JP7696748B2 - Search method for wurtzite crystal structure ferroelectric material and wurtzite crystal structure ferroelectric material - Google Patents

Description

Article 30, paragraph 2 of the Patent Act applies. Website posting date: December 7, 2020. Website address: https://aip.scitation.org/doi/10.1063/5.0023626. Website posting date: December 10, 2020. Website address: https://www.jfcc.or.jp/press/r20_6.html. Website posting date: December 10, 2020. Website address: https://www.kyushu-u.ac.jp/ja/researches/view/536

The present invention relates to a method for searching for ferroelectric materials with a wurtzite crystal structure and a low coercive electric field using first-principles calculations, and to ferroelectric materials with a wurtzite crystal structure and a low coercive electric field.

Ferroelectric materials such as lead zirconate titanate (PZT) have been widely used in non-volatile ferroelectric memories, filters and actuators for mobile phones and personal computers, but lead has been used in many of these materials. In recent years, due to environmental concerns, research and development of lead-free ferroelectric materials has been actively conducted, but many high-performance ferroelectric materials have a perovskite crystal structure consisting of oxygen octahedra or a similar structure.
On the other hand, crystals with a wurtzite structure (space group P6 ₃ mc) are not centrally symmetric, and therefore have been conventionally considered to be non-ferroelectric. However, in recent years, demonstration experiments have been conducted on their ferroelectricity. For example, a P-E hysteresis loop of a Sc-doped AlN thin film with a wurtzite structure has been reported (see Non-Patent Document 1). However, the polarization inversion barrier of the Sc-doped AlN thin film is very high, about two orders of magnitude higher than that of BaTiO ₃ , PbTiO ₃ , and the like, which are typical conventional perovskite-type ferroelectric materials. When a ferroelectric material is used in a device such as a ferroelectric memory, the polarization inversion barrier must be low (for example, about 100 kV/cm), and the actual applications of ferroelectric materials with a wurtzite structure have been limited.

S. Fichtner, N. Wolff, F. Lofink, L. Kienle, and B. Wagner, J. Appl. Phys., 125, 114103 (2019). H. Moriwake, A. Konishi, T. Ogawa, K. Fujimura, C. A. J. Fisher, A. Kuwabara, T. Shimizu, S. Yasui, and M. Itoh, Appl. Phys. Lett. 104, 242909 (2014). A. Konishi, T. Ogawa, C. A. J. Fisher, A. Kuwabara, T. Shimizu, S. Yasui, M. Itoh, and H. Moriwake, Appl. Phys. Lett. 109, 102903 (2016).

As mentioned above, many of the high-performance non-lead ferroelectric materials have a perovskite-type crystal structure consisting of oxygen octahedra or a similar structure. These have been thoroughly investigated, and for a new breakthrough, it is desirable to discover a ferroelectric material with a crystal structure that does not have oxygen octahedra.
The present inventors focused on a simple wurtzite crystal structure without oxygen octahedra, as shown in Figure 1. Figure 1(a) shows the hexagonal wurtzite structure of the binary compound MX (space group P6 ₃ mc). Figure 1(b) shows the polarization switching mechanism, with a ferroelectric state of P = +P 2 _S , a paraelectric (intermediate) state of P = 0, and a ferroelectric state of P = -P 2 _S after inversion of the MX ₄ tetrahedra by applying an electric field parallel to the c-axis, where δ is the displacement of the ions relative to their positions in the intermediate state.
The inventors then investigated the possibility of using this material as a ferroelectric material by first-principles calculations, and found that the polarization reversal barrier energy, which is a necessary characteristic for a ferroelectric, in ZnO is comparable to that of lead titanate (PbTiO ₃ ), a representative ferroelectric material, and clarified the possibility of developing ferroelectric materials at the atomic level with simple wurtzite crystal structures that do not have oxygen octahedra (see Non-Patent Documents 2 and 3). However, since the coercive field, which is the electric field required to reverse the electric polarization of a ferroelectric material, is very large in ZnO, it was necessary to find a material with an even lower coercive field for practical use.

Ferroelectrics are materials with spontaneous electric polarization _{Ps that can be switched between two or more symmetry variants by applying an electric field E. Such compounds usually change between polar (low symmetry) and non-polar (high symmetry) phases corresponding to ferroelectric and paraelectric states as a function of temperature (or pressure). The wurtzite structure (P63mc )} is not centrosymmetric, and binary compounds of this crystal type are polar (Figure 1(a)). Until recently, crystals with the wurtzite structure were thought to be non-ferroelectric because of the difficulty in switching the cation-centered tetrahedra that compose them, and early theoretical calculations investigating the polarization and piezoelectricity of wurtzite crystals considered only the displacement of cations within the tetrahedra. Subsequent observations, however, have led to the possibility that wurtzite crystals may exhibit ferroelectricity by reversing the orientation of the cation-anion tetrahedra. The inventors have used first-principles calculations to show that for Zn and Be chalcogenides, the relative displacement of the cations with respect to the anions along the c-axis produces a metastable centrosymmetric structure that is paraelectric (space group _P63 /mmc) and intermediate between two polar structures with opposite tetrahedral orientations, as shown in Figure 1(b). If the energy required for this displacement is low enough, it should be possible to switch the polarization, and so they speculated that ferroelectric materials containing tetrahedra, also known as tetrahedral ferroelectrics, could be developed as an alternative to conventional perovskite materials.

The present invention has been made in consideration of the above-mentioned current situation, and aims to provide a method for searching for a wurtzite crystal structure ferroelectric material with a low coercive electric field using first-principles calculations, and a wurtzite crystal structure ferroelectric material with a low coercive electric field.

The present invention is as follows.
1. A method for searching for a wurtzite crystal structure ferroelectric material, the method comprising searching for a wurtzite crystal structure ferroelectric material capable of being polarized by using first-principles calculations.
2. The method for searching for a wurtzite crystal structure ferroelectric material according to 1 above, using one of the 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, as the first-principles calculation.
3. The first-principles calculation includes a structural optimization calculation step of performing a structural optimization calculation and an extraction step of extracting a target composition,
In the structural optimization calculation step, energies in the space group P6 ₃ mc and the space group P6 ₃ /mmc are determined;
3. The method for searching for a wurtzite crystal structure ferroelectric material according to 1. or 2., wherein in the extraction step, an energy difference between the space group _P63mc and the space group _P63 /mmc is defined as a polarization inversion barrier energy, and a composition having the polarization inversion barrier energy of 0.22 eV/fu or less is extracted.
4. The method for searching for a wurtzite crystal structure ferroelectric material according to 3 above, wherein the calculation condition in the structural optimization calculation step is a k-point density of 0.5/(10 ⁻¹⁰ m) or less.
5. The method for searching for a wurtzite crystal structure ferroelectric material according to either 3. or 4., wherein a cutoff energy is set to 400 eV or more as a calculation condition in the structural optimization calculation step.
6. The method for searching for a wurtzite crystal structure ferroelectric material according to any one of 3. to 5., wherein the force acting on atoms at the termination of the structural optimization is set to 0.1 eV/(10 ⁻¹⁰ m) or less as a calculation condition in the structural optimization calculation step.
7. A ferroelectric material having a wurtzite crystal structure, characterized in that the ferroelectric material has a wurtzite crystal structure and is selected from the group consisting of CdO, MgO, AgCl, AgBr, AgI, CuCl and CuBr.
8. A ferroelectric material with a wurtzite crystal structure according to the above 7, in which the coercive electric field is further reduced by extending the ab plane of the wurtzite crystal structure.

According to the method for searching for a wurtzite crystal structure ferroelectric material of the present invention, it is possible to find a wurtzite crystal structure ferroelectric material that is a composition having a wurtzite crystal structure capable of reversing polarization and has a low coercive electric field, by using first-principles calculations.
The wurtzite crystal structure ferroelectric material of the present invention has a polarization inversion barrier energy close to that of the conventional representative ferroelectric perovskite _PbTiO3 , and is expected to be put to practical use as an alternative non-lead ferroelectric material with a low coercive field.
Furthermore, by adding epitaxial strain to the wurtzite crystal structure ferroelectric material, the barrier energy for polarization inversion can be reduced, and it is expected that a ferroelectric material with an even lower coercive field can be realized by synthesizing it as a thin film having epitaxial strain.

The present invention will be further described by the following detailed description, which gives non-limiting examples of exemplary embodiments according to the invention, and with reference to the mentioned drawings, in which like reference numerals refer to like parts throughout the several views of the drawings.
FIG. 1 is a schematic diagram showing a simple wurtzite crystal structure that does not have an oxygen octahedral structure. FIG. 1 shows calculated potential surfaces for ferroelectric cation displacements in monovalent halides. FIG. 1 shows a calculated potential surface for ferroelectric cation displacement in a divalent chalcogenide (1/2). FIG. 2 shows the calculated potential surface for ferroelectric cation displacement in a divalent chalcogenide (2/2). FIG. 1 shows a diagram (1/2) of calculated potential surfaces for ferroelectric cation displacements in trivalent pnictogenides and silicon carbide. FIG. 2 shows calculated potential surfaces for ferroelectric cation displacements in trivalent pnictogenides and silicon carbide (part 2). FIG. 1 is a graph showing the relationship between the anion/cation radius ratio and the polarization inversion barrier energy. FIG. 1 shows the effect of ab epitaxial strain on the ferroelectric potential barrier for AgCl, CuCl, and CuBr in the wurtzite structure. FIG. 1 is a diagram showing a schematic configuration of a method for searching for a wurtzite crystal structure ferroelectric material according to an embodiment. 1 is a table (1) showing the calculated lattice constants, band gaps, effective charges and spontaneous polarizations for binary compounds. 1 is a table (2) showing the calculated lattice constants, band gaps, effective charges and spontaneous polarizations for binary compounds.

The present invention will now be described in detail with reference to the accompanying drawings.
The matters shown herein are illustrative and are intended to exemplify the embodiments of the present invention, and are described for the purpose 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 in conjunction with the drawings will make it clear to those skilled in the art how some forms of the present invention can be actually embodied.

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

Previously, the inventors estimated the coercive field of a limited number of wurtzite structure compounds by calculating the tetrahedral polarization reversal barrier energy (Non-Patent Documents 2 and 3). In this invention, the search of the composition phase space is extended to cover a wider range of binary compounds and identify new ferroelectrics with low coercive field. The search started with compounds that have been experimentally confirmed to have the wurtzite structure under standard or non-standard conditions (high temperature, high pressure, nanosizing, etc.). Many of these compounds have the wurtzite polymorphism included in the International Crystal Structure Database. Specifically, these are CuI, AgI, BeO, MgTe, MnO, MnS, ZnO, ZnS, ZnSe, CdS, CdSe, CdTe, AlN, GaN, InN, InSb, 2H-SiC, etc. For compounds whose wurtzite structure has not been reported in detail (CuCl, CuBr, BeS, MgS, MgSe, MnSe, MnTe, ZnTe, AlP, AlAs, AlSb, GaP, GaAs, GaSb, InP, InAs, etc.), the same structure containing the same cations was used and the appropriate X element was used to construct the starting structure for the first-principles calculations. For comparison, several hypothetical wurtzite structure compounds (AgCl, AgBr, BeSe, BeTe, MgO, CdO, etc.) were also considered and their initial structures were constructed in a similar manner.

The search method (1) for a wurtzite crystal structure ferroelectric material according to the present embodiment is characterized in that it searches for a wurtzite crystal structure ferroelectric material capable of being polarized and having a polarization reversible barrier energy of less than 0.22 eV/f.u. by using first-principles calculation (3), and performs first-principles calculation by inputting data contained in a crystal structure database (2). The first-principles calculation (3) includes a structural optimization calculation step (32) for performing a structural optimization calculation and an extraction step (34) for extracting a target composition, and the structural optimization calculation step (32) can have the following conditions: the k-point density is set to 0.5/( ^10-10 m) or less, the cutoff energy is set to 400 eV or more, and the structural optimization is performed until the force acting on the atoms at the structural optimization termination is 0.1 eV/( ^10-10 m) or less. Then, in the structural optimization calculation step (32), the energies in the space group _P63mc and the space group _P63 /mmc are determined, and in the extraction step (34), the energy difference between the space group _P63mc and the space group _P63 /mmc is set as the polarization inversion barrier energy, and a composition having a polarization inversion barrier energy of 0.22 eV/fu or less is extracted (see FIG. 9).
"fu" stands for formula unit.

In this embodiment, the first-principles calculations use density functional theory (DFT) calculations implemented in VASP (Vienna Ab initio Simulation Package, 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 the first-principles calculations, the vasp code, castep code, Quantum espresso code, pwscf code, PHASE code, STATE-SENRI code, QMAS code, ABINIT code, etc., which use plane waves as basis functions, can be used.

All calculations were performed using the Perdew-Burke-Ernzerhof formulation of the generalized gradient approximation (GGA-PBE _sol ) optimized for solids to treat the exchange-correlation terms (Reference: JP Perdew, K. Burke, and M. Ernzerhof, Phys. Rev. Lett. 77, 3865 (1996)).
A plane-wave based projector augmented-wave method (reference: PE 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, and 3d and 4s electrons for Mn, Cu and Zn treated as valence electrons.

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

In this embodiment, in the structural optimization calculation step (32), the cutoff energy must be set to 400 eV or more. The cutoff energy is set to 400 eV or more in order to ensure sufficient calculation accuracy (energy, force, structure).

Numerical integration was performed using a Γ-centered k-point mesh with 0.25/(10−10 m) spacing generated according to the Monkhorst-Pack scheme (see H. J. Monkhorst and J. D. Pack, Phys. Rev. B 13, 5188 ( ¹⁹⁷⁶ )) within the first Brillouin zone of a 4-atom wurtzite unit cell.

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 value cannot ensure sufficient calculation accuracy (energy, force, structure).

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.

To reconcile known underestimations of the electronic band gaps of transition metal-containing compounds using the GGA method, a Hubbard U-term of _Ueff = 3.6 eV was added for Mn-containing compounds (see 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)).

The atomic positions and lattice constants of each unit cell were relaxed until the residual forces were smaller than 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 DR Hamann, Phys. Rev. B 72, 035105 (2005)). The spontaneous polarization P _S was calculated as the difference in polarization between the paraelectric and ferroelectric structures. The polarization P is guided by the periodic displacement δ for the atomic positions. In the nonpolar centrosymmetric ( _P63 /mmc) structure, it is related to the resulting effective charge Z ^* ₃₃ of the cations in the c-direction and the volume V of the unit cell according to equation (1):

10 and 11 are tables showing the calculated lattice constants, band gaps (E _bg ), generated effective charges (Z ^* ₃₃ ) and spontaneous polarizations (P _S ) of the binary compounds investigated in this study. In the tables, the numbers in parentheses are the known experimental lattice constants and the calculated deviations therefrom. The calculated lattice constants, band gaps (E _g ), Z* ₃₃ and P _S of each compound are compared to the known experimental data in the tables. The calculated lattice constants reproduce the experimental data well and are within the usual DFT error range, validating the use of the PBE _sol potential to model the ferroelectric transformation.

In addition to a low coercive field, ferroelectric materials must be electronically insulating, i.e., have a sufficiently wide band gap. Although DFT calculations using the GGA functional are known to significantly underestimate the band gap, all compounds except MnO exhibited nonzero E _g values and therefore must be electronic insulators in the polar regime. Due to the lack of a band gap, MnO was not considered further, even though the Hubbard U term was included. Also, AlAs, AlSb, GaP, GaAs, GaSb, InP, InAs and InSb were calculated to have metallic band structures in their respective nonpolar (transition) states, and therefore these compounds were also deemed unsuitable for use as ferroelectric materials.

Unlike typical perovskite ferroelectric compounds, the calculated Z ^* ₃₃ values of each ion deviate slightly from the nominal charge in most cases. All compounds exhibit relatively large P _S values, with the trivalent compounds being the largest (e.g., 1.24 C/m ² for GaN and 1.21 C/m ² for AlN), resulting in an effective charge magnitude of about 3. In contrast, the monovalent compounds exhibit relatively small polarizations (e.g., 0.27 C/m ² for CuI and 0.27 C/m ² for AgI), resulting in effective charges of about +1 and -1 for the cations and anions, respectively. Nevertheless, the P _S values of these monovalent compounds were found to be close in _magnitude to that of the perovskite BaTiO ₃ (0.25 C/m ² ), as a result of the large displacement of the cations and anions from their centrosymmetric positions.

The coercive field of a ferroelectric crystal can be evaluated by calculating the magnitude of the polarization reversal barrier energy E _SW from the DFT energies of the crystal structure in various states among the polar variants using the fixed displacement method.
Figure 2 shows the calculated relative potential surfaces (vertical axis) versus normalized ferroelectric cation displacements (horizontal axis) for monovalent halides (a) CuX and (b) AgX, where X = Cl, Br, and I.
3 and 4 show the calculated potential surfaces for the ferroelectric cation displacement in divalent chalcogenides, as in the previous figures. Fig. 3(a) shows BeX, (b) shows MgX, (c) shows MnX, (d) shows ZnX, and (e) shows CdX, where X = O, S, Se, and Te. MnO is excluded because it is electronically conductive.
5 and 6 show the calculated potential surfaces for the ferroelectric cation displacement in trivalent pnictogens and silicon carbide, as in the previous figures. Fig. 5(a) shows AlX, (b) shows GaX, and Fig. 6(c) shows InX, where X = N, P, As, and Sb, respectively, and Fig. 6(d) shows 2H-SiC.

The calculated potential surfaces are plotted in Figure 2 for monovalent compounds (Cu and Ag halides), in Figures 3 and 4 for divalent compounds (Be, Mg, Mn, Zn and Cd chalcogenides), as described above, and in Figures 5 and 6 for trivalent compounds (Al, Ga and In pnictogenides, and 2H-SiC) (for completeness, results for compounds with an electronically conducting ferroelectric phase are included).
The calculations show that all compounds exhibit double well potentials, with maxima corresponding to non-polar states intermediate between the minima of the two polar variants. Among all the above compounds, the monovalent compounds (Cu and Ag halides) have the lowest polarization reversal barrier energies: 0.17 eV/fu for CuCl, 0.21 eV/fu for CuBr, 0.29 eV/fu for CuI, 0.11 eV/fu for AgCl, 0.15 eV/fu for AgBr, and 0.22 eV/fu for AgI. These barriers are close in magnitude to the known barrier of _0.2 eV/fu for the ferroelectric perovskite PbTiO3 (see RE Cohen, Nature (London) 358, 136 (1992)). In all cases, the potential barrier decreases with decreasing atomic number (and therefore ionic radius) of the anion.

7 shows the polarization reversal barrier energy E SW (vertical axis) versus anion/cation radius ratio χ (horizontal axis) using the known Shannon ionic radii for six coordinations (reference: _RD Shannon, Acta Cryst. A 32, 751 (1976)). For the anions N ^3- and P ^3- , whose ionic radii have only been reported for four coordinations, the radii were estimated using the ratio of the Madelung constants for the wurtzite and rocksalt structures with six and eight coordinations, respectively (reference: RD Shannon, Acta Cryst. A 32, 751 (1976)).
In this diagram, compounds that have the wurtzite structure under standard conditions are labeled in bold and boxed text, 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 normal typeface. Compounds that can be prepared in the wurtzite structure under non-equilibrium conditions are underlined. For example, both nickeline-type compounds MnSe and MnTe are stabilized in the wurtzite structure when prepared in the form of nanowires, nanoribbons, or nanoparticles (see JE Huheey, EA Keiter, and RL 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 a relatively simple relationship between χ and E _SW over a wide range of chemical compositions for both hypothetical and real wurtzite, with E _SW increasing monotonically with increasing χ. Deviations from linearity may be due to differences in the nature of the chemical bonding (ionic to covalent), especially at higher χ values beyond the usual range for ground-state wurtzite compounds (roughly 1.9≦χ≦3.1).

The linear relationship between E _SW and χ can be considered as follows: E _SW derived from DFT is the energy difference between the polar (P6 ₃ mc) and non-polar (P6 ₃ /mmc) structures. As χ decreases, 6-coordinate structures (e.g., rock salt) become more stable, while 4-coordinate structures such as wurtzite become less stable, thus decreasing the energy difference between the polar (P6 ₃ mc) and non-polar (P6 ₃ /mmc) structures. In other words, the non-polar state becomes energetically favorable. For χ≦1.9, the rock salt (Fm3m) structure is the most stable, as seen in AgCl, AgBr, CdO, and MgO. In terms of topological stability, MnX compounds are most different from the other compounds. This is believed to be a result of the significantly different bonding states associated with the d-orbital electrons of Mn ²⁺ . MgS also appears to be unusual, having a rock-salt structure at room temperature, but has been shown to adopt the wurtzite structure in thin film form (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 that it has a low polarization reversal barrier energy. It has been reported experimentally to have a zinc-blende structure (F43m), but transforms to wurtzite at about 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 suitable synthesis conditions. According to DFT calculations, the energy difference between wurtzite and zincblende CuCl is only 1.4 meV/fu. In contrast, for the well-known rock-salt compound AgCl, χ _AgCl = 1.6, which falls outside the wurtzite region. It appears to be very difficult to stabilize in the wurtzite form. This is also consistent with the larger calculated energy difference (29 meV/fu) between rock-salt and wurtzite AgCl compared to alternative forms of CuCl.

As already discussed by the inventors (see Non-Patent Document 3), one of the effective ways to lower the polarization barrier energy is to apply epitaxial strain to expand the crystal of the basal plane. This was found to be true for all the compounds investigated in this invention. As an example, FIG. 8 shows the effect of ab epitaxial strain (%) on the polarization barrier energy for (a) AgCl, (b) CuCl, and (c) CuBr with the wurtzite structure. When applying 5% epitaxial strain, the polarization barrier energy decreases from 0.17 to 0.04 eV/fu for CuCl, the polarization barrier energy decreases from 0.21 to 0.08 eV/fu for CuBr, and the polarization barrier energy decreases from 0.22 to 0.09 eV/fu for AgCl. These low polarization barrier energies are similar to those of conventional perovskite ferroelectrics, e.g., 0.02 eV/fu for _BaTiO3 (see YM Rumyantsev, FA Kuznetsov, and SA Stroitelve, Kristallografiya 10, 263 (1965)). Therefore, it is expected that low coercive fields (less than 100 kV/cm) can be realized in strained thin films of these compounds. Regarding the substrate, hexagonal _ScAlMgO4 is one of the promising candidates because it has a very small in-plane (0001) lattice constant and is often used as a substrate for heteroepitaxial growth of ZnO thin films with the wurtzite structure (see U. Ozgur, Ya. I. Alivov, C. Liu, A. Teke, MA Reshchikov, S. Dogan, V. Avrutin, S.-J. Cho, and H. Morkoc, J. Appl. Phys. 98, 041301 (2005)). It is believed that _ScAlMgO4 can be substituted with a wide variety of isovalent cations (e.g., Y3 ⁺ or In3 ⁺ for Sc3 ⁺ , Ga3 ⁺ or Fe3 ⁺ for Al3 ⁺ , and Zn2 ⁺ , Mn2 ⁺ , Co2 ⁺ or Cu2 ⁺ for ^Mg2 +) to precisely tune the lattice constant of the substrate to induce the appropriate epitaxial strain in the thin film.

From the above, in this embodiment, in the first-principles calculation (3), the energy is determined in the space group _P63mc and the space group _P63 /mmc, and a composition with an energy difference of 0.22 eV/fu or less is extracted. This makes it possible to extract CuCl, CuBr, AgI, CdO, MgO, AgCl, AgBr, etc. as wurtzite crystal structure ferroelectric materials with low coercive electric field.
In addition, in this embodiment, the coercive electric field can be further reduced by expanding the ab plane of the wurtzite crystal structure.

In summary, using first-principles calculations, we have systematically investigated binary compounds in search of new tetrahedral ferroelectrics, in particular those with wurtzite structures and low coercive fields, and three main conclusions can be drawn from this.
(1) Of the wurtzite binary compounds examined, the two lowest polarization barrier energies found were 0.11 eV/fu for AgCl and 0.15 eV/fu for AgBr, both of which have rock salt structures and are very stable. The third lowest was 0.17 eV/fu for CuCl, which typically has a zinc-blende structure that is slightly more stable than the wurtzite structure. This polarization barrier energy is similar in magnitude to that of the ferroelectric perovskite _PbTiO3 , suggesting a low coercive field for CuCl when prepared in the wurtzite structure. The wurtzite AgI and CuBr also have polarization barrier energies below 0.22 eV/fu and are considered promising tetrahedral ferroelectrics.

(2) The polarization reversal barrier energy decreases with decreasing anion-cation radius ratio (r _anion /r _cation ), which is related to the decreased stability of the cation-anion tetrahedron as anions become smaller and cations become larger, decreasing the energy difference between the polar variant (P6 ₃ mc symmetry) and the nonpolar state (P6 ₃ /mmc symmetry).

(3) Applying epitaxial tensile strain to the (0001) plane is effective in lowering the polarization reversal barrier energy. In wurtzite CuCl, the potential barrier decreased from 0.17 to 0.04 eV/fu after expanding the crystal by 5% parallel to the (0001) plane. Therefore, it is believed that a low coercive field (less than 100 kV/cm) can be achieved by synthesizing this compound as a thin film with a few percent epitaxial strain.

The present invention is not limited to the above-described embodiment, and various modifications may be made within the scope of the present invention depending on the purpose and application.

The search method of the present invention makes it possible to discover ferroelectric materials with a wurtzite crystal structure that have low polarization reversal barrier energy and extremely low coercive electric field. It is expected that such new materials will promote the further development of high-performance lead-free ferroelectric materials, making them applicable to practical devices such as non-volatile memories.

1: Search method for wurtzite crystal structure ferroelectric materials, 2: Crystal structure database, 3: First-principles calculation, 32: Structure optimization calculation step, 34: Extraction step.

Claims (3)

A method for searching for a wurtzite crystal structure ferroelectric material using first-principles calculations to search for a ferroelectric material having a wurtzite crystal structure capable of being polarized, comprising the steps of:
The first-principles calculation includes a structural optimization calculation step of performing a structural optimization calculation on a binary compound having a known wurtzite crystal structure, which is a candidate for the search, and an extraction step of determining whether to extract the candidate as a target composition based on a result of the structural optimization calculation step,
In the structural optimization calculation step, energies in the space group P6 ₃ mc and the space group P6 ₃ /mmc of the candidate for the structural optimization calculation are determined by density functional theory calculation using a VASP code ;
As calculation conditions in the structural optimization calculation step, the k-point density is set to 0.5/(10 ⁻¹⁰ m) or less, the force applied to the atoms at the structural optimization cutoff is set to 0.1 eV/(10 ⁻¹⁰ m) or less, and the cutoff energy is set to 400 eV or more;
a difference between the energy of the space group P63mc _and the energy of the space group P63 _/ mmc being taken as a polarization inversion barrier energy, and the candidate having the polarization inversion barrier energy of 0.22 eV/fu or less is extracted as the composition in the extraction step . 2. The method for searching for a wurtzite crystal structure ferroelectric material according to claim 1, wherein the search candidates are selected from the group consisting of CdO, MgO, AgCl , AgBr, AgI, CuCl and CuBr . The method for searching for a wurtzite crystal structure ferroelectric material according to claim 2, in which the coercive electric field of the ferroelectric material is less than 100 kV/cm due to the extension of the ab plane of the wurtzite crystal structure.

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