Charged defect potential alignment method, apparatus, device, and storage medium

Abstract

The present disclosure provides a charged defect potential alignment method, device, equipment and storage medium, which can be applied to the field of first-principle charged defect formation energy calculation based on density functional theory. The method comprises: obtaining the potentials of each sampling point in the reference unit cell and the defect unit cell, and constructing a potential difference sample; layering the defect unit cell according to a preset distance, and determining the shell layer region to which each sampling point belongs based on the shortest periodic distance from each sampling point in the defect unit cell to the defect center, to obtain a plurality of shell sample set; in the case that the robust scale corresponding to each of the plurality of shell sample set and the robust center drift of adjacent shell layers satisfy the stability criterion condition, a far-field sample set is determined; performing robust position estimation on the potential difference corresponding to each sampling point in the far-field sample set to determine a potential alignment constant, so as to realize the potential alignment between the defect unit cell and the reference unit cell.

Description

Technical Field

[0001] This disclosure relates to the field of calculating the formation energy of charged defects based on first-principles calculations of density functional theory, and particularly to a method, apparatus, device, and storage medium for aligning the potential of charged defects. Background Technology

[0002] When performing DFT (Density Functional Theory) calculations of charged defects under periodic boundary conditions, a uniform compensation background charge and a numerical specification with a fixed potential zero are usually introduced to ensure the feasibility and convergence of the calculation.

[0003] However, since the potential itself is determined only in the sense of a difference of a constant, the zero potential point between a perfect crystal (i.e., a perfect supercell) and a defective supercell may have a constant shift, which means that the charge state-related terms in the charged defect formation energy need to be corrected by introducing potential alignment. However, in related technologies, common potential alignment processes have problems such as dependence on experience in selecting the far-field region, sensitivity to outliers, lack of reliability quantification, and difficulty in mass engineering. Summary of the Invention

[0004] In view of the above problems, this disclosure provides a method, apparatus, device and storage medium for aligning charged defect potentials.

[0005] According to a first aspect of this disclosure, a method for aligning the potential of charged defects is provided, comprising:

[0006] The potential of each sampling point in the reference cell and the defect cell is obtained, and the potential difference sample between the corresponding sampling points in the reference cell and the defect cell is constructed. The defect cell is obtained by introducing a defect into the reference cell.

[0007] Using the defect center of the defect cell as the shell center, the defect cell is divided into layers according to a preset distance to obtain multiple shells. Based on the shortest periodic distance from each sampling point in the defect cell to the defect center, the shell region to which the sampling point belongs is determined to obtain multiple shell sample sets. The shell region is determined by two adjacent shells.

[0008] For any of the multiple shell sample sets mentioned above, based on the potential difference corresponding to each sampling point in any of the shell sample sets, the robust center, robust scale, and adjacent shell robust center drift corresponding to any of the shell sample sets are determined, wherein the adjacent shell robust center drift is determined by the robust center of the adjacent shell region.

[0009] The far-field sample set is determined when the robust scales corresponding to the above multiple shell sample sets and the drift of the robust center of the adjacent shells satisfy the stability criterion.

[0010] Robust position estimation is performed on the potential difference corresponding to each sampling point in the above far-field sample set to determine the potential alignment constant, which is used to achieve potential alignment between the defect cell and the reference cell.

[0011] A second aspect of this disclosure provides a charged defect potential alignment device, comprising: an acquisition module, a layering module, a first determination module, a second determination module, and a third determination module.

[0012] The module includes several sub-modules: an acquisition module for acquiring the potential of each sampling point in the reference cell and the defect cell, and constructing potential difference samples between corresponding sampling points in the reference cell and the defect cell. The defect cell is obtained by introducing defects into the reference cell. A layering module is used to layer the defect cell according to a preset distance, using the defect center of the defect cell as the shell center, to obtain multiple shells. Based on the shortest period distance from each sampling point in the defect cell to the defect center, the module determines the shell region to which the sampling point belongs, resulting in multiple shell sample sets. The shell region is determined by two adjacent shells. A first determination module is used to determine, for any shell sample set among the multiple shell sample sets, the robust center, robust scale, and adjacent shell robust center drift corresponding to any shell sample set, based on the potential difference corresponding to each sampling point in any shell sample set. The adjacent shell robust center drift is determined by the robust center of the adjacent shell region. The second determination module is used to determine the far-field sample set when the robust scales corresponding to the multiple shell sample sets and the drift of the robust centers of adjacent shells satisfy the stability criterion. The third determination module is used to perform robust position estimation on the potential difference corresponding to each sampling point in the above-mentioned far-field sample set and determine the potential alignment constant to achieve potential alignment between the defect cell and the reference cell.

[0013] A third aspect of this disclosure provides an electronic device comprising: one or more processors; and a memory for storing one or more computer programs, wherein the one or more processors execute the one or more computer programs to implement the steps of the method described above.

[0014] A fourth aspect of this disclosure also provides a computer-readable storage medium having a computer program or instructions stored thereon, which, when executed by a processor, implement the steps of the above-described method.

[0015] The fifth aspect of this disclosure also provides a computer program product, including a computer program or instructions that, when executed by a processor, implement the steps of the above-described method.

[0016] According to the charged defect potential alignment method, apparatus, device, and storage medium provided in this disclosure, the defect cell is divided into layers using the defect center as the shell center. The shortest period distance from each sampling point in the defect cell to the defect center is calculated to determine the nearest defect center to the sampling point. This allows for accurate division of the shell region to which the sampling point belongs, avoiding incorrect partitioning of the sampling points and obtaining multiple shell sample sets. Based on this, the robust center, robust scale, and drift of the robust center of adjacent shells corresponding to any shell sample set are determined based on the potential difference of each sampling point in any shell sample set. This determines whether the corresponding shell region is far from the defect and is not disturbed by the defect. Then, if the robust scale and drift of the robust center of adjacent shells corresponding to each of the multiple shell sample sets satisfy the stability criterion, reliable sampling points are selected as the far-field sample set, and the potential alignment constant is determined based on the far-field sample set. Therefore, by performing distance-layered and robust statistical estimation on the potential difference samples between the reference cell and the defect cell, the automatic identification of the far-field region and the robust estimation of the potential alignment constant are realized, and the repeatability and reliability of the calculated results of the charged defect formation energy are improved. Attached Figure Description

[0017] The foregoing contents, as well as other objects, features, and advantages of this disclosure, will become clearer from the following description of embodiments with reference to the accompanying drawings, in which:

[0018] Figure 1 This diagram schematically illustrates an application scenario of the charged defect potential alignment method according to an embodiment of the present disclosure.

[0019] Figure 2 A flowchart illustrating a method for aligning the potential of charged defects according to an embodiment of the present disclosure is shown schematically.

[0020] Figure 3 A schematic diagram illustrating a plurality of shells divided in a defective unit cell according to an embodiment of the present disclosure is shown.

[0021] Figure 4 The diagram illustrates the curves showing the robust center, robust scale, and drift of the robust center of adjacent shells according to embodiments of the present disclosure.

[0022] Figure 5 This schematically illustrates the mapping relationship between the shortest periodic distance from the sampling point to the defect center according to an embodiment of the present disclosure and the potential difference between the reference cell and the defect cell at the sampling point;

[0023] Figure 6 A flowchart illustrating a method for aligning the potential of charged defects according to an embodiment of the present disclosure is shown schematically.

[0024] Figure 7A schematic block diagram of a charged defect potential alignment device according to an embodiment of the present disclosure is shown; and

[0025] Figure 8 A block diagram schematically illustrates an electronic device suitable for implementing a method for aligning charged defect potentials according to an embodiment of the present disclosure. Detailed Implementation

[0026] The embodiments of the present disclosure will now be described with reference to the accompanying drawings. However, it should be understood that these descriptions are exemplary only and are not intended to limit the scope of the disclosure. In the following detailed description, numerous specific details are set forth to provide a thorough understanding of the embodiments of the present disclosure for ease of explanation. However, it will be apparent that one or more embodiments may be practiced without these specific details. Furthermore, descriptions of well-known structures and techniques are omitted in the following description to avoid unnecessarily obscuring the concepts of the present disclosure.

[0027] The terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit this disclosure. The terms “comprising,” “including,” etc., as used herein indicate the presence of the stated features, steps, operations, and / or components, but do not exclude the presence or addition of one or more other features, steps, operations, or components.

[0028] All terms used herein (including technical and scientific terms) have the meanings commonly understood by those skilled in the art, unless otherwise defined. It should be noted that the terms used herein are to be interpreted in a manner consistent with the context of this specification, and not in an idealized or overly rigid way.

[0029] When using expressions such as "at least one of A, B and C", they should generally be interpreted in accordance with the meaning that is commonly understood by those skilled in the art (e.g., "a system having at least one of A, B and C" should include, but is not limited to, a system having A alone, a system having B alone, a system having C alone, a system having A and B, a system having A and C, a system having B and C, and / or a system having A, B and C, etc.).

[0030] In the process of realizing this disclosure, it was discovered that the common potential alignment process in related technologies includes: extracting potential data from perfect supercells and defective supercells, selecting a region far from the defect, calculating the average value of the potential difference in that region as an alignment constant, and using the alignment constant as a correction term for the formation energy of charged defects.

[0031] However, the potential alignment process in related technologies often suffers from the following problems:

[0032] The selection of far-field regions relies on experience: often, a fixed radius (such as outside the Wigner-Seitz radius) or a range of artificial observation platforms is used to select far-field regions, which makes it difficult to guarantee robustness under different systems, different levels of disorder, or different supercell sizes.

[0033] Sensitive to outliers: Local chemical environment of atoms, strong relaxation or amorphous structure can cause strong fluctuations in site potential, and simply calculating the average potential difference is easily biased by outliers.

[0034] Lack of reliability quantification: It usually only outputs a single alignment value, but lacks uncertainty measures such as confidence intervals, making it impossible for users to judge whether the result is reliable, and also lacking a closed-loop basis for when a larger supercell / reselection area is needed.

[0035] Difficult to scale up for engineering: When faced with a large number of defect configurations, different charge states or different material systems, manual selection and judgment will become bottlenecks and difficult to reproduce.

[0036] Therefore, embodiments of this disclosure provide a method for aligning the potential of charged defects, which can automatically determine the far-field stable region, be robust to outliers, and output uncertainty and engineering suggestions, thereby improving the repeatability and reliability of the calculated results of charged defect formation energy.

[0037] Figure 1 The diagram illustrates an application scenario of the charged defect potential alignment method according to an embodiment of the present disclosure.

[0038] like Figure 1 As shown, application scenario 100 according to this embodiment may include a first terminal device 101, a second terminal device 102, a third terminal device 103, a network 104, and a server 105. The network 104 serves as a medium for providing a communication link between the first terminal device 101, the second terminal device 102, the third terminal device 103, and the server 105. The network 104 may include various connection types, such as wired or wireless communication links, or fiber optic cables, etc.

[0039] Users can use the first terminal device 101, the second terminal device 102, and the third terminal device 103 to interact with the server 105 via the network 104 to receive or send messages, etc. Various communication client applications can be installed on the first terminal device 101, the second terminal device 102, and the third terminal device 103, such as shopping applications, web browser applications, search applications, instant messaging tools, email clients, social media platform software, etc. (for example only).

[0040] The first terminal device 101, the second terminal device 102, and the third terminal device 103 can be various electronic devices with displays and support web browsing, including but not limited to smartphones, tablets, laptops, and desktop computers.

[0041] For example, users can upload data such as the cell structure of the reference cell and the defect cell to the server 105 through the first terminal device 101, the second terminal device 102, and the third terminal device 103.

[0042] In one embodiment, the defect cell is obtained by introducing defects into a reference cell.

[0043] Server 105 can be a server that provides various services, such as a backend management server that supports websites browsed by users using the first terminal device 101, the second terminal device 102, and the third terminal device 103 (this is just an example). The backend management server can analyze and process data such as received user requests, and feed back the processing results (such as web pages, information, or data obtained or generated according to user requests) to the terminal devices.

[0044] For example, the potential of each sampling point in the reference cell and the defect cell can be obtained through server 105, and potential difference samples between corresponding sampling points in the reference cell and the defect cell can be constructed. Taking the defect center of the defect cell as the shell center, the defect cell is divided into layers according to a preset distance to obtain multiple shells. Based on the shortest period distance from each sampling point in the defect cell to the defect center, the shell to which the sampling point belongs is determined to obtain multiple shell sample sets. Then, for any shell sample set in the multiple shell sample sets, based on the potential difference corresponding to each sampling point in any shell sample set, the robust center, robust scale and adjacent shell robust center drift corresponding to any shell sample set are determined, wherein the adjacent shell robust center drift is determined by the robust center of the adjacent shell. Based on this, when the robust scales corresponding to the multiple shell sample sets and the drift of the robust centers of adjacent shells satisfy the stability criterion, the far-field sample set is determined, and the potential difference corresponding to each sampling point in the far-field sample set is robustly estimated to determine the potential alignment constant, which is used to achieve potential alignment between the defect cell and the reference cell.

[0045] It should be noted that the charged defect potential alignment method provided in this embodiment can generally be executed by server 105. Correspondingly, the charged defect potential alignment device provided in this embodiment can generally be located in server 105. The charged defect potential alignment method provided in this embodiment can also be executed by a server or server cluster that is different from server 105 and capable of communicating with the first terminal device 101, the second terminal device 102, the third terminal device 103, and / or server 105. Correspondingly, the charged defect potential alignment device provided in this embodiment can also be located in a server or server cluster that is different from server 105 and capable of communicating with the first terminal device 101, the second terminal device 102, the third terminal device 103, and / or server 105.

[0046] It should be understood that Figure 1 The number of terminal devices, networks, and servers shown is merely illustrative. Depending on implementation needs, any number of terminal devices, networks, and servers can be included.

[0047] The following will be based on Figure 1 The described scene, through Figures 2-6 The method for aligning charged defect potentials according to embodiments of this disclosure will be described in detail.

[0048] Introducing a charge of [value] into a perfect unit cell After the defect is formed, the perfect unit cell becomes a defective unit cell. The total energy change of the defective unit cell relative to the perfect unit cell is the energy required to form the defect. This energy is defined as the charged defect formation energy.

[0049] Under the Jellium (gel model) approximation, the charge is... defects The energy for formation can be represented by the following formula (1).

[0050] (1);

[0051] in, Indicates the charge is defects Formation energy; This represents the total energy of a charged unit cell containing defects, i.e., the total energy of a defective unit cell. This represents the total energy of a perfect unit cell; This represents the total number of defect atoms present in a defective unit cell relative to a perfect unit cell. The first defect is represented in the unit cell. The chemical potential (i.e., atomic potential) corresponding to each defect atom. greater than or equal to 1 and less than or equal to 1 Integers; Represents the charge state related terms; Indicates relative valence band terms; Indicates the relative price band top The Fermi level; This indicates a correction term for finite-size charged components.

[0052] Furthermore, potential alignment correction The following formula (2) can be used.

[0053] (2);

[0054] in, It represents the zero-potential offset between a perfect unit cell and a defective unit cell, i.e., the potential alignment constant.

[0055] Based on the above, since the zero potential point between perfect and defective unit cells may have a constant shift, the inconsistency between their zero potential points makes comparison impossible. Therefore, a potential alignment correction is introduced into the charge state-related term in the charged defect formation energy to correct the potential zero potential shift between perfect and defective unit cells. Accordingly, to achieve potential alignment between defective and perfect unit cells, it is necessary to determine the potential alignment constant. This is to achieve potential alignment of charged defects (i.e., substituting the potential alignment correction into the above formula (1)). Therefore, the main process in achieving potential alignment of charged defects is to determine the potential alignment constant (i.e., the zero-potential offset) between the perfect unit cell and the defective unit cell. To this end, through... Figure 2 The method for aligning the potential of charged defects shown can illustrate the process of achieving the alignment of the potential of charged defects.

[0056] Figure 2 A flowchart illustrating a method for aligning the potential of charged defects according to an embodiment of the present disclosure is shown schematically.

[0057] like Figure 2 As shown, the method 200 includes operations S210 to S250.

[0058] In operation S210, the potential of each sampling point in the reference cell and the defect cell is obtained, and potential difference samples between corresponding sampling points in the reference cell and the defect cell are constructed.

[0059] The defect cell is obtained by introducing defects into the reference cell.

[0060] In one embodiment, the reference cell is a periodic simulated cell without introduced defects, which may be a primitive cell, a conventional cell, or a supercell obtained by extending a primitive cell / conventional cell; in the calculation of charged defect formation energy, the reference cell is preferably a perfect supercell.

[0061] Since electric potential has only a relative meaning, there is a constant offset between the zero potential points of the reference cell and the defect cell. Therefore, it is necessary to calculate the potential difference between the reference cell and the defect cell in the defect-free far-field region to obtain the zero potential offset, and then complete the zero potential calibration between the reference cell and the defect cell to achieve potential alignment.

[0062] Based on this, it is necessary to determine the sampling points far from the defects in the reference cell and the defect cell, and obtain the potential of each sampling point in the reference cell and the defect cell, so as to calculate the potential difference between the corresponding sampling points in the reference cell and the defect cell, and then construct the potential difference sample between the corresponding sampling points in the reference cell and the defect cell for subsequent calculation of the zero-point offset.

[0063] Among them, the potential difference sample includes the potential difference between each sampling point in the reference cell and the defect cell.

[0064] In operation S220, the defect center of the defect cell is used as the shell center. The defect cell is divided into layers according to a preset distance to obtain multiple shells. Based on the shortest period distance from each sampling point in the defect cell to the defect center, the shell region to which the sampling point belongs is determined to obtain multiple shell sample sets.

[0065] The shell region is determined by two adjacent shells.

[0066] In one embodiment, the reference unit cell can be used to obtain three types of defect units through different atomic operations: vacancy-type defect units (obtained by removing some lattice atoms from the reference unit cell), substitution-type defect units (obtained by replacing the original lattice atoms in the reference unit cell with other atoms), and interstitial defect units (obtained by embedding additional atoms in the interstitial positions of the reference unit cell).

[0067] Based on this, when the defect cell is a vacancy-type defect cell, if the defect cell is obtained by removing one atom, the defect cell has one defect center, and the defect center is the coordinate of the removed atom. When the defect cell is a substitution-type or interstitial defect cell, if the defect cell is obtained by replacing one atom or inserting an additional atom, the defect cell has one defect center, and the defect center is the coordinate of the replaced atom or the additionally inserted atom. If the defect cell has multiple defect centers, a defect center set is defined to calculate the shortest period distance from each sampling point to each defect center in the defect center set.

[0068] In one embodiment, the defect center of the defect cell is used as the shell center, and the defect cell is layered according to a preset distance to obtain multiple shells. The preset distance represents the distance between two adjacent shells and is set as needed.

[0069] Figure 3 A schematic diagram of multiple shells divided in a defective unit cell according to an embodiment of the present disclosure is shown.

[0070] like Figure 3 As shown, taking the three shells divided in the defect cell as an example, with the defect center 310 of the defect cell as the shell center, according to a preset distance... By dividing the defect cell into layers, we can obtain the first shell 320, the second shell 330, and the third shell 340.

[0071] Wherein, the shell region corresponding to the first shell layer 320 is region A enclosed by the first shell layer 320, the shell region corresponding to the second shell layer 330 is region B between the second shell layer 330 and the first shell layer 320, and the shell region corresponding to the third shell layer 340 is region C between the third shell layer 340 and the second shell layer 330.

[0072] For example, the preset distance is set to The first shell corresponds to a shell region of 0.0~0.5 Å, the second shell corresponds to a shell region of 0.5~1.0 Å, and so on, dividing the defect cell into multiple shells with the defect center as the shell center. Here, 0.0 can represent the upper boundary of the first shell region, and 0.5 Å can represent the lower boundary of the first shell region or the upper boundary of the second shell region.

[0073] To use distance stratification for each sampling point in the defect cell, it is necessary to determine the shortest periodic distance from each sampling point in the defect cell to the defect center, so as to determine the shell region to which the sampling point belongs. Specifically, the distance can be calculated using the following formula (3). The shortest period distance from each sampling point to the defect center .

[0074] (3);

[0075] in, Represents the set of lattice translation vectors. Indicating the first defect in the unit cell The coordinates of each sampling point; The coordinates representing the center of the defect; Indicates the th defect in the current unit cell The position vector of each sampling point relative to the defect center; The vector representing lattice translation is used to shift the defect center. Translate to all periodic mirror positions; Indicates the first Each sampling point was shifted. The position vector of the center of the mirror defect after reflection; This represents the set of lattice translation vectors. All The corresponding position vectors are taken as the minimum distance, i.e., the first... The shortest periodic distance from each sampling point to the center of all periodically repeating defects. .

[0076] Based on this, the shortest periodic distance from the sampling point to the defect center is calculated to adapt to the periodic boundary conditions, find the nearest defect center for each sampling point, and thus accurately complete the division of the shell region to which the sampling point belongs, avoiding the partitioning error of the sampling point.

[0077] Therefore, based on the shortest periodic distance from each sampling point in the defect cell to the defect center, the shell region to which the sampling point belongs can be determined to obtain multiple shell sample sets. The samples in the shell sample set are all the sampling points in the corresponding shell region.

[0078] Based on the above, if there are multiple defect centers in a defect cell, the shell region to which a certain sampling point in the defect cell belongs is determined. First, the defect center that is closest to the sampling point among the multiple defect centers is determined. This defect center is used as the shell center, and the layers are divided according to a preset distance to determine the shell region to which the sampling point belongs. That is, different sampling points correspond to different defect centers used as shell centers.

[0079] For example, considering sampling points E and F, if the nearest defect centers to sampling points E and F are different (e.g., sampling point E is closest to defect center E1, and sampling point F is closest to defect center F1), then when determining the shell region to which sampling point E belongs, defect center E1 is used as the shell center for stratification; similarly, when determining the shell region to which sampling point F belongs, defect center F1 is used as the shell center for stratification. If sampling point E is in the second shell region defined by defect center E1, and sampling point F is in the second shell region defined by defect center F1, then both sampling points E and F belong to the sample set of the second shell region.

[0080] In one embodiment, the first A set of shell samples It can be shown in the following formula (4).

[0081] (4);

[0082] in, Indicates the first A set of shell samples The number of sampling points (i.e., the number of samples); Indicates the first The distance from each shell layer to the center of the defect Indicates the first The distance from each shell layer to the center of the defect It is an integer greater than or equal to 1. Therefore, the... A set of shell samples Taken from the first The first shell layer and the first Sampling points within the region between the shell layers.

[0083] by Taking the value 2 as an example, combined with Figure 3 As shown in the layering diagram, the samples in the second shell sample set are taken from all sampling points within region B between the first shell 320 and the second shell 330. Therefore, the shortest period distance is selected. exist and sampling points between As the first A set of shell samples Samples within.

[0084] In operation S230, for any shell sample set among multiple shell sample sets, based on the potential difference corresponding to each sampling point in any shell sample set, the robust center, robust scale, and drift of the robust center of adjacent shells corresponding to any shell sample set are determined.

[0085] Among them, the drift of the robust center of adjacent shell layers is determined by the robust center of the adjacent shell layer region.

[0086] In one embodiment, due to lattice distortion and uneven potential distribution around the defect, a few "extreme points" may contaminate the average value. Therefore, a robust center is calculated based on the potential difference corresponding to each sampling point in any shell sample set to resist distortion, thereby truly reflecting the average position of the shell sample set in the corresponding shell region within the defect unit cell, ensuring that the center positioning of the shell region is stable and comparable.

[0087] In one embodiment, the robust scale reflects the strength of the disturbance of the potential distribution in the shell region by the defect and is not affected by outliers. Therefore, the robust scale is calculated based on the potential difference corresponding to each sampling point in any shell sample set to reflect the strength of the disturbance of the potential distribution in the shell region by the defect.

[0088] In one embodiment, defects also cause the robust center of each shell region to shift relative to the perfect lattice center. The drift of the robust center between adjacent shells can then reflect the quantitative shift layer by layer, demonstrating the spatial propagation characteristics of defect perturbations. Therefore, based on the potential difference corresponding to each sampling point in any shell sample set, the drift of the robust center between adjacent shells is calculated to show how the robust centers of adjacent shell regions shift.

[0089] In operation S240, the far-field sample set is determined when the robust scales corresponding to the multiple shell sample sets and the drift of the robust centers of adjacent shells satisfy the stability criterion.

[0090] Since a potential alignment constant needs to be determined to achieve potential alignment, if the potential difference used to determine the potential alignment constant is disturbed by defects, the determined potential alignment constant will introduce errors, making potential alignment impossible. Furthermore, defects cause the center of the shell region to shift and the intralayer distribution to become scattered, manifesting as continuous changes in the drift of the robust center of adjacent shell layers and constant fluctuations in the robust scale. However, as the distance from the defect center increases, the drift of the robust center of adjacent shell layers approaches zero, and the robust scale remains constant, meaning that the defect disturbance gradually weakens.

[0091] Based on this, a stability criterion is set. When the robust scales corresponding to multiple shell sample sets and the drift of the robust centers of adjacent shells satisfy the stability criterion, the far-field sample set is determined. The far-field sample set includes the sampling points in the shell sample set that satisfy the stability criterion.

[0092] Among them, the stability criterion condition characterizes the judgment condition that the sampling points in the shell region corresponding to the set of shell samples are far away from the defect and are not disturbed by the defect.

[0093] In operation S250, robust position estimation is performed on the potential difference corresponding to each sampling point in the far-field sample set to determine the potential alignment constant, which is used to achieve potential alignment between the defect cell and the reference cell.

[0094] Since the sampling points included in the far-field sample set are far from the defect and are not disturbed by the defect, the potential alignment constant calculated based on the potential difference of each sampling point in the far-field sample set can effectively correct the zero potential offset between the reference cell and the defect cell.

[0095] In one embodiment, the potential alignment constant is defined as a robust position estimate of the far-field sample set, which can be obtained by the following formula (5). .

[0096] (5);

[0097] in, Represents the far-field sample set, Indicates the first sampling points (i.e., sampling points) ), Indicates the first The potential difference corresponding to the sampling point, i.e., the potential difference in the reference unit cell at the sampling point. The sampling point and the defect cell in the th sampling point Potential difference between sampling points.

[0098] Therefore, the potential alignment constant obtained by using the above formula (5) Substituting into the above formula (1), the potential alignment between the defect cell and the reference cell can be achieved.

[0099] According to embodiments of this disclosure, the defect center of the defect cell is used as the shell center. The defect cell is divided into layers, and the shortest period distance from each sampling point in the defect cell to the defect center is calculated to determine the nearest defect center to the sampling point. This allows for accurate division of the shell region to which the sampling point belongs, avoiding partitioning errors and obtaining multiple shell sample sets. Based on this, the robust center, robust scale, and adjacent shell robust center drift corresponding to any shell sample set are determined based on the potential difference corresponding to each sampling point in any shell sample set. This determines whether the corresponding shell region is far from the defect and is not disturbed by the defect. Then, if the robust scale and adjacent shell robust center drift of each of the multiple shell sample sets satisfy the stability criterion, reliable sampling points are selected as the far-field sample set, and the potential alignment constant is determined based on the far-field sample set. Thus, by performing distance layering and robust statistical estimation on the potential difference samples between the reference cell and the defect cell, automatic identification of the far-field region and robust estimation of the potential alignment constant are achieved, improving the repeatability and reliability of the charged defect formation energy calculation results.

[0100] In one embodiment, to determine the sampling points in the reference cell and the defect cell, random space sampling or a combination of random space sampling and atomic site sampling can be used. The process of determining the sampling points in the reference cell and the defect cell using random space sampling is as follows.

[0101] According to embodiments of this disclosure, sampling points in the reference cell and the defect cell are determined by the following operations: randomly selecting multiple candidate sampling points from the defect cell; calculating a first distance between each candidate sampling point and the defect center; calculating a second distance between each candidate sampling point and each atom in the defect cell; and selecting candidate sampling points from the multiple candidate sampling points whose first distance is greater than or equal to a preset defect distance and whose second distance is greater than or equal to a preset atomic distance as sampling points in the defect cell and the reference cell.

[0102] The first distance represents the shortest period distance between the candidate sampling point and the defect center; the second distance represents the shortest period distance between the candidate sampling point and each atom in the defect cell, and the sampling points in the defect cell are the same as those in the reference cell.

[0103] If there are multiple defect centers, the first distance represents the minimum distance among the shortest period distances from any candidate sampling point to each defect center; the second distance represents the minimum distance among the shortest period distances from any candidate sampling point to each defect center.

[0104] In one embodiment, multiple candidate sampling points are randomly selected in the defective unit cell, for example, M spatial sampling points are randomly selected in the defective unit cell. (That is, select M candidate sampling points) M is an integer greater than 1.

[0105] Because of lattice distortion and charge localization effects around the defect center in a defective unit cell, the potential in this region is significantly disturbed by the defect and cannot represent the intrinsic bulk potential of the crystal. However, in regions far from the defect center, the lattice, electronic structure, and potential distribution all revert to the intrinsic state of the crystal, consistent with the physical environment of a perfect unit cell. Therefore, selecting sampling points far from the defect center ensures that the potential obtained at these sampling points avoids potential interference caused by defects, guaranteeing the accuracy of subsequent potential difference calculations and zero-point potential offset calculations.

[0106] Furthermore, the sampling points should ideally be far away from the atoms to avoid them falling in regions of drastic potential changes near the atoms, thereby reducing outliers.

[0107] Based on the above, calculate the first distance between each candidate sampling point and the defect center; calculate the second distance between each candidate sampling point and each atom in the defect cell; select candidate sampling points from multiple candidate sampling points whose first distance is greater than or equal to the preset defect distance and whose second distance is greater than or equal to the preset atom distance, and use them as sampling points in the defect cell and the reference cell.

[0108] Based on this, the sampling points selected from the candidate sampling points need to satisfy the rejection sampling constraints shown in the following formulas (6) and (7).

[0109] (6);

[0110] (7);

[0111] in, This represents the shortest period distance (minimum-image). The defect center represents the defect cell. Indicates the first One candidate sampling point; Indicates the preset defect distance; Represents the first in the reference cell (or defect cell) One atom; Indicates the preset atomic distance; This represents the first distance, which is the shortest periodic distance from the candidate sampling point to the defect center; This represents the second distance, which is the shortest periodic distance between the candidate sampling point and the atom.

[0112] Therefore, by using the above formula (6), sampling points far from the defect center can be selected from the candidate sampling points, and by using the above formula (7), sampling points far from the atom can be selected from the candidate sampling points. Furthermore, by using the above formulas (6) and (7), sampling points far from both the defect center and the atom can be selected from the candidate sampling points.

[0113] In one embodiment, the preset defect distance characterizes the near-field exclusion distance of the defect. The preset defect distance is used in the sampling stage to exclude sampling points near the defect center. The preset defect distance is set according to the actual situation.

[0114] In one embodiment, the preset atomic distance indicates that candidate sampling points within a region above a certain distance from the atom are not affected by the electric field near the atom. The preset atomic distance is set according to the actual situation.

[0115] In one embodiment, since the potential difference between the defective unit cell and the perfect unit cell needs to be calculated subsequently, it is necessary to ensure that the sampling points in the defective unit cell and the perfect unit cell are consistent.

[0116] According to embodiments of this disclosure, sampling points that are far from the defect center and far from atoms are selected from candidate sampling points to ensure that the sampling points in the reference cell and defect cell used for subsequent potential difference calculation can avoid potential interference caused by defects and interference from the electric field near atoms, thereby further improving the accuracy of potential difference calculation and potential zero-point offset calculation.

[0117] Based on the above, sampling points that are far from the defect center and far from atoms are selected from the M candidate sampling points. The index of the sampling point remains unchanged, and the sampling points are not reordered. For example, if M is 5, then the candidate sampling points include the candidate sampling points. Candidate sampling points Candidate sampling points Candidate sampling points and candidate sampling points If candidate sampling points Candidate sampling points and candidate sampling points If the filtering criteria are met, the sampling points are obtained. Sampling points and sampling points .

[0118] In one embodiment, sampling points in the reference cell and defect cell are determined by atomic site sampling, that is, atoms in the reference cell and defect cell are used as sampling points.

[0119] Based on the above, the number of samples in the atomic site sampling method and the random space sampling method are different. The number of sampling points in the atomic site sampling method is the number of atoms. For example, the number of sampling points in the atomic site sampling method is 80, while the number of sampling points in the random space sampling method is 2000.

[0120] Based on this, samples obtained by random space sampling are closer to the smooth potential of the intercellular space region, while samples obtained by atomic site sampling are more susceptible to the influence of local chemical environment, atom type, and local relaxation. The potential difference corresponding to the sample obtained by atomic site sampling may fluctuate more than that corresponding to the potential difference of the sample obtained by random space sampling. Therefore, random space sampling is used as the main sample for far-field determination and calculation of the final potential alignment constant, while atomic site sampling is only used as an auxiliary sample for site marking, outlier diagnosis, and comparison with traditional methods.

[0121] Based on the above, since the number of samples in random space sampling is much larger than that in atomic site sampling, the results of obtaining sampling points are basically dominated by the random space sampling method. This allows sampling points to be determined through random space sampling, or by random space sampling and atomic site sampling in parallel.

[0122] After determining the sampling points in the reference cell and the defect cell, it is necessary to obtain the potential difference between each corresponding sampling point in the reference cell and the defect cell for the calculation of the zero potential offset. Based on this, it is necessary to first obtain the potential of each sampling point in the reference cell and the defect cell. The potential of the sampling point can be obtained through the following operations.

[0123] According to embodiments of this disclosure, obtaining the potential of each sampling point in the reference cell and the defect cell includes: performing uniform mesh division and self-consistent electrostatic potential calculation on the reference cell and the defect cell respectively to obtain the three-dimensional potential mesh of the reference cell and the defect cell respectively; and performing trilinear interpolation on the three-dimensional potential mesh of the reference cell and the defect cell based on the sampling points in the reference cell and the defect cell respectively to obtain the potential of each sampling point in the reference cell and the defect cell.

[0124] In one embodiment, uniform meshing and self-consistent electrostatic potential calculation are performed on the reference cell (i.e., perfect cell) and the defect cell, respectively. That is, LOCPOT data are extracted based on the reference cell and the defect cell to obtain the three-dimensional potential mesh of the reference cell and the defect cell respectively.

[0125] The grid points of the three-dimensional potential grid store the potential.

[0126] Based on this, trilinear interpolation is performed on the three-dimensional potential grids of the reference cell and the defect cell, respectively, using sampling points in the reference cell and the defect cell, to obtain the potential of each sampling point in the reference cell and the defect cell. and ,in, Indicates the sampling point within the reference unit cell after trilinear interpolation. The potential, i.e., the obtained reference unit cell sampling point. The electric potential; This represents the sampling point within the defect cell after trilinear interpolation. The potential, i.e., the sampling point within the defect cell. The electric potential.

[0127] In one embodiment, three-dimensional linear interpolation refers to estimating the potential corresponding to a sampling point in a three-dimensional potential grid by linear weighting based on the potentials of eight grid points surrounding the sampling point. Furthermore, when performing three-dimensional linear interpolation on the three-dimensional potential grid, index wrap-around processing can be performed at the cell boundaries according to periodic conditions to avoid interpolation failure.

[0128] According to the embodiments of this disclosure, for the selected sampling points that satisfy the above-mentioned rejection sampling constraints, the potential of the sampling points is solved by three-dimensional linear interpolation of the three-dimensional potential grid. This ensures that the potential of the sampling points obtained by three-dimensional linear interpolation has no abnormal deviation, smooths the sawtooth error caused by the three-dimensional potential grid, and guarantees the rationality and reliability of the potential values ​​of the sampling points.

[0129] According to embodiments of this disclosure, determining the robust center, robust scale, and robust center drift corresponding to any shell sample set based on the potential difference corresponding to each sampling point in any shell sample set includes: estimating the local robust position of the potential difference corresponding to each sampling point in any shell sample set to obtain the robust center corresponding to any shell sample set; calculating the median absolute deviation of the potential difference corresponding to each sampling point in any shell sample set to obtain the robust scale corresponding to any shell sample set; and determining the adjacent shell robust center drift based on the absolute difference between the robust center corresponding to any shell sample set and the robust center of the shell sample set corresponding to the shell adjacent to the shell of any shell sample set.

[0130] In one embodiment, shell robust statistics include robust center, robust scale, and robust center drift.

[0131] Specifically, regarding the first The first shell can be calculated using the following formula (8). The robust center of the shell sample set corresponding to each shell. .

[0132] (8);

[0133] in, Indicates the first A set of shell samples, Indicates the first In the set of shell samples, the first Potential difference corresponding to each sampling point.

[0134] Based on the above formula (8). You can use the median, truncated mean, or Huber estimate.

[0135] For example, the median of the potential difference corresponding to each sampling point in any shell sample set can be used as a robust center.

[0136] The first can be calculated using the following formula (9). Robust scaling of the shell sample set corresponding to each shell .

[0137] (9);

[0138] in, The appropriate value is MAD (Median Absolute Deviation).

[0139] Taking MAD as an example, the first Robust Scale of Shell Sample Set Further, it can be shown in the following formula (10).

[0140] (10);

[0141] in, Indicating the first unit cell The first atom and defect cell in the unit cell The potential difference between atoms This represents all atoms within the shell region corresponding to the k-th shell. The median of Let represent the set of atoms within the shell region corresponding to the k-th shell. The k-th shell can be calculated using the following formula (11). Robust center drift of adjacent shells in a set of shell samples .

[0142] (11);

[0143] in, Indicates the first Robust centers of a set of shell samples Indicates the first Robust center of a set of shell samples.

[0144] Figure 4 The diagram illustrates a schematic representation of the robust center, robust scale, and drift curves of the robust center of adjacent shells according to an embodiment of the present disclosure.

[0145] like Figure 4 As shown, the horizontal axis represents the distance from the sampling point to the defect center (unit: Å), and the vertical axis, from top to bottom, represents the drift of the robust center of the adjacent shell. , robust scale Stable Center .

[0146] pass Figure 4 As shown, the farther the sampling point is from the defect center, the smaller the fluctuations in the curves corresponding to the robust center drift, robust scale, and robust center of the adjacent shell.

[0147] According to embodiments of this disclosure, in order to determine whether the sampling points in the corresponding shell region are affected by defects, it is necessary to calculate the robust center, robust scale, and drift of the robust center of the corresponding shell sample set with those of the adjacent shells, so as to reflect whether the sampling points are reliable and whether they are affected by defects.

[0148] According to embodiments of this disclosure, when the robust scale corresponding to each of the multiple shell sample sets and the drift of the robust center of adjacent shells satisfy the stability criterion, the far-field sample set is determined, including: when the number of sampling points of the shell sample set corresponding to m consecutive shells is greater than or equal to a sample number threshold, the robust scale is less than or equal to a robust scale threshold, and the drift of the robust center of adjacent shells is less than or equal to a drift threshold, the shell sample set corresponding to m consecutive shells satisfies the stability criterion; the sampling points in the shell sample set corresponding to the k-th shell in the defect cell and the shells after the k-th shell are determined as the far-field sample set.

[0149] Where m is an integer greater than 1, and m consecutive shells represent the k-th to k+m-1-th shells in the defect cell, where k is an integer greater than or equal to 1.

[0150] In one embodiment, the stability criterion may include the constraints shown in Equation (12) and Equation (13) below.

[0151] (12);

[0152] (13);

[0153] in, Indicates the threshold for the number of samples. Indicates the robust scaling threshold. Indicates the drift threshold. This indicates an indicator function; if the condition within the parentheses is true... Take 1 if the conditions within the parentheses are not entirely true. Set to 0; This represents the number of samples (i.e., the number of sampling points) in the k-th shell sample set. This indicates taking the smallest index k that satisfies the condition that m consecutive indicator functions all have the value 1, i.e., when m consecutive indicator functions all have the value 1. The value is the smallest subscript of the m indicator functions; m represents the number of continuous stable shells.

[0154] In one embodiment, a robust scale threshold is used to determine whether the fluctuation of the potential difference within the same shell region is small enough, and a drift threshold is used to determine whether the change in the drift of the robust center of adjacent shells is small enough.

[0155] Therefore, given that the set of shell samples corresponding to m consecutive shells satisfies the stability criterion (i.e., the number of consecutive stable shells is m), the far-field sample set can be represented by the following formula (14). .

[0156] (14);

[0157] in, This means setting the index to be greater than or equal to the smallest index. All shell sample sets Merging them into a single set yields the far-field sample set. .

[0158] According to embodiments of this disclosure, when the robust scales corresponding to each of the multiple shell sample sets and the drift of the robust centers of adjacent shells satisfy the stability criterion, a far-field sample set is determined, that is, sampling points far from defects and not affected by defects are selected as sample points of the far-field sample set, so that the potential alignment constant calculated based on the potential difference of each sampling point in the far-field sample set can effectively correct the zero potential offset between the reference cell and the defect cell.

[0159] For example, it can be done through Figure 5 Display the determination results of the far-field starting point in the far-field sample set.

[0160] Figure 5 The diagram illustrates the mapping relationship between the shortest periodic distance from the sampling point to the defect center according to an embodiment of the present disclosure and the potential difference between the reference cell and the defect cell at the sampling point.

[0161] like Figure 5 As shown, the horizontal axis represents the shortest period distance from the sampling point to the defect center. (Unit: Å), the vertical axis represents the potential difference between the sampling point in the reference unit cell and the sampling point in the defect unit cell. (Unit: eV). Among them, This represents the potential difference calculated from the potential of the reference cell and the potential of the defect cell at the same sampling point.

[0162] exist Figure 5 In the sampled area, the potential difference fluctuates more significantly at sampling points closer to the defect center, indicating that this region is still affected by localized defect disturbances. As the shortest period distance from the sampling point to the defect center increases, the potential difference gradually stabilizes. After judging the shell robustness statistics and stability criteria, the starting distance of the plateau region where the potential difference begins to stabilize can be determined as the far-field starting point.

[0163] For example, Figure 5 The far-field starting point d, as illustrated in the diagram, is approximately 5.2 Å. This far-field starting point is used to subsequently determine the far-field sample set; that is, sampling points in the defect cell above this far-field starting point from the defect center can be used as samples in the far-field sample set, such as... Figure 5 The sampling points corresponding to the region to the right of the mid-far field starting point can be used as the far field sample set, which is different from the preset defect near field exclusion distance (i.e., preset defect distance) used to exclude the near field of the defect core during the random sampling stage.

[0164] According to embodiments of this disclosure, the above-described charged defect potential alignment method further includes: when the robust scales corresponding to the multiple shell sample sets and the drift of the robust centers of adjacent shells do not meet the stability criterion conditions, obtaining a distance dataset based on the shortest period distance from each sampling point in the defect cell to the defect center; determining the quantile threshold corresponding to the distance dataset at a preset quantile based on the distance dataset; and selecting sampling points from the sampling points of the defect cell whose shortest period distance is greater than or equal to the quantile threshold as the far-field sample set.

[0165] In one embodiment, if the robust scale corresponding to each of the multiple shell sample sets and the drift of the robust center of the adjacent shell do not meet the stability criterion conditions, that is, there are no consecutive m shells whose number of sampling points is greater than or equal to the sample number threshold, the robust scale is less than or equal to the robust scale threshold, and the drift of the robust center of the adjacent shell is less than or equal to the drift threshold, a fallback strategy can be adopted to determine the far-field sample set.

[0166] Specifically, the far-field sample set can be determined using the following formula (15). .

[0167] (15);

[0168] in, Represents the distance dataset, Indicates the preset quantile. This represents the quantile threshold corresponding to the distance dataset at a preset quantile.

[0169] Based on the above formula (15), the shortest period distance is selected from the sampling points of the defect cell. Greater than or equal to the quantile threshold sampling points As a far-field sample set .

[0170] According to the embodiments of this disclosure, when the robust scales corresponding to the multiple shell sample sets and the drift of the robust centers of adjacent shells do not meet the stability criterion conditions, the far-field sample set can also be selected by the above formula (15) for subsequent calculation of the zero potential offset.

[0171] According to embodiments of this disclosure, the above-described method for aligning charged defect potentials further includes: performing a preset number of resampling operations with replacement on the sampling points in the far-field sample set to obtain multiple sample point sample sets; performing robust position estimation on the potential difference corresponding to the sampling points in each sample point sample set to obtain a robust center corresponding to each sample point sample set, and constructing a sample dataset based on the robust center corresponding to each sample point sample set; using the quantile threshold corresponding to the first quantile of the sample dataset as an upper bound and the quantile threshold corresponding to the second quantile of the sample dataset as a lower bound to obtain a confidence interval for the potential alignment constant, which is used to evaluate the stability of the potential alignment constant.

[0172] In one embodiment, sampling points in the far-field sample set are resampled with replacement a preset number of times. For example, bootstrap resampling of the far-field sample set can yield multiple sample sets of sampling points, with the number of sample sets being the same as the preset number of times.

[0173] For example, samples with replacement are drawn from the far-field sample set, with the same number of samples as those in the far-field sample set, to form a sampling point sample set. This process is repeated a preset number of times B, and finally B sampling point sample sets are obtained.

[0174] In one embodiment, the robust position estimation of the potential difference corresponding to the sampling point in each sampling point sample set can be performed by the following formula (16) to obtain the robust center corresponding to each sampling point sample set.

[0175] (16);

[0176] in, Indicates the first A sample set of sampling points Indicates the first The potential difference corresponding to each sampling point in the sample set of sampling points Indicates the first The robust center corresponding to the sample set of each sampling point.

[0177] In one embodiment, the confidence interval for the potential alignment constant can be obtained by using the following formula (17), with the quantile threshold corresponding to the first quantile of the sample dataset as the upper bound and the quantile threshold corresponding to the second quantile of the sample dataset as the lower bound, so as to evaluate the stability of the potential alignment constant.

[0178] (17);

[0179] in, This represents the sample dataset constructed based on the robust centers corresponding to the sample sets at each sampling point. It is the second quantile. The first quantile, This represents the quantile threshold corresponding to the second quantile in the sample dataset. This represents the quantile threshold corresponding to the first quantile in the sample dataset. This represents a 95% confidence interval.

[0180] In one embodiment, the first quantile, the second quantile, and the confidence level (e.g., 95%) can be set as needed.

[0181] In one embodiment, given a confidence interval, the stability of the potential alignment constant can be evaluated based on this interval. Specifically, the stability of the potential alignment constant is evaluated based on the width of the confidence interval. When the confidence interval width is less than or equal to a preset uncertainty threshold, the potential alignment constant is considered to have good stability; when the confidence interval width is greater than the preset uncertainty threshold, it indicates problems such as a too-small supercell, and the potential alignment constant is considered inaccurate. Therefore, suggestions to increase the supercell size, adjust the sampling parameters, or adjust the far-field criterion parameters can be output.

[0182] According to embodiments of this disclosure, after calculating the potential alignment constant, the far-field sample set is bootstrap resampled to give the confidence interval of the potential alignment constant, thereby realizing the quantification of uncertainty (i.e., confidence interval), which facilitates the judgment of whether the unit cell is sufficient and whether the alignment is reliable, so that when the uncertainty is large, a closed-loop suggestion (e.g., increasing the supercell, adjusting the far-field selection threshold, excluding abnormal atoms, etc.) can be given.

[0183] Based on the above, during the process of aligning the potential of charged defects, diagnostic information for far-field determination will also be output. This diagnostic information includes at least the starting distance of the far-field sample set. (i.e., far-field starting point), the number of samples in the far-field sample set, the number of samples in the shell sample set, robust statistics, the satisfaction / non-satisfaction flags of the stability criterion, and the triggering reason and the fallback parameter (i.e., preset quantile) when the fallback strategy is triggered. ).

[0184] Therefore, compared with related technologies, the charged defect potential alignment method proposed in this disclosure has at least the following beneficial effects: Automated far-field selection: Transforming traditional manual / empirical region selection into reproducible stability criteria, lowering the barrier to entry; Enhanced robustness: Employing robust statistics (such as median, truncated mean, or Huber estimation) to reduce outlier influence, adapting to strongly relaxed, disordered, and amorphous systems; Output reliability and closed-loop basis: Quantifying uncertainty through confidence intervals facilitates judgment on whether the supercell is sufficient and whether the alignment is reliable; Engineering feasibility and scalability: Capable of batch processing multi-configuration, multi-charge-state, and multi-material systems, improving the scalability of the defect calculation workflow; Auditable and traceable: Outputting diagnostic information such as far-field starting point, shell statistics, and stability markers, facilitating verification and reporting.

[0185] Figure 6 A flowchart illustrating a method for aligning the potential of charged defects according to an embodiment of the present disclosure is shown.

[0186] like Figure 6 As shown, the method includes operations S610 to S618.

[0187] When operating S610, input preparation: input LOCPOT and cell parameters.

[0188] In one embodiment, LOCPOT can be a file in VASP that stores a three-dimensional grid of local or total potentials, and can be written as a "potential field file, such as LOCPOT," and is not limited to a single input format. Cell parameters can include data such as the cell structure of the reference cell and defect cells.

[0189] When operating S611, consistency check: resampling to the same grid.

[0190] In one embodiment, the consistency of the lattice size, grid size, and coordinate mapping between the reference cell and the defect cell is checked. If inconsistencies exist, the potential fields of the reference cell and the defect cell need to be mapped to the same fractional coordinate system or the same spatial coordinate system to ensure that the same sampling point corresponds to the same physical location in the two potential fields. If the lattice size and grid size are consistent, no additional resampling is required.

[0191] In operation S612, the distance metric is defined as follows: to determine the defect center, define the PBC (Periodic Boundary Conditions) distance function.

[0192] In one embodiment, the PBC distance function characterizes a function used for calculating the minimum-image periodic distance, which is used to calculate the closest distance from the sampling point to the defect center and its periodic mirror image.

[0193] Sampling is performed using S613.

[0194] In one embodiment, sampling can be performed using the above formulas (6) and (7).

[0195] When operating S614, the shortest period distance and potential difference are calculated for each sampling point.

[0196] In operation S615, define the stability criterion conditions.

[0197] In one embodiment, the stability criterion may include the constraints shown in formulas (12) and (13) above.

[0198] In operation S616, the far-field starting point is determined based on the stability criterion, and the potential alignment constant and confidence interval are calculated.

[0199] In operation S617, stability diagnosis: verify the stability of the potential alignment constant based on confidence intervals.

[0200] During the S618 operation, check if the diagnostics are successful.

[0201] In one embodiment, the stability of the potential alignment constant is evaluated based on the width of the confidence interval. The diagnosis is considered successful when the confidence interval width is less than or equal to a preset uncertainty threshold; the diagnosis is considered unsuccessful when the confidence interval width is greater than the preset uncertainty threshold.

[0202] In one embodiment, if the diagnosis passes, the result is output, namely the output potential alignment constant and the diagnostic information; if the diagnosis fails, the sampling parameters and the far-field criterion parameters are adjusted to re-execute the above operations S613 to S617.

[0203] In one embodiment, the sampling parameters may include the number of candidate sampling points and a preset defect distance. Preset atomic distance Far-field criterion parameters may include preset distances between shells. Sample size threshold Robust scalar threshold Drift threshold .

[0204] Based on the above-mentioned method for aligning charged defect potentials and combined with Figure 6 ,by Taking an 80-atom cubic unit cell as an example, how to realize the... The potential alignment calculation is as follows.

[0205] (1) Take An 80-atom cubic symmetric unit cell was used as the perfect unit cell. Four input files were prepared: POSCAR (structure coordinate file), POTCAR (pseudopotential file), INCAR (control parameter file), and KPOINTS (K-point mesh file). The ENCUT (cutoff energy) was set to 520 eV. The LVTOT (total local potential) was opened to obtain the total potential file. The EDIFF (electronic step convergence threshold) was set to 1E-7. Static single-point calculations were performed to output the potential field. .

[0206] (2) Selecting oxygen atom sites as vacancy sites in the perfect unit cell: Select atom number 41 (O, labeled O7), with fractional coordinates (0.38200, 0.61002, 0.34584). Removing this oxygen atom yields the defective unit cell. and set the charge state After geometric relaxation (fixed lattice), static single-point calculation is performed again with the same settings as in step (1) to output its potential field. The coordinates of the removed oxygen atom are the coordinates of the defect center.

[0207] (3) Potential difference samples are constructed using random spatial sampling and rejection sampling constraints. The number of candidate sampling points is set to M=2000, and the near-field exclusion radius of atoms (i.e., the preset atomic distance) is set. =1.2Å. For each candidate sampling point Requires candidate sampling points To the Defect Center Shortest period distance ,in, The shell robustness statistics are used for automatic determination; if the automatic determination fails, it will fall back to using [other methods]. Å. The potential difference is defined as electric potential value and It is obtained by trilinear interpolation from the LOCPOT three-dimensional potential grid.

[0208] (4) Use shell width (i.e., preset distance) Å, the defect cell is divided into layers; the automatic far-field determination adopts a continuous stable shell strategy, the number of continuous stable shells m=3, and the minimum number of samples in the shell sample set. =60. Robust scaling and drift thresholds can be determined based on preset empirical thresholds, tail shell statistics, or sampling sensitivity tests to automatically determine the far-field starting point. For example, robust scaling thresholds and drift thresholds can be combined. Figure 4 Sure.

[0209] (5) For the far-field sample set Huber robust position estimation is used to determine the potential alignment constant, where the tuning constant used in Huber robust position estimation is... And for the far-field sample set Perform bootstrap resampling B=2000 times to output a 95% confidence interval; when the defect charge state is When the potential alignment constant is obtained, .

[0210] Based on the above-described method for aligning charged defect potentials, this disclosure also provides a device for aligning charged defect potentials. The following will be combined with... Figure 7 The device is described in detail.

[0211] Figure 7 A schematic block diagram of a charged defect potential alignment device according to an embodiment of the present disclosure is shown.

[0212] like Figure 7 As shown, the charged defect potential alignment device 700 of this embodiment includes an acquisition module 710, a layering module 720, a first determination module 730, a second determination module 740 and a third determination module 750.

[0213] The acquisition module 710 is used to acquire the potential of each sampling point in the reference cell and the defect cell, and to construct a potential difference sample between corresponding sampling points in the reference cell and the defect cell. The defect cell is obtained by introducing a defect into the reference cell. In one embodiment, the acquisition module 710 can be used to perform the operation S210 described above, which will not be repeated here.

[0214] The layering module 720 is used to layer the defect cell according to a preset distance, using the defect center of the defect cell as the shell center, to obtain multiple shells. Based on the shortest periodic distance from each sampling point in the defect cell to the defect center, it determines the shell region to which the sampling point belongs, thus obtaining multiple shell sample sets. The shell region is determined by two adjacent shells. In one embodiment, the layering module 720 can be used to perform the operation S220 described above, which will not be repeated here.

[0215] The first determining module 730 is used to determine, for any shell sample set among multiple shell sample sets, the robust center, robust scale, and adjacent shell robust center drift corresponding to any shell sample set based on the potential difference corresponding to each sampling point in any shell sample set, wherein the adjacent shell robust center drift is determined by the robust center of the adjacent shell. In one embodiment, the first determining module 730 can be used to perform the operation S230 described above, which will not be repeated here.

[0216] The second determining module 740 is used to determine the far-field sample set when the robust scales corresponding to the multiple shell sample sets and the drift of the robust centers of adjacent shells satisfy the stability criterion. In one embodiment, the second determining module 740 can be used to perform the operation S240 described above, which will not be repeated here.

[0217] The third determining module 750 is used to perform robust position estimation of the potential difference corresponding to each sampling point in the far-field sample set, and determine the potential alignment constant to achieve potential alignment between the defect cell and the reference cell. In one embodiment, the third determining module 750 can be used to perform the operation S250 described above, which will not be repeated here.

[0218] According to embodiments of this disclosure, any plurality of modules among the acquisition module 710, layering module 720, first determination module 730, second determination module 740, and third determination module 750 can be combined into one module, or any one of these modules can be split into multiple modules. Alternatively, at least part of the functionality of one or more of these modules can be combined with at least part of the functionality of other modules and implemented in one module. According to embodiments of this disclosure, at least one of the acquisition module 710, layering module 720, first determination module 730, second determination module 740, and third determination module 750 can be at least partially implemented as hardware circuitry, such as a field-programmable gate array (FPGA), a programmable logic array (PLA), a system-on-a-chip, a system-on-a-substrate, a system-on-package, an application-specific integrated circuit (ASIC), or implemented in hardware or firmware by any other reasonable means of integrating or packaging circuitry, or implemented in any one of software, hardware, and firmware methods, or in a suitable combination of any of these methods. Alternatively, at least one of the acquisition module 710, the layering module 720, the first determining module 730, the second determining module 740, and the third determining module 750 may be implemented at least partially as a computer program module, which can perform corresponding functions when the computer program module is run.

[0219] Figure 8 A block diagram schematically illustrates an electronic device suitable for implementing a method for aligning charged defect potentials according to an embodiment of the present disclosure.

[0220] like Figure 8 As shown, an electronic device 800 according to an embodiment of this disclosure includes a processor 801, which can perform various appropriate actions and processes according to a program stored in a read-only memory (ROM) 802 or a program loaded from a storage portion 808 into a random access memory (RAM) 803. The processor 801 may include, for example, a general-purpose microprocessor (e.g., a CPU), an instruction set processor and / or an associated chipset and / or a special-purpose microprocessor (e.g., an application-specific integrated circuit (ASIC)), etc. The processor 801 may also include onboard memory for caching purposes. The processor 801 may include a single processing unit or multiple processing units for performing different actions of the method flow according to an embodiment of this disclosure.

[0221] RAM 803 stores various programs and data required for the operation of electronic device 800. Processor 801, ROM 802, and RAM 803 are interconnected via bus 804. Processor 801 performs various operations of the method flow according to embodiments of the present disclosure by executing programs in ROM 802 and / or RAM 803. It should be noted that the programs may also be stored in one or more memories other than ROM 802 and RAM 803. Processor 801 may also perform various operations of the method flow according to embodiments of the present disclosure by executing programs stored in said one or more memories.

[0222] According to embodiments of this disclosure, the electronic device 800 may further include an input / output (I / O) interface 805, which is also connected to a bus 804. The electronic device 800 may also include one or more of the following components connected to the input / output (I / O) interface 805: an input section 806 including a keyboard, mouse, etc.; an output section 807 including a cathode ray tube (CRT), liquid crystal display (LCD), etc., and a speaker, etc.; a storage section 808 including a hard disk, etc.; and a communication section 809 including a network interface card such as a LAN card, modem, etc. The communication section 809 performs communication processing via a network such as the Internet. A drive 810 is also connected to the input / output (I / O) interface 805 as needed. A removable medium 811, such as a disk, optical disk, magneto-optical disk, semiconductor memory, etc., is installed on the drive 810 as needed so that computer programs read from it can be installed into the storage section 808 as needed.

[0223] This disclosure also provides a computer-readable storage medium, which may be included in the device / apparatus / system described in the above embodiments; or it may exist independently and not assembled into the device / apparatus / system. The computer-readable storage medium carries one or more programs that, when executed, implement the method according to the embodiments of this disclosure.

[0224] According to embodiments of this disclosure, the computer-readable storage medium can be a non-volatile computer-readable storage medium, such as including, but not limited to: portable computer disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), portable compact disk read-only memory (CD-ROM), optical storage devices, magnetic storage devices, or any suitable combination thereof. In this disclosure, the computer-readable storage medium can be any tangible medium that contains or stores a program that can be used by or in conjunction with an instruction execution system, apparatus, or device. For example, according to embodiments of this disclosure, the computer-readable storage medium may include ROM 802 and / or RAM 803 and / or one or more memories other than ROM 802 and RAM 803 described above.

[0225] Embodiments of this disclosure also include a computer program product comprising a computer program containing program code for performing the methods shown in the flowchart. When the computer program product is run on a computer system, the program code is used to enable the computer system to implement the charged defect potential alignment method provided in the embodiments of this disclosure.

[0226] When the computer program is executed by the processor 801, it performs the functions defined in the system / apparatus of this disclosure embodiments. According to embodiments of this disclosure, the systems, apparatuses, modules, units, etc., described above can be implemented by computer program modules.

[0227] In one embodiment, the computer program may rely on a tangible storage medium such as an optical storage device or a magnetic storage device. In another embodiment, the computer program may also be transmitted and distributed in the form of signals over a network medium, and may be downloaded and installed via the communication section 809, and / or installed from a removable medium 811. The program code contained in the computer program can be transmitted using any suitable network medium, including but not limited to: wireless, wired, etc., or any suitable combination thereof.

[0228] In such an embodiment, the computer program can be downloaded and installed from a network via communication section 809, and / or installed from removable medium 811. When the computer program is executed by processor 801, it performs the functions defined in the system of this disclosure embodiment. According to embodiments of this disclosure, the systems, devices, apparatuses, modules, units, etc., described above can be implemented by computer program modules.

[0229] According to embodiments of this disclosure, program code for executing the computer programs provided in embodiments of this disclosure can be written in any combination of one or more programming languages. Specifically, these computational programs can be implemented using high-level procedural and / or object-oriented programming languages, and / or assembly / machine languages. Programming languages ​​include, but are not limited to, languages ​​such as Java, C++, Python, "C", or similar programming languages. The program code can execute entirely on a user's computing device, partially on a user's device, partially on a remote computing device, or entirely on a remote computing device or server. In cases involving remote computing devices, the remote computing device can be connected to the user's computing device via any type of network, including a local area network (LAN) or a wide area network (WAN), or it can be connected to an external computing device (e.g., via the Internet using an Internet service provider).

[0230] The flowcharts and block diagrams in the accompanying drawings illustrate the architecture, functionality, and operation of possible implementations of systems, methods, and computer program products according to various embodiments of this disclosure. In this regard, each block in a flowchart or block diagram may represent a module, segment, or portion of code containing one or more executable instructions for implementing a specified logical function. It should also be noted that in some alternative implementations, the functions indicated in the blocks may occur in a different order than those indicated in the drawings. For example, two consecutively indicated blocks may actually be executed substantially in parallel, and they may sometimes be executed in reverse order, depending on the functions involved. It should also be noted that each block in a block diagram or flowchart, and combinations of blocks in a block diagram or flowchart, may be implemented using a dedicated hardware-based system that performs the specified function or operation, or using a combination of dedicated hardware and computer instructions.

[0231] Those skilled in the art will understand that the features described in the various embodiments of this disclosure can be combined and / or combined in various ways, even if such combinations or combinations are not explicitly described in this disclosure. In particular, the features described in the various embodiments of this disclosure can be combined and / or combined in various ways without departing from the spirit and teachings of this disclosure. All such combinations and / or combinations fall within the scope of this disclosure.

[0232] The embodiments of this disclosure have been described above. However, these embodiments are for illustrative purposes only and are not intended to limit the scope of this disclosure. Although various embodiments have been described above, this does not mean that the measures in the various embodiments cannot be used advantageously in combination. Various substitutions and modifications can be made by those skilled in the art without departing from the scope of this disclosure, and all such substitutions and modifications should fall within the scope of this disclosure.

Claims

1. A method for aligning the potential of charged defects, characterized in that, The method includes: The potential of each sampling point in the reference cell and the defect cell is obtained, and the potential difference sample between the corresponding sampling points in the reference cell and the defect cell is constructed. The defect cell is obtained by introducing a defect into the reference cell. Using the defect center of the defect cell as the shell center, the defect cell is divided into layers according to a preset distance to obtain multiple shells. Based on the shortest periodic distance from each sampling point in the defect cell to the defect center, the shell region to which the sampling point belongs is determined to obtain multiple shell sample sets. The shell region is determined by two adjacent shells. For any shell sample set among the multiple shell sample sets, based on the potential difference corresponding to each sampling point in any shell sample set, determine the robust center, robust scale, and adjacent shell robust center drift corresponding to any shell sample set, wherein the adjacent shell robust center drift is determined by the robust center of the adjacent shell region. The far-field sample set is determined when the robust scale corresponding to each of the multiple shell sample sets and the drift of the robust center of the adjacent shell satisfy the stability criterion condition. Robust position estimation is performed on the potential difference corresponding to each sampling point in the far-field sample set to determine the potential alignment constant, which is used to achieve potential alignment between the defect cell and the reference cell.

2. The method according to claim 1, characterized in that, The process of obtaining the potential at each sampling point in the reference cell and the defect cell includes: Uniform meshing and self-consistent electrostatic potential calculation are performed on the reference cell and the defect cell respectively to obtain the three-dimensional potential mesh of the reference cell and the defect cell. The grid points of the three-dimensional potential mesh store the potential. Based on the sampling points in the reference cell and the defect cell, trilinear interpolation is performed on the three-dimensional potential grids of the reference cell and the defect cell respectively to obtain the potential of each sampling point in the reference cell and the defect cell.

3. The method according to claim 2, characterized in that, The sampling points in the reference cell and the defect cell are determined by the following operation: Multiple candidate sampling points are randomly selected from the defective unit cell; Calculate the first distance between each candidate sampling point and the defect center, where the first distance characterizes the shortest period distance between the candidate sampling point and the defect center; Calculate the second distance between each candidate sampling point and each atom in the defect cell, where the second distance characterizes the shortest period distance between the candidate sampling point and each atom in the defect cell; From the plurality of candidate sampling points, candidate sampling points with a first distance greater than or equal to a preset defect distance and a second distance greater than or equal to a preset atomic distance are selected as sampling points in the defect cell and the reference cell, wherein the sampling points in the defect cell and the reference cell are the same.

4. The method according to claim 1, characterized in that, The determination of the robust center, robust scale, and robust center drift corresponding to any shell sample set based on the potential difference corresponding to each sampling point in the shell sample set includes: Local robust position estimation is performed on the potential difference corresponding to each sampling point in any shell sample set to obtain the robust center corresponding to any shell sample set; Calculate the median absolute deviation of the potential difference corresponding to each sampling point in any shell sample set to obtain the robust scale corresponding to any shell sample set; Based on the absolute difference between the robust center corresponding to any shell sample set and the robust center of the shell sample set corresponding to the shell adjacent to the shell sample set, the drift of the robust center of the adjacent shell is determined.

5. The method according to claim 1, characterized in that, The determination of the far-field sample set, under the condition that the robust scales corresponding to the multiple shell sample sets and the drift of the robust centers of adjacent shells satisfy the stability criterion, includes: If the number of sampling points in the shell sample set corresponding to m consecutive shells is greater than or equal to the sample number threshold, the robust scale is less than or equal to the robust scale threshold, and the drift of the robust center of adjacent shells is less than or equal to the drift threshold, then the shell sample set corresponding to m consecutive shells is determined to satisfy the stability criterion condition, where m is an integer greater than 1, and the m consecutive shells represent the k-th to k+m-1-th shells in the defect cell, where k is an integer greater than or equal to 1. The sampling points in the sample set corresponding to the k-th shell and the shells after the k-th shell in the defective unit cell are determined as the far-field sample set.

6. The method according to claim 5, characterized in that, The method further includes: When the robust scales corresponding to the multiple shell sample sets and the drift of the robust centers of adjacent shells do not meet the stability criterion, a distance dataset is obtained based on the shortest periodic distance from each sampling point in the defect cell to the defect center. Based on the distance dataset, determine the quantile threshold corresponding to the distance dataset at the preset quantile; From the sampling points of the defective unit cell, the sampling points with the shortest period distance greater than or equal to the quantile threshold are selected as the far-field sample set.

7. The method according to any one of claims 1 to 6, characterized in that, The method further includes: The sampling points in the far-field sample set are resampled with replacement a preset number of times to obtain multiple sample sets of sampling points; Robust location estimation is performed on the potential difference corresponding to the sampling point in the sample set of each sampling point to obtain the robust center corresponding to the sample set of each sampling point, and the sample dataset is constructed based on the robust center corresponding to the sample set of each sampling point. Using the quantile threshold corresponding to the first quantile of the sample dataset as the upper bound and the quantile threshold corresponding to the second quantile of the sample dataset as the lower bound, a confidence interval for the potential alignment constant is obtained, which is used to evaluate the stability of the potential alignment constant.

8. A device for aligning the potential of charged defects, characterized in that, The device includes: The acquisition module is used to acquire the potential of each sampling point in the reference cell and the defect cell, and to construct the potential difference sample between the corresponding sampling points in the reference cell and the defect cell. The defect cell is obtained by introducing a defect into the reference cell. The layering module is used to divide the defect cell into layers according to a preset distance, with the defect center of the defect cell as the shell center, to obtain multiple shells. Based on the shortest period distance from each sampling point in the defect cell to the defect center, the shell region to which the sampling point belongs is determined to obtain multiple shell sample sets. The shell region is determined by two adjacent shells. The first determining module is used to determine, for any shell sample set among the plurality of shell sample sets, the robust center, robust scale and adjacent shell robust center drift corresponding to any shell sample set based on the potential difference corresponding to each sampling point in any shell sample set, wherein the adjacent shell robust center drift is determined by the robust center of the adjacent shell region. The second determining module is used to determine the far-field sample set when the robust scale corresponding to each of the multiple shell sample sets and the drift of the robust center of the adjacent shell satisfy the stability criterion condition. The third determining module is used to perform robust position estimation on the potential difference corresponding to each sampling point in the far-field sample set and determine the potential alignment constant to achieve potential alignment between the defect cell and the reference cell.

9. An electronic device, comprising: One or more processors; Memory, used to store one or more computer programs. The characteristic feature is that the one or more processors execute the one or more computer programs to implement the steps of the method according to any one of claims 1 to 7.

10. A computer-readable storage medium having a computer program or instructions stored thereon, characterized in that, When the computer program or instructions are executed by a processor, they implement the steps of the method according to any one of claims 1 to 7.

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