SANTOS AND KAXIRAS VOL. 7 ’ NO. 12 ’ 10741–10746 ’ 2013 www.acsnano.org 10741 November 11, 2013 C 2013 American Chemical Society Electrically Driven Tuning of the Dielectric Constant in MoS 2 Layers Elton J. G. Santos †,§, * and Efthimios Kaxiras †,‡ † School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, United States and ‡ Department of Physics, Harvard University, Cambridge, Massachusetts 02138, United States. § Present address: Department of Chemical Engineering, Stanford University, Stanford, California 94305, United States, and SUNCAT Center for Interface Science and Catalysis, SLAC National Accelerator Laboratory, Menlo Park, California 94025, United States L ayered molybdenum disulfide has been attracting increasing interest as a building block of a new class of nano- devices. MoS 2 offers a novel set of features, for example, as an alternative 2D material that overcomes the limitation of a zero band gap in graphene. The sizable band gap observed in monolayer MoS 2 1 has opened new avenues for the creation of field-effect transistors with power dissipation lower than conventional transistors, 2,3 optoelectronics devices in high-performance flexible elec- tronics, 4 and thin-film solar cells 5À7 that can absorb light in the visible range. 8 One of the main features that influences all these prop- erties is the MoS 2 thickness, which deter- mines the charge distribution in the device as well as the electronic structure through the band gap and the electric field screen- ing that depends on the dielectric constant ε. The large range of values for ε found by different experiments 9À13 (from 4 to 17) has become a subject of considerable discus- sion. As is also the case in graphene, 14 the presence of substrates plays a role in the experimental attempts to measure the intrinsic dielectric constant in MoS 2 layers. In particular, recent electrical transport mea- surements 15 have shown that the dielectric response of MoS 2 layers is sensitive to the substrate used and the effect depends on the sample thickness. In practical terms, the effective dielectric constant of a two- dimensional crystal is given by ε =(ε sub þ ε vac )/2, with ε sub and ε vac being the dielectric con- stant values for the underlying substrate and vacuum, respectively. However, using this approach requires detailed knowledge of the dielectric constant of the environ- ment in which MoS 2 is embedded, which is not always accessible. The determination of the intrinsic value of ε is thus of great interest and importance as it can lead to novel routes for improving the performance of MoS 2 -based devices and reveal the role of electric-field screening in van der Waals layered structures. Here we show that ε can be manipulated by an external electric field E ext , with result- ing values in the range of 4À16. Bilayer (2L) MoS 2 does not show substantial modifica- tions with the external field, while N-layer MoS 2 (N > 2) displays a dependence of ε on the external bias. The linear response of the * Address correspondence to eltonjos@stanford.edu. Received for review July 19, 2013 and accepted November 11, 2013. Published online 10.1021/nn403738b ABSTRACT The properties of two-dimensional materials, such as molybdenum disulfide, will play an important role in the design of the next generation of electronic devices. Many of those properties are determined by the dielectric constant which is one of the fundamental quantities used to characterize conductivity, refractive index, charge screening, and capacitance. We predict that the effective dielectric constant (ε) of few-layer MoS 2 is tunable by an external electric field (E ext ). Through first-principles electronic structure calculations, including van der Waals interactions, we show that at low fields (E ext < 0.01 V/Å) ε assumes a nearly constant value ∼4 but increases at higher fields to values that depend on the layer thickness. The thicker the structure, the stronger the modulation of ε with the electric field. Increasing of the external field perpendicular to the dichalcogenide layers beyond a critical value can drive the system to an unstable state where the layers are weakly coupled and can be easily separated. The observed dependence of ε on the external field is due to charge polarization driven by the bias. Implications on the optical properties as well as on the electronic excitations are also considered. Our results point to a promising way of understanding and controlling the screening properties of MoS 2 through external electric fields. KEYWORDS: MoS 2 dielectric constant . dielectric response . tunable dielectric properties . electrostatic exfoliation . excitations ARTICLE