Method for searching for ferroelectric materials and ferroelectric materials

Abstract

A method for searching for ferroelectric materials, such as wurtzite crystal structures, that have low coercive fields and high spontaneous polarization values ​​using first-principles calculations is provided. [Solution] The method includes a first extraction step of obtaining, from a crystal structure database, ferroelectric material candidates with non-centrosymmetric symmetry as first candidates; a calculation step of calculating the band gap value, polarization reversal barrier energy value, and spontaneous polarization value of each first candidate obtained in the first extraction step using first-principles calculations; an insulating property determination step of determining whether the calculated band gap value satisfies insulating properties; a polarization reversal determination step of determining whether the calculated polarization reversal barrier energy value is within a range in which polarization reversal is possible; a spontaneous polarization determination step of determining whether the calculated spontaneous polarization value is within a range in which ferroelectric properties are exhibited; and a second extraction step of extracting, as ferroelectric materials, first candidates for which the determination results in the insulating property determination step, polarization reversal determination step, and spontaneous polarization determination step are all acceptable.

Description

[Technical Field]

[0001] The present invention relates to a search method for ferroelectric materials of various crystal structures, such as a wurtzite crystal structure, which have a low coercive field and a high spontaneous polarization value, using first-principles calculations, and to ferroelectric materials of various crystal structures, such as a wurtzite crystal structure, which have a low coercive field and a high spontaneous polarization value, searched for by the search method. [Background technology]

[0002] Ferroelectric materials such as lead zirconate titanate (PZT) have traditionally been widely used in nonvolatile ferroelectric memories, and in filters and actuators for mobile phones and personal computers, but many of these materials contain lead. In recent years, due to environmental concerns, there has been active research and development into lead-free ferroelectric materials, but many high-performance ferroelectric materials have a perovskite-type crystal structure consisting of oxygen octahedra or a similar structure. On the other hand, crystals with a wurtzite structure (space group P63mc) have been considered non-ferroelectric because of their non-centrosymmetric crystal structure, which makes polarization reversal difficult. However, in recent years, experimental demonstrations have been conducted to demonstrate their ferroelectricity. For example, the PE hysteresis loop of a Sc-doped AlN thin film with a wurtzite structure has been reported (see Non-Patent Document 1). However, the polarization reversal barrier energy of Sc-doped AlN thin films is very high, approximately two orders of magnitude higher than that of typical perovskite-type ferroelectric materials such as BaTiO3 and PbTiO3. To use ferroelectric materials in devices such as ferroelectric memories, a low polarization reversal barrier energy (e.g., approximately 100 kV / cm) is required, which has limited the practical applications of ferroelectric materials with a wurtzite structure.

[0003] As mentioned above, many high-performance lead-free ferroelectric materials have a perovskite-type crystal structure consisting of oxygen octahedra or similar structures. These have been thoroughly investigated, and a new breakthrough is needed: the discovery of a ferroelectric material with a crystal structure that does not contain oxygen octahedra. The present inventors focused on a simple wurtzite crystal structure that does not have an oxygen octahedron structure, as shown in Figure 12. Figure 12(a) shows the hexagonal wurtzite structure of the binary compound MX (space group P63mc). Figure 12(b) shows the polarization switching mechanism, where P = +P S ferroelectric state with P = 0, paraelectric (intermediate) state with P = -P after inversion of the MX4 tetrahedron by applying an electric field parallel to the c-axis S where δ is the displacement of the ion relative to its position in the intermediate state. The inventors then investigated its potential as a ferroelectric material using first-principles calculations and found that the polarization reversal barrier energy, a necessary characteristic for a ferroelectric, in ZnO is comparable to that of lead titanate (PbTiO3), a typical ferroelectric, and clarified at the atomic level the possibility of developing ferroelectric materials with simple wurtzite crystal structures that do not have oxygen octahedra (see Non-Patent Documents 2 and 3). Furthermore, they demonstrated that by examining the conditions for calculating the polarization reversal barrier energy using first-principles calculations, it is possible to search for ferroelectric materials with a wurtzite crystal structure (see Patent Document 1). [Prior art documents] [Non-patent literature]

[0004] [Patent Document 1] Japanese Patent Publication No. 2022-165348 [Non-Patent Document 1] S. Fichtner, N. Wolff, F. Lofink, L. Kienle, and B. Wagner, J. Appl. Phys., 125, 114103 (2019). [Non-patent document 2] H. Moriwake, A. Konishi, T. Ogawa, K. Fujimura, CAJ Fisher, A. Kuwabara, T. Shimizu, S. Yasui, and M. Itoh, Appl. Phys. Lett. 104, 242909 (2014). [Non-patent document 3] A. Konishi, T. Ogawa, CAJ Fisher, A. Kuwabara, T. Shimizu, S. Yasui, M. Itoh, and H. Moriwake, Appl. Phys. Lett. 109, 102903 (2016). Summary of the Invention [Problem to be solved by the invention]

[0005] On the other hand, the search method for wurtzite crystal structure ferroelectric materials shown in Patent Document 1 requires determining the spontaneous polarization from the centrosymmetric structure of the candidate dielectric material, and therefore cannot be applied to dielectric materials whose centrosymmetric structure is unknown. Furthermore, since no study has been conducted as to whether the dielectric materials searched for can be synthesized, it has been desired to be able to simultaneously determine whether the dielectric materials can be synthesized.

[0006] The present invention has been made in view of the above-mentioned current situation, and aims to provide a method for searching for ferroelectric materials of various crystal structures, such as a wurtzite crystal structure, which have a low coercive field and a high spontaneous polarization value, using first-principles calculations, and a ferroelectric material, such as a wurtzite crystal structure, which has a low coercive field and a high spontaneous polarization value, searched for by the above-mentioned searching method. [Means for solving the problem]

[0007] The present invention is as follows. 1. A method for searching for a ferroelectric material, characterized by searching for a ferroelectric material having a crystal structure with a low coercive field and a high spontaneous polarization value, a first extraction step of acquiring, as a first candidate, a ferroelectric material candidate having a non-centrosymmetric symmetry from a crystal structure database in which crystal structures of the ferroelectric material candidates are stored; a calculation step of calculating a band gap value, a polarization inversion barrier energy value, and a spontaneous polarization value of each of the first candidates obtained in the first extraction step by first-principles calculation; an insulating property determining step of determining whether the band gap value calculated in the calculating step satisfies insulating properties; a polarization reversal determination step of determining whether the polarization reversal barrier energy value calculated in the calculation step is within a range in which polarization reversal is possible; a spontaneous polarization determination step of determining whether the spontaneous polarization value calculated in the calculation step is within a range that indicates ferroelectricity; a second extraction step of extracting, as the ferroelectric material, the first candidate for which the results of the insulation determining step, the polarization reversal determining step, and the spontaneous polarization determining step are all acceptable; A method for searching for a ferroelectric material, comprising: 2. The calculation of the polarization inversion barrier energy value includes enumerating one or more centrosymmetric structure candidates from the first candidate space group, The method for searching for a ferroelectric material according to paragraph 1, further comprising: comparing an energy difference between the space group of the first candidate and the space group of the centrosymmetric structure candidate; extracting the centrosymmetric structure candidate with the shortest distance as an inverted structure; and setting the energy difference as a polarization inversion barrier energy. 3. The method for searching for ferroelectric materials according to 2. above, wherein the centrosymmetric structure candidates are enumerated using the PSEUDO code. 4. The calculation step calculates the phonon dispersion curve of each of the first candidates by first-principles calculation; an imaginary mode determination step of determining whether or not the phonon dispersion curve calculated in the calculation step does not include a curve indicating an imaginary mode; The method for searching for a ferroelectric material according to any one of 1. to 3., wherein the second extraction step extracts the first candidate as the ferroelectric material, the first candidate being one for which the judgment results of the insulation judgment step, the polarization reversal judgment step, the spontaneous polarization judgment step, and the imaginary mode judgment step are all acceptable. 5. The method for searching for a ferroelectric material according to 4 above, wherein the spontaneous polarization value is calculated by Berry phase calculation. 6. A method for searching for ferroelectric materials according to 5. above, in which one of the following codes is used for first-principles calculations: VASP code, CASTEP code, Quantum Espresso code, PWSCF code, PHASE code, STATE-SENRI code, QMAS code, and ABINIT code, with plane waves as basis functions. 7. A wurtzite crystal structure ferroelectric material having a wurtzite crystal structure selected from CdO, MgO, AgBr, AgI, CuCl and CuBr, or having an orthorhombic crystal structure of Li3AlF6, characterized in that the band gap value satisfies insulating properties, the polarization reversal barrier energy value is within a range in which polarization reversal is possible, the spontaneous polarization value is within a range in which ferroelectricity is exhibited, and the phonon dispersion curve does not include a curve indicative of an imaginary mode. [Effects of the Invention]

[0008] The method for searching for a ferroelectric material and the obtained wurtzite crystal structure ferroelectric material of the present invention include a first extraction step of acquiring a non-centrosymmetric ferroelectric material candidate as a first candidate from a crystal structure database in which crystal structures of ferroelectric material candidates having a wurtzite crystal structure or the like are stored; a calculation step of calculating a band gap value, a polarization inversion barrier energy value, and a spontaneous polarization value of each of the first candidates obtained in the first extraction step by first-principles calculation; an insulating property determination step of determining whether the band gap value calculated in the calculation step satisfies insulating properties; By providing a polarization reversal determination step of determining whether the calculated polarization reversal barrier energy value is within a range in which polarization reversal is possible, a spontaneous polarization determination step of determining whether the spontaneous polarization value calculated in the calculation step is within a range in which ferroelectricity is exhibited, and a second extraction step of extracting the first candidate for which the determination results in the insulating property determination step, the polarization reversal determination step, and the spontaneous polarization determination step are all acceptable as the ferroelectric material, it is possible to find a crystal structure with a high spontaneous polarization value that allows polarization reversal by confirming that the calculated band gap value, polarization reversal barrier value, and spontaneous polarization value are low, thereby making it easy to extract a target dielectric from a large number of candidates.

[0009] The polarization inversion barrier energy value is calculated by enumerating one or more centrosymmetric structure candidates from the first candidate space group, comparing the energy difference between the space group of the first candidate and the space group of the centrosymmetric structure candidate, and extracting the centrosymmetric structure candidate with the shortest distance as an inverted structure. When the energy difference is used as the polarization inversion barrier energy, it is possible to uniquely determine the inverted structure and the centrosymmetric structure used to determine whether or not a material is a ferroelectric, and to find a ferroelectric material with a low coercive field. Previously, the polarization reversal barrier energy value could not be calculated unless the inverted structure and centrosymmetric structure were known. However, by using the PSEUDO code to enumerate the centrosymmetric structure candidates, it was possible to enumerate centrosymmetric structure candidates based on the supergroup-subgroup of group theory, which is based on the space group, and to uniquely determine the centrosymmetric structure used to determine whether a material is ferroelectric, thereby discovering ferroelectric materials with low coercive fields.

[0010] The calculation step further includes an imaginary mode determination step of calculating the phonon dispersion curve of each of the first candidates by first-principles calculation and determining whether or not the phonon dispersion curve calculated in the calculation step does not include a curve indicating an imaginary mode. When the second extraction step extracts the first candidate for which the determination results in the insulation determination step, the polarization reversal determination step, the spontaneous polarization determination step, and the imaginary mode determination step are all positive, it is possible to search for candidates that are highly likely to be used to synthesize a ferroelectric material, and to significantly reduce candidate noise.

[0011] When the spontaneous polarization value is calculated by Berry phase calculation, it can be calculated based on first-principles calculation even for a crystal having periodicity. When using one of the following codes for first-principles calculations, which use plane waves as basis functions: VASP code, CASTEP code, Quantum Espresso code, PWSCF code, PHASE code, STATE-SENRI code, QMAS code, and ABINIT code, various values ​​calculated in the calculation step can be obtained reliably.

[0012] A wurtzite crystal structure ferroelectric material having a wurtzite crystal structure selected from CdO, MgO, AgBr, AgI, CuCl, and CuBr, or having an orthorhombic crystal structure which is Li3AlF6, characterized in that the band gap value satisfies insulating properties, the polarization reversal barrier energy value is in a range in which polarization reversal is possible, the spontaneous polarization value is in a range in which ferroelectricity is exhibited, and the phonon dispersion curve does not contain a curve indicating an imaginary mode, is a ferroelectric material with a low coercive field, a high spontaneous polarization value, and high synthesizability, and is expected to be put into practical use as a lead-free ferroelectric material with a low coercive field. [Brief explanation of the drawings]

[0013] The present invention will be further described by the following detailed description, which provides non-limiting examples of exemplary embodiments according to the present invention, and with reference to the mentioned drawings, in which like reference numerals refer to like parts throughout the several views of the drawings. [Figure 1] 1 is a flowchart illustrating the present method for searching for ferroelectric materials. [Figure 2] 1 is a table (1) showing the calculated lattice constants, band gaps, effective charges and spontaneous polarizations for binary compounds. [Figure 3] 1 is a table (2) showing the calculated lattice constants, band gaps, effective charges and spontaneous polarizations for binary compounds. [Figure 4] FIG. 1 is a graph showing the relationship between the anion / cation radius ratio and the polarization inversion barrier energy. [Figure 5] FIG. 1 shows the effect of ab-epitaxial strain on the ferroelectric potential barrier for AgCl, CuCl, and CuBr with the wurtzite structure. [Figure 6] Schematics showing the polarization reversal mechanism of MgO, showing (a) polarization upward, (b) no polarization, and (c) polarization downward. [Figure 7] 1 is a graph showing the phonon dispersion curve of MgO. [Figure 8] 1 is a graph showing the phonon dispersion curve of LiAgF2. [Figure 9] 1 is a graph showing the phonon dispersion curve of κ-Al2O3. [Figure 10] 1 shows the polarization reversal mechanism of LiAgF2, with (a) polarization upward, (b) no polarization, and (c) polarization downward. [Figure 11] Schematics showing the polarization reversal mechanism of κ-Al2O3, showing (a) polarization upward, (b) no polarization, and (c) polarization downward. [Figure 12] FIG. 1 is a schematic diagram showing a simple wurtzite crystal structure that does not have an oxygen octahedron structure. DETAILED DESCRIPTION OF THE INVENTION

[0014] The present invention will be described in detail below with reference to the drawings. The matters set forth herein are for illustrative purposes only and are intended to provide an illustrative description of the embodiments of the present invention, with the aim of providing what is believed to be the most effective and easily understandable explanation of the principles and conceptual features of the present invention. In this respect, it is not intended to show structural details of the present invention beyond the extent necessary for a fundamental understanding of the present invention, and the description, taken together with the drawings, will make clear to those skilled in the art how some aspects of the present invention may be actually embodied.

[0015] In the method for searching for ferroelectric materials according to this embodiment, a theoretical calculation method called first-principles calculation and materials informatics was used to comprehensively search for new materials with a wurtzite crystal structure.

[0016] Previously, the inventors estimated the coercive fields of a limited number of wurtzite-structure compounds by calculating the tetrahedral polarization reversal barrier energy (Non-Patent Documents 2 and 3). In this study, we expand the search of the compositional phase space to encompass a wider range of binary compounds and identify new ferroelectrics with low coercive fields (less than 100 kV / cm) under specified conditions. Furthermore, the ferroelectrics were searched from compounds experimentally confirmed to have the wurtzite structure under standard or non-standard conditions (e.g., high temperature, high pressure, nanosizing) and registered in the International Crystal Structure Database.

[0017] The method for searching for a ferroelectric material according to this embodiment includes a first extraction step (3) of acquiring, as a first candidate, a ferroelectric material candidate having a non-centrosymmetric symmetry from a crystal structure database (2) storing crystal structures of candidate ferroelectric materials; a calculation step (4) of calculating a band gap value, a polarization inversion barrier energy value, and a spontaneous polarization value of each of the first candidates obtained in the first extraction step (3) by first-principles calculation; and an insulating property determination step of determining whether the band gap value calculated in the calculation step (4) satisfies insulating properties. (51), a polarization reversal determination step (52) of determining whether the polarization reversal barrier energy value calculated in the calculation step (4) is within a range in which polarization reversal is possible, a spontaneous polarization determination step (53) of determining whether the spontaneous polarization value calculated in the calculation step (4) is within a range in which ferroelectricity is exhibited, and a second extraction step (6) of extracting the first candidate, whose determination results in the insulation determination step (51), the polarization reversal determination step (52) and the spontaneous polarization determination step (53) are all acceptable, as a ferroelectric material (see FIG. 1).

[0018] The calculation step (4) can calculate a phonon dispersion curve, and further includes an imaginary mode determination step (54) for determining whether or not the calculated phonon dispersion curve does not include a curve indicating an imaginary mode. The second extraction step (6) can extract, as a ferroelectric material, a first candidate for which the determination results of the insulation determination step (51), the polarization reversal determination step (52), the spontaneous polarization determination step (53), and the imaginary mode determination step (54) are all positive.

[0019] The crystal structure database is a database containing candidate ferroelectric materials, which are compositions whose crystal structures are known, and stores information on the atoms constituting the crystal of each composition and the arrangement of each atom in the crystal as a crystal structure. Such a database can be a known database such as the International Crystal Structure Database. The first-principles calculation for calculating the band gap value, polarization inversion barrier energy value, and spontaneous polarization value of each of the first candidates is performed by setting the k-point density to 0.5 / (10 -10 m) or less, the cutoff energy is 400 eV or more, and the force applied to atoms when the structure optimization is terminated is 0.1 eV / (10 -10 The structural optimization can be performed until the band gap value, the polarization inversion barrier energy value, and the spontaneous polarization value are calculated quickly. Then, the energies in the space group of the first candidate and the space group of the centrosymmetric structure candidate are determined, and the energy difference between the space group of the first candidate and the space group of the centrosymmetric structure candidate is taken as the polarization inversion barrier energy, and the polarization inversion barrier energy can be set to a certain value (for example, 0.22 eV / fu or less, and particularly preferably 0.2 eV / fu or less; here, "fu" represents a formula unit).

[0020] In this embodiment, first-principles calculations are performed using density functional theory (DFT) calculations implemented in VASP (Vienna Ab initio Simulation Package, plane wave basis method, reference: G. Kresse and J. Furthmuller, Phys. Rev. B 54, 11169 (1996)) to characterize each compound and evaluate its suitability as a candidate tetrahedral ferroelectric. For first-principles calculations, VASP code, CASTEP code, Quantum Espresso code, PWSCF code, PHASE code, STATE-SENRI code, QMAS code, ABINIT code, or the like, which use plane waves as basis functions, can be used.

[0021] All calculations are performed using the Perdew-Burke-Ernzerhof form of the generalized gradient approximation (GGA-PBE), optimized for solids, to handle the exchange-correlation terms. sol ) (Reference: J.P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev. Lett. 77, 3865 (1996)). A plane-wave based projector augmented-wave method (reference: P.E. Blochl, Phys. Rev. B 50, 17953 (1994)) was used with 2s and 2p electrons for Be, N, O, C and F, 3s and 3p electrons for Mg, Al, SiP, S and Cl, 4s and 4p electrons for As, Se and Br, 5s and 5p electrons for In, Sb, Te and I, 1s and 2s electrons for Li, 1s, 2s and 2p electrons for F, and 3d and 4s electrons for Mn, Cu and Zn treated as valence electrons.

[0022] A plane wave cutoff energy of 550 eV was used in all cases. The convergence of the total energy for cutoff energies up to 800 eV was better than 0.015 eV / fu.

[0023] In this embodiment, it is preferable to set the cutoff energy to 400 eV or more in the structural optimization calculation step (32) in order to ensure sufficient calculation accuracy (energy, force, structure).

[0024] Numerical integration is performed for the Γ-center generated according to the Monkhorst-Pack scheme (see HJ Monkhorst and JD Pack, Phys. Rev. B 13, 5188 (1976)) within the first Brillouin zone of a 4-atom wurtzite unit cell. -10 The calculation was performed using a k-point mesh with m spacing.

[0025] In this embodiment, in the structural optimization calculation step (32), the k-point density is set to 0.5 / (10 -10 m) or less, because a k-point density exceeding this level cannot ensure sufficient calculation accuracy (energy, force, structure).

[0026] In this embodiment, in the structural optimization calculation step (32), the force applied to the atoms at the structural optimization termination is set to 0.1 eV / (10 -10 m) or less, because if this is exceeded, sufficient calculation accuracy (energy, force, structure) cannot be ensured.

[0027] To reconcile the known underestimation of the electronic band gap of transition metal-containing compounds using the GGA method, we used U in the case of Mn-containing compounds. eff Added Hubbard U term of =3.6eV (Reference: SL Dudarev, GA Botton, SY Savrasov, CJ Humphreys, and AP Sutton, Phys. Rev. B 57, 1505-1509 (1998)., F. Zhou, M. Cococcioni, CA Marianetti, D. Morgan, and G. Ceder, Phys. Rev. B 70, 235121 (2004)).

[0028] The atomic positions and lattice constants of each unit cell are determined by the residual force of 0.005 eV / (10 -10 m). The resulting effective charge tensor was calculated using the Berry phase approach within density functional perturbation theory (see X. Wu, D. Vanderbilt, and D. R. Hamann, Phys. Rev. B 72, 035105 (2005)). The spontaneous polarization P S The spontaneous polarization value (P) was calculated as the difference in polarization between the paraelectric and ferroelectric structures. S is 0.15C / m 2 or more (more preferably 0.2 C / m 2 (or more). Spontaneous polarization P S is 0.15C / m 2 This is because sufficient ferroelectricity comparable to that of BaTiO3 can be obtained if the spontaneous polarization P S can be calculated by any method, and the Berry phase calculation (Phys. Rev. B (1993), 47, 1651.) is a good example. The Berry phase calculation is used to calculate the spontaneous polarization P S Although it is not used in the calculation of the spontaneous polarization P S This is useful for evaluating the stability of dielectrics by calculating lattice vibrations.

[0029] Figures 2 and 3 show the calculated lattice constants and band gaps (E bg ), generated effective charge (Z * 33 ) and spontaneous polarization (P S ) in the table. In the table, the values ​​in parentheses are the known experimental lattice constants and the deviation calculated based on them. The calculated lattice constants and band gaps (E g ), Z 33 and P S are compared with known experimental data in the same table. The calculated lattice parameters reproduce the experimental data well, are within the usual DFT error range, and are suitable for PBE to model the ferroelectric transformation. solThe use of potential is verified.

[0030] In addition to a low coercive field, ferroelectric materials must be electronically insulating, i.e., have a sufficiently wide band gap. DFT calculations using the GGA functional are known to significantly underestimate the band gap, but all wurtzite-structure compounds except MnO have a non-zero E g values, it must be an electronic insulator in the polar regime. MnO was not considered further, even though the Hubbard U term was included, due to its lack of a band gap. Also, AlAs, AlSb, GaP, GaAs, GaSb, InP, InAs, and InSb were calculated to have metallic band structures in their respective nonpolar (transition) states, so these compounds were also deemed unsuitable for use as ferroelectric materials.

[0031] Unlike typical perovskite ferroelectric compounds, the calculated Z of each ion in wurtzite structure compounds * 33 The values ​​deviate slightly from the nominal charge in most cases. All compounds have relatively large P S The maximum value for trivalent compounds is 1.24 C / m for GaN. 2 , and 1.21 C / m for AlN. 2 ), the magnitude of the generated effective charge was about 3. In contrast, monovalent compounds exhibited relatively small polarizations (e.g., 0.27 C / m for CuI). 2 , and 0.27 C / m for AgI. 2 ), the resulting effective charges of the cations and anions were calculated to be approximately +1 and -1, respectively. Nevertheless, the P S The P value of perovskite BaTiO3 is a result of the large displacement of cations and anions from their centrosymmetric positions. S value (0.25C / m 2 ) was found to be close in size to

[0032] The coercive field of a ferroelectric crystal can be calculated by using the fixed displacement method to obtain the polarization reversal barrier energy E from the DFT energy of the crystal structure in various states between the polar variants. SW It can be evaluated by calculating the magnitude of

[0033] Figure 4 shows the polarization reversal barrier energy E versus the anion / cation radius ratio χ (horizontal axis) using the known Shannon ionic radius for six-coordination systems (reference: R.D. Shannon, Acta Cryst. A 32, 751 (1976)). SW The ionic radius of the anion N is reported only for tetracoordinated anions. 3- and P 3- In this case, the radius was estimated using the ratio of the Madelung constants for the wurtzite and rocksalt structures with six and eight coordinations, respectively (reference: R.D. Shannon, Acta Cryst. A 32, 751 (1976)). In Figure 4, compounds that have the wurtzite crystal structure under standard conditions are labeled in bold and boxed. Compounds whose ground state has the zincblende structure are labeled in italics, compounds with the nickelate (NiAs) structure are labeled in curly brackets, and compounds with the rocksalt structure are labeled in regular type. Compounds that can be prepared in the wurtzite structure under non-equilibrium conditions are underlined. For example, the nickel-type compounds MnSe and MnTe are both stabilized in the wurtzite structure when prepared in the form of nanowires, nanoribbons, or nanoparticles (see J.E. Huheey, E.A. Keiter, and R.L. Keiter, "Inorganic Chemistry," 4th ed., Harper Collins, New York, USA, 1993; Y. Jiang, X.-M. Meng, W.-C. Yiu, J. Liu, J.-X. Ding, C.-S. Lee, and S.-T. Lee, J. Phys. Chem. B, 108, 2784 (2004)). The results presented here show that the χ and E values ​​for both hypothetical and real wurtzite structure compounds are comparable across a wide range of chemical compositions. SWIn the relatively simple relationship, as χ increases, E SW increases monotonically. Deviations from linearity may be due to differences in the nature of chemical bonding (ionic to covalent), especially at high χ values ​​above the normal range for ground-state wurtzite compounds (roughly 1.9 ≤ χ ≤ 3.1).

[0034] E SW The linear relationship between and χ can be considered as follows: E derived from DFT SW is the energy difference between the polar structure (P63mc) and the non-polar structure (P63 / mmc). As χ decreases, hexa-coordinated structures (e.g., rock salt structure) become more stable, while tetra-coordinated structures such as wurtzite become less stable, so the energy difference between the polar structure (P63mc) and the non-polar state (P63 / mmc) decreases. In other words, the non-polar state becomes energetically favorable. When χ≦1.9, the rock salt (Fm3m) structure is the most stable, as seen in CdO, MgO, AgBr, and AgCl. In terms of phase stability, MnX compounds are most different from other compounds. This is because Mn 2+This is thought to be the result of significantly different bonding states related to the d-orbital electrons. MgS also appears to be anomalous, having a rock-salt structure at room temperature, but has been shown to adopt the wurtzite structure in thin films (see S. Siol, Y. Han, J. Mangum, P. Schulz, AM Holder, TR Klein, MFAM van Hest, B. Gormand, and A. Zakutayev J. Mater. Chem. C, 6, 6297 (2018)). CuCl is within the wurtzite zone in terms of its low polarization reversal barrier energy. Although experimentally reported to have a zinc-blende structure (F43m), it transforms to wurtzite at approximately 400 °C (see YH Lai, QL He, WY Cheung, SK Lok, KS Wong, SK Ho, KW Tam, and IK Sou, Appl. Phys. Lett. 102, 171104 (2013)), making it a suitable tetrahedral ferroelectric when prepared under appropriate synthetic conditions. DFT calculations show that the energy difference between wurtzite and zinc-blende CuCl is only 1.4 meV / fu. In contrast, the well-known rock-salt compound AgCl has a χ AgCl = 1.6, which falls outside the wurtzite region. It appears that stabilization in the wurtzite form is very difficult. This is consistent with the large calculated energy difference (29 meV / fu) between rocksalt AgCl and wurtzite AgCl compared to the alternative form of CuCl.

[0035] As previously discussed by the inventors (see Non-Patent Document 3), one effective method for lowering the polarization barrier energy is to apply epitaxial strain to expand the basal plane crystal. This was found to be true for all wurtzite crystal structure compounds investigated in this study. As an example, Figure 5 shows the effect of ab epitaxial strain (%) on the polarization barrier energy for (a) AgCl, (b) CuCl, and (c) CuBr, all of which have wurtzite crystal structures. Applying 5% epitaxial strain reduces the polarization barrier energy in CuCl from 0.17 to 0.04 eV / fu. In CuBr, the polarization barrier energy decreases from 0.21 to 0.08 eV / fu. It can also be seen that the polarization barrier energy in AgCl decreases from 0.22 to 0.09 eV / fu. These low polarization barrier energies are similar to those of conventional perovskite ferroelectrics. For example, the coercive field for BaTiO3 is 0.02 eV / fu (Reference: Y.M. Rumyantsev, F.A. Kuznetsov, and S.A. Stroitelve, Kristallografiya 10, 263 (1965)). Therefore, low coercive fields (less than 100 kV / cm) are expected to be achievable in strained thin films of these compounds. Regarding substrates, hexagonal ScAlMgO4 is one promising candidate because it has a very small in-plane (0001) lattice parameter and is often used as a substrate for heteroepitaxial growth of wurtzite-structured ZnO thin films (Reference: U. Ozgur, Ya. I. Alivov, C. Liu, A. Teke, M.A. Reshchikov, S. Dogan, V. Avrutin, S.-J. Cho, and H. Morkoc, J. Appl. Phys. 98, 041301 (2005)). ScAlMgO4 can be synthesized with a wide variety of isovalent cations (e.g., Sc 3+ If Y 3+ or In 3+ , Al 3+ In the case of Ga 3+ or Fe 3+ , Mg 2+ In the case of Zn 2+ , Mn2+ , Co 2+ or Cu 2+ ), and it is believed that the lattice constant of the substrate can be adjusted with high precision so as to induce appropriate epitaxial strain in the thin film.

[0036] As described above, in this embodiment, the energy is determined for a non-centrosymmetric structure and a centrosymmetric structure in the first-principles calculation (3), and compositions with an energy difference of 0.22 eV / fu or less are extracted. As a result, CdO, MgO, AgBr, AgI, CuCl, CuBr, etc. can be extracted as ferroelectric materials with a wurtzite crystal structure and low coercive field.

[0037] Using this first-principles calculation method, we searched for new ferroelectric materials with low coercive fields and high spontaneous polarization values. Specific steps of the method were performed as shown in Figure 1. Furthermore, this method is not limited to hexagonal wurtzite crystal structures, but can also be applied to non-centrosymmetric crystal structures such as cubic perovskite crystal structures. (1) First extraction step 3 In the first extraction step 3, compositions having a space group with non-centrosymmetric properties were comprehensively listed as candidate ferroelectric materials from the International Crystal Structure Database 2, and the resulting candidate ferroelectric materials were extracted as first candidates. Whether the crystal structure of the composition is non-centrosymmetric can be determined by any means. For example, the composition may be listed based on the type of crystal structure that is known to be non-centrosymmetric, such as a wurtzite structure, or the composition may be calculated to determine whether its crystal structure is centrosymmetric, and if it is non-centrosymmetric, the composition may be listed.

[0038] (2) Calculation step 4 Next, in the calculation step, the band gap value, polarization inversion barrier energy value, spontaneous polarization value, and phonon dispersion curve of each first candidate were calculated by first-principles calculation. [1] Calculation of band gap value41 The lattice constants of the initial structures of these first candidates were calculated as the product of the ionic radii of each ion, and the structure was optimized using first-principles calculations, after which the band gap value (Eg) was calculated. The first-principles calculations were performed using the VASP code, and the GGA-PBE exchange-correlation term was used. sol was used. [2] Calculation of polarization reversal barrier energy value42 From the first candidate structure, we created inverted structures as shown in Figures 6, 10, and 11. From the resulting inverted structures, we determined the transition state structure using the NEB method and calculated the polarization reversal energy (Esw). To create the inverted structures, we used the PSEUDO code (PSEUDO, J. Appl. Cryst. (2001), 34, 783-784.) to enumerate possible centrosymmetric structure candidates based on the space group of the first candidate structure and the supergroup-subgroup structure of group theory. From the resulting centrosymmetric structure candidates, we then selected the inverted structure with the smallest polarization reversal barrier energy. [3] Calculation of spontaneous polarization value43 The spontaneous polarization value was determined by Berry phase calculation using the first candidate crystal structure and the first candidate inverted structure obtained when calculating the polarization inversion barrier energy value. [4] Calculation of phonon dispersion curves44 A phonon dispersion curve was created from the first candidate structure. The phonon dispersion curve can be created using known means, such as phonopy code, MedeA Phonon code, and ALAMODE code.

[0039] (3) Insulation determination step 51 The band gap value calculated in the calculation step was determined to satisfy the insulating property. Specifically, when the band gap value is 1.0 eV or more, it was determined to satisfy the insulating property. This is because when the band gap is small, the material becomes a conductor due to thermal excitation of electrons.

[0040] (4) Polarization reversal determination step 52 The polarization inversion barrier energy value calculated in the calculation step was used to determine whether polarization inversion was possible. Specifically, when the polarization inversion barrier energy value was 0.3 eV / fu or less (more preferably 0.22 eV / fu or less), it was determined that polarization inversion was possible. This is because if the polarization inversion barrier energy value is high, ferroelectric inversion cannot occur and ferroelectricity is not exhibited.

[0041] (5) Spontaneous polarization determination step 53 The spontaneous polarization value calculated in the calculation step was judged to be within the range showing ferroelectricity. Specifically, if the spontaneous polarization value was 0.1 C / m 2 or more (more preferably 0.2 C / m 2 It was determined that ferroelectricity was exhibited when the temperature was 0.1 C / m or more. 2 If this is the case, the spontaneous polarization value of the ferroelectric BaTiO3 (approximately 0.3 C / m 2 ) and exhibits sufficient ferroelectricity.

[0042] (6) Imaginary mode determination step 54 We determined whether the phonon dispersion curves calculated in the calculation step contained any curves indicating imaginary modes. Specifically, if all frequencies of the phonon dispersion curves were equal to or greater than 0, we determined that the phonon dispersion curves did not contain any imaginary modes. For example, as shown in Figure 7, the phonon dispersion curves of MgO, which has a known wurtzite crystal structure, show that all phonon dispersion curves have frequencies equal to or greater than 0. On the other hand, κ-Al2O3, which has an unstable crystal structure as shown in Figure 9, has phonon dispersion curves with negative frequencies, i.e., imaginary modes. Thus, the presence of imaginary modes indicates dynamic instability, and the possibility of synthesis is considered extremely low.

[0043] (7) Second extraction step 6 The first candidate that satisfied all the conditions in the insulation determining step 51, the polarization reversal determining step 52, the spontaneous polarization determining step 53, and the imaginary mode determining step 54 was extracted as the ferroelectric material. That is, the first candidate has a band gap value of 1.0 eV or more, a polarization inversion barrier energy value of 0.3 eV / fu or less, and a spontaneous polarization value of 0.1 C / m 2 If the above conditions were satisfied and the phonon dispersion curve did not include a curve indicating an imaginary mode, the material was determined to be a ferroelectric material and extracted. If there are multiple first candidates, calculation step 4, insulation determination step 51, polarization reversal determination step 52, spontaneous polarization determination step 53, imaginary mode determination step 54, and second extraction step 6 are performed for each first candidate to determine whether it is a ferroelectric material.

[0044] To verify the effectiveness of this ferroelectric material search method, known compositions were listed as first-choice candidates. Each first-choice candidate was then subjected to calculation step 4, insulation determination step 51, polarization reversal determination step 52, spontaneous polarization determination step 53, imaginary mode determination step 54, and second extraction step 6 to determine whether it was a ferroelectric material. Table 1 shows the band gap value, polarization reversal barrier energy value, spontaneous polarization value, and various values ​​indicating the presence or absence of phonon imaginary modes in the phonon dispersion curves obtained in calculation step 4, as well as the results of each determination step 51-54 (items with a positive result are marked with an ◯). Table 1 also shows the results of second extraction step 6, indicating whether the candidate was a ferroelectric material. Figure 8 shows an example of a phonon dispersion curve for LiAgF2, which does not have an imaginary mode. For comparison, Figure 9 shows the phonon dispersion curve for κ-Al2O3, which has an imaginary mode. Furthermore, the polarization reversal mechanism of LiAgF2 and κ-Al2O3 is shown in Figures 10 and 11.

[0045] [Table 1]

[0046] As shown in Table 1, the known dielectric compositions TiPbO3, LaN, and BaGa 12 O 19 , Li3AlF6, LiAgF2, BaNa2Ti2Si4O 14Of these, TiPbO3, LaN, and Li3AlF6 were extracted as ferroelectric materials, demonstrating the effectiveness of this method for searching for ferroelectric materials.

[0047] The present invention is not limited to the above-described embodiment, but can be modified in various ways within the scope of the present invention depending on the purpose and application. [Industrial Applicability]

[0048] It is expected that these new materials will promote the further development of high-performance lead-free ferroelectric materials, which will find application in nonvolatile ferroelectric memories, filter circuits and actuators for mobile phones and personal computers, and more.

Claims

1. A method for searching for a ferroelectric material, the method comprising: searching for a ferroelectric material having a crystal structure with a low coercive field and a high spontaneous polarization value, a first extraction step of acquiring, as a first candidate, a ferroelectric material candidate having a non-centrosymmetric symmetry from a crystal structure database in which crystal structures of the ferroelectric material candidates are stored; a calculation step of calculating a band gap value, a polarization inversion barrier energy value, and a spontaneous polarization value of each of the first candidates obtained in the first extraction step by first-principles calculation; an insulating property determining step of determining whether the band gap value calculated in the calculating step satisfies insulating properties; a polarization reversal determination step of determining whether the polarization reversal barrier energy value calculated in the calculation step is within a range in which polarization reversal is possible; a spontaneous polarization determination step of determining whether the spontaneous polarization value calculated in the calculation step is within a range that indicates ferroelectricity; a second extraction step of extracting, as the ferroelectric material, the first candidate for which the results of the insulation determining step, the polarization reversal determining step, and the spontaneous polarization determining step are all acceptable; A method for searching for a ferroelectric material, comprising:

2. The calculation of the polarization inversion barrier energy value includes enumerating one or more centrosymmetric structure candidates from the first candidate space group, 2. The method for searching for a ferroelectric material according to claim 1, wherein an energy difference between the space group of the first candidate and the space group of the centrosymmetric structure candidate is compared, the centrosymmetric structure candidate with the shortest distance is extracted as an inverted structure, and the energy difference is used as a polarization inversion barrier energy.

3. 3. The method for searching for ferroelectric materials according to claim 2, wherein the centrosymmetric structure candidates are enumerated using the PSEUDO code.

4. the calculating step calculates a phonon dispersion curve of each of the first candidates by first-principles calculation; an imaginary mode determination step of determining whether or not the phonon dispersion curve calculated in the calculation step does not include a curve indicating an imaginary mode; 4. The method for searching for a ferroelectric material according to claim 1, wherein the second extraction step extracts the first candidate as the ferroelectric material, the first candidate being one for which the judgment results of the insulation judgment step, the polarization reversal judgment step, the spontaneous polarization judgment step, and the imaginary mode judgment step are all acceptable.

5. 5. The method for searching for a ferroelectric material according to claim 4, wherein the spontaneous polarization value is calculated by Berry phase calculation.

6. 6. The method for searching for ferroelectric materials according to claim 5, wherein the first-principles calculation uses one of the VASP code, the CASTEP code, the Quantum Espresso code, the PWSCF code, the PHASE code, the STATE-SENRI code, the QMAS code, and the ABINIT code, each of which uses a plane wave as a basis function.

7. having a wurtzite crystal structure selected from CdO, MgO, AgCl, AgBr, AgI, CuCl and CuBr, or Li ３ AlF ６ It has an orthorhombic crystal structure in which The band gap value satisfies the insulating property, The polarization reversal barrier energy value is within a range in which polarization reversal is possible, The spontaneous polarization value is in the range in which ferroelectricity is exhibited, The ferroelectric material is characterized in that the phonon dispersion curve does not include a curve indicating an imaginary mode.

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