Design method for wearable two-dimensional asymmetric materials with high thermoelectric conversion efficiency

Abstract

The present invention discloses a design method for a wearable two-dimensional asymmetric material with high thermoelectric conversion efficiency. The method comprises: (1) designing a two-dimensional chalcogenide MXY with an asymmetric Janus structure, wherein M = {Mo, W, Hf, Zr} and X / Y = {S, Se, Te}; (2) calculating the stable configurations of 12 systems based on density functional theory, and calculating the electronic structure characteristics under the condition of spin-orbit coupling; (3) using electron Boltzmann transport theory, and considering the electron-phonon interaction, calculating the electrical conductivity, electronic thermal conductivity and Seebeck coefficient of the material; (4) simultaneously, using the phonon Boltzmann equation, obtaining the group velocity, scattering intensity and lattice thermal conductivity of the phonons, and obtaining the thermoelectric figure of merit of the material; (5) calculating the flexible mechanical properties of the system based on density functional theory, including fracture toughness and elastic modulus. The two-dimensional asymmetric material designed by the method of the present invention has the advantages of high room temperature thermoelectric conversion efficiency, high stability, and excellent mechanical properties.

Description

Technical Field

[0001] The present invention belongs to the field of wearable thermoelectric materials and relates to a design method for a wearable two-dimensional asymmetric material with high thermoelectric conversion efficiency. Background Art

[0002] The development of the Internet of Things (IoT) today urgently requires its components to harvest energy from the surrounding environment, thereby freeing them from the spatial constraints imposed by power transmission lines and batteries. Thermoelectric materials, utilizing the Seebeck effect, offer an ideal solution for extracting energy from ambient heat and converting it into the electrical energy required by the device. The parameter used to evaluate thermoelectric conversion efficiency is called the thermoelectric figure of merit, which is expressed as ZT = S 2 σ / (k e +k l ), S is the Seebeck coefficient, σ is the electrical conductivity, k is the thermal conductivity, and T is the absolute temperature. High-performance thermoelectric materials require a slow return to thermal equilibrium in their environment and high electrical transport properties. However, in real-world materials, due to the tight coupling of electrical and thermal transport, it is difficult to effectively achieve both high electrical and low thermal conductivity in the same material.

[0003] Wearable thermoelectric materials demand even higher intrinsic performance: they must simultaneously achieve high room-temperature thermoelectric conversion rates and stable mechanical properties. However, to date, most high-performance thermoelectric conversion materials require temperatures as high as 600K. Furthermore, the brittleness and poor ductility of thermoelectric materials have limited their application in the IoT. Organic thermoelectric materials exhibit excellent mechanical properties and flexibility, but their low power factor makes it difficult to provide sufficient power for practical wearable devices. For two-dimensional chalcogenides, M={Pd,Pt}, X / Y={S,Se,Te} have been reported as potential thermoelectric materials, but the mechanical properties of the materials as potential flexible wearable materials have not been described (Tao WL, Lan JQ, Hu CE, et al. Thermoelectric properties of Janus MXY(M=Pd,Pt;X,Y=S,Se,Te)transition-metal dichalcogenide monolayers from first principles[J]. J Appl Phys, 2020, 127(3):035101.).

[0004] In recent years, studies have shown that the Rashba effect can be used to effectively decouple various thermoelectric parameters, thereby dividing and conquering them and breaking through the bottleneck of low room-temperature thermoelectric conversion efficiency. Specifically, the unique electronic structure characteristics brought by the Rashba effect can simultaneously improve the Seebeck coefficient and electrical conductivity, which is difficult to achieve in traditional thermoelectric materials. In two-dimensional materials, the breaking of spatial symmetry can bring about significant vertical electric dipole effects. This electric dipole can cause the material to produce a strong Rashba effect, thereby improving the Seebeck coefficient and electrical conductivity. At present, many research groups have noticed the use of two-dimensional chalcogenides to improve the room-temperature thermoelectric conversion rate of materials, but the improvement is not significant (Hippalgaonkar K, Wang Y, Ye Y, et al. High thermoelectric power factor in two-dimensional crystals of MoS2[J]. Phys. Rev. B, 2017, 95(11): 115407.). The fundamental reason is that the spatial inversion symmetry of this type of material hinders the simultaneous improvement of the Seebeck coefficient and electrical conductivity. Summary of the Invention

[0005] To address the low room-temperature thermoelectric conversion efficiency, poor mechanical stability, and difficulty in simultaneously improving various thermoelectric transport parameters of existing thermoelectric materials, this paper provides a design method for wearable, two-dimensional asymmetric materials with high thermoelectric conversion efficiency. This design method, based on first-principles research and combined with Boltzmann transport theory, calculates the Rashba effect, thermoelectric transport, and mechanical properties of two-dimensional Janus-structured asymmetric chalcogenides. By screening Janus systems with different components, a design scheme that utilizes the Rashba effect to improve room-temperature thermoelectric conversion efficiency is proposed.

[0006] The technical solutions of the present invention are as follows:

[0007] The design method of wearable two-dimensional asymmetric materials with high thermoelectric conversion efficiency includes the following steps:

[0008] (1) Using Materials Studio software to model, the sulfur elements in the upper and lower layers of molybdenum disulfide were replaced by X / Y = {S, Se, Te}, while keeping the upper and lower layer elements different. Then, the metal elements were replaced by M = {Mo, W, Hf, Zr} to obtain the initial structures of twelve systems.

[0009] (2) Using VASP density functional calculation software, fully relaxed structural optimization is performed on the twelve systems. When the system reaches the preset energy and force convergence standards, the calculation is terminated to obtain a stable Janus structure. Then, the electronic structure characteristics are calculated under the stable Janus structure, including band structure, charge transfer, state density, projected state density, and projected band structure.

[0010] (3) Using PBE as the exchange-correlation functional approximation in the generalized gradient approximation, the electron spin-orbit coupling is considered to further calculate the band structure and state density of the material, and the magnetic anisotropy characteristics of the material;

[0011] (4) According to the Rashba effect judgment criteria, the estimated band edge Rashba splitting size is calculated, the characteristic energy range of the electronic structure in different dimensions caused by Rashba splitting is calculated, the energy value of the intersection point of the electronic structure dimension is determined, and the energy state density after considering the Rashba effect is further calculated;

[0012] (5) Based on the lattice scattering theory and electron-phonon coupling theory, calculate the scattering of electrons by lattice vibrations, and calculate the electron scattering intensity and electron scattering lifetime during the carrier transport process;

[0013] (6) Calculate the phonon spectrum of the material based on the density functional theory, and on this basis, obtain the phonon energy state density distribution and calculate the phonon group velocity;

[0014] (7) Based on the second and third order differentials of the energy of the density functional theory, the three-phonon scattering time, that is, the lifetime of the phonon in the lattice thermal conductivity, is obtained;

[0015] (8) According to the electron Boltzmann transport equation, the electron scattering lifetime obtained in step (5) is used to calculate the electron transport parameters, including electron mobility, electron conductivity, Seebeck coefficient, and electron thermal conductivity;

[0016] (9) Calculating the lattice thermal conductivity of the material using the phonon group velocity calculated in step (6) and the phonon lifetime calculated in step (7) according to the phonon Boltzmann equation;

[0017] (10) calculating the thermoelectric figure of merit of the material at a specific temperature and a specific doping concentration based on the electronic conductivity, electronic thermal conductivity, and Seebeck coefficient calculated in step (8) and the lattice thermal conductivity calculated in step (9);

[0018] (11) The fracture toughness and in-plane stiffness of the material were calculated based on the VASP density functional calculation software. By applying biaxial strain, the stress-strain curve of the system was calculated. The elastic modulus of the material was determined by performing six finite deformations on the lattice and deriving the elastic constants from the stress-strain relationship.

[0019] Furthermore, in step (2), the calculation methods of the band structure, charge transfer, density of states, projected density of states, and projected band structure are as follows:

[0020] Electronic structure calculations are performed on the stable Janus structure to obtain the optimized electron density function of the system, as well as the potential energy functional and kinetic energy functional with electron density as the variable. The kinetic energy and potential energy functionals are introduced into the Kohn-Sham equation to increase the number of electron wave vectors in the Brillouin zone and obtain the detailed energy state density distribution of the system; the high symmetry points in the Brillouin zone are determined, the electron wave vectors on the special path are determined, and the optimized Kohn-Sham equation is introduced to obtain the electron energy on the special path and the electronic band structure.

[0021] Furthermore, in step (5), the calculation method of the electron scattering intensity and the electron scattering lifetime is as follows:

[0022] The density functional theory is used to calculate the second-order potential energy differential and obtain the electron-phonon coupling matrix. The Wannier interpolation technique is used to obtain the high-density electron-phonon coupling matrix in the Brillouin zone. The electron self-energy is calculated using the electron-phonon coupling matrix, and the imaginary part of the electron self-energy, Im(Σ αk ) multiplied by a constant That is the electron lifetime τ αk , electron scattering intensity It is inversely proportional to the electron lifetime and its calculation formula is as follows:

[0023]

[0024] Among them, g αβ (k,q) is the electron-phonon matrix element, is the Bose-Einstein distribution function to describe the distribution of equilibrium phonon states, is the phonon energy corresponding to the wave vector q, f β,k is the Fermi-Dirac distribution function used to describe the distribution of equilibrium electronic states, ε β,k is the electron energy corresponding to the wave vector k. α(β) is the electron energy band (phonon mode) index, and k and q are the wave vectors of the electron and phonon states, respectively.

[0025] Furthermore, in step (8), the calculation formulas for the Seebeck coefficient, electronic conductivity, and electronic thermal conductivity are as follows:

[0026]

[0027]

[0028]

[0029] Where S is the Seebeck coefficient, σ is the conductivity, and k e is the electronic thermal conductivity; N is the total number of wave vectors in the Brillouin zone of the system, V is the effective volume of the two-dimensional system, ν nk is the electron group velocity.

[0030] Furthermore, in step (11), the calculation formula of the stress-strain curve is as follows:

[0031]

[0032] Where σ and ε are stress and strain respectively, V(ε) is the effective volume of the material, is the partial derivative of the total energy of the system with respect to strain;

[0033] The elastic modulus is calculated as follows:

[0034]

[0035] Among them, C ij is the elastic strain tensor matrix element, the coefficient

[0036] Compared with the prior art, the present invention has the following beneficial effects:

[0037] (1) By using first-principles calculation methods and combining the electron and phonon Boltzmann transport theory, the electrical conductivity, Seebeck coefficient, lattice thermal conductivity, power factor, thermoelectric conversion efficiency, and mechanical properties of two-dimensional Janus-structured asymmetric chalcogenides are calculated. The calculation of electrical and thermal transport, as well as the calculation of mechanical properties, provides a comprehensive and reliable theoretical basis for the design of room-temperature wearable thermoelectric materials.

[0038] (2) A new idea based on the synergistic effect of electric dipole and Rashba splitting to improve the room-temperature thermoelectric performance of materials was proposed, and it was found that the WSTe system has a very high room-temperature thermoelectric conversion efficiency, which is expected to provide sufficient power support for small wearable devices in the Internet of Things. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 This is a schematic diagram of the working principle of the Janus structure two-dimensional chalcogenide thermoelectric compound of the present invention.

[0040] Figure 2 This is the Janus structure two-dimensional chalcogenide compound crystal structure diagram and three-view drawing of the present invention.

[0041] Figure 3 This is the energy band diagram of the Janus structure MoSTe, MoSeTe, and MoSSe of the present invention.

[0042] Figure 4 This is the energy band diagram of the Janus structure WTe, WSeTe, and WSSe of the present invention.

[0043] Figure 5 This is the energy band diagram of the Janus structures HfSTe, HfSeTe, and HfSSe of the present invention.

[0044] Figure 6 It is the energy band diagram of the Janus structure ZrSTe, ZrSeTe and ZrSSe of the present invention.

[0045] Figure 7 This is a diagram of the electrostatic potential change of the Janus structure WSTe two-dimensional material of the present invention along the vertical plane direction.

[0046] Figure 8 This is the phonon dispersion diagram of the lattice vibration eigenmode of the Janus structure WSTe two-dimensional material of the present invention.

[0047] Figure 9 This is the energy state density diagram of the Janus structure WSTe two-dimensional material of the present invention.

[0048] Figure 10 This is the atomic orbital diagram near the band gap of the Janus structure WSTe two-dimensional material of the present invention.

[0049] Figure 11 This is a spin topology diagram of the Rashba effect in the Janus structure WSTe two-dimensional material of the present invention.

[0050] Figure 12 This is a graph showing the change in electrical conductivity of the Janus structure WSTe two-dimensional material of the present invention with temperature and doping concentration.

[0051] Figure 13 This is a graph showing the variation of the Seebeck coefficient of the Janus structure WSTe two-dimensional material of the present invention with temperature and doping concentration.

[0052] Figure 14 This is a graph showing how the power factor of the Janus structure WSTe two-dimensional material of the present invention changes with temperature and doping concentration.

[0053] Figure 15 This is a graph showing the change in lattice thermal conductivity of the Janus structure WSTe two-dimensional material of the present invention with temperature.

[0054] Figure 16 This is a graph showing how the quality factor of the Janus structure WSTe two-dimensional material of the present invention changes with temperature and doping concentration.

[0055] Figure 17 This is a comparison chart of the stress-strain curves of the Janus structure WSTe two-dimensional material and MoS2 of the present invention.

[0056] Figure 18 This is a comparison chart of the angle-dependent elastic modulus of the Janus structure WSTe two-dimensional material of the present invention and MoS2. DETAILED DESCRIPTION

[0057] The present invention will be further described in detail below with reference to the embodiments and accompanying drawings.

[0058] Example 1

[0059] (1) Using Materials Studio software to model, the sulfur elements in the upper and lower layers of molybdenum disulfide were replaced by X / Y = {S, Se, Te}, and the upper and lower layer elements were kept different. Then the metal elements were replaced by M = {Mo, W, Hf, Zr} to obtain the initial structures of the twelve systems. Then, the crystal information was exported and the structural information file POSCAR required by the VASP density functional calculation software was prepared, as shown in the figure. Figure 1 , 2;

[0060] (2) Using VASP density functional calculation software, the PBE in the generalized gradient approximation is used as the exchange correlation functional to describe the interaction between electrons. The two-dimensional layered structure adopts vacuum The model is simulated to reduce the interaction between layers, and the fully relaxed structure optimization is performed on the twelve systems. When the system reaches the preset energy and force convergence standards, the calculation is ended and a stable Janus structure is obtained. Then the electronic structure characteristics of the twelve stable Janus systems are calculated, including band structure, charge transfer, state density, projected state density, and projected band structure. Figure 3 , 4, 5, 6, after screening, the WSTe system has the optimal electronic structure - a large Rashba splitting and located at the top of the valence band. Then the electrostatic potential curve of the stable WSTe system along the vertical plane direction is calculated and divided by the effective thickness of the system to obtain the built-in electric field strength of the system, such as Figure 7 , and simultaneously calculate the phonon dispersion spectrum of the WSTe system, using an 8×8×1 q grid and increasing the energy convergence criterion to 10 -9 Ry, determines the thermodynamic stability of the WSTe system, such as Figure 8 ;

[0061] (3) Under the PBE as the exchange-correlation functional approximation in the generalized gradient approximation, the electron spin-orbit coupling effect is considered to obtain the wave function and charge density of the material, and the state density and orbital charge density of the WSTe system are further calculated to calculate the magnetic anisotropy characteristics of the material, such as Figure 9 , 10;

[0062] (4) According to the Rashba effect judgment criteria, the estimated band edge Rashba splitting size is calculated, the characteristic energy range of the electronic structure in different dimensions caused by Rashba splitting is calculated, the energy value of the intersection point of the electronic structure dimension is determined, and the electron spin orientation of the WST system after considering the Rashba effect is further calculated, such as Figure 11 ;

[0063] (5) Based on the lattice scattering theory and the electron-phonon coupling theory, the scattering of electrons by the lattice vibration of the WSTe system is calculated, in which the scattering caused by the acoustic and optical branches of phonons is fully considered. The interpolation method based on the Wannier function is used to achieve accurate interpolation of the electron-phonon matrix element. A dense K grid interpolation of 240×240×1 is used to accurately describe the state of electrons and phonons. Based on the electron scattering intensity calculation formula (1), the scattering intensity of carriers in the WSTe system during transport is calculated;

[0064] (6) Based on the phonon dispersion spectrum of the WSTe system calculated by density functional micro-winding theory, the phonon energy state density distribution is obtained and the phonon group velocity of the WSTe system is calculated;

[0065] (7) Based on the density functional theory, the second-order and third-order differentials of the energy of the WSTe system are calculated, and the three-phonon scattering time, that is, the lifetime of the phonons in the WSTe system lattice, is further obtained;

[0066] (8) According to the electron Boltzmann transport equation, the electron scattering lifetime obtained in step 5 is used to calculate the electron transport parameters of the WSTe system according to formulas (2), (3), and (4), including: electron conductivity, Seebeck coefficient, electron thermal conductivity, and power factor curves varying with temperature and carrier concentration, as shown in the following example: Figure 12 , 13, 14;

[0067] (9) According to the phonon Boltzmann equation, considering the four-neighbor interaction, using the phonon group velocity calculated in step 6 and the phonon lifetime calculated in step 7, the converged lattice thermal conductivity of the WSTe system is calculated under a q grid of 128×128×1, as follows: Figure 15 ;

[0068] (10) Based on the electronic conductivity, electronic thermal conductivity, and Seebeck coefficient calculated in step 8 and the lattice thermal conductivity calculated in step 9, the thermoelectric figure of merit of the WSTe system at a specific temperature and a specific doping concentration is calculated, as follows: Figure 16 The doping concentration of WSTe system at room temperature is 1.5×10 20 cm 3 The thermoelectric figure of merit is 0.41, which is 24 times higher than that of molybdenum disulfide;

[0069] (11) The fracture toughness and in-plane stiffness of the material were calculated based on the VASP density functional calculation software. By applying biaxial strain, the stress-strain curve of the WSTe system was calculated according to formula (5). Convergence tests were performed using cutoff energies of 500 eV, 550 eV, and 600 eV. When the cutoff energy was 550 eV, the elastic modulus had converged. In the calculation, the parameters IBRION = 6 and ISIF = 3 were set. The elastic tensor was determined by applying six finite deformations to the lattice and deriving the elastic constants from the stress-strain relationship. In this process, the relaxation of rigid ions was allowed. The elastic modulus calculated according to formula (6) includes the contribution of rigid ion deformation and the contribution of ion relaxation, as shown in the following example: Figure 17 ,18,The flexible mechanical properties of the WSTe system are comparable to those of molybdenum disulfide and have good flexibility.

[0070] The present invention is not limited to these. The above description is only a representative embodiment of the present invention and does not limit the patent scope of the present invention. Any equivalent structure or equivalent process transformation made by using the contents of the present invention description and drawings, or directly or indirectly applied in other related technical fields, are also included in the patent protection scope of the present invention.

Claims

1. A design method for wearable two-dimensional asymmetric materials with high thermoelectric conversion efficiency, characterized in that: The following steps are involved: (1) Using Materials Studio software to model, the sulfur elements in the upper and lower layers of molybdenum disulfide were replaced by X / Y = {S, Se, Te}, while keeping the upper and lower layer elements different. Then, the metal elements were replaced by M = {Mo, W, Hf, Zr} to obtain the initial structures of twelve systems. (2) Using VASP density functional calculation software, fully relaxed structural optimization is performed on the twelve systems. When the system reaches the preset energy and force convergence standards, the calculation is terminated to obtain a stable Janus structure. Then, the electronic structure characteristics are calculated under the stable Janus structure, including band structure, charge transfer, state density, projected state density, and projected band structure. (3) Using PBE as the exchange-correlation functional approximation in the generalized gradient approximation, the electron spin-orbit coupling is considered to calculate the band structure and state density of the material, and the magnetic anisotropy characteristics of the material; (4) According to the Rashba effect judgment criteria, the estimated band edge Rashba splitting size is calculated, the characteristic energy range of the electronic structure in different dimensions caused by Rashba splitting is calculated, the energy value of the intersection point of the electronic structure dimension is determined, and the energy state density after considering the Rashba effect is calculated; (5) Based on the lattice scattering theory and electron-phonon coupling theory, calculate the scattering of electrons by lattice vibrations, and calculate the electron scattering intensity and electron scattering lifetime during the carrier transport process; (6) Calculate the phonon spectrum of the material based on the density functional theory, and on this basis, obtain the phonon energy state density distribution and calculate the phonon group velocity; (7) Based on the second and third order differentials of the energy of the density functional theory, the three-phonon scattering time, that is, the lifetime of the phonon in the lattice thermal conductivity, is obtained; (8) According to the electron Boltzmann transport equation, the electron scattering lifetime obtained in step (5) is used to calculate the electron transport parameters, including electron mobility, electron conductivity, Seebeck coefficient, and electron thermal conductivity; (9) Calculating the lattice thermal conductivity of the material using the phonon group velocity calculated in step (6) and the phonon lifetime calculated in step (7) according to the phonon Boltzmann equation; (10) calculating the thermoelectric figure of merit of the material at a set temperature and a set doping concentration based on the electronic conductivity, electronic thermal conductivity, and Seebeck coefficient calculated in step (8) and the lattice thermal conductivity calculated in step (9); (11) The fracture toughness and in-plane stiffness of the material were calculated based on the VASP density functional calculation software. By applying biaxial strain, the stress-strain curve of the system was calculated. The elastic modulus of the material was determined by performing six finite deformations on the lattice and deriving the elastic constants from the stress-strain relationship.

2. The design method according to claim 1, characterized in that: In step (2), the calculation methods of band structure, charge transfer, density of states, projected density of states, and projected band structure are as follows: Electronic structure calculations are performed on the stable Janus structure to obtain the optimized electron density function of the system, as well as the potential energy functional and kinetic energy functional with electron density as the variable. The kinetic energy and potential energy functionals are introduced into the Kohn-Sham equation to increase the number of electron wave vectors in the Brillouin zone and obtain the detailed energy state density distribution of the system; the high symmetry points in the Brillouin zone are determined, the electron wave vectors on the special path are determined, and the optimized Kohn-Sham equation is introduced to obtain the electron energy on the special path and the electronic band structure.

3. The design method according to claim 1, characterized in that: In step (5), the calculation method of the electron scattering intensity and the electron scattering lifetime is as follows: The density functional theory is used to calculate the second-order potential energy differential and obtain the electron-phonon coupling matrix. The Wannier interpolation technique is used to obtain the high-density electron-phonon coupling matrix in the Brillouin zone. The electron self-energy is calculated using the electron-phonon coupling matrix, and the imaginary part of the electron self-energy, Im(Σ αk ) multiplied by a constant That is the electron lifetime τ αk , electron scattering intensity It is inversely proportional to the electron lifetime and its calculation formula is as follows: Among them, g αβ (k,q) is the electron-phonon matrix element, is the Bose-Einstein distribution function to describe the distribution of equilibrium phonon states, is the phonon energy corresponding to the wave vector q, f β,k is the Fermi-Dirac distribution function used to describe the distribution of equilibrium electronic states, ε β,k is the electron energy corresponding to the wave vector k, α is the electron energy band index, β is the phonon mode index, and k and q are the wave vectors of the electron and phonon states, respectively.

4. The design method according to claim 1, characterized in that: In step (8), the calculation formulas for the Seebeck coefficient, electronic conductivity, and electronic thermal conductivity are as follows: Where S is the Seebeck coefficient, τ αk is the electron lifetime, α is the electron band index, k is the wave vector of the electron state, σ is the conductivity, k e is the electronic thermal conductivity; N is the total number of wave vectors in the Brillouin zone of the system, V is the effective volume of the two-dimensional system, v αk is the electron group velocity.

5. The design method according to claim 1, characterized in that: In step (11), the calculation formula of the stress-strain curve is as follows: Where σ and ε are stress and strain respectively, V(ε) is the effective volume of the material, is the partial derivative of the total energy of the system with respect to the strain.

6. The design method according to claim 1, characterized in that: In step (11), the elastic modulus is calculated as follows: Among them, C ij is the elastic strain tensor matrix element, the coefficient

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