Method and system for calculating dielectric property of hafnium-based oxide solid solution based on deep learning potential function

Abstract

The invention relates to a deep learning potential function-based hafnium-based oxide solid solution dielectric property calculation method and system, and the method comprises the steps: S1, building a hafnium-based oxide solid solution model with HfO2 as a parent phase structure, and building an initial data set through first principle molecular dynamics simulation; s2, training an inter-atomic interaction potential function by using a deep neural network; s3, performing large-scale molecular dynamics simulation based on the potential function, screening candidate configurations, constructing an incremental data set, and iteratively optimizing the potential function; s4, verifying the precision of the potential function optimized in the step S3 by the system, comparing and predicting the equilibrium state physical property of the material, and ensuring the accuracy of the potential function model; and S5, performing deep potential energy molecular dynamics simulation based on the potential function optimized in S3, and researching the phase stability and dielectric property of the system. Compared with the prior art, the device structure of the dynamic random access memory is combined, and a prospective solution is provided for improving the capacitor performance of the dynamic random access memory.

Description

Technical Field

[0001] This invention relates to the field of new materials technology, and in particular to a method and system for calculating the dielectric properties of hafnium-based oxide solid solutions based on deep learning potential functions. Background Technology

[0002] With the deepening innovation in the information and electronics industry, intelligent technologies such as artificial intelligence, the Internet of Things, and cloud computing are placing higher demands on data storage performance. Dynamic Random Access Memory (DRAM), as a core component of computer storage systems, faces a critical challenge in improving capacitor performance: the continuous miniaturization of devices has pushed the thickness of traditional SiO2 dielectric layers to their physical limits, leading to an exponential increase in leakage current due to the quantum tunneling effect. To address this bottleneck, using dielectric materials with high dielectric constants (high k) (such as hafnium-based oxide HfO2 with k≈25) has become a promising technological approach. While maintaining the same capacitance density, the dielectric thickness using high-k dielectric layers can be increased to 6-8 nm, reducing carrier tunneling probability by three orders of magnitude, providing crucial support for the evolution of DRAM towards advanced nodes.

[0003] In recent years, quasi-isomorphic phase boundaries (MPBs) have emerged as a novel strategy for achieving high k-values ​​and low equivalent oxide thickness (EOT) dielectric layers due to their unique physical properties. The dielectric properties of hafnium-based oxides are closely related to their phase structure; their MPBs exhibit a mixed crystalline structure of ferroelectric orthorhombic phase (o phase) and antiferroelectric tetragonal phase (t phase). Experimentally, the MPB effect in hafnium-based oxides can be induced by introducing dopants such as Zr, Si, and Al to form solid solutions, combined with strain engineering and temperature control. Further manipulation of the solid solution composition allows the leakage current density to be effectively controlled within 10 while maintaining a dielectric constant k > 50. -7 A / cm 2 The following provides practical solutions for the integrated application of high-performance memory.

[0004] Hafnium-based oxides exhibit various crystal phase structures, including monoclinic (m-phase), tetragonal (t-phase), and orthorhombic (o-phase), with significant differences in dielectric constant among the phases. This makes precise control of the crystal phase structure crucial for achieving their high k-values. First-principles studies have shown that local lattice distortions in hafnium-based oxide solid solutions (such as oxygen octahedral tilting caused by Zr doping) can significantly enhance the spontaneous polarization intensity of the system. However, when dealing with finely doped solid solution structures, the composition-structure-property relationship exhibits a highly nonlinear coupling relationship, posing a significant challenge to predicting complex solid solution systems using first-principles methods. Furthermore, the physical mechanisms underlying the ultra-high k-values ​​exhibited by hafnium-based oxide solid solutions in the MPB region remain poorly understood, and material optimization still heavily relies on empirical trial-and-error experiments.

[0005] Existing technologies suffer from the following problems: The experimental development of stable hafnium-based oxide solid solutions with high k-values ​​has a long development cycle and high trial-and-error costs; traditional first-principles calculations, when dealing with solid solution systems with a large number of atoms, exhibit a computational complexity that increases proportionally with the number of atoms N (N < k). 3 The growth of the dielectric properties makes it difficult to simulate them. Elemental doping, stress-strain, and temperature play important roles in enhancing the stability of hafnium-based oxides, and these mechanisms require further investigation. Summary of the Invention

[0006] The purpose of this invention is to overcome the shortcomings of the existing technology by providing a method and system for calculating the dielectric properties of hafnium-based oxide solid solutions based on deep learning potential functions. The method combines first-principles calculations, deep learning potential function training, and molecular dynamics simulations. Based on linear response theory, the method can calculate the accurate dielectric constant of large-scale systems at finite temperatures, enabling precise prediction of the dielectric constant of hafnium-based oxide solid solution materials. This provides a theoretical basis and underlying logic support for improving the dielectric properties of dielectric materials in DRAM capacitors.

[0007] The objective of this invention can be achieved through the following technical solutions:

[0008] The first aspect of this invention provides a method for calculating the dielectric properties of hafnium-based oxide solid solutions based on deep learning potential functions, comprising the following steps:

[0009] S1. Using bulk HfO2 as the parent phase structure, a supercell model of hafnium-based oxide solid solution with different component concentrations was built, and an initial training dataset containing multiphase features was constructed through first-principles molecular dynamics simulation.

[0010] S2. Based on the initial training dataset, use a deep neural network to train a potential function model to describe the interactions between atoms in the system and construct a deep learning potential function model.

[0011] S3. Large-scale molecular dynamics simulations are performed based on deep learning potential function models. Candidate configurations are screened by confidence analysis. First-principles single-point energy calculations are performed on the candidate configurations to build an incremental dataset. After multiple iterations, a high-precision potential function model covering various target temperatures and pressures is obtained.

[0012] S4. Based on the obtained high-precision potential function model, perform deep potential energy molecular dynamics simulation to study and calculate the phase stability and dielectric properties of hafnium-based oxide solid solution materials.

[0013] Further, step S1 includes the following process:

[0014] Using bulk HfO2 as the parent phase structure, a supercell model of hafnium-based oxide solid solution with different component concentrations was built by atomic substitution method. First-principles molecular dynamics (AIMD) simulations were performed over a wide temperature range. The system collected the energy eigenvalues, atomic force tensors, and virial tensor parameters of the system to construct an initial training dataset containing multiphase characteristics.

[0015] Furthermore, in step S1, the bulk HfO2 is obtained from a crystal structure database.

[0016] Further, in step S1, the chemical formula of the hafnium-based oxide is (Hf x M 1-x O2, where M = one or more of Zr, Si, and Al, and x = 0-1.

[0017] Furthermore, in step S1, the size of the hafnium-based oxide solid solution supercell is set to be greater than 2×2×2.

[0018] Furthermore, in step S1, the wide temperature range is 300-1200K.

[0019] Further, step S1 includes the following process:

[0020] S1.1 Using the bulk HfO2 obtained from the crystal structure database as the parent phase structure, hafnium-based oxides (HfO2) with different component concentrations were constructed using crystal structure modeling software through the atomic random substitution method. x M 1-x O2 (M = Zr, Si, Al, ...; x = 0-1) solid solution supercell model, with the supercell size set to be greater than 2×2×2 to satisfy the randomness of atomic arrangement, and converted into the input file format required by DFT calculation software;

[0021] S1.2. First-principles molecular dynamics (AIMD) simulations were performed over a wide temperature range (300-1200K) for the stability temperatures of different hafnium-based oxide phase structures. At the same time, the system collected the energy eigenvalues, atomic force tensors and virial stress parameters of the system.

[0022] S1.3 Use the data standardization interface to uniformly convert the data collected in step S1.2 into an initial training dataset containing multiphase (physical) characteristics.

[0023] Further, step S2 includes the following process:

[0024] S2.1 Based on the initial training dataset, set the basic neural network training parameters, which include the residual network, dynamic loss weights, learning rate exponent, and cutoff radius to describe the local interactions of atoms.

[0025] S2.2. Multiple potential functions are trained in parallel using deep neural networks to accurately describe the interactions between atoms and construct a deep learning potential function model.

[0026] Furthermore, step S3 includes the following process:

[0027] S3.1 Based on the deep learning potential function model, parameters such as simulation step size, ensemble, temperature and pressure, and number of iterations are set to carry out large-scale molecular dynamics simulation. Atomic force deviation is used as the standard, and candidate configurations are marked through confidence analysis.

[0028] S3.2 Perform first-principles density functional theory (DFT) single-point energy calculations on the labeled candidate configurations, and then standardize the obtained energy, atomic force and virial stress data and incorporate them into the training set to form an incremental dataset;

[0029] S3.3. Perform new iterative training based on the updated dataset. Each iteration includes neural network weight updates and potential energy surface parameter space optimization.

[0030] S3.4 Repeat the above process (steps S3.1 to S3.3) for multiple iterations until a high-precision potential function covering each target temperature and pressure is obtained.

[0031] Furthermore, after step S3, the following step S3' is performed to systematically verify the accuracy of the high-precision potential function:

[0032] S3' Systematically verify the accuracy of the high-precision potential function, including the convergence of the loss function, atomic forces, energy assessment, and the prediction comparison of material equilibrium properties: equation of state (EOS), elastic constant tensor, phonon dispersion relation, etc., to ensure the accuracy of the model in material simulation;

[0033] The material equilibrium properties include the equation of state (EOS), the elastic constant tensor, and the phonon dispersion relation.

[0034] Furthermore, step S3' includes the following process:

[0035] System verification of the high-precision potential function accuracy: Monitor the convergence of the energy and force loss functions during training to ensure that the root mean square (RMS) values ​​of the energy and force loss functions reach the threshold; compare the atomic force and energy results of the high-precision potential function with those of the DFT to ensure that the root mean square error (RMSE) of the typical configuration is less than the target value.

[0036] Equilibrium property prediction verification: The equation of state (EOS) is verified by sampling within ±5% of the equilibrium volume V0, and the energy-volume curve is fitted with an appropriate equation; the elastic constant tensor is calculated by the energy-strain method to verify whether it meets the Born-Huang elastic stability criterion; the high-symmetric path phonon dispersion relation is calculated to verify whether the characteristic phonon branch is consistent with the DFT calculation.

[0037] Further, step S4 includes the following process:

[0038] S4.1. Based on the obtained high-precision potential function model, deep potential energy molecular dynamics simulation is carried out. Multiple feature points are selected within the target temperature and pressure range, and the influence of different component concentrations is considered. By comparing the structural characteristics and free energy change trends of each phase, the relative stability of each phase structure is quantitatively evaluated, thereby revealing the regulation mechanism of temperature, concentration and pressure conditions on the phase equilibrium relationship of hafnium-based oxide solid solution and screening stable phase structures.

[0039] S4.2. Based on deep potential energy molecular dynamics simulation, the dielectric response characteristics of hafnium-based oxide solid solution materials are simulated. According to the stable phase structure obtained in step S4.1, the polarization behavior of the material under the action of an applied electrostatic field is simulated. The static dielectric constant of hafnium-based oxide solid solution under different temperatures, concentrations and pressures is calculated. The correlation mechanism between microstructure and macroscopic properties is further analyzed, and candidate material systems with high dielectric constants are screened.

[0040] Further, step S4.2 includes the following process:

[0041] S4.2.1. Using deep potential energy molecular dynamics, under target temperature and pressure conditions, a suitable ensemble is selected for structural relaxation calculations. The relaxation process lasts for no less than 20 ps. After the system reaches a steady state, the final relaxed structure and the average stable structure during the relaxation process are output. This step eliminates stress concentration in the initial configuration through sufficient relaxation, ensuring that the system reaches thermodynamic equilibrium.

[0042] S4.2.2 Based on the relaxed final-state structure, an external electric field is applied using the equivalent force field method. Specifically, a long-term relaxation simulation is first performed after the electric field is applied. Once the system reaches equilibrium again, the stable average structure under the electric field (>20 ps) is recorded. The macroscopic electric field E is transformed into the equivalent force F on each atom i through the Born effective charge tensor. i :

[0043]

[0044] Among them, Z * i,αβThe Born effective charge tensor of the atom is calculated using the density functional perturbation theory (DFPT) method in DFT software. α,β∈{x,y,z} correspond to the orthogonal basis vector directions in the crystal coordinate system, and e represents the unit charge. This method accurately simulates the synergistic effect of ionic real displacement and electronic polarization induced by an external electric field through an equivalent atomic force field.

[0045] S4.2.3. Based on the simulation in step S4.2.2, the dielectric constant is calculated based on the linear response theory framework, assuming that the external electric field is insufficient to significantly change the intrinsic properties of the dielectric material. In this case, the polarization P of the dielectric exhibits a linear response under the applied electrostatic field E:

[0046]

[0047] Where ε0 is the vacuum permittivity, δ αβ Denotes the identity matrix and the dielectric constant tensor ε. αβ The above formula can be directly derived as follows:

[0048]

[0049] Here, the relative cell polarization ΔP is induced by the relative atomic displacement u by Born's effective charge and the electric field ΔE. i And the calculation of the unit cell volume V:

[0050]

[0051] In the formula, the relative atomic displacement u i The calculation requires obtaining the equilibrium lattice coordinates R of the material when there is no external field (E=0). i (0) and the equilibrium atomic coordinates R under the action of an external electric field E i (E), and then the relative displacement of each atom is calculated using vector difference:

[0052] u i,αβ =R i,αβ (E)-R i,αβ (0)

[0053] Considering the second-order tensor properties of the dielectric constant of anisotropic crystals, a complete characterization requires systematic calculations by applying electric fields along the three crystal axes (

[100] ,

[010] ,

[001] ). Specifically, for each orthogonal direction α (α = x, y, z) of the crystal axis, an electric field E needs to be applied along that direction. α Calculate the corresponding polarization intensity change ΔP β (β=x,y,z), and then calculate the complete dielectric constant tensor element based on the linear response theory.

[0054] A second aspect of the present invention provides a calculation system for the dielectric properties of hafnium-based oxide solid solutions based on deep learning potential functions, the calculation system being used to implement the aforementioned calculation method.

[0055] Furthermore, the computing system includes:

[0056] A deep learning potential function training module is used for iterative training of the interatomic interaction potential function of hafnium-based oxide solid solution materials;

[0057] The phase stability and dielectric properties calculation module is used to conduct deep potential energy molecular dynamics simulations, and to systematically study and calculate the phase stability and dielectric properties of hafnium-based oxide solid solution materials.

[0058] Furthermore, the computing system also includes:

[0059] The deep learning potential function testing module is used to test the accuracy of the potential function model of hafnium-based oxide solid solution materials and to compare the prediction of the material's equilibrium properties, thereby evaluating the accuracy of the potential function.

[0060] Furthermore, the computing system includes:

[0061] A deep learning potential function training module is used for iterative training of the interatomic interaction potential function of hafnium-based oxide solid solution materials. The hafnium-based oxide solid solution structure is constructed using an atomic substitution method with a quasi-random doping strategy. The iteration employs a "training-exploration-labeling" loop mechanism to progressively optimize the potential function under various thermodynamic conditions. The "training" step generates the potential function using deep learning training based on the dataset. The "exploration" step performs large-scale molecular dynamics simulations based on the potential function to screen candidate configurations. The "labeling" step performs first-principles calculations based on the candidate configurations to refine the training dataset for the next round of potential function optimization training.

[0062] A deep learning potential function testing module is used for the accuracy testing of potential functions and the prediction and comparison of equilibrium properties of hafnium-based oxide solid solution materials, to evaluate the accuracy of the potential functions. The potential function accuracy testing includes loss function convergence, atomic interaction forces, and energy assessment. The material equilibrium properties include equation of state (EOS), elastic constant tensor, phonon dispersion relation, etc.

[0063] The phase stability and dielectric property calculation module is used to conduct deep potential energy molecular dynamics simulations to systematically study the phase stability and dielectric properties of hafnium-based oxide solid solution materials. The phase stability calculation obtains the fundamental thermodynamic parameters of the material through equilibrium state property calculations and examines the phase transition behavior under different temperature and pressure conditions. The dielectric property study simulates the linear polarization response process of the material by applying an external electric field, establishing a quantitative relationship between polarization intensity and electric field intensity, and finally calculating key performance indicators such as the dielectric constant.

[0064] Compared with the prior art, the present invention has the following technical advantages:

[0065] 1. This invention provides a method and system for calculating the dielectric properties of hafnium-based oxide solid solutions based on deep learning potential functions. It employs an advanced neural network potential function method to accurately describe the interatomic interactions of the system, significantly improving the accuracy and efficiency of finite-temperature simulations and greatly reducing the cost of theoretical research. This provides a new platform for studying the dielectric properties of hafnium-based oxide solid solutions. Furthermore, the developed potential function model can be widely applied to the thermodynamic analysis, phase-field simulation, and material design of corresponding systems, aiding in the prediction of properties such as structural phase transitions and domain structure evolution.

[0066] 2. This invention provides a method and system for calculating the dielectric properties of hafnium-based oxide solid solutions based on deep learning potential functions. Starting from the microscopic definition of the dielectric constant, and based on linear response theory, the static dielectric constant can be obtained by calculating the polarization response of the linearly polarized region under an applied electric field. The electric field is introduced into the molecular dynamics simulation in the form of a force, and the Born effective charge implies the contribution of electronic polarization by correcting the atomic charge. This makes up for the deficiency of traditional molecular dynamics in handling electronic polarization, and provides an important theoretical basis and calculation tool for the dielectric property design of new materials.

[0067] 3. This invention provides a method and system for calculating the dielectric properties of hafnium-based oxide solid solutions based on deep learning potential functions. It establishes an integrated model for predicting and optimizing the dielectric properties of hafnium-based oxide solid solutions. This model can complete the dielectric property calculations of a large number of materials in a short time, significantly improving the efficiency of material research and development. By guiding experimental design through theoretical calculations, it can effectively shorten the material research and development cycle and reduce trial-and-error costs, avoiding resource waste and blind spots in traditional research and development processes, thereby accelerating the research and development process of high-performance dielectric materials. Attached Figure Description

[0068] Figure 1 This invention provides an embodiment of Hf based on a deep learning potential function. x Zr 1-x Flowchart of the method for calculating the dielectric properties of O2(HZO) solid solution.

[0069] Figure 2This invention provides an embodiment of Hf based on a deep learning potential function. x Zr 1-x Module diagram of the O2(HZO) solid solution dielectric property calculation system.

[0070] Figure 3 This is a schematic diagram of the HZO system structure constructed using the atomic substitution method with different phase bulk HfO2 as the parent phase structure in the embodiment. The doping ratio shown in the figure is 50%, i.e., Hf 0.5 Zr 0.5 O2. (Among them) Figure 3 (a) is an m-phase (P21 / c)HZO structure; Figure 3 (b) is a t-phase (P42 / nmc)HZO structure; Figure 3 (c) is o I Phase (Pbca)HZO structure; Figure 3 (d) is o III The (Pca21)HZO structure.

[0071] Figure 4 This is a schematic diagram illustrating the accuracy verification of the deep learning potential function. Figure 4 (a) shows the convergence trend of the energy and force training and testing loss functions with the number of training steps during the potential function training process; Figure 4 (b) shows the distribution of the maximum force deviation of the system during the 30th to 34th iterations; Figure 4 (c) is a comparison of the energies of the HZO system predicted by the potential function and calculated by DFT; Figure 4 (d) is a comparison of the atomic forces of the HZO system predicted by the potential function and calculated by DFT; in particular, Figure 4 The illustrations in (c) and 4(d) show in detail the distribution of the root mean square error (RMSE) of the prediction results.

[0072] Figure 5 For m phase, t phase, o I With o III Hf with four phase structures 0.5 Zr 0.5 Equations of state for the O2 system under different lattice volumes.

[0073] Figure 6 The results show a comparison between the potential function prediction and the DFT calculation of the phonon spectrum curves of the HfO2 system; among which... Figure 6 (a) shows the phonon spectrum of the m-phase HfO2 structure; Figure 6 (b) is o III Phonon spectrum curves of the HfO2 phase structure.

[0074] Figure 7This describes the dynamic changes of physical quantities in the m-phase HfO2 structure during relaxation simulation based on the potential function at a target temperature of 1000 K and a pressure of 1 bar. Figure 7 (a)-(d) are the fluctuation curves of temperature, pressure, total energy, and volume as a function of the number of simulation steps, respectively.

[0075] Figure 8 The results show a comparison of phase stability of the HZO system in the experimental temperature range based on potential function calculations; among them Figure 8 (a)-(d) correspond to four temperature ranges of 700K, 750K, 800K, and 850K, respectively. Using the m phase as the reference ground state, the m phase, t phase, and o phase are compared. I With o III The relative energy of the HZO system varies with the Zr doping concentration.

[0076] Figure 9 This section presents the variation of the dielectric constant of the HZO system with Zr doping concentration under finite temperature conditions, calculated based on the potential function. For comparison between different phase structures, a doping concentration interval of 0.25 is selected, and the results at 300 K are shown for the m phase and o phase. I Phase, o III The average dielectric constant of the phase and the t-phase HZO at 2100K high temperature is calculated.

[0077] Figure 10 Apply 0.004 eV / m² along the y-direction (

[010] crystal orientation). Under electric field conditions, phase t Hf 0.25 Zr 0.75 The atomic displacements of the O2 system are shown in 10(a)-(c), which respectively show the displacement distribution characteristics of Hf, Zr and O atoms in the

[100] ,

[010] and

[001] crystal directions (corresponding to the three orthogonal directions x, y and z). Detailed Implementation

[0078] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments. Component models, material names, connection structures, control methods, algorithms, and other features not explicitly described in this technical solution are considered common technical features disclosed in the prior art.

[0079] This invention provides a method for calculating the dielectric properties of hafnium-based oxide solid solutions based on deep learning potential functions, the specific steps of which include:

[0080] S1, using HfO2 as the parent phase structure to construct a hafnium-based oxide (Hf x M 1-x The O2 (M = Zr, Si, Al, ...; x = 0-1) solid solution model was used to construct the initial dataset through first-principles molecular dynamics simulations.

[0081] S2, using a deep neural network to train the interatomic interaction potential function;

[0082] S3, based on deep learning potential functions, performs large-scale molecular dynamics simulations, screens candidate configurations and constructs incremental datasets, and iteratively optimizes the potential function;

[0083] S4. Systematically verify the accuracy of the potential function after optimization in step S3, compare the predicted material equilibrium properties, and ensure the accuracy of the potential function model.

[0084] S5. Based on the potential function optimized in step S3, deep potential energy molecular dynamics simulations are performed to study the phase stability and dielectric properties of the system.

[0085] This invention provides a prediction of the dielectric constant of hafnium-based oxide solid solution materials that balances accuracy and efficiency, thereby solving the technical problem of limited improvement of the dielectric constant of existing hafnium-based oxide materials.

[0086] Furthermore, the following implementation steps are included:

[0087] S1. Using bulk HfO2 as the parent phase structure, a supercell model of hafnium-based oxide solid solution with different component concentrations was built by atomic substitution method. First-principles molecular dynamics (AIMD) simulations were performed over a wide temperature range. The system collected the energy eigenvalues, atomic force tensors, and virial tensor parameters of the system during the simulation process to construct an initial training dataset containing multiphase characteristics.

[0088] S2. Based on the initial training dataset, use a deep neural network to train a potential function model to describe the interactions between atoms in the system and construct a deep learning potential function model.

[0089] S3. Large-scale molecular dynamics simulations are performed based on deep learning potential function models. Candidate configurations are screened by confidence analysis, and first-principles single-point energy calculations are performed to construct an incremental dataset. After multiple iterations, a high-precision potential function model covering various target temperatures and pressures is obtained.

[0090] S4. Systematically verify the potential function accuracy of the high-precision potential function model, including loss function convergence, atomic interaction force, energy assessment, and prediction comparison of material equilibrium properties: equation of state (EOS), elastic constant tensor, phonon dispersion relation, etc., to ensure the accuracy of the model in material simulation.

[0091] S5. Based on the obtained high-precision potential function model, deep potential energy molecular dynamics simulation is carried out to study and calculate the phase stability and dielectric properties of hafnium-based oxide solid solution materials, analyze the correlation mechanism between microstructure and macroscopic properties, and screen candidate material systems with high dielectric constants.

[0092] It should be noted that the potential function training methods and calculation methods in this invention can be adjusted according to actual needs, and the specific implementation steps and parameter settings may differ. This embodiment provides an optional technical solution: DFT calculation relies on the Vienna Ab-initio Simulation Package (VASP) software to obtain the system's energy, atomic force, and virial tensor information; a deep learning potential function training framework is constructed using the DeepMD-kit software, and training iterations are implemented using the DP-GEN software; molecular dynamics simulations are performed using the Large-scale Atomic / Molecular Massively ParallelSimulator (LAMMPS) software to calculate the system's phase stability and dielectric properties. The Hf function obtained through other methods... x Zr 1-x The O2 structure is also applicable to this invention and will not affect the final calculation results. In this embodiment, the crystal structure data comes from the Materials Project (MP) database. Crystal modeling of hafnium-based oxide solid solution structures of different concentrations was completed using ATAT-mcsqs software, and the Atomsk tool was used for input file format conversion.

[0093] Example 1

[0094] In this embodiment, the hafnium-based oxide is selected as Hf. x Zr 1-x O2(HZO), x=0-1, provides a zirconium hafnium Hf based on deep learning potential function. x Zr 1-x Methods for calculating the dielectric properties of O2(HZO) solid solutions, such as Figure 1 As shown, the specific implementation steps include the following:

[0095] S1. Using bulk HfO2 as the parent phase structure, a supercell model of hafnium-based oxide solid solution with different component concentrations was built by atomic substitution method. First-principles molecular dynamics (AIMD) simulations were performed over a wide temperature range. The system collected the energy eigenvalues, atomic force tensors, and virial tensor parameters of the system during the simulation process to construct an initial training dataset containing multiphase characteristics.

[0096] S1 includes:

[0097] S1.1. Four bulk HfO2 phases were selected from the crystal structure database MP as the parent phase structures, including the m phase (space group: P21 / c), the t phase (space group: P42 / nmc), and the o phase. I Phase (space group: Pbca), o IIIPhase (space group: Pca21), using the crystal structure modeling software ATAT-mcsqs, the atomic random substitution method was employed to randomly replace Hf atoms in the system with Zr atoms in different proportions, in order to construct hafnium-based oxides Hf with different Zr concentrations. x Zr 1-x O2 solid solution model. Considering the requirements of computational efficiency and the randomness of atomic arrangement, a 2×2×2 supercell model was constructed, with each supercell containing 96 atoms (32 metal atoms and 64 oxygen atoms). Seven representative Zr doping concentration gradients (0% (pure HfO2), 12.5%, 25%, 50%, 75%, 87.5%, and 100% (pure ZrO2)) were selected to ensure that the system can still reflect the statistical characteristics of random solid solutions well within a finite size. A schematic diagram of the crystal structure of the HZO system is shown below. Figure 3 As shown. Finally, the generated supercell model is converted into a POSCAR format structure input file required by the DFT calculation software VASP for subsequent first-principles calculations.

[0098] S1.2. Based on the stability temperatures of different HZO phase structures, first-principles molecular dynamics (AIMD) simulations were performed over a wide temperature range (300-1200 K). Specifically, for the aforementioned 28 HZO structures with 4 crystal phases and 7 doping concentrations, perturbation structures were obtained by applying ±3% lattice strain and atomic position perturbations, thus expanding the sampling range of the system's potential energy surface. Subsequently, all perturbation structures were subjected to short-step AIMD simulations at multiple temperature points with 100 K intervals under the NPT ensemble. The Langevin thermobath method was used for temperature control, with a time step of 2 fs and a total of 10 simulation steps. For computation, a modified PBEsol exchange-correlation functional was used, which has higher accuracy in predicting the structural parameters of solid-state systems. The computational parameters underwent rigorous convergence testing, with the plane wave cutoff energy set to 600 eV and the K-point grid density set to... Simultaneously, the system records key data (multidimensional thermodynamic data) such as the energy eigenvalues, atomic force tensors, and virial stress parameters of the system during the simulation process.

[0099] S1.3. The multidimensional thermodynamic data collected in step S1.2 above is systematically processed using the data standardization interface to finally construct a standardized initial training dataset containing the multiphase structural features of HZO, providing a high-quality data foundation for the subsequent training of deep learning potential functions.

[0100] S2. Based on the initial training dataset, use a deep neural network to train a potential function model to describe the interactions between atoms in the system and construct a deep learning potential function model.

[0101] S2 includes:

[0102] S2.1. Based on the initial training dataset, a neural network model is constructed using the Deep Potential framework. In terms of model architecture, an embedded atomic neural network (se_e2_a) with symmetry-preserving properties is used as the descriptor, and the truncation radius is set... Smooth radius The size of the embedding grid is set to [25, 50, 100], while the size of the fitting grid is [240, 240, 240]. For the optimization strategy, an exponentially decaying learning rate is used, with an initial learning rate of 0.001 decaying over 20,000 steps to a final learning rate of 3.51E-8. The loss function design incorporates a dynamic weight adjustment mechanism to balance the contributions of different physical quantities during training.

[0103] S2.2. Four potential functions were trained in parallel using a deep neural network, with a total of 800,000 iterations. An independent test set was used to monitor the model's generalization performance, thus constructing a deep learning potential function model. To ensure reproducibility, all training was initialized with a fixed random seed, and training time was recorded to evaluate computational efficiency. A multi-task learning strategy was employed to accurately describe the interatomic interactions between Zr, Hf, and O atoms in different phase structures within the HZO system.

[0104] S3. Large-scale molecular dynamics simulations are performed based on deep learning potential function models. Candidate configurations are screened by confidence analysis, and first-principles single-point energy calculations are performed on the candidate configurations to construct an incremental dataset. After multiple iterations, a high-precision potential function model covering various temperatures and pressures is obtained.

[0105] S3 includes:

[0106] S3.1. Based on the deep learning potential function obtained in the current iteration, a large-scale NPT ensemble molecular dynamics simulation is performed, setting a temperature range from 100K to 3200K and a pressure range from -50 bar to 50000 bar. During the simulation, the system's atomic force F... i The maximum standard deviation is used as the configuration error criterion, and it is defined as follows: Where F i This represents the predicted force on the i-th atom. The principle of model labeling is: when σ f max >σ high At that time, the corresponding configuration is marked as a failure only if 0.15 = σ low <σ f max <σ high When the value is 0.30, the corresponding configuration will be marked as a candidate configuration that can improve the accuracy of the model.

[0107] S3.2. Perform first-principles density functional theory (DFT) single-point energy calculations on the labeled candidate configurations. In the single-point energy calculations, the selection of the exchange-correlation functional, cutoff energy, and K-point grid density parameters remains consistent with the settings used in the previous AIMD simulations. Subsequently, the obtained energy, atomic force, and virial stress data are standardized and incorporated into the training set to form an incremental dataset.

[0108] S3.3. Based on the updated incremental dataset, perform a new round of iterative training. Each iteration includes updating the neural network weights and optimizing the potential energy surface parameter space.

[0109] S3.4 Repeat steps S3.1 to S3.3 for multiple iterations until the percentage of the accurate configuration (σ) is reached. f max <σ low When the probability of convergence is greater than 99%, the phase space exploration of the system can be considered to have converged. Finally, all datasets are collected and merged into the final training dataset for a long-term training of 4,000,000 steps to obtain a high-precision potential function covering various target temperatures and pressures.

[0110] S4. Systematically verify the accuracy of the high-precision potential function, including the convergence of the loss function, atomic forces, energy assessment, and the prediction comparison of material equilibrium properties: equation of state (EOS), elastic constant tensor, phonon dispersion relation, etc., to ensure the accuracy of the model in material simulation.

[0111] S4 includes:

[0112] S4.1 System verification of the accuracy of the high-precision potential function is as follows: Figure 4 As shown in (a), the training and testing loss functions for energy and force both converge steadily with increasing training steps, with final root mean square values ​​of 2.533E-3 and 1.36E-1, respectively, reaching the set thresholds; further analysis... Figure 4 (b) shows the change in the maximum force deviation distribution from iterations 30 to 34. As the dataset becomes more comprehensive, the peak value of the maximum force deviation predicted by the potential function shows a clear leftward shift, indicating a continuous improvement in model prediction accuracy. To quantitatively evaluate model performance, the potential function is compared with the atomic force and energy results from the DFT, such as... Figure 4 (c) and Figure 4 As shown in (d), both are basically linearly distributed, and the energy (ΔE=|E) DFT -E DP |) and atomic force (ΔF=|F DFT -F DP The root mean square errors (RMSE) of |) were 3.703 meV / atom and 0.205 eV / atom, respectively. It is shown that the potential function based on the deep neural network has excellent representability and flexibility, and can learn the highly nonlinear complex high-dimensional energy function of solid solutions with different components without manual intervention.

[0113] S4.2. Prediction and verification of physical properties at equilibrium state: At the equilibrium state of 0 K, potential function prediction and DFT calculation are carried out on HfO2, Hf 0.5 Zr 0.5 O2 and ZrO2 with m-phase and t-phase structures. As shown in Table 1, the lattice constants a, b, c and energy results predicted by the potential function are highly consistent with the DFT calculation results. The error of the lattice parameters is controlled within 0.2%, and the energy difference is only 0.004%.

[0114] Table 1 Lattice parameters and energies at 0 K predicted by the potential function and calculated by DFT. The conventional values are the DFT calculation results, the bold ones represent the potential function prediction results, and the percentages reflect the relative errors of the potential function prediction values compared with the DFT results.

[0115]

[0116] Further sampling is carried out in the range of ±5% near the equilibrium volume V0 to verify the equation of state (EOS). The Murnaghan equation of state is used to fit the energy-volume curve, and the calculation and comparison results are as Figure 5 shown. It can be seen that the potential function can well reproduce the EOS curve calculated by DFT and the phase stability order: E(m) < E(o I ) < E(o III ) < E(t). In particular, the potential function can accurately capture the small energy difference between the o I phase and the o III phase, which highlights the advantage of the deep potential function method over the traditional empirical potential function in the prediction accuracy of the system energy.

[0117] In addition, the elastic constant tensor of the HfO2 bulk system is calculated by the energy-strain method, and the results are shown in Table 2. The values of the elastic constants of the HfO2 bulk are distributed between 0 - 600 GPa, all of which satisfy the Born-Huang elastic stability criterion. The maximum relative error between the potential function and the DFT calculation results reaches 56%, but this deviation is mainly due to the significant change of some elastic constants caused by the sensitivity of the phase structure to the strain. The potential function can accurately predict the elastic properties of phases not explicitly included in the training database (such as the c phase, space group: ), and this result not only verifies the accuracy of the model, but also highlights its good portability in the prediction of material properties.

[0118] Table 2 compares the elastic constants (unit: GPa) of HfO2 bulk materials of different phases predicted by potential function and DFT. The standard volume represents the DFT calculation result, the bold text represents the potential function prediction result, and the percentage reflects the relative error between the potential function prediction value and the DFT result.

[0119]

[0120] The force constant, as the second derivative of energy with respect to atomic displacement, provides a more rigorous standard for evaluating the accuracy of the potential function. Figure 6 This demonstrates the potential function and DFT calculations of m-HfO2 and o III The phonon spectrum of -HfO2. Although the training iteration process did not explicitly consider the second derivative information describing the local minima of different phases, the potential function and DFT results still showed quite good consistency, and correctly predicted the vibrational modes that make the system dynamically stable throughout the Brillouin zone. These results demonstrate that the potential function can accurately describe the characteristics of interatomic interactions, providing a reliable foundation for subsequent large-scale molecular dynamics simulations.

[0121] S5. Based on the obtained high-precision potential function (deep potential energy function) model, molecular dynamics simulations are performed to study the phase stability and dielectric properties of the material, analyze the correlation mechanism between microstructure and macroscopic properties, and screen candidate material systems with high dielectric constants.

[0122] S5 includes:

[0123] S5.1. Based on the obtained high-precision potential function model, deep potential energy molecular dynamics simulations were performed using the LAMMPS software package. Periodic boundary conditions were employed under standard pressure (1 bar), and the simulation system used an 8×8×8 supercell structure (6144 atoms). For non-orthogonal systems, the simulation allowed complete relaxation of the lattice constant and lattice angles. First, MD (molecular dynamics) equilibrium simulations were performed on the m-HfO2 structure at 1000 K and standard atmospheric pressure, and the changes in various physical properties with the number of simulation steps were statistically analyzed. The simulation was conducted under the NPT ensemble, and the trends of temperature, pressure, total energy, and total volume are shown below. Figure 7 As shown, in the initial stage of the simulation, the various physical properties of the system exhibited significant fluctuations, but after about 2 ps, they began to stabilize and fluctuate around the set values, indicating that the system had reached thermal equilibrium. Therefore, to ensure the reliability of subsequent calculation results, the simulation duration for phase stability calculation was set to 40 ps, ​​and the statistical data from the last 20 ps were averaged to more accurately analyze the stability of various physical properties.

[0124] Multiple characteristic points were selected within the target temperature and pressure range, and the influence of different component concentrations was considered. By comparing the structural characteristics and free energy change trends of each phase, the relative stability of each phase structure was quantitatively evaluated, thereby revealing the regulation mechanism of temperature, concentration, and pressure on the phase equilibrium relationship of hafnium-based oxide solid solutions. Currently, preliminary calculations of the HZO solid solution phase diagram in the experimental temperature range (700-850 K) have been obtained to explore the possible MPB phase transition regions, such as... Figure 8 As shown. Here, the m-phase structure with the lowest energy reported experimentally is taken as the ground state, and other phase structures (t-phase, o-phase, t ... I With o III The energy of the m-phase relative to the ground state is considered. As the Zr doping concentration increases, the energy of the system generally shows an upward trend. Meanwhile, among all regions of HZO, the energy of the m-phase structure remains the lowest, and no obvious phase transition phenomenon was observed, which is consistent with previous experimental results. This further verifies the stability of the m-phase at low temperatures.

[0125] S5.2. Dielectric response characteristics of materials calculated based on deep potential energy molecular dynamics. The polarization behavior of hafnium-based oxide solid solutions under an applied electrostatic field was simulated, and the static dielectric constant of hafnium-based oxide solid solutions under different temperatures, concentrations, and pressures was calculated. The correlation mechanism between microstructure and macroscopic properties was further analyzed, and candidate material systems with high dielectric constants were screened.

[0126] Example 2

[0127] As a preferred embodiment of the present invention, this embodiment provides a method for calculating the dielectric properties of hafnium-based oxide solid solutions based on deep learning potential functions, which, based on Embodiment 1, further includes the following steps:

[0128] In step S5.2, the method further includes the following steps:

[0129] S5.2.1. Using deep potential energy molecular dynamics, under target temperature and pressure conditions, structural relaxation calculations are performed using the NPT ensemble. The relaxation time is 40 ps. After the system reaches a steady state, the final relaxed structure and the stable average structure during the last 20 ps of relaxation are output. This step eliminates stress concentration in the initial configuration through sufficient relaxation, ensuring that the system reaches thermodynamic equilibrium.

[0130] S5.2.2 Based on the stable structure after relaxation, an external electric field is applied using the equivalent force field method. In practice, a relaxation simulation is first performed after the electric field is applied, with a relaxation time of 40 ps. After the system reaches equilibrium again, the stable average structure under the electric field is recorded. The macroscopic electric field E is transformed into the equivalent force F on each atom i through the Born effective charge tensor. i :

[0131]

[0132] Among them, Z * i,αβ The Born effective charge tensor of the atom is calculated using the density functional perturbation theory (DFPT) method in VASP software. α,β∈{x,y,z} correspond to the orthogonal basis vector directions in the crystal coordinate system, and e represents the unit charge. This method accurately simulates the synergistic effect of ionic real displacement and electronic polarization induced by an external electric field through an equivalent atomic force field.

[0133] It should be noted that during the DFPT calculation, the selection of the exchange-correlation functional, cutoff energy, and K-point grid density parameters should be consistent with the settings of the previous AIMD simulation. In addition, high-precision structural optimization is required, and the energy convergence criterion should be set to 10. -8 eV, the maximum force convergence criterion for each atom is set to be less than 10 eV. -3 eV / To ensure the accuracy of Born's effective charge calculation results.

[0134] For the HZO system, the atomic Born effective charge tensors calculated by the DFPT method are as follows:

[0135]

[0136] S5.2.3 Based on the above simulation, the dielectric constant is calculated based on the linear response theory framework, assuming that the external electric field is insufficient to significantly change the intrinsic properties of the dielectric material. In this case, the polarization P of the dielectric exhibits a linear response under the applied electrostatic field E:

[0137]

[0138] Where ε0 is the vacuum permittivity, δ αβ Denotes the identity matrix and the dielectric constant tensor ε. αβ The above formula can be directly derived as follows:

[0139]

[0140] Here, the relative cell polarization ΔP is induced by the relative atomic displacement u by Born's effective charge and the electric field ΔE. i And the calculation of the unit cell volume V:

[0141]

[0142] In the formula, the relative atomic displacement u i The calculation requires obtaining the equilibrium lattice coordinates R of the material when there is no external field (E=0). i (0) and the applied electric field E = 0.004 eV / Equilibrium atomic coordinates R under action i (E), and then the relative displacement of each atom is calculated using vector difference:

[0143] u i,αβ =R i,αβ (E)-R i,αβ (0)

[0144] Considering the second-order tensor properties of the dielectric constant of anisotropic crystals, its complete characterization requires applying 0.004 eV / m² along the three crystal axes (

[100] ,

[010] ,

[001] ). The magnitude of the electric field is calculated systematically. Specifically, for each orthogonal direction α (α = x, y, z) of the crystal axis, an electric field E along that direction needs to be applied. α Calculate the corresponding polarization intensity change ΔP β (β=x,y,z), and then the complete dielectric constant tensor element is calculated based on the linear response theory. Table 3 compares the m-phase, t-phase, and o-phase values ​​calculated by the potential function and DFT methods. I Phase, o III The diagonal elements and average values ​​of the dielectric constant tensor of HfO2 phase were obtained. The results show that the potential function accurately predicts the magnitude of the dielectric constant of each phase, with phase t exhibiting the highest dielectric response characteristics and an average dielectric constant of 65.05. Of particular note is the good agreement between the potential function calculation results and the DFT data, verifying the reliability of this potential function in predicting the dielectric properties of polycrystalline phases of hafnium-based oxide solid solutions.

[0145] Table 3 compares the dielectric property predictions of HfO2 bulk materials with potential function and DFT. The standard figures represent DFT calculation results, the bold figures represent potential function prediction results, and the percentages reflect the relative error between the potential function predictions and the DFT results.

[0146]

[0147] To further investigate the effect of Zr doping on the dielectric properties of the HfO2 system, a series of models with Zr doping concentrations of 0%, 25%, 50%, 75%, and 100% were constructed and their dielectric properties were calculated. Figure 9 The changes in average dielectric constant for four phase structures under different doping concentrations are shown. With increasing Zr doping concentration, the dielectric properties of all phase structures show a significant increasing trend, with Hf showing the most significant improvement. 0.25 Zr 0.75 The O2 structure exhibits the best dielectric properties, with an average dielectric constant of 70.55, which is about 8.5% higher than that of the undoped system.

[0148] To gain a deeper understanding of the microscopic mechanism of the high dielectric response of hafnium-based oxide structures, the t-phase Hf was analyzed in detail. 0.25 Zr 0.75 Polarization characteristics of the O2 system. Figure 10 It demonstrates the application of 0.004 eV / along the

[010] crystal orientation. Atomic displacement distribution characteristics under an external electric field. Microscopic mechanism analysis shows that Zr doping significantly enhances the ionic displacement polarization effect of the system. Specifically, Zr atoms exhibit a more significant displacement response than Hf atoms, which directly leads to a significant increase in the dielectric constant. Notably, the polarization response along the

[010] crystal orientation mainly originates from the displacement of oxygen atoms, and its displacement distribution probability is nearly twice that of Zr and Hf atoms, dominating the polarization response of the system.

[0149] Example 3

[0150] This application also relates to a calculation system for the dielectric properties of hafnium-based oxide solid solutions based on deep learning potential functions, such as... Figure 2 As shown, a zirconium hafnium Hf based on a deep learning potential function, as described in Example 1 or Example 2, is used. x Zr 1-x A method for calculating the dielectric properties of O2(HZO) solid solutions, wherein the calculation system includes:

[0151] A deep learning potential function training module is used for iterative training of the interatomic interaction potential function of hafnium-based oxide solid solution materials. The hafnium-based oxide solid solution structure is constructed using a quasi-random doping strategy implemented with ATAT-mcsqs software. The iteration employs a "training-exploration-labeling" loop mechanism implemented with DP-GEN software to progressively optimize the potential function under various thermodynamic conditions. The "training" step uses the DeepMD-kit software package to construct the deep learning potential function based on the dataset. The "exploration" step uses the LAMMPS software package to perform large-scale molecular dynamics simulations based on the potential function to screen candidate configurations. The "labeling" step uses the VASP software package to perform first-principles calculations based on the candidate configurations to refine the training dataset for the next round of potential function optimization training.

[0152] The deep learning potential function testing module is used for the accuracy testing of the potential function of hafnium-based oxide solid solution materials and the prediction and comparison of the material equilibrium properties to evaluate the accuracy of the potential function. The potential function accuracy testing includes loss function convergence, atomic interaction forces, and energy assessment. The material equilibrium properties include equation of state (EOS), elastic constant tensor, phonon dispersion relation, etc.

[0153] The phase stability and dielectric property calculation module is used to conduct deep potential energy molecular dynamics simulations to systematically study the phase stability and dielectric properties of hafnium-based oxide solid solution materials. The phase stability calculation obtains the fundamental thermodynamic parameters of the material through equilibrium state property calculations and examines the phase transition behavior under different temperature and pressure conditions. The dielectric property study simulates the linear polarization response process of the material by applying an external electric field, establishing a quantitative relationship between polarization intensity and electric field intensity, and finally calculating key performance indicators such as the dielectric constant.

[0154] The embodiments of the method of the present invention have been described above in conjunction with the accompanying drawings. However, the present invention is not limited to the above embodiments. Various changes can be made according to the purpose of the invention. Any parameter changes or calculation simplifications made based on the principle of the technical solution of the present invention, as long as they meet the purpose of the invention and do not deviate from the principle and concept of the method and system for calculating the dielectric properties of hafnium-based oxide solid solutions based on deep learning potential functions, are all within the protection scope of the present invention.

[0155] The above description of the embodiments is provided to enable those skilled in the art to understand and use the invention. It will be apparent to those skilled in the art that various modifications can be made to these embodiments, and the general principles described herein can be applied to other embodiments without inventive effort. Therefore, the present invention is not limited to the above embodiments, and any improvements and modifications made by those skilled in the art based on the disclosure of the present invention without departing from the scope of the invention should be within the protection scope of the present invention.

Claims

1. A method for calculating the dielectric properties of hafnium-based oxide solid solutions based on deep learning potential functions, characterized in that, Includes the following steps: S1. Using bulk HfO2 as the parent phase structure, a supercell model of hafnium-based oxide solid solution with different component concentrations was built, and an initial training dataset containing multiphase features was constructed through first-principles molecular dynamics simulation. S2. Based on the initial training dataset, use a deep neural network to train a potential function model to describe the interactions between atoms in the system and construct a deep learning potential function model. S3. Molecular dynamics simulations are performed based on deep learning potential function models to screen candidate configurations, and an incremental dataset is constructed. The potential function is iteratively optimized to obtain a high-precision potential function model covering the target temperature and pressure. S4. Based on the obtained high-precision potential function model, molecular dynamics simulations were performed to study and calculate the phase stability and dielectric properties of hafnium-based oxide solid solution materials.

2. The method for calculating the dielectric properties of hafnium-based oxide solid solutions based on deep learning potential functions according to claim 1, characterized in that, Step S1 includes the following process: Using bulk HfO2 as the parent phase structure, a supercell model of hafnium-based oxide solid solution with different component concentrations was built by atomic substitution method. First-principles molecular dynamics simulations were performed over a wide temperature range. The system collected the energy eigenvalues, atomic force tensors, and virial tensor parameters of the system and constructed an initial training dataset containing multiphase characteristics. In step S1, the bulk HfO2 is obtained from a crystal structure database; In step S1, the chemical formula of the hafnium-based oxide is (Hf x M 1-x O2, where M = one or more of Zr, Si, and Al, and x = 0-1; In step S1, the size of the hafnium-based oxide solid solution supercell is set to be greater than 2×2×2; In step S1, the wide temperature range is 300-1200K.

3. The method for calculating the dielectric properties of hafnium-based oxide solid solutions based on deep learning potential functions according to claim 1, characterized in that, Step S2 includes the following process: S2.1 Based on the initial training dataset, set the neural network training parameters, which include the residual network, dynamic loss weights, learning rate exponent, and cutoff radius to describe the local interactions of atoms. S2.

2. Multiple potential functions are trained in parallel using deep neural networks to describe the interactions between atoms and to construct a deep learning potential function model.

4. The method for calculating the dielectric properties of hafnium-based oxide solid solutions based on deep learning potential functions according to claim 1, characterized in that, Step S3 includes the following process: S3.1 Based on the deep learning potential function model, set parameters including simulation step size, ensemble, temperature and pressure, and number of iterations to perform molecular dynamics simulation, use atomic force deviation as the standard, and label candidate configurations through confidence analysis; S3.2 Perform first-principles density functional theory single-point energy calculations on the labeled candidate configurations, and then standardize the obtained energy, atomic force and virial stress data and incorporate them into the training set to form an incremental dataset; S3.

3. Perform new iterative training based on the updated dataset. Each iteration includes neural network weight updates and potential energy surface parameter space optimization. S3.4 Repeat steps S3.1 to S3.3 for multiple iterations until a high-precision potential function covering all target temperatures and pressures is obtained.

5. The method for calculating the dielectric properties of hafnium-based oxide solid solutions based on deep learning potential functions according to claim 1, characterized in that, Following step S3, the following step S3' is performed to systematically verify the accuracy of the high-precision potential function: S3' , Systematically verify the accuracy of the high-precision potential function, including the convergence of the loss function, atomic forces, energy assessment, and prediction comparison of material equilibrium properties, to ensure the accuracy of the model in material simulation; The material equilibrium properties include the equation of state, the elastic constant tensor, and the phonon dispersion relation.

6. The method for calculating the dielectric properties of hafnium-based oxide solid solutions based on deep learning potential functions according to claim 5, characterized in that, Step S3' includes the following process: System verification of the high-precision potential function accuracy: Monitor the convergence of the energy and force loss functions during training to ensure that the root mean square values ​​of the energy and force loss functions reach the threshold; compare the atomic force and energy results of the high-precision potential function with those of DFT to ensure that the root mean square error of typical configurations is less than the target value; Prediction and verification of equilibrium properties: The equation of state was verified by sampling in the range of -5% to 5% near the equilibrium volume V0, and the energy-volume curve was fitted; the elastic constant tensor was calculated by the energy-strain method to verify whether the Born-Huang elastic stability criterion was satisfied. Calculate the phonon dispersion relation of the high-symmetric path and verify whether the characteristic phonon branches are consistent with the DFT calculation.

7. The method for calculating the dielectric properties of hafnium-based oxide solid solutions based on deep learning potential functions according to claim 1, characterized in that, Step S4 includes the following process: S4.

1. Based on the obtained high-precision potential function model, deep potential energy molecular dynamics simulation is carried out. Multiple feature points are selected within the target temperature and pressure range, and the influence of different component concentrations is considered. By comparing the structural characteristics and free energy change trends of each phase, the relative stability of each phase structure is quantitatively evaluated, thereby revealing the regulation mechanism of temperature, concentration and pressure conditions on the phase equilibrium relationship of hafnium-based oxide solid solution and screening stable phase structures. S4.

2. Based on deep potential energy molecular dynamics simulation of the dielectric response characteristics of hafnium-based oxide solid solutions, according to the stable phase structure obtained in step S4.1, the polarization behavior of the material under the action of an applied electrostatic field is simulated, and the static dielectric constant of hafnium-based oxide solid solutions under different temperatures, concentrations and pressures is calculated. The correlation mechanism between microstructure and macroscopic properties is further analyzed, and candidate material systems with high dielectric constants are screened.

8. The method for calculating the dielectric properties of hafnium-based oxide solid solutions based on deep learning potential functions according to claim 7, characterized in that, Step S4.2 includes the following process: S4.2.1 Using deep potential energy molecular dynamics, structural relaxation calculations are performed under target temperature and pressure conditions. After the system reaches a steady state, the final relaxation structure and the stable average structure during the relaxation process are output. S4.2.2 Based on the relaxed final state structure, an external electric field is applied using the equivalent force field method. A long-term relaxation simulation is first performed after the electric field is applied. After the system reaches equilibrium again, the stable average structure under the action of the electric field is recorded. The synergistic effect of ion real displacement and electronic polarization induced by the external electric field is simulated by the equivalent atomic force field. S4.2.

3. Based on the simulation in step S4.2.2, calculate the dielectric constant.

9. A calculation system for the dielectric properties of hafnium-based oxide solid solutions based on deep learning potential functions, characterized in that, The computing system is used to implement the computing method as described in any one of claims 1-8; The computing system includes: A deep learning potential function training module is used for iterative training of the interatomic interaction potential function of hafnium-based oxide solid solution materials; The phase stability and dielectric properties calculation module is used to conduct deep potential energy molecular dynamics simulations, and to systematically study and calculate the phase stability and dielectric properties of hafnium-based oxide solid solution materials.

10. The calculation system for the dielectric properties of hafnium-based oxide solid solutions based on deep learning potential functions according to claim 9, characterized in that, The computing system also includes: The deep learning potential function testing module is used to test the accuracy of the potential function model of hafnium-based oxide solid solution materials and to compare the prediction of the material's equilibrium properties, thereby evaluating the accuracy of the potential function.

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