Geometric structure and piezoelectric polarization of MoS2 nanoribbons under 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 = 2.18, = 2.20, = 2.26, = 2.37, and = 2.51 nm for edge angles of 0, 8, 16, 23, and 30, respectively. The total energy appears parabolic around the initial length . 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)
- et al.
Theoretical study of hydrogenation process of formate on clean and Zn deposited Cu(111) surfaces
Appl. Surf. Sci.
(2001) - et al.
Electric field effect in atomically thin carbon films
Science
(2004) - et al.
Heteroepitaxial graphite on 6H-SiC(0001): Interface formation through conduction-band electronic structure
Phys. Rev. B
(1998) - et al.
Electronic confinement and coherence in patterned epitaxial graphene
Science
(2006) - et al.
Catalytic growth of graphene: toward large-area single-crystalline graphene
J. Phys. Chem. Lett.
(2012) - et al.
Epitaxial growth and electronic properties of large hexagonal graphene domains on Cu(111) thin film
Appl. Phys. Express
(2013) - et al.
Large scale growth and characterization of atomic hexagonal boron nitride layers
Nano Lett.
(2010) - et al.
Synthesis of few-layer hexagonal boron nitride thin film by chemical vapor deposition
Nano Lett.
(2010) - et al.
Synthesis of monolayer hexagonal boron nitride on Cu foil using chemical vapor deposition
Nano Lett.
(2012) - et al.
Atomic-scale structure of single-layer MoS2 nanoclusters
Phys. Rev. Lett.
(2000)