Piezoelectric properties in two-dimensional materials ...nesel.skku.edu/paper files/203.pdf · the 2D layered structure is also important and can lead to ﬂexo-electricity [15–17],

Materials Today d Volume xxx, Number xx d xxxx 2017 RESEARCH

Piezoelectric properties

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in two-dimensional materials:
Simulations and experiments RES

Ronan Hinchet 1,†, Usman Khan 1,†, Christian Falconi 2, Sang-Woo Kim 1,3,⇑

1 School of Advanced Materials Science and Engineering, Sungkyunkwan Un
iversity (SKKU), Suwon 440-746, Republic of Korea2Department of Electronic Engineering, University of Rome Tor Vergata, Roma 00133, Italy3 SKKU Advanced Institute of Nanotechnology (SAINT), Sungkyunkwan University (SKKU), Suwon 440-746, Republic of Korea
The piezoelectric effect, discovered in 1880 by Jacques and Pierre Curie, effectively allows to transducesignals from the mechanical domain to the electrical domain and vice versa. For this reason,piezoelectric devices are already ubiquitous, including, for instance, quartz oscillators, mechanicalactuators with sub-atomic resolution and microbalances. However, the ability to synthesize two-dimensional (2D) materials may enable the fabrication of innovative devices with unprecedentedperformance. For instance, many materials which are not piezoelectric in their bulk form becomepiezoelectric when reduced to a single atomic layer; moreover, since all the atoms belong to the surface,piezoelectricity can be effectively engineered by proper surface modifications. As additional advan-tages, 2Dmaterials are strong, flexible, easy to be co-integrated with conventional integrated circuits ormicro-electromechanical systems and, in comparison with bulk or quasi-1D materials, easier to besimulated at the atomistic level. Here, we review the state of the art on 2D piezoelectricity, withreference to both computational predictions and experimental characterization. Because of theirunique advantages, we believe 2D piezoelectric materials will substantially expand the applications ofpiezoelectricity.

IntroductionElectromechanical coupling is crucial for sensing [1,2], actuating[3,4], and energy harvesting [5,6]. Since piezoelectric materialscan be electrically polarized under an externally applied strainand, vice versa, can be deformed by an applied voltage [7,8],piezoelectricity effectively allows to bring signals from themechanical domain to the electrical domain and vice versa.Piezoelectricity is only possible in materials which havenon-centrosymmetric structures and a bandgap, i.e., arenon-metallic [7,9]. Most remarkably, several materials are cen-trosymmetric and, therefore, not piezoelectric, in their bulkform, but the inversion center disappears when they are thinneddown to monolayer [8,10,11], thus resulting in piezoelectricity.

⇑ Corresponding author at: School of Advanced Materials Science and Engineering,Sungkyunkwan University (SKKU), Suwon, 440-746, Republic of Korea.

E-mail address: Kim, S.-W. ([email protected])† Ronan Hinchet and Usman Khan contributed equally to this work.

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This is the case of hexagonal boron nitride (h-BN), manytransition-metal dichalcogenides (TMDCs), transition-metaldioxides (TMDOs), II-VI semiconductors (SCs), III-V SCs, III-monochalcogenides (III-MCs) and IV-monochalcogenides (IV-MCs). The emergence of two-dimensional (2D) piezoelectricityin materials that are not piezoelectric in their bulk form hasalready been the subject of several theoretical predictions [8,10]and experimental characterizations [9,11]. In these 2D piezoelec-tric materials, similar to bulk piezoelectric materials, the crystalstructure plays a very important role in piezoelectricity and canlead to flexoelectricity [12] like in thin films [13,14]. However,the 2D layered structure is also important and can lead to flexo-electricity [15–17], for example in some bilayers. Lastly, sincemost atoms in 2D materials belong to the surface, the influenceof the surface on physical phenomena cannot be neglected.Thereby, piezoelectric properties of 2D materials can bedramatically altered by surface modifications, including the

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RESEARCH Materials Today d Volume xxx, Number xx d xxxx 2018

introduction of adatoms and defects [18,19] leading to surfacepiezoelectricity and ferroelectricity [20]. This general surfaceproperty of 2D materials is especially interesting for engineeringpiezoelectricity. In fact, some 2D materials which are intrinsi-cally non-piezoelectric because their inversion symmetry ispreserved even in themonolayer form, can still bemade piezoelec-tric by means of surface or structure modifications. For instance,graphene (Gr) is intrinsically non-piezoelectric because bothatoms in the planar hexagonal unit cell are identical [11,21];nevertheless, piezoelectricity can be effectively engineered in Grby adatom adsorption or by incorporating non-centrosymmetricin-plane defects [7,18,22]. As a result, in two-dimensions, not onlymanymore piezoelectricmaterials exist, but, in principle, superiorpiezoelectric properties can be engineered.

Besides these specific advantages, namely the existence ofmore piezoelectric materials and piezoelectricity engineering,the other advantages of 2D materials [19,23–27] can also be cru-cial for the design of piezoelectric 2D devices. For instance, whileapproaching monolayer dimensions, the band structure canundergo major transformation [28,29] so that, as an example,monolayer MoS2, unlike its bulk form, has a direct band gapand is therefore a candidate for optoelectronics [28] and forpiezo-photo-tronics [30,31]. Besides, 2D materials are inherentlyflexible and strong [32–35]. As an additional advantage, the lim-ited number of atoms in 2Dmaterials greatly facilitates atomistic-level simulations of practical 2D devices. Moreover, free chargesin semiconductive 2D materials can be electrostatically con-trolled by gates [24], similar to quasi-1D and bulk devices, buteven by ghost gates [36], which do not require to materially fab-ricate gates and interconnects. Finally, at least in principle, 2Dmaterials are fully compatible with state-of-the-art microfabrica-tion technologies; as a result, in comparison with quasi-1D nan-odevices, devices based on 2Dmaterials may be easier to fabricate[37,38] and to be co-integrated with conventional integratedcircuits or micro-electromechanical systems (MEMS).

Here, we shall review the state of the art on piezoelectricity in2D materials. In section ‘Piezoelectric characterization of 2Dmaterials’, we shall outline several 2D materials systems, describetheir stability, crystal structures, and review the theoreticalpredictions of piezoelectricity. Thereafter, in section ‘2D piezo-electric devices’, we shall discuss notable experimental investiga-tions of piezoelectricity in 2D materials which were carried outusing atomic force microscopy (AFM) and piezoresponse forcemicroscopy (PFM). In section ‘Conclusion and perspectives’, weshall outline some 2D piezoelectric devices for energy harvestingand sensing [39].

2D piezoelectricity theoretical predictionsMany theoretical works have investigated the heat formationand the probability to exist of several 2D materials by takingadvantage of simulations based on the density functional theory(DFT). Depending on the material simulated, different methodshave been used, such as the projector-augmented wave potential[8,10,40,41] or the norm-conserving pseudopotential [8,42]methods. Different approaches can be used to calculate piezo-electric coefficients [43]. As explained by Alyörük et al. [44],piezoelectric coefficients are often calculated using Berry’s Phaseapproximation, but in some cases the density functional

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perturbation theory (DFPT) [45,46] can be advantageous [47].DFT Berry’s phase approximation method enables to calculatemany properties arising from small applied strain or lattice dis-placements, whereas the DFPT enables to compute these proper-ties without multiple ground-state calculations. Thereby, itfacilitates the calculations of the piezoelectric properties of awide range of materials having weak electronic correlations withgreat accuracy. We mention that small variations among differ-ent results found in the literature may be due to the differentcomputational approaches or also to differences in the valuesof the elastic constants and of other parameters which are usedin the simulations. Another important and challenging aspectis the computational modeling of fracture problems in 2D piezo-electric materials and structures [48–52]. We shall mention that,like in 1D piezoelectricity, fracture problems can reduce the effec-tive properties and practical use of 2D materials and, therefore,must be taken into account.

2D materials systemsHundreds of 2D materials have been discussed in the literature[53–56]. Recently, an intensive data mining over 50,000 inor-ganic crystals [57] allowed identifying 1173 2D weakly bondedsolids. Among them the authors found 325 potential 2D piezo-electric monolayers, defined by a non-zero electronic band gapand a lack of centrosymmetry in their monolayer crystal, butnot necessarily in their 3D bulk structure. In fact, since manymaterials lose their inversion symmetry in their monolayer form,many materials which are not piezoelectric in their bulk form,become piezoelectric at single-atomic thickness. Thereby, multi-ple well-known materials and specific material families havebeen reported as 2D piezoelectric monolayers, and numerousexotic material families are expected to be 2D piezoelectric[57]. Here we restrict to some piezoelectric 2D materials whosepiezoelectric coefficients have already been estimated in theliterature.

First, we distinguish (Figure 1a) the groups of SCs II–VI andIII–V that have already been intensively studied and used to syn-thesize quasi 1D piezoelectric structures such as ZnO [5] and GaN[58] nanowires. More recent studies have highlighted newTMDCs and TMDOs (both referred as TMD materials) piezoelec-tric materials. In particular, 2D MoS2 [59] was first experimen-tally demonstrated as piezoelectric in 2014 [11] whereas it isnot piezoelectric in its 3D form. Lastly, with the developmentof nanoelectronics beyond silicon, the groups of IV-MCs andIII-MCs started drawing attention, for example with Ge- andGa-based material systems such as GeSe [60] and GaS [61].

Only some materials can exist in 2D form. For instance, Ras-mussen et al. [40] performed intensive DFT calculations of theheat of formation (Figure 1b) for most 2D TMDO and TMDCmaterials; in fact, the heat of formation gives an indication onthe possibility to synthesize [62] the material and on their rela-tive stability. Among the 216 material systems tested, 171 werefound stable as defined by a negative heat of formation relativeto the standard states. Overall, we can see that oxides have thehighest stability followed by the sulfides, selenides, and tel-lurides. The stability also decreases as the radius of the transitionmetal (TM) ion decreases (go through the left of TM series). Asmentioned, the heat of formation gives an indication on the

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FIGURE 1

Elements considered in this review. (a) Periodic table of the atom candidates to create 2D material systems. (b) Calculation of the heat of formation necessaryto create TMD monolayer in a trigonal prismatic 2H phase and an octahedral 1T phase [40].

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possibility to synthetize a material, but does not take intoaccount the mechanical instabilities and the competing phasesof lower energy. As a result, while a material may be possible tosynthetize in 2D form, a 3D form could also exist and be morestable, so that the material will preferably grow in its 3D forminstead of its 2D form, making the 2D form very challenging tosynthetize. Among the 171 stable 2D materials, 76 TMDCs arealready known as 3D multilayered bulk materials. The failure tofind bulk layered TMDOs in the Inorganic Crystal Structure Data-base (ICSD) [63] may indicate that TMDOs could have nonlay-ered bulk phases of higher stability than their 2D phases whichwould be metastable. To overcome this issue, works proposedto stabilize metastable 2D materials by taking advantage of theirinteraction with substrate or by encapsulating the monolayer, forinstance, with h-BN [64]. Another approach would be to usemechanical instability-driven manipulation as an approach toreach new 2D material phases and structures [65].


Prerequisite to 2D piezoelectricityA 2D material should have a low heat of formation to be stable.In addition, its 2D structure should be more stable than otherpossible 3D structures to have a chance to be synthesized. Intheir simulations, Ataca et al. [41] took into account the mechan-ical instabilities and the competing lower energy phases by carry-ing out molecular dynamics simulations on a restricted pool of88 TMDs. Their results are in total agreement with Rasmussenet al. [40]. Existing 2D materials are piezoelectric if and only ifthey fulfill two criteria: they must have a non-symmetric crystalstructure and they must be non-metallic (i.e., have a band gap).First, within the 171 stable 2D materials investigated by Ras-mussen et al. [40], only 52 TMDs were found to be non-metallic and non-magnetic. They can have a 1T and/or a 2H2D crystal structure. Here, the 2H refers to the Ramsdell notationfor the bulk stacking sequence (two-layer periodic) and the unitcell’s basal plane shape (hexagonal). As explained by Duerloo

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et al. [8], this notation is inaccurate in the case of monolayermaterials because the 2H notation provides insufficient informa-tion about the in-plane structure to differentiate it from the octa-hedral structure commonly called 1T. In addition, the 2 isirrelevant in the case of a monolayer. However, for consistencywe adopt the widely used 2H notation. In addition, a distortedoctahedral structure has also been reported experimentally [66]when synthesizing TMDs by exfoliation in aqueous solution[67], but we will not consider it here as it has not yet been studiedtheoretically. 1T 2D structures (Figure 2a) have an octahedralarrangement with hexagonal lattice. This structure has a sym-metric arrangement with a symmetric charge density distribu-tion. As a consequence, 1T crystals cannot be piezoelectric. Onthe other hand, 2H 2D crystals (Figure 2b) have a trigonalarrangement with hexagonal lattice. Normally, 2H crystals arecentrosymmetric [68], but, in case of monolayers, have no inver-sion center and non-symmetric arrangement with a non-symmetric charge density distribution. Therefore, 2H structurescan be piezoelectric. Overall, the results of Ataca et al. [41] aresummarized in Figure 2c. Among the 44 TMD materials thatcan form stable 1T and/or 2H monolayers, only the SCs withthe 2H structure being the most stable can be piezoelectric. Asa result, only the Mo, W and Cr-based TMDs are intrinsicallypiezoelectric in their 2D form. By contrast, other materials, likeSc-based TMDs, could be piezoelectric if their 2H structures werefound or artificially stabilized over their 1T structure, whichmotivate their piezoelectric study under their 2H form.

For other material groups, because of their smaller number ofcombinations and the special cases they represent, 2D piezoelec-tric properties of IV-MC and III-MC SC groups have been mostlystudied one by one or by small groups. II–VI SC monolayers aremore numerous and were investigated recently by Zheng et al.[69] who carried out a systematic study of 32 planar hexagonalmonolayer II–VI SCs. They found that these materials are notstable under their 2D planar hexagonal form but many of themare dynamically stable, meaning that they are at a local mini-mum of potential energy surface rather than at a saddle point(metastable), which is consistent with the previous II-oxide study[70]. They also found that tetragonal BaS and orthorhombic HgSare metastable which could lead in future to potentially moreunexpected metastable 2D crystal structures in the II–VI SCgroup. Similarly, several (III–V) SC monolayer structures werealso found metastable or unstable [71,72], having a planar hexag-onal structure for the (B-V), (III-N) and AlP compounds and abuckled hexagonal structure for the others. As explained byZhuang et al. [72] the formation energies of these 2D layers rela-tive to their bulk phases range from 0.38 eV/atom for InSb to0.52 eV/atom for AlP, which is rather high and could suggest thatthese materials may be unstable. Nevertheless, these energies arecomparable to the energy of a SiC monolayer (0.50 eV/atom),which has been successfully fabricated. Therefore, it should befeasible to synthesize (III–V) monolayers on a suitable hexagonalsubstrate that minimizes the formation energy and stabilizestheir 2D structure [73,74]. Interestingly, researchers found thatsome (III–V) compounds can organize into a buckled tetragonalbilayer structure which is more stable than the buckled hexago-nal structure. Indeed, buckled tetragonal bilayers have formationenergies around 0.2 eV/atom which is lower than that of buckled

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hexagonal structures and is close to the energy formation of syn-thesized ZnO monolayer at 0.19 eV/atom [75]. Nevertheless, thisstructure is symmetric and, therefore, may not be piezoelectric.Therefore, we will only consider the hexagonal structures of(III–V) SCs for their piezoelectric properties.

2D piezoelectric structuresRecently, several papers investigated the piezoelectric propertiesof potential 2D materials systems. Even if they can crystallizeinto various 2D structures, which are not all stable but also meta-stable, it is still interesting to evaluate their potential piezoelec-tric properties. Figure 3 shows the 2D crystal structures thatcan be piezoelectric. First, we can see that they all have a hexag-onal or a deformed hexagonal lattice which make these 2D mate-rials piezoelectric in the 11 direction. Then, depending on theirlayered structure, they can have other non-zero piezoelectriccoefficients. For example, the planar hexagonal and the 2Hhexagonal structures have only a non-zero d11 coefficient,whereas the buckled hexagonal structure has non-zero d11 andd31 coefficients [10]. Several studies considered the piezoelectricproperties of three structures, namely the planar hexagonalstructure for the (II–VI) SCs and some (III–V) SCs (Figure 3a),the buckled hexagonal structure for the other (III–V) SCs andsome (IV-MC) SCs, and the 2H hexagonal structure for TMDmaterials (Figure 3b). The TMD 2H hexagonal structure is partic-ularly remarkable as it is stable in a 2D as well as in a 3D layeredform called 3R. This 3D 3R layered structures can be found innumerous natural bulk TMD materials such as for MoS2 whichwas first isolated in its 2D monolayer form in 1986 [76] by exfo-liation of bulk MoS2. Nonetheless, 3D MoS2 crystal is not piezo-electric because its 2H monolayers stack into a top-to-tailconfiguration [59]. Therefore, the piezoelectric axis of eachmonolayer is opposed to its adjacent ones, the piezoelectric con-tribution of each layer is screened by others and the global rem-nant piezoelectric effect is negligible for more than a small oddnumber of monolayers [9]. Concerning (III-MC) SCs, a zigzagedges hexagonal nanoribbon [61] (X-M-M-X) of 4 atoms thick(Figure 3d) has been studied. This structure is the thickest of all2D monolayers considered having 2D piezoelectric properties.As a consequence of its more complex structure and consideringthe formation energy per atom (0.33 to 0.62 eV/atom) it mightbe possible to modify this type of monolayer with different com-bination of atoms following a (X-M-M-X0) or a (X-M-M0-X) pat-tern [77]. This could lead to an increase in their d11 coefficientand the appearance of a non-zero d31 coefficient. Finally, the caseof (IV-MC) SCs is especially interesting as three very differentstructures have been investigated, namely the buckled hexagonalstructure Figure 3c, the puckered anisotropic hexagonal structureFigure 3e and the puckered rectangular structure Figure 3f;remarkably, different structures result in very different piezoelec-tric coefficients[78].

2D piezoelectric coefficientsIn many cases, for each 2D material, different values of the samepiezoelectric coefficient have been reported. Because of thesevariations, we compare the relaxed-ion d11 and, eventually, thed31 and d12 piezoelectric coefficients taken from several refer-ences. The piezoelectric coefficient d measures the mechanical

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FIGURE 2

Potential 2D crystal structures and properties of TMD monolayers. (a) Octahedral 1T phase and (b) trigonal prismatic 2H phase structures and charge densitydistribution in the structure (contour plots and isosurfaces). (c) Summary of the stability simulation results on 44 TMD material systems that can form stablemonolayers in the 2H and/or 1T structure. The bottom structure (2H or 1T) is the ground state and the electrical state of the structure is indicated by theexponent (half-metallic+, metallic* or semiconducting**) [41].

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to electrical energy conversion ratio of the material and dependson the piezoelectric coefficient e and the elastic stiffness param-eters C of the material. Because of the variability of C dependingon materials, the trends observed for the e and d coefficients arenot necessarily the same. Usually, the relaxed-ion elastic con-stants C are mostly smaller than the clamped-ion ones becausethe internal relaxation of the ions allows releasing some of thestress in the former. This explains why clamped-ion piezoelectriccoefficients are smaller than relaxed-ion ones. Results agreerather well for well-known materials like common TMD com-pounds. However, for more recently investigated 2D materialslike (IV-MC) SCs, there are fewer and less consistent values inthe literature. For comparison, it is useful to consider the piezo-electric coefficients of the most widely used bulk piezoelectricmaterials and nanostructures. The a-quartz has a d11 of 2.3 pm/V [79], the wurtzite AlN has a d33 of 5.1 pm/V [80], the wurtziteGaN has a d33 of 3.1 pm/V [80], and the wurtzite ZnO thin filmhas a d33 of 12.4 pm/V [81]. DFT simulations can be rather


accurate; as an example, the calculated piezoelectric coefficientsof GaN are in agreement with experimental measurementswithin approximately 20% [82].

The piezoelectric coefficient d11 of known piezoelectric 2DTMD materials is given in Table 1. As a first remark, the calcu-lated relaxed-ion d11 coefficients of TMD monolayers are of thesame order as piezoelectric coefficients of typical bulk piezoelec-tric materials. Secondly, the piezoelectric coefficient follows twochemical trends: WO2 possesses the smallest piezoelectric coeffi-cient, and moving upward and to the left in the TM elements ordownward the chalcogenide elements increase the piezoelectriceffect until MoTe2 which has the largest piezoelectric coefficient.Duerloo et al. [8] clarified that this trend is especially noticeableon the d11 coefficient because the elastic stiffness coefficients C11

and C12 have an opposite trend, which amplifies the small trendin the e11 coefficient following Eq. (1).

d11 ¼ e11=ðC11 � C12Þ ð1Þ

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FIGURE 3

Monolayer structures that are non-centrosymmetric and can exhibit piezoelectricity. (a) Planar hexagonal monolayer structure [8]. (b) Trigonal prismatichexagonal monolayer structure [83]. (c) Buckled hexagonal monolayer structure [42]. (d) Nanoribbon hexagonal monolayer structure [61]. (e) Puckeredanisotropic hexagonal monolayer structure [60]. (f) Puckered rectangular monolayer structure [78].

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We found the same trend, in agreement, in all large piezoelec-tric theoretical studies on TMD monolayers [8,10,83]. Accordingto Alyörük et al. [83], this trend can be correlated with the polar-izability of chalcogenide atoms since atoms are more easily polar-ized when going downward in a group of the periodic table. Theyalso noted that the chalcogenide atoms dominate the piezoelec-tric effect in TMD monolayers; it has a much bigger impact onthe d11 coefficient than the TM atoms. This trend has beenconfirmed by Blonsky et al. [10] who found a very good propor-tionality between the d11 coefficient and the ratio of the polariz-ability of the anions and cation (Figure 4a). It means that d11 canbe maximized using a smaller TM atom (lower polarizability) and

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a larger chalcogenide atom (higher polarizability). This indicatesthat the piezoelectricity of TMD monolayers mostly originatesfrom the change in polarization of the ions due to the appliedstrain. The TM Zr makes an exception to this trend because theC11 elastic constant of Zr-X2 is smaller than that of Ti and Hf-based TMDCs. Similarly, TMDOs usually have a much larger elas-tic constant which induce a much smaller d11 coefficient com-pared to TMDCs. In these cases, the mechanical propertieshave a strong impact on the d11 coefficient. The softer the mate-rial, the bigger the d11 coefficient.

Similar properties have been found in (II–VI) SC oxides in theplanar hexagonal configuration using DFT for calculating their

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TABLE 1

d11 piezoelectric coefficients of TMD monolayers extracted from [8,10,83]. TMD monolayers were considered in a 2H structure.

d11 TMD (M-X2)

(pm/V) O S Se Te

Cr 3.24 6.15 6.82 8.25 9.96 13.5 17.1Mo 2.49 3.65 4.94 3.73 4.55 6.47 4.72 7.39 10.2 9.13W 1.39 2.12 3.23 2.19 2.64 4.98 2.79 4.39 6.78 4.60Nb 3.12 3.87 4.45Ta 3.44 3.94 4.72Ti 6.64 6.34 7.50Zr 8.48 8.87 9.87 10.4Hf 4.16 4.40 4.80 5.11

Refs. [10] [83] [8] [10] [83] [8] [10] [83] [8] [10] [83] [8]

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d11 piezoelectric properties (Table 2) [10,44]. Alyörük et al. [44]performed additional DFPT simulations and, in some cases,found very different results, probably because of the non negligi-ble electronic correlations in some of these materials. Concern-ing non-oxide (II–VI) SC monolayers, Sevik et al. [84] analyzedthat the ionic contribution is larger than the electronic contribu-tion except for Be-MC. The e coefficient of these materials areclose, therefore, their d coefficient is strongly correlated to theirelastic stiffness except for Be-MCs and Mg-MCs which havemuch larger stiffness. Overall, (II–VI) SCs follow a similar trendto TMDs, but their d11 is proportional to not only the ratio ofthe anion and cation polarizabilities, but also to the product ofthe Bader charge and the in-plane lattice parameter (Figure 4b).

(III–V) SCs are more complex because they can crystallize intotwo different piezoelectric monolayer forms, namely the planarand the buckled hexagonal structures, which the most stabledepends on the material (Figure 4c). A third form (tetragonal) isalso possible and can be sometimes more stable than others (Fig-ure 4d) but it is not piezoelectric. Therefore, only hexagonalforms were considered for calculating (III–V) SCs’ d11 and d31coefficients (Tables 3 and 4). (B-V) and (III-N) compounds havea stable planar hexagonal structure, but AlP is unstable. Other(III-V) SC monolayers have a buckled hexagonal structure: AlAs,AlSb, GaSb, and InSb being unstable and GaP, GaAs, InP, andInAs being metastable (there 2D tetragonal structure being morestable [72]). Globally, (III–V) SCs’ piezoelectric coefficients followthe same proportional curve (Figure 4e) as (II–VI) SCs [10]. How-ever, this is not the case for AlN, GaN, and InN, possibly due tothe large electronegativity and small size of nitrogen comparedto other pnictogens (V). DFT simulation results [8,10,42] showthat the d11 coefficient of (III–V) SCs monolayers is around twotimes smaller than that of TMD monolayers. Interestingly, buck-led hexagonal structured (III–V) SC monolayers also exhibit anon-zero d31 coefficient. Since the d33 piezoelectric coefficientis ill-defined and the C31 elastic stiffness coefficient does not existfor 2D materials [10,85], the d31 piezoelectric coefficient can bedefined following Eq. (2) [10,86]:

d31 ¼ e31=ðC11 þ C12Þ ð2ÞWe noticed a quite big difference between the two main stud-

ies evaluating the d33 [10,42]. It is somewhat unclear why andthey did not discuss this issue nor compared their methods.However, both studies predict the same trend regarding the d11and d31 coefficient distribution.


There are very few studies on the piezoelectricity in (III-MC)SC monolayers. The d11 coefficients are summarized in Table 5.The two studies indexed exhibit different coefficients which areall lower than those of TMDs. Moreover, there are not enoughresults to draw a clear trend. This lack of data is probably relatedto the high complexity of this material system. Indeed, becauseof their compound properties and their more complex 2D struc-ture of 4 atoms thick, these materials can create multiple differ-ent monolayers which are more difficult to investigate in termsof stability, synthesis, and piezoelectricity. Guo et al. [77] startedinvestigating some of them like (X-M-M0-X) and (X-M-M-X0)(Table 6) called Janus group III chalcogenide monolayers inopposition to (X-M-M-X) materials called perfect group IIIchalcogenide monolayers.

Monolayers formed by (IV-MC) SCs are also difficult to ana-lyze because they can have multiple monolayer structures whosestability depends on materials [78] and conditions. Moreover,similar to Phosphorene [87,88], different structures could coexistand have very different properties [89] and piezoelectric coeffi-cients [60,78]. Therefore, we highlighted the structure consid-ered (Figure 4f) for each coefficient value (Tables 7 and 8). Herewe only indexed (IV-MC) SCs, but (IV-DC) SC monolayers arepossible like SnO2 and SnS2 which have a 2H hexagonal structure[83]. Interestingly, some (IV-MC) materials can be ferroelectric[12]. In this case, more data are needed to establish and confirma clear piezoelectric trend.

Parameters influencing the 2D piezoelectricityPiezoelectricity is a well-known phenomenon that has been dee-ply studied theoretically and experimentally. However, there arestill important obstacles to the accurate characterization of piezo-electric materials. For example, piezoelectric properties may sig-nificantly depend on frequency [90] and on the dimensions.For instance, piezoelectric coefficients can substantially changeand often increase when shrinking down nanostructures to theirlimit sizes [91–93]; as a remarkable example, it has been pre-dicted [93] that the piezoelectric coefficient of GaN nanowiresmay increase by about 2 orders of magnitude, in comparisonwith the bulk value, when shrinking the diameter down to 2.4nm or less. Finally, the output piezopotential of a strained piezo-electric semiconductor greatly depends on its doping and freecharge density [6,94–100].

The dependence of the piezopotential in strained piezo-semiconductor on the charge density is especially interesting

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FIGURE 4

Piezoelectric trend and stability of 2D piezoelectric crystals. (a) Proportional trend between the d11 coefficient of TMD monolayers and the ratio of the anionand cation polarizabilities a [10]. (b) Proportional trend between the d11 coefficient of (II–VI) SC monolayers and a linear combination of the ratio of the anionand cation polarizabilities a and the product of the Bader charge QB and in-plane lattice parameter a0 [84]. (c) Energy difference between the planar andbuckled hexagonal structures, and (d) between the hexagonal and tetragonal structures as a function of Q2/a2 (Q being the ionic charge and a being thelattice parameter). (e) Proportional trend between the d11 coefficient of (III–V) SC monolayers and a linear combination of the ratio of the anion and cationpolarizabilities a and the product of the Bader charge Q and in-plane lattice parameter a0 [10]. (f) Binding energies of (IV-MC) SC monolayers depending onthe crystal structures [78].

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because the density of free charges inside a semiconductor can beelectrostatically controlled by a gate terminal [24]. Nevertheless,in many applications, for instance in battery-less energy har-vesters, both the generation of a gate voltage and the co-integration of patterned gates and interconnects would be, atleast, complex. As a possible solution, immaterial (i.e., made ofcharges-only and not of a conductor) ghost floating gates [36]

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can be defined under a 2D material in order to locally controlthe polarity and density of charges in the 2D material itself. Asan example, Figure 5a schematically shows that by rubbingchemical vapor deposition (CVD)-synthesized monolayer gra-phene transferred on a SiO2 insulator with an AFM tip, fixedcharges can be stored at the SiO2-air gap interface by tunnelingtriboelectrification [36], and act as ghost floating gates.

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TABLE 2

d11 relaxed-ion piezoelectric coefficients of (II–VI) SC monolayers extracted from [10,44,84].

d11 SC group (II–VI)

(pm/V) O S Se Te

Be 1.39 1.52 �0.01 �0.47 �1.16Mg 6.63 7.75 7.19 6.54 5.11Ca 8.47 9.98 18.6 22.4 26.7Sr 7.22 15.5 18.6 23.2Ba 1.04 11.2 14.3 19.8Zn 8.65 8.87 1.70 0.63 �0.32Cd 21.7 23.7 5.38 3.92 2.19

Refs. [10] [44] [84] [10] [44] [84] [10] [44] [84] [10] [44] [84]

TABLE 3

d11 piezoelectric coefficients of (III–V) SC monolayers extracted from [8,10,42]. (III–V) SC monolayerswere considered in a planar hexagonal structure (blue) and in a buckled hexagonal structure (green).

TABLE 4

d31 piezoelectric coefficient of the planar hexagonal (blue) and buckledhexagonal (green) structured (III-V) SC monolayers.

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Remarkably, due to the excellent insulating properties of the air-gap, these floating ghost gates may survive for a few days, whichmay already be sufficient for some applications. Tunneling tribo-electrification is almost exclusively possible for 2D materials; forinstance, Figure 5b shows that the potential difference betweenthe rubbed and the unrubbed parts becomes smaller withincreasing the number of graphene layers and completely van-ishes for highly oriented pyrolytic graphite (HOPG). Until now,

TABLE 5

d11 piezoelectric coefficient of (III-MC) SC monolayers extracted from [61,77

d11 SC group (III-MC)

(pm/V) S Se

Ga 1.72 2.06 1.7In 1.12 1.9

Refs. [77] [61] [77


tunneling triboelectrification has only been reported for CVDgraphene; however, its advantages for piezosemiconductive 2Dmaterials may be crucial. In fact, though tunneling triboelectrifi-cation requires an AFM for initially drawing the ghost gates, itdoes not require to apply biasing voltages to the gates and alsoallows to draw ghost gates with the extraordinary resolution ofAFMs (e.g., for defining non-uniform free charges densities) with-out adding and patterning gates, insulators, and the intercon-nects to the gate. As an example Figure 5c shows the potentialmap of a CVD graphene layer after four deep sub-micron floatingghost gates and, correspondently, four p/n+ junctions have beendrawn by selectively rubbing the graphene with a biased AFMtip [36].

In 2D piezoelectricity, boron nitride (BN) is a particular casewhich has been deeply investigated under numerous crystalstructures [101] and forms like nanotubes [102–105]. At 2D scale,BN has a stable planar hexagonal structure and these BN nanosheets, usually called h-BN, are a good electrical insulator [106].Studies agree well on the piezoelectric coefficient e11 of h-BNwhich range from 118 to 139 pC/m [8,10,107–109]. 2D h-BN is

].

Te

7 2.30 1.938 1.46 1.18

] [61] [77] [61]

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TABLE 6

Piezoelectric coefficients of the Janus group (III-MC) monolayers [77].

SC group (III-MC) Piezo coefficients (pm/V)

d11 d31

Ga2SSe 5.23 0.07Ga2STe 2.46 0.25Ga2SeTe 2.32 0.21In2SSe 8.47 0.18In2STe 1.91 0.25In2SeTe 4.73 0.13GaInS2 8.33 0.38GaInSe2 3.19 0.46GaInTe2 2.99 0.32R

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the structurally most simple crystal which is piezoelectric [107].As a consequence, it is a relatively easy and simple 2D materialto simulate compared to others and many studies focused onits piezoelectric layer dependence. Theoretical studies [110]showed that, similar to MoS2 [59], h-BN sheets stacked into a3D prismatic h-BN structure and the piezoelectric coefficientsdepend on the number of h-BN layers. In this 3D configuration,h-BN monolayers are stacked in a top-to-tail configuration withopposite direction piezoelectric axis. Therefore, for an even num-ber of layers, the piezoelectric contributions compensate them-selves and multilayer h-BN is not piezoelectric. On the otherhand, for an odd number of h-BN layers, the study concludesthat the piezoelectric coefficient of the whole h-BN multilayerstack is inversely proportional to the number of layers N: e11|3D= 0.731/N = e11|2D/(d � N) in C/m2, where d is the monolayereffective thickness. Remarkably, these results are in agreementwith the piezoelectric trend found in MoS2 [9,111], hydrofluori-nated graphene [112], and in multi-walled BN nanotubes [113].Experimentally, this piezoelectric trend in h-BN has been con-firmed in some piezoelectric planar hexagonal monolayer mate-rials like for MoS2 [11] and SnSe [114].

TABLE 7

d11 piezoelectric coefficients of (IV-MC) SC monolayethe buckled hexagonal (grey), puckered hexagonaorange) monolayer structures. The exponent u standhexagonal structures.

TABLE 8

d12 piezoelectric coefficient of (IV-MC) SC monolayebuckled hexagonal (grey), puckered hexagonal (darkmonolayer structures.

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Another property of h-BN is flexoelectricity, which is theappearance of a polarization induced by the effect of strain gradi-ents on crystal structures through curvature [15–17]. Whenapplied using piezoelectric materials like h-BN, a nanocompositecan potentially enhance its piezoelectric properties [115]. Forinstance, a bilayer in flexion can transform and amplify a verticaldisplacement into a lateral strain. Of course, each layer fromeither side of the bending neutral axis will experience an oppo-site strain: a compression on the concave side and an extensionon the convex side. Thereby, it is possible to create a non-zero d31piezoelectric effect if the piezoelectric axis of each layer isopposed. Planar hexagonal 2D piezoelectric materials like h-BNare especially adapted to this technique as each monolayer isstacked into a top-to-tail configuration with opposite piezoelec-tric axis. However, the curvature and the flexoelectric effect areemergent properties of bilayers only, because if the number oflayers is higher, the strain-mismatch between the layers cannoteasily be kept coherently aligned by simply introducing a curva-ture. Duerloo et al. [109] found that flexoelectricity in h-BN issimilar in magnitude to the flexoelectric effect found on curvedcarbon nanoshells [116]. Michel et al. [117] corroborated flexo-electricity in bilayer h-BN and recently started investigating flex-oelectricity in TMD materials such as MoS2.

Engineering piezoelectricityOverall, the piezoelectric coefficient of h-BN is one order of mag-nitude smaller than that of TMDmonolayers. Nevertheless, h-BNremains a very attractive material as it is an insulator with goodchemical and thermal stability. Moreover, it is thermally conduc-tive, mechanically robust, and highly resistant to oxidation[118–120]. Such unique properties make h-BN a promising nano-material. Unfortunately, it does not have any out-of-plane piezo-electric property because of its planar structure, which limitspotential applications. To solve this issue and increase its

rs extracted from [10,60,78]. The colors refer tol (dark green) and puckered rectangular (darks for unstable and the indice p indicates a planar

rs extracted from [60,78]. The colors refer to thegreen) and puckered rectangular (dark orange)

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FIGURE 5

AFM triboelectric writing of ghost gates on 2D materials. (a) Schematic of the friction process and the KPFM measurement system. (b) DVr of triboelectricallywritten ghost gates on graphene and DVu for different types of CVD graphene (1, 2 or 3 layers) and for HOPG. (c) KPFM image of 4 deep sub-micron n+ ghostgates and p/n+ junctions defined by selectively rubbing arbitrary graphene regions with the AFM tip biased by 10 V [36].

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piezoelectric coefficient, researches inspired by works done on h-BN surface functionalization [121–124] tried to modify h-BN tocontrol its piezoelectricity. To study piezoelectricity engineeringon h-BN, Noor-A-Alam et al. [86] conducted simulations of h-BNmonolayers decorated with H or F atoms. The monolayers cre-ated are 3 atoms thick, they can have 4 configurations: (HBNH),(FBNH), (HBNF), and (FBNF) and 2 structures: chair and boat.The chair structures are stable with a negative formation energy,but their hydrogenation might be difficult in the presence ofhydrogen molecules. The boat structures are slightly more stable,but they are not piezoelectric because of their symmetry. Resultsshow that hydrogenation and or fluorination on h-BN canimprove the d11 coefficient, which range from 0.50 pm/V inthe HBNF configuration to 1.27 pm/V in the FBNH configura-tion. In addition, they also noted the appearance of a non-zeroout-of-plane d31 coefficient comparable to other (III–V) SCmonolayers. The new d31 ranges from �0.10 pm/V in the HBNHconfiguration to 0.13 pm/V in the FBNF configuration. It isimportant to note that it is possible to control the polarity ofthe d31 piezoelectric coefficient by choosing the surface decora-tion. These results highlight that the surface chemistry and theelectronic properties of 2D piezoelectric materialsare very impor-tant when considering their piezoelectricity.

Piezoelectricity engineering has been further developed to addpiezoelectric properties to intrinsically non-piezoelectric 2Dmaterials like graphene. Taking inspiration from works done ongraphene doping [125] using adatoms [126–129] and vacancies[130], two major techniques emerged: adding adatoms on gra-phene [7,18] or digging vacancies [22] in graphene.

First, Ong et al. [7,18] calculated that piezoelectricity can beengineered onto graphene by chemical doping. In practice, theycontrolled the absorption of adatoms on the surfaces of graphene


to break its inversion symmetry and generate a piezoelectriceffect. In their simulations they considered adding Li, K, F, andH adatoms on graphene. H [131–133] and F [134,135] coveredgraphene has both been realized experimentally and were foundstable in ambient conditions. Alkali metals [136,137] Li [138–140] and K [141–143] adatoms have also been investigated. Asshown on Figure 6, these adatoms localize at different sites ongraphene. Li and K prefer to bind at the hollow site at the centerof the hexagon (Figure 6a), whereas H (Figure 6b) and F (Figure6c) prefer to bind at the top site bonding of covalent interactions(directly over a C atom). The authors also tested different combi-nations of dopant on each side like (Li,F) (Figure 6d) and (F,H)(Figure 6e). The crystals created by these configurations of gra-phene doping are non-centrosymmetric. By consequence, theyare piezoelectric and will exhibit an out-of-plane d31 coefficient.The results show that the d31 coefficient may greatly changedepending on the dopant. Binding F or (F,H) to grapheneresulted in a small variation of the d31, binding Li or K providedan average modification of the d31 and binding (Li,F) gave thehigher d31 value of 0.30 pm/V (Figure 6f), which is comparableto wurtzite BN d31 = 0.33 pm/V [82] and three times smaller thanwurtzite GaN d31 = �1.05 pm/V [144]. But the trend is differentfor the e31 coefficients and Li gave the strongest e31. Interestingly,Ong et al. noted that the polarization magnitudes in graphenehave the potential to be larger than those of wurtzite GaN dueto the larger elastic strains achievable in graphene before elasticfailure (critical strain larger than 10%) [34]. Following theseresults, they examined the impact of the percentage of dopantcoverage on the d31 coefficient. They considered different Lidopant to C atom ratio ranging from C2Li to C32Li (Figure 6g).The maximum piezoelectric coefficient occurs for the C8Lidopant ratio (Figure 6h). This is the result of the competition

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FIGURE 6

Piezoelectric engineering of graphene. (a) Unit cell structure when adding Li, (b) F, and (c) H adatoms on graphene. (d) Unit cell structure when adding Li,Fand (e) H,F adatoms on both sides of graphene. (f) Low-density coverage of one Li adatom for 8C atoms of graphene. (g) Polarization change offunctionalized graphene depending on the equibiaxial in-plane strain applied to graphene. The slope gives twice the e31 coefficient and depends on theadatom type and (h) on the adatom density [18]. (i) Graphene, (j) circular and (k) triangular vacancy geometries considered for the piezoelectric simulation ofgraphene in [22]. The gray atom is C and the white is H which marks the termination of graphene.

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between two effects: first, the static dipole moment of Li on gra-phene gets stronger as the coverage decreases; second, the influ-ence of this increased interaction on the d31 decreases with thenumber of Li leading to an optimum piezoelectric effect for C8Li.

In view of these last results, it would be expected that a similarsymmetry break would occur when creating vacancies in

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graphene, which would make it piezoelectric. Normally,graphene conductivity depends on shapes [145] and defect[146,147], and it should screen piezoelectricity. However, porousgraphene can act as a dielectric [148] and therefore it is justifiedto study if porous graphene could have piezoelectric properties.Chandratre et al. [22] investigated this aspect of graphene by

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simulating different nanosize and geometry of hole in graphene(Figure 6i–k). The concept is that when graphene is strained, thevacancies serve as stress concentrators where strain gradientsaround vacancies may break the inversion symmetry and inducea polarization, similar to flexoelectricity induced by straingradients and assuming that graphene has a proper vacanciesgeometry. For example, circular holes would not generate apiezoelectric behavior because of their circular symmetry, whichwould result in a zero average polarization. However, triangularholes aligned in the same direction would generate a piezoelec-tric behavior. Of course, the porosity should be high enough toexhibit SC or insulating properties. Within these condition,Chandratre et al. [22] found that graphene with triangular holecould achieve a e11|1D coefficient of 0.124 C/m2. It is difficult tointerpret this 1D section value which is not directly comparablewith common values, but considering a graphene effective thick-ness of 300 pm, e11|2D is equal to 37.2 pC/m, which is smaller bya factor less than 10 compared to other 2D materials.

Piezoelectric characterization of 2D materialsHere, we shall report the experimental observations of piezoelec-tricity in both intrinsic and non-intrinsic piezoelectric 2Dmaterials.

Intrinsic piezoelectric 2D materialsTMDCs are non piezoelectric in the bulk form as they are centro-symmetric. However, their inversion centers disappear in mono-layers, resulting in piezoelectricity [10,11]. As an experimentalevidence, Zhu et al. [9] characterized the piezoelectricity inmonolayer MoS2 and its dependence on the number of layers.Monolayer MoS2 consists of S-Mo-S stack (Figure 7a) having atrigonal prismatic structure which has no inversion symmetry.As a consequence, when an in-plane electric field is applied fromthe S site to the Mo site, the unit cell is elongated due to thestretching of the Mo-S bond (Figure 7b). The resulting piezoelec-tric stress tensor, Drp, can be described as follows [149]:

Drp ¼ �e11 � E1 ð3Þwhere e11 is the piezoelectric coefficient along the armchair directionand E1 is the applied electric field.

The characterization of piezoelectricity by conventional PFMmeasurements is not suited for MoS2 as its vertical symmetrydoes not offer electromechanical coupling in the vertical direc-tion. In order to overcome this challenge, the coauthors adopteda novel characterization method that combines a laterallyapplied electric field and the nanoindentation of a free-standing film using an AFM tip (Figure 7c). The indentation ofthe membrane converts the in-plane piezoelectric stress inducedby the electric field into an out-of-plane force that changes theload on the tip. Besides, due to the suspension of the MoS2, thismethod characterizes the intrinsic piezoelectricity of the MoS2which is free from substrate effects.

The MoS2 was exfoliated from natural 2H-MoS2 crystals. Fig-ure 7d shows the scanning electron microscope (SEM) image ofthe free-standing MoS2 monolayer. Au electrodes are defined par-allel to the zigzag edges of the monolayer flakes for applying elec-tric field along the armchair direction. Figure 7e shows thepiezoelectric stress induced by a ramping applied voltage at fixed


indentation. The results show that monolayer MoS2 has a piezo-electric coefficient e11 = 290 (±50) pC/m (the equivalent bulk/3Dcoefficient is 0.5 C/m2 which is obtained by normalizing withthe layer thickness) which is very similar to the theoretical DFTvalue [8]. Figure 7f shows the thickness dependence of the piezo-electric coefficient. Even-layer membranes do not possess piezo-electricity due to the cancelation of the piezoelectricity due tothe alternating orientations of the adjacent layers in 2H-MoS2.In contrast, the odd-layers are piezoelectric due to the non-total compensation.

Non-intrinsic piezoelectric 2D materialsGraphene is intrinsically non-piezoelectric, but Rodrigues et al.[21] experimentally observed piezoelectricity in graphene onSiO2 calibration grating substrates using PFM measurementsand confocal Raman spectroscopy. Figure 8a schematicallydescribes the PFM measurements of the single layer graphene(SLG) on a Si/SiO2 calibration grating substrate. Figure 8b showsthe variation of G-band position and strain across the grating.The strains are relatively high (�2.5 times) in supported gra-phene (Figure 8b shaded rectangles) than in the suspendedregions. In order to characterize the vertical piezoresponse fromthe SLG, electric field was applied between the tip and the sub-strate and the corresponding piezoelectric graphene vibrations(pm level) were detected. Figure 8c shows the piezoresponsealong a line on graphene across the grating structure due to anapplied AC voltage (5 V). The piezoresponse is zero on bareSiO2 substrate (Figure 8c right part) and becomes negative alonggraphene. However, the PFM signal on the supported graphene(shaded areas) is significantly higher (�4 times) than on the sus-pended one. Nevertheless, the tensile strain distribution and thepiezoresponse distribution correlate well, but the piezoresponseis not amplified near the grating edges where the maximumstrain gradients are present. Therefore, the observed out-of-plane polarization is not due to the in-plane symmetry breakinginduced by lateral strain in graphene. Figure 8d shows thepiezoresponse on the supported graphene due to a sweepingDC voltage from �10 V to +10 V with a driving AC voltage of1 V. Unlike conventional ferroelectric materials, there was nohysteresis and polarization switching. Besides, the magnitudeof the piezoresponse was increasing with an increase in the neg-ative DC voltage and was decreasing with an increase in positiveDC voltage. Figure 8e shows the piezoresponse of the supportedgraphene as a function of applied AC voltage at the resonancefrequency of the cantilever (262 kHz). The linear dependenceof piezoresponse on the AC amplitude demonstrates that thesupported graphene is piezoelectric.

The authors have attributed the observed out-of-plane piezo-electricity to the chemical interaction of graphene with theunderlying SiO2 substrate. A chemical bond between the carbonatoms of graphene with oxygen atoms of the substrate inducednon-zero net dipole moment as schematically described in Fig-ure 8f. The C+-O� dipoles are suggested to possess random orien-tation due to the random orientation of the SiO2 complexes onthe surface layer. Therefore, a negative electric bias orients thedipoles in the normal direction and increases the net polariza-tion. In contrast, a positive electric field to the tip deviatesthe dipoles from the normal direction and decreases the net

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FIGURE 7

Piezoelectric property of free-standing MoS2 [9]. (a) Schematics of the structure of an MoS2 monolayer. (b) Elongation of the unit cell due to an externalelectric field applied from the S to the Mo site. (c) Schematic of the measurement setup. (d) SEM image showing the free-standing MoS2 monolayers clampedbetween the Au electrodes and HSQ posts; scale bar is 1 lm. (e) Measured piezoelectric stress as a function of ramping voltage at a fixed depth ofindentation; the error bars were estimated from the noise level; the red curves show the linear fit according to Eq. (3). (f) Measured piezoelectric coefficient ofmono, bi, and tri layers MoS2; error bars were estimated from the noise level of the force measurement and variations in the device geometry.

FIGURE 8

Piezoelectricity in SLG deposited on SiO2 grating substrates [21]. (a) Schematics of the PFMmeasurements of SLG on grating substrate. (b) Variation of G-bandposition and strain across the grating; shaded rectangles correspond to supported graphene. (c) Piezoresponse along a line on graphene across the gratingstructure; the measurements were carried out at 90 kHz and Va.c. = 5 V. (d) Piezoresponse measured on supported graphene; driving a.c. voltage is 1 V andfrequency is 20 kHz. (e) Piezoresponse amplitude at the resonance as a function of applied a.c. voltage. (f) Schematic of graphene layer on SiO2 substrate withO termination (left) and chemical interaction of C and O atoms inducing dipoles (right).

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Please cite this article in press as: R. Hinchet et al., (2018), https://doi.org/10.1016/j.mattod.2018.01.031


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polarization (Figure 8d). Based on the experimental results, thecalculated vertical piezocoefficient, d33, of the SLG is about 1.4nm/V; the piezoelectric coefficient is more than twice of the con-ventional piezoelectric material of lead zirconate titanate [150]and is comparable to that of relaxor single crystals [151].

Controlled shape in-plane defects can produce polarization ina non-piezoelectric dielectric material due to strain gradientsaround defects [22,152]. However, realization of suchnanometer-scale shape defect like triangular nano–holes is extre-mely challenging. Therefore, as an experimental evidence ofengineering piezoelectricity using triangular-shaped holes,Zelisko et al. [152] used an alternative material: carbone nitride(C3N4) nanosheets that naturally comprise triangular holes. Theycarried out PFM characterization on C3N4 nanosheets. Consider-ing the crystal structure, C3N4 is non-piezoelectric and is pre-dicted to exist in a, b, cubic, pseudo-cubic, and 2D graphitic (g)forms [153]. g-C3N4, is the graphitic form of carbon nitride; amonolayer is represented in Figure 9a. Since g-C3N4 is non-conducting and naturally comprises non-centrosymmetric trian-gular holes, it is expected to possess in-plane piezoelectricity. Fig-ure 9b shows an AFM image of the sample which is around 800nm wide, while its thicknesses is in the 1–2-nm range (Figure 9c).

In order to examine the piezoelectricity, a conductive AFM tipis brought into contact with the g-C3N4 sample and an electricfield is applied in the normal direction (Figure 9a e3) in such amanner it has spherically symmetric components along thein-plane axes (Figure 9a e1 and e2). Local vibrations of the piezo-electric materials underneath the AFM tip due to the applied elec-tric field cause a deflection of the cantilever. Figure 9d and eshows the in-plane (lateral) PFM response as a function of AC fre-quency and voltage. The lateral PFM response is due to cantilevertwisting induced by the in-plane piezoelectric shear strain andexhibits a resonant peak near 778 kHz. At the cantilever-sampleresonance, the sensitivity of the measurement is enhanced andthe piezoelectric vibration is greatly magnified. Besides, thepiezoresponse increases linearly with an increase in the ampli-tude of the applied AC voltage, which also confirms the linearityof the piezoelectricity in g-C3N4 nanosheets.

The g-C3N4 is non-piezoelectric. However, Zelisko et al. [152]suggest that the occurrence of the anomalous piezoelectricity ing-C3N4 is due to flexoelectricity and the presence of non-centrosymmetric triangular holes in the sheet. For instance, Fig-ure 9f shows a non-piezoelectric sheet with triangular holes.Under a uniform stretch, there is an appearance of local polariza-tion, i.e., P(x)– 0 due to flexoelectricity caused by strain gradi-ents around the hole. Non centro-symmetry of the triangular-shaped hole causes a net average polarization, i.e., P – 0 acrossthe sheet. By the same argument, the non-centrosymmetric, tri-angular nano pores and flexoelectricity lead to piezoelectricity ingraphene nitride sheet as well. Zelisko et al. also determined thepiezoelectric coefficient, e11, using quantum calculations. Thecalculated coefficients, e11, for single and a stack of layers are0.732 C/m2 and 0.758 C/m2, respectively, which are almost fourtimes higher than that of a-quartz (0.171 C/m2 [79]). Besides, e11coefficient for the single sheet in units of C/m is 218 pC/m,which is lower than MoS2 (364 pC/m [8]) and WS2 (2.47 pC/m[8]) and higher than h-BN (1.38 pC/m [8]). However, MoS2,WS2, and h-BN are not piezoelectric in bulk/stacked form due


to ant-parallel stacking of the individual layers. In contrast, g-C3N4 is piezoelectric even in bulk/stacked form as the stackingsequence is analogous to that in graphite. As a consequence,the manufacturing becomes very easy as synthesis of monolayeris not a major constraint unlike for MoS2, WS2, and h-BN. There-fore, g-C3N4, in either bulk or single-layer form, is a promisingcandidate for NEMS.

2D piezoelectric devicesThe unique advantages of 2D piezoelectricity may open the wayto many innovative devices. In fact, in just a few years since thefirst experimental studies on 2D materials, 2D devices and 2Dpiezoelectric devices have already been demonstrated for a widevariety of applications, including pressure sensors [154,155],strain sensors [156–158], displacement sensors [159], mass sen-sors [160], gas sensors [161–163], light sensors [164–167], energyharvesting [5,11,111,168–172], energy storage [173–178], high-frequency switches [179–183], motors [184] and tweezers [185].Furthermore, 2D materials are very promising for nanoelectron-ics [38,186–195], optoelectronics [196–203], piezo-phototronics[11,204–208], tribo-phototronics [209,210], and catalysis[62,211,212]. Here, we shall concisely discuss, as importantexamples, 2D piezoelectric devices for mechanical energy har-vesting and strain sensing.

Mechanical energy harvestingPiezoelectricity in monolayer MoS2 has been theoretically pre-dicted and experimentally measured [8–10]. Wu et al. demon-strated the first 2D MoS2-based piezoelectric devices [11]; thedevices were meant for both energy harvesting and strain sensingapplications. Figure 10a schematically describes the operation ofa single-layer MoS2-based piezoelectric device. When the deviceis strained along the MoS2 armchair direction, piezoelectricpolarization charges of opposite polarities are induced at the zig-zag edges, which drives a flow of electrons in an external resistor.When the device is released, the piezoelectric polarization disap-pears and the electrons flow back in the opposite direction. Theelectrical contacts to the piezoelectric 2D material are thereforecrucial for proper operations of piezoelectric devices [11,213].For instance, for a semiconducting 2D material, such as MoS2,the contacts must constitute a Schottky junction in order to pre-vent the electrons from crossing the interface and, thereby, neu-tralizing the piezoelectric polarization charges. The fabrication ofSchottky contacts depends upon the work function difference ofthe contacting materials, and is also influenced by the interfacestates and environmental parameters [213–216]. Figure 10bshows an optical image of the single atomic layer MoS2 flake withschematic of the lattice orientation superimposed on the flakeimage.

As explained in Figure 10d, the piezoelectric outputs comprisealternating pulses due to cycling stretching and releasing of thedevice. However, the piezoelectric response is reversed whenthe strain is rotated from the x (‘armchair’) to the y (‘zigzag’)direction. Such dependence of piezoelectric charge polarizationon the directions of the strain can be explained by consideringthe crystalline D3h symmetry of single layer MoS2 [9,11]. Dueto the D3h symmetry, single-layer MoS2 has only one non-zero

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FIGURE 9

Piezoelectricity in 2D g-C3N4 nanosheets [152]. (a) g-C3N4; blue and gray spheres represent N and C atoms, respectively. (b) AFM image of the g-C3N4; scalebar is 200 nm. (c) AFM thickness along the white line in b. (d) Frequency dependence of PFM signal at different a.c. voltages. (e) Piezoresponse as a functionof the applied voltage. (f) Schematic of effects of non-centrosymmetric triangular holes on the polarization of a non-piezoelectric sheet under uniform stress.

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coefficient e11 and the in-plane polarization P1 along the x axiscan be expressed as below

P1 ¼ e11ðe11 � e22Þ ð4Þwhere e11 and e22 are the strain along x and y directions. It is evidentfrom Eq. (4) that the piezoelectric output is expected to reverse signwhen the strain is rotated from the x (‘armchair’) to the y (‘zigzag’)direction. Nevertheless, the current and the voltage output of thedevice due to strain in Figure 10d unambiguously demonstrate theconversion of mechanical energy into electricity.

In order to quantify the output power of the piezoelectricdevice, the coauthors also characterized the voltage and currentoutputs as a function of load resistance as shown in Figure 10e.The output current remains almost constant until a load resis-tance of �1 MX and then starts decreasing with the increasingload. On the other hand, the output voltage remains �0 V ini-tially and starts increasing as load resistance exceeds �1 MX.The maximum instantaneous power (�55.3 fW) is delivered ata load resistance of �220 MX with a corresponding power den-sity of 2 mW/m2. The conversion efficiency of the monolayerMoS2 nanogenerator (NG) was estimated to be �5%. Figure 10fshows the output current of the piezoelectric nanogenerator(PENG) due to cyclic loading up to 0.43% strain at 0.5 Hz for300 min. Though the output slightly decreased, the deviceremained functional which demonstrates the stability ofmechanical energy conversion and its potential for a sustainedoperation. Recently, Lee et al. [217] have demonstrated thatthe devices based on bilayer TMDCs could be mechanically moredurable than monolayer devices. The bilayer TMDCs are howevernot piezoelectric due to the anti-parallel Bernal stacking in themost common 2H form [217]. In contrast, if the bilayer TMDCs

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are realized through turbostratic stacking, i.e., layer- by-layertransfer of CVD grown monolayers, they are piezoelectric dueto the non-centrosymmetry induced due to the transfer [217].Piezoelectric devices based on turbostratic bilayer WSe2 havebeen shown to withstand higher strains than the monolayerWSe2-based piezoelectric devices [217].

Strain/force/pressure sensing2D TMDCs such as MoS2 are semiconducting piezoelectric [8,11].They are therefore suitable candidates for piezotronic devices[204,218,219] whose carrier transport is modulated by strain-induced piezoelectric charges, thereby enabling strain sensing.Qi et al. [37] experimentally investigated the coupling of in-plane piezoelectric polarization and carrier transport in CVD-grown triangular shaped monolayer MoS2 and, as an applicationof the observed piezotronic effect, demonstrated a strain/forcesensor. Monolayer MoS2 films were synthesized on a sapphireor Si substrate using CVD method. Unlike exfoliated MoS2, thefilms have a regular triangular shape with three zigzag edges. Inorder to fabricate the characterization devices, MoS2 film wastransferred onto a Si/SiO2 substrate and drain and source elec-trodes were then realized using e-beam lithography. Figure 11adescribes the measurement setup where contact-mode AFM isused to apply local isotropic strain to the MoS2 film and corre-sponding conductivity modulation is measured by applying anexternal bias. In order to apply a compressive strain, AFM loadis applied at the center of the MoS2 film (Figure 11b); the filmwas imagined to deform in a concave shape under the compres-sive strain. On the other hand, AFM load is applied near the edgeof the triangular MoS2 film in order to apply a tensile strain

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FIGURE 10

Monolayer MoS2-based PENG for mechanical energy harvesting [11]. (a) Schematics of a single-layer MoS2 piezoelectric device. When stretched, piezoelectriccharges are induced at the zigzag edges. Periodic stretching and releasing of the device generates alternating piezoelectric current in an external circuit. (b)Optical image of a single-atomic layer MoS2 flake with superimposed lattice orientation schematic; blue and yellow spheres represent Mo and S atoms,respectively. Inset: atomic force microscopy image of the flake. Scale bar 2 mm. (c) A flexible single-layer MoS2-based device with electrodes at its zigzagedges. Inset: optical image of the flexible device. (d) Output voltage with 1 GX external load and short-circuit current of the single-layer MoS2 device due to aperiodic strain applied along x, armchair direction (top), and along y, zigzag direction (bottom). (e) Output voltage and current of the device under 0.53%strain as a function of load resistance; indicated values are the mean from 20 technical replicates; error bars represent s.d. (f) Cyclic test showing the stabilityof the single-layer MoS2-based PENG.

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(Figure 11c); the film was imagined to deform in a convex shapeunder the tensile strain. Under compressive strain, the currentdecreases with increasing force, whereas, under tensile strain,the current increases with an increasing force. The current mod-ulation in the MoS2 devices is due to the changes in Schottky bar-rier height (SBH) due to the applied strain. The barrier heightincreases with compressive strain thereby decreasing current


and decreases with increasing tensile strain thereby increasingcurrent.

As an application of the observed piezotronic effect, theauthors demonstrated a strain/force sensor. Figure 11d and eshows current response and proposed working mechanism ofthe sensor. Its current decreases due to compressive strains andincreases due to tensile strains. As to the energy band diagrams,

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FIGURE 11

Piezotronic effect in CVD grown monolayer MoS2 for strain sensing applications [37]. (a) Schematic of applying strain to an MoS2 using an AFM tip. (b) I–Vbcharacteristics of the MoS2 device at varying loads under compressive and (c) tensile strains; the forces were applied at locations denoted in upper insets,whereas the lower insets schematically show the resulting strains. (d) Current response and energy band diagram of the MoS2 device under compressivestrain. (e) Current response and energy band diagram of the MoS2 device under tensile strain. The red arrows show the directions of the piezoelectricpolarizations. EF is the Fermi level of monolayer MoS2, EC is conduction band, EV is valence band, Vbias is the external bias and D is the piezopotential-inducedchange of barrier height. The quasi-Fermi level is raised at the source contact due to the external bias.

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a compressive strain induces negative piezoelectric polarizationcharges at three zigzag edges of the triangular MoS2 (Figure11d). The resulting negative piezopotential depletes free elec-trons near the interfaces with the metal and therefore increasesSBHs at both contacts, thereby producing a decrease in the cur-rent under the compressive strain. On the other hand, a tensilestrain produces positive piezoelectric polarization charges atthe three zigzag edges of the MoS2 triangle (Figure 11e). Theresulting positive piezoelectric field attracts free electrons nearthe interfaces with metal contacts and so reduces the SBHs atboth contacts, thereby causes an increase in the current undertensile strain. Nevertheless, for both cases, the sensor’s responseis repeatable, indicating the stability of its operation. The gaugefactor, which is defined as ½DI e=I0�=De, of the sensor was foundto be �1160 which is much larger than that of the strain sensorsbased on metal (1–5), graphene (�2) [220], doped-Si (�200)[221], and even higher than the highest known gauge factor ofCNTs (�1000) [222]. These results demonstrate that 2D materialshave strong potential for realizinghigh-performance strain sensors.

Conclusion and perspectivesThough the piezoelectric effect has been discovered almost 140years ago, the recent emergence of 2D materials may offerentirely new opportunities. In fact, first, at 2D scale, more piezo-electric materials may exist as, for instance, some materialswhich are not piezoelectric in their bulk form become piezoelec-tric when reduced to a single atomic layer; moreover, since all theatoms of 2D materials belong to the surface, piezoelectricity canbe effectively engineered by proper surface modifications. In

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addition, the limited number of atoms, which is typical of 2Dmaterials, uniquely reduces the computational complexity ofatomistic-level simulations and, therefore, offers an extraordi-nary tool for material design. As additional advantages, 2D mate-rials are strong, flexible and, in principle, easy to be co-integratedwith conventional integrated circuits or MEMS. Furthermore,reducing the thickness of a material to a single atomic layer oreven to a few atomic layers obviously has major effects on theband structure, so that, as an example, monolayer MoS2, unlikeits bulk form, has a direct band gap and therefore may becomeuseful for both optoelectronics and piezo-photo-tronics. Besides,the 2D nature permits to take advantage of techniques whichwould be impossible with conventional materials; for instance,different 2D materials can be properly combined to constitutevan derWaals heterostructures or, as another example, immaterial,rewritable ghost floating gates can be drawn under 2D materials.

In this review, first, we discussed the crystal structures,stability, and piezoelectric properties of different groups of 2Dmaterials (TMD, (II–VI), (III–V), (III-MC), and (IV-MC), andfunctionalized h-BN and graphene). Afterward, we have dis-cussed piezoelectricity engineering by surface modifications,with special reference to graphene [19,23,223,224] and to otherplanar hexagonal piezoelectric monolayers such as group IV ele-ments and III-V binary compounds [71]; obviously many morematerials, including for instance more complex carbon-basedmonolayers like C3N4 [152], silicene [225,226], germanene[227,228], and phosphorene [229–232] could benefit frompiezoelectric engineering. Beyond that, 2D material composites[233] and Van der Waals heterostructures [25,26,234,235] arecertainly very promising for the development of innovative 2D

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piezoelectric devices and 2D ferroelectric devices [236,237].Moreover, we have discussed experimental investigations ofpiezoelectricity in 2D materials by means of AFM and PFM char-acterization. Finally, we have described some 2D piezoelectricdevices for energy harvesting and sensing.

Overall, so far, the piezoelectric coefficients of 2D materialswere found of the same order of magnitude than their bulk coun-ter parts, but remain lower than some specific high-performancebulk piezoelectric materials like PZT. Nevertheless, both theoret-ical predictions and experimental results consistently confirmthe outstanding potential of 2D piezoelectricity for developinginnovative piezoelectric devices and new nanosystems. Thoughonly very recently it has become possible to synthesize 2D piezo-electric materials, there is already a very high and growing inter-est in exploring the rich physics and unique possibilities of the2D piezoelectric materials, including the piezoelectricity of mate-rials which would not be piezoelectric when in the bulk form.We envision, in addition to growing future research activitiesrelated to 2D piezoelectric materials, innovative and uniqueapplications enabled by 2D piezoelectricity engineering. For thisreason, we believe 2D piezoelectricity will soon substantiallyadvance and further expand the impact of piezoelectricity onsociety and on our daily lives.

AcknowledgmentsThe authors acknowledge financial support from the

Framework of International Cooperation Program managedby National Research Foundation of Korea (NRF-2015K2A2A7056357) and “Human Resources Program in EnergyTechnology” of the Korea Institute of Energy TechnologyEvaluation and Planning (KETEP), granted financial resourcefrom the Ministry of Trade, Industry & Energy, Republic of Korea(No. 20154030200870).

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Documents

Piezoelectric properties in two-dimensional materials ...nesel.skku.edu/paper files/203.pdf · the 2D layered structure is also important and can lead to ﬂexo-electricity [15–17],