阅读说明：本技术 自动矫正样品带轴偏离的电子层叠成像方法及装置 (Electronic lamination imaging method and device for automatically correcting tape axis deviation of sample ) 是由 于荣 沙浩治 崔吉哲 于 2021-08-10 设计创作，主要内容包括：本发明公开了一种自动矫正样品带轴偏离的电子层叠成像方法及装置,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；初始化物函数和电子束函数,构建正向传播模型,计算损失函数；求解损失函数关于物函数、电子束函数和样品倾角等参数的梯度,根据梯度优化待优化参数；重新计算损失函数进行迭代,直至满足迭代终止条件,输出样品偏离正带轴的角度和样品在正带轴下的投影势。该方法和装置解决了层叠成像中样品带轴偏离带来的图像质量降低的问题,能提高图像分辨率。(The invention discloses an electronic stack imaging method and device for automatically correcting tape axis deviation of a sample, comprising the following steps: scanning a sample through an electron beam, and collecting a diffraction pattern of each scanning point of the sample; initializing a materialization function and an electron beam function, constructing a forward propagation model, and calculating a loss function; solving the gradient of the loss function with respect to parameters such as an object function, an electron beam function, a sample inclination angle and the like, and optimizing the parameter to be optimized according to the gradient; and recalculating the loss function for iteration until an iteration termination condition is met, and outputting the angle of the sample deviating from the positive belt axis and the projection potential of the sample under the positive belt axis. The method and the device solve the problem of image quality reduction caused by sample belt axis deviation in laminated imaging and can improve image resolution.)

1. An electronic stacking imaging method for automatically correcting tape axis deviation of a sample is characterized by comprising the following steps:

s1, scanning the sample through the electron beam, and collecting a diffraction pattern of each scanning point of the sample;

s2, initializing a materialization function and an electron beam function, and when a forward propagation model is constructed, using the tilting angle of the sample relative to the electron beam as a variable parameter, including the variable parameter into the propagation function between sample slices, and calculating the loss function of the forward propagation model;

s3, solving the gradient of the loss function about the parameter to be optimized, and optimizing the parameter to be optimized according to the gradient;

and S4, executing the S2 to recalculate the loss function until an iteration termination condition is met, outputting the parameter to be optimized, wherein the obtained tilting angle is the angle of the deviation of the sample tape axis relative to the electron beam direction, and the objective function is the projection of the sample under the positive tape axis.

2. The method of claim 1, wherein the parameters to be optimized include an objective function, an incident electron beam function, and a deviation of a sample strip axis from an electron beam direction.

3. The method of claim 1, wherein the exit wave function in the forward propagation model is:

wherein, P (r-r)_j) Representing the electron beam scanned to the jth location,represents the objective function of the ith layer,represents a Fresnel near-field diffraction effect factor, and the effect is expressed as:

p(k；Δz，θ)＝exp[-iπΔz(λk²-2k_xtanθ_x-2k_ytanθ_y)]，

wherein Δ z represents the thickness of each layer of the physical function, (θ)_x，θ_y) Representing the angle of the object off the positive belt axis, (theta)_x，θ_y) Are variable parameters.

4. The method of claim 1, wherein the optimizing the parameter to be optimized according to the gradient comprises:

wherein the content of the first and second substances,α_P、andis a function of an objectElectron beam function P and inclination angle of sample off positive band axis (θ)_x，θ_y) The learning rate of (a) is determined,is the gradient of the object function and is,is the gradient of the function of the electron beam,andare respectively an inclination angle (theta)_x，θ_y) Of the gradient of (c).

5. The method of claim 1, wherein the iteration termination condition comprises:

converging a loss function; or

Reaching the preset iteration times.

6. An electronic stack imaging apparatus for automatically correcting tape axis misalignment of a sample, comprising:

the acquisition module is used for scanning a sample through an electron beam and acquiring a diffraction pattern of each scanning point of the sample;

the calculation module is used for initializing a materialization function and an electron beam function, and when a forward propagation model is constructed, the tilting angle of the sample relative to the electron beam is used as a variable parameter and is included in the propagation function between sample slices, and the loss function of the forward propagation model is calculated;

the optimization module is used for solving the gradient of the loss function about the parameter to be optimized and optimizing the parameter to be optimized according to the gradient;

and the imaging module is used for executing the calculation module to recalculate the loss function until an iteration termination condition is met, outputting the parameter to be optimized, wherein the obtained tilting angle is the angle of the sample belt shaft deviating relative to the direction of the electron beam, and the objective function is the projection of the sample under the positive belt shaft.

7. The apparatus of claim 6, wherein the parameters to be optimized include an objective function, an incident electron beam function, and a deviation of a sample strip axis from an electron beam direction.

8. The apparatus of claim 6, wherein the exit wave function in the forward propagation model is:

wherein, P (r-r)_j) Representing the electron beam scanned to the jth location,represents the objective function of the ith layer,represents a Fresnel near-field diffraction effect factor, and the effect is expressed as:

p(k；Δz，θ)＝exp[-iπΔz(λk²-2k_xtanθ_x-2k_ytanθ_y)]，

wherein Δ z represents the thickness of each layer of the physical function, (θ)_x，θ_y) Representing the angle of the object off the positive belt axis, (theta)_x，θ_y) Are variable parameters.

9. The apparatus of claim 6, wherein the optimizing the parameter to be optimized according to the gradient comprises:

wherein the content of the first and second substances,α_P、andis a function of an objectElectron beam function P and inclination angle of sample off positive band axis (θ)_x，θ_y) The learning rate of (a) is determined,is the gradient of the object function and is,is the gradient of the function of the electron beam,andare respectively an inclination angle (theta)_x，θ_y) Of the gradient of (c).

10. The apparatus of claim 6, wherein the iteration termination condition comprises:

converging a loss function; or

Reaching the preset iteration times.

Technical Field

The invention relates to the technical field of microscopic imaging, in particular to an electronic stack imaging method and device for automatically correcting tape axis deviation of a sample.

Background

Traditional electron microscopy imaging methods play an important role in characterizing the microstructure of materials. Conventional electron microscopy imaging methods include high resolution transmission electron microscopy, annular dark field imaging, annular bright field imaging, differential phase contrast imaging in scanning transmission electron microscopy, and the like. However, the high resolution image quality obtained by these imaging methods is affected by sample tilt. When the sample band axis deviates, contrast artifacts may appear in the atom resolution image, and different atom columns generate false relative displacement due to different channel effects, which brings great difficulty to quantitative characterization of sample structure information. At present, no effective method for solving the influence of the belt axis deviation of the sample exists.

Stacked imaging is a method for achieving ultra-high resolution in the field of electron microscopy, and has the advantage that electron beams can be reconstructed simultaneously, so that the resolution of images is not limited by aberrations any more. After a multi-slice method is introduced, the problem of multiple scattering in the field of electron microscopy can be solved by laminated imaging, and the depth resolution ratio is certain. However, the current cascade imaging also requires the sample to be on the positive band axis to obtain high quality reconstruction results, and this requirement limits the application scenarios of cascade imaging.

Disclosure of Invention

The present invention is directed to solving, at least to some extent, one of the technical problems in the related art.

Therefore, an object of the present invention is to provide an electronic stack imaging method for automatically correcting the sample tape axis deviation, which solves the problem of image quality degradation caused by the sample tape axis deviation in stack imaging.

Another object of the present invention is to provide an electronic stack imaging apparatus for automatically correcting tape axis deviation of a sample.

In order to achieve the above object, an embodiment of the present invention provides an electronic stack imaging method for automatically correcting tape axis deviation of a sample, including the following steps:

s1, scanning the sample through the electron beam, and collecting a diffraction pattern of each scanning point of the sample;

s2, initializing a materialization function and an electron beam function, and when a forward propagation model is constructed, using the tilting angle of the sample relative to the electron beam as a variable parameter, including the variable parameter into the propagation function between sample slices, and calculating the loss function of the forward propagation model;

s3, solving the gradient of the loss function about the parameter to be optimized, and optimizing the parameter to be optimized according to the gradient;

and S4, executing the S2 to recalculate the loss function until an iteration termination condition is met, outputting the parameter to be optimized, wherein the obtained tilting angle is the angle of the deviation of the sample tape axis relative to the electron beam direction, and the objective function is the projection of the sample under the positive tape axis.

In order to achieve the above object, according to another embodiment of the present invention, an electronic stacked imaging apparatus for automatically correcting tape axis deviation of a sample is provided, including:

the acquisition module is used for scanning a sample through an electron beam and acquiring a diffraction pattern of each scanning point of the sample;

the calculation module is used for initializing a materialization function and an electron beam function, and when a forward propagation model is constructed, the tilting angle of the sample relative to the electron beam is used as a variable parameter and is included in the propagation function between sample slices, and the loss function of the forward propagation model is calculated;

the optimization module is used for solving the gradient of the loss function about the parameter to be optimized and optimizing the parameter to be optimized according to the gradient;

and the imaging module is used for executing the calculation module to recalculate the loss function until an iteration termination condition is met, outputting the parameter to be optimized, wherein the obtained tilting angle is the angle of the sample belt shaft deviating relative to the direction of the electron beam, and the objective function is the projection of the sample under the positive belt shaft.

According to the electronic stack imaging method and device for automatically correcting the tape axis deviation of the sample, a series of diffraction patterns obtained by scanning an electron beam on the sample are used as data, an inclination angle is introduced into a Fresnel (Fresnel) near-field diffraction propagation function describing the propagation of an electronic wave function in the sample, the inclination angle is updated through the gradient of a loss function relative to the inclination angle in an iterative optimization algorithm of stack imaging, and finally the tape axis deviation angle of the sample and the projection potential of the sample under a positive tape axis are obtained. The defect that an electron microscope is difficult to obtain high-spatial resolution images and high-precision structural information when a sample belt axis deviates is overcome, and the sample projection potential with sub-angstrom resolution can be obtained under the condition that the sample belt axis deviates.

Additional aspects and advantages of the invention will be set forth in part in the description which follows and, in part, will be obvious from the description, or may be learned by practice of the invention.

Drawings

The foregoing and/or additional aspects and advantages of the present invention will become apparent and readily appreciated from the following description of the embodiments, taken in conjunction with the accompanying drawings of which:

FIG. 1 is a flow chart of an electronic stack imaging method for automatically correcting tape-axis misalignment of a sample according to one embodiment of the present invention;

FIG. 2 is a projection structure of barium titanate along [001] direction of a sample used according to an embodiment of the present invention;

FIG. 3 is a distribution diagram of electron beam scanning spots according to one embodiment of the present invention;

FIG. 4 is a schematic representation of the average of the diffraction patterns at all scan positions according to one embodiment of the present invention;

FIG. 5 is an algorithm initialized object function amplitude image according to one embodiment of the present invention;

FIG. 6 is an algorithm initialized object function phase image according to one embodiment of the present invention;

FIG. 7 is an algorithm initialized beam function amplitude according to one embodiment of the present invention;

FIG. 8 is an algorithm initialized electron beam function phase according to one embodiment of the present invention;

FIG. 9 is an object function mean phase image reconstructed by the algorithm according to one embodiment of the present invention;

FIG. 10 is an amplitude image of the electron beam function reconstructed by the algorithm according to one embodiment of the present invention;

FIG. 11 is a graphical representation of the variation of the tilt of an object in the x and y directions during an iteration of the algorithm in accordance with one embodiment of the present invention;

fig. 12 is a schematic structural diagram of an electronic stacked imaging device for automatically correcting tape-axis deviation of a sample according to an embodiment of the invention.

Detailed Description

Reference will now be made in detail to embodiments of the present invention, examples of which are illustrated in the accompanying drawings, wherein like or similar reference numerals refer to the same or similar elements or elements having the same or similar function throughout. The embodiments described below with reference to the drawings are illustrative and intended to be illustrative of the invention and are not to be construed as limiting the invention.

An electronic stack imaging method and apparatus for automatically correcting tape axis deviation of a sample according to an embodiment of the present invention will be described with reference to the accompanying drawings. Scanning transmission electron microscopy is applicable but not limited.

FIG. 1 is a flow chart of an electronic stack imaging method for automatically correcting tape axis misalignment of a sample according to one embodiment of the invention.

As shown in fig. 1, the electronic stack imaging method for automatically correcting the tape axis deviation of the sample comprises the following steps:

in step S1, the sample is scanned by the electron beam, and a diffraction pattern is acquired for each scanning point of the sample.

In the embodiment of the invention, the device comprises a sample, an electron source and a detector, wherein an electron beam is emitted by the electron source to scan on the sample, a scattering signal of each scanning position is recorded by the detector, and a diffraction pattern of each scanning point is acquired.

In step S2, the initialization function and the electron beam function are included in the propagation function between sample slices as variable parameters when constructing the forward propagation model, and the loss function of the forward propagation model is calculated.

Further, in one embodiment of the present invention, the initialization function and the electron beam function. All-1 amplitude and random phase are adopted for each layer of objective function, and the electron beam function is constructed according to the diaphragm size and the defocusing amount:

where A (k) is the diaphragm function and χ (k) is the aberration function.

Further, in one embodiment of the present invention, the loss function is written as a function with respect to an object function, an electron beam function, and the like. Wherein the loss function includes, but is not limited to, the following form:

where j represents the serial number of the scan location, | - | represents the modulus of each element in the computation matrix,representing the Fourier transform of the computational matrix, | · |. non-woven phosphor_FA frobenius norm (frobeniuusnnorm) representing the computation matrix,is the outgoing wave function to be optimized, and I is the collected diffraction intensity matrix.

Function of outgoing waveCan be expressed as:

wherein, P (r-r)_j) Representing the electron beam scanned to the jth location,representing the objective function of the ith layer. It can be assumed that each layer of the objective function has the same thickness and inclination,represents a Fresnel near-field diffraction effect factor, and the effect can be expressed as:

p(k；Δz，θ)＝exp[-iπΔz(λk²-2k_xtanθ_x-2k_ytanθ_y)]，

wherein Δ z represents the thickness of each layer of the physical function, (θ)_x，θ_y) Representing the angle of the object off the positive belt axis, will be (theta)_x，θ_y) Considered as the parameter to be optimized, by solving the loss functionTo pairP、(θ_x，θ_y) The gradients of the isoparametric iteratively optimize the corresponding parameters.

In step S3, the gradient of the loss function with respect to the parameter to be optimized is solved, and the parameter to be optimized is optimized according to the gradient.

In an embodiment of the invention, the parameters to be optimized include the objective function, the incident electron beam function, and the deviation of the sample strip axis from the electron beam direction. I.e. solving the loss function with respect to the object functionElectron beam function P, inclination angle (theta)_x，θ_y) Isoparametric gradients.

Specifically, the gradient may be obtained by using a software library with an automatic derivation function, or by using the following analytical expression:

wherein the content of the first and second substances,method and apparatus for obtainingSimilarly, the fresnel propagation function of any layer is replaced with the derivative of the fresnel propagation function to the tilt angle, for example, when the objective function contains an even number of slices (N), the fresnel propagation function of the N/2 th layer is replaced.

After calculating the gradient, the target parameter is updated by using the calculated gradient, which may be updated by the following formula as an embodiment:

wherein the content of the first and second substances,αP、andis a function of an objectElectron beam function P and inclination angle of sample off positive band axis (θ)_x，θ_y) The learning rate of (a) is determined,is the gradient of the object function and is,is the gradient of the function of the electron beam,andare respectively an inclination angle (theta)_x，θ_y) Of the gradient of (c).

In step S4, S2 is executed to recalculate the loss function until the iteration end condition is satisfied, and the parameter to be optimized is output, the obtained tilt angle is the angle of the deviation of the sample tape axis from the electron beam direction, and the objective function is the projection of the sample on the positive tape axis.

Further, in one embodiment of the present invention, the iteration termination condition includes: converging a loss function; or, a preset number of iterations is reached.

Specifically, the loss function is recalculated through the parameters updated in the step S3, S2-S3 are repeatedly executed, iteration is repeated until the loss function converges or reaches the set iteration number, the iteration is ended, the parameters to be optimized are finally obtained, and then the parameters to be optimized are used for sample imaging.

The method of the embodiment can automatically correct the influence of the sample belt axis deviation on the resolution and the structure measurement precision, relaxes the experimental requirements of electron microscopy, and enables the laminated imaging to obtain the structure measurement with ultrahigh resolution and picometer precision even when the sample obviously deviates from the positive belt axis.

The electronic stack imaging method for automatically correcting tape axis deviation of a sample according to the present invention is described in detail with reference to an embodiment.

In this example, it is observed that the projection of barium titanate along the [001] direction is structured as shown in FIG. 2. for the conventional imaging method, the electron beam is required to be substantially parallel to the [001] direction of barium titanate to obtain a correct high-resolution image.

In this example, the sample is shifted by 8mrad in the [001] direction, the electron beam is scanned over the sample, the scan points are as shown in fig. 3, the detector collects the diffraction patterns at each scan position, the average of all diffraction patterns is as shown in fig. 4, the convergence half angle is 22mrad, and the under focus is 8 nm.

The initialization function is the same as the electron beam function, all slices of the object function have the same amplitude of 1, as shown in FIG. 5, and the phase is random, as shown in FIG. 6, and the electron beam function is formulated asInitialization is performed with the amplitude shown with reference to fig. 7 and the phase shown with reference to fig. 8.

Calculating a loss functionAnd a gradient of the target parameter, and iteratively updating the target parameter using the following formula:

wherein P represents an electron beam, wherein,representing the objective function of the i-th layer, (theta)_x，θ_y) Representing the angle of deflection of the sample belt axis,α_P、andis the learning rate of each parameter.

The mean phase of the objective function for all the slices is shown in fig. 9, the amplitude of the electron beam function is shown in fig. 10, and the tilt of the sample with respect to the positive band axis as a function of the number of iterations is shown in fig. 11.

According to the electronic stack imaging method for automatically correcting the sample tape axis deviation, a series of diffraction patterns obtained by scanning an electron beam on a sample are used as data, a tilt angle is introduced into a Fresnel (Fresnel) near-field diffraction propagation function describing the propagation of an electron wave function in the sample, the tilt angle is updated through the gradient of a loss function relative to the tilt angle in an iterative optimization algorithm of stack imaging, and finally the angle of the sample tape axis deviation and the projection potential of the sample under a positive tape axis are obtained. The defect that an electron microscope is difficult to obtain high-spatial resolution images and high-precision structural information when a sample belt axis deviates is overcome, and the sample projection potential with sub-angstrom resolution can be obtained under the condition that the sample belt axis deviates.

Next, an electronic stacked imaging apparatus for automatically correcting tape axis deviation of a sample according to an embodiment of the present invention will be described with reference to the drawings.

Fig. 12 is a schematic structural diagram of an electronic stacked imaging device for automatically correcting tape-axis deviation of a sample according to an embodiment of the invention.

As shown in fig. 12, the electronic stack imaging apparatus for automatically correcting tape axis deviation of a sample includes: an acquisition module 100, a calculation module 200, an optimization module 300 and an imaging module 400.

The acquisition module 100 is configured to scan a sample through an electron beam, and acquire a diffraction pattern of each scanning point of the sample. The module may be, but is not limited to, a scanning transmission microscope. And the calculation module 200 is used for initializing the objective function and the electron beam function, and calculating the loss function of the forward propagation model by using the tilting angle of the sample relative to the electron beam as a variable parameter and including the variable parameter in the propagation function between sample slices when the forward propagation model is constructed. And the optimization module 300 is configured to solve a gradient of the loss function with respect to the parameter to be optimized, and optimize the parameter to be optimized according to the gradient. And the imaging module 400 is used for executing the function of the calculation module to recalculate the loss function until an iteration termination condition is met, outputting a parameter to be optimized, wherein the obtained tilting angle is the angle of the sample belt axis deviating relative to the direction of the electron beam, and the objective function is the projection of the sample under the positive belt axis.

Further, in one embodiment of the present invention, the initialization function includes all 1 amplitudes and random phases for each layer of the objective function.

Further, in one embodiment of the present invention, the parameters to be optimized include an objective function, an incident electron beam function, and a deviation of the sample strip axis from the electron beam direction.

Further, in one embodiment of the present invention, the exit wave function in the forward propagation model is:

wherein, P (r-r)_j) Representing the electron beam scanned to the jth location,represents the objective function of the ith layer,represents a Fresnel near-field diffraction effect factor, and the effect is expressed as:

p(k；Δz，θ)＝exp[-iπΔz(λk²-2k_xtanθ_x-2k_ytanθ_y)]，

wherein Δ z represents the thickness of each layer of the physical function, (θ)_x，θ_y) Representing the angle of the object off the positive belt axis, (theta)_x，θ_y) Are variable parameters.

Further, in an embodiment of the present invention, optimizing the parameter to be optimized according to the gradient includes:

wherein the content of the first and second substances,α_P、andis a function of an objectElectron beam function P and inclination angle of sample off positive band axis (θ)_x，θ_y) The learning rate of (a) is determined,is the gradient of the object function and is,is the gradient of the function of the electron beam,andare respectively an inclination angle (theta)_x，θ_y) Of the gradient of (c).

Further, in one embodiment of the present invention, the iteration termination condition includes:

converging a loss function; or

Reaching the preset iteration times.

It should be noted that the foregoing explanation of the method embodiment is also applicable to the apparatus of this embodiment, and is not repeated herein.

According to the electronic stacking imaging device for automatically correcting the sample tape axis deviation, a series of diffraction patterns obtained by scanning an electron beam on a sample are used as data, a tilt angle is introduced into a Fresnel (Fresnel) near-field diffraction propagation function describing the propagation of an electron wave function in the sample, the tilt angle is updated through the gradient of a loss function relative to the tilt angle in an iterative optimization algorithm of the stacking imaging, and finally the angle of the sample tape axis deviation and the projection potential of the sample under a positive tape axis are obtained. The defect that an electron microscope is difficult to obtain high-spatial resolution images and high-precision structural information when a sample belt axis deviates is overcome, and the sample projection potential with sub-angstrom resolution can be obtained under the condition that the sample belt axis deviates.

Furthermore, the terms "first", "second" and "first" are used for descriptive purposes only and are not to be construed as indicating or implying relative importance or implicitly indicating the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one such feature. In the description of the present invention, "a plurality" means at least two, e.g., two, three, etc., unless specifically limited otherwise.

In the description herein, references to the description of the term "one embodiment," "some embodiments," "an example," "a specific example," or "some examples," etc., mean that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the invention. In this specification, the schematic representations of the terms used above are not necessarily intended to refer to the same embodiment or example. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples. Furthermore, various embodiments or examples and features of different embodiments or examples described in this specification can be combined and combined by one skilled in the art without contradiction.

Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention, and that variations, modifications, substitutions and alterations can be made to the above embodiments by those of ordinary skill in the art within the scope of the present invention.