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Binary Compound Bilayer and Multilayer with Vertical Polarizations: Two-Dimensional Ferroelectrics, Multiferroics, and Nanogenerators Lei Li and Menghao Wu* School of Physics and Wuhan National High Magnetic Field Center, Huazhong University of Science and Technology, Wuhan 430074, China S Supporting Information *

ABSTRACT: Vertical ferroelectricity in two-dimensional (2D) materials is desirable for high-density data storage without quantum tunneling or high power consumption/dissipation, which still remains elusive due to the surfacedepolarizing field. Herein, we report the first-principles evidence of 2D vertical ferroelectricity induced by interlayer translation, which exists extensively in the graphitic bilayer of BN, AlN, ZnO, MoS2, GaSe, etc.; the bilayer of some 2D ferromagnets like MXene, VS2, and MoN2 can be even multiferroics with switchable magnetizations upon ferroelectric switching, rendering efficient reading and writing for high-density data storage. In particular, the electromechanical coupling between interlayer translation and potential can be used to drive the flow of electrons as nanogenerators for harvesting energy from human activities, ocean waves, mechanical vibration, etc. A ferroelectric superlattice with spatial varying potential can be formed in a bilayer Moire pattern upon a small twist or strain, making it possible to generate periodic n/p doped-domains and shape the periodicity of the potential energy landscape. Finally, some of their multilayer counterparts with wurtzite structures like a ZnO multilayer are revealed to exhibit another type of vertical ferroelectricity with greatly enhanced polarizations. KEYWORDS: two-dimensional ferroelectrics, vertical polarizations, multiferroic bilayer, ferroelectric nanogenerators, ferroelectric Moire superlattice depolarizing field. Another challenge for both FeRAMs and MRAMs is the integration into semiconductor circuits: although intensive research has been devoted to diluted magnetic semiconductors trying to incorporate ferromagnetism (FM) into semiconductors, their Curie temperature can scarcely reach room temperature;5 efforts on combining FE with semiconductors have been scarcely reported, as FE cannot be induced simply by doping magnetic ions, while traditional ferroelectrics like perovskites2 with large bandgaps are insulators rather than semiconductors. Actually, neither FeRAMs nor MRAMs have commercially substituted current silicon-based RAMs, which can be integrated in silicon wafers utilizing a mature silicon process. Since the isolation of graphene from graphite in 2004,6 a series of two-dimensional (2D) layered materials such as

T

he prevailing silicon-based random access memories (RAMs) have been disturbed by two major problems, which will become almost unsolvable with the downscaling of integrated circuit size to nanoscale: (1) Their logic “0” and “1” states are not degenerate in energy, giving rise to quantum tunneling and memory wear. (2) They are volatile as their states are lost upon power outage, and the required continuous supply of power will be a challenge to power dissipation, limiting the performance of electronics from handheld devices to massive data centers. Both issues may be solved in ferroelectric RAMs (FeRAMs) or magnetic RAMs (MRAMs): the “0” and “1” states in ferroics are equivalent, and both types of ferroic memories are nonvolatile. FeRAMs can be even more energy saving than MRAMs in data writing with a much lower energy cost in switching.1 However, for the ultrathin films of traditional ferroelectrics,2 in-plane ferroelectricity (FE) is generally not suitable for high-density data storage, while their vertical FE will vanish below critical film thickness (24 Å in BaTiO3, 12 Å in PbTiO3)3,4 due to the © 2017 American Chemical Society

Received: April 20, 2017 Accepted: June 11, 2017 Published: June 11, 2017 6382

DOI: 10.1021/acsnano.7b02756 ACS Nano 2017, 11, 6382−6388

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Figure 1. (a) Ferroelectric switching pathway of BN bilayer; (b)different stacking configurations of graphene/BN heterobilayer with distinct interlayer potentials, which can be utilized as nanogenerators. Gray, pink, and blue spheres denote C, B, and N atoms, and black and red arrows denote the direction of charge transfer and polarizations, respectively.

hexagonal boron nitride (h-BN)7,8 and transition-metal dichalcogenides (for example, MoS2)9 have also been exfoliated by following the same procedure of micromechanical cleavage. As the performance of traditional transistors at nanosize will be seriously influenced by quantum effects, 2D materials with atomic thickness and much higher performance are likely to replace the current semiconductor materials in microelectronics and facilitate the extension of Moore’s Law in the future. They may be also endowed with nonvolatile memory upon the incorporation of FE and their range of applications will be greatly enhanced, rendering the direct integration of FE into semiconductor circuits. Compared with FM that is usually weak in semiconductors, FE does not have such conflicts and may possess a high Curie temperature and a moderate bandgap simultaneously. Meanwhile FE has been much less explored in 2D compared with FM: since the first prediction of 2D van der Waals FE in graphanol years ago,10 later theoretical studies have proposed that 2D FE may also emerge in distorted 1T MoS2,11 buckled honeycomb AB monolayer,12 phosphorene analogues (GeS, GeSe, SnS, SnSe),13 hydrogenated carbon nitride,14 and chemically functionalized 2D materials;15 it was not until 2016 that 2D FE was realized experimentally in thin-layer SnTe16 and CuInP2S6.17 Here, by first-principles calculations, we reveal the wide existence of 2D vertical FE in a series of van der Waals bilayers (like BN, MoS2, GaSe) or even their bulk phase, as well as some wurtzite multilayer, which may enable the direct integration of nonvolatile memories into semiconductor circuits. Their interlayer translation can change the interlayer potential and drive the flow of electrons, which can be utilized as nanogenerators. Some magnetic bilayer like MXene, VS2, and

MoN2 can be even multiferroics with switchable magnetizations upon ferroelectric switching.

RESULTS AND DISCUSSION It is known that graphene and hexagonal boron nitride (h-BN) possess similar crystal structures with only 2% lattice constant difference. First, we investigate the case of the BN bilayer, where AB1 stacking has already been revealed to be the ground state in previous studies.18,19 The geometric structure of the BN bilayer in AB1 stacking is displayed in Figure 1a, where the optimized interlayer distance is 3.10 Å. For this configuration, the N atom in the upper layer is over the hexagon center in the down layer, while the B atom in the upper layer is right over the N atom in the down layer. Here, the closer interlayer B−N distance may lead to a stronger charge transfer, giving rise to a net charge transfer from the upper layer to the down layer (marked by black arrow) and a vertical polarization upward (marked by red arrow). This polarization can be switched upon the interlayer translation by one B−N bond length, moving the N atoms in the upper layer right over the B atoms of the down layer, as shown in Figure 1a. The translation pathway, i.e., the ferroelectric switching pathway, has been computed by using nudged elastic band (NEB)20 method, as shown in Figure 1a. It turns out that the barrier is only ∼9 meV per unitcell, revealing the feasibility of ferroelectric switching under ambient conditions. According to Berry phase calculations, the switchable vertical polarization will be 2.08 × 10−12 C/m in 2D and 0.68 μC·cm−2 in 3D, more than three times higher than 1T MoS2 reported previously(0.22 μC·cm−2).11 6383


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Figure 2. Ferroelectric Moire superlattice upon (a) a small twist angle or (b) a slight difference in strain between upper and down layer. ABup, AB-down, and AA regions are marked in yellow, green, and red circles, respectively.

It is known that a small twisted angle in the van der Waals bilayer can give rise to a Moire superlattice,34−36 where the large-scale modulation of local stacking can generate different ferroelectric domains in the BN bilayer, as displayed in Figure 2a: the polarization is vanished in AA stacking domains (marked in red circle), while for AB stacking domains, the polarization can be either upward (in AB-up domains with B atoms of upper layer right over the N atoms in the down layer, marked in yellow circle) or downward (in AB-down domains with N atoms of upper layer right over the B atoms in the down layer, marked in green circle), depending on the direction of interlayer charge transfer from B to N. A slight difference in strain between the upper and down layer can induce another type of ferroelectric Moire superlattice, with periodic stripes of AB-up, AA, and AB-down domains, as well as periodic varying interlayer voltage, as shown in Figure 2b. Similar types of Moire pattern for C/BN heterobilayer can be constructed, where periodic n- or p-doped graphene domains can be generated and the electronic properties of graphene can be tuned; note that the modulation of local potential of graphene placed on a BN monolayer can give rise to fractional quantum Hall effect and Hofstadter’s butterfly according to previous observations.37,38 Computation of electrostatic potential reveals that the difference in work function between AB1 and AB2 domains of the C/BN heterobilayer is 0.11 eV. Although the local bandgap can be enhanced upon vertical compression as mentioned above, it is not so dependent on lateral interlayer displacement. However, for the BN bilayer, it has been shown by our previous calculations34 that the bandgap is 4.57 eV for AB stacking but only 3.99 eV for AA stacking, which even declines to 3.49 eV as the interlayer distance is compressed by 10%. It turns out that the local electronic structures vary with lateral and vertical interlayer displacements, akin to previous predictions on bilayer blue phosphorus.39 Similar 2D vertical FE may emerge in other AB stacking bilayers of binary compounds with hexagonal lattice, like layered AlN, SiC, ZnO, and so on. Note that it has been revealed that many cubic or wurtzite structures share a graphitization tendency in ultrathin films terminated by (111) or (0001) surfaces,40,41 while graphitic few-layer GaN,42 SiC,43

If the upper BN layer is substituted by a graphene layer, in the ground state denoted as AB1 stacking shown in Figure 1b, the B atoms of the BN layer will be right below the upper C atoms, while the N atoms will be over the hexagon centers of graphene layer. Similarly, a vertical polarization of 1.5 × 10−12 C/m pointing downward can be formed, and the graphene monolayer is essentially n-doped. By a coarse estimation using qd

the formula U = εS , the interlayer voltage for BN bilayer and C/BN heterobilayer are, respectively, 0.23 and 0.17 V. For another configuration of C/BN heterobilayer denoted as AB2 stacking with a slightly higher energy, where the N atoms are right below the C atoms, the polarization will be 3.3 × 10−13 C/ m pointing upward. Here, the graphene monolayer will be pdoped and the interlayer potential difference will be −0.04 V. If the graphene on the BN monolayer is dragged along the armchair direction, the interlayer voltage will oscillate between 0.17 V for AB1 stacking and −0.04 V for AB2 stacking, generating an alternating current output signal, which can be used as nanogenerator. Here the mechanism of ferroelectric generator is somewhat akin to a previously designed triboelectric nanogenerator21−28 where variations in the potential as well as capacitance of the system can be used to drive the flow of electrons and harvest energies. We also explored their applications in piezotronics:29−31 as the interlayer distance is further decreased upon vertical pressure, the polarization as well as the interlayer voltage can be further enhanced. For example, as shown in Figure S1, when the interlayer distance is compressed by 10%, the polarization of the BN bilayer and the C/BN heterobilayer can be approximately doubled. Moreover, a bandgap of 0.31 eV can be opened in the graphene/BN bilayer upon such a pressure, which will be highly desirable for zero-bandgap graphene applied in nanoelectronics. It can be used as a pressurizing fieldeffect transistor; note that similar devices have been experimentally realized in few-layer MoS232 and halide perovskite33 with a bandgap revealed to be closed at 56 GPa. Somewhat differently, the compression on the C/BN bilayer switches the system from a semimetallic “on” to a semiconducting “off” state. 6384


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ACS Nano Table 1. Polarization of Bilayer Binary Compounds Such as BN, ZnO, AlN, etc. polarization (×10−12 C/m)

BN

ZnO

AlN

GaN

SiC

MoS2

InSe

GaSe

2.08

8.22

10.29

9.72

6.17

0.97

0.24

0.46

Figure 3. (a) FE in bulk MoS2 and InSe. (b) Switchable magnetization for MXene Cr2NO2, VS2, and MoN2 upon ferroelectric switching.

Figure 4. Ferroelectric switching pathway of bulk ZnO and 20-atom-thick ZnO multilayer.

and ZnO44 have already been experimentally realized. The critical number of layers up to which the graphitic structure has a lower cleavage energy compared with (0001) surfaces are, respectively, 24, 8, and 18 for AlN, SiC, and ZnO, so the ground states of the bilayer are graphitic akin to BN bilayer with AB stacking. Their polarizations as well as interlayer voltage can be much higher, as summarized in Table 1, where the AlN bilayer possesses the largest polarization almost five times higher than that of the BN bilayer. Other van der Waals bilayers like MoS2 and GaSe can also exhibit vertical FE, where interlayer charge transfer between Mo−S or Ga−Se atoms can induce interlayer voltage difference. It is worth mentioning that for MoS2 and InSe their ground state of the 3D bulk phase with R3m symmetry can also exhibit FE, as shown in Figure 3a. Meanwhile they are also semiconductors with suitable bandgaps and high mobility for nanoelectronics,45 rendering nonvolatile

memories directly integrated into semiconductor circuits possible.46 Multiferroic materials entailing both magnetism and FE are known to be elusive, and strong magnetoelectric coupling for electric field control of magnetization remains challenging.47 Herein, it is demonstrated that the multiferroic bilayer can be designed upon combination of magnetism. There are a few choices of 2D ferromagnetic monolayer that have been synthesized to date, such as MXenes,48 VS2,49 MoN2,50 and LaCl/LaBr with room-temperature ferromagetism.51 For two monolayers that are antiferromagnetically coupled in the ground state, which are inequivalent due to the interlayer charge transfer and voltage difference, their total magnetic moments may be a non-zero value upon an incomplete compensation. The total magnetization can be switched with the reversal of polarization and interlayer voltage, rendering the ideal mode of “electrical writing + magnetic reading”. To our 6385


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and pressurizing field-effect transistors. Finally, some of their multilayer counterparts with wurtzite structures like ZnO multilayer are revealed to exhibit another type of vertical FE with much enhanced polarizations.

computation, the switchable magnetization for MXene Cr2NO2,52 VS2, and MoN2 (all revealed to be ferromagnetic in previous studies) are, respectively, 0.008, 0.016, and 0.09 μB per unit cell, which verifies the magnetoelectric coupling in 2D multiferroics. For the binary compounds in Table 1 like ZnO, the wurtzite structure will be more energically favorable than graphitic structure over critical thickness, where another type of vertical FE will be formed. It has been demonstrated that binary wurtzite structure (S.G.: P63mc) can be a polar but nonferroelectric crystal due to the large energy barrier for its polarization switching. For example, the polarization of bulk ZnO was estimated to be 90 μC·cm−2 in a previous study,53 while the switching barrier for ZnO can be as high as 0.25 eV/ fu, making its polarization unlikely to be switchable under ambient conditions. Although this barrier will be lowered to 0.15 eV/fu upon a 5% epitaxial tensile strain, the experimental realization of such a large strain is still a challenge. However, this value can be greatly reduced in ultrathin film, as long as the structure can still keep wurtzite from graphitization over critical thickness, which is 18-atoms thick for ZnO. As shown in Figure 4, the FE in wurzite ZnO can be understood by structure distortion from centrosymmetric P63/mmc by relative vertical displacement of Zn against O atoms, which is marked by black arrows. For 20-atomic-thick multilayer ZnO, this barrier can be reduced to 0.099 eV/fu, turning its FE switchable at ambient conditions. Similarly, for 14 atom thin-layer InN and ZnS that can maintain the wurtzite structure, the ferroelectric switching barrier can be reduced to 0.18 and 0.063 eV/fu, respectively. A wurtzite multilayer with relatively stronger spin−orbit coupling (SOC) and Rashba splitting, e.g., InN multilayer, can also be candidates for ferroelectric Rashba semiconductors, where electric fields can be used to control spin via ferroelectric switching. Some wurtzite multilayer structure like the SiC thin film can even be multiferroic with both FE and FM, and the spin distribution can change upon ferroelectric switching, as displayed in Figure S2. Note that the rare coexistence of FE and FM remains to date: almost all of the multiferroic materials reported are either antiferromagnetic or ferrimagnetic, except EuTiO3, which will be FM upon a large strain.14

COMPUTATIONAL METHODS Our calculations are performed by using DFT implemented in the VASP54,55 code. The generalized gradient approximation with the Perdew−Burke−Ernzerhof56 exchange-correlation functional and the projector augmented wave57 potentials are adopted. The kinetic energy cutoff is set to be 400 eV, and a large vacuum space is set in the vertical direction so the nearest distance between two neighboring bilayer is greater than 15 Å. For geometric optimization, the Brillouin zone is sampled with 12 × 12 × 1 k points using the Monkhorst-pack scheme,58 while the forces on all atoms are optimized to be less than 0.005 eV/ Å and the tolerance for the energy convergence is set to 10−5 eV. The PBE-D2 functional of Grimme59 is used to take into account dispersive forces, and the Berry-phase method is employed to evaluate crystalline polarization.60

ASSOCIATED CONTENT S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acsnano.7b02756. Additional details for the piezoelectric effect of AB stacking bilayer BN and BN/C heterobilayer and ferroelectric switching of a 10-layer thin film of wurtzite SiC (PDF)

AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected]. ORCID

Menghao Wu: 0000-0002-1683-6449 Notes

The authors declare no competing financial interest.

ACKNOWLEDGMENTS M.W. is supported by the National Natural Science Foundation of China (No. 21573084). We thank Prof. Ju Li (MIT) and Prof. Jun Zhou (HUST) for helpful discussions and also the Shanghai Supercomputing Center for providing computational resources.

CONCLUSIONS In summary, through density functional theory (DFT) calculations we demonstrate that the graphitic bilayer of BN, AlN, ZnO, MoS2, GaSe, etc., can be 2D ferroelectrics with vertical polarizations, while MXene Cr2NO2, VS2, and MoN2 bilayers can even be multiferroics with switchable magnetizations upon ferroelectric switching, rendering efficient reading and writing for high-density data storage with low energy consumptions. A similar rule can be applied to the bulk phase of van der Waals semiconductors like MoS2 and InSe with suitable bandgaps and high mobility for nanoelectronics, rendering nonvolatile memories directly integrated into semiconductor circuits. Such 2D FE induced by interlayer translation may possess a much extended range of potential applications. For example, a small twist or strain difference in bilayer can give rise to a ferroelectric superlattice with spatial varying potential and periodic n/p-doped domains. Moreover, their interlayer translation can change the interlayer potential and drive the flow of electrons, which can be utilized as nanogenerators, with great applications in self-powered systems for personal electronics, environmental monitoring, etc. Such an electromechanical coupling may be also utilized in piezotronics

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