A computational search for wurtzite-structured ferroelectrics with low coercive voltages

Ferroelectricity has recently been observed in wurtzite-structured Sc-doped AlN thin films, five years after our initial prediction of ferroelec-tricity in wurtzite compounds based on first-principles calculations. The thin films exhibited a much higher coercive voltage (3 MV/cm) than that of conventional perovskite-structured ferroelectric material PbTiO 3 , however, making it difficult to switch the films’ polarity and limiting their practical application. To identify tetrahedral ferroelectric materials with low coercive voltages, we have carried out a wider exploration of candidate binary compounds, from halides to chalcogenides to pnictogenides, using first-principles methods. The overall trend is for polarization switching barriers to decrease with decreasing anion-to-cation radius ratio, with

(http://creativecommons.org/licenses/by/4.0/).https://doi.org/10.1063/5.0023626., s Ferroelectrics are materials possessing a spontaneous electric polarization, Ps, that can be switched between two or more symmetry-related variants by application of an electric field, E. Such compounds typically transform between polar (low symmetry) and non-polar (high symmetry) phases corresponding to ferroelectric and paraelectric states, respectively, as a function of temperature (or pressure).The wurtzite structure (S.G.P6 3 mc) is non-centrosymmetric and thus stoichiometric binary compounds with this crystal type are polar [Fig.1(a)].2][3][4][5] However, as early as 1973, Sawada et al. 6 traced the electric displacementelectric field (D-E) hysteresis loop of wurtzite BeO and measured a small polarization of 0.061 C/m 2 at 805 ○ C. Similarly, in 1996, when measuring the P-E hysteresis loop of Li-doped ZnO, Onodera et al. 7 detected a dielectric anomaly at 330 K with a small polarization of 0.044 μC/cm 2 at room temperature, and Joseph et al. 8 in 1999 reported a dielectric anomaly at 340 K in the same material.Such observations motivated us to consider the possibility of wurtzite crystals exhibiting ferroelectricity by a reversal in orientation of the cation-anion tetrahedra. 9,10We showed using first-principles calculations of Zn and Be chalcogenides that displacement of the cations relative to the anions parallel to the c axis produces a metastable centrosymmetric structure, which is paraelectric (space group P6 3 /mmc) and halfway between the two polar structures of opposite tetrahedral orientation, as illustrated in Fig.  to be the correct reference structure for accurately calculating polarization constants.If the energy required for this displacement is sufficiently low, it should be possible to switch the polarization, thereby holding out the promise that ferroelectric materials consisting of tetrahedral networks, otherwise known as tetrahedral ferroelectrics, can be developed as an alternative to the conventional perovskite materials.A similar method was used by Bennett et al. to examine a large number of stuffed wurtzites. 124][15][16][17][18][19][20][21][22] In particular, in 2019, Fichtner et al. 23 reported a well-defined P-E hysteresis loop with a high spontaneous polarization of 1.00 C/m 2 in Sc-doped AlN thin films, their work providing further stimulus to the search for tetrahedral ferroelectrics.To be practical, a ferroelectric material requires a moderate-to-low coercive voltage, especially if it is to be used in ferroelectric memory or similar devices, but the coercive voltage of their material was reported to be very high; at 2 MV/cm-5 MV/cm, the coercive voltages of their Al(Sc)N thin films are around two orders of magnitude higher than those of conventional perovskite-type ferroelectric materials, such as BaTiO 3 (25 kV/cm) 24 and PbTiO 3 (121 kV/cm). 25There is thus a strong impetus to discover new materials with coercive voltages <100 kV/cm.
In our previous reports, 9,10 we estimated the coercive voltages of a limited number of wurtzite-structured compounds by calculating activation energies for (homogeneous) polarization switching of tetrahedra.In this report, we expand our exploration of the compositional phase space to encompass a wider range of binary compounds, thereby identifying novel ferroelectrics with low coercive voltages.We began with compounds that have been experimentally confirmed to have the wurtzite structure, whether under standard or non-standard (high temperature, high pressure, nanosizing, and so on) conditions.Many of these compounds have their wurtzite polymorphs included in the International Crystal Structure Database, 26 viz., CuI, AgI, BeO, MgTe, MnO, MnS, ZnO, ZnS, ZnSe, CdS, CdSe, CdTe, AlN, GaN, InN, InSb, and 2H-SiC.For those whose wurtzite form has not been reported in detail (viz., CuCl, CuBr, BeS, MgS, MgSe, MnSe, MnTe, ZnTe, AlP, AlAs, AlSb, GaP, GaAs, GaSb, InP, and InAs), we used an analog structure containing the same cation and substituted the appropriate X element to construct starting structures relaxed using first-principles methods.We also considered a number of hypothetical wurtzite-structured compounds, viz., AgCl, AgBr, BeSe, BeTe, MgO, and CdO, for comparison, their initial structures constructed in a similar way.
Similar to our earlier study, density functional theory (DFT) calculations, as implemented in VASP, 27,28 were used to characterize each of the above compounds and assess their suitability as candidate tetrahedral ferroelectrics.All calculations were performed using the Perdew-Burke-Ernzerhof form of the generalized gradient approximation optimized for solids (GGA-PBEsol) to treat exchange-correlation interactions. 29The plane wave basis projector augmented wave method 30 was used with 2s and 2p electrons for Be, N, O, C, and F, 3s and 3p electrons for Mg, Al, Si P, 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.The convergence of the total energies with respect to cutoff energies up to 800 eV was better than 0.015 eV/f.u.Numerical integration was carried out using a Γ-centered 0.25 Å −1 spaced k-point mesh, generated according to the Monkhorst-Pack scheme, 31 within the first Brillouin zone of the four-atom wurtzite unit cell.To adjust for the known underestimation of electronic bandgaps in transition metal-containing compounds using the GGA method, a Hubbard U term 32 of U eff = 3.6 eV was added in the case of Mn-containing compounds. 33tom positions and lattice parameters of each unit cell were relaxed until residual forces were smaller than 0.005 eV/Å.Born effective charge tensors were calculated using the Berry phase approach within density functional perturbation theory. 34Spontaneous polarizations, Ps, were calculated as the difference in polarization between paraelectric and ferroelectric structures, where polarization P induced by periodic displacement δ of atoms relative to their positions in the non-polar centrosymmetric (P6 3 /mmc) structure is related to the Born effective charge of the cation in the c direction, Z * 33 , and the volume of the unit cell, V, according to the following equation: Calculated lattice parameters, bandgaps (Eg), Z * 33 , and Ps of each compound are compared with available experimental data in Table I.The calculated lattice parameters reproduce the experimental data well and are within the usual DFT error, validating the use of PBEsol potentials for modeling ferroelectric transformations.
In addition to a low coercive voltage, conventional ferroelectric materials also need to be electronically insulating, i.e., have sufficiently wide bandgaps, to undergo switching by an applied electric field.Although DFT calculations using GGA functionals are known to underestimate bandgaps significantly, all compounds apart from MnO exhibited non-zero Eg values and thus should be electronic insulators in their polar forms.Because of its lack of bandgap, even with a Hubbard U term included, MnO was not considered further.In addition, AlAs, AlSb, GaP, GaAs, GaSb, InP, InAs, and InSb were each calculated to have a metallic band structure in their nonpolar (transition) state, so these compounds are likely unsuitable for use as ferroelectric materials according to the modern theory of polarization. 35,36nlike in typical perovskite ferroelectric compounds, the calculated Z * 33 values of each ion in most cases deviated only slightly from their nominal charges.All compounds exhibited relatively large Ps values, with trivalent compounds having the largest (e.g., 1.24 C/m 2 for GaN and 1.21 C/m 2 for AlN), consistent with the magnitudes of their Born effective charges being around 3. In contrast, monovalent compounds were calculated to have relatively small polarizations (e.g., 0.27 C/m 2 for CuI and 0.27 C/m 2 for AgI) with small Born effective charges of around +1 and −1 for cations and anions, respectively.Despite this, Ps values for these monovalent compounds were found to be similar in magnitude to that of perovskite BaTiO 3 (0.25 C/m 2 ) as a result of the large displacement of their cations and anions from the centrosymmetric positions.
In many ferroelectrics, polarization switching may occur by more complicated (inhomogeneous) processes, such as domain nucleation and growth (typically around defects) or order-disorder processes.Although it is possible to construct models encompassing these more complex phenomena, they require tailoring to each particular material and are thus time-consuming and computationally expensive, which is impractical in terms of developing an efficient materials exploration method.For the purposes of this study, we have thus assumed a direct switching mechanism, with the coercive field estimated by calculating the magnitude of the polarization switching potential, Esw, from DFT energies of the crystal structure in various states between the polar variants using the fixed displacement-field (or fixed D-field) method. 54,55his may mean that the coercive fields are overestimated in some cases, but it has the merit of revealing trends within a reasonable time frame, thereby providing insight into which materials are promising as tetrahedral ferroelectrics.Efforts to determine the precise details of the switching mechanism can then be focused on those systems, which exhibit interesting ferroelectric behavior.
The calculated potential surfaces from which Esw values were extracted are plotted in Figs.2-4 for monovalent compounds (Cu and Ag halides), divalent compounds (Be, Mg, Mn, Zn,  and Cd chalcogenides), and trivalent compounds (Al, Ga, and In pnictogenides and 2H-SiC), respectively (results for compounds with electronically conducting paraelectric phases are included for completeness).The results reveal that all compounds exhibit a double-well potential, with the maximum corresponding to the intermediate non-polar state between the minima of the two polar variants.Out of all the compounds examined, the monovalent compounds (Cu and Ag halides) have the lowest Esw values, viz., 0.17 eV/f.u. for CuCl, 0.21 eV/f.u. for CuBr, 0.29 eV/f.u. for CuI, 0.11 eV/f.u. for AgCl, 0.15 eV/f.u. for AgBr, and 0.22 eV/f.u. for AgI.These barriers are close in magnitude to that of ferroelectric perovskite PbTiO 3 at 0.2 eV/f.u. 56In all cases, the potential barrier decreases with decreasing atomic number (thus ion radius) of the anion.Figure 5 shows a plot of Esw vs anion/cation radius ratio, χ (=r anion /r cation ), using Shannon's ionic radii 57 in sixfold coordination where available.In the case of anions N 3− and P 3− for which ionic radii are only reported for fourfold coordination, radii were estimated using the ratio of Madelung constants for wurtzite and rock-salt structures with a Born exponent of 6 and 8, respectively. 58n this figure, compounds that have the wurtzite structure under standard conditions are labeled in bold and in boxes; compounds FIG. 5. Relationship between polarization switching barrier, Esw, and ionic radius ratio, χ = r anion /r cation .Compounds with the wurtzite structure under standard conditions are labeled in bold within boxes, those with the zinc blende structure in italics, those with the nickeline structure in curly brackets, and those with the rock-salt structure in normal font.Compounds known to be synthesizable in the wurtzite structure under non-equilibrium or non-standard conditions are underlined.
whose ground state is the zinc blende structure are labeled in italics, those with the nickeline (NiAs) structure in curly brackets, and those with the rock-salt structure in normal style.Compounds that have been reported to be prepared in the wurtzite form under non-equilibrium conditions are underlined.For example, both of the nickeline-type compounds, MnSe and MnTe, have been stabilized with the wurtzite structure when prepared in nanowire, nanoribbon, or nanoparticle form. 59,60The results show that, for both hypothetical and actual wurtzites, there is a comparatively simple relationship between χ and Esw over a wide range of chemical compositions, with Esw increasing monotonically with increasing χ.Deviations from linearity can be ascribed to differences in the nature of the chemical bonding (from ionic to covalent), especially at higher χ values beyond the normal range of ground-state wurtzite compounds (roughly 1.9 ≲ χ ≲ 3.1).
We rationalize the linear relationship between Esw and χ as follows: A decrease in χ means that structures with sixfold coordinated sites (e.g., the rock-salt structure) become more stable compared to structures with fourfold coordinated sites such as wurtzite compounds so that the energy difference between polar variants (P6 3 mc) and the non-polar (P6 3 /mmc) state, i.e., Esw, decreases; in other words, the non-polar state becomes energetically more favorable.When χ ≲ 1.9, the rock-salt (Fm 3m) structure is the most stable, as found for AgCl, AgBr, CdO, and MgO.In terms of phase stability, the MnX compounds are the most different to the others, which we posit is a result of the markedly different bonding states associated with the d-orbital electrons of Mn 2+ ions.MgS also appears to be an anomaly, having the rock-salt structure at room temperature, although it has been shown to take on the wurtzite structure in thinfilm form. 61In regard to compounds with low switching barriers, CuCl lies just within the wurtzite zone; experimentally, it is reported to have the zincblende structure (F 43m) but transforms to wurtzite at around 400 ○ C, 62 making it a good candidate for being a tetrahedral ferroelectric if prepared under suitable synthesis conditions.According to our DFT calculations, the energy difference between wurtzite CuCl and zincblende CuCl is as little as 1.4 meV/f.u.In contrast, for the well-known rock-salt-structured compound AgCl, χ AgCl = 1.6, which is well outside the wurtzite zone, and so is predicted to be very difficult to stabilize in wurtzite form, in good agreement with experiment.Indeed, the energy difference between rock-salt AgCl and wurtzite AgCl 29 meV/f.u.) is much larger than that between the analogous forms of CuCl.

FIG. 1 .
FIG. 1. (a)Hexagonal wurtzite structure of binary compound MX (space group P6 3 mc).(b) Polarization switching mechanism: ferroelectric state with P = +Ps, paraelectric (intermediate) state with P = 0, and ferroelectric state with P = -Ps after inversion of MX 4 tetrahedra by applying an electric field parallel to the c axis, where δ is displacement of an ion relative to its position in the intermediate structure.

TABLE I .
Calculated lattice parameters, bandgaps (E bg ), Born effective charges (Z * 33 ), and spontaneous polarizations (Ps) of binary compounds examined in this study.Where available, experimental lattice parameters (in parentheses) and calculated deviations are also included.