A method, system, device and medium for calculating a coercive electric field of a ferroelectric material

Abstract

The application discloses a coercive electric field calculation method, system, equipment and medium of ferroelectric material, relates to the technical field of coercive electric field estimation, and comprises the following steps: selecting an initial state and a final state of the ferroelectric material; the initial state is a stable state of the ferroelectric material, and the final state is another stable state; or the initial state is a ferroelectric state of the ferroelectric material, and the final state is a central symmetric state; a minimum energy path method of a first principle is used to generate a polarization reversal path from the initial state to the final state and a continuous inversion path; a double polarization strategy is used to obtain the polarization value of each structure point in the continuous inversion path, and the maximum energy point is determined according to the energy distribution of the structure point; the polarization difference and the reversal barrier of the ferroelectric phase and the paraelectric phase are extracted; and the coercive electric field is obtained by the ratio of the reversal barrier to the polarization difference. The application obtains the real polarization reversal path through the minimum energy path algorithm, avoids the energy distortion and polarization error that may be introduced by the non-physical linear interpolation path, and thus accurately captures the reversal barrier and the polarization evolution.

Description

Technical Field

[0001] This invention relates to the field of coercive electric field estimation technology, and in particular to a method, system, device and medium for calculating the coercive electric field of ferroelectric materials. Background Technology

[0002] Ferroelectric materials are a class of functional materials exhibiting spontaneous polarization, where the polarization direction can reversibly reverse under an applied electric field. Therefore, they are widely used in novel micro / nanoelectronic devices such as non-volatile RAM (FeRAM), ferroelectric field-effect transistors (FeFETs), ferroelectric tunnel junctions (FTJs), and spintronic devices. When evaluating the performance of ferroelectric materials, the coercive electric field (E) is crucial. c E c It is one of the core physical parameters for measuring polarization switchability and device operability. The smaller the coercive electric field, the easier it is for the material to achieve low-power writing; while an excessively high or unstable coercive electric field will limit its application in low-power devices.

[0003] In existing technologies, first-principles methods have been widely used to predict the polarization properties and coercive electric fields of ferroelectric materials. One typical method is based on Berry phase theory combined with the Landau-Ginzburg-Devonshire (LGD) estimation model. However, existing first-principles-based coercive electric field calculation methods have high requirements for the band structure of the system, and in the prediction process, they usually need to be fitted with experimental data or set a priori parameters, resulting in strong parameter dependence and poor reliability and universality. Summary of the Invention

[0004] The purpose of this invention is to address the shortcomings of the prior art by providing a method, system, device, and medium for calculating the coercive electric field of ferroelectric materials, thereby solving the problems in the prior art.

[0005] This invention specifically provides the following technical solution: a method for calculating the coercive electric field of ferroelectric materials, comprising:

[0006] The initial state and the final state of the ferroelectric material are selected. The initial state is a stable state of the ferroelectric material and the final state is another stable state. Alternatively, the initial state is the ferroelectric state of the ferroelectric material and the final state is a centrosymmetric state.

[0007] The first-principles minimum energy path method is used to generate a polarization reversal path from the initial state to the final state. Through local structure optimization and self-consistent calculation methods, several interpolation point structures and total energy in the polarization reversal path are obtained, forming a continuous inversion path from the initial state to the final state.

[0008] A dual polarization strategy is used to obtain the polarization value of each structure point in the continuous inversion path. The polarization difference is obtained by subtracting the polarization values ​​of the structure points at both ends of the continuous inversion path. The maximum energy point is determined according to the energy distribution of the structure points, and the flip barrier is extracted based on the maximum energy point. The coercive electric field is obtained by the ratio of the flip barrier to the polarization difference.

[0009] Preferably, the method of generating the polarization reversal path from the initial state to the final state using the first-principles minimum energy path method specifically involves:

[0010] By analyzing atomic displacements in the lattice coordinate space of ferroelectric materials, rotations around the central site, microstructural distortions of dimers / triangular / tetrahedral / octahedral structures, and symmetry evolution, the paths from the relatively initial ferroelectric phase to the nearest centrosymmetric phase, and the paths from the relatively initial ferroelectric phase to the polarization-reversed ferroelectric configuration are determined. These two paths are then used as polarization-reversal paths.

[0011] Among them, the initial ferroelectric phase is the stabilized state or ferroelectric state of the ferroelectric material, the nearest centrosymmetric phase is the centrosymmetric state, and the ferroelectric configuration is another stabilized state of the ferroelectric material.

[0012] Preferably, the method of using a dual polarization strategy to obtain the polarization value of each structure point in the continuous inversion path specifically involves:

[0013] The polarization values ​​of ferroelectric materials belonging to the insulating system were generated using the Berry phase method.

[0014] The polarization values ​​of ferroelectric materials belonging to metallic or narrow bandgap systems are generated using the Born effective charge tensor method.

[0015] Preferably, the method of generating polarization values ​​for ferroelectric materials belonging to metallic or narrow bandgap systems using the Born effective charge tensor method specifically involves:

[0016] The polarization value of ferroelectric materials belonging to metallic or narrow bandgap systems is obtained by summing the effective charge tensor and the product of the relative displacement of each ion per unit cell volume; the specific expression is:

[0017] ;

[0018] in, For ferroelectric materials that belong to metallic or narrow bandgap systems, the polarization value is... For the first Effective charge tensor of each ion This is relative displacement. For unit cell volume, in two-dimensional materials, it is... Replace with unit cell area S.

[0019] Preferably, after obtaining the coercive electric field by the ratio of the flipping potential barrier to the polarization difference, the method further includes:

[0020] The Landau free energy of ferroelectric materials is expressed as follows:

[0021] ;

[0022] in, F ( P The total free energy of the system is denoted as . Landau coefficient; For coercive electric field strength;

[0023] Utilizing polarization paths The Landau coefficients were obtained by least-squares fitting of the data to the Landau free energy of ferroelectric materials. ;in, The polarization value at each structural point, The coercive electric field strength at each structural point;

[0024] Build The temperature dependence of the Curie temperature; specifically expressed as:

[0025] ;

[0026] in, These are temperature-dependent second-order coefficients. T For temperature, Curie temperature; Related to the material itself, It is a constant;

[0027] The fitted Landau coefficients Substitute into the formula In the middle, the Curie temperature was obtained. Then through Generate at different temperatures Substituting this into the Landau free energy formula for ferroelectric materials, we obtain the coercive electric field at different temperatures.

[0028] Preferably, the polarization difference is obtained by subtracting the polarization values ​​of the structure points at both ends of the continuous inversion path, and the maximum energy point is determined according to the energy distribution of the structure points. The flip barrier is extracted, and the coercive electric field is obtained by the ratio of the flip barrier to the polarization difference. Specifically:

[0029] The maximum energy point is determined based on the energy distribution of the structural points at both ends of the continuous inversion path, and the barrier difference between the maximum energy point and the minimum energy point is used as the inversion barrier between the ferroelectric phase and the paraelectric phase; the polarization difference between the ferroelectric phase and the paraelectric phase is obtained by the polarization difference between the polarization values ​​of the ferroelectric phase and the paraelectric phase; wherein, the ferroelectric phase and the paraelectric phase are the states of the ferroelectric material below the Curie temperature and the states of the ferroelectric material above the Curie temperature, respectively.

[0030] The coercive electric field is obtained by the ratio of the flipping potential barrier to the polarization difference.

[0031] This invention provides a coercive electric field calculation system for ferroelectric materials, comprising:

[0032] The data selection module is used to select the initial state and the final state of the ferroelectric material. The initial state is a stable state of the ferroelectric material and the final state is another stable state, or the initial state is the ferroelectric state of the ferroelectric material and the final state is a centrosymmetric state.

[0033] The path generation module is used to generate a polarization reversal path from the initial state to the final state using the first-principles minimum energy path method. Through local structure optimization and self-consistent calculation methods, it obtains several interpolation point structures and total energy in the polarization reversal path, forming a continuous inversion path from the initial state to the final state.

[0034] The electric field calculation module is used to obtain the polarization value of each structure point in the continuous inversion path using a dual polarization strategy. The polarization difference is obtained by subtracting the polarization values ​​of the structure points at both ends of the continuous inversion path. The maximum energy point is determined according to the energy distribution of the structure points, and the flipping barrier is extracted based on the maximum energy point. The coercive electric field is obtained by the ratio of the flipping barrier to the polarization difference.

[0035] The present invention provides a computer device, including a memory and a processor. The memory stores a program, and when the program is executed by the processor, the processor performs the steps of the above-described method for calculating the coercive electric field of a ferroelectric material.

[0036] The present invention provides a storage medium storing a computer program thereon, wherein the computer program, when executed by a processor, implements the steps of the above-described method for calculating the coercive electric field of a ferroelectric material.

[0037] Compared with the prior art, the present invention has the following significant advantages:

[0038] This invention employs a first-principles minimum energy path method to generate a polarization reversal path from the initial state to the final state. Through local structure optimization and self-consistent calculation methods, it obtains the structure of several interpolation points and the total energy in the polarization reversal path, forming a continuous inversion path from the initial state to the final state. This avoids energy distortion and polarization errors that may be introduced by non-physical linear interpolation paths. At the same time, based on the obtained path, it obtains the polarization value of the structure point, the polarization difference at both ends of the continuous inversion path, and the reversal barrier, improving the physical reliability of obtaining the coercive electric field. Moreover, it is calculated entirely based on first-principles calculations, avoiding experimental dependence or empirical fitting of the Landau free energy function coefficient, and has strong universality and reliability. Attached Figure Description

[0039] Figure 1 This is a graph showing the calculation results of polarization in this invention;

[0040] Figure 2 This is the polarization and energy curve diagram in this invention;

[0041] Figure 3 This is a scatter plot of the electric field and polarization in this invention;

[0042] Figure 4 This is a flowchart of a method for calculating the coercive electric field of ferroelectric materials provided by the present invention. Detailed Implementation

[0043] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0044] In existing technologies, the estimation model method based on Berry phase theory combined with Landau-Ginzburg-Devonshire (LGD) is completed through the following steps:

[0045] 1) Select the ferroelectric state and nonpolar reference state of the material.

[0046] 2) Construct the inversion path using linear interpolation or the NEB method.

[0047] 3) Calculate the total energy of each structural point in the path to obtain the polarization reversal barrier.

[0048] 4) Calculate polarization using the Berry phase method.

[0049] 5) Finally, the coercive electric field is calculated using the Landau-Ginzburg-Devonshire (LGD) theoretical formula and its free energy coefficients. The free energy coefficients need to be fitted by experiments or a large amount of experience.

[0050] This method is applicable to most wide-bandgap insulator ferroelectric materials (such as BaTiO3, PbTiO3, etc.). 3, Relatively reliable results can be obtained from BiTiO3, which has a certain degree of physical consistency within the first-principles framework.

[0051] Disadvantages of existing technology:

[0052] I. Applicability Limitations of Material Systems: The Berry phase polarization calculation method has high requirements for the band structure of the system and is only applicable to materials with well-defined insulating states. For metals and narrow bandgap materials, due to their divergence near the Fermi level, the metallic state is limited in E... FThe calculation of the nearby Berry curvature fails, and its factor is: , where the denominator approaches 0.

[0053] 2. The polarization path is not unique or is not physical: If a simple linear interpolation method is used to construct the ferroelectric reversal path, the intermediate interpolation structure may contain non-physical bond lengths and excessive atomic shifts, thus failing to accurately reflect the real polarization reversal barrier.

[0054] III. Free energy coefficients depend on experimental or empirical fitting: lacking universality: the free energy expansion coefficients used in the Landau-Ginzburg-Devonshire (LGD) theoretical formulas for calculating the coercive electric field (e.g.) Typically, models need to be fitted with experimental data or set priors, lacking a unified mechanism for working backward from first principles. This results in strong dependence on model parameters, poor repeatability, and weak generalization ability across materials.

[0055] Fourth, the inability to predict temperature dependence: Most traditional methods predict potential barriers and polarization at 0K, which is difficult to extend to limited temperatures. In particular, it is difficult to reliably predict coercive electric fields in the operating environment of traditional devices (such as above room temperature), which limits the application value of the methods in engineering design.

[0056] To address the technical problems of existing first-principles-based coercive electric field calculation methods, such as limited applicability, inaccurate polarization path construction, non-universal polarization calculation methods, and free energy parameter dependence on experimental fitting, this invention proposes a universal calculation method for coercive electric fields. This method has the following objectives:

[0057] Materials applicable to various electronic structure types: This paper provides a coercive electric field calculation framework that is applicable to wide bandgap insulators, narrow bandgap semiconductors, and even metallic ferroelectric systems. It solves the problem that the Berry phase method is not applicable to metallic / small bandgap materials, and improves the versatility and material coverage of the method.

[0058] Constructing a physically realistic polarization reversal path: The minimum energy path during polarization reversal is accurately obtained through the NEB (Nudged Elastic Band) algorithm, avoiding unreasonable deformations and energy anomalies in linear interpolation results, and ensuring physical consistency between the potential barrier calculation and the polarization change trajectory.

[0059] Calculating the coercive electric field without the participation of experimental parameters: The coercive electric field is directly generated by the energy difference and polarization difference in the first principle path, without relying on external experimental data or empirically fitted free energy coefficients, thereby achieving theoretical self-consistency and model-controllable performance prediction.

[0060] Introducing a back-calculation mechanism for Landau-Ginzburg-Devonshire theoretical parameters: By fitting the energy-polarization point along the first-principles path, the coefficient parameters in Landau-Ginzburg-Devonshire (such as...) can be deduced. Based on this, a temperature-dependent model is constructed to predict the changing trend of the coercive electric field at different temperatures, thereby expanding the practical engineering applicability of the method.

[0061] like Figure 4 As shown, this invention provides a universal method for calculating the coercive electric field applicable to insulators, semiconductors, narrow bandgap materials, and even metallic ferroelectric systems. This method is based on first-principles minimum energy path search and polarization difference extraction, combined with discrete electric field formulas and LGD theoretical coefficient fitting, to predict the coercive electric field at different temperatures. The method includes the following steps:

[0062] Step S1: Select the initial state and final state of the ferroelectric material. The initial state is the stable state of the ferroelectric material, and the final state is another stable state. Alternatively, the initial state is the ferroelectric state of the ferroelectric material, and the final state is a centrosymmetric state. Among these, there are two stable states (+P or -P).

[0063] Step S2: Constructing the polarization reversal path of ferroelectric materials: Using the first-principles minimum energy path method, such as NEB (Nudged Elastic Band) or CI-NEB, a polarization reversal path between the initial state and the final state is generated. Through local structure optimization and self-consistent calculation methods, several interpolation point structures and total energy in the polarization reversal path are obtained, forming a continuous inversion path from the initial state to the final state, capturing the real transition state evolution during the polarization reversal process.

[0064] The process of generating the polarization reversal path between the initial and final states using the first-principles minimum energy path method is as follows:

[0065] By analyzing atomic displacements in the lattice coordinate space of ferroelectric materials, rotations around the central site, microstructural distortions of dimers / triangular / tetrahedral / octahedral structures, and symmetry evolution, the paths from the relatively initial ferroelectric phase to the nearest centrosymmetric phase, and the paths from the relatively initial ferroelectric phase to the polarization-reversed ferroelectric configuration are determined. These two paths are then used as polarization-reversal paths.

[0066] Among them, the initial ferroelectric phase is the stabilized state or ferroelectric state of the ferroelectric material, the nearest centrosymmetric phase is the centrosymmetric state, and the ferroelectric configuration is another stabilized state of the ferroelectric material.

[0067] Step S3: Calculate the polarization value of each structure point in the path, and calculate the coercive electric field based on the polarization difference and potential barrier: Use a dual polarization strategy to obtain the polarization value of each structure point in the continuous inversion path. The polarization difference is obtained by subtracting the polarization values ​​of the structure points at both ends of the continuous inversion path, and the maximum energy point is determined according to the energy distribution of the structure points. The flipping barrier is extracted based on the maximum energy point. The coercive electric field is obtained by the ratio of the flipping barrier to the polarization difference.

[0068] Dual polarization strategies include the Berry phase method and the Born effective charge tensor method. The calculation results for the polarization of ferroelectric materials are as follows: Figure 1 As shown. The polarization values ​​of ferroelectric materials belonging to the insulator system are generated using the Berry phase method. The polarization values ​​of ferroelectric materials belonging to the metallic or narrow bandgap system are generated using the Born effective charge (BEC) tensor method, specifically:

[0069] The polarization value of ferroelectric materials belonging to metallic or narrow bandgap systems is obtained by summing the effective charge tensor and the product of the relative displacement of each ion per unit cell volume; the specific expression is:

[0070] ;

[0071] in, For ferroelectric materials that belong to metallic or narrow bandgap systems, the polarization value is... For the first Effective charge tensor of each ion This is relative displacement. For unit cell volume, in two-dimensional materials, it is... Instead, we use unit cell area S. This step introduces the BEC method, which ensures that polarization calculations remain universal and numerically stable when the Berry phase method is unavailable.

[0072] The polarization difference is obtained by subtracting the polarization values ​​at both ends of the continuous inversion path. The maximum energy point is determined based on the energy distribution of the structural points. The flip barrier is extracted, and the coercive electric field is obtained by the ratio of the flip barrier to the polarization difference. Specifically:

[0073] The polarization difference between the ferroelectric and paraelectric phases is obtained by comparing the polarization values ​​of the ferroelectric and paraelectric phases; where the ferroelectric and paraelectric phases represent the states of the ferroelectric material below and above the Curie temperature, respectively; the specific expression is as follows:

[0074] ;

[0075] in This represents the polarization difference between the ferroelectric and paraelectric phases. The polarization value of the ferroelectric phase; This represents the polarization value of the paraelectric phase.

[0076] The maximum energy point (saddle point) is determined based on the energy distribution of structural points in the continuous inversion path. The potential barrier difference between the maximum and minimum energy points in the NEB path is used as the switching barrier between the ferroelectric and paraelectric phases. The polarization and energy curves are shown below. Figure 2 As shown; the specific expression is:

[0077] ;

[0078] in The potential barrier difference between the ferroelectric and paraelectric phases is... This is the highest energy point in the NEB path. This is the lowest point of energy in the NEB path.

[0079] The coercive electric field is approximately obtained by using the ratio of the flipping potential barrier to the polarization difference. E c The specific expression is:

[0080] ;

[0081] in, For unit cell volume, two-dimensional materials will... Instead, we use the unit cell area S. This discrete formula is derived from an approximate average field expression of the contribution of electro-polarization energy during the flipping process. It can take into account both the energy barrier and the polarization driving factors. The resulting coercive electric field and polarization scatter plot are shown below. Figure 3 As shown.

[0082] By employing a dual polarization calculation strategy using Berry phase and Born effective charge BEC tensor, this method is applicable not only to traditional wide bandgap insulators but also to small bandgap semiconductors and even ferroelectric systems with weak metallic properties, significantly expanding the material applicability range for coercive field calculations.

[0083] After obtaining the coercive electric field by using the ratio of the flip potential barrier to the polarization difference, the process also includes: fitting the Landau free energy model and predicting the coercive electric field at the temperature, specifically:

[0084] The Landau free energy of ferroelectric materials is expressed as follows:

[0085] ;

[0086] in, F ( P The total free energy of the system is denoted as . Let be the Landau coefficient, where The quadratic coefficients indicate the phase transition type and critical temperature. It appears only in first-order phase transitions and breaks the even symmetry of free energy; The coefficient is a sixth-order phase coefficient, which ensures the stability of the ordered phase at low temperatures and dominates the low-temperature behavior in the second-order phase transition; For coercive electric field strength; It represents the polarization value of a metallic or narrow bandgap system.

[0087] Utilizing polarization paths The Landau coefficients were derived by least-squares fitting of the data to the Landau free energy of ferroelectric materials. ;in, The polarization value at each structural point, The coercive electric field strength at each structural point.

[0088] Build Temperature dependence of Curie temperature, combined with the actual Curie temperature of the material Predicting the changes in the coercive electric field at different temperatures; specifically expressed as:

[0089] ;

[0090] in, It is a temperature-dependent second-order coefficient (which determines the curvature of the energy curve near P=0 and is a stability criterion for paraelectric and ferroelectric phases). T For temperature, Curie temperature (critical temperature for phase transition); Related to the material itself (describes the material's sensitivity to temperature changes; a larger value indicates a more significant impact of temperature changes on phase transitions). It is a constant.

[0091] The coercive electric field at the corresponding temperature is calculated by varying the barrier height and polarization well width under the free energy curve. The Landau coefficients to be fitted are then used. Substitute into the formula In the middle, the Curie temperature was obtained. Then through Generate at different temperatures Substituting this into the Landau free energy formula for ferroelectric materials, we obtain the coercive electric field at different temperatures.

[0092] This step extends the zero-temperature static prediction results of the coercive electric field, improving the method's engineering applicability and predictive capability.

[0093] This invention also possesses temperature prediction capabilities, expanding its engineering applicability: by fitting the polarization-energy relationship along the first-principles path, the temperature correlation coefficient in the Landau-Ginzburg-Devonshire model is derived, thereby establishing a model of the coercive electric field changing with temperature. This method can be used to evaluate the performance stability of materials in actual operating temperature ranges (such as room temperature, device heating environments, etc.). It is particularly suitable for research on two-dimensional ferroelectric and low-dimensional materials: this invention is highly adaptable to changes in structural dimension and symmetry, and is especially suitable for two-dimensional ferroelectric materials (such as...) currently a research hotspot. Performance evaluation of low-dimensional systems such as In2Se3, SnTe, heterojunctions, and superlattices provides theoretical support for novel low-power non-volatile devices.

[0094] In summary, this invention achieves a comprehensive upgrade in coercive electric field calculation from traditional limited models to one that combines universality, physical rigor, engineering practicality, and automation capabilities, and has significant theoretical value and promising prospects for industrial application.

[0095] This invention proposes a coercive electric field calculation system for ferroelectric materials, comprising: a data selection module, a path generation module, and an electric field calculation module.

[0096] The data selection module selects the initial and final states of the ferroelectric material. The initial state is a stable state of the ferroelectric material, and the final state is another stable state, or the initial state is the ferroelectric state of the ferroelectric material, and the final state is a centrosymmetric state. The path generation module generates a polarization reversal path from the initial state to the final state using the first-principles minimum energy path method. Through local structure optimization and self-consistent calculation methods, it obtains several interpolation point structures and total energy in the polarization reversal path, forming a continuous inversion path from the initial state to the final state. The electric field calculation module uses a dual polarization strategy to obtain the polarization value of each structure point in the continuous inversion path. It obtains the polarization difference by subtracting the polarization values ​​of the structure points at both ends of the continuous inversion path, determines the maximum energy point based on the energy distribution of the structure points, and extracts the reversal barrier based on the maximum energy point. The coercive electric field is obtained by the ratio of the reversal barrier to the polarization difference.

[0097] The present invention also provides a computer device, including a memory and a processor. The memory stores a program, and when the program is executed by the processor, the processor performs the steps of a method for calculating the coercive electric field of a ferroelectric material.

[0098] According to the disclosed embodiments, the computer device can communicate with one or more external devices (e.g., keyboard, pointing device, Bluetooth communication, etc.) or with any device that enables the computing device to communicate with one or more other computing devices (e.g., router, demodulator, etc.).

[0099] The present invention also provides a storage medium storing a computer program thereon, wherein the computer program, when executed by a processor, implements the steps of a method for calculating the coercive electric field of a ferroelectric material.

[0100] The above description, in conjunction with specific preferred embodiments, provides a more detailed explanation of the present invention. For those skilled in the art, various simple deductions or substitutions can be made without departing from the concept of the present invention, and all such deductions or substitutions should be considered to fall within the scope of protection of the present invention.

Claims

1. A method for calculating the coercive electric field of ferroelectric materials, characterized in that, include: The initial state and the final state of the ferroelectric material are selected. The initial state is a stable state of the ferroelectric material and the final state is another stable state. Alternatively, the initial state is the ferroelectric state of the ferroelectric material and the final state is a centrosymmetric state. The first-principles minimum energy path method is used to generate a polarization reversal path from the initial state to the final state. Through local structure optimization and self-consistent calculation methods, several interpolation point structures and total energy in the polarization reversal path are obtained, forming a continuous inversion path from the initial state to the final state. A dual polarization strategy is used to obtain the polarization value of each structure point in the continuous inversion path. The polarization difference is obtained by subtracting the polarization values ​​of the structure points at both ends of the continuous inversion path. The maximum energy point is determined according to the energy distribution of the structure points, and the flip barrier is extracted based on the maximum energy point. The coercive electric field is obtained by the ratio of the flip barrier to the polarization difference. The first-principles minimum energy path method generates the polarization reversal path between the initial and final states, specifically as follows: By analyzing atomic displacements in the lattice coordinate space of ferroelectric materials, rotations around the central site, microstructural distortions of dimers / triangular / tetrahedral / octahedral structures, and symmetry evolution, the paths from the relatively initial ferroelectric phase to the nearest centrosymmetric phase, and the paths from the relatively initial ferroelectric phase to the polarization-reversed ferroelectric configuration are determined. These two paths are then used as polarization-reversal paths. Among them, the initial ferroelectric phase is the stabilized state or ferroelectric state of the ferroelectric material, the nearest centrosymmetric phase is the centrosymmetric state, and the ferroelectric configuration is another stabilized state of the ferroelectric material.

2. The method for calculating the coercive electric field of ferroelectric materials as described in claim 1, characterized in that, The method of using a dual polarization strategy to obtain the polarization value of each structure point in the continuous inversion path is as follows: The polarization values ​​of ferroelectric materials belonging to the insulating system were generated using the Berry phase method. The polarization values ​​of ferroelectric materials belonging to metallic or narrow bandgap systems are generated using the Born effective charge tensor method.

3. The method for calculating the coercive electric field of ferroelectric materials as described in claim 2, characterized in that, The method of generating polarization values ​​for ferroelectric materials belonging to metallic or narrow bandgap systems using the Born effective charge tensor method is specifically as follows: The polarization value of ferroelectric materials belonging to metallic or narrow bandgap systems is obtained by summing the effective charge tensor and the product of the relative displacement of each ion per unit cell volume; the specific expression is: ； in, For ferroelectric materials that belong to metallic or narrow bandgap systems, the polarization value is... For the first Effective charge tensor of each ion This is relative displacement. For unit cell volume, in two-dimensional materials, it is... Replace with unit cell area S.

4. The method for calculating the coercive electric field of ferroelectric materials as described in claim 3, characterized in that, After obtaining the coercive electric field by the ratio of the flipping potential barrier to the polarization difference, the method further includes: The Landau free energy of ferroelectric materials is expressed as follows: ； in, F ( P The total free energy of the system is denoted as . Landau coefficient; For coercive electric field strength; Utilizing polarization paths The Landau coefficients were obtained by least-squares fitting of the data to the Landau free energy of ferroelectric materials. ;in, The polarization value at each structural point, The coercive electric field strength at each structural point; Build The temperature dependence of the Curie temperature; specifically expressed as: ； in, These are temperature-dependent second-order coefficients. T For temperature, Curie temperature; Related to the material itself, It is a constant; The fitted Landau coefficients Substitute into the formula In the middle, the Curie temperature was obtained. Then through Generate at different temperatures Substituting this into the Landau free energy formula for ferroelectric materials, we obtain the coercive electric field at different temperatures.

5. The method for calculating the coercive electric field of ferroelectric materials as described in claim 1, characterized in that, The polarization difference is obtained by subtracting the polarization values ​​of the structure points at both ends of the continuous inversion path, and the maximum energy point is determined according to the energy distribution of the structure points. The flip barrier is extracted based on the maximum energy point. The coercive electric field is obtained by the ratio of the flip barrier to the polarization difference. Specifically: The maximum energy point is determined based on the energy distribution of the structural points at both ends of the continuous inversion path, and the barrier difference between the maximum energy point and the minimum energy point is used as the inversion barrier between the ferroelectric phase and the paraelectric phase; the polarization difference between the ferroelectric phase and the paraelectric phase is obtained by the polarization difference between the polarization values ​​of the ferroelectric phase and the paraelectric phase; wherein, the ferroelectric phase and the paraelectric phase are the states of the ferroelectric material below the Curie temperature and the states of the ferroelectric material above the Curie temperature, respectively. The coercive electric field is obtained by the ratio of the flipping potential barrier to the polarization difference.

6. A coercive electric field calculation system for ferroelectric materials, characterized in that, include: The data selection module is used to select the initial state and the final state of the ferroelectric material. The initial state is a stable state of the ferroelectric material and the final state is another stable state, or the initial state is the ferroelectric state of the ferroelectric material and the final state is a centrosymmetric state. The path generation module is used to generate a polarization reversal path from the initial state to the final state using the first-principles minimum energy path method. Through local structure optimization and self-consistent calculation methods, it obtains several interpolation point structures and total energy in the polarization reversal path, forming a continuous inversion path from the initial state to the final state. The electric field calculation module is used to obtain the polarization value of each structure point in the continuous inversion path using a dual polarization strategy. The polarization difference is obtained by subtracting the polarization values ​​of the structure points at both ends of the continuous inversion path. The maximum energy point is determined according to the energy distribution of the structure points, and the flip barrier is extracted based on the maximum energy point. The coercive electric field is obtained by the ratio of the flip barrier to the polarization difference. The first-principles minimum energy path method generates the polarization reversal path between the initial and final states, specifically as follows: By analyzing atomic displacements in the lattice coordinate space of ferroelectric materials, rotations around the central site, microstructural distortions of dimers / triangular / tetrahedral / octahedral structures, and symmetry evolution, the paths from the relatively initial ferroelectric phase to the nearest centrosymmetric phase, and the paths from the relatively initial ferroelectric phase to the polarization-reversed ferroelectric configuration are determined. These two paths are then used as polarization-reversal paths. Among them, the initial ferroelectric phase is the stabilized state or ferroelectric state of the ferroelectric material, the nearest centrosymmetric phase is the centrosymmetric state, and the ferroelectric configuration is another stabilized state of the ferroelectric material.

7. A computer device, characterized in that, The device includes a memory and a processor, wherein the memory stores a program, and when the program is executed by the processor, the processor performs the steps of the method for calculating the coercive electric field of a ferroelectric material as described in any one of claims 1 to 5.

8. A storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the steps of the method for calculating the coercive electric field of a ferroelectric material according to any one of claims 1 to 5.

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