A high-throughput calculation method for electrical transport performance based on deformation potential approximation

Abstract

The application discloses a high-throughput calculation method of electric transport performance based on deformation potential approximation. In the method, the electron relaxation time involved in the calculation of the electric transport performance is only considered as the electric-acoustic interaction, and the electric-acoustic interaction is described by using the deformation potential approximation. A high-throughput calculation method of the deformation potential constant is developed, the average value of the first band is used as a reference state, and the obtained deformation potential constant dataset is used for high-throughput electric transport performance calculation. Compared with the constant relaxation time approximation and the constant mean free path approximation method, the method has higher precision, and compared with the precise electric-acoustic coupling method, the method is more suitable for high-throughput calculation in terms of cost and time. The method is based on the MatHub-3d database, 11993 semiconductor materials are screened from the database, the deformation potential constants of the 11993 semiconductor materials are high-throughput calculated, and the electric transport performance of 10195 semiconductor materials is high-throughput predicted by using the deformation potential constant dataset.

Description

TECHNICAL FIELD

[0001] The present application relates to the performance prediction of thermoelectric materials, and particularly relates to a high-throughput calculation method for predicting the electrical transport performance of thermoelectric materials based on deformation potential approximation. BACKGROUND

[0002] In recent years, environmental pollution is increasing, and energy crisis is brewing. Fossil fuels are prone to emit a large amount of exhaust gas and waste heat during use. Direct emission of exhaust gas and waste heat can cause serious air pollution, such as greenhouse effect. Researchers have proposed many solutions, one of which is the multi-element and multi-stage efficient utilization of exhaust gas and waste heat. Through thermoelectric conversion technology, bidirectional conversion of heat and electricity can be realized. This technology not only converts exhaust gas and waste heat, but also fully utilizes solar energy, geothermal energy and other resources to realize thermoelectric energy conversion, so as to achieve full and effective utilization of resources. In addition, under the reverse effect, thermoelectric refrigeration can also be realized. Thermoelectric materials have the advantages of small size, light weight, low noise, no environmental pollution, precise temperature control, and have important application value in many fields. In the new energy automobile, electronic information and other new fields, thermoelectric materials are also needed to realize micro space efficient and rapid temperature control, local high heat flux density active thermal control and other functions. Therefore, it is of great significance to select efficient research tools and research methods to accelerate the application and development of thermoelectric materials.

[0003] The proposal of the material genome project makes the performance prediction of new materials by high-throughput calculation a new research paradigm. Under this background, researchers in the field of thermoelectric materials gradually break the traditional trial-and-error research mode, combine electronic information technology, and carry out high-throughput calculation research and high-throughput screening exploration to screen new potential thermoelectric materials with higher efficiency. The development of current high-throughput technology is maturing, and has become an important means of thermoelectric material research and development. However, most of the high-throughput electrical transport calculation is based on the constant relaxation time approximation, that is, the change of relaxation time in different systems or different carrier concentrations in the same system is ignored, and the precision is limited. If high-throughput calculation is combined with high-precision electrical transport method to realize higher precision method to predict the electrical transport performance of thermoelectric materials, it will be of great benefit to the search and research of new thermoelectric materials. SUMMARY

[0004] The purpose of the present application is to improve the prediction accuracy of electrical transport performance while not increasing the calculation cost and calculation time, and to propose a high-throughput calculation method for electrical transport performance based on deformation potential approximation. The method for predicting the electrical transport performance of thermoelectric materials does not depend on any empirical constant, and the deformation potential constant required is obtained through automatic calculation.

[0005] The introduction of the deformation potential approximation method is based on the following reasons:

[0006] Since the scattering terms of the material are mainly phonon scattering and impurity scattering, the phonon scattering is most affected by temperature, the higher the temperature, the more intense the phonon scattering, and the impurity scattering is affected by the impurity ions or crystal defects, the higher the impurity or defect concentration, the more significant the impurity scattering. Therefore, under low temperature environment, phonon scattering is weak, and impurity scattering has a greater impact, while under high temperature environment, phonon scattering will be dominant among all scattering terms. The accurate relaxation time calculation under the action of electroacoustic scattering can be expressed as:

[0007]

[0008] Where g mk’,nk is the electroacoustic coupling matrix element, n is the Bose-Einstein distribution of phonons, and q is the phonon frequency. The constant electroacoustic coupling approximates the electron scattering contribution under the action of electroacoustic interaction, and combines the contribution of the energy band change in the whole space, considering that only near the Fermi level, the energy band change has the greatest contribution to the scattering term, so g mk’,nk in equation (1) is regarded as a constant, and equation (1) is simplified as:

[0009]

[0010] Where C n,k is the approximate constant of electroacoustic coupling. The direct processing scheme for this constant is to select the empirical constant value of electroacoustic coupling. For this approximate constant, the deformation potential approximation theory is introduced. In the deformation potential theory, the average value of the electron-longitudinal acoustic phonon coupling probability is expressed as:

[0011]

[0012] Where E n is the deformation potential of the nth energy band, and for the sake of simplifying the calculation, the elastic modulus is replaced by the bulk modulus B. This theory only considers longitudinal acoustic phonons because the shear deformation potential generated by transverse acoustic phonons is negligible in the above research. Substituting equation (3) into equation (2), the relaxation time calculation formula of the deformation potential method is obtained:

[0013]

[0014] Under this approximate theory, only the deformation potential constant and the elastic constant need to be calculated to predict the electron relaxation time, and part of the electron-phonon interaction is considered, and it can also be realized under the background of high flux research.

[0015] The deformation potential constant of semiconductor material is an important physical parameter for describing the electron-phonon interaction of semiconductor, which contains important information of part of the energy level wave function, and can be represented by the phenomenon that the energy level in the semiconductor moves under a certain strain:

[0016]

[0017] where E is the energy at the valence band maximum and the conduction band minimum, E ref is the reference energy level, and lnV is the volume deformation. From the perspective of high-throughput implementation, the reference energy level calculated using the average value of the first band is determined.

[0018] The present application adopts the following technical solutions to achieve:

[0019] 1. A high-throughput calculation method for electrical transport performance based on deformation potential approximation, comprising the following steps:

[0020] 1) Using VASP software, the deformation potential and bulk modulus of 11993 semiconductor materials in the database are calculated by a high-throughput calculation method, the volume of the crystal unit cell is changed, and electronic self-consistent calculation is performed to obtain the deformation potential and bulk modulus constants of 11993 compounds. The deformation potential calculation formula is as follows:

[0021]

[0022] where E is the energy value at the valence band maximum and the conduction band minimum, E ref is the energy value of the reference energy level, which is taken as the average value of the first band, and lnV is the volume change rate;

[0023] 2) Set the linear fitting determination coefficient standard to screen compounds with good deformation potential constant fitting;

[0024] 3) Use VASP software to perform electronic structure calculation and screen out 10195 converged structures;

[0025] 4) Based on the calculation results of the above step 3), combined with the TransOpt2.0 program for post-processing, the electrical transport performance is calculated using the semi-empirical Boltzmann transport theory, and the calculation formula is as follows:

[0026]

[0027]

[0028] where ε nk and v nk are the energy eigenvalue and electron group velocity at the band number n and the inverse spatial coordinate k, respectively, and parameters T, μ, V, f μ , e are absolute temperature, Fermi energy level, unit cell volume, Fermi-Dirac distribution, and electron charge, respectively, and τ nk is the electron relaxation time. The deformation potential method is introduced for the processing of the electron relaxation time, and the relaxation time calculation formula under this method is as follows:

[0029]

[0030] k B TE 2 The electroacoustic coupling matrix element is approximately represented by n, which is the energy band number, k is the wave vector, E is the deformation potential, B is the bulk modulus, the deformation potential constant and the bulk modulus constant calculated in step 1) are substituted into formula (4) to calculate the relaxation time, T is the temperature, the temperature is 700K, and the electrical transport properties of 10195 compounds, including conductivity, Zerbach coefficient, Lorentz number and power factor, are obtained in this step.

[0031] Further, in step 1), the change of the unit cell lattice constant makes the volume of the unit cell become 98%, 99%, 100%, 101%, 102% of the equilibrium volume, the crystal parameters of the crystal structure are a, b, c, the high symmetry k point is set to 60 / a+1, 60 / b+1, 60 / c+1, and the energy convergence standard is 10 -4 eV, the cutoff energy is 520eV. When the deformation potential constant is calculated, the reference energy level E ref is determined, and the average value of the first energy band is set as the reference energy level for calculation.

[0032] Further, in step 2), the fitting conditions under different fitting parameters are comprehensively measured, and R 2 >0.95 is set as the criterion for good fitting.

[0033] Further, in step 3), the crystal parameters of the crystal structure are a, b, c, the high symmetry k point of the Brillouin zone is set to 240 / a+1, 240 / b+1, 240 / c+1, and the energy convergence standard is 10 -4 eV, and the cutoff energy is 520eV.

[0034] Further, in step 4), in the input file of TransOpt2.0, the energy zero point is set as the Fermi energy level, the energy starting point is the energy under the carrier concentration of 10 18 cm -3 , the energy interval is 0.001eV, the absolute temperature is 700K, the Gaussian smoothing factor is 0.5, and the deformation potential and bulk modulus parameters are the values calculated in step 1).

[0035] Compared with the prior art, the present application has the following obvious and substantial characteristics and advantages:

[0036] (1) The method of the present application realizes high-throughput calculation of deformation potential constant for the first time, which is of great significance for deformation potential data analysis on a large data scale.

[0037] (2) The method of the present application introduces a deformation potential approximation to predict the electrical transport properties of thermoelectric materials, which has higher calculation accuracy compared with the constant relaxation time approximation method, without increasing the calculation cost, calculation time and calculation difficulty; compared with the constant free path approximation method, the application object is wider, and it is suitable for all semiconductor materials.

[0038] (3) The method of the present application predicts more than ten thousand electrical transport properties, which can analyze the distribution trend of electrical conductivity, Zeebeck coefficient and power factor at the big data level, and has practical significance in the high-throughput field of electrical transport property prediction. BRIEF DESCRIPTION OF DRAWINGS

[0039] Figure 1 The high-throughput calculation flowchart of the present application;

[0040] Figure 2 The deformation potential constant fitting diagram under five volumes;

[0041] Figure 3 The change diagram of electrical conductivity, Zeebeck and power factor of TiCoSb at a temperature of 700K under different carrier concentrations;

[0042] Figure 4 The distribution relationship between the power factor and the absolute value of the deformation potential constant at a temperature of 700K and a Zeebeck coefficient of 180μV / K. DETAILED DESCRIPTION

[0043] The embodiments of the present application will be described in detail below through specific specific embodiments, and those skilled in the art can easily understand other advantages and effects of the present application from the content disclosed in the specification.

[0044] The present application will be described in detail below with reference to the accompanying drawings.

[0045] A high-throughput calculation method of electrical transport properties based on deformation potential approximation, comprising the following steps:

[0046] 1) Use VASP software to automatically calculate the deformation potential and bulk modulus of 11993 semiconductor materials in MatHub-3d database. Change the lattice constant of the crystal unit cell, simulate the deformation of the crystal, and perform electronic self-consistent calculation on the crystal structure under different deformations. The calculation in this step prepares for obtaining the deformation potential constant and the bulk modulus constant in step 2).

[0047] 2) Set the energy reference level as the average value of the first band, obtain the relative energy change value of the valence band top and the conduction band bottom under different deformations, and obtain the deformation potential constant according to formula (5), and set the linear fitting determination coefficient standard to screen the compounds with good deformation potential constant fitting. At the same time, use phonopy-qha to obtain the bulk modulus constant of the compound.

[0048] 3) Full-space electronic structure calculations were performed using VASP software, employing DFT+U. Because the calculated system included some systems with strongly correlated electrons, such as some 3d transition metal oxide systems, this calculation method can account for the interaction forces between electrons. Therefore, the calculation accuracy was improved by introducing a Coulomb repulsion term, i.e., using the DFT+U method for correction. A total of 10195 convergent structures were identified.

[0049] 4) Based on the calculation results of step 3), post-processing was performed using the TransOpt 2.0 program, and the electrical transport properties were calculated using the semi-empirical Boltzmann transport theory. This step yielded the electrical transport properties of 10195 compounds, including conductivity, Seebeck coefficient, Lorentz number, and power factor.

[0050] Example

[0051] This embodiment presents a high-throughput calculation method for electrical transport performance based on deformation potential approximation, comprising the following steps:

[0052] 1) The unit cell lattice constants of 11993 compounds were changed so that the unit cell volume became 98%, 99%, 100%, 101%, and 102% of the equilibrium volume. Electronic self-consistent calculations were then performed on the crystal structures at different volumes, and the energy converged to 10. - 4 The plane wave cutoff energy is 520 eV, and the high symmetry k-points are set to 60 / a+1, 60 / b+1, and 60 / c+1, where a, b, and c are the lattice parameters of the crystal.

[0053] 2) Extract the energy values ​​at the top of the valence band and the bottom of the conduction band of the compound at different volumes, and extract the average value of the first energy band as the reference energy level to obtain the relative changes in energy at the top of the valence band and the bottom of the conduction band. Obtain the deformation potential constant through linear fitting, and set R... 2 A value of >0.95 was used as the screening criterion for good fit, and 10,387 compounds with effective deformation potential constants were screened out. Figure 2 This is a fitting diagram of the deformation potential.

[0054] 3) Electrical transport calculations were performed using VASP. The crystal parameters of the crystal structure were a, b, and c. The high-symmetry k-points in the Brillouin zone were set to 240 / a+1, 240 / b+1, and 240 / c+1. The energy convergence criterion was 10. -4 The cutoff energy is 520 eV. 10195 convergent structures were calculated.

[0055] 4) Using the calculation results of step 3), the electrical transport process is carried out in combination with the TransOpt2.0 program, wherein in the input file of TransOpt2.0, the energy zero point is set as the Fermi energy level, the energy starting point is the energy under the carrier concentration 10 18 cm -3 , the energy interval is 0.001eV, the absolute temperature is 700K, the Gaussian smoothing factor is 0.5, and the deformation potential and bulk modulus parameters are the values calculated in step 1). The electrical transport performance of 10195 compounds is calculated, wherein Figure 3 is the distribution diagram of the electrical conductivity, the Zerbeck coefficient and the power factor of one of the materials TiCoSb at 700K under different carrier concentrations. And the relationship between the deformation potential and the power factor is revealed from the big data level, as shown in Figure 4 .

[0056] According to the traditional material research and development mode, it may take several years or even more than ten years to realize an effective electrical transport performance prediction of these materials. The above embodiment method can overcome the shortcomings of the traditional material screening method, and quickly realize the accurate electrical transport performance prediction of more than ten thousand compounds, which has higher accuracy than other methods such as constant relaxation time approximation, and is more cost-effective and time-saving than precise electroacoustic coupling method, and has strong high-throughput operability.

[0057] In summary, the above embodiment calculates the deformation potential constant of more than ten thousand compounds based on the MatHub-3d database, and uses the calculated deformation potential constant to introduce the deformation potential approximation method to calculate the electron relaxation time, and predicts the electrical transport performance of more than ten thousand compounds based on the Boltzmann transport equation, which improves the high-throughput prediction accuracy and ensures the feasibility, accuracy and time cost of high-throughput. It is the basis for subsequent experimental verification of potential new thermoelectric materials.

[0058] The above describes the embodiments of the present application in combination with the drawings, but the present application is not limited to the above embodiments, and various changes can be made according to the purpose of the present application. Any change, modification, substitution, combination or simplification made according to the spirit and principles of the technical solution of the present application shall be an equivalent replacement method, as long as it meets the purpose of the present application, as long as it does not deviate from the method of the present application for predicting the electrical transport performance of thermoelectric materials with high throughput. It belongs to the protection scope of the present application.

Claims

1. A method for high-throughput calculation of electrical transport properties based on deformation potential approximation, characterized in that, Comprising the following steps: 1) Calculate the deformation potential and bulk modulus of 11993 semiconductor materials in the database by high-throughput calculation method using VASP software, change the volume of the crystal unit cell, perform electronic self-consistent calculation, obtain the deformation potential and bulk modulus constants of 11993 compounds, and the calculation formula of the deformation potential is as follows: where E is the energy value of the valence band top and the conduction band bottom, E ref is the energy value of the reference energy level, here the average value of the first band, lnV is the volume change rate; 2) Set a linear fitting coefficient standard to screen compounds with good deformation potential constant fitting; 3) Perform electronic structure calculation using VASP software and screen out 10195 converged structures; 4) Based on the calculation results of the above step 3), combined with the post-processing of TransOpt2.0 program, calculate the electrical transport performance by semi-empirical Boltzmann transport theory, and the calculation formula is as follows: where ε nk and v nk are the energy eigenvalue and electron group velocity at the energy band number n and the inverse space coordinate k, respectively, and T, μ, V, f μ , e are the absolute temperature, Fermi energy level, unit cell volume, Fermi-Dirac distribution, and electron charge, respectively, and τ nk is the electron relaxation time, and the deformation potential method is introduced for the processing of the electron relaxation time, and the calculation formula of the relaxation time under the method is as follows: k B TE 2 / B approximates the matrix element of the electro- acoustic coupling, n is the band number, k is the wave vector, E is the deformation potential, B is the bulk modulus, the deformation potential constant and the bulk modulus constant calculated in step 1) are substituted into formula (4) for the calculation of the relaxation time, T is the temperature, the temperature is taken as 700K, and the electrical transport properties of 10195 compounds, including conductivity, Zabek coefficient, Lorentz number and power factor, are obtained in this step.

2. The method of claim 1, wherein, In the step 1), the lattice constant of the primitive cell is changed so that the volume of the primitive cell becomes 98%, 99%, 100%, 101%, 102% of the equilibrium volume, the crystal parameters of the crystal structure are a, b, c respectively, the high symmetry k point is set to 60 / a+1, 60 / b+1, 60 / c+1, and the energy convergence standard is 10 -4 eV, the cutoff energy is 520 eV, and the reference energy level E is determined when calculating the deformation potential constant ref , and the average value of the first band is set as the reference energy level for calculation.

3. The method of claim 1, wherein, In step 2), the fitting condition under different fitting parameters is comprehensively measured, and R 2 >0.95 is set as the criterion for good fitting.

4. The method of claim 1, wherein, In the step 3), the crystal parameters of the crystal structure are a, b, and c respectively, the high-symmetry k points of the Brillouin zone are set as 240 / a+1, 240 / b+1, and 240 / c+1, and the energy convergence standard is 10 -4 eV, and the cutoff energy is 520 eV.

5. The method of claim 1, wherein, In the step 4), in the input file of TransOpt2.0, the energy zero point is set as the Fermi level, the energy start point is the energy under the carrier concentration 10 18 cm -3 , the energy interval is 0.001eV, the absolute temperature is 700K, the Gaussian smoothing factor is 0.5, and the deformation potential and bulk modulus parameters are the calculated values in the step 1).

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