First-principles study of strained 2D MoS2

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Abstract

The electronic and vibrational properties of 2D honeycomb structures of molybdenum disulfide (MoS2) subjected to strain have been investigated using first-principles calculations based on density functional theory. We have studied the evolution of the electronic properties of bulk and layered MoS2, going down from a few layers up to a mono-layer, and next investigated the effect of bi-axial strain on their electronic structure and vibrational frequencies. Both for tensile and compressive bi-axial strains, the shrinking of the energy band-gap of MoS2 with increasing level of applied strain is observed and a transition limit of the system from semiconducting to metallic is predicted to occur for strains in the range of 8–10%. We also found a progressive downshift (upshift) of both the E12g and A1g Raman active modes with increasing level of applied tensile (compressive) strain. Interestingly, significant changes in the curvature of the conduction and valence band near their extrema upon the application of strain are also predicted, with correlated variations of the electron and hole effective masses. These changes present interesting possibilities for engineering the electronic properties of 2D structures of MoS2.

Introduction

2D materials are attracting a lot of interest as possible candidate for replace traditional semiconductors in the next generation of nanoelectronic devices. Several advantages could be obtained by using these materials, going from excellent electronic properties, such as very high mobility [1], to the use of extremely thin layers allowing an easy integration in novel transistor architectures [2], [3], [4].

The most known and widely studied 2D material, graphene, has no bandgap in its electronic structures, in its pristine form. This characteristic electronic property limits its application in Integrated Circuits. Several methodologies of bandgap engineering in graphene have been investigated [5], [6], [7], but the proposed solutions result in an increase of fabrication complexity and reduced mobility. In fact, the opening of a gap between the Dirac cones [8] leads to a perturbation of the linear relationship between energy (ε) and momentum (k) with a consequent considerable reduction of mobility to values often lower than that observable for silicon.

2D materials other than graphene, but with an intrinsic bandgap, may represent an attractive possibility for use as conductive channel in field effect transistors (FETs) [2], [4] and either as tunneling barrier in tunneling field effect transistors (TFETs) [3] and other novel transistor architectures.

Molybdenum disulfide is an indirect band-gap semiconductor, consisting of S–Mo–S sheets with a hexagonal structure held together by van der Waals interactions. Single layer MoS2 is a direct gap semiconductor with a band-gap of about 1.9 eV [11], [12], [13], so potentially interesting for electronic, optoelectronic and photovoltaic applications. The formation of suspended mono-layer MoS2 has been recently demonstrated [9], [10] and its properties have been investigated both experimentally [11], [12], [13] and theoretically [12], [13], [14], [15], [16]. Furthermore, mono-layer MoS2 has been recently used as a conductive channel to realize a low-power field effect transistor [2], [4] and as tunneling barrier in between graphene layers for vertical TFET [3]. Both the theoretical and experimental studies on single layer and bulk MoS2 [17], [18] demonstrated that carrier mobility of MoS2 is lower than that of silicon. These low values for the carrier mobility in both bulk and single layer MoS2 (in the range 0.1–10 cm2 V−1 s−1) can be enhanced (200–500 cm2 V−1 s−1) by using a high-κ dielectric on top of the MoS2 channel, but the obtained mobility values [2], [4] are still not so attractive for the use in MOS devices.

Enhancement of mobility in silicon by introducing strain has been exploited since 2003 [19] for commercial N and PMOS transistor and its investigation started more than 10 yrs before [20]. Strain is in fact responsible for an alteration of the band structure in silicon and consequent enhancement of carrier mobility. If similar effect of strain can be used for 2D materials and particularly for MoS2, another step towards the introduction of these materials in novel technology process of low power and high performance transistor could be done.

Here, by using a first-principle modeling approach, we investigate the evolution of the electronic properties of bulk and layered MoS2, going down from a few layers up to a mono-layer and then study the effect of bi-axial strain on their electronic structure. We observe a progressive shrinking of the energy band-gap upon the applied strain. Both for tensile and compressive strains, a transition limit is reached where the bottom of the conduction band and the top of the valence band cross the Fermi energy, changing the nature of the system from semiconducting to metallic. Tensile strain causes a drastic reduction of the effective mass both for electrons and holes. Effect of strain in single and few layers MoS2 could thus potentially be used to tune its electronic transport properties, with possible application for flexible electronic and other nano or optoelectronic devices. Changes of the electronic properties are also associated to a considerable shift of the vibrational frequencies. Particularly we found a trend in the shift of the out-of-plane (A1g) and in-plane (E12g) Raman active modes which is markedly different to the anomalous trend reported in the case of reduction of the number of layers in MoS2 [21]. The shift of the Raman peaks could thus be helpful for the identification and quantification of strain in the experiments.

Section snippets

Calculation methods

The first-principles calculations were performed within the density-functional theory (DFT) using the local density approximation (LDA) [22] as implemented in the ABINIT package [23]. The valence electrons for sulfur and the valence and semi-core states (4s2 and 4p6) for molybdenum were explicitly treated in the calculations using Hartwigsen–Goedecker–Hutter pseudopotentials[24]. The electronic wave functions were described by plane-wave basis sets with a kinetic energy cutoff of 60 Ha and the

Results

After geometry relaxation, the in-plane (a=b) and out-of-plane (c) structural parameters for the bulk phase are 3.13 Å and 11.89 Å, which underestimate the experimental values by 1% and 3%, respectively. The studied multilayer MoS2 structures with 1, 2 and 3 S–Mo–S sheets do not show significant differences in term of Mo–S bond lengths and S–S distances with respect to the bulk structure. On the contrary, the calculated phonon modes frequencies, particularly the two Raman active modes

Conclusions

In summary, the electronic and vibrational properties of quasi-2D MoS2 have been investigated, focusing on the effect of bi-axial strain. Mono-layer MoS2 is predicted to be a direct gap semiconductor (Eg=1.86 eV), while multilayers MoS2 are found to be indirect gap compounds. Upon the application of bi-axial strain, we found that the two Raman active modes (A1g and E12g) of MoS2 are characterized by a shift of frequencies, which is downwards for the tensile strain and upwards for the compressive

Acknowledgment

Part of this work has been financially supported by the Research Funds of KU Leuven, Project OT/09/031 and the European Project 2D –NANOLATTICES, FET-Open Grant no. 270749.

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