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WO2023011569A1 - 自动矫正样品晶带轴偏离的电子叠层成像方法及装置 - Google Patents

自动矫正样品晶带轴偏离的电子叠层成像方法及装置 Download PDF

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WO2023011569A1
WO2023011569A1 PCT/CN2022/110146 CN2022110146W WO2023011569A1 WO 2023011569 A1 WO2023011569 A1 WO 2023011569A1 CN 2022110146 W CN2022110146 W CN 2022110146W WO 2023011569 A1 WO2023011569 A1 WO 2023011569A1
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function
sample
electron beam
inclination angle
optimized
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French (fr)
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于荣
沙浩治
崔吉哲
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Tsinghua University
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Tsinghua University
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N23/00—Investigating or analysing materials by the use of wave or particle radiation, e.g. X-rays or neutrons, not covered by groups G01N3/00 – G01N17/00, G01N21/00 or G01N22/00
    • G01N23/20—Investigating or analysing materials by the use of wave or particle radiation, e.g. X-rays or neutrons, not covered by groups G01N3/00 – G01N17/00, G01N21/00 or G01N22/00 by using diffraction of the radiation by the materials, e.g. for investigating crystal structure; by using scattering of the radiation by the materials, e.g. for investigating non-crystalline materials; by using reflection of the radiation by the materials
    • G01N23/2055—Analysing diffraction patterns

Definitions

  • the invention relates to the technical field of microscopic imaging, in particular to an electronic lamination imaging method and device for automatically correcting the axis deviation of a sample crystal band.
  • Traditional electron microscopy imaging methods play an important role in characterizing the microstructure of materials.
  • Traditional electron microscopy imaging methods include high-resolution transmission electron microscopy imaging, annular dark field image in scanning transmission electron microscopy imaging, annular bright field image, bright field image, differential phase contrast imaging, etc.
  • the quality of high-resolution images obtained by these imaging methods is affected by sample tilt.
  • the crystal band axis of the sample deviates, contrasting artifacts may appear in the atomic resolution image, and different atomic columns produce false relative displacements due to the different strength of the channel effect, which brings great difficulties to quantitatively characterize the structural information of the sample.
  • Stack imaging is a method to achieve ultra-high resolution in the field of electron microscopy, which has the advantage of being able to reconstruct the electron beam at the same time, so that the resolution of the image is no longer limited by aberrations.
  • stack imaging can solve the problem of multiple scattering in the field of electron microscopy, and has a certain depth resolution.
  • the current stack imaging also requires the sample to be in the normal crystal zone axis to obtain high-quality reconstruction results, which limits the application scenarios of stack imaging.
  • the present invention aims to solve one of the technical problems in the related art at least to a certain extent.
  • an object of the present invention is to propose an electronic stack imaging method that automatically corrects the deviation of the sample crystal zone axis, which solves the problem of image quality degradation caused by the deviation of the sample crystal band axis in stack imaging.
  • Another object of the present invention is to provide an electronic stack imaging device that automatically corrects the deviation of the sample crystal zone axis.
  • an embodiment of the present invention proposes an electronic stack imaging method for automatically correcting the deviation of the sample ribbon axis, including the following steps: scanning the sample with an electron beam, and collecting the image of each scanning point of the sample Diffraction pattern;
  • the initializer function and the electron beam function according to the propagation function between the sample sheets, construct a forward propagation model, calculate the loss function of the forward propagation model, and the propagation function between the sample sheets
  • the variable parameters include the deviation angle of the sample zone axis relative to the direction of the electron beam;
  • an electronic stack imaging device for automatically correcting the sample ribbon axis deviation, including an acquisition module, a calculation module, an optimization module, and an imaging module.
  • the collection module is used to scan the sample with an electron beam, and collect the diffraction pattern of each scanning point of the sample;
  • the calculation module is used to initialize the object function and the electron beam function, construct a forward propagation model according to the propagation function between the sample sheets, and calculate the loss function of the forward propagation model, wherein the sample sheet Variable parameters of the propagation function include the angle of deviation of the sample zone axis relative to the direction of the electron beam.
  • the optimization module is configured to solve the gradient of the loss function with respect to the parameter to be optimized, and optimize the parameter to be optimized according to the gradient.
  • the imaging module is configured to execute the calculation module to recalculate the loss function of the forward propagation model until an iteration termination condition is met, and output optimized parameters.
  • the electronic lamination imaging method and device for automatically correcting the deviation of the sample zone axis in the embodiment of the present invention scans the electron beam on the sample, and obtains a series of diffraction patterns as data, which is used to describe the Fresnel of the electron wave function propagating in the sample Fresnel (Fresnel) near-field diffraction propagation function, that is, the inclination angle is introduced into the propagation function between the sample layers.
  • the inclination angle includes the first inclination angle and the second inclination angle.
  • the loss function is compared with the first inclination angle and The gradient of the second dip angle updates the first dip angle and the second dip angle, and finally obtains the deviation angle of the sample crystal zone axis relative to the electron beam direction and the projected potential of the sample under the normal crystal zone axis. It overcomes the shortcomings of the electron microscope that is difficult to obtain high spatial resolution images and high-precision structural information when the sample crystal band axis deviates, and can obtain the projected potential of the sample with sub-angstrom resolution when the sample crystal band axis deviates
  • FIG. 1 is a flow chart of an electronic stack imaging method for automatically correcting sample zone axis deviation according to an embodiment of the present invention.
  • Fig. 2 is a projected structure along the direction [001] of the barium titanate sample used according to an embodiment of the present invention.
  • FIG. 3 is a distribution diagram of electron beam scanning points according to an embodiment of the present invention.
  • FIG. 4 is a schematic diagram of the average of diffraction patterns at all scanning positions according to an embodiment of the present invention.
  • Fig. 5 is a diagram of the amplitude of the physical function initialized by the iterative optimization algorithm according to an embodiment of the present invention.
  • Fig. 6 is a phase diagram of a physical function initialized by an iterative optimization algorithm according to an embodiment of the present invention.
  • FIG. 7 is an amplitude diagram of an electron beam function initialized by an iterative optimization algorithm according to an embodiment of the present invention.
  • FIG. 8 is a phase diagram of an electron beam function initialized by an iterative optimization algorithm according to an embodiment of the present invention.
  • FIG. 9 is an average phase diagram of an object function reconstructed by an iterative optimization algorithm according to an embodiment of the present invention.
  • FIG. 10 is an amplitude diagram of an electron beam function reconstructed by an iterative optimization algorithm according to an embodiment of the present invention.
  • FIG. 11 is a schematic diagram of the change curve of the first inclination angle of the object along the x direction and the second inclination angle in the y direction during the iterative process of the iterative optimization algorithm according to an embodiment of the present invention.
  • FIG. 12 is a schematic structural diagram of an electronic stack imaging device for automatically correcting the sample zone axis deviation according to an embodiment of the present invention.
  • FIG. 13 is a schematic diagram of the internal structure of a computer device in an embodiment of the present application.
  • FIG. 1 is a flow chart of an electronic stack imaging method for automatically correcting sample zone axis deviation according to an embodiment of the present invention.
  • the electronic stack imaging method for automatically correcting the sample zone axis deviation includes the following steps S1-S4.
  • step S1 the sample is scanned by an electron beam, and a diffraction pattern of each scanning point of the sample is collected.
  • the present invention includes a sample, an electron source and a detector.
  • the electron beam is emitted by the electron source to scan the sample, and the detector records the scattering signal at each scanning position, and collects the diffraction pattern of each scanning point.
  • step S2 the object function and the electron beam function are initialized, and the forward propagation model is constructed according to the propagation function between the sample sheets, and the loss function of the forward propagation model is calculated.
  • Variable parameters of the propagation function between the sample sheets include the angle of deviation of the sample zone axis relative to the direction of the incident electron beam.
  • the object function and the electron beam function are initialized.
  • the object function of each layer adopts all 1 amplitude and random phase, and the electron beam function P(r) is constructed according to the aperture function and aberration function:
  • A(k) is the aperture function
  • ⁇ (k) is the aberration function
  • the loss function is defined as a function about an object function, an electron beam function, and the like.
  • the loss function Including but not limited to the following forms:
  • j represents the serial number of the scanning position
  • represents the modulus of each element in the calculation matrix
  • ⁇ F' represents the Frobenius norm of the calculation matrix
  • I is the collected diffraction intensity matrix.
  • the outgoing wave function in the forward propagation model It can be expressed as:
  • P(rr j ) represents the electron beam scanned to the j-th position
  • O i represents the object function of the i-th layer. It can be assumed that the physical function of each layer has the same thickness and inclination angle, Represents the Fresnel near-field diffraction factor, which can be expressed as:
  • step S3 the gradient of the loss function with respect to the parameter to be optimized is calculated, and the parameter to be optimized is optimized according to the gradient.
  • the parameters to be optimized include the physical function, the electron beam function, the deviation angle of the sample zone axis relative to the electron beam direction, that is, the first inclination angle and the second inclination angle. Solve the gradient of the loss function with respect to parameters such as the object function O i , the electron beam function P, the first inclination angle ⁇ x , and the second inclination angle ⁇ y .
  • the calculation of the gradient can be realized by using a software library with an automatic derivation function.
  • the Fresnel propagation function of any layer is replaced by the derivative of the Fresnel propagation function to the dip angle ⁇ k .
  • the Fresnel propagation function of the N/2th layer is replaced.
  • the parameters to be optimized are updated using the calculated gradient.
  • the parameters to be optimized can be updated by the following formula:
  • O′ i is the updated object function
  • P′ is the updated electron beam function
  • ⁇ x ′ is the updated first inclination angle
  • ⁇ y ′ is the updated second inclination angle
  • O i is the learning rate of the object function
  • ⁇ P is the learning rate of the electron beam function P
  • is the gradient of the loss function with respect to the object function is the gradient of the loss function with respect to the electron beam function, and are the gradients of the loss function with respect to the first inclination angle ⁇ x , and the second inclination angle ⁇ y , respectively.
  • step S4 return to step S2, recalculate the loss function, and output optimized parameters until the iteration termination condition is satisfied.
  • the optimized first inclination angle and the optimized second inclination angle are the angles at which the final sample crystal zone axis deviates from the direction of the electron beam, and the optimized material function is the projected potential of the final sample under the normal crystal zone axis.
  • the iteration termination condition includes: the loss function converges; or, the number of iterations reaches a preset threshold of iterations.
  • step S3 recalculate the loss function through the parameters updated in step S3, repeat S2-S3, and iterate repeatedly until the loss function converges or the number of iterations reaches the set threshold of iteration times, and the iteration ends, and finally the optimized parameters are obtained, and then Sample imaging with optimized parameters.
  • the method of the above embodiment can automatically correct the deviation of the crystal zone axis of the sample, thereby reducing the impact on the resolution and structure measurement accuracy, relaxing the experimental requirements of electron microscopy, and making stack imaging even when the sample obviously deviates from the orthocrystal Ultra-high resolution and picometer-accurate structural measurements can still be obtained with a shaft.
  • the inclination angle of the sample from the direction [001] is 8 mrad
  • the electron beam scans on the sample
  • the scanning position is shown in Figure 3
  • the scanning points are distributed in a uniform grid distribution
  • the detector collects the diffraction pattern of each scanning position
  • the average of all diffraction patterns is shown in Fig. 4, using a convergence half angle of 22mrad and an underfocus amount of 8nm.
  • the distribution of the scanning points may also be non-uniform, for example, the intervals of the scanning points in the x-axis direction and the y-axis direction may not be equal.
  • the scan points are distributed in a helical shape.
  • the initial scanning point can also be set arbitrarily.
  • the amplitude of the physical function is 1, as shown in Figure 5; the phase of the physical function is a random number, as shown in Figure 6.
  • the electron beam function uses the formula For initialization, the amplitude of the electron beam function is shown in Figure 7, and the phase is shown in Figure 8.
  • the electron beam is scanned on the sample, and a series of diffraction patterns obtained are used as data to describe the Fresnel of the electron wave function propagating in the sample.
  • Fresnel (Fresnel) near-field diffraction propagation function that is, the inclination angle is introduced into the propagation function between the sample layers.
  • the inclination angle includes the first inclination angle and the second inclination angle.
  • the loss function is compared with the first inclination angle and The gradient of the second inclination angle updates the first inclination angle and the second inclination angle, and finally obtains the deviation angle of the crystal zone axis of the sample relative to the direction of the incident electron beam and the projected potential of the sample under the normal crystal zone axis. It overcomes the shortcomings of the electron microscope that it is difficult to obtain high spatial resolution images and high-precision structural information when the sample band axis deviates, and can obtain the projected potential of the sample with sub-angstrom resolution when the sample band axis deviates.
  • FIG. 12 is a schematic structural diagram of an electronic stack imaging device for automatically correcting the sample zone axis deviation according to an embodiment of the present invention.
  • the electronic lamination imaging device for automatically correcting the sample ribbon axis deviation includes: an acquisition module 100 , a calculation module 200 , an optimization module 300 and an imaging module 400 .
  • the collection module 100 is configured to scan the sample by electron beams, and collect the diffraction pattern of each scanning point of the sample.
  • This module can be, but is not limited to, a scanning transmission microscope.
  • the calculation module 200 is used to initialize the object function and the electron beam function, construct a forward propagation model according to the propagation function between the sample sheets, and calculate a loss function of the forward propagation model.
  • Variable parameters of the propagation function between the sample sheets include the angle of deviation of the sample zone axis relative to the direction of the incident electron beam.
  • the optimization module 300 is used to solve the gradient of the loss function with respect to the parameter to be optimized, and optimize the parameter to be optimized according to the gradient.
  • the imaging module 400 is configured to execute the function of the calculation module to recalculate the loss function until the iteration termination condition is met, and output optimized parameters.
  • the optimized first inclination angle and the optimized second inclination angle are the angles at which the crystal zone axis of the final sample deviates from the electron beam direction, and the optimized matter function is the projected potential of the final sample under the positive crystal zone axis.
  • the initialization of the physical function includes that the physical function of each layer adopts all 1 amplitudes and random phases.
  • the parameters to be optimized include the physical function, the electron beam function, the deviation angle of the sample zone axis relative to the electron beam direction, that is, the first inclination angle and the second inclination angle.
  • the outgoing wave function in the forward propagation model for:
  • P(rr j ) represents the electron beam scanned to the j-th position
  • O i represents the object function of the i-th layer
  • ⁇ z represents the thickness of the object function of each layer
  • the first inclination angle ⁇ x and the second inclination angle ⁇ y are variable parameters to be optimized.
  • optimizing the parameters to be optimized according to the gradient includes:
  • O′ i is the updated object function
  • P′ is the updated electron beam function
  • ⁇ x ′ is the updated first inclination angle
  • ⁇ y ′ is the updated second inclination angle
  • O i is the learning rate of the object function
  • ⁇ P is the learning rate of the electron beam function P
  • is the gradient of the loss function with respect to the object function is the gradient of the loss function with respect to the electron beam function, and are the gradients of the loss function with respect to the first inclination angle ⁇ x and the second inclination angle ⁇ y , respectively.
  • the iteration termination condition includes:
  • the loss function converges, or the number of iterations reaches the preset threshold of iterations.
  • the electron beam is scanned on the sample, and a series of diffraction patterns obtained are used as data to describe the Fresnel of the electron wave function propagating in the sample.
  • the first dip and the second dip are introduced into the Fresnel near-field diffraction propagation function, that is, the propagation function between the sample sheets, and the loss function relative to the first dip and the second dip is used in the iterative optimization algorithm of stack imaging.
  • the gradient updates the first dip angle and the second dip angle, and finally obtains the deviation angle of the sample crystal zone axis relative to the electron beam direction and the projected potential of the sample under the normal crystal zone axis. It overcomes the shortcomings of the electron microscope that it is difficult to obtain high spatial resolution images and high-precision structural information when the sample band axis deviates, and can obtain the projected potential of the sample with sub-angstrom resolution when the sample band axis deviates.
  • a computer device is provided.
  • the computer device may be a terminal, and its internal structure is shown in FIG. 13 .
  • the computer device includes a processor, a memory, a communication interface, a display screen and an input device connected through a system bus.
  • the processor of the computer device is used to provide calculation and control capabilities.
  • the memory of the computer device includes a non-volatile storage medium and an internal memory.
  • the non-volatile storage medium stores an operating system and computer programs.
  • the internal memory provides an environment for the operation of the operating system and computer programs in the non-volatile storage medium.
  • the communication interface of the computer device is used to communicate with an external terminal in a wired or wireless manner, and the wireless manner can be realized through WIFI, an operator network, NFC (Near Field Communication) or other technologies.
  • the computer program is executed by a processor, the electronic stack imaging method for automatically correcting the deviation of the crystal band axis of the sample is realized.
  • the display screen of the computer device may be a liquid crystal display screen or an electronic ink display screen, and the input device of the computer device may be a touch layer covered on the display screen, or a button, a trackball or a touch pad provided on the casing of the computer device , and can also be an external keyboard, touchpad, or mouse.
  • FIG. 13 is only a block diagram of a part of the structure related to the solution of this application, and does not constitute a limitation on the computer equipment on which the solution of this application is applied.
  • the specific computer equipment can be More or fewer components than shown in the figures may be included, or some components may be combined, or have a different arrangement of components.
  • a computer device including a memory and a processor, where a computer program is stored in the memory, and the processor implements the steps in the above method embodiments when executing the computer program.
  • a computer-readable storage medium on which a computer program is stored, and when the computer program is executed by a processor, the steps in the foregoing method embodiments are implemented.
  • Non-volatile memory may include read-only memory (Read-Only Memory, ROM), magnetic tape, floppy disk, flash memory or optical memory, etc.
  • Volatile memory can include Random Access Memory (RAM) or external cache memory.
  • RAM can take many forms, such as Static Random Access Memory (SRAM) or Dynamic Random Access Memory (DRAM).
  • first and second are used for descriptive purposes only, and cannot be interpreted as indicating or implying relative importance or implicitly specifying the quantity of indicated technical features.
  • the features defined as “first” and “second” may explicitly or implicitly include at least one of these features.
  • “plurality” means at least two, such as two, three, etc., unless otherwise specifically defined.

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Abstract

一种自动矫正样品晶带轴偏离的电子叠层成像方法及装置，方法包括：通过电子束对样品进行扫描，采集样品每个扫描点的衍射图（S1）；初始化物函数和电子束函数，根据样品片层之间的传播函数，构建正向传播模型，计算正向传播模型的损失函数，其中样品片层之间的传播函数的可变参数包括样品带轴相对电子束方向的偏离角度（S2）；求解损失函数关于待优化参数的梯度，根据梯度优化待优化参数（S3）；返回执行初始化物函数和电子束函数，根据样品片层之间的传播函数，构建正向传播模型，重新计算正向传播模型的损失函数，直至满足迭代终止条件，输出优化的参数（S4）。

Description

自动矫正样品晶带轴偏离的电子叠层成像方法及装置
相关申请的交叉引用
本申请要求于2021年8月6日提交的，申请号为202110900738.3的中国专利申请，和2021年8月10日提交的，申请号为202110914428.7的中国专利申请的优先权,在此将其全文引入作为参考。
技术领域
本发明涉及显微成像技术领域，特别涉及一种自动矫正样品晶带轴偏离的电子叠层成像方法及装置。
背景技术
传统电子显微学成像方法在表征材料微观结构方面起到了重要作用。传统电子显微学成像方法包括高分辨透射电子显微成像、扫描透射电子显微成像中的环形暗场像、环形明场像、明场像、微分相位衬度成像等。然而，这些成像方法获得的高分辨图像质量均受到样品倾斜的影响。当样品晶带轴偏离时，原子分辨图像中可能出现衬度假象，不同原子柱由于通道效应强弱不同而产生虚假的相对位移，这给定量表征样品结构信息带来了巨大困难。目前尚无解决样品晶带轴偏离影响的有效方法。
叠层成像是一种在电子显微学领域实现超高分辨率的方法，其优势在于能够同时重构电子束，使图像的分辨率不再受到像差的限制。再引入多片层法后，叠层成像能够解决电子显微学领域的多重散射问题，并具有一定深度分辨率。然而，目前叠层成像也需要样品处于正晶带轴以获得高质量重构结果，这种要求限制了叠层成像的应用场景。
发明内容
本发明旨在至少在一定程度上解决相关技术中的技术问题之一。
为此，本发明的一个目的在于提出一种自动矫正样品晶带轴偏离的电子叠层成像方法，该方法解决了叠层成像中样品晶带轴偏离带来的图像质量降低的问题。
本发明的另一个目的在于提出一种自动矫正样品晶带轴偏离的电子叠层成像装置。
为达到上述目的，本发明一方面实施例提出了一种自动矫正样品晶带轴偏离的电子叠层成像方法，包括以下步骤：通过电子束对样品进行扫描，采集所述样品每个扫描点的衍射图；
初始化物函数和电子束函数，根据所述样品片层之间的传播函数，构建正向传播模型，计算所述正向传播模型的损失函数，所述样品片层之间的所述传播函数的可变参数包括样 品晶带轴相对电子束方向的偏离角度；
求解所述损失函数关于待优化参数的梯度，根据所述梯度优化所述待优化参数；
返回执行所述初始化物函数和电子束函数，根据所述样品片层之间的传播函数，构建正向传播模型，重新计算所述正向传播模型的所述损失函数，直至满足迭代终止条件，输出优化的参数。
为达到上述目的，本发明另一方面实施例提出了一种自动矫正样品晶带轴偏离的电子叠层成像装置，包括采集模块，计算模块，优化模块，和成像模块。
所述采集模块，用于通过电子束对样品进行扫描，采集所述样品每个扫描点的衍射图；
所述计算模块，用于初始化物函数和电子束函数，根据所述样品片层之间的传播函数，构建正向传播模型，计算所述正向传播模型的损失函数，其中所述样品片层之间的所述传播函数的可变参数包括样品晶带轴相对电子束方向的偏离角度。
所述优化模块，用于求解所述损失函数关于待优化参数的梯度，根据所述梯度优化所述待优化参数。
所述成像模块，用于执行所述计算模块重新计算所述正向传播模型的损失函数，直至满足迭代终止条件，输出优化的参数。
本发明实施例的自动矫正样品晶带轴偏离的电子叠层成像方法及装置，将电子束在样品上扫描，获得的一系列衍射图作为数据，在描述电子波函数在样品中传播的菲涅尔(Fresnel)近场衍射传播函数即样品片层之间的传播函数中引入倾角，倾角包括第一倾角和第二倾角，在叠层成像的迭代优化算法中通过损失函数相对于第一倾角和第二倾角的梯度更新第一倾角和第二倾角，最终获得样品晶带轴相对电子束方向的偏离角度和样品在正晶带轴下的投影势。克服了样品晶带轴偏离时电子显微镜难以获得高空间分辨图像和高精度结构信息的缺点，可以在样品晶带轴偏离的情况下获得具有亚埃分辨率的样品投影势
本发明附加的方面和优点将在下面的描述中部分给出，部分将从下面的描述中变得明显，或通过本发明的实践了解到。
附图说明
图1为根据本发明一个实施例的自动矫正样品晶带轴偏离的电子叠层成像方法的流程图。
图2为根据本发明一个实施例的所用样品钛酸钡沿方向[001]的投影结构。
图3为根据本发明一个实施例的电子束扫描点的分布图。
图4为根据本发明一个实施例的所有扫描位置衍射图案的平均的示意图。
图5为根据本发明一个实施例的迭代优化算法初始化的物函数振幅图。
图6为根据本发明一个实施例的迭代优化算法初始化的物函数相位图。
图7为根据本发明一个实施例的迭代优化算法初始化的电子束函数振幅图。
图8为根据本发明一个实施例的迭代优化算法初始化的电子束函数相位图。
图9为根据本发明一个实施例的迭代优化算法重构出的物函数平均相位图。
图10为根据本发明一个实施例的迭代优化算法重构出的电子束函数的振幅图。
图11为根据本发明一个实施例的迭代优化算法的迭代过程中物体沿x方向的第一倾角和y方向的第二倾角变化曲线示意图。
图12为根据本发明一个实施例的自动矫正样品晶带轴偏离的电子叠层成像装置结构示意图。
图13为本申请一个实施例中计算机设备的内部结构示意图。
具体实施方式
下面详细描述本发明的实施例，所述实施例的示例在附图中示出，其中自始至终相同或类似的标号表示相同或类似的元件或具有相同或类似功能的元件。下面通过参考附图描述的实施例是示例性的，旨在用于解释本发明，而不能理解为对本发明的限制。
下面参照附图描述根据本发明实施例提出的自动矫正样品晶带轴偏离的电子叠层成像方法及装置，可应用但不局限于扫描透射电子显微镜。
图1为根据本发明一个实施例的自动矫正样品晶带轴偏离的电子叠层成像方法的流程图。
如图1所示，该自动矫正样品晶带轴偏离的电子叠层成像方法包括以下步骤S1-S4。
在步骤S1中，通过电子束对样品进行扫描，采集样品每个扫描点的衍射图。
在本发明的实施例中，包括样品，电子源和探测器，通过电子源发出电子束在样品上进行扫描，由探测器记录每个扫描位置的散射信号，采集每个扫描点的衍射图。
在步骤S2中，初始化物函数和电子束函数，根据样品片层之间的传播函数，构建正向传播模型，计算正向传播模型的损失函数。样品片层之间的传播函数的可变参数包括样品晶带轴相对入射电子束方向的偏离角度。
进一步地，在本发明的一个实施例中，初始化物函数和电子束函数。每一层物函数均采用全1幅值和随机相位，电子束函数P(r)根据光阑函数和像差函数构建：
Figure PCTCN2022110146-appb-000001
其中A(k)为光阑函数，χ(k)为像差函数。
进一步地，在本发明的一个实施例中，将损失函数定义为关于物函数、电子束函数等的函数。其中，损失函数
Figure PCTCN2022110146-appb-000002
包括但不限于以下形式：
Figure PCTCN2022110146-appb-000003
其中，j代表扫描位置的序号，|·|代表计算矩阵中每个元素的模，
Figure PCTCN2022110146-appb-000004
代表计算矩阵的傅里叶变换，‖·‖ F’代表计算矩阵的弗罗贝尼乌斯范数(Frobeniusnorm)，
Figure PCTCN2022110146-appb-000005
是待优化的出射波函数，I是采集到的衍射强度矩阵。
在本发明的一个实施例中，正向传播模型中的出射波函数
Figure PCTCN2022110146-appb-000006
可以表示为：
Figure PCTCN2022110146-appb-000007
其中，P(r-r j)代表扫描到第j个位置的电子束，O i代表第i层的物函数。可以假设每层物函数具有相同的厚度和倾角，
Figure PCTCN2022110146-appb-000008
代表菲涅尔近场衍射作用因子，可以表示为：
Figure PCTCN2022110146-appb-000009
其中，p(k；Δz,θ)＝exp[-iπΔz(λk 2-2k xtanθ x-2k ytanθ y)],Δz代表每一层物函数的厚度，θ＝(θ x,θ y)代表样品晶带轴相对电子束方向的偏离角度，包括第一倾角θ x,第二倾角θ y。将第一倾角θ x,和第二倾角θ y做为待优化参数，通过求解损失函数
Figure PCTCN2022110146-appb-000010
对物函数O i、电子束函数P、第一倾角θ x,第二倾角θ y等参数的梯度，对相应参数进行迭代优化。
在步骤S3中，求解损失函数关于待优化参数的梯度，根据梯度优化待优化参数。
在本发明的实施例中，待优化参数包括物函数、电子束函数、样品晶带轴相对电子束方向的偏离角度即第一倾角和第二倾角。求解损失函数关于物函数O i、电子束函数P、第一倾角θ x,和第二倾角θ y等参数的梯度。
具体地，梯度的求取可以利用具有自动求导功能的软件库来实现。在一实施例中，例如损失函数关于倾角θ x(k＝x或y)的梯度可以通过以下表达式实现：
Figure PCTCN2022110146-appb-000011
Figure PCTCN2022110146-appb-000012
Figure PCTCN2022110146-appb-000013
其中，
Figure PCTCN2022110146-appb-000014
的求取方法与
Figure PCTCN2022110146-appb-000015
类似，将任意一层的菲涅尔传播函数替换为菲涅尔传播函数对倾角θ k的导数。例如，当物函数包含偶数(N)个片层时，将第N/2层的菲涅尔传播函数进行替换。
Figure PCTCN2022110146-appb-000016
Figure PCTCN2022110146-appb-000017
Figure PCTCN2022110146-appb-000018
Figure PCTCN2022110146-appb-000019
在本申请的一实施例中，计算出梯度后，利用计算的梯度对待优化参数进行更新。作为一种实施例方式，可以通过下述公式对待优化参数进行更新：
Figure PCTCN2022110146-appb-000020
Figure PCTCN2022110146-appb-000021
Figure PCTCN2022110146-appb-000022
Figure PCTCN2022110146-appb-000023
其中，O′ i为更新后的物函数、P′为更新后的电子束函数、θ x′为更新后的第一倾角、θ y′更新后的第二倾角，
Figure PCTCN2022110146-appb-000024
为物函数O i的学习率、α P为电子束函数P的学习率、
Figure PCTCN2022110146-appb-000025
和
Figure PCTCN2022110146-appb-000026
是第一倾角θ x,第二倾角θ y的学习率，
Figure PCTCN2022110146-appb-000027
为损失函数关于物函数的梯度，
Figure PCTCN2022110146-appb-000028
为损失函数关于电子束函数的梯度，
Figure PCTCN2022110146-appb-000029
和
Figure PCTCN2022110146-appb-000030
分别为损失函数关于第一倾角θ x,和第二倾角θ y的梯度。
在步骤S4中，返回执行步骤S2，重新计算损失函数，直至满足迭代终止条件，输出优化的参数。
优化的第一倾角和优化的第二倾角，为最终的样品晶带轴相对电子束方向偏离的角度，优化的物函数为最终的样品在正晶带轴下的投影势。
进一步地，在本发明的一个实施例中，迭代终止条件包括：损失函数收敛；或，迭代次数达到预设迭代次数阈值。
具体地，通过步骤S3中更新的参数，重新计算损失函数，重复执行S2-S3，反复迭代，直至损失函数收敛或迭代次数达到设定的迭代次数阈值，结束迭代，最终得到优化的参数，进而利用优化的参数进行样品成像。
通过上述实施例的方法可以自动矫正样品晶带轴偏离，从而减小对分辨率和结构测量精度产生的影响，放宽了电子显微学的实验要求，使叠层成像即使在样品明显偏离正晶带轴时仍能获得超高分辨率和皮米精度结构测量。
下面通过一个具体实施例，对本发明的自动矫正样品晶带轴偏离的电子叠层成像方法进行详细说明。
本实例中需要观察的是钛酸钡沿方向[001]的投影，投影结构如图2所示，对于传统成像方法，电子束需与钛酸钡的投影方向[001]基本平行，才能得到正确的高分辨图像。
本例中样品偏离方向[001]的倾角为8mrad，电子束在样品上进行扫描，扫描位置如图3所示，扫描点分布为均匀的网格分布，探测器收集每个扫描位置的衍射图案，所有衍射图案的平均如图4所示，采用的会聚半角为22mrad，欠焦量为8nm。
在本申请的其他实施例中，扫描点的分布也可以是不均匀的，例如扫描点在x轴方向和y轴方向的间距可以不相等。在一些实施例中，扫描点的分布呈螺旋状。在其他实施例中，起始扫描点也可以任意设置。
初始化物函数与电子束函数，物函数的所有片层都相同，物函数的振幅为1，如图5所示；物函数的相位为随机数，参照图6所示。电子束函数采用公式
Figure PCTCN2022110146-appb-000031
Figure PCTCN2022110146-appb-000032
进行初始化，电子束函数的振幅如图7所示，相位如图8所示。
计算损失函数
Figure PCTCN2022110146-appb-000033
以及损失函数关于各参数的梯度，并用以下公式对各参数进行迭代更新：
Figure PCTCN2022110146-appb-000034
Figure PCTCN2022110146-appb-000035
Figure PCTCN2022110146-appb-000036
Figure PCTCN2022110146-appb-000037
最终得到所有片层的物函数的平均相位如图9所示，电子束函数的振幅如图10所 示，样品晶带轴相对入射电子束方向的偏离角度随迭代次数的变化如图11所示。
根据本发明实施例提出的自动矫正样品晶带轴偏离的电子叠层成像方法，将电子束在样品上扫描，获得的一系列衍射图作为数据，在描述电子波函数在样品中传播的菲涅尔(Fresnel)近场衍射传播函数即样品片层之间的传播函数中引入倾角，倾角包括第一倾角和第二倾角，在叠层成像的迭代优化算法中通过损失函数相对于第一倾角和第二倾角的梯度更新第一倾角和第二倾角，最终获得样品晶带轴相对入射电子束方向的偏离角度和样品在正晶带轴下的投影势。克服了样品晶带轴偏离时电子显微镜难以获得高空间分辨图像和高精度结构信息的缺点，可以在样品晶带轴偏离的情况下获得具有亚埃分辨率的样品投影势。
以下参照附图描述根据本发明实施例提出的自动矫正样品晶带轴偏离的电子叠层成像装置。
图12为根据本发明一个实施例的自动矫正样品晶带轴偏离的电子叠层成像装置结构示意图。
如图12所示，该自动矫正样品晶带轴偏离的电子叠层成像装置包括：采集模块100、计算模块200、优化模块300和成像模块400。
其中，采集模块100，用于通过电子束对样品进行扫描，采集样品每个扫描点的衍射图。该模块可以但不局限于扫描透射显微镜。计算模块200，用于初始化物函数和电子束函数，根据样品片层之间的传播函数，构建正向传播模型，计算正向传播模型的损失函数。样品片层之间的传播函数的可变参数包括样品晶带轴相对入射电子束方向的偏离角度。优化模块300，用于求解损失函数关于待优化参数的梯度，根据梯度优化待优化参数。成像模块400，用于执行计算模块的功能重新计算损失函数，直至满足迭代终止条件，输出优化的参数。
优化的第一倾角和优化的第二倾角，为最终的样品晶带轴相对电子束方向偏离的角度，优化后的物函数为最终的样品在正晶带轴下的投影势。
进一步地，在本发明的一个实施例中，初始化物函数包括每一层物函数均采用全1幅值和随机相位。
进一步地，在本发明的一个实施例中，待优化参数包括物函数、电子束函数、样品晶带轴相对电子束方向的偏离角度即第一倾角和第二倾角。
进一步地，在本发明的一个实施例中，正向传播模型中的出射波函数
Figure PCTCN2022110146-appb-000038
为：
Figure PCTCN2022110146-appb-000039
其中，P(r-r j)代表扫描到第j个位置的电子束，O i代表第i层的物函数，
Figure PCTCN2022110146-appb-000040
代 表菲涅尔近场衍射作用因子，表示为：
Figure PCTCN2022110146-appb-000041
其中，p(k；Δz,θ)＝exp[-iπΔz(λk 2-2k xtanθ x-2k ytanθ y)]，
Δz代表每一层物函数的厚度，θ＝(θ x,θ y)代表样品晶带轴相对电子束方向的偏离角度，包括第一倾角θ x和第二倾角θ y。第一倾角θ x和第二倾角θ y为可变的待优化参数。
进一步地，在本发明的一个实施例中，根据梯度优化待优化参数，包括：
Figure PCTCN2022110146-appb-000042
Figure PCTCN2022110146-appb-000043
Figure PCTCN2022110146-appb-000044
Figure PCTCN2022110146-appb-000045
其中，O′ i为更新后的物函数、P′为更新后的电子束函数、θ x′为更新后的第一倾角、θ y′为更新后的第二倾角、
Figure PCTCN2022110146-appb-000046
为物函数O i的学习率、α P为电子束函数P的学习率、
Figure PCTCN2022110146-appb-000047
和
Figure PCTCN2022110146-appb-000048
是第一倾角θ x和第二倾角θ y的学习率，
Figure PCTCN2022110146-appb-000049
为损失函数关于物函数的梯度，
Figure PCTCN2022110146-appb-000050
为损失函数关于电子束函数的梯度，
Figure PCTCN2022110146-appb-000051
和
Figure PCTCN2022110146-appb-000052
分别为损失函数关于第一倾角θ x和第二倾角θ y的梯度。
进一步地，在本发明的一个实施例中，迭代终止条件包括：
损失函数收敛,或迭代次数达到预设迭代次数阈值。
需要说明的是，前述对方法实施例的解释说明也适用于该实施例的装置，此处不再赘述。
根据本发明实施例提出的自动矫正样品晶带轴偏离的电子叠层成像方法，将电子束在样品上扫描，获得的一系列衍射图作为数据，在描述电子波函数在样品中传播的菲涅尔(Fresnel)近场衍射传播函数即样品片层之间的传播函数中引入第一倾角和第二倾角，在叠层成像的迭代优化算法中通过损失函数相对于第一倾角和第二倾角的梯度更新第一倾角和第二倾角，最终获得样品晶带轴相对电子束方向的偏离角度和样品在正晶带轴下的投影势。克服了样品晶带轴偏离时电子显微镜难以获得高空间分辨图像和高精度结构信息的缺点，可以在样品晶带轴偏离的情况下获得具有亚埃分辨率的样品投影势。
在一个实施例中，提供了一种计算机设备，该计算机设备可以是终端，其内部结构如图13所示。该计算机设备包括通过系统总线连接的处理器、存储器、通信接口、显示屏和输入装置。其中，该计算机设备的处理器用于提供计算和控制能力。该计算机设备的存储器包括非易失性存储介质、内存储器。该非易失性存储介质存储有操作系统和计算机程序。该内存储器为非易失性存储介质中的操作系统和计算机程序的运行提供环境。该计算机设备的通信接口用于与外部的终端进行有线或无线方式的通信，无线方式可通过WIFI、运营商网络、NFC(近场通信)或其他技术实现。该计算机程序被处理器执行时以实现自动矫正样品晶带轴偏离的电子叠层成像方法。该计算机设备的显示屏可以是液晶显示屏或者电子墨水显示屏，该计算机设备的输入装置可以是显示屏上覆盖的触摸层，也可以是计算机设备外壳上设置的按键、轨迹球或触控板，还可以是外接的键盘、触控板或鼠标等。
本领域技术人员可以理解，图13中示出的结构，仅仅是与本申请方案相关的部分结构的框图，并不构成对本申请方案所应用于其上的计算机设备的限定，具体的计算机设备可以包括比图中所示更多或更少的部件，或者组合某些部件，或者具有不同的部件布置。
在一个实施例中，还提供了一种计算机设备，包括存储器和处理器，存储器中存储有计算机程序，该处理器执行计算机程序时实现上述各方法实施例中的步骤。
在一个实施例中，提供了一种计算机可读存储介质，其上存储有计算机程序，该计算机程序被处理器执行时实现上述各方法实施例中的步骤。
本领域普通技术人员可以理解实现上述实施例方法中的全部或部分流程，是可以通过计算机程序来指令相关的硬件来完成，所述的计算机程序可存储于一非易失性计算机可读取存储介质中，该计算机程序在执行时，可包括如上述各方法的实施例的流程。其中，本申请所提供的各实施例中所使用的对存储器、存储、数据库或其它介质的任何引用，均可包括非易失性和易失性存储器中的至少一种。非易失性存储器可包括只读存储器(Read-Only Memory，ROM)、磁带、软盘、闪存或光存储器等。易失性存储器可包括随机存取存储器(Random Access Memory，RAM)或外部高速缓冲存储器。作为说明而非局限，RAM可以是多种形式，比如静态随机存取存储器(Static Random Access Memory，SRAM)或动态随机存取存储器(Dynamic Random Access Memory，DRAM)等。
此外，术语“第一”、“第二”仅用于描述目的，而不能理解为指示或暗示相对重要性或者隐含指明所指示的技术特征的数量。由此，限定有“第一”、“第二”的特征可以明示或者隐含地包括至少一个该特征。在本发明的描述中，“多个”的含义是至少两个，例如两个，三个等，除非另有明确具体的限定。
在本说明书的描述中，参考术语“一个实施例”、“一些实施例”、“示例”、“具体示例”、或“一些示例”等的描述意指结合该实施例或示例描述的具体特征、结构、材料或者特点包含于本发明的至少一个实施例或示例中。在本说明书中，对上述术语的示意性表述不必须针对的是相同的实施例或示例。而且，描述的具体特征、结构、材料或者特点可以在任一个或多个实施例或示例中以合适的方式结合。此外，在不相互矛盾的情况下，本领域的技术人员可以将本说明书中描述的不同实施例或示例以及不同实施例或示例的特征进行结合和组合。
尽管上面已经示出和描述了本发明的实施例，可以理解的是，上述实施例是示例性的，不能理解为对本发明的限制，本领域的普通技术人员在本发明的范围内可以对上述实施例进行变化、修改、替换和变型。

Claims (13)

  1. 一种自动矫正样品晶带轴偏离的电子叠层成像方法，其特征在于，包括：
    通过电子束对样品进行扫描，采集所述样品每个扫描点的衍射图；
    初始化物函数和电子束函数，根据所述样品片层之间的传播函数，构建正向传播模型，计算所述正向传播模型的损失函数，其中所述样品片层之间的所述传播函数的可变参数包括样品晶带轴相对电子束方向的偏离角度；
    求解所述损失函数关于待优化参数的梯度，根据所述梯度优化所述待优化参数；
    返回执行所述初始化物函数和电子束函数，根据所述样品片层之间的传播函数，构建正向传播模型，重新计算所述正向传播模型的损失函数，直至满足迭代终止条件，输出优化的参数。
  2. 根据权利要求1所述的方法，其特征在于，所述待优化参数包括所述物函数、所述电子束函数、所述样品晶带轴相对所述电子束方向的偏离角度，所述偏离角度包括第一倾角和第二倾角。
  3. 根据权利要求1所述的方法，其特征在于，所述正向传播模型中的出射波函数为：
    Figure PCTCN2022110146-appb-100001
    其中，P(r-r j)代表扫描到第j个位置的电子束，O i代表第i层的物函数，
    Figure PCTCN2022110146-appb-100002
    代表菲涅尔近场衍射作用因子，所述作用因子为：
    Figure PCTCN2022110146-appb-100003
    其中，p(k；Δz,θ)＝exp[-iπΔz(λk 2-2k xtanθ x-2k ytanθ y)]，Δz代表每一层物函数的厚度；θ＝(θ x,θ y)代表所述样品晶带轴相对电子束方向的所述偏离角度，所述偏离角度包括第一倾角和第二倾角，θ x为所述第一倾角，θ y为所述第二倾角，为所述待优化参数。
  4. 根据权利要求1所述的方法，其特征在于，所述根据所述梯度优化所述待优化参数，包括：
    Figure PCTCN2022110146-appb-100004
    Figure PCTCN2022110146-appb-100005
    Figure PCTCN2022110146-appb-100006
    Figure PCTCN2022110146-appb-100007
    其中，所述偏离角度包括第一倾角和第二倾角；O i为所述物函数、p为所述电子束函数、θ x为所述第一倾角、θ y所述第二倾角；O′ i为更新后的物函数、P′为更新后的电子束函数、θ x′为更新后的第一倾角、θ y′更新后的第二倾角；
    Figure PCTCN2022110146-appb-100008
    为所述物函数O i的学习率、α P为所述电子束函数P的学习率、
    Figure PCTCN2022110146-appb-100009
    和
    Figure PCTCN2022110146-appb-100010
    是所述第一倾角θ x和所述第二倾角θ y的学习率，
    Figure PCTCN2022110146-appb-100011
    为所述损失函数关于所述物函数的梯度，
    Figure PCTCN2022110146-appb-100012
    为所述损失函数关于所述电子束函数的梯度，
    Figure PCTCN2022110146-appb-100013
    和
    Figure PCTCN2022110146-appb-100014
    分别为所述损失函数关于所述第一倾角θ x和所述第二倾角θ y的梯度。
  5. 根据权利要求1所述的方法，其特征在于，所述迭代终止条件包括：
    损失函数收敛；或
    迭代次数达到预设迭代次数阈值。
  6. 根据权利要求1所述的方法，其特征在于，所述优化的参数包括优化的第一倾角和优化的第二倾角，以及优化的物函数，其中，所述优化的物函数为最终的样品在正晶带轴下的投影势。
  7. 一种自动矫正样品晶带轴偏离的电子叠层成像装置，其特征在于，包括：
    采集模块，用于通过电子束对样品进行扫描，采集所述样品每个扫描点的衍射图；
    计算模块，用于初始化物函数和电子束函数，根据所述样品片层之间的传播函数，构建正向传播模型，计算所述正向传播模型的损失函数，其中所述样品片层之间的所述传播函数的可变参数包括样品晶带轴相对电子束方向的偏离角度；
    优化模块，用于求解所述损失函数关于待优化参数的梯度，根据所述梯度优化所述待优化参数；
    成像模块，用于执行所述计算模块重新计算所述正向传播模型的损失函数，直至满足迭代终止条件，输出优化的参数。
  8. 根据权利要求7所述的装置，其特征在于，所述待优化参数包括所述物函数、所述电子束函数、所述样品晶带轴相对所述电子束方向的偏离角度，所述偏离角度包括第一倾 角和第二倾角。
  9. 根据权利要求7所述的装置，其特征在于，所述正向传播模型中的出射波函数为：
    Figure PCTCN2022110146-appb-100015
    其中，P(r-r j)代表扫描到第j个位置的电子束，O i代表第i层的物函数，
    Figure PCTCN2022110146-appb-100016
    代表菲涅尔近场衍射作用因子，所述作用因子为：
    Figure PCTCN2022110146-appb-100017
    其中，p(k；Δz,θ)＝exp[-iπΔz(λk 2-2k xtanθ x-2k ytanθ y)]，Δz代表每一层物函数的厚度；θ＝(θ x,θ y)代表所述样品晶带轴相对电子束方向的所述偏离角度，所述偏离角度包括第一倾角和第二倾角，θ x为所述第一倾角，θ y为所述第二倾角，为所述待优化参数。
  10. 根据权利要求7所述的装置，其特征在于，所述根据所述梯度优化所述待优化参数，包括：
    Figure PCTCN2022110146-appb-100018
    Figure PCTCN2022110146-appb-100019
    Figure PCTCN2022110146-appb-100020
    Figure PCTCN2022110146-appb-100021
    其中，所述偏离角度包括第一倾角和第二倾角；O i为所述物函数、p为所述电子束函数、θ x为所述第一倾角、θ y所述第二倾角；O′ i为更新后的物函数、P′为更新后的电子束函数、θ x′为更新后的第一倾角、θ y′更新后的第二倾角；
    Figure PCTCN2022110146-appb-100022
    为所述物函数O i的学习率、α P为所述电子束函数P的学习率、
    Figure PCTCN2022110146-appb-100023
    和
    Figure PCTCN2022110146-appb-100024
    是所述第一倾角θ x和所述第二倾角θ y的学习率，
    Figure PCTCN2022110146-appb-100025
    为所述损失函数关于所述物函数的梯度，
    Figure PCTCN2022110146-appb-100026
    为所述损失函数关于所述电子束函数的梯度，
    Figure PCTCN2022110146-appb-100027
    和
    Figure PCTCN2022110146-appb-100028
    分别为所述损失函数关于所述第一倾角θ x和所述第二倾角θ y的梯度。
  11. 根据权利要求7所述的装置，其特征在于，所述迭代终止条件包括：
    损失函数收敛；或
    迭代次数达到预设迭代次数阈值。
  12. 一种计算机设备，包括存储器和处理器，所述存储器存储计算机程序，其中，所述处理器执行所述计算机程序时，执行权利要求1-6所述的任一方法的步骤。
  13. 一种非易失计算机可读存储介质，其上存储有计算机程序，其中，所述计算机程序被处理器执行时，执行权利要求1-6所述的任一方法的步骤。
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