Method for high-throughput calculation of electronic structure of half-heusler materials at different temperatures

Abstract

The application discloses a method for high-throughput calculation of electronic structures of different temperatures of semi-Hasler materials. The calculation is mainly based on a MatHub-3d database. There are 274 semi-Hasler materials in the database. First, the structures of the 274 materials are optimized, and then the electronic structures and phonon spectra are calculated, and 109 stable semiconductor structures with no virtual frequency and a band gap greater than 0.1 eV are screened. Then, the electronic structures at 11 temperatures from 0 to 1000K are calculated by applying Allen-Heine-Cardona (AHC) theory. The method can improve the efficiency by high-throughput calculation, achieve the purpose of quickly calculating the target material system, and provide a theoretical reference for the design of photoelectric and thermoelectric materials.

Description

Technical Field

[0001] This invention relates to the field of computational materials with electronic structures at different temperatures, specifically a method for high-throughput computation of the electronic structures of semi-Hassler materials at different temperatures. Background Technology

[0002] As early as the 1960s and 70s, researchers discovered that temperature could induce changes in the electronic structure of traditional semiconductor materials such as diamond and silicon carbide, primarily manifested in changes in the band gap. These changes stem from two main factors: lattice thermal expansion and phonon-induced lattice thermal vibrations, i.e., electro-acoustic renormalization, which includes zero-point renormalization and finite-temperature renormalization. Subsequent research has also revealed that electro-acoustic renormalization can affect the width of the energy band or cause band degeneracy. These changes could potentially have a positive impact on the optoelectronic and thermoelectric properties of materials, benefiting the development and application of functional devices. However, previous research has mostly focused on individual systems, with relatively little research on a class of functional materials.

[0003] Semi-Hassler materials are ternary intermetallic compounds, usually represented by the chemical formula ABX. The high symmetry of their crystal structure gives them a large band degeneracy, and the electronic density of states near the Fermi level is usually dominated by d electrons of transition metals (such as Fe, Co, Ni, etc.), resulting in a large effective mass of states. Therefore, this system often has high electrical performance and is a promising class of thermoelectric materials.

[0004] In recent years, thanks to the rapid development of high-performance and high-throughput computing, various research fields in materials science have made great strides, which has also driven the emergence of digital materials information databases. By using automated processes to perform calculations and screenings on a large number of materials, from structural optimization to property prediction, it is helpful to solve, to some extent, the problems of long R&D cycles and high trial-and-error costs in materials design. Summary of the Invention

[0005] This invention proposes a high-throughput method for calculating the electronic structure of semi-Hassler materials at different temperatures. The aim is to screen for structurally stable semi-Hassler materials using high throughput and systematically calculate their electronic structures at different temperatures, providing theoretical reference for the design of subsequent optoelectronic and thermoelectric materials. This invention primarily uses 274 semi-Hassler materials from the MATLAB-3D database. First, structural optimization is performed, followed by calculation of the electronic structure and phonon spectrum, resulting in the selection of 109 stable semiconductor structures with no imaginary frequencies in the phonon spectrum and a band gap greater than 0.1 eV. Then, the AHC theory is applied to calculate the electronic structure at 11 temperatures ranging from 0 to 1000 K. Based on the MATLAB-3D database, this invention uses AHC theory to perform high-throughput calculations of the band structure at different temperatures. This is a relatively accurate method that yields clear band structure diagrams, facilitating the analysis of band gap changes and the observation of band width variations and band degeneracy. This information will greatly contribute to the understanding of the electronic structure of semi-Hassler materials at different temperatures and is beneficial for obtaining potential high-performance optoelectronic and thermoelectric materials.

[0006] To achieve the above-mentioned objectives, the technical solution adopted by this invention is as follows: a method for high-throughput calculation of the electronic structure of a semi-Hassler material at different temperatures, comprising the following steps:

[0007] 1) The equilibrium lattice constants of 274 semi-Hassler materials in the database were obtained by high-throughput calculation using VASP software;

[0008] 2) Phonon spectrum calculations were performed using the optimized crystal structure;

[0009] 3) The optimized crystal structure is used to perform self-consistent calculations to obtain the charge density of the system;

[0010] 4) Calculate the band structure using charge density;

[0011] 5) From the results obtained in steps 2) and 4), 109 stable structures with no imaginary frequencies in the phonon spectrum and a band gap greater than 0.1 eV were selected.

[0012] 6) Using Abinit software, the 109 stable structures were subjected to electroacoustic coupling renormalization calculations using a high-throughput calculation method to obtain the electronic structures at 11 temperatures from 0 to 1000 K.

[0013] Further, in step 1), the lattice parameters of the crystal structure are a, b, and c, the high-symmetry k-points during structure optimization are set to 60 / a+1, 60 / b+1, and 60 / c+1, and the energy convergence criterion is 10. -8 eV, cutoff energy is 520eV.

[0014] Furthermore, in step 2), the phonon spectrum calculation constructs a 4×4×4 supercell structure.

[0015] Furthermore, in step 3), during the self-consistent calculation, the high-symmetry k-points are set to 60 / a+1, 60 / b+1, and 60 / c+1, and the energy convergence criterion is 10. -4 eV, cutoff energy is 520eV.

[0016] Furthermore, in step 4), each system has a total of 6 band segments, each segment has 40 points, and the cutoff energy is 520eV.

[0017] Furthermore, in step 6), the calculation of the electronic structure at different temperatures is mainly based on the Allen-Heine-Cardona (AHC) theory, that is, the electron-phonon interaction is perturbed and consists of two terms representing the second-order Taylor expansion in the nuclear shift, called the Fan-Migdal (Fan) and Debye-Waller (DW) self-energy terms. The cutoff energy in the calculation is 35 Hatree, the k-grid is 6×6×6, the q-grid is 10×10×10, and the temperature is set to 0-1000K in 100K intervals. The calculation formula is as follows:

[0018] ∑ e-ph (ω, T)=∑ FM (ω,T)+∑ DW (T) (1)

[0019]

[0020]

[0021] Where f mk+q (ε F (n, T) is the Fermi-Dirac distribution function at temperature T, and n qv (T) is the Bose-Einstein distribution at temperature T, ε F It is the Fermi level, and the integral is in the volumetric Brillouin zone Ω. BZ The process takes place at point q, where η is a positive real infinitesimal.

[0022] Compared with the prior art, the present invention has the following obvious substantive features and significant advantages:

[0023] (1) The present invention adopts a high-throughput computing method, which can quickly screen the target system, with high efficiency and accuracy.

[0024] (2) This invention can theoretically reproduce the electronic structure of the semi-Hassler material at different temperatures, providing a theoretical reference for the improvement of electrical transport performance caused by band gap changes or band degeneracy observed in experiments.

[0025] (3) The method of the present invention does not involve experimental operations and does not generate chemical pollution throughout the process. It conforms to the concept of green environmental protection and is simple to operate and easy to implement. It is suitable for promotion to other semiconductor materials. Attached Figure Description

[0026] Figure 1 This is a flowchart of the high-throughput computing process of the present invention.

[0027] Figure 2 The phonon spectrum of ZrNiSn.

[0028] Figure 3 This is a diagram of the band structure of ZrNiSn.

[0029] Figure 4 The diagram shows the band structure of ZrNiSn in the range of 0-1000K, where the solid lines represent unit cell bands and the dashed lines represent bands at different temperatures.

[0030] Figure 5 The phonon spectrum of TiRhBi is shown.

[0031] Figure 6 This is the band structure diagram of TiRhBi.

[0032] Figure 7 The diagram shows the band structure of TiRhBi in the range of 0-1000K, where the solid lines represent unit cell bands and the dashed lines represent bands at different temperatures. Detailed Implementation

[0033] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0034] Example 1

[0035] like Figure 1 As shown, the present invention provides a method for high-throughput calculation of the electronic structure of a semi-Hassler material at different temperatures, comprising the following steps:

[0036] 1) The structure of the semi-Hassler material ZrNiSn was optimized using VASP software. The lattice parameters of the crystal structure were as follows: The high-symmetry k-point for structural optimization is set to 14×14×14, and the energy convergence criterion is 10. - 8 eV, cutoff energy is 520eV;

[0037] 2) Phonon spectrum calculations were performed using the optimized crystal structure. A 4×4×4 supercell structure was constructed. The phonon spectrum results are shown below. Figure 2 ;

[0038] 3) Self-consistent calculations were performed using the optimized crystal structure to obtain the charge density of the system. The high-symmetry k-point was set to 14×14×14, and the energy convergence criterion was 10. -4 eV, cutoff energy is 520eV;

[0039] 4) The energy band structure was calculated using the charge density. There are 6 band segments, each with 40 points. The cutoff energy is 520 eV. The band structure results are shown below. Figure 3 ;

[0040] 5) Based on the results obtained in steps 2) and 4), determine that the ZrNiSn phonon spectrum has no imaginary frequency and the band gap is greater than 0.1 eV;

[0041] 6) Electroacoustic coupled renormalization calculations of ZrNiSn were performed using Abinit software with high-throughput computation methods. The electronic structure was obtained at 11 temperatures ranging from 0 to 1000 K. The cutoff energy was 35 Hatree, and the k-grid was 6×6×6 with a 10×10×10 grid. The temperature range was 0-1000 K, with 100 K intervals. The band structure results at different temperatures are shown in [Figure number missing]. Figure 4 The bandgap value at 1000K decreased by 0.15 eV compared to 0K.

[0042] Example 2

[0043] This step is basically the same as the above embodiment, but the difference lies in the calculation of a semi-Hassler material that can undergo conduction band degeneracy at medium and high temperatures, which is beneficial to the improvement of thermoelectric performance:

[0044] 1) The structure of the semi-Hassler material TiRhBi was optimized using VASP software. The lattice parameters of the crystal structure were as follows: The high-symmetry k-point for structural optimization is set to 14×14×14, and the energy convergence criterion is 10. - 8 eV, cutoff energy is 520eV;

[0045] 2) Phonon spectrum calculations were performed using the optimized crystal structure. A 4×4×4 supercell structure was constructed. The phonon spectrum results are shown below. Figure 5 ;

[0046] 3) Self-consistent calculations were performed using the optimized crystal structure to obtain the charge density of the system. The high-symmetry k-point was set to 14×14×14, and the energy convergence criterion was 10. -4 eV, cutoff energy is 520eV;

[0047] 4) The energy band structure was calculated using the charge density. There are 6 band segments, each with 40 points. The cutoff energy is 520 eV. The band structure results are shown below. Figure 6 ;

[0048] 5) Based on the results obtained in steps 2) and 4), determine that the TiRhBi phonon spectrum has no imaginary frequency and the band gap is greater than 0.1 eV;

[0049] 6) Electroacoustic coupled renormalization calculations were performed on TiRhBi using Abinit software with high-throughput computation methods. The electronic structure was obtained at 11 temperatures ranging from 0 to 1000 K. The cutoff energy was 35 Hatree, and the k-grid was 6×6×6 with a 10×10×10 grid. The temperature range was 0-1000 K, with 100 K intervals. The band structure results at different temperatures are shown in [reference needed]. Figure 7 As the temperature increases, the conduction band bottom and the second conduction band at point X become degenerate, and the electronic density of states increases. This is beneficial for obtaining a larger Seebeck coefficient while keeping the carrier concentration constant, thereby improving the thermoelectric properties of the material.

[0050] The methods described above overcome the problems of long development times and high costs associated with traditional materials research and development, and can quickly screen for structurally stable target systems. The automated process used in electroacoustic renormalization calculations can systematically obtain the band structure of semi-Hassler materials at different temperatures, facilitating direct observation of band gap changes or alterations in band shape and energy level positions, providing theoretical reference for the development of optoelectronic and thermoelectric materials. Furthermore, this calculation method is relatively simple and suitable for application to other semiconductor materials.

[0051] In summary, this invention provides a high-throughput method for calculating the electronic structure of semi-Hassler materials at different temperatures. Based on the MatHub-3d materials database, 109 structurally stable semi-Hassler semiconductor materials were screened through phonon spectrum and band structure calculations. Using AHC theory, the electronic structures at temperatures ranging from 0 to 1000 K were calculated. This invention is simple to operate, easy to promote, and provides guidance for the research and development of optoelectronic and thermoelectric materials.

[0052] 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 for high-throughput calculation of the electronic structure of a semi-Hassler material at different temperatures, are within the protection scope of the present invention.

Claims

1. A method for high-throughput calculation of the electronic structure of a semi-Hassler material at different temperatures, characterized in that, The method includes the following steps: 1) The equilibrium lattice constants of 274 semi-Hassler materials in the database were obtained by high-throughput calculation using VASP software; 2) Phonon spectrum calculations were performed using the optimized crystal structure; 3) The optimized crystal structure is used to perform self-consistent calculations to obtain the charge density of the system; 4) Calculate the band structure using the charge density; 5) From the results obtained in steps 2) and 4), 109 stable structures with no imaginary frequencies in the phonon spectrum and a band gap greater than 0.1 eV were selected. 6) Using Abinit software, high-throughput calculations were performed on the 109 stable structures to obtain the electronic structures at 11 temperatures from 0 to 1000 K by performing electroacoustic coupling renormalization calculations. In step 6), the calculation of the electronic structure at different temperatures is mainly based on the Allen-Heine-Cardona (AHC) theory. That is, the electron-phonon interaction is perturbed and consists of two terms representing the second-order Taylor expansion of the nuclear shift, called the Fan-Migdal (Fan) and Debye-Waller (DW) self-energy terms. The cutoff energy in the calculation is 35 Hatree, the k-grid is 6×6×6, the q-grid is 10×10×10, and the temperature is set to 0-1000K in 100K intervals. The calculation formula is as follows: S e-ph (ω,T)=Σ FM (ω,T)+Σ DW (T) (1) Where f mk+q (ε F (n, T) is the Fermi-Dirac distribution function at temperature T, and n qv (T) is the Bose-Einstein distribution at temperature T, ε F It is the Fermi level, and the integral is in the volumetric Brillouin zone Ω. BZ The process takes place at point q, where η is a positive real infinitesimal.

2. The method for high-throughput calculation of the electronic structure of a semi-Hassler material at different temperatures according to claim 1, characterized in that, In step 1), the lattice parameters of the crystal structure are a, b, and c, respectively. The high-symmetry k-points during structure optimization are set to 60 / a+1, 60 / b+1, and 60 / c+1, and the energy convergence criterion is 10. -8 eV, cutoff energy is 520eV.

3. The method for high-throughput calculation of the electronic structure of a semi-Hassler material at different temperatures according to claim 1, characterized in that, In step 2), the phonon spectrum calculation constructs a 4×4×4 supercell structure.

4. The method for high-throughput calculation of the electronic structure of a semi-Hassler material at different temperatures according to claim 1, characterized in that, In step 3), during the self-consistent calculation, the high-symmetry k-points are set to 60 / a+1, 60 / b+1, and 60 / c+1, with an energy convergence criterion of 10. -4 eV, cutoff energy is 520eV.

5. The method for high-throughput calculation of the electronic structure of a semi-Hassler material at different temperatures according to claim 1, characterized in that, In step 4), each system corresponds to a total of 6 band segments, with 40 points in each segment and a cutoff energy of 520 eV.

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