A method for calculating the band structure of a wurtzite aluminum nitride ferroelectric material

Abstract

The application discloses a kind of band structure calculation methods of aluminium nitride wurtzite ferroelectric material, belong to semiconductor electronic technical field, the band structure calculation method of aluminium nitride wurtzite ferroelectric material, using the first kind of spherical shell type density functional theory algorithm is carried out self-energy correction and obtains cut-off radius, using the second kind of spherical shell type density functional theory algorithm obtains multiple band gap theory value, find out the covalent bond strength value corresponding to the band gap experimental value with the least difference, the cation self-energy potential of actual element is stronger than the case of atomic state, simultaneously with the A value of cation corresponding self-energy potential and the value of covalent bond strength value, the band structure of aluminium nitride wurtzite ferroelectric material is reasonably corrected, finally carries out the band calculation of aluminium nitride wurtzite ferroelectric material, can accurately and efficiently describe the band structure of aluminium nitride wurtzite ferroelectric material.

Description

Technical Field

[0001] This invention belongs to the field of semiconductor electronics technology, and more specifically, relates to a method for calculating the band structure of aluminum zinc nitride ferroelectric materials. Background Technology

[0002] Aluminum nitride (ANH3), as an ultrawide bandgap material, has a thermodynamically stable wurtzite structure with a direct bandgap of approximately 6.2 eV, making it a key material for blue and ultraviolet light emitting devices. ANH3 possesses low dielectric constant and dielectric loss, good thermal conductivity, high resistivity, and high breakdown field strength, further enhancing its application potential in high-temperature, high-frequency, and high-power devices. The wurtzite structure exhibits a non-centrosymmetric crystal structure, a polarized c-axis, and piezoelectric properties, with a piezoelectric coefficient higher than gallium nitride (GaN) or indium nitride (INH3). Solid solutions composed of ANH3 and scandium nitride exhibit ferroelectricity and can serve as a novel ferroelectric material. However, this new ferroelectric wurtzite type III nitride solid solution may have other forms, requiring theoretical calculations, simulations, and derivations. While electronic structure simulations can effectively predict material performance, first-principles calculations of semiconductor band structures based on density functional theory suffer from a systematic underestimation of the bandgap.

[0003] Currently, there are many solutions to the density functional bandgap problem, the root of which lies in addressing the lack of derivative discontinuity in exchange-correlated functionals. For example, hybrid functionals can improve the treatment of electron exchange effects by introducing a certain amount of nonlocal electron exchange; electron self-interaction correction methods subtract electron self-interactions through post-processing; the GW method is based on the Green's function method in quantum field theory to handle excited states; and the scissor operator is based on the basic electronic structure of the local density approximation and the generalized gradient approximation, shifting the conduction band or valence band to increase the bandgap value. However, the computational cost of hybrid functionals and self-potential correction methods increases dramatically, and electron self-interaction correction methods are complex to operate. Only the scissor operator method is easy to use and generalize, offering a trade-off between speed and accuracy.

[0004] Based on the scissor operator method, two charge stripping schemes were derived. For binary ionic semiconductors, the shell DFT-0-1 / 2 method is used, stripping 0.5 electrons from the anion; for binary covalent semiconductors, the shell DFT-1 / 4-1 / 4 method is used, stripping 0.25 electrons from each of the anion and cation. However, in reality, the actual bonds are not ideal ionic or covalent bonds, but a mixture of both. Therefore, although the band gap can be improved by correcting the band gap using the above methods, there is still a certain difference from the experimental values. For aluminum nitride, the band gap value calculated using the ordinary local density approximation is 4.4 eV, with an error of 29.37% compared to the experimental value of 6.23 eV (T=0K); while the band gap value calculated using the shell LDA-1 / 4-1 / 4 method is 5.57, with an error of 10.59% compared to the experimental value, both showing a certain discrepancy from the experimental values. Accurately describing the electronic structure of aluminum nitride wurtzite ferroelectric materials is of great significance for exploring novel ferroelectric wurtzite type III nitride solid solutions and novel aluminum nitride-based devices. Summary of the Invention

[0005] In view of the above-mentioned defects or improvement needs of the prior art, the present invention provides a method for calculating the band structure of aluminum nitride zinc ferroelectric materials, the purpose of which is to solve the technical problem of low accuracy in describing the electronic structure of aluminum nitride zinc ferroelectric materials in the prior art.

[0006] To achieve the above objectives, according to one aspect of the present invention, a method for calculating the band structure of aluminum nitride zircon ferroelectric materials is provided, comprising:

[0007] S1: Determine the first POSCAR file corresponding to the original crystal structure of the aluminum nitride zinc ferroelectric material, and input the first INCAR file, the first POSCAR file, the first POTCAR file, and the first KPOINTS file into VASP software to optimize the original crystal structure to obtain the second POSCAR file;

[0008] S2: Using the second INCAR file, the second POSCAR file, the first POTCAR file, and the second KPOINTS file, the first spherical shell density functional theory algorithm is used to perform self-energy correction to obtain the cutoff radius;

[0009] S3: Calculation of trivalent aluminum ions (Al) 3+ The enhancement factor value corresponding to the self-energy potential is obtained by inputting the cutoff radius and the enhancement factor value into the second type of spherical shell density functional theory algorithm to obtain multiple band gap theoretical values. The multiple band gap theoretical values ​​are compared with the band gap experimental values ​​to find the covalent bond strength value corresponding to the band gap experimental value with the smallest difference.

[0010] S4: Use the POTCAR file in the covalent bond strength value directory as the second POTCAR file; input the second INCAR file, the second POSCAR file, the second POTCAR file, and the third KPOINTS file into the VASP software for self-consistent calculation to obtain the CHGCAR file;

[0011] S5: Input the CHGCAR file, the third INCAR file, the second POSCAR file, the second POTCAR file, and the row-mode KPOINTS file into the VASP software to perform band structure calculations for aluminum nitride zinc ferroelectric materials.

[0012] Furthermore, prior to S2, the following is also included:

[0013] The second INCAR file, the second POSCAR file, the first POTCAR file, and the second KPOINTS file are input into the VASP software for self-consistent calculation to export the WAVECAR file;

[0014] S2 includes:

[0015] The cutoff radius is obtained by performing self-energy correction using the WAVECAR file, the second INCAR file, the second POSCAR file, the first POTCAR file, and the second KPOINTS file.

[0016] Furthermore, the cutoff radius is Al: 1.4-3.3, N: 0.8-2.4.

[0017] Furthermore, the first type of spherical shell density functional theory algorithm is the shell DFT-1 / 4-1 / 4 algorithm.

[0018] Furthermore, the second type of spherical shell density functional theory algorithm is: shell DFT-xy; where x is the covalent bond strength value, y is an intermediate variable, and x+y=1 / 2.

[0019] Furthermore, the theoretical values ​​of the multiple band gaps include 0.09-0.16.

[0020] Furthermore, the enhancement factor value corresponding to the self-potential of the trivalent aluminum ion is 3.47.

[0021] Furthermore, in the first INCAR file, the plane wave cutoff kinetic energy ENCUT = 600 eV;

[0022] The pseudopotentials selected in the first POTCAR file are the 3-electron aluminum and 5-electron nitrogen pseudopotentials of PAW provided by VASP software;

[0023] The product of the K-point value and the lattice constant in the first KPOINTS file is...

[0024] Further, S5 includes:

[0025] The CHGCAR file, the third INCAR file, the second POSCAR file, the second POTCAR file, and the row-mode KPOINTS file are input into the VASP software, and the band structure of the aluminum nitride zinc ferroelectric material is calculated according to the path of ALMGAHKG with the high symmetry point selected.

[0026] Furthermore, the product of the K-point value in the third KPOINTS file and the lattice constant is...

[0027] In summary, compared with the prior art, the above-described technical solutions conceived by this invention can achieve the following beneficial effects:

[0028] (1) This invention provides a method for calculating the band structure of aluminum zinc nitride ferroelectric materials. The method uses a first type of spherical density functional theory algorithm to obtain the cutoff radius by self-energy correction, and a second type of spherical density functional theory algorithm to obtain multiple theoretical band gap values. The method finds the covalent bond strength value of the experimental band gap value that has the smallest difference from the experimental band gap value. The method considers the case where the self-energy potential of the actual element is stronger than that of the atomic state. At the same time, the A value of the self-energy potential corresponding to the cation and the value of the covalent bond strength are used to reasonably correct the band structure of aluminum zinc nitride ferroelectric materials. Finally, the band structure of aluminum zinc nitride ferroelectric materials is calculated, which can accurately and efficiently describe the band structure of aluminum zinc nitride ferroelectric materials. Attached Figure Description

[0029] Figure 1 A flowchart illustrating a method for calculating the band structure of a zinc nitride ferroelectric material provided in an embodiment of the present invention;

[0030] Figure 2a A schematic diagram of the original crystal structure of the aluminum nitride zinc ferroelectric material provided in an embodiment of the present invention;

[0031] Figure 2b This is a schematic diagram of the local density approximation calculation of the aluminum nitride band structure provided in an embodiment of the present invention;

[0032] Figure 3 A schematic diagram illustrating the calculation of the aluminum nitride band structure using the shell local density approximation of -1 / 4 to -1 / 4, provided in an embodiment of the present invention;

[0033] Figure 4A schematic diagram illustrating the calculation of the aluminum nitride band structure using the shell local density approximation of -0.12A3.47-0.38, provided for embodiments of the present invention;

[0034] Figure 5 The partial density of states diagram of scandium-doped aluminum nitride provided in an embodiment of the present invention. Detailed Implementation

[0035] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0036] like Figure 1 As shown, this embodiment of the invention provides a method for calculating the band structure of aluminum nitride zircon ferroelectric materials, including:

[0037] S1: Determine the first POSCAR file corresponding to the original crystal structure of the aluminum nitride zinc ferroelectric material, and input the first INCAR file, first POSCAR file, first POTCAR file and first KPOINTS file into VASP software to optimize the original crystal structure and obtain the second POSCAR file;

[0038] S2: The cutoff radius is obtained by performing self-energy correction using the second INCAR file, the second POSCAR file, the first POTCAR file, and the second KPOINTS file.

[0039] S3: Calculation of trivalent aluminum ions (Al) 3+ The enhancement factor value corresponding to the self-energy potential is obtained by inputting the cutoff radius and enhancement factor value into the second type of spherical shell density functional theory algorithm to obtain multiple band gap theoretical values. The multiple band gap theoretical values ​​are compared with the band gap experimental values ​​to find the covalent bond strength value corresponding to the band gap experimental value with the smallest difference.

[0040] S4: Use the POTCAR file in the covalent bond strength value directory as the second POTCAR file; input the second INCAR file, the second POSCAR file, the second POTCAR file, and the third KPOINTS file into VASP software for self-consistent calculation to obtain the CHGCAR file;

[0041] S5: Input the CHGCAR file, third INCAR file, second POSCAR file, second POTCAR file, and line-mode KPOINTS file into VASP software to perform band structure calculations for aluminum nitride zinc ferroelectric materials.

[0042] As a preferred embodiment, the original crystal structure is a unit cell.

[0043] As a preferred embodiment, the plane wave cutoff kinetic energy ENCUT = 600 eV in the first INCAR file; the pseudopotential in the first POTCAR file is selected as the 3-electron aluminum and 5-electron nitrogen pseudopotentials of PAW provided by VASP software; the K-point value in the first KPOINTS file multiplied by the lattice constant is...

[0044] in, Figure 2a This is a schematic diagram of the atomic structure of aluminum wurtzite ferroelectric material. The positions of the two Al atoms are represented by fractional coordinates as (0.667, 0.333, 0.500) and (0.333, 0.667, 1.000), respectively, and the positions of the two N atoms are (0.667, 0.333, 0.878) and (0.333, 0.667, 0.378), respectively. A POSCAR input file for VASP is established; the POTCAR pseudopotential file selects the PAW-local density approximation pseudopotential provided by VASP; KPOINTS uses a Gamma-centered mesh to sample the Brillouin zone, with each K point having a value of 31×31×19; INCAR selects the local density approximation exchange correlation functional, the plane wave cutoff kinetic energy ENCUT is set to 600 eV, and the electronic step convergence criterion EDIFF is set to 1E-4.

[0045] In a preferred embodiment, before S2, the method further includes: inputting the second INCAR file, the second POSCAR file, the first POTCAR file, and the second KPOINTS file into VASP software for self-consistent calculation to export a WAVECAR file. S2 includes: using the WAVECAR file, the second INCAR file, the second POSCAR file, the first POTCAR file, and the second KPOINTS file to perform self-energy correction using a first type of spherical shell density functional theory algorithm to obtain the cutoff radius.

[0046] The optimized structure is the CONTCAR generated in S1. Importing it into VASP software, its lattice constant is... Therefore, the KPOINTS value in this step is 11×11×7; the INCAR electronic step convergence criterion EDIFF is set to 1E-5, and LWAVE = .TRUE. The WAVECAR file, second INCAR file, second POSCAR file, first POTCAR file, and second KPOINTS file are modified using the Tool.exe program to perform a shell local density approximation -1 / 4 to -1 / 4 correction on the POTCAR file, obtaining the cutoff inner and outer diameters of the two atoms. These inner and outer diameters must maximize the band gap of the semiconductor to satisfy the variational method requirements. Among these... Figure 2b A schematic diagram of the band structure of aluminum nitride for local density approximation calculation. Figure 3 A schematic diagram of the aluminum nitride band structure calculated for shell LDA-1 / 4-1 / 4.

[0047] In this embodiment, the cutoff radius of A1 is (1.4, 3, 3), and the cutoff radius of N is (0.8, 2.4), where the exponential factor n of the self-potential cutoff function is 20; Al is exported using the Tool.exe program. 3+ The self-potential of the ion was calculated, and the scaling factor A was found to be 3.47 at a radius of 1 Bohr. The cutoff radius and A value were written into a file named xy.in, with the first line showing 20, the second line showing 11.43.33.47, and the third line showing 20.82.41. This xy.in file, along with the four input files and the WAVECAR file, was placed in the same folder. Running Tool.exe yielded the bandgap values ​​for x values ​​from 0.01 to 0.25 using the shell DFT-xy method. We found that the bandgap values ​​of the aluminum nitride wurtzite ferroelectric material were in good agreement with experimental values ​​when x = 0.09-0.16. As shown in Table 1, the maximum error was 1.35%, and the minimum error was only 0.16%. In contrast, the error of the ordinary local density approximation was as high as 29.37%, and the error of the shell local density approximation method (-1 / 4 to 1 / 4) was 10.59%, demonstrating the excellent effect of this invention.

[0048] Table 1

[0049] 9 6.31 1.35 10 6.29 0.97 11 6.27 0.6 12 6.24 O.16 13 6.22 0.16 14 6.2 0.51 15 6.18 0.88 16 6.15 1.24

[0050] As a preferred implementation, the first spherical density functional theory algorithm is the shellDFT-1 / 4-1 / 4 algorithm.

[0051] As a preferred implementation, the second spherical shell density functional theory algorithm is: shellDFT-xy; where x is the covalent bond strength value, y is an intermediate variable, and x+y=1 / 2.

[0052] S4 involves using the value of x obtained from S3 to find the corrected POTCAR file in the corresponding directory, placing it in the same folder as the other three input files in S2, setting the value of KPOINTS to 17×17×11, and performing self-consistent calculations.

[0053] As a preferred implementation, S5 includes: inputting the CHGCAR file, the third INCAR file, the second POSCAR file, the second POTCAR file, and the row-mode KPOINTS file into the VASP software, and performing band structure calculations for the aluminum zinc nitride ferroelectric material according to the path where the high symmetry point is selected as ALMGAHKG.

[0054] As a preferred implementation, the K-point value in the third KPOINTS file is multiplied by the lattice constant to a value of 40-50.

[0055] As a preferred implementation, the third INCAR file contains SIGMA=0.01, NBANDS=24, and ICHARG=11.

[0056] S5 places the CHGCAR obtained in S4, the corrected POTCAR, and the structure-optimized POSCAR into the same folder. The KPOINTS here are different from those in the above steps and need to be written in line mode. In this embodiment, the high symmetry point is selected as ALMGAHKG, and the corresponding fractional coordinates are (0.0 0.0 0.5)(0.0 0.5 0.5)(0.0 0.5 0.0)(0.0 0.0 0.0)(0.00.0 0.5)(-0.333 0.667 0.5)(-0.333 0.667 0.0)(0.0 0.0 0.0). The number of k points sampled in the middle of each high symmetry point is 101. Since this step involves a non-self-consistent calculation, INCAR needs to be configured with NBANDS. In this embodiment, NBNDS is 24, SIGMA = 0.01, and ICHARG = 11 to construct the initial charge density. The electronic step convergence criterion EDIFF is set to 1E-5. After the calculation is complete, Tool.exe is run for post-processing. The energy range is selected as (-20, 20). The obtained K-points and eigenvalues ​​are processed to generate an Ek.txt file, which is then imported into Origin software for plotting. (See attached...) Figure 4 The image shows the aluminum nitride band structure after correction to the shell local density approximation of -0.12A3.47-0.38. The band gap is in excellent agreement with experimental values. (See attached image.) Figure 5 The figure shown is a partial density of states diagram of scandium-doped aluminum nitride calculated further. This method is applicable to aluminum nitride wurtzite ferroelectric materials.

[0057] The terms “first,” “second,” etc. (if present) in this invention and its accompanying drawings are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence.

[0058] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present 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 calculating the band structure of alumina zirconium ferroelectric material, characterized in that, include: S1: Determine the first POSCAR file corresponding to the original crystal structure of the aluminum nitride zinc ferroelectric material, and input the first INCAR file, the first POSCAR file, the first POTCAR file, and the first KPOINTS file into VASP software to optimize the original crystal structure to obtain the second POSCAR file; S2: Using the second INCAR file, the second POSCAR file, the first POTCAR file, and the second KPOINTS file, the first spherical shell density functional theory algorithm is used to perform self-energy correction to obtain the cutoff radius; S3: Calculation of trivalent aluminum ions The enhancement factor value corresponding to the self-energy potential is obtained by inputting the cutoff radius and the enhancement factor value into the second type of spherical shell density functional theory algorithm to obtain multiple band gap theoretical values. The multiple band gap theoretical values ​​are compared with the band gap experimental values ​​to find the covalent bond strength value corresponding to the band gap experimental value with the smallest difference. S4: Use the POTCAR file in the covalent bond strength value directory as the second POTCAR file; input the second INCAR file, the second POSCAR file, the second POTCAR file, and the third KPOINTS file into the VASP software for self-consistent calculation to obtain the CHGCAR file; S5: Input the CHGCAR file, the third INCAR file, the second POSCAR file, the second POTCAR file, and the line-mode KPOINTS file into the VASP software to perform band structure calculations for the aluminum zinc nitride ferroelectric material; Before step S2, the method further includes: inputting the second INCAR file, the second POSCAR file, the first POTCAR file, and the second KPOINTS file into the VASP software for self-consistent calculation to export the WAVECAR file; step S2 includes: using the WAVECAR file, the second INCAR file, the second POSCAR file, the first POTCAR file, and the second KPOINTS file to perform self-energy correction using the first type of spherical shell density functional theory algorithm to obtain the cutoff radius; In the first INCAR file, the plane wave cutoff kinetic energy ENCUT = 600 eV, or can be reduced to between 450 eV and 500 eV as needed; The pseudopotentials selected in the first POTCAR file are the 3-electron aluminum and 5-electron nitrogen pseudopotentials of PAW provided by VASP software; The value of point K in the first KPOINTS file multiplied by the lattice constant is 90-100 Å; S5 includes: inputting the CHGCAR file, the third INCAR file, the second POSCAR file, the second POTCAR file, and the row-mode KPOINTS file into the VASP software, and performing non-self-consistent band structure calculations for aluminum nitride zirconite ferroelectric materials according to the path with the high symmetry point selected as ALMGAHKG.

2. The method for calculating the band structure of aluminum nitride zirconium ferroelectric materials as described in claim 1, characterized in that, The cutoff radius is Al: 1.4-3.3, N: 0.8-2.

4.

3. The method for calculating the band structure of aluminum nitride zinc ferroelectric materials as described in claim 1, characterized in that, The first type of density functional theory algorithm for spherical shells is the shell DFT-1 / 4-1 / 4 algorithm.

4. The method for calculating the band structure of aluminum nitride zinc ferroelectric materials as described in claim 3, characterized in that, The second type of density functional theory algorithm for spherical shells is: shell DFT-xy; Where x is the covalent bond strength value, y is an intermediate variable, and x+y=1 / 2.

5. The method for calculating the band structure of aluminum nitride zinc ferroelectric materials as described in claim 4, characterized in that, The theoretical values ​​for multiple band gaps range from 0.09 to 0.

16.

6. The method for calculating the band structure of aluminum nitride zirconium ferroelectric materials as described in claim 4, characterized in that, The enhancement factor value corresponding to the self-potential of the trivalent aluminum ion is 3.

47.

7. The method for calculating the band structure of aluminum nitride zinc ferroelectric materials as described in claim 1, characterized in that, The K-point value in the third KPOINTS file, multiplied by the lattice constant, is 40-50 Å.

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