Elsevier

FlatChem

Volume 29, September 2021, 100289
FlatChem

Geometric structure and piezoelectric polarization of MoS2 nanoribbons under uniaxial strain

https://doi.org/10.1016/j.flatc.2021.100289Get rights and content

Highlights

  • Piezoelectric polarization across MoS2 nanoribbons with zigzag edges.

  • Substantial edge reconstruction on MoS2 nanoribbons with chiral edges under large compressive strain.

  • Electronic structure of MoS2 nanoribbons is insensitive to the strains.

Abstract

Using density functional theory with the generalized gradient approximation and effective screening medium method, we investigated the geometric and piezoelectric properties of MoS2 nanoribbons under uniaxial strain in terms of their edge shapes. The strain ranged from 6% compressive to 6% tensile. Ribbons with zigzag and armchair edges are stiffer than those with chiral edges under compressive strain. Substantial edge reconstruction occurs at the chiral edges where S atomic sites are dominant under 6% compressive strain. Relative piezoelectric polarity between edges decreases and increases under compressive and tensile strains, respectively, when a ribbon possesses the zigzag edges, indicating possible application to piezoelectric devices. Polarity across a ribbon with armchair and chiral edges is insensitive to uniaxial strain except when there is edge reconstruction under a large compressive strain. The electronic structure of a ribbon slightly depends on uniaxial strain.

Introduction

Following syntheses of graphene [1], [2], [3], [4], [5], various two-dimensional materials have been exfoliated from their bulk layered structures and synthesized through chemical vapor deposition on appropriate substrates [6], [7], [8], [9]. These materials have atomic layers of covalent two-dimensional networks and have versatile physical properties depending on their covalent network topology and constituent elements. The honeycomb covalent network of C atoms in graphene makes it a unique material in which pairs of conical dispersion bands emerge at the Fermi level and at six corners of the hexagonal Brillouin zone [10], [11], [12]. Accordingly, graphene exhibits an unusual Hall effect and remarkable carrier mobility [13], [14], [15], [16]. A binary honeycomb sheet of boron and nitrogen (h-BN) is an insulator version of graphene that possesses a wide band gap of approximately 5 eV at the K point, owing to the chemical difference between B and N atoms [17], [18]. Thus, h-BN is used as a substrate to investigate various atomic-layer materials and apply their unique physical properties [19]. Transition metal dichalcogenides (TMDCs) such as MoS2, MoSe2, WS2, WSe2, and MoTe2 are another example of such atomic-layer materials. These consist of an atomic layer of transition metals forming a triangular lattice sandwiched by atomic layers of chalcogens arranged in prismatic manner, resulting in a hexagonal network of these elements with a thickness of about 3Å. Most TMDCs are semiconductors with a direct band gap at the K point [20] that strongly depends on the constituent elements, even though their thin films or bulks are indirect band gap semiconductors [21].

TMDCs have chemically inert surfaces owing to their two-dimensional covalent networks, so they could be building blocks of various heterostructures in which each layer is bound via weak van der Waals interaction. Because of the variation of the constituent layers in such van der Waals heterostructures, we can tailor their physical properties by properly controlling the stacking arrangement and external conditions [22], [23], [24], [25], [26], [27], [28]. Atomic-layer materials are also building blocks for other low-dimensional materials such as nanoribbons [29], [30], [31], [32], [33], [34], nanoflakes [35], [36], and in-plane heterostructures [37], [38], [39], [40], [41] when additional boundary conditions are imposed. These are emerging materials for designing functional devices such as electronics, photonics, and photoelectronic devices owing to their physical properties. In addition, TMDCs have flexible sheet structures without inversion symmetry that cause piezoelectricity [42], [43]. Tensile and compressive strains along a particular direction cause electricity in TMDCs. Although experiments have found piezoelectricity in TMDCs, the microscopic correlation between their structural and piezoelectric properties is not yet fully understood. Therefore, in this paper, we aim to elucidate the correlation between the atomic structure and piezoelectric property of MoS2 nanoribbons as representatives of TMDC nanostructures under uniaxial tensile and compressive strains, using density functional theory combined with the effective screening medium method. Piezoelectric polarization is only observed between the zigzag edges of a MoS2 ribbon under tensile and compressive strains along the length direction, which cause both decreases and increases in the ribbon width. For ribbons with chiral edges, the piezoelectricity is insensitive to tensile and small compressive strains irrespective of their edge angles, while a large compressive strain causing edge reconstruction induces polarization.

Section snippets

Calculation methods and structural model

All calculations were performed within density functional theory (DFT) [44], [45] using the Simulation Tool for Atom TEchnology (STATE) package [46], [47]. To calculate the exchange–correlation energy among the interacting electrons, we used the generalized gradient approximation (GGA) with the Perdew-Burke-Ernzerhof (PBE) functional form [48]. Ultrasoft pseudopotentials generated with the Vanderbilt scheme were used to describe the interaction between electrons and nuclei [49].In constructing

Results and discussion

Fig. 2 shows the total energy per MoS2 of MoS2 nanoribbons with armchair, chiral, and zigzag edges as a function of nanoribbon length normalized by the initial lengths L0 = 2.18, L0 = 2.20, L0 = 2.26, L0 = 2.37, and L0 = 2.51 nm for edge angles of 0°, 8°, 16°, 23°, and 30°, respectively. The total energy appears parabolic around the initial length L0. Note that the optimum length of nanoribbons with armchair and zigzag edges are slightly longer than those previously reported, owing to the

Conclusion

Using DFT combined with the ESM, we investigated the correlation between the atomic structure and electric properties of MoS2 nanoribbons under uniaxial tensile and compressive strains in terms of their edge shapes. Piezoelectric polarization is observed between the zigzag edges of MoS2 nanoribbons under tensile and compressive strains along the length direction of the nanoribbons, which cause decreases and increases in the nanoribbon width. Furthermore, the polarization monotonically increases

CRediT authorship contribution statement

Mina Maruyama: Conceptualization, Investigation, Data curation, Formal analysis. Yanlin Gao: Investigation, Data curation, Formal analysis. Ayaka Yamanaka: Investigation, Data curation, Formal analysis. Susumu Okada: Investigation, Data curation, Formal analysis, Writing - original draft.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgement

This work was supported by the Japan Science and Technology Agency Core Research for Evolutionary Science and Technology (JST-CREST; Grant Nos. JPMJCR1715 and JPMJCR20B5), the Japan Society for the Promotion of Science Grants-in-Aid for Scientific Research (JSPS KAKENHI; Grant Nos. JP21K14484, JP20K22323, JP20H00316, JP20H02080, JP20K05253, JP20H05664, and JP16H06331), the Joint Research Program on Zero-Emission Energy Research of the Institute of Advanced Energy at Kyoto University, and the

References (51)

  • Y. Morikawa et al.

    Theoretical study of hydrogenation process of formate on clean and Zn deposited Cu(111) surfaces

    Appl. Surf. Sci.

    (2001)
  • K.S. Novoselov et al.

    Electric field effect in atomically thin carbon films

    Science

    (2004)
  • I. Forbeaux et al.

    Heteroepitaxial graphite on 6H-SiC(0001): Interface formation through conduction-band electronic structure

    Phys. Rev. B

    (1998)
  • C. Berger et al.

    Electronic confinement and coherence in patterned epitaxial graphene

    Science

    (2006)
  • H. Ago et al.

    Catalytic growth of graphene: toward large-area single-crystalline graphene

    J. Phys. Chem. Lett.

    (2012)
  • H. Ago et al.

    Epitaxial growth and electronic properties of large hexagonal graphene domains on Cu(111) thin film

    Appl. Phys. Express

    (2013)
  • L. Song et al.

    Large scale growth and characterization of atomic hexagonal boron nitride layers

    Nano Lett.

    (2010)
  • Y. Shi et al.

    Synthesis of few-layer hexagonal boron nitride thin film by chemical vapor deposition

    Nano Lett.

    (2010)
  • K.K. Kim et al.

    Synthesis of monolayer hexagonal boron nitride on Cu foil using chemical vapor deposition

    Nano Lett.

    (2012)
  • S. Helveg et al.

    Atomic-scale structure of single-layer MoS2 nanoclusters

    Phys. Rev. Lett.

    (2000)
  • G.S. Painter et al.

    Electronic band structure and optical properties of graphite from a variational approach

    Phys. Rev.

    (1970)
  • F. Bassani et al.

    Band structure and optical properties of graphite and of the layer compounds GaS and GaSe

    Nuovo Cimento B

    (1967)
  • M. Posternak et al.

    Prediction of electronic interlayer states in graphite and reinterpretation of alkali bands in graphite intercalation compounds

    Phys. Rev. Lett.

    (1983)
  • K.S. Novoselov et al.

    Two-dimensional gas of massless Dirac fermions in graphene

    Nature

    (2005)
  • Y. Zhang et al.

    Experimental observation of the quantum Hall effect and Berry’s phase in graphene

    Nature

    (2005)
  • X. Du et al.

    Fractional quantum Hall effect and insulating phase of Dirac electrons in graphene

    Nature

    (2009)
  • K.I. Bolotin et al.

    Observation of the fractional quantum Hall effect in graphene

    Nature

    (2009)
  • A. Catellani et al.

    Bulk and surface electronic structure of hexagonal boron nitride

    Phys. Rev. B

    (1987)
  • X. Blase et al.

    Quasiparticle band structure of bulk hexagonal boron nitride and related systems

    Phys. Rev. B

    (1995)
  • C.R. Dean et al.

    Boron nitride substrates for high-quality graphene electronics

    Nat. Nanotechnol.

    (2010)
  • K.F. Mak et al.

    Atomically thin MoS2: A new direct-gap semiconductor

    Phys. Rev. Lett.

    (2010)
  • N.T. Cuong et al.

    Gate-induced electron-state tuning of MoS<texmath type=”inline”>_2</texmath>: first-principles calculations

    J. Phys.: Condens. Matter

    (2014)
  • A.K. Geim et al.

    Van der Waals heterostructures

    Nature

    (2013)
  • S. Masubuchi et al.

    Autonomous robotic searching and assembly of two-dimensional crystals to build van der Waals superlattices

    Nat. Commun.

    (2018)
  • C.-H. Lee et al.

    Atomically thin p–n junctions with van der Waals heterointerfaces

    Nat. Nanotechnol.

    (2014)
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