A calculation method for the defect properties of β-Ga2O3 single crystals

Abstract

The present invention provides a method for calculating the defect properties of β-Ga₂O₃ single crystals, including: constructing a primitive cell of β-Ga₂O₃, and by adjusting the ratio of HSE to PBE, selecting a hybrid parameter with a band gap consistent with the experimental value as the experimental parameter; expanding the primitive cell of β-Ga₂O₃ to obtain a supercell of β-Ga₂O₃; constructing a defect model in the β-Ga₂O₃ supercell, and performing structural optimization on the defect model, and performing self-consistent calculations on the defect model structure using the experimental parameter obtained in step S3; extracting the data of the calculation file in step S5 to obtain the defect formation energy and charge transfer energy level of the stable defect model. The method for calculating the defect properties of β-Ga₂O₃ single crystals provided by the present invention can avoid the problem of underestimating the band gap in β-Ga₂O₃ by using the hybrid functionals of HSE and PBE to calculate the defect formation energy and charge transfer energy level, and obtain calculation results closer to the experimental data.

Description

Technical Field

[0001] The present invention relates to the field of electronic technologies, and more particularly, to a method for calculating the defect properties of β-Ga2O3 single crystals. Background Art

[0002] Gallium oxide (Ga2O3) has five polycrystalline forms: α, β, γ, δ, and ε. Among them, the thermodynamically most stable one is the monoclinic β-phase, which has strong ionicity and a band gap close to 5 eV. It is also the only phase that can be grown by melt growth techniques (including the floating zone method, edge-defined film growth, and the Czochralski method), which makes it possible to mass-produce large-sized single crystal substrates. Based on these characteristics, β-Ga2O3 has become a candidate material for high-temperature gas sensors, high-voltage field-effect transistors, and solar-blind ultraviolet photodetectors. Moreover, β-Ga2O3 has also been proposed for use in low-wavelength tunable lasers, the n-type layer in thin-film heterojunction solar cells, and deep-ultraviolet transparent conductive oxides (TCOs) used as antistatic layers, etc.

[0003] Before applying the β-Ga2O3 material, it is necessary to comprehensively understand its electrical and optical active defects. At present, first-principles calculations based on density functional theory (DFT) have been used in the study of many material properties, such as optics, magnetism, and electronic structure. Theoretical calculations can provide in-depth understanding of materials and help us further understand the materials themselves. The formation energy of oxygen vacancies in β-Ga2O3 has been studied in the past few years, but different functionals and approximation methods will lead to differences in results. Among them, the generalized gradient approximation (GGA) and local density approximation (LDA) functionals cannot well describe the electronic structure of semiconductors, will underestimate the band gap in semiconductor materials, and thus the defect states caused by defects cannot be correctly processed. On the other hand, accurate methods such as the Hartree-Fock (HF) density functional, the Heyd-Scuseria-Ernzerhof (HSE) functional, and screened exchange are limited by computing resources and are difficult to obtain accurate results. Summary of the Invention

[0004] The problem to be solved by the present invention is how to provide a method that can quickly and accurately calculate the defect properties of β-Ga2O3 single crystals.

[0005] To solve at least one aspect of the above problems, the present invention provides a method for calculating the defect properties of β-Ga2O3 single crystals, including the following steps:

[0006] Step S1: Construct a primitive cell of β-Ga2O3, adjust the lattice parameters of the primitive cell of β-Ga2O3 to experimental values, and then perform ionic relaxation and structural optimization on it to obtain an optimized primitive cell of β-Ga2O3;

[0007] Step S2: Perform self-consistent calculations on the optimized β-Ga2O3 primitive cell using different k-points until the total energy of the primitive cell no longer changes with the variation of k-points. Then, select the k-points at this time to perform band structure calculations on the optimized β-Ga2O3 primitive cell. During the band structure calculation process, by adjusting the ratio of HSE to PBE, test the band gap widths of the optimized β-Ga2O3 primitive cell under different mixing parameters, and select the mixing parameter with a band gap width consistent with the experimental value as the experimental parameter;

[0008] Step S3: Expand the optimized β-Ga2O3 primitive cell to obtain a β-Ga2O3 supercell;

[0009] Step S4: Construct a defect model in the β-Ga2O3 supercell and perform structural optimization on the defect model until the structure of the defect model can reach one-step self-consistency to obtain a stable defect model structure;

[0010] Step S5: Select the experimental parameter obtained in Step S2 to perform self-consistent calculations on the stable defect model structure;

[0011] Step S6: Extract the data from the calculation files in Step S5 to obtain the defect formation energy and charge transfer energy level of the stable defect model, and establish a β-Ga2O3 defect property database.

[0012] Preferably, in Step S1, use the FINDIT software to find the lattice parameters of β-Ga2O3, and obtain the experimental values of the lattice parameters of β-Ga2O3 as a = 12.23, b = 3.04, c = 5.8, α = 90°, β = 103.7°, γ = 90°; where a, b, and c are the unit cell side length parameters of the lattice, and α, β, and γ are the three angle parameters of the unit cell of the lattice.

[0013] Preferably, in Step S1, use the VASP software to perform ion relaxation and structural optimization on the adjusted β-Ga2O3 primitive cell to minimize the energy of the β-Ga2O3 primitive cell.

[0014] Preferably, in Step S3, the scales of the β-Ga2O3 supercell in three directions are kept consistent, and the lattice size of the β-Ga2O3 supercell is greater than

[0015] Preferably, in Step S4, during the construction of the defect model, consider the lattice positions of different crystal structures, thereby constructing different defect models.

[0016] Preferably, in Step S4, perform structural optimization on the defect model to find the structure with the lowest energy of the defect model until the structure of the defect model can reach one-step self-consistency.

[0017] Preferably, in the step S6, the defect formation energy is calculated by the following formula:

[0018] E f [X q = E tot [X q - E tot [bulk] - ∑ i n i μ i + q[E F + E v + ΔV];

[0019] Wherein, E tot [X q is the total energy of the defect system, E tot [bulk] is the total energy of the supercell, n is the number of atoms increased or decreased in the defect system, μ is the chemical potential of the atoms increased or decreased in the defect system, q is the charge amount of the defect system, EF is the Fermi level, E v is the valence band bottom of the defect, ΔV is the correction term, and i is the atomic number.

[0020] Preferably, in the step S6, the charge transfer energy level is calculated by the following formula:

[0021]

[0022] Wherein, q1 is the charge state before transfer, q2 is the charge state after transfer, E f (X q1 ; E F = 0) is the defect formation energy with the Fermi level of 0 in the q1 charge state, E f (X q2 ; E F = 0) is the defect formation energy with the Fermi level of 0 in the q2 charge state, and ε(q1 / q2) is the conversion energy level between the q1 and q2 charge states of the defect.

[0023] In the present invention, by adjusting the lattice parameters of the β-Ga2O3 primitive cell to experimental values and optimizing its structure, a primitive cell structure consistent with the experimental values is constructed, enabling it to have the ability to accurately simulate experiments. Then, band calculations are performed under the K-point condition when the total energy no longer changes with the K-point, and by adjusting the ratio of HSE and PBE in the calculation process, the changes in the band gap under different hybrid parameter systems are tested. The hybrid parameters with a calculated structure consistent with the experimental values are selected as experimental parameters. Finally, calculations are performed on the supercell defect structure of the expanded β-Ga2O3 based on the hybrid functionals of HSE and PBE, thereby obtaining accurate data such as defect formation energy and charge transfer energy levels. The calculation method for the defect properties of β-Ga2O3 single crystals provided by the present invention uses the hybrid functionals of HSE and PBE to calculate the defect formation energy and charge transfer energy levels, which can avoid the problem of underestimating the band gap in β-Ga2O3 caused by GGA and LDA, and can obtain calculation results closer to experimental data. BRIEF DESCRIPTION OF THE DRAWINGS

[0024] Figure 1 It is a flowchart of the calculation method for the defect properties of β-Ga2O3 single crystals in the embodiments of the present invention;

[0025] Figure 2 It is a schematic diagram of the β-Ga2O3 primitive cell structure in the embodiments of the present invention;

[0026] Figure 3 It is a trend diagram of the energy change of the β-Ga2O3 primitive cell under different K-points in the embodiments of the present invention;

[0027] Figure 4 It is a trend diagram of the band gap change of the β-Ga2O3 primitive cell under different hybrid parameters in the embodiments of the present invention;

[0028] Figure 5 It is a schematic diagram of the β-Ga2O3 supercell structure in the embodiments of the present invention;

[0029] Figure 6 It is a schematic diagram of the gallium vacancy defect structure of the β-Ga2O3 supercell in the embodiments of the present invention;

[0030] Figure 7 It is a schematic diagram of the defect formation energy and conversion energy levels under different charge states of the gallium vacancy defect structure of β-Ga2O3 in the embodiments of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0031] To make the above objects, features, and advantages of the present invention more apparent and understandable, the following provides a detailed description of the specific embodiments of the present invention.

[0032] It should be noted that, without conflict, the features in the embodiments of the present invention can be combined with each other. The meanings of the terms "comprising", "including", "containing", and "having" are non-restrictive, that is, other steps and other components that do not affect the result can be added. The above terms cover the terms "consisting of" and "consisting essentially of". Unless otherwise specified, the materials, equipment, and reagents are commercially available.

[0033] An embodiment of the present invention provides a calculation method for the defect properties of β-Ga2O3 single crystals, as Figure 1 shown, including the following steps:

[0034] Step S1: Construct a primitive cell of β-Ga2O3, adjust the lattice parameters of the primitive cell of β-Ga2O3 to the experimental values, and then perform ion relaxation and structure optimization on it to obtain an optimized primitive cell of β-Ga2O3;

[0035] Step S2: Perform self-consistent calculations on the optimized primitive cell of β-Ga2O3 using different k-points respectively until the total energy of the primitive cell no longer changes with the change of the k-points. Then select the k-point at this time to perform band calculations on the optimized primitive cell of β-Ga2O3. During the band calculation process, by adjusting the ratio of HSE to PBE, test the band gap widths of the optimized primitive cell of β-Ga2O3 under different mixing parameters, and select the mixing parameter with the band gap width consistent with the experimental value as the experimental parameter;

[0036] Step S3: Expand the optimized primitive cell of β-Ga2O3 to obtain a supercell of β-Ga2O3;

[0037] Step S4: Construct a defect model in the supercell of β-Ga2O3 and perform structure optimization on the defect model until the structure of the defect model can reach one-step self-consistency to obtain a stable defect model structure;

[0038] Step S5: Select the experimental parameter obtained in Step S2 to perform self-consistent calculations on the stable defect model structure;

[0039] Step S6: Extract the data of the calculation file in Step S5 to obtain the defect formation energy and charge transfer energy level of the stable defect model, and establish a β-Ga2O3 defect property database.

[0040] In step S1, first, a primitive cell of β-Ga2O3 is constructed. The lattice parameters of β-Ga2O3 are found through the FINDIT software, and the experimental values of the lattice parameters of β-Ga2O3 are obtained as a = 12.23, b = 3.04, c = 5.8, α = 90°, β = 103.7°, γ = 90°. Here, a, b, and c are the side length parameters of the unit cell of the lattice, and α, β, and γ are the three angle parameters of the unit cell of the lattice. The lattice parameters of the constructed primitive cell of β-Ga2O3 are adjusted to the experimental values. Then, the VASP software is used to perform ionic relaxation and structural optimization on the primitive cell of β-Ga2O3 to minimize the energy of the primitive cell of β-Ga2O3, thereby obtaining a stable structure of the primitive cell of β-Ga2O3 and getting the optimized primitive cell of β-Ga2O3. Adjusting the lattice parameters of the primitive cell of β-Ga2O3 to the experimental values can more accurately simulate the real situation of the primitive cell of β-Ga2O3 and improve the accuracy of the result calculation.

[0041] In step S2, self-consistent calculations are performed on the optimized primitive cell of β-Ga2O3 using different k-points until the total energy of the primitive cell no longer changes with the change of the k-points. Then, the k-points at this time are selected to perform band calculations on the optimized primitive cell of β-Ga2O3. During the band calculation process, by adjusting the ratio of HSE to PBE, the band gap of the optimized primitive cell of β-Ga2O3 under different mixing parameters is tested, and the mixing parameter with the band gap consistent with the experimental value is selected as the experimental parameter. Calculating through the hybrid functional of HSE and PBE can avoid the problem of underestimating the band gap in β-Ga2O3 caused by GGA and LDA, thereby obtaining a calculation result closer to the experimental data. By adjusting the ratio of HSE and PBE to make the calculated band gap consistent with the experimental value, the accuracy of the calculation can be further improved, making the obtained calculation structure closer to the experimental data.

[0042] Specifically, the band gap of the primitive cell of β-Ga2O3 is 4.5 - 5.0 eV. When the ratio of HSE and PBE is adjusted, if the calculated band gap is within this range, it is used as the experimental parameter for subsequent calculations.

[0043] In step S3, the primitive cell of β-Ga2O3 is expanded. To balance the calculation accuracy and calculation resources, the size of the supercell of β-Ga2O3 after expansion is above. In addition, for the convenience of subsequent data processing, the scales of the β-Ga2O3 supercell in three directions should be kept consistent.

[0044] In step S4, a defect model is constructed in the β-Ga2O3 supercell. Among them, there are three lattice points for O atoms and two lattice points for Ga atoms in β-Ga2O3. When constructing the Ga vacancy defect model, there are two defect forms. For different lattice points, different defect models can be constructed. Then, the constructed defect models are structurally optimized to find the structure with the lowest energy of the defect model, and a stable defect model is obtained. In actual situations, the formation of defects is not simply removing or adding atoms from the supercell structure. The constructed defect models need to be structurally optimized to find the structure with the lowest energy of the defect model and then used for calculations, which can be closer to the experimental data.

[0045] Specifically, when structurally optimizing the defect model, the defect model needs to be optimized repeatedly until the structure after optimization can be self-consistent in one step when optimized again.

[0046] In step S5, the β-Ga2O3 supercell is self-consistently calculated using the experimental parameters obtained in step S3 to obtain the calculation results.

[0047] In step S6, key parameters are extracted from the calculation results of step S5, and the defect formation energy and charge transfer energy level of the defect model are calculated. Among them, the defect formation energy is calculated using the following formula:

[0048] E f [X q =E tot [X q -E tot [bulk]-∑ i n i μ i +q[E F +E v +ΔV];

[0049] Among them, E tot [X q is the total energy of the defect system, E tot [bulk] is the total energy of the supercell, n is the number of atoms increased or decreased in the defect system, μ is the chemical potential of the atoms increased or decreased in the defect system, q is the charge quantity of the defect system, EF is the Fermi level, E v is the valence band bottom of the defect, △V is the correction term, and i is the atomic number.

[0050] The charge transfer energy level is calculated using the following formula:

[0051]

[0052] Among them, q1 is the charge state before transfer, q2 is the charge state after transfer, E f (X q1 ;EF = 0) is the defect formation energy with the Fermi level of 0 for the q1 charge state, E f (X q2 ; E F = 0) is the defect formation energy with the Fermi level of 0 for the q2 charge state, and ε(q1 / q2) is the transition energy level between the q1 and q2 charge states of the defect;

[0053] Then, the calculation results are summarized to construct a defect property database of β-Ga2O3.

[0054] The following introduces the calculation method of the defect properties of β-Ga2O3 single crystal in combination with specific embodiments:

[0055] Embodiment

[0056] 1.1. First, construct the primitive cell of β-Ga2O3. By using the FINDIT software to search for the lattice parameters of β-Ga2O3, the experimental values of the lattice parameters of β-Ga2O3 are obtained as a = 12.23, b = 3.04, c = 5.8, α = 90°, β = 103.7°, γ = 90°. Among them, a, b, and c are the unit cell side length parameters of the lattice, and α, β, and γ are the three angle parameters of the unit cell of the lattice. Adjust the lattice parameters of the constructed β-Ga2O3 primitive cell to the experimental values; then, use the VASP software to perform ion relaxation and structure optimization on the β-Ga2O3 primitive cell. The geometric optimization calculation is completed using the PBE exchange correlation function. The Ga3d electrons are regarded as valence electrons, the cutoff energy of the plane wave basis is set to 400 eV, and the 3×3×3 Monkhorst-Pack k-point is used to minimize the energy of the β-Ga2O3 primitive cell, thereby obtaining a stable β-Ga2O3 primitive cell structure, where the structure of the β-Ga2O3 primitive cell is as Figure 2 shown;

[0057] 1.2. Perform self-consistent calculations on the optimized β-Ga2O3 primitive cell using different k-points until the total energy of the primitive cell no longer changes with the change of the k-point. Then, select the k-point at this time to perform band calculations on the optimized β-Ga2O3 primitive cell. During the band calculation process, by adjusting the ratio of HSE to PBE, test the band gap of the optimized β-Ga2O3 primitive cell under different mixing parameters, and select the mixing parameter with the band gap consistent with the experimental value as the experimental parameter. Among them, for HSE self-consistency, the Monkhorst-Pack k-point is set to 0.25, 0.25, 0.25;

[0058] Among them, Figure 3 is the schematic diagram of the change of the energy of the β-Ga2O3 primitive cell under different k-points. It can be seen from the figure that after the k-point is 6, the total energy of the primitive cell no longer changes with the change of the k-point; Figure 4The figure shows the variation trend of the band gap of the β-Ga2O3 primitive cell under different mixing parameters. Since the experimental value of the band gap of the β-Ga2O3 primitive cell is 4.5 - 5.0 eV, according to Figure 4 It can be seen that when AEXX of the HSE and PBE hybrid functionals is 0.30 and 0.32 respectively, the calculated band gap is within the range of the experimental values;

[0059] 1.3 Expand the cell of the β-Ga2O3 primitive cell. To balance the calculation accuracy and computational resources, the supercell structure of β-Ga2O3 after cell expansion is as shown in Figure 5 Figure, including 120 atoms. In addition, to facilitate subsequent data processing, the scales of the β-Ga2O3 supercell in three directions should be kept consistent;

[0060] 1.4 Construct a defect model in the β-Ga2O3 supercell. Among them, remove the Ga atom at the Ga1 lattice point to construct a gallium vacancy defect structure; optimize the structure of the constructed defect model to find the structure with the lowest energy of the defect model, obtain a stable defect model, and through repeated optimization in turn until the optimized structure can achieve self-consistency in one step when optimized again. Among them, the schematic diagram of the structure of the gallium vacancy defect model of the β-Ga2O3 supercell is as shown in Figure 6 Figure;

[0061] 1.5 Use AEXX = 0.30 as the experimental parameter to perform self-consistent calculations on the β-Ga2O3 supercell to obtain the calculation results;

[0062] 1.6 Extract key parameters from the calculation results in step 1.5, and calculate the defect formation energy and charge transfer energy level of the defect model. Among them, the defect formation energy is calculated using the following formula:

[0063] E f [X q = E tot [X q - E tot [bulk] - ∑ i n i μ i + q[E F + E v + ΔV];

[0064] Among them, E tot [X q is the total energy of the defect system, E tot [bulk] is the total energy of the supercell, n is the number of atoms increased or decreased in the defect system, μ is the chemical potential of the atoms increased or decreased in the defect system, q is the charge amount of the defect system, EF is the Fermi level, E v is the valence band bottom of the defect, △V is the correction term, and i is the atomic number.

[0065] The charge transfer energy level is calculated using the following formula:

[0066]

[0067] where q1 is the charge state before transfer, q2 is the charge state after transfer, and E f (X q1 ; E F = 0) is the defect formation energy with the Fermi level of the q1 charge state being 0, and E f (X q2 ; E F = 0) is the defect formation energy with the Fermi level of the q2 charge state being 0, and ε(q1 / q2) is the conversion energy level between the q1 and q2 charge states of the defect;

[0068] Figure 7 is the result diagram of the defect formation energy of the gallium vacancy defect structure and the conversion energy level under different charge states. As Figure 7 shown, the abscissa is the Fermi level E F , and when the Fermi level E F is 0 eV, it is called the valence band top E v , and when the Fermi level E F is 4.7 eV, it is called the conduction band bottom E C . The ordinate is the defect formation energy of V Ga1 . The kink points of the curve are the defect conversion energy levels of different charge states. For example, ε(0 / 1-) is E V +1.19, ε(1- / 2-) is E V +1.96, and ε(2- / 3-) is E V +2.24.

[0069] 1.7. Summarize the calculation results of step 1.6 to construct a defect property database of β-Ga2O3.

[0070] Although the present disclosure is disclosed as above, the protection scope of the present disclosure is not limited thereto. Those skilled in the art can make various changes and modifications without departing from the spirit and scope of the present disclosure, and these changes and modifications will all fall within the protection scope of the present invention.

Claims

1. A calculation method for the defect properties of β-Ga2O3 single crystals, characterized in that, It includes the following steps: Step S1: Construct a β-Ga2O3 primitive cell, adjust the lattice parameters of the β-Ga2O3 primitive cell to the experimental values, and then perform ionic relaxation and structural optimization on it to obtain the optimized β-Ga2O3 primitive cell; Step S2: Perform self-consistent calculations on the optimized β-Ga2O3 primitive cell using different k-points respectively until the total energy of the primitive cell no longer changes with the change of k-points. Then select the k-point at this time to perform band calculations on the optimized β-Ga2O3 primitive cell. During the band calculation process, by adjusting the ratio of HSE to PBE, test the band gap widths of the optimized β-Ga2O3 primitive cell under different mixing parameters, and select the mixing parameter with the band gap width consistent with the experimental value as the experimental parameter; Step S3: Expand the optimized β-Ga2O3 primitive cell to obtain a β-Ga2O3 supercell; Step S4: Construct a defect model in the β-Ga2O3 supercell and perform structural optimization on the defect model until the structure of the defect model can reach one-step self-consistency to obtain a stable defect model structure; Step S5: Select the experimental parameter obtained in Step S2 to perform self-consistent calculations on the stable defect model structure; Step S6: Extract the data of the calculation file in Step S5, obtain the defect formation energy and charge transfer energy level of the stable defect model, and establish a β-Ga2O3 defect property database.

2. The calculation method of the defect properties of β-Ga2O3 single crystal according to claim 1, characterized in that, In Step S1, use the FINDIT software to find the lattice parameters of β-Ga2O3, and the experimental values of the lattice parameters of β-Ga2O3 are obtained as a = 12.23, b = 3.04, c = 5.8, α = 90°, β = 103.7°, γ = 90°; where a, b, and c are the unit cell side length parameters of the lattice, and α, β, and γ are the three angle parameters of the unit cell of the lattice.

3. The calculation method for the defect properties of β-Ga2O3 single crystal according to claim 1, characterized in that, In Step S1, use the VASP software to perform ionic relaxation and structural optimization on the adjusted β-Ga2O3 primitive cell to make the energy of the β-Ga2O3 primitive cell reach the minimum value.

4. The calculation method of the defect properties of β-Ga2O3 single crystal according to claim 1, wherein In the step S3, the scales of the β-Ga2O3 supercell in three directions are kept consistent, and the lattice size of the β-Ga2O3 supercell is greater than 5. The calculation method for the defect properties of β-Ga2O3 single crystals according to claim 1, characterized in that, In Step S4, during the process of constructing the defect model, consider the lattice point positions of different crystal structures, so as to construct different defect models.

6. The calculation method for the defect properties of β-Ga2O3 single crystal according to claim 1, characterized in that, In Step S4, perform structural optimization on the defect model to find the structure with the lowest energy of the defect model until the structure of the defect model can reach one-step self-consistency.

7. The calculation method of the defect properties of β-Ga2O3 single crystal according to claim 1, characterized in that In Step S6, the defect formation energy is calculated using the following formula: E f [X q = E tot [X q - E tot [bulk] - ∑ i n i μ i + q[E F + E v + ΔV]; Among them, E tot [X q is the total energy of the defect system, E tot [bulk] is the total energy of the supercell, n is the number of atoms added or reduced in the defect system, μ is the chemical potential of the atoms added or reduced in the defect system, q is the charge quantity of the defect system, E F is the Fermi level, E v is the valence band bottom of the defect, ΔV is the correction term, and i is the atomic number.

8. The calculation method for the defect properties of β-Ga2O3 single crystal according to claim 1, wherein In Step S6, the charge transfer energy level is calculated using the following formula: Among them, q1 is the charge state before transfer, q2 is the charge state after transfer, and E f (X q1 ; E F = 0) is the defect formation energy with the Fermi level of the q1 charge state being 0, and E f (X q2 ; E F = 0) is the defect formation energy with the Fermi level of the q2 charge state being 0, and ε(q1 / q2) is the conversion energy level between the q1 and q2 charge states of the defect.

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