the same time and is difficult to perform high-precision reconstruction of the phase, the present application provides an electronic laminography imaging method combining local orbitals and plane waves. In the method, the actual diffraction intensity generated when the electron beam scans the sample at each scanning position is first obtained. Then, the to-be-optimized parameters of all scanning positions are initialized, the beam spot function of all scanning positions is calculated, and 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 to-be-optimized parameters are updated using the loss value 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 electronic laminography imaging. The method combines the advantages of local orbitals in representing high spatial frequency information and the advantages of plane waves in representing low spatial frequency, and obtains a more accurate sample potential function. Thus, the problem that the related art lacks the ability to accurately represent high-frequency and low-frequency information at the same time and is difficult to perform high-precision reconstruction of the phase is solved.

[0039] Specifically, Figure 1 A flowchart of an electronic laminography imaging method combining local orbitals and plane waves provided by an embodiment of the present application is shown in FIG. 1.

[0040] As Figure 1 shown, the electronic laminography imaging method combining local orbitals and plane waves includes the following steps:

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

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

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

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

[0045] Wherein, the local orbit refers to an orbit function concentrated in the vicinity of the atomic nucleus or in some specific region, which is usually approximated by a set of local basis functions; the plane wave is a simple wave form, and each point in the diffraction pattern in the embodiment of the application represents a plane wave; the aberration coefficients of each order are related to the aberrations generated in the imaging process, which are represented by an aberration function.

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

[0047] In the embodiment of the application, the local orbit represents high spatial frequency information, and the plane wave represents low spatial frequency information.

[0048] Wherein, the high spatial frequency information refers to characteristics that change rapidly in space, which corresponds to steep change regions in the potential function, such as the atomic nucleus and the core electron part that change rapidly in the potential function; the low spatial frequency information refers to characteristics that change slowly in space, such as the valence electron part that changes relatively smoothly and slowly in the potential function. The high-frequency oscillation potential function characteristics are captured by using the high spatial frequency local orbit part, and the low-frequency smooth potential function characteristics are described by using the low spatial frequency plane wave part.

[0049] It can be understood that the embodiment of the application uses the local orbit to describe the high spatial frequency information in the sample, i.e. those steeply changing parts, and uses the plane wave to represent the low spatial frequency information in the sample, i.e. those gently changing parts, and the combination of the information of the two can accurately represent both high-frequency and low-frequency information, obtaining 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 orbit expansion coefficients and the plane wave Fourier coefficients.

[0051] Wherein, the beam spot function represents the characteristics of the electron beam spot formed by the electron beam passing through the sample at each scanning position, and the calculation method will be described in detail below, and will not be described here again.

[0052] It can be understood that, according to the aberration coefficients and the electron beam intensity at each scanning position, the beam spot function at each position is calculated, then the potential function distribution of each layer of the sample is calculated by using the local orbital expansion coefficient and the plane wave Fourier coefficient, that is, the local atomic nucleus and inner shell electron part with rapid local change in the sample is accurately captured by combining the local orbital, and the valence electron part with relatively smooth and slow change is expressed by using the plane wave, through the method, the high frequency and low frequency information can be accurately expressed at the same time, and the details of the internal structure of the sample and the overall trend are more accurately reconstructed.

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

[0054]

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

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

[0057]

[0058] Wherein, Real{·} represents taking the real part of each element in the matrix, C n,m,i,j is the aberration coefficient C m,m of the i,jth scanning position, that is, the aberration coefficient of each order, R2(ω) represents other high-order expansion terms in the aberration of two orders or more, wherein ω is a complex representation of the inverse space vector k, and the value is defined as ω=k u +i·k v , wherein k u and k v are inverse space coordinates, ω represents the conjugate matrix of ω.

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

[0060]

[0061] Wherein, r is the real space coordinate; l represents the longitudinal coordinate of the potential function distribution of the sample; φ i (r) is the base 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 inverse space vector, a l,Gcorresponding 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, wherein, is the local orbital potential function, is the plane wave potential function, and the potential function calculation formula is as follows,

[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 to-be-optimized parameter is updated by using the loss value until the loss function converges to the target value.

[0064] The potential function distribution describes the electric potential distribution inside the sample; the diffraction intensity is calculated based on the beam spot function and the potential function distribution, and represents the theoretical diffraction pattern intensity distribution, and the calculation method will be described in detail below, and will not be described here; the loss function is used to quantify the difference between the diffraction intensity calculated based on the beam spot function and the potential function distribution and the actual diffraction intensity, and the parameter is optimized by minimizing the loss value; the target value is specifically set according to actual requirements, and is not specifically limited here; the method of updating the to-be-optimized parameter by using the loss value until the loss function converges to the target value will be described in detail below, and will not be described here.

[0065] It can be understood that the embodiments of the present application first calculate the diffraction intensity by using the beam spot function and the potential function distribution, compare the diffraction intensity with the actual diffraction intensity measured actually, calculate the loss value, which reflects the difference between the prediction and the actual observation, use the loss value as feedback to adjust the to-be-optimized parameter to reduce the difference between the theoretical calculation and the actual situation, and repeatedly perform the process until the loss function converges, that is, the parameter set that can most accurately reflect the actual potential function distribution of the sample is found, so that the high-precision reconstruction of the sample structure is realized.

[0066] In the embodiments 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 calculating the diffraction intensity when the electron beam is located at each scanning position by using the exit wave function.

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

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

[0069] In the embodiments of the present application, the calculation formula of the exit wave function is:

[0070]

[0071] wherein 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 of the i,jth scanning position.

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

[0073]

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

[0075] It should be noted that the loss value is used to update the to-be-optimized parameters until the loss function converges to the target value. First, the loss function Regarding the gradient of each to-be-optimized parameter, for θ t = c i,l , a l,G , C n,m,i,j , s i,j each to-be-optimized parameter, wherein 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, and s i,j is the electron beam intensity. The gradient obtained by calculation is used to update the target parameters: wherein a is the learning rate of each parameter, ∈ is a calculation precision quantity, and are the first-order and second-order momentum estimates of the gradient, wherein β1 and β2 are the attenuation rates of the first-order and second-order momentum estimates, respectively. The gradient optimization algorithms such as the Adam algorithm, the SGD algorithm, and the Adagrad algorithm are used to optimize each parameter in the updating process. 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 , the steps of calculating the beam spot function to updating the to-be-optimized parameters are repeated, and iteration is repeated until the loss function converges to the target value, that is, the optimized parameter values are obtained.

[0076] In step S105, the potential function distribution of each layer of the sample after the loss function converges is used to realize electron tomography.

[0077] It can be understood that, by iteratively optimizing and adjusting the to-be-optimized parameters, the loss function gradually converges, so that the predicted diffraction pattern is as accurately matched as possible with the actual diffraction pattern observed in the experiment. When the loss function converges, it means that the potential function distribution that best reflects the real situation of the sample is found. The image of the sample is reconstructed using the optimized potential function distribution, thereby realizing high-precision electron tomography imaging.

[0078] According to the electron tomography imaging method combining the local orbital and the plane wave provided in the embodiments of the present application, the actual diffraction intensity generated when the electron beam scans each scanning position of the sample is first obtained, then the to-be-optimized parameters of all scanning positions are initialized, the beam spot function of all scanning positions is calculated, 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 to-be-optimized parameters are updated using the loss value until the loss function converges, and finally the electron tomography imaging is realized using the potential function distribution of each layer of the sample after the loss function converges. The advantages of the local orbital in representing high spatial frequency information and the advantages of the plane wave in representing low spatial frequency are combined, and a more accurate potential function of the sample is obtained.

[0079] The electron tomography imaging method combining the local orbital and the plane wave is further described below through a specific embodiment, as shown in Figure 2 The method includes the following steps:

[0080] In step S201, the to-be-optimized parameters such as the local orbital expansion coefficient and the plane wave Fourier coefficient are initialized.

[0081] In step S202, the beam spot function is calculated according to the aberration coefficient of each order and the electron beam intensity.

[0082] In step S203, 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.

[0083] In step S204, the outgoing wave function is calculated according to the beam spot function and the potential function distribution of each layer.

[0084] In step S205, the diffraction intensity is calculated according to the outgoing wave function.

[0085] In step S206, the loss function is calculated according to the calculated diffraction intensity and the experimentally acquired diffraction intensity. The experimentally acquired diffraction intensity is calculated by sequentially moving the electron beam to scan each position to obtain a four-dimensional diffraction intensity.

[0086] In step S207, it is determined whether the loss function converges to a target value. If yes, step S210 is performed, otherwise step S208 is performed.

[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 the scanning matrix position of the iron oxide sample point by point, 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 the figure, the amplitude of the beam spot function is as follows: 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 the potential function of each layer 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 Figure 9 shown.

[0099] Secondly, the electron tomography device combining local orbitals and plane waves is described with reference to the accompanying drawings according to the embodiments of the present application.

[0100] Figure 10 is a block schematic diagram of the electron tomography device combining local orbitals and plane waves according to the embodiments of the present application.

[0101] As shown in the figure, the electron tomography device combining local orbitals and plane waves 10 comprises an acquisition module 301, an initialization module 302, a calculation module 303, an updating module 304 and an imaging module 305. Figure 10

[0102] The acquisition module 301 is configured to acquire actual diffraction intensity generated when an electron beam scans a sample at each scanning position; the initialization module 302 is configured to initialize to-be-optimized parameters of all scanning positions, wherein the to-be-optimized parameters comprise local orbital expansion coefficients, plane wave Fourier coefficients, aberration coefficients of each order and electron beam intensity; the calculation module 303 is configured to calculate beam spot functions of all scanning positions according to the aberration coefficients of each order and the electron beam intensity, and calculate potential function distributions of each layer of the sample according to the local orbital expansion coefficients and the plane wave Fourier coefficients; the updating module 304 is configured to calculate diffraction intensity according to the beam spot functions and the potential function distributions, calculate loss values of a loss function according to the actual diffraction intensity and the calculated diffraction intensity, and update the to-be-optimized parameters by using the loss values until the loss function converges; and the imaging module 305 is configured to realize electron tomography by using the potential function distributions of each layer of the sample after the loss function converges.

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

[0104]

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

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

[0107]

[0108] wherein r is a real space coordinate; l represents a longitudinal coordinate of the sample potential function distribution; φ i (r) is a base function of the i th local orbital; c i,l is a corresponding expansion coefficient; R i,l is a center position of the local orbital; G is an inverse space vector, a​l,G are the corresponding Fourier coefficients.

[0109] In the embodiment of the present application, the diffraction intensity is calculated according to the beam spot function and the potential function distribution, and the updating module 304 is further configured to: generate an exit wave function according to the beam spot function and the potential function distribution; and calculate the diffraction intensity of the electron beam scanning at each scanning position by using the exit wave function.

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

[0111]

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

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

[0114]

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

[0116] In the embodiment of the present application, the local orbital represents high spatial frequency information and the plane wave represents low spatial frequency information.

[0117] It should be noted that the aforementioned explanation and description of the embodiment of the electron laminography imaging method combining the local orbital and the plane wave also applies to the embodiment of the electron laminography imaging device combining the local orbital and the plane wave, which will not be described here.

[0118] According to the embodiment of the electron laminography imaging device combining the local orbital and the plane wave, the actual diffraction intensity generated when the electron beam scans the sample at each scanning position is first obtained, then the to-be-optimized parameters of all scanning positions are initialized, the beam spot function of all scanning positions is calculated, 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 to-be-optimized parameters are updated by using the loss value until the loss function converges, and finally the electron laminography imaging is realized by using the potential function distribution of each layer of the sample after the loss function converges, which combines the advantages of the local orbital in representing high spatial frequency information and the advantages of the plane wave in representing low spatial frequency, and obtains a more accurate sample potential function.

[0119] Figure 11A structural schematic diagram of an electronic device is provided in the embodiments of the present application. The electronic device can include

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

[0121] The processor 402 implements the method of the electronic layer imaging provided in the above embodiments when executing the program.

[0122] Further, the electronic device further includes

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

[0124] The memory 401 is used for storing the computer program executable on the processor 402.

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

[0126] If the memory 401, the processor 402 and the communication interface 403 are independently implemented, the communication interface 403, the memory 401 and the processor 402 can be connected to each other through a bus and complete communication between each other. The bus can be an ISA (Industry Standard Architecture) bus, a PCI (Peripheral Component) 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 the convenience of representation, Figure 11 Only one thick line is used in the figure, but it does not mean that there is only one bus or only one type of bus.

[0127] Optionally, in 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 complete communication between each other through an internal interface.

[0128] The processor 402 can 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] The embodiment of the present application also provides a computer readable storage medium, which stores a computer program, and the computer program is executed by a processor to implement the electronic layer imaging method combining local orbitals and plane waves as described above.

[0130] In the description of the present specification, the description of the terms "one embodiment", "some embodiments", "an example", "a specific example", or "some examples" and the like means that the specific features, structures, materials or characteristics described in connection with the embodiment or example are included in at least one embodiment or example of the present application. In the present specification, the illustrative description of the above terms is not necessarily directed to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described can be combined in any one or N embodiments or examples in a suitable manner. In addition, the person skilled in the art can combine and combine the different embodiments or examples described in the present specification and the features of the different embodiments or examples without contradiction.

[0131] In addition, the terms "first", "second" are only for descriptive purposes and cannot be understood as indicating or implying relative importance or implicitly indicating the number of the indicated technical features. Therefore, the features defined with "first", "second" can explicitly or implicitly include at least one of the features. In the description of the present application, the meaning of "N" is at least two, for example, two, three, etc., unless otherwise explicitly specified.

[0132] Any process or method descriptions in flow charts or described elsewhere herein can be understood as representing code modules, segments, or portions of code that include one or more executable instructions for implementing the specified logical functions or steps, and the preferred embodiments of the present application also include the possibility that the described functions may be implemented by alternative means, such as using an alternative order of steps, or using the functions of others, or using a combination of some of the above, or utilizing some or all of the features, without departing from the scope of the present application, which should be understood as encompassing such alternative implementations.

[0133] It should be understood that parts of the present application can be implemented in hardware, software, firmware or a combination thereof. In the above-described embodiments, the steps or methods can be implemented by software or firmware stored in a memory and executed by a suitable instruction execution system. As in another embodiment, if implemented in hardware, any of the following technologies known in the art or their combinations can be used: discrete logic circuit with logic gate circuit for implementing logical functions on data signals, application specific integrated circuit with suitable combination of logic gate circuit, programmable gate array, field programmable gate array, etc.

[0134] Those skilled in the art can understand that all or part of the steps of the method for implementing the above-mentioned embodiments can be instructed by a program to complete the relevant hardware, and the above-mentioned program can be stored in a computer readable storage medium. When the program is executed, it 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 should be understood that the above-mentioned embodiments are exemplary and cannot be understood as limiting the present application. Those skilled in the art can make changes, modifications, replacements and variations to the above-mentioned embodiments within the scope of the present application.

Claims

1. An electron stack imaging method combining localized orbits and plane waves, characterized in that: The following steps are involved: Obtain the actual diffraction intensity generated when the electron beam is 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, various order aberration coefficients, 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 orbital expansion coefficient and the plane wave Fourier coefficient; Calculating a diffraction intensity according to the beam spot function and the potential function distribution, calculating a loss value of a loss function according to the actual diffraction intensity and the diffraction intensity, and updating the parameter to be optimized using the loss value until the loss function converges to a target value; The potential function distribution of each layer of the sample after the loss function converges is used to realize electron stack imaging.

2. The electron stack imaging method combining localized orbits and plane waves 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 reciprocal 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 localized orbits and plane waves 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 localized orbits and plane waves according to claim 1, characterized in that: The calculating the diffraction intensity according to the beam spot function and the potential function distribution includes: generating an output 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 localized orbits and plane waves 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 localized orbits and plane waves 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 localized orbits and plane waves 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 localized 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 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, various order aberration coefficients and electron beam intensity; a calculation module, configured 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; an updating module, configured to calculate the diffraction intensity according to the beam spot function and the potential function distribution, calculate a loss value of a loss function according to the actual diffraction intensity and the diffraction intensity, and update the parameter to be optimized using the loss value until the loss function converges; An 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 localized orbits and plane waves according to 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 instructions are executed, the electron stack imaging method combining localized orbits and plane waves according to any one of claims 1 to 7 is implemented.

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