A method for predicting the dielectric properties and phase diagrams of multi-component nitrides

Abstract

The application discloses a method for predicting dielectric properties and phase diagrams of multi-component nitride, comprising the following steps: step 1, determining special quasi-random arrangement of atoms in different structural phases of multi-component materials; step 2, performing structural optimization calculation; step 3, performing self-consistent calculation of electronic structure to obtain formation energy and band gap of different chemical compositions and structural phases; step 4, performing density functional linear response calculation to obtain spontaneous polarization of the material and response to external electric field; and step 5, comparing formation energy and structural information of different structural phases under the same chemical composition to determine thermodynamic stable phase and obtain an equilibrium phase diagram. The application can save resources and time, quickly and efficiently predict ferroelectric properties and phase diagrams of materials in a highly automated manner, shorten the research and development cycle of new nitride ferroelectric materials, and has important practical significance.

Description

Technical Field

[0001] This invention belongs to the field of ferroelectric materials technology, specifically relating to a method for predicting the dielectric properties and phase diagrams of multi-component nitrides based on high-throughput first-principles calculations. Background Technology

[0002] Ferroelectric materials possess stable spontaneous polarization states, capable of transitioning from one stable polarization state to another under an external electric field. The polarization intensity is influenced by factors such as temperature, stress, and strain. They also exhibit pyroelectric and piezoelectric properties, leading to a wide range of applications in thermal management, energy storage and utilization, information storage, and information sensing. The search for novel ferroelectric materials with superior properties is of great significance for promoting technological progress and socio-economic development.

[0003] Nitrides with wurtzite structure are a new type of ferroelectric material discovered in recent years. Their spontaneous polarization intensity is greater than that of traditional perovskite ferroelectric materials such as Pb(Zr,Ti)O3 and HfO2-based ferroelectric materials that have been widely studied in recent years. They are also suitable for integration with GaN-based semiconductor technology, making them a ferroelectric material with better performance and huge application prospects. They are expected to be commercialized in the next 5 to 10 years.

[0004] AlN is a typical polar nitride material with a wurtzite structure, but ferroelectric polarization reversal has not yet been detected in pure AlN. In 2019, Fichtner et al., by doping AlN with Sc, measured the hysteresis loop within the range of Sc content from 27% to 43%, thus confirming the ferroelectricity of wurtzite-structured nitrides for the first time. In 2021, John Hayden et al., by doping AlN with B, measured the hysteresis loop of the ferroelectric material within the range of B content from 2% to 19%. In addition, experimental and theoretical calculations have also studied the ferroelectric properties of AlN doped with elements such as Ga and Y. These studies confirm that the ferroelectric properties can be tuned by doping other elements into wurtzite ferroelectric materials.

[0005] However, existing wurtzite-structured nitride ferroelectric materials typically exhibit large coercive fields, hindering their application. Furthermore, the range of existing wurtzite ferroelectric materials remains relatively limited, concentrating on a few elements, and mostly consisting of compounds composed of three elements. Expanding the range of chemical compositions and introducing more elements can significantly broaden the selection space, potentially leading to ferroelectric materials with superior performance. However, the experimental synthesis of multi-element materials is challenging and costly. Therefore, screening materials with ideal ferroelectric properties and complex chemical compositions using high-throughput first-principles calculations has significant practical value. Summary of the Invention

[0006] The purpose of this invention is to provide a method for predicting the dielectric properties and phase diagrams of nitrides with a certain chemical composition based on high-throughput first-principles calculations.

[0007] To achieve the above-mentioned objectives, the technical solution adopted by the present invention is as follows:

[0008] Step 1: Using the mcsqs program in the ATAT package, determine the specific quasi-random arrangement of the ideal atomic positions in the common structures of metal nitrides for a given composition.

[0009] Step 2: Using VASP software, the conjugate gradient method is used to optimize the atomic structure of the material to obtain the optimized unit cell structure.

[0010] Step 3: Perform self-consistent calculations on the structure after convergence of structural optimization calculations to obtain Kohn-Sham energy and band information, and calculate formation energy.

[0011] Step 4: Calculate the linear response of the structure after the structural optimization calculation has converged, and calculate the dielectric properties of the material.

[0012] Step 5: Compare the formation energies of different phases under various chemical compositions, and determine the thermodynamically stable phase by combining the band gap and polarization properties.

[0013] Step 2 includes:

[0014] Step 2.1: Optimize the atomic positions, lattice shape, and size using VASP software to generate the maximum spacing of the reciprocal space K-points. The energy convergence criterion for the ion step is 10. -6 eV, the convergence criterion for atomic forces is

[0015] Step 2.2: Using the structure obtained in Step 2.1, compare it with the initial structure to calculate the atomic coordinate relaxation coefficient CR and the lattice relaxation coefficient LR2.

[0016] Step 3 includes:

[0017] Step 3.1: Using the optimized crystal structure, perform self-consistent electronic structure calculations using VASP software to generate the maximum spacing of the reciprocal space K-points. Set the parameter "ISMEAR=-5".

[0018] Step 3.2: Calculate the band gap size based on the electronic structure obtained from the self-consistent calculation in Step 3.1.

[0019] Step 3.3: Calculate the formation energy based on the Kohn-Sham energy obtained from the self-consistent calculation in Step 3.1.

[0020] Step 4 includes:

[0021] Step 4.1: Use VASP software to calculate the density functional linear response, set the parameter "LEPSILON=.TRUE.", and calculate the Born effective charge tensor.

[0022] Step 4.2: Based on the initial atomic structure obtained in Step 1, construct a nonpolarized reference phase crystal structure.

[0023] Step 4.3: Compare the optimized crystal structure in Step 2 with the reference phase crystal structure constructed in Step 4.2, calculate the atomic shifts, and use the Born effective charge tensor obtained in Step 4.1 to calculate the polarization intensity.

[0024] Step 4.4: Starting from the optimized crystal structure obtained in Step 2, apply an electric field with gradually changing intensity. For each electric field intensity, optimize the atomic positions, lattice shape and size, and calculate the polarization intensity to obtain the hysteresis loop.

[0025] Step 5 includes:

[0026] Step 5.1: Compare the formation energies of each phase under the same chemical composition, and take the one with the lowest energy to preliminarily determine it as the thermodynamically stable phase.

[0027] Step 5.2: Based on the atomic coordinate relaxation coefficient CR and lattice relaxation coefficient LR2 calculated in Step 2.2, filter the calculation results. If CR is greater than... If LR2 is greater than 0.20, it is considered that the optimized structure is no longer the initial phase, and the calculation result is excluded.

[0028] Step 5.3: Compare stable phases with similar chemical compositions, identify outliers, specifically compare the optimized crystal structure, band gap, polarization intensity and their variation with chemical composition, determine whether the structure optimization has resulted in other phases, and correct the thermodynamically stable phase under the given chemical composition.

[0029] Step 5.4: Summarize the stable phases under all chemical compositions, determine the phase boundaries, and obtain the equilibrium phase diagram.

[0030] The technical solution of the present invention has the following beneficial technical effects:

[0031] 1. Overcomes the blindness of traditional "trial and error" experiments, saves resources and time, does not involve experiments, does not produce chemical pollution, and is green and environmentally friendly;

[0032] 2. Based on high-throughput first-principles calculations, the dielectric properties and phase diagrams of materials can be rapidly predicted, ferroelectric materials with good performance can be screened, providing theoretical guidance for experimental preparation and improving experimental efficiency;

[0033] 3. It is simple to operate and can achieve a high degree of automation. It can predict the dielectric properties and stable phase of a material by only providing the initial structure and chemical composition. Attached Figure Description

[0034] Figure 1 This is a flowchart of the method of the present invention.

[0035] Figure 2 This is a schematic diagram of a common structure of metal nitrides.

[0036] Figure 3 The atomic position relaxation factor CR varies with the Sc component content in the examples.

[0037] Figure 4 The variation of lattice relaxation factor LR2 with Sc component content is shown in the example.

[0038] Figure 5 The band gap varies with the Sc component content in the examples.

[0039] Figure 6 The variation in the formation energy with the content of the Sc component is shown in the examples.

[0040] Figure 7 The polarization intensity varies with the Sc component content in the example.

[0041] Figure 8 The hysteresis loop is shown in the example when the Sc component content is 31.25%. Detailed Implementation

[0042] The present invention will now be described in detail with reference to the accompanying drawings and embodiments, but the scope of protection of the present invention is not limited to the following description.

[0043] The flowchart of the method for predicting the dielectric properties and phase diagrams of multi-component nitrides in this invention is as follows: Figure 1 As shown.

[0044] Example:

[0045] Taking the (Al,Ga,Sc)N system as an example, the thermodynamically stable phase and its dielectric properties are calculated when the Ga composition is fixed at 12.5%, and the composition ratio of Sc and Al is changed. The steps include:

[0046] Step 1: Use the mcsqs program to calculate the specific quasi-random arrangement of atoms for a given composition. Select five common structures of nitrides: wurtzite (WZ), layered hexagonal (HEX), β-beryllium oxide (BB), zincblende (ZB), and rock salt (RS), as follows: Figure 2As shown. The wz phase is a polarized phase, while the other four phases are non-polarized and, in principle, do not spontaneously polarize. A supercell with 32 atoms is used for the wz, hex, and bb phases, and a supercell with 64 atoms is used for the zb and rs phases. Of the 32 atoms in the selected supercells for the wz, hex, and bb phases, 16 are nitrogen atoms; therefore, the Al, Ga, and Sc compositions can vary in steps of 1 / 16 = 6.25%. Considering the Ga composition is fixed at 12.5%, there are 2 Ga atoms in the wz, hex, and bb phase supercells and 4 Ga atoms in the zb and rs supercells. The Sc composition is set to vary from 0% to 87.5% in 6.25% steps, resulting in 15 different chemical compositions and 75 different structures. Input the percentage of each element and run the mcsqs program. After running for about 4 hours on a single core for each structure, the atomic occupancy remains basically unchanged, and the program can be stopped to convert the final atomic arrangement into the VASP input file POSCAR.

[0047] Step 2: Optimize the crystal structure.

[0048] Step 2.1: Using the POSCAR file generated in Step 1 as the initial input structure, set the maximum spacing of the generated reciprocal space K-points to be... The energy convergence criterion for the ion step is 10. -6 eV, the convergence criterion for atomic forces is The atomic positions, lattice size, and shape were optimized. The PBEsol functional under the generalized gradient approximation (GGA) framework was adopted, and the selected plane wave cutoff energy was 550 eV.

[0049] Step 2.2: Compare the optimized structure obtained in Step 2.1 with the initial structure, and calculate the atomic relaxation factor CR and the lattice relaxation factor LR2. The changes of CR and LR2 with the Sc atom content are as follows: Figure 3 and Figure 4 As shown.

[0050] Step 3: Perform self-consistent calculations on the optimized structure obtained in Step 2.1.

[0051] Step 3.1: Using the optimized crystal structure, perform self-consistent electronic structure calculations using VASP software to generate the maximum spacing of the reciprocal space K-points. Set the parameter "ISMEAR=-5".

[0052] Step 3.2: Based on the electronic structure obtained from the self-consistent calculation in Step 3.1, calculate the band gap. For example... Figure 5 The figure shows how the band gap changes with the Sc component content.

[0053] Step 3.3: Based on the Kohn-Sham energy obtained from the self-consistent calculation in Step 3.1, calculate the formation energy using the following formula.

[0054]

[0055] Where E KS The value is the Kohn-Sham energy obtained from the self-consistent calculation in step 3.1; N is the ratio of the number of atoms in the selected structure to the number of atoms in the formal unit (fu), which is 8 for the wz, hex, and bb phases and 16 for the zb and rs phases; x Sc ,x Al ,x Ga These represent the percentage content of Sc, Al, and Ga elements, respectively, where x is the percentage content of Sc, Al, and Ga Ga Fixed at 12.5%; E(N2), E(Sc), E(Al), E(Ga) are the Kohn-Sham energies of N2, Sc, Al, and Ga, respectively. Figure 6 The figure shows the variation of the formation energy of each phase with the content of the Sc component.

[0056] Step 4: Calculate the linear response of the structure after the structural optimization calculation has converged, and calculate the dielectric properties of the material.

[0057] Step 4.1: Using the optimized crystal structure obtained in Step 2, perform density functional linear response calculations using VASP software, set the parameter "LEPSILON=.TRUE.", and calculate the Born effective charge tensor.

[0058] Step 4.2: Based on the initial atomic structure obtained in Step 1, construct a non-polarized reference phase crystal structure. For the non-polarized phases hex, bb, zb, and rs, only the structure obtained in Step 1 before structural optimization needs to be used as the reference phase. For the polarized phase wz, since the initial structure obtained in Step 1 has spontaneous polarization, it cannot be directly used as the reference phase. Instead, based on the initial structure obtained in Step 1, the coordinates of the N atoms need to be adjusted so that the N atoms and Al, Sc, and Ga atoms are in the same plane along the c-direction of the crystal lattice, resulting in a layered hexagonal phase with the same atomic arrangement as the initial structure, which serves as the reference phase structure.

[0059] Step 4.3: Compare the optimized crystal structure from Step 2 with the reference phase crystal structure constructed in Step 4.2, calculate the atomic shifts, and use the Born effective charge tensor obtained in Step 4.1 to calculate the polarization. Note that the influence of lattice periodic boundary conditions must be considered when calculating atomic shifts. Figure 7 The figure shows the relationship between polarization intensity and Sc component content.

[0060] Step 4.4: Starting from the optimized crystal structure obtained in Step 2, apply an electric field with progressively linearly varying intensity. For each electric field strength, optimize the atomic positions, lattice shape, and size, and calculate the polarization intensity to obtain the hysteresis loop. Taking the wz phase structure with a Sc composition content of 31.25% as an example, its spontaneous polarization magnitude is approximately 1.09 C / m. 2 The direction is along the c-direction of the lattice. Therefore, the applied electric field is directed along the -c-direction of the lattice, with a maximum electric field strength of 6.7 MV / cm chosen. The electric field strength starts from 0, first increasing to the maximum along the -c direction, then decreasing to 0, then increasing to the maximum along the +c direction, and finally decreasing to 0, completing one cycle. The resulting hysteresis loop is shown below. Figure 8 As shown, the obtained hysteresis loop belongs to a typical ferroelectric material, with a coercive field of approximately 3.3 MV / cm. Note that since the electric field strength calculated by first-principles methods is usually several to tens of times larger than the experimental field strength, the calculated electric field strength often needs to be scaled. This is generally attributed to the Landauer paradox. In nitride systems, the ratio of the electric field strength predicted by first-principles methods to the experimental electric field strength has been reported in previous studies to be around 3. The electric field strength value here is 1 / 3 of the original calculated electric field strength value.

[0061] Step 5: Compare the formation energies of different phases under various chemical compositions, and determine the thermodynamically stable phase by combining the band gap and polarization properties.

[0062] Step 5.1: Compare the formation energies of different phases with the same chemical composition to preliminarily determine the thermodynamically stable phase. For example... Figure 6 The figure shows the variation of formation energy of each phase with the Sc component content. Specifically, the wz phase has the lowest formation energy when the Sc component content is no greater than 37.5%; the bb phase has the lowest formation energy when the Sc component content is 43.75%; and the rs phase has the lowest formation energy when the Sc component content is no less than 50%. Therefore, it is preliminarily determined that the bb phase is the stable phase when the Sc component content is around 43.75%; the wz phase is the stable phase in the lower Sc component content range; and the rs phase is the stable phase in the higher Sc component content range.

[0063] Step 5.2: Based on the atomic coordinate relaxation coefficient CR and lattice relaxation coefficient LR2 calculated in Step 2.2, filter the calculation results. If CR is greater than... If LR2 is greater than 0.20, then the optimized structure is considered to be no longer the initial phase, and the calculation result is excluded. Figure 3 The figure shows the change in CR with the content of Sc component. When the Sc component content is above 37.5%, the CR of the bb phase exceeds [the value missing]. The threshold; when the Sc component content is above 56.25%, the CR of the WZ phase exceeds [the threshold value]. The threshold. In both of the above cases, these structures should be considered to have strong atomic relaxation, and the optimized structure is no longer the original structure, and should be excluded. Figure 3 The figure shows the variation of LR2 with the Sc component content. It can be seen that LR2 does not exceed the threshold for all components. Compared with the equilibrium phase initially obtained in step 5.1, it can be seen that the bb phase has been excluded at the Sc content of 43.75%, and the bb phase is not the thermodynamically stable phase of this component.

[0064] Step 5.3 compares stable phases with similar chemical compositions, specifically comparing the optimized crystal structure, band gap, polarization intensity, and their variation with chemical composition to determine whether the structure optimization has resulted in a different phase, and corrects the thermodynamically stable phase under that chemical composition. For example... Figure 5 As shown, near the Sc component at 37.5%, the initial bb phase structural band gap undergoes an abrupt change; as... Figure 6 As shown, in the portion where the Sc composition is above 37.5%, the structure initially in the bb phase exhibits significant spontaneous polarization, even though the bb phase is inherently non-polarizable. This evidence further indicates that when the Sc composition is above 37.5%, the initial bb phase undergoes a phase transition during structure optimization calculations and is no longer the bb phase, consistent with the conclusion of step 5.2. Similarly, the abrupt change in band gap and polarization intensity of the initial wz phase near the Sc composition of 56.25% indicates that the wz phase undergoes a phase transition near this composition, also consistent with the conclusion of step 5.2.

[0065] Examine the structure at the Sc component concentration of 43.75%. (From...) Figure 5 It can be seen that when the Sc composition is above 43.75%, the band gap of the initial bb phase structure is quite close to that of the initial hex phase. Observing and comparing the optimized atomic structures at a Sc composition of 43.75%, the initial bb phase structure is already very close to the initial hex phase structure. Further examination of the structure at a Sc composition of 37.5% shows that the initial wz phase with the lowest energy remains a wz phase after optimization. Examination of the structure at a Sc composition of 50% shows that the initial rs phase with the lowest energy remains an rs phase after optimization.

[0066] Step 5.4: Summarize the stable phases under all chemical compositions, determine the phase boundaries, and obtain the equilibrium phase diagram. Based on the above discussion, it can be seen that for the (Al,Ga,Sc)N system with a Ga content of 12.5%, the equilibrium phases varying with the Sc content are as follows: in a narrow composition range around 43.75% Sc content, the thermodynamically stable phase is the hex phase; in the region with a lower Sc content, the thermodynamically stable phase is the wz phase; and in the region with a higher Sc content, the thermodynamically stable phase is the rs phase.

[0067] In summary, the above embodiments, based on the high-throughput first-principles method for predicting the dielectric properties and phase diagrams of multi-component nitrides, first determine the specific arrangement of different atoms within the supercell, then perform structural optimization calculations, then use self-consistent electronic structure calculations to obtain the band gap and formation energy, and use density functional linear response calculations to obtain the material's response to an external electric field, thus predicting the dielectric properties. Finally, by comparing the formation energy and structural information of different structural phases under the same chemical composition, the thermodynamically stable phases under different chemical compositions are determined, and the phase diagram is obtained.

[0068] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for predicting the dielectric properties and phase diagrams of multi-component nitrides, characterized in that, The method includes the following steps: Step 1: Using the mcsqs program in the ATAT package, determine the specific quasi-random arrangement of the ideal atomic positions in the common structures of metal nitrides for a given composition; Step 2: Using VASP software, the conjugate gradient method is used to optimize the atomic structure of the material to obtain the optimized crystal structure. Step 3: Perform self-consistent calculations on the structure after convergence of structural optimization calculations to obtain Kohn-Sham energy and band information, and calculate formation energy; Step 4 involves calculating the linear response of the converged structure obtained from the structural optimization calculation, and then calculating the dielectric properties of the material. Step 4 includes: Step 4.1: Use VASP software to calculate the density functional linear response, set the parameter "LEPSILON=.TRUE.", and calculate the Born effective charge tensor; Step 4.2: Based on the initial atomic structure obtained in Step 1, construct a nonpolar reference phase crystal structure; Step 4.3: Compare the optimized crystal structure in Step 2 with the reference phase crystal structure constructed in Step 4.2, calculate the atomic shifts, and use the Born effective charge tensor obtained in Step 4.1 to calculate the polarization intensity. Step 4.4: Starting from the optimized crystal structure obtained in Step 2, apply an electric field with gradually changing intensity. For each electric field intensity, optimize the atomic positions, lattice shape and size, and calculate the polarization intensity to obtain the hysteresis loop. Step 5: Compare the formation energies of different phases under various chemical compositions, and determine the thermodynamically stable phase by combining the band gap and polarization properties.

2. The method for predicting the dielectric properties and phase diagrams of multi-component nitrides according to claim 1, characterized in that, Step 1 involves selecting the composition ratio of each element, obtaining common structures of metal nitrides, using the mcsqs program to calculate until the objective function converges or runs for a predetermined time, obtaining the optimal atomic arrangement, and converting it into a VASP input file format.

3. The method for predicting the dielectric properties and phase diagrams of multi-component nitrides according to claim 1, characterized in that, Step 2 includes: Step 2.1: The atomic positions, lattice shape, and size are optimized using VASP software to generate a reciprocal space K-point with a maximum spacing of 0.3 Å. -1 The energy convergence criterion for the ion step is 10. -6 eV, the atomic force convergence standard is 0.005 eV / Å; Step 2.2: Compare the structure obtained in Step 2.1 with the initial structure to calculate the atomic coordinate relaxation coefficient CR and the lattice relaxation coefficient LR2.

4. The method for predicting the dielectric properties and phase diagrams of multi-component nitrides according to claim 1, characterized in that, Step 3 includes: Step 3.1: Using the optimized crystal structure, perform self-consistent electronic structure calculations using VASP software to generate a reciprocal space K-point maximum spacing of 0.2 Å. -1 Set the parameter "ISMEAR=-5"; Step 3.2: Calculate the band gap size based on the electronic structure obtained from the self-consistent calculation in Step 3.1; Step 3.3: Calculate the formation energy based on the Kohn-Sham energy obtained from the self-consistent calculation in Step 3.

1.

5. The method for predicting the dielectric properties and phase diagrams of multi-component nitrides according to claim 3, characterized in that, Step 5 includes: Step 5.1: Compare the formation energies of each phase under the same chemical composition, and take the one with the lowest energy to preliminarily determine it as the thermodynamically stable phase; Step 5.2: Based on the atomic coordinate relaxation coefficient CR and lattice relaxation coefficient LR2 calculated in Step 2.2, the calculation results are screened. If CR is greater than 0.25 Å or LR2 is greater than 0.20, it is considered that the structure is no longer the initial phase after optimization, and the calculation result is excluded. Step 5.3: Compare stable phases with similar chemical compositions, identify outliers, specifically compare the optimized crystal structure and band gap, polarization intensity and their variation with chemical composition, determine whether the structure optimization has resulted in other phases, and correct the thermodynamically stable phase under the given chemical composition. Step 5.4: Summarize the stable phases under all chemical compositions, determine the phase boundaries, and obtain the equilibrium phase diagram.

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