Piezoelectricity in Monolayers and Bilayers of Inorganic Two-Dimensional Crystals
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Piezoelectricity in Monolayers and Bilayers of Inorganic Two-Dimensional Crystals Karel-Alexander N. Duerloo1*, Mitchell T. Ong2 and Evan J. Reed1 1 Department of Materials Science and Engineering, Stanford University, Stanford, CA 94305, U.S.A. 2 Condensed Matter and Materials Division, Physical and Life Sciences Directorate, Lawrence Livermore National Laboratory, Livermore, CA 94550, U.S.A. ABSTRACT The symmetry properties of many inorganic two-dimensional monolayer crystals make them piezoelectric, whereas their three-dimensional parent crystals are not. The emergence of piezoelectricity in the single-layer limit points toward intriguing electromechanical effects and applications in the single- or few-layer regime. We use density functional theory to calculate the piezoelectric coefficients of BN, MoS2, MoSe2, MoTe2, WS2, WSe2 and WTe2. These coefficients are found to be comparable to, and in some cases greater than those of commonly used wurtzite piezoelectrics. The centrosymmetry of a BN bilayer prevents a piezoelectric effect for this structure. However, by developing an elastic model, we find that the bilayer exhibits an unusual electromechanical coupling to the curvature, similar to that of a bimorph. A BN bilayer is found to amplify the constituent monolayers’ in-plane piezoelectric displacements by factors on the order of 103-104 into out-of plane deflections. INTRODUCTION Piezoelectric crystals are key components in a variety of actuating, sensory and generator devices in both microscopic and macroscopic contexts. Their desirable electromechanical coupling is also applied in the nanometer regime, in nanowires and thin films, for example. Piezoelectricity (linear coupling between mechanical stress or strain and the electrical polarization of a crystal) exists only in a certain subset of materials: those whose crystal structures possess no center of inversion symmetry and are semiconductors or insulators. These requirements significantly constrain the selection of piezoelectrics available to scientists and engineers working at all length scales. Graphene has placed atomically thin two-dimensional (2D) crystals at the center of considerable research attention. One reason why the discovery of 2D monolayer crystals is important is that these materials have a number of emergent properties that do not exist in their bulk (3D) parent crystal. These 2D emergent properties include: very high mechanical strength [1, 2], graphene’s anomalous electronic properties [3], and direct band gaps in the transition metal dichalcogenides [4]. We have discovered that many commonly studied two-dimensional crystals are piezoelectric, unlike their stacked 3D counterparts. These inorganic 2D piezoelectrics are BN, *
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MoS2, MoSe2, MoTe2, WS2, WSe2 and WTe2. Piezoelectricity can thus be established as a new emergent property of certain 2D crystals. Rather than being just a theoretical curiosity, we will show that th
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