Mechanically-Controllable Strong 2D Ferroelectricity and Optical

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Mechanically-controllable strong 2D ferroelectricity and optical properties of semiconducting BiN monolayer Peng Chen, Xuejing Zhang, and Bang-Gui Liu ACS Appl. Nano Mater., Just Accepted Manuscript • DOI: 10.1021/acsanm.8b01628 • Publication Date (Web): 21 Dec 2018 Downloaded from http://pubs.acs.org on December 26, 2018

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ACS Applied Nano Materials

Mechanically-Controllable Strong 2D Ferroelectricity and Optical Properties of Semiconducting BiN Monolayer Peng Chen,1, 2 Xue-Jing Zhang,1, 2 and Bang-Gui Liu1, 2, ∗ 1

Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China. 2 School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100190, China. (Dated: December 21, 2018) Structural, electronic, ferroelectric, and optical properties of two-dimensional (2D) BiN monolayer material with phosphorene-like structure are studied in terms of the density functional theory and modern Berry phase method of ferroelectric calculation. Both phonon spectra, molecular dynamics simulations, and total energy comparison indicate that the BiN monolayer is a stable 2D ferroelectric with polarization as large as 580 pC/m, with ferroelectric polarization being sustainable up to 500 K. Further study shows that the polarization in the BiN monolayer can be easily switched from [100] to [010] direction over the bridging saddle phase by applying a tensile [010] stress of 2.54 N/m or compressive [100] stress of -1.18 N/m. This phase transition makes its lattice constants vary in a large range compared to other non-ferroelectric 2D materials. Moreover, through applying uniaxial tensile stress parallel to the polarization, one can fix the polarization and change the semiconductor energy gap, from direct to indirect one. The optical properties feature a very strong anisotropy in reflectivity below the photon energy of 4 eV. All these significant ferroelectric, mechanical, electronic, and optical properties make us believe that the 2D BiN monolayer can be used to make stretchable electronic devices and optical applications. Keywords: 2D semiconductor, 2D ferroelectricity, monolayer, mechanical manipulation, optical property, 2D material

I.

INTRODUCTION

The two-dimensional material has attracted more and more attention in both condensed matter physics and material science because of its wealth of physical phenomena due to the confinement of electrons[1–7]. These special structural and electronic properties can produce many unique optical, mechanical, and electronic functions[7] and can be used to design novel electronic devices[8–10]. In most of the applications of ferroelectric materials, one used thin-film materials[11–13], because they allow an achievable moderate voltage to switch the polarization[14]. However, to guarantee the devices to work reliably, the high quality of the thin films and the interfaces is demanded. Moreover, there exists a critical thickness[15] for the ferroelectricity in the traditional perovskite ferroelectric ultrathin films, because of the imperfect screening of depolarizing field at the ferroelectricmetal interfaces[16]. Therefore, two-dimensional ferroelectric materials should be highly desirable. The idea of two-dimensional ferroelectricity is very attractive because 2D materials, such as black phosphorus, graphene, and MoS2 , usually have great mechanical flexibility and can allow large strains (∼25%) [17–20], and ferroelectricity often coexists with tensile strains, in addition to lone pair or second-order Jahn-Teller effect[10, 14, 16]. Unlike the low-dimensional ferromagnetism whose Curie temperature Tc is often far below room temperature (for two-dimensional isotropic Heisenberg spin

∗

[email protected]

models, one has Tc = 0 according to Mermin-Wagner theorem[21]), two-dimensional ferroelectricity can survive at a relatively high temperature. It is also of interest that two-dimensional ferroelectricity is compatible with two-dimensional semiconductors[16]. Recently, ferroelectric and even multiferroic phenomenon have been observed in several types of two-dimensional materials[22– 27]. Because the ridged structure of black phosphorus has a unique atomic arrangement order[28], ferroelectricity can be formed in phosphorene-like structures[22– 24, 26, 27].

In this paper, considering similar ionic radii of Gd3+ and Bi3+ , we construct a BiN monolayer in terms of stable GdN compound, and use the Bi 6s lone pair (as in the famous BiFeO3 ) to induce a strong ferroelectric polarization in the BiN monolayer with the phosphorenelike structure. Our first-principles investigation proves that this two-dimensional BiN is thermally and dynamically stable and ferroelectricity can persists up to 500 K. Strain engineering calculations indicate that the ferroelectric polarization and the semiconductor band gap can be easily manipulated by applying uniaxial stress. Our analysis of mechanical properties prove that the BiN monolayer is mechanically flexible. Its anisotropic features have a significant effect on its optical properties. These features make us believe that this BiN monolayer with Phosphorene-like structure may be applicable for stretchable electronic devices and optical applications. More detailed results will be presented in the following.

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II.

METHOD

The calculations are performed in terms of the density functional theory (DFT)[29, 30] and projectoraugmented wave potentials[31], as implemented in VASP[32]. We use the exchange-correlation functional PBEsol[33], and adopt usual atomic pseudopotentials of Bi:6s2 5d1 06p3 and N:2s2 2p3 . Our computational model is a supercell consisting of the BiN monolayer and a vacuum layer of 20 ˚ A. The plane wave energy cutoff is set to 500 eV. The 11 × 8 × 1 k-point mesh in the Brillouin zone is constructed within Monkhorst-Pack scheme[34]. Phonopy package[35] is used in the phonon spectrum calculations. All the structures have been fully relaxed until the largest forces between the atoms become less than 1 meV/˚ A. Phase-switching paths are determined with the help of the ‘Nudged Elastic Band’ (NEB)[36] method which can give the most energetically favorable intermediate configuration between the initial and final structures. To calculate the ferroelectric polarization, we use the modern Berry phase method[37]. When estimating the 3D polarization of stacked two-dimensional ferroelectric material (to show how strong a 2D ferroelectricity is in comparison to usual 3D one), the Van der Waals correction is included in the GGA scheme. Ab-initial molecular dynamics simulations st different temperatures are adopted to show the finite temperature stability of ferroelectric phase of the BiN monolayer.

III. A.

RESULTS AND DISCUSSION

Stable structure and ferroelectricity

It is well known that the strong ferroelectricity in BiFeO3 originates from the lone pair of Bi atom. We believe that Bi can cause two-dimensional ferroelectricity in appropriate chemical environment. Considering that the radius of Bi3+ ion is almost the same as that of Gd3+ ion, we construct the BiN monolayer in terms of the structure of GdN compound. On the other hand, this BiN monolayer can be considered to be made by substituting the P atoms in the famous phosphorene structure by Bi and N atoms. It has center inversion symmetry, as shown in Fig. 1 (a.1) and (a.2). It can be seen that the centers of anions and cations coincide, which indicates no ferroelectric polarizations. We will call this phosphorene-like structure as reference phase in the following. We calculate its zero K phonon spectrum, and find that the largest soft mode frequency can be found at Γ point, as shown in Fig. 1 (a.3). Further analysis shows that this imaginary frequency is two-fold degenerate and they imply possible ferroelectric displacements along [100] and/or [010] direction. Then, we distort the reference structure according to the two soft phonon modes. When applying the two modes together, we can get a ferroelectric phase described in Fig. 1 (b.1) and (b.2), and its polarization is along [110] direction. Fur-

FIG. 1. (Color online) Top views, side views, and phonon spectra of reference phase (a.1, a.2, a.3), saddle phase (b.1, b.2, b.3), and ferroelectric phase (c.1, c.2, c.3) of BiN monolayer. The large green balls represent Bi, and the black ball N. The red circle in reference means inversion center, and the red arrows in the structures indicate the ferroelectric distortions.

ther calculated phonon spectra show that the structure with [110] polarization still has soft modes, as shown in Fig. 1(b.3), which indicates this phase is a saddle point on the energy surface (saddle phase). When adopting only one of the modes, we obtain the ferroelectric phase in Fig. 1 (c.1) and (c.2) and the polarization is along either [100] or [010] direction. The space group of the supercell is Pmn21 (#31), and the lattice constants of the supercell are a = 3.469˚ A, b = 3.624˚ A, and c = 15˚ A. The internal coordinates of Bi is (0.5000,0.0000,0.4132) and those of N (0.3866,0.0000,0.5562). There are four atom planes, in the series of Bi-N-N-Bi, and the Bi-Bi plane distance is 2.606˚ A. The Bi-N bond lengthes are 2.184˚ A and 2.278˚ A. Further phonon spectra show that there is no imaginary frequency in this case, as shown in Fig. 1(c.3), and therefore the structure with [100] or [010] polarization is dynamically stable. Furthermore, we perform ab-initial molecular dynamic simulations of the BiN monolayer at 300 K, 400 K, 500 K, 700 K, and 1100 K. The structures of 300 K and 500K at 7.5 ps are shown in Fig. 2. We can see that the twodimensional BiN monolayer can preserve its ferroelectric properties at least up to 500 K; and when temperature is as high as 700 K, the structure is still stable, but the polarization is substantially reduced; and when temperature is higher than 1100 K, the structure is broken by the thermal fluctuation. Actually, when temperature is higher than 500 K, the local dipoles start to orient randomly, which makes the net polarization decrease. Since the reference structure has higher energy than the saddle phase, the reference structure is supposed to show up at higher


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(G2D ), and Poisson’s ratios (ν 2D ) for the 2D system[39]:  C 2D C 2D − C 2D C 2D   Y∥2D = 11 22 2D 12 21 ,   C22    2D 2D 2D 2D  C11 C22 − C12 C21  2D Y⊥ = , 2D C11  2D   G2D = C66 ,   2D 2D   C C12 2D   ν∥2D = 21 , ν = ⊥ 2D 2D C22 C11

FIG. 2. (Color online) Top view snapshots and side view snapshots of ferroelectric BiN monolayer at 300 K (a.1, a.2) and 500 K (b.1, b.2), from the ab-initio molecular-dynamics simulations for 7.5 ps.

temperature. It can be seen by noting that around 700 K, there are center-symmetry-like structures in some of the cells. Therefore, we believe that the ferroelectric twodimensional BiN monolayer is thermodynamically stable beyond 500 K. In addition, we compare the total energy of the BiN monolayer with those of other similar two-dimensional structures of BiN, summarizing detail in Supporting Information. It is confirmed again that the BiN monolayer is lowest in the total energy and therefore is stable. It is noted that the ferroelectric [100] and [010] phases are equivalent to each other, with their polarization orientating in the two directions, but we still distinguish them by their different polarization directions because these equivalent phases can have different behavior under different strains. This is crucial to the discussion of the ferroelectric switching in the following.

B.

Mechanical flexibility

The elastic stiffness constants Cij can be determined by making six finite distortions of the lattice and deriving the elastic constants from the strain-stress relationship[38]. Since the system is treated as a bulk (in the VASP package) which is a combination of the monolayer and vacuum, the Cij are in GPa. As a result, the 2D elastic stiffness constants should be recovered by 2D Cij = Cij × c, in which c is the lattice constant contain2D ing the vacuum, accordingly the Cij are in J/m2 . Then, 2D we can derive Young’s modulus (Y ), shear modulus

(1)

TABLE 1. The two-dimensional Young’s modulus (Y2D and ∥ 2D 2 2 Y⊥ in J/m ), shear modulus (G in J/m ), and Poisson’s 2D ratios (ν∥2D and ν⊥ ) for the Phosphorene, Graphene, MoS2 , and monolayer BiN. The ∥ and ⊥ indicate the ferroelectric direction and the direction perpendicular to the ferroelectric orientation respectively. Y∥2D Y⊥2D G2D ν∥2D 2D ν⊥

Phosphorene[20] 24.42 92.13 22.75 0.17 0.62

Graphene[40] 366.4 366.4 162.8 0.125 0.125

MoS2 [41] 123 123 47.9[42] 0.25 0.25

BiN 47.14 101.41 11.78 0.08 0.21

Our calculated Young’s modulus and Poisson’s ratios are listed in Table 1. Due to the polarization, the Young’s modulus (Poisson’s ratio) are anisotropic in the plane of the monolayer, being different when the direction is parallel (∥) and perpendicular (⊥) to the ferroelectric orientation. The Young’s modulus in the ⊥ direction is two times larger than that in the ∥ direction. As shown in Table 1, Graphene has the largest Young’s and shear modulus, and MoS2 and phosphorene have smaller values. It can be seen that the moduli of the BiN monolayer are larger than those of phosphorene and the in-plane anisotropy is less than that of phosphorene. Although the moduli are the second smallest among the four monolayer systems, the shear modulus of the BiN monolayer is the smallest, nearly half that of phosphorene. For the Poisson’s ratio, we notice that the BiN monolayer has the smallest ν∥2D , which means that when we squeeze (stretch) the BiN monolayer along the ferroelectric direction, it expands (shrinks) the smallest in the perpendicular direction. We believe that the BiN monolayer can preserve its superior mechanical flexibility as phosphorene does.

C.

Ferroelectric polarization and mechanical switching

We calculate the ferroelectric polarization with the modern berry phase ferroelectric theory. The polarization of the BiN monolayer reaches to 580 pC/m which is larger than that of the predicted GeSn. In order to make a simple comparison with the famous room-temperature



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FIG. 3. (Color online) Total energies (a) and ferroelectric polarizations (b) of ferroelectric [100] and [010] phases as functions of the lattice constant. The two black dashed vertical lines indicate the equivalent lattice constants in the two directions. (c) Energy values along the switching path from ferroelectric [010] phase to ferroelectric [100] phase through the saddle phase whose polarization is along [110] direction.

multiferroic BiFeO3 [43–45], we stack the BiN monolayers to form a 3D layered structure, and obtain a threedimensional polarization of 88.8 µC/cm2 . Because this 3D polarization is comparable with that of BiFeO3 , it is clear that the BiN monolayer has very strong 2D ferroelectricity. The ferroelectric polarization of the BiN monolayer can take one of the [100] and [010] directions, and then we think that the BiN monolayer can take one of the two phases defined to have polarization along the [100] and [010] directions, respectively. The uniaxial stresses parallel and perpendicular to the polarization will produce different effects on the BiN monolayer. When a uniaxial stress is applied, there will be a corresponding strain parallel to the stress and an opposite strain perpendicular to the stress. The perpendicular strain is determined by optimizing the total energy along this direction. In Fig. 3 (a), we present the total energies of the two ferroelectric phases as functions of the parallel strains. The two vertical black lines indicate the equivalent lattice constants along [100] direction (lattice constant a) for the [100] and [010] phases. For the [100] (or [010]) phase, as marked in blue (or in red) in Fig. 3(a), we performed structural optimizations with a given lattice constant a and plot the total energies as functions of a. Some representative data, with (a − a0 )/a0 =-5%∼5%, are summarized in Supporting Information. The mini-

ma of the two quadratic curves indicate the equilibrium lattice constant a0 for [100] and [010] phase respectively. The crossing point of the two curves, a0 =3.5388 ˚ A, indicate the phase transition point. Smaller the lattice constant a is, more favorable the [010] phase becomes, and a larger a favors the [100] phase more. If focusing on the red line (ferroelectric [010]) in Fig. 3 (a), the strains at the left lattice constant means the compressive strains perpendicular to the polarization direction and the strains at the right lattice constant indicate the tensile strain perpendicular to the polarization direction. The same configurations are applied to the blue line (ferroelectric [100]) in Fig. 3 (a), the only difference is that the strains are parallel to the polarization direction. We can see that there is an energy crossing between the ferroelectric [100] (blue line in Fig. 3) and the ferroelectric [010] (red line in Fig. 3) at a = 3.5388˚ A, which means that there will be a phase transition at this point, and accordingly a polarization switching between the [100] and [010] directions is shown in Fig. 3 (b). The strain to induce the phase transition of the [100] phase is only 2%. This strain can be produced by applying a parallel compressive stress of -1.18 N/m, or a perpendicular tensile stress of 2.54 N/m, which can be easily achieved in the two-dimensional materials. The energy barrier between these two phases has been calculated with the NEB method, as shown in Fig. 3 (c). We find out that the energy barrier is equivalent to 81 meV/f.u. if the ferroelectric [100] phase is switched through the reference phase (Fig. 1 (a.1) and (a.2)), but the energy barrier reduces to 10.5 meV/f.u. if the ferroelectric [100] phase is switched through the saddle phase (Fig. 1 (b.1) and (b.2)) that has polarization along the [110] direction. Because of the stress-induced phase transition, the lattice constant of the BiN monolayer can vary in a very large range, which makes it very flexible. From the blue line of the tensile strain part (ferroelectric [100]) in Fig. 3 (a), we can also see that the energy increases very slowly with the strain, which indicates the BiN monolayer is very mechanically flexible. On the other hand, we can also fix the polarization by applying tensile stress parallel to the polarization, as shown in Fig. 3(a). All these properties can make the BiN monolayer a very promising candidate for stretchable electronic devices.

D.

Mechanical manipulation of optical properties

Because strain (stress) is powerful to manipulating properties and functionals of materials[46, 47], we calculated the band structures of the BiN monolayer under a series of uniaxial stresses. We have found that the energy band gaps can be tuned by the uniaxial stress, changing from direct gap to indirect gap. In Fig. 4, the black dashed lines in (a) and (b) indicate the band structures of the ferroelectric [010] and [100] phases, respectively. In the Fig. 4 (a), we can see that it is a direct gap of 1.5 eV for the ferroelectric [010] phase, and it becomes


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FIG. 4. (Color online) Energy bands of the the ferroelectric [010] (a) and [100] (b) phases, with the [100] lattice constant changing from 3.30 to 3.80 ˚ A.

is applied, reaching to an indirect gap of 1.0 eV at the parallel strain of −5%. In the Fig. 4 (b), the direct gap is 1.5 eV at the equilibrium position, and the indirect gap is about 1.4 eV for a parallel tensile strain of 5%. Comparing (a) and (b) in Fig. 4, we can see that the gap transition, from direct to indirect, is much easy to achieve by applying uniaxial stress perpendicular to the polarization direction, but it cannot be tuned much by applying uniaxial stress parallel to the polarization direction. Therefore, while stretching the BiN momolayer as a two-dimensional material, we can achieve not only directional switching of its ferroelectric polarization but also manipulation of its semiconductor band gap.

(a)

(b)

FIG. 5. (Color online) The imaginary part of dielectric function (a) and reflectivity (b) of the BiN monolayer as functions of photon energy parallel (red) and perpendicular (blue) to the ferroelectric directions. The inset describes the partial energy band structure with arrows indicating the transitions.

an indirect band gap when compressive uniaxial stress

We calculate frequency-dependent dielectric constants and present the dielectric functions parallel and perpendicular to the ferroelectric directions in Fig. 5. As shown in the anisotropic Young’s modulus, the anisotropic feature is also reflected in the optical properties of the BiN monolayer. The peak ∆⋆ along the ferroelectric direction can only be found around 1.5 eV in the Fig. 5(a). This unique peak comes from the direct band gap along the Γ → X (∆) direction. Since the compressive stress applied to the ⊥ direction can tune the direct gap into an indirect gap, the ∆⋆ feature can be changed by applying such stress. The reflectivity below 4 eV is strongly anisotropic, as shown in Fig. 5(b), which implies that for the photon energy between 0 and 3.5 eV, the perpendicular reflectivity is at least twice the parallel reflectivity. Such strong anisotropy should be useful for designing new applications.



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E.

Further discussion

The crystal structure of the BiN monolayer originates from the famous faced center cubic GdN[48]. It is well known that GdN can preserve ferroelectric under strains[49]. It is reasonable to believe that the ferroelectric distortion without strain in the BiN monolayer comes from the Bi3+ lone-pair 6s electrons. The BiN monolayer is mechanically flexible according to our Young’s modulus calculation, being comparable with the phosphorene which has been proved to be the superior mechanical flexibility material[20]. The shear modulus of the BiN monolayer is even smaller than that of phosphorene, which explains why the energy barrier is so small for switching the ferroelectric polarization from [100] to [010] direction through the saddle phase. From the Fig. 3, the ferroelectric phase transition between [100] and [010] can be induced by 2% strain, corresponding to the lattice constant ranging from 3.469 ˚ A to 3.642 ˚ A. Considering the superior mechanical flexibilities, the BiN monolayer can be very easily stretched in a large range of lattice constant. Moreover, due to the ferroelectric polarization, the symmetry was broken between the [100] and [010] direction, which induces the anisotropic features of the energy band structure and the optical properties. As Fig. 3 shows, it should be easy to reoriented the BiN dipole from [100] to [010] direction (or other equivalent directions) by applying external stress. We performed larger-supercell calculations, in collinear cases in which the dipoles are parallel ([100] and [100]) and antiparallel ([100] and [-100]), and in non-collinear cases in which the dipoles are [100] and [010]. Both of the antiparallel and non-collinear cases converge into the reference phase after relaxation, which have higher energy than the parallel case. These implies that our results are robust against orientation fluctuations of Bi-N dipoles. Because Bi usually has strong spin-orbits effect, we also performed band calculations with the spin-orbits coupling taken into account. It is shown that the main results are not affected by the spin-orbits effect, as shown in Supporting Information.

being comparable with BiFeO3 in the 3D case. Further mechanical studies show that the polarization in this BiN monolayer can be easily switched from [100] to [010] direction over a saddle phase through overcoming a 10.5 meV/f.u. barrier by applying small tensile [010] stress of 2.54 N/m or compressive [100] stress of -1.18 N/m, corresponding to a strain of 2%. This phase transition in this 2D BiN monolayer makes its lattice constant change in a very large range in comparison with other non-ferroelectric materials. Moreover, through applying uniaxial tensile stress perpendicular to the polarization, one can fix the ferroelectric polarization and change the semiconductor energy gap, between direct and indirect. A very strong anisotropy has been found in the optical reflectivity when the photon energy is below 4 eV. All these features make us believe that the BiN monolayer as a two-dimensional material can be used to achieve stretchable electronic devices and optical applications.

SUPPORTING INFORMATION

The Supporting Information is available: Total energy comparison of different 2D structures of BiN monolayer; Structural parameters of the BiN monolayer under uniaxial stress; Effect of the spin-orbits coupling on the band structures.

AUTHOR INFORMATION

Corresponding Author *E-mail: [email protected] (B.G.L.). ORCID Bang-Gui Liu: 0000-0002-6030-6680 Notes The authors declare no competing financial interest.

ACKNOWLEDGMENTS IV.

CONCLUSION

In summary, we have studied a two-dimensional BiN monolayer with phosphorene-like structure which has been proven to tending to preserve ferroelectricity. Our calculated phonon spectra and MD calculations have show that it is structurally stable. Our DFT and Berry phase based modern ferroelectric theory studies have shown that the BiN monolayer has a 2D ferroelectricity with as large polarization as 580 pC/m,

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This work is supported by the Nature Science Foundation of China (No.11574366), by the Strategic Priority Research Program of the Chinese Academy of Sciences (Grant No.XDB07000000), and by the Department of Science and Technology of China (Grant No.2016YFA0300701). The calculations were performed in the Milky Way #2 supercomputer system at the National Supercomputer Center of Guangzhou, Guangzhou, China.

erostructures. Science, 353(6298):9439, July 2016.


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FIG. 6. For Table of Contents Only


Mechanically-Controllable Strong 2D Ferroelectricity and Optical

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